---
title: Official College Board Digital SAT Question Bank items ported into Meridian
---

# Official Question Bank items

Every item on this page is real, verbatim College Board Digital SAT Question Bank content, ported into Meridian's curriculum. Extracted directly from the three commits that added it (`64a698a`, `58d72c5`, `4c18340`) rather than reconstructed from memory, so what's below is exactly what those commits introduced — nothing paraphrased.

**Provenance:** the question text, stimulus passages, and choice text are College Board's own — this project claims no authorship over them and is not affiliated with or endorsed by College Board. The worked explanation under every choice (including the wrong ones) and the difficulty tagging are original analysis added by this project, not part of the official source.

**Total: 1694 items across 30 skills** — all 30 officially tested Digital SAT skill points.

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## Reading & Writing

### Craft & Structure

#### Cross-Text Connections (41 items)

##### Q1
> Text 1: Public policy researcher Anthony Fowler studied the history of elections in Australia, a country that requires citizens to vote. Fowler argues that requiring citizens to vote leads to a significant increase in voters who would otherwise not have the time or motivation to vote. Thus, election results in countries that require citizens to vote better reflect the preferences of the country as a whole. Text 2: Governments in democratic countries function better when more people vote. However, forcing people to vote may have negative consequences. Shane P. Singh and Jason Roy studied what happens when a country requires its citizens to vote. They found that when people feel forced to vote, they tend to spend less time looking for information about their choices when voting. As a result, votes from these voters may not reflect their actual preferences.

Based on the texts, how would Singh and Roy (Text 2) most likely respond to the research discussed in Text 1?

**A.** Only countries of a certain population size should implement mandatory voting. 

  *Population size never appears in either text. This is an imported qualifier with no textual basis — Singh and Roy's objection is about the quality of information voters gather, not about how large a country's population is.*

**B.** People who are forced to vote are likely to become politically engaged in other ways, such as volunteering or running for office. 

  *Text 2 says nothing about volunteering or holding office. It invents a compensating benefit that runs opposite to Singh and Roy's actual finding, which is that forced voters research less, not that they become more engaged elsewhere.*

**C.** Requiring people to vote does not necessarily lead to election outcomes that better represent the preferences of the country as a whole. **(Correct)**

  *Correct. This directly denies Text 1's causal conclusion using Text 2's own finding: because forced voters spend less time researching their choices, their votes may not reflect their actual preferences — so results are not guaranteed to represent the country's preferences better, contrary to Fowler's claim.*

**D.** Countries that require voting must also make the process of voting easier for their citizens. 

  *Ease of access to voting is not part of either text. Singh and Roy's objection concerns how much information forced voters gather before choosing, not how convenient the act of voting itself is.*

*Difficulty: medium*

---

##### Q2
> Text 1: Dance choreographer Alvin Ailey's deep admiration for jazz music can most clearly be felt in the rhythms and beats his works were set to. Ailey collaborated with some of the greatest jazz legends, like Charles Mingus, Charlie Parker, and perhaps his favorite, Duke Ellington. With his choice of music, Ailey helped bring jazz to life for his audiences. Text 2: Jazz is present throughout Ailey's work, but it's most visible in Ailey's approach to choreography. Ailey often incorporated improvisation, a signature characteristic of jazz music, in his work. When managing his dance company, Ailey rarely forced his dancers to an exact set of specific moves. Instead, he encouraged his dancers to let their own skills and experiences shape their performances, as jazz musicians do.

Based on the texts, both authors would most likely agree with which statement?

**A.** Dancers who worked with Ailey greatly appreciated his supportive approach as a choreographer. 

  *Neither text reports how dancers felt about Ailey's approach. Text 2 describes the approach itself — encouraging improvisation — not the dancers' reaction to it.*

**B.** Ailey's work was strongly influenced by jazz. **(Correct)**

  *Correct. Text 1 grounds this in his choice of music and his jazz-legend collaborators; Text 2 grounds it in his choreographic method, built around jazz-style improvisation. Both texts independently converge on jazz as the defining influence — the shared premise underneath two different kinds of evidence.*

**C.** Audiences were mostly unfamiliar with the jazz music in Ailey's works. 

  *Text 1 says Ailey 'helped bring jazz to life for his audiences,' which implies exposure and engagement, not that audiences began unfamiliar with the music. This detail is invented.*

**D.** Ailey blended multiple genres of music together when choreographing dance pieces. 

  *Neither text describes genre-blending. Both describe a single, consistent jazz influence running through his choice of music and his choreographic method, not a mixture of genres.*

*Difficulty: easy*

---

##### Q3
> Text 1: Historians studying pre-Inca Peru have looked to ceramic vessels to understand daily life among the Moche people. These mold-made sculptures present plants, animals, and human faces in precise ways—vessels representing human faces are so detailed that scholars have interpreted facial markings to represent scars and other skin irregularities. Some historians have even used these objects to identify potential skin diseases that may have afflicted people at the time. Text 2: Art historian and archaeologist Lisa Trever has argued that the interpretation of Moche "portrait" vessels as hyper-realistic portrayals of identifiable people may inadvertently disregard the creativity of the objects' creators. Moche ceramic vessels, Trever argues, are artworks in which sculptors could free their imagination, using realistic objects and people around them as inspiration to explore more abstract concepts.

Based on the texts, what would Lisa Trever (Text 2) most likely say about the interpretation of facial markings described in Text 1?

**A.** Depictions of human faces are significantly more realistic than depictions of plants and other animals are. 

  *Text 1 lists faces, plants, and animals as equally precise. No comparative ranking of realism across subjects appears in either text.*

**B.** It is likely that some depictions of human faces with extensive markings are intended to portray the same historical individual. 

  *This doubles down on the literal-portraiture reading Trever's entire argument works against. Her point is that sculptors used realistic elements as material for imaginative, not documentary, work.*

**C.** Some vessels may have been damaged during their excavation and thus provide little insight into Moche culture. 

  *Excavation damage appears in neither text. Trever's objection is about interpretive method — treating art as a literal biographical record — not about artifact condition.*

**D.** Markings on depictions of human faces are not necessarily intended to portray particular details about the physical appearance of individuals. **(Correct)**

  *Correct. This matches Trever's argument directly: reading markings as a literal record of scars or disease treats the vessels as hyper-realistic portraiture, exactly the assumption she says overlooks the sculptors' creative and abstract use of realistic material.*

*Difficulty: medium*

---

##### Q4
> Text 1: Italian painters in the 1500s rarely depicted themselves in their work. Even more rare were self-portrait paintings that portrayed the artist as a painter. At the time, painting was not yet respected as a profession, so painters mostly chose to emphasize other qualities in their self-portraits, like their intellect or social status. In the city of Bologna, the first artist to depict themself painting was a man named Annibale Carracci. A painting of his from around 1585 shows Carracci in front of an easel holding a palette. Text 2: In their self-portraits, Bolognese artists typically avoided referring to the act of painting until the mid-1600s. However, Lavinia Fontana's 1577 painting, Self-Portrait at the Keyboard, stands out as the earliest example of such a work by an artist from Bologna. Although the artist is depicted playing music, in the background, one can spot a painting easel by a window.

Based on the texts, how would the author of Text 2 most likely respond to the claim in Text 1 that Carracci was the first Bolognese artist to depict himself painting?

**A.** Carracci and Fontana were among the most well-respected painters in Bologna at the time. 

  *Neither text discusses the painters' reputations or professional standing. Text 2's point is about chronological priority and the content of the self-portraits, not esteem.*

**B.** The depiction of Fontana in Self-Portrait at the Keyboard was intended to underscore the artist's creativity. 

  *Text 2 never states Fontana's intent regarding 'creativity.' It reports what the painting depicts — music, with an easel visible in the background — not why she chose to include it.*

**C.** Fontana likely inspired the reference to an easel and palette in Carracci's painting. 

  *No influence between the two painters is claimed in either text. This invents a causal relationship neither author asserts.*

**D.** Self-Portrait at the Keyboard was painted earlier than Carracci's painting and also refers to the artist's craft. **(Correct)**

  *Correct. Fontana's 1577 painting predates Carracci's c. 1585 painting by roughly eight years, and its background easel is a reference to painting — satisfying the same 'depict themself painting' criterion Text 1 used to credit Carracci as first. Text 2 supplies both the earlier date and the qualifying detail, directly displacing Text 1's claim.*

*Difficulty: hard*

---

##### Q5
> Text 1: Today the starchy root cassava is found in many dishes across West Africa, but its rise to popularity was slow. Portuguese traders brought cassava from Brazil to the West African coast in the 1500s. But at this time, people living in the capitals further inland had little contact with coastal communities. Thus, cassava remained relatively unknown to most of the region's inhabitants until the 1800s. Text 2: Cassava's slow adoption into the diet of West Africans is mainly due to the nature of the crop itself. If not cooked properly, cassava can be toxic. Knowledge of how to properly prepare cassava needed to spread before the food could grow in popularity. The arrival of formerly enslaved people from Brazil in the 1800s, who brought their knowledge of cassava and its preparation with them, thus directly fueled the spread of this crop.

Based on the texts, the author of Text 1 and the author of Text 2 would most likely agree with which statement?

**A.** Cassava did not become a significant crop in West Africa until long after it was first introduced. **(Correct)**

  *Correct. Text 1 dates introduction to the 1500s and widespread adoption to the 1800s; Text 2 independently locates the crop's spread in the 1800s, via preparation knowledge. Both texts, for different reasons — limited contact versus toxicity risk — place a long gap between introduction and popularity.*

**B.** Several of the most commonly grown crops in West Africa are originally from Brazil. 

  *Both texts discuss cassava specifically. Neither generalizes to several other crops of Brazilian origin, an unsupported extension beyond the single crop discussed.*

**C.** The climate of the West African coast in the 1500s prevented cassava's spread in the region. 

  *Text 1 attributes the delay to lack of contact between coastal and inland communities, and Text 2 attributes it to the toxicity of unprepared cassava — neither text mentions climate as a barrier.*

**D.** The most commonly used methods to cook cassava today date to the 1500s. 

  *Text 2 traces safe preparation knowledge to people arriving in the 1800s, not the 1500s. This misdates the very mechanism Text 2 describes.*

*Difficulty: medium*

---

##### Q6
> Text 1: On April 26th, 1777, Sybil Ludington rode 40 miles by horse through Putnam County, New York, to gather up local militia. British forces were burning nearby Danbury, Connecticut, and Ludington wanted to rally rebel troops to meet them. Although she was only 16 years old at the time, her brave feat made Ludington one of the heroes of the American Revolution. Since then, Ludington has been widely celebrated, inspiring postage stamps, statues, and even children's TV series. Text 2: Historian Paula D. Hunt researched the life and legacy of Sybil Ludington but found no evidence for her famous ride. Although many articles and books have been written about Ludington, Hunt believes writers may have been inventing details about Ludington as they retold her story. Ludington is revered by Americans today, but there simply isn't a strong historical record of her heroic ride.

Based on the texts, both authors would most likely agree with which statement?

**A.** Sybil Ludington was crucial to the outcome of the Revolutionary War. 

  *Text 1 celebrates Ludington's ride but never claims it decided the war's outcome, and Text 2 doubts the ride is even well documented. Neither text supports a claim about the war's outcome.*

**B.** Historians have confirmed which route Sybil Ludington took. 

  *This contradicts Text 2 directly, which states there 'isn't a strong historical record' of the ride at all, let alone a confirmed route.*

**C.** Sybil Ludington was likely not a real person. 

  *Text 2 questions the evidence for the ride, not Ludington's existence as a person. Doubting a specific event is not the same as doubting the person existed.*

**D.** Many people have come to admire the story of Sybil Ludington's ride. **(Correct)**

  *Correct. Text 1 documents her wide celebration — stamps, statues, TV series. Text 2, while skeptical of the historical record, explicitly states Ludington 'is revered by Americans today.' Both texts agree on the story's popularity even while disagreeing on its accuracy.*

*Difficulty: easy*

---

##### Q7
> Text 1: For decades, bluegrass musicians have debated whether their genre should exclude influences from mainstream genres such as rock. Many insist that bluegrass is defined by its adherence to the folk music of the US South, out of which bluegrass emerged. Such "purists," as they are known, regard the recordings of Bill Monroe, which established the bluegrass sound in the 1940s, as a standard against which the genre should still be measured. Text 2: Bluegrass isn't simply an extension of folk traditions into the era of recorded music. In reality, Bill Monroe created the bluegrass sound in the 1940s by combining Southern folk music with commercial genres that had arisen only a few decades before, such as jazz and the blues. Since bluegrass has always been a mixed genre, contemporary bluegrass musicians should not be forbidden from incorporating into it influences from rock and other mainstream genres.

Based on the texts, how would the author of Text 2 most likely regard the perspective of bluegrass purists, as described in Text 1?

**A.** As inconsistent, since bluegrass purists themselves enjoy other musical genres 

  *Neither text says anything about purists' personal listening habits. Text 2's objection is about the genre's own origin, not the purists' private tastes.*

**B.** As unrealistic, since bluegrass purists have no way of enforcing their musical preferences 

  *Enforceability of a preference is never raised in either text. Text 2's argument concerns whether the purist standard is historically accurate, not whether it is practically enforceable.*

**C.** As shortsighted, because bluegrass could enlarge its audience by including influences from mainstream genres 

  *Text 2 does argue for allowing mainstream influence, but on the grounds that bluegrass was always a mixed genre — audience size is never mentioned as the reason. This borrows Text 2's conclusion but attaches the wrong justification.*

**D.** As illogical, because the purists overlook crucial aspects of how the bluegrass sound first originated. **(Correct)**

  *Correct. Text 2's entire argument is that Monroe's 'original' bluegrass sound was itself a combination of folk with commercial genres like jazz and blues. Treating that mixed origin as a pure folk standard is the exact inconsistency Text 2 identifies in the purist position.*

*Difficulty: medium*

---

##### Q8
> Text 1: Most scientists agree that the moon was likely formed after a collision between Earth and a large planet named Theia. This collision likely created a huge debris field, made up of material from both Earth and Theia. Based on models of this event, scientists believe that the moon was formed from this debris over the course of thousands of years. Text 2: Researchers from NASA's Ames Research Center used a computer to model how the moon could have formed. Although simulations of the moon's formation have been done in the past, the team from NASA ran simulations that were much more detailed. They found that the formation of the moon was likely not a slow process that took many years. Instead, it's probable that the moon's formation happened immediately after impact, taking just a few hours.

Which choice best describes a difference in how the author of Text 1 and the author of Text 2 view the evidence for the formation of the moon?

**A.** The author of Text 1 argues that the formation of the moon occurred much earlier than the author of Text 2 argues. 

  *Neither text discusses when in cosmic history the collision occurred. The disagreement is about the duration of formation — thousands of years versus hours — not about the timing of the collision itself.*

**B.** The author of Text 1 suggests there is more evidence confirming the existence of Theia than the author of Text 2 suggests. 

  *Both texts accept the Theia collision as the starting premise. Neither text disputes or discusses the quantity of evidence for Theia's existence.*

**C.** The author of Text 1 claims that the moon's surface is more similar to Earth's surface than the author of Text 2 claims. 

  *Surface similarity between Earth and moon is not addressed in either text; both discuss the debris field and the speed of accretion, not surface composition.*

**D.** The author of Text 1 believes that the moon formed more slowly than the author of Text 2 believes. **(Correct)**

  *Correct. Text 1 states formation took 'the course of thousands of years'; Text 2's more detailed simulations found it 'probable' the moon formed 'immediately after impact, taking just a few hours.' A direct, quantified disagreement about duration.*

*Difficulty: easy*

---

##### Q9
> Text 1: Literary scholars have struggled with the vastness of Nigerian writer Wole Soyinka's collective works of drama (spanning over 20 plays in total). It is best, however, to understand Soyinka's body of work as a dramatist chronologically. Soyinka's progression as a playwright can be considered to fall into three periods, with each one representing a particular thematic and stylistic cohesion: the 1960s, the two decades between 1970 and 1990, and lastly, from roughly 1990 onwards. Text 2: It is tempting to impose a linear sense of order on the expanse of Wole Soyinka's body of work as a dramatist. However, critics who have considered Soyinka's plays to fit neatly into three phases overlook potential commonalities in Soyinka's work that span across these phases. Additionally, this view may discount significant differences in the styles and content of plays written around the same time.

Which choice best describes a difference in how the author of Text 1 and the author of Text 2 view the study of Soyinka's works of drama?

**A.** While the author of Text 1 believes that thinking about Soyinka's works of theater in phases is useful, the author of Text 2 views such an approach as limiting. **(Correct)**

  *Correct. Text 1 recommends the three-period framework as the best way to understand Soyinka's body of work. Text 2 calls that framework 'tempting' but argues it overlooks commonalities across phases and differences within them — exactly the limiting view this choice describes.*

**B.** Although the author of Text 1 claims that Soyinka's style as a dramatist has evolved over time, the author of Text 2 argues that his style has remained consistent throughout his career. 

  *This reverses Text 2's actual claim. Text 2 does not argue for consistency — it argues that phase-based critics discount real differences even within a single period, while also noting overlooked similarities across periods, a more nuanced position than flat consistency.*

**C.** The author of Text 1 considers Soyinka's plays to showcase his strongest writing, whereas the author of Text 2 believes that Soyinka's poetry is where he is most skilled. 

  *Neither text compares Soyinka's drama to his poetry or ranks his skill across genres; poetry never appears in either passage.*

**D.** The author of Text 1 argues that Soyinka's early plays were his most politically charged, whereas the author of Text 2 claims that Soyinka's most recent plays are the most politicized. 

  *Neither text discusses the political content of Soyinka's plays; both focus on how to periodize or study his body of work structurally.*

*Difficulty: medium*

---

##### Q10
> Text 1: In a study of insect behavior, Samadi Galpayage and colleagues presented bumblebees with small wooden balls and observed many of the bees clinging to, rolling, and dragging the objects. The researchers provided no external rewards (such as food) to encourage these interactions. The bees simply appeared to be playing—and for no other reason than because they were having fun. Text 2: Insects do not have cortexes or other brain areas associated with emotions in humans. Still, Galpayage and her team have shown that bumblebees may engage in play, possibly experiencing some kind of positive emotional state. Other studies have suggested that bees experience negative emotional states (for example, stress), but as Galpayage and her team have acknowledged, emotions in insects, if they do indeed exist, are likely very rudimentary.

Based on the texts, how would the author of Text 2 most likely respond to the claim in Text 1 that the bees were playing purely because they were having fun?

**A.** By objecting that the bees were actually experiencing a negative feeling akin to stress rather than a positive feeling 

  *Text 2 associates play specifically with 'some kind of positive emotional state'; stress is mentioned only as something other studies found in other contexts, not as an alternative account of play.*

**B.** By arguing that some insects other than bumblebees may be capable of experiencing complex emotional states 

  *Text 2 explicitly calls insect emotions 'likely very rudimentary,' the opposite of complex, and never discusses insects besides bees.*

**C.** By pointing out that even humans sometimes struggle to have fun while engaging in play 

  *This is an outside comparison to human experience that appears nowhere in either text, which is entirely about bees.*

**D.** By noting that if the bees were truly playing, any positive feelings they may have experienced were probably quite basic **(Correct)**

  *Correct. Text 2 grants that bees 'may engage in play, possibly experiencing some kind of positive emotional state,' but immediately qualifies that insect emotions, if they exist, are 'likely very rudimentary.' This accepts the fun-based reading in Text 1 while capping its emotional weight — matching the hedge exactly.*

*Difficulty: medium*

---

##### Q11
> Text 1: Although food writing is one of the most widely read genres in the United States, literary scholars have long neglected it. And within this genre, cookbooks attract the least scholarly attention of all, regardless of how well written they may be. This is especially true of works dedicated to regional US cuisines, whose complexity and historical significance are often overlooked. Text 2: With her 1976 cookbook The Taste of Country Cooking, Edna Lewis popularized the refined Southern cooking she had grown up with in Freetown, an all-Black community in Virginia. She also set a new standard for cookbook writing: the recipes and memoir passages interspersing them are written in prose more elegant than that of most novels. Yet despite its inarguable value as a piece of writing, Lewis's masterpiece has received almost no attention from literary scholars.

Based on the two texts, how would the author of Text 1 most likely regard the fact, presented in Text 2, that Lewis's cookbook has received almost no scholarly attention?

**A.** As typical, because scholars are dismissive of literary works that achieve popularity with the general public 

  *Text 1 attributes scholarly neglect to genre — cookbooks, especially regional ones — not to a work's general popularity; popularity as a cause of neglect appears nowhere in Text 1.*

**B.** As unsurprising, because scholars tend to overlook the literary value of food writing in general and of regional cookbooks in particular **(Correct)**

  *Correct. Text 1's claim is precisely that cookbooks, and especially those 'dedicated to regional US cuisines,' receive the least scholarly attention 'regardless of how well written they may be.' A regional Southern cookbook of exceptional prose receiving no scholarly attention is exactly what Text 1 predicts.*

**C.** As justifiable, because Lewis incorporated memoir into The Taste of Country Cooking, thus undermining its status as a cookbook 

  *Text 1 never suggests that mixing genres within a cookbook would justify neglect; Text 1's author is critical of the neglect, not sympathetic to reasons for it.*

**D.** As inevitable, because The Taste of Country Cooking was marketed to readers of food writing and not to readers of other genres 

  *Marketing and target readership are never discussed in either text; Text 1's explanation is about scholarly attention patterns, not commercial audience.*

*Difficulty: medium*

---

##### Q12
> Text 1: Some animal species, like the leopard, can be found in many kinds of areas. On the other hand, tropical mountain bird species tend to be limited in the types of spaces they can call home. This is because many mountain bird species are only able to survive at very specific elevations. Over time, these species have likely become used to living at a specific temperature. Therefore, these species struggle to survive at elevations that are warmer or colder than they are used to. Text 2: A new study reviewed observations of nearly 3,000 bird species to understand why tropical mountain bird species live at specific elevations. They noted that when a mountain bird species was found in an area with many other bird species, it tended to inhabit much smaller geographic areas. It is thus likely that competition for resources with other species, not temperature, limits where these birds can live.

Based on the texts, both authors would most likely agree with which statement?

**A.** Tropical mountain bird species are restricted in where they can live. **(Correct)**

  *Correct. Text 1 opens by stating these species 'tend to be limited in the types of spaces they can call home,' and Text 2's entire study investigates 'why tropical mountain bird species live at specific elevations.' Both texts take the restriction itself as a given; they disagree only about its cause.*

**B.** Scientists have better tools to observe tropical mountain birds than they did in the past. 

  *Neither text compares current observational methods to past ones; Text 2 mentions a large observational study but says nothing about improved tools or historical comparison.*

**C.** Little is known about how tropical mountain birds build their nests. 

  *Nest-building is not discussed in either text, which focus on geographic range and its causes, not nesting behavior.*

**D.** Tropical mountain bird species that live at high elevations tend to be genetically similar. 

  *Genetics is never mentioned in either text; Text 1 discusses temperature adaptation and Text 2 discusses competition for resources, neither of which is a genetic claim.*

*Difficulty: easy*

---

##### Q13
> Text 1: American sculptor Edmonia Lewis is best known for her sculptures that represent figures from history and mythology, such as The Death of Cleopatra and Hagar. Although Lewis sculpted other subjects, her career as a sculptor is best represented by the works in which she depicted these historical and mythical themes. Text 2: Art historians have typically ignored the many portrait busts Edmonia Lewis created. Lewis likely carved these busts (sculptures of a person's head) frequently throughout her long career. She is known for her sculptures that represent historical figures, but Lewis likely supported herself financially by carving portrait busts for acquaintances who paid her to represent their features. Thus, Lewis's portrait busts are a central aspect of her career as a sculptor.

Based on the texts, both authors would most likely agree with which statement?

**A.** Lewis's portrait busts have overshadowed her other work. 

  *Text 1 barely mentions portrait busts and centers Lewis's reputation on historical and mythical works, and Text 2 argues busts have been ignored by art historians — the opposite of overshadowing her other work.*

**B.** The Death of Cleopatra is Lewis's most famous piece. 

  *Text 1 lists The Death of Cleopatra alongside Hagar as examples but never ranks them by fame, and Text 2 does not mention this specific work at all.*

**C.** Sculpting representations of historical figures was a short-lived trend. 

  *Both texts describe Lewis's historical and mythical sculpture as a lasting, defining feature of her career, or ongoing alongside busts throughout her 'long career'; neither text calls it short-lived.*

**D.** Lewis's works are varied in the subjects they depict. **(Correct)**

  *Correct. Text 1 explicitly notes Lewis 'sculpted other subjects' beyond historical and mythical themes, and Text 2 adds that she also carved many portrait busts of acquaintances. Both texts, while disagreeing about which body of work is most central to her career, agree that her output spanned multiple kinds of subjects.*

*Difficulty: medium*

---

##### Q14
> Text 1: A team led by Bernardo Strassburg has found that rewilding farmland (returning the land to its natural state) could help preserve biodiversity and offset carbon emissions. The amount of farmland that would need to be restored, they found, is remarkably low. Rewilding a mere 15% of the world's current farmland would prevent 60% of expected species extinctions and help absorb nearly 299 gigatons of carbon dioxide—a clear win in the fight against the biodiversity and climate crises. Text 2: While Strassburg's team's findings certainly offer encouraging insight into the potential benefits of rewilding, it's important to consider potential effects on global food supplies. The researchers suggest that to compensate for the loss of food-producing land, remaining farmland would need to produce even more food. Thus, policies focused on rewilding farmland must also address strategies for higher-yield farming.

Which choice best describes a difference in how the author of Text 1 and the author of Text 2 view Strassburg's team's study?

**A.** The author of Text 2 approaches the study's findings with some caution, whereas the author of Text 1 is optimistic about the reported potential environmental benefits. **(Correct)**

  *Correct. Text 1 calls the findings 'a clear win' — unqualified enthusiasm. Text 2 opens by calling the same findings 'encouraging' but immediately raises a caveat about food supply that Text 1 never mentions — accepting the data while qualifying its implications.*

**B.** The author of Text 2 claims that the percentage of farmland identified by Strassburg's team is too low for rewilding to achieve meaningful results, whereas the author of Text 1 thinks the percentage is sufficient. 

  *Text 2 never disputes the 15% figure or calls it insufficient; its concern is about the food-supply consequences of that rewilding, not about whether 15% is enough land to rewild.*

**C.** The author of Text 2 believes that the results described by Strassburg's team are achievable in the near future, whereas the author of Text 1 argues that they likely aren't. 

  *Neither text discusses feasibility or timeline for achieving the results; Text 1 reports the findings and Text 2 raises a food-supply consideration, not a timeline dispute.*

**D.** The author of Text 2 focuses on rewilding's effect on carbon emissions, whereas the author of Text 1 focuses on biodiversity. 

  *This reverses the actual emphasis — Text 1 discusses both biodiversity and carbon emissions, while Text 2's focus is specifically on food supply, a topic neither text ties to carbon emissions specifically.*

*Difficulty: medium*

---

##### Q15
> Text 1: Flamingos are known for their vibrant pink coloring, but they're actually born with gray feathers. Their pink color comes from eating brine shrimp, but brine shrimp aren't naturally pink either. Animals can't produce carotenoids, the pigments that provide the pink hue. The algae that brine shrimp feed on, however, can produce these pigments. Thus, the pinker the flamingo, the more shrimp it has eaten. Text 2: Ecologist Juan Amat has found that flamingos apply a kind of makeup to make themselves appear pinker. A gland near their tail contains pigments that come from the food they eat. When the flamingos groom themselves using the pigments, their feathers become pinker. Flamingos may do this to improve their success during mating season, when they would benefit from looking pinker.

Based on the texts, how would the ecologist in Text 2 most likely respond to the author's conclusion in Text 1 that a flamingo's pinkness reflects how much shrimp it has eaten?

**A.** By emphasizing that flamingos' tail feathers are pinker than their other feathers are 

  *Text 2 locates the pigment gland near the tail but says grooming spreads it across the feathers generally; it never claims tail feathers specifically end up pinker than the rest.*

**B.** By claiming that the coloring of flamingos' feathers doesn't change significantly enough for most observers to notice 

  *Text 2's entire point is that grooming visibly increases pinkness, an effect worth studying and tied to mating success; it never suggests the change is imperceptible.*

**C.** By pointing out that the amount of shrimp eaten isn't the only thing that influences flamingos' coloring **(Correct)**

  *Correct. Text 1 makes diet the sole determinant of pinkness. Text 2 adds a second mechanism — self-applied grooming with gland pigments, intensified for mating season — that changes pinkness independent of how much has been freshly eaten. Diet still matters, but it isn't the whole story.*

**D.** By arguing that flamingos' diet doesn't include much shrimp except during mating season 

  *Text 2 never disputes how much shrimp flamingos eat or when; its claim is about a grooming behavior applied to already-acquired pigments, not about seasonal diet composition.*

*Difficulty: medium*

---

##### Q16
> Text 1: Imagine you and your friend are trying to decide where to eat lunch. When people try to make joint decisions like this, they often don't reveal their true preferences. Instead, they say they would be happy with all options because they think this response will help them appear more easygoing and likable to the other person. Text 2: Research shows that people who don't state their preferences when making a decision with others aren't more likable in the eyes of others. In fact, stating that you have no preference actually makes the decision more difficult for other people. It can also cause them to feel less happy with their ultimate decision and with you.

Based on the texts, what response would the author of Text 2 most likely suggest for someone deciding where to eat lunch with a friend, as described in Text 1?

**A.** Cancel the plan to have lunch together. 

  *Text 2 addresses how to communicate within the decision, not whether to make the decision at all; canceling the plan isn't a response to a preference-stating problem.*

**B.** Ask where the friend typically likes to eat. 

  *Text 2's remedy concerns the person's own withheld preference, not researching the other person's habits; deflecting to the friend's preferences doesn't address the problem Text 2 identifies.*

**C.** State a preference about where to eat. **(Correct)**

  *Correct. Text 2 shows that withholding a preference doesn't make a person more likable and makes the decision harder and less satisfying for the other person. The direct fix implied is to do the opposite of what Text 1's hypothetical friend does: state an actual preference.*

**D.** Change the subject to talk about something else. 

  *This avoids the decision rather than resolving the preference problem Text 2 describes; Text 2's finding is about the cost of not stating a preference, not about avoiding the topic altogether.*

*Difficulty: easy*

---

##### Q17
> Text 1: Microbes are tiny organisms in the soil, water, and air all around us. They thrive even in very harsh conditions. That's why Noah Fierer and colleagues were surprised when soil samples they collected from an extremely cold, dry area in Antarctica didn't seem to contain any life. The finding doesn't prove that there are no microbes in that area, but the team says it does suggest that the environment severely restricts microbes' survival. Text 2: Microbes are found in virtually every environment on Earth. So it's unlikely they would be completely absent from Fierer's team's study site, no matter how extreme the environment is. There were probably so few organisms in the samples that current technology couldn't detect them. But since a spoonful of typical soil elsewhere might contain billions of microbes, the presence of so few in the Antarctic soil samples would show how challenging the conditions are.

Based on the texts, Fierer's team and the author of Text 2 would most likely agree with which statement about microbes?

**A.** Most microbes are better able to survive in environments with extremely dry conditions than in environments with harsh temperatures. 

  *Neither text ranks dry conditions against temperature conditions; both discuss the Antarctic site as a single environment that is both cold and dry, without separating the two variables.*

**B.** A much higher number of microbes would probably be found if another sample of soil were taken from the Antarctic study site. 

  *Text 2 argues the opposite — that only a very small number of microbes are present at the site, too few for current technology to detect, not that resampling would reveal abundant life.*

**C.** Microbes are likely difficult to detect in the soil at the Antarctic study site because they tend to be smaller than microbes found in typical soil elsewhere. 

  *Text 2 attributes detection difficulty to how few organisms are present, not to their size; size is never discussed in either text.*

**D.** Most microbes are probably unable to withstand the soil conditions at the Antarctic study site. **(Correct)**

  *Correct. Text 1's team concludes the environment 'severely restricts microbes' survival.' Text 2, while insisting microbes are not completely absent, agrees the harsh conditions explain why 'so few' organisms are detectable there — both texts converge on the site being inhospitable to most microbes, even as they disagree on whether any are present at all.*

*Difficulty: medium*

---

##### Q18
> Text 1: The idea that time moves in only one direction is instinctively understood, yet it puzzles physicists. According to the second law of thermodynamics, at a macroscopic level some processes of heat transfer are irreversible due to the production of entropy—after a transfer we cannot rewind time and place molecules back exactly where they were before, just as we cannot unbreak dropped eggs. But laws of physics at a microscopic or quantum level hold that those processes should be reversible. Text 2: In 2015, physicists Tiago Batalhão et al. performed an experiment in which they confirmed the irreversibility of thermodynamic processes at a quantum level, producing entropy by applying a rapidly oscillating magnetic field to a system of carbon-13 atoms in liquid chloroform. But the experiment "does not pinpoint … what causes [irreversibility] at the microscopic level," coauthor Mauro Paternostro said.

Based on the texts, what would the author of Text 1 most likely say about the experiment described in Text 2?

**A.** It would suggest an interesting direction for future research were it not the case that two of the physicists who conducted the experiment disagree on the significance of its findings. 

  *Text 2 quotes only one coauthor's caveat about what the experiment doesn't pinpoint; this is not a disagreement between physicists about the finding's significance, and no second physicist's dissenting view appears in either text.*

**B.** It provides empirical evidence that the current understanding of an aspect of physics at a microscopic level must be incomplete. **(Correct)**

  *Correct. Text 1 states that quantum-level physics holds irreversible processes 'should be reversible.' Text 2 reports an experiment that found genuine irreversibility at the quantum level — in tension with that theoretical expectation. Since existing microscopic-level theory predicts reversibility but the experiment observed irreversibility, the finding indicates something in the current understanding is incomplete, even though it doesn't yet explain the cause.*

**C.** It is consistent with the current understanding of physics at a microscopic level but not at a macroscopic level. 

  *This inverts the actual tension. Text 2's finding of irreversibility at the microscopic level conflicts with the microscopic-level theory Text 1 describes (which predicts reversibility); it is the macroscopic-level physics (irreversibility via entropy) that the finding resembles, not the microscopic-level theory.*

**D.** It supports a claim about an isolated system of atoms in a laboratory, but that claim should not be extrapolated to a general claim about the universe. 

  *Text 1 makes no statement about the scope of extrapolation from laboratory systems to the universe; this is an outside methodological concern not raised by either text.*

*Difficulty: sat-hardest*

---

##### Q19
> Text 1: The live music festival business is growing in event size and genre variety. With so many consumer options, organizers are finding ways to cement festival attendance as a special experience worth sharing. This phenomenon is linked to the growing "experiential economy," where many find it gratifying to purchase lived experiences. To ensure a profitable event, venues need to consider the overall consumer experience, not just the band lineup. Text 2: Music festival appearances are becoming a more important part of musicians' careers. One factor in this shift is the rising use of streaming services that allow access to huge numbers of songs for a monthly fee, subsequently reducing sales of full-length albums. With this shift in consumer behavior, musicians are increasingly dependent on revenue from live performances.

Based on the texts, both authors would most likely agree with which statement?

**A.** Consumers are more interested in paying subscription fees to stream music than in attending music festivals in person. 

  *Both texts describe festival attendance as growing in importance, not declining relative to streaming; Text 2 links streaming to reduced album sales, not reduced festival interest.*

**B.** Consumers' growing interest in purchasing experiences is mostly confined to the music industry. 

  *Text 1 frames the 'experiential economy' as a broader trend that music festivals participate in, not one confined to music; neither text claims the phenomenon is unique to this industry.*

**C.** Changing consumer behaviors are leading to changes in music-related businesses. **(Correct)**

  *Correct. Text 1 ties the growth of festivals to the broader experiential-economy shift in consumer behavior; Text 2 ties musicians' growing dependence on live performance to the consumer shift toward streaming. Both texts describe a changing music-related business responding to changing consumer behavior — different behaviors, same underlying pattern.*

**D.** The rising consumer demand for live music festivals also generates higher demand for music streaming. 

  *Neither text claims a causal link running from festival demand to streaming demand; Text 2 describes streaming as reducing album sales and increasing reliance on festivals, the reverse direction of causation.*

*Difficulty: easy*

---

##### Q20
> Text 1: Stage lighting theorist Adolphe Appia was perhaps the first to argue that light must be considered alongside all the various elements of a stage to create a single, unified performance. Researcher Kelly Bremner, however, has noted that Appia lacked technical expertise in the use of light in the theater. As a result of Appia's inexperience, Bremner argues, Appia's theory of light called for lighting practices that weren't possible until after the advent of electricity around 1881. Text 2: Adolphe Appia was not an amateur in the practice of lighting. Instead, it is precisely his exposure to lighting techniques at the time that contributed to his theory on the importance of light. When working as an apprentice for a lighting specialist in his youth, Appia observed the use of portable lighting devices that could be operated by hand. This experience developed his understanding of what was possible in the coordination of elements on the stage.

Based on the texts, how would the author of Text 2 most likely respond to the claim about Appia's level of technical expertise made by Bremner in Text 1?

**A.** Many lighting technicians dismissed Appia's ideas about light on the stage. 

  *Neither text discusses how other technicians received Appia's ideas; Text 2's argument is about Appia's own hands-on experience, not other professionals' reactions to him.*

**B.** Appia likely gained a level of technical expertise during his time as an apprentice. **(Correct)**

  *Correct. This is nearly a direct restatement of Text 2: Appia 'was not an amateur,' and his apprenticeship for a lighting specialist gave him direct exposure to lighting devices and practical understanding — the opposite of Bremner's claim that inexperience shaped his theory.*

**C.** Theater practitioners who worked with Appia greatly admired his work. 

  *Admiration from collaborators is not discussed in either text; Text 2's evidence concerns Appia's apprenticeship experience, not others' opinions of his later work.*

**D.** Appia was unfamiliar with the use of music and sound in theater. 

  *Neither text discusses Appia's familiarity with music or sound; both texts concern lighting specifically, and this choice introduces an unrelated domain of expertise.*

*Difficulty: easy*

---

##### Q21
> Text 1: In 2021, a team led by Amir Siraj hypothesized that the Chicxulub impactor—the object that struck the Yucatán Peninsula sixty-six million years ago, precipitating the mass extinction of the dinosaurs—was likely a member of the class of long-period comets. As evidence, Siraj cited the carbonaceous chondritic composition of samples from the Chicxulub impact crater as well as of samples obtained from long-period comet Wild 2 in 2006. Text 2: Although long-period comets contain carbonaceous chondrites, asteroids are similarly rich in these materials. Furthermore, some asteroids are rich in iridium, as Natalia Artemieva points out, whereas long-period comets are not. Given the prevalence of iridium at the crater and, more broadly, in geological layers deposited worldwide following the impact, Artemieva argues that an asteroid is a more plausible candidate for the Chicxulub impactor.

Based on the texts, how would Artemieva likely respond to Siraj's hypothesis, as presented in Text 1?

**A.** By insisting that it overestimates how representative Wild 2 is of long-period comets as a class 

  *Text 2 never questions whether Wild 2 is representative of comets generally; Artemieva's objection is about which material actually distinguishes comets from asteroids, not about sampling representativeness.*

**B.** By arguing that it does not account for the amount of iridium found in geological layers dating to the Chicxulub impact **(Correct)**

  *Correct. Text 2's core objection is that carbonaceous chondrites don't discriminate between comets and asteroids — both contain them — but iridium does, and iridium is abundant at the crater and in worldwide impact-layer deposits, a composition that points to an asteroid rather than Siraj's comet. Siraj's hypothesis, built entirely on the chondritic composition, never engages with the iridium evidence.*

**C.** By praising it for connecting the composition of Chicxulub crater samples to the composition of certain asteroids 

  *Siraj's hypothesis connects the crater samples to comet Wild 2, not to asteroids; Artemieva's argument is a rebuttal, not praise, and it argues for an asteroid origin rather than endorsing any comet-asteroid link Siraj made.*

**D.** By concurring that carbonaceous chondrites are prevalent in soil samples from sites distant from the Chicxulub crater 

  *Text 2 discusses iridium's prevalence in geological layers worldwide, not carbonaceous chondrites at distant sites; this swaps which substance is described as widespread.*

*Difficulty: hard*

---

##### Q22
> Text 1: Philosopher G.E. Moore's most influential work entails the concept of common sense. He asserts that there are certain beliefs that all people, including philosophers, know instinctively to be true, whether or not they profess otherwise: among them, that they have bodies, or that they exist in a world with other objects that have three dimensions. Moore's careful work on common sense may seem obvious but was in fact groundbreaking. Text 2: External world skepticism is a philosophical stance supposing that we cannot be sure of the existence of anything outside our own minds. During a lecture, G.E. Moore once offered a proof refuting this stance by holding out his hands and saying, "Here is one hand, and here is another." Many philosophers reflexively reject this proof (Annalisa Coliva called it "an obviously annoying failure") but have found it a challenge to articulate exactly why the proof fails.

Based on the texts, how would the author of Text 1 most likely respond to proponents of the philosophical stance outlined in Text 2?

**A.** By agreeing with those proponents that Moore's treatment of positions that contradict his own is fundamentally unserious 

  *Text 1 presents Moore's work as 'groundbreaking,' not dismissive of opposing views; nothing in Text 1 supports the idea that Moore treats other positions unseriously, and this choice puts a critical judgment in Text 1's mouth that it never makes.*

**B.** By suggesting that an instinctive distaste for Moore's position is preventing external world skeptics from constructing a sufficiently rigorous refutation of Moore 

  *This is a plausible-sounding psychological explanation for why philosophers reject Moore's proof, but it appears only in Text 2 (via Coliva's reaction), and Text 1 says nothing about skeptics' motivations or the rigor of their refutations.*

**C.** By arguing that if it is valid to assert that some facts are true based on instinct, it is also valid to assert that some proofs are inadequate based on instinct 

  *This would undercut Moore's own instinct-based method by validating instinctive rejections of his proof, contradicting Text 1's framing of instinctive common-sense belief as Moore's central, defensible insight.*

**D.** By pointing out that Moore would assert that external world skepticism is at odds with other beliefs those proponents most unavoidably hold **(Correct)**

  *Correct. Text 1 establishes that, per Moore, all people — including philosophers — instinctively know certain things to be true, such as having bodies and existing in a three-dimensional world with other objects. External world skepticism directly conflicts with those very commonsense beliefs Text 1 says even skeptics cannot help but hold, licensing a response built entirely from Text 1's content.*

*Difficulty: sat-hardest*

---

##### Q23
> Text 1: Because literacy in Nahuatl script, the writing system of the Aztec Empire, was lost after Spain invaded central Mexico in the 1500s, it is unclear exactly how meaning was encoded in the script's symbols. Although many scholars had assumed that the symbols signified entire words, linguist Alfonso Lacadena theorized in 2008 that they signified units of language smaller than words: individual syllables. Text 2: The growing consensus among scholars of Nahuatl script is that many of its symbols could signify either words or syllables, depending on syntax and content at any given site within a text. For example, the symbol signifying the word huipil (blouse) in some contexts could signify the syllable "pil" in others, as in the place name Chipiltepec. Thus, for the Aztecs, reading required a determination of how such symbols functioned each time they appeared in a text.

Based on the texts, how would the author of Text 2 most likely characterize Lacadena's theory, as described in Text 1?

**A.** By praising the theory for recognizing that the script's symbols could represent entire words 

  *Lacadena's theory as described in Text 1 argues symbols signified syllables, not entire words — the older, word-based assumption is what his theory revised. Crediting his theory with the word-based view reverses it.*

**B.** By arguing that the theory is overly influenced by the work of earlier scholars 

  *Text 1 frames Lacadena's syllabic theory as a departure from earlier scholars' word-based assumption, not a continuation of it; influence from earlier scholars is never discussed in either text.*

**C.** By approving of the theory's emphasis on how the script changed over time 

  *Neither text discusses change over time in the script; Text 2's consensus view is about context-dependent function at a given site within a text, not historical evolution of the writing system.*

**D.** By cautioning that the theory overlooks certain important aspects of how the script functioned **(Correct)**

  *Correct. Text 2's consensus holds that Nahuatl symbols could signify either words or syllables depending on context, requiring readers to determine function case by case. Lacadena's theory, as reported in Text 1, treats the symbols as uniformly syllabic — a narrower account that misses the word/syllable flexibility Text 2 says is now the consensus view.*

*Difficulty: hard*

---

##### Q24
> Text 1: Many studies in psychology have shown that people seek out information even when they know in advance that they have no immediate use for it and that they won't directly benefit from it. Such findings support the consensus view among researchers of curiosity: namely, that curiosity is not instrumental but instead represents a drive to acquire information for its own sake. Text 2: While acknowledging that acquiring information is a powerful motivator, Rachit Dubey and colleagues ran an experiment to test whether emphasizing the usefulness of scientific information could increase curiosity about it. They found that when research involving rats and fruit flies was presented as having medical applications for humans, participants expressed greater interest in learning about it than when the research was not presented as useful.

Based on the texts, how would Dubey and colleagues (Text 2) most likely respond to the consensus view discussed in Text 1?

**A.** By suggesting that curiosity may not be exclusively motivated by the desire to merely acquire information **(Correct)**

  *Correct. Text 1's consensus is that curiosity is purely non-instrumental, acquiring information 'for its own sake.' Dubey's experiment found that framing information as medically useful increased interest in it — meaning perceived usefulness, an instrumental factor, also drives curiosity. This is a scope limitation on the consensus view: information-seeking still happens, but usefulness measurably affects it too.*

**B.** By conceding that people may seek out information that serves no immediate purpose only because they think they can use it later 

  *This reframes the consensus as delayed instrumentalism, but Dubey's finding is about perceived usefulness increasing interest in real time, not about people secretly banking information for later use — a mechanism neither text describes.*

**C.** By pointing out that it is challenging to determine when information-seeking serves no goal beyond acquiring information 

  *Dubey's experiment doesn't raise a measurement difficulty; it directly demonstrates a specific effect (usefulness framing increases interest), a substantive finding, not a methodological complaint about ambiguity.*

**D.** By disputing the idea that curiosity can help explain apparently purposeless information-seeking behaviors 

  *Dubey's team 'acknowledges that acquiring information is a powerful motivator,' accepting that curiosity does explain such behavior; their finding qualifies the consensus's exclusivity claim, it doesn't dispute curiosity's explanatory role altogether.*

*Difficulty: medium*

---

##### Q25
> Text 1: Polar bears sustain themselves primarily by hunting seals on the Arctic sea ice, but rising ocean temperatures are causing the ice to diminish, raising concerns about polar bear population declines as these large predators' seal-hunting habitats continue to shrink. A 2020 study examining polar bear populations across the Arctic concluded that populations affected by sea-ice loss are at great risk of extinction by the end of the twenty-first century. Text 2: Monitoring carried out by researchers from the Norwegian Polar Institute shows that the polar bear population on the Arctic archipelago of Svalbard remains stable and well nourished despite rapidly declining sea ice in recent years. The researchers attribute this population's resilience in part to a shift in feeding strategies: in addition to hunting seals, the Svalbard polar bears have begun relying on a diet of reindeer meat and birds' eggs.

Based on the texts, how would the researchers in Text 2 most likely respond to the conclusion, presented in Text 1, that populations affected by sea-ice loss are at great risk of extinction?

**A.** By noting that it neglects the possibility of some polar bear populations adapting to changes in their environment **(Correct)**

  *Correct. The Svalbard population faces the same sea-ice decline as the populations in Text 1's study, yet remains 'stable and well nourished' because the bears shifted their diet to reindeer and birds' eggs — a concrete case of adaptation the extinction-risk conclusion in Text 1 doesn't account for.*

**B.** By suggesting that it is likely incorrect about the rates at which warming ocean temperatures have caused sea ice to melt in the Arctic 

  *Text 2 doesn't dispute the rate of sea-ice decline — it explicitly describes 'rapidly declining sea ice' at Svalbard too; its point is about the bears' response to that decline, not about the accuracy of ice-melt data.*

**C.** By asserting that it overlooks polar bear populations that have not yet been affected by loss of seal-hunting habitats 

  *The Svalbard population in Text 2 has been affected by sea-ice loss (it is explicitly 'rapidly declining'); the researchers' point is about resilience despite being affected, not about populations untouched by the problem.*

**D.** By arguing that it fails to account for polar bears' reliance on a single seal-hunting strategy 

  *Text 2's resilience explanation is that Svalbard bears diversified beyond seal-hunting to reindeer and eggs; this choice describes a critique about seals specifically, but the researchers' actual point is about supplementing, not the risks of relying on one hunting method.*

*Difficulty: medium*

---

##### Q26
> Text 1: It seems clear that emotional contagion (the unintentional transfer of an emotional state from one person to another) requires physical interaction and the observation of body language. After all, research shows that talking to someone who is smiling and expressing positive feelings often causes people to respond in a comparably positive way. Similarly, displays of nervous fidgeting have been found to prompt others to begin behaving more nervously, too. Text 2: In an experiment using a social networking service, Zeyao Yang and Emilio Ferrara found evidence of emotional contagion in text-based online interactions. The researchers discovered that reading social media posts that expressed a positive outlook led people to make more positive posts themselves, while posts with a negative emotional tone led people to make more negative posts.

Based on the texts, what would the researchers in Text 2 most likely say about the claim in Text 1 that emotional contagion requires physical interaction and the observation of body language?

**A.** It perpetuates a flawed understanding of emotional contagion, because there isn't enough evidence to suggest that smiling is a sign of emotional contagion. 

  *Text 2 doesn't dispute that smiling can transmit emotion in person; its finding is about a separate channel (text-based posts) working without physical interaction at all, not about the validity of the smiling example itself.*

**B.** It reflects an incomplete view of emotional contagion, because this phenomenon can occur even without in-person interaction. **(Correct)**

  *Correct. Yang and Ferrara found emotional contagion in purely 'text-based online interactions' — no physical presence, body language, or in-person contact involved. This directly demonstrates that Text 1's claimed requirement is not actually necessary, without denying that in-person contagion also occurs.*

**C.** It's fairly persuasive, because studies attempting to identify emotional contagion in situations without in-person interaction have thus far yielded unclear results. 

  *This misrepresents Text 2's own finding as inconclusive, when Yang and Ferrara's experiment 'found evidence' of contagion in text-based interactions — a clear, not unclear, result that undercuts rather than supports Text 1's claim.*

**D.** It's mostly accurate, because the social networking study confirmed that emotional contagion primarily occurs in response to negative emotions like nervousness. 

  *Text 2 reports contagion effects for both positive and negative posts symmetrically, with no claim that negative emotions predominate; nervousness specifically belongs to Text 1's in-person example, not Text 2's online study.*

*Difficulty: medium*

---

##### Q27
> Text 1: One challenge faced by researchers studying global urbanization is that countries may define urban settlements differently. Many countries define urban settlements based on the number of people living in them. However, countries do not all use the same number; for example, Iceland uses a minimum population of 200, while the Netherlands uses 20,000. Other countries use a combination of population and other factors. This variation makes it difficult for researchers to compare aspects of urbanization in different countries. Text 2: Recently, a group of six international organizations developed global definitions of common types of settlements. The group developed a new measure called the "degree of urbanization." This new measure establishes global criteria used to define three types of settlements (cities, towns, and rural areas) and allows researchers to better understand global urbanization rates.

Based on the texts, how would the author of Text 2 most likely respond to the problem presented in Text 1?

**A.** By recommending that a specific institution should further investigate the problem 

  *Text 2 describes a completed measure already developed by six organizations, not a recommendation that some single institution should investigate further; the measure is presented as an existing solution, not a call for more study.*

**B.** By suggesting that researchers focus on topics besides urbanization 

  *Text 2 is entirely about improving urbanization research through a new standardized measure, not about redirecting researchers away from the topic.*

**C.** By supplying additional ways in which urbanization research is difficult 

  *Text 2 doesn't add new difficulties; it presents a resolution — the degree-of-urbanization measure — to the specific difficulty Text 1 raises, moving toward a solution rather than compounding the problem.*

**D.** By noting that a possible solution to the problem is available **(Correct)**

  *Correct. Text 1's problem is that inconsistent national definitions of 'urban' make cross-country comparison difficult. Text 2 reports that six international organizations developed a new standardized 'degree of urbanization' measure with global criteria, which 'allows researchers to better understand global urbanization rates' — precisely a solution to the definitional inconsistency Text 1 describes.*

*Difficulty: easy*

---

##### Q28
> Text 1: In 1916, H. Dugdale Sykes disputed claims that The Two Noble Kinsmen was coauthored by William Shakespeare and John Fletcher. Sykes felt that Fletcher's contributions to the play were obvious—Fletcher had a distinct style in his other plays, so much so that lines with that style were considered sufficient evidence of Fletcher's authorship. But for the lines not deemed to be by Fletcher, Sykes felt that their depiction of women indicated that their author was not Shakespeare but Philip Massinger. Text 2: Scholars have accepted The Two Noble Kinsmen as coauthored by Shakespeare since the 1970s: it appears in all major one-volume editions of Shakespeare's complete works. Though scholars disagree about who wrote what exactly, it is generally held that on the basis of style, Shakespeare wrote all of the first act and most of the last, while John Fletcher authored most of the three middle acts.

Based on the texts, both Sykes in Text 1 and the scholars in Text 2 would most likely agree with which statement?

**A.** John Fletcher's writing has a unique, readily identifiable style. **(Correct)**

  *Correct. Sykes treats lines matching Fletcher's 'distinct style' as 'sufficient evidence of Fletcher's authorship,' and the scholars in Text 2 likewise attribute most of the three middle acts to Fletcher 'on the basis of style.' Both attributions depend on Fletcher's style being distinctive enough to identify — the shared premise underneath their otherwise different conclusions about the play's authorship.*

**B.** The women characters in John Fletcher's plays are similar to the women characters in Philip Massinger's plays. 

  *Sykes uses depictions of women to argue for Massinger's authorship of certain lines instead of Fletcher's, implying a difference in style, not a similarity between Fletcher and Massinger; Text 2 never discusses Massinger at all.*

**C.** The Two Noble Kinsmen belongs in one-volume compilations of Shakespeare's complete plays. 

  *This is Text 2's own claim about current scholarly practice; Sykes, writing in 1916, disputed Shakespeare's coauthorship altogether, so nothing indicates he would agree the play belongs in Shakespeare compilations.*

**D.** Philip Massinger's style in the first and last acts of The Two Noble Kinsmen is an homage to Shakespeare's style. 

  *Text 2 attributes the first and most of the last act to Shakespeare himself, not to Massinger; Sykes attributes only the lines about women, not full acts, to Massinger. This choice misassigns which author wrote which acts.*

*Difficulty: medium*

---

##### Q29
> Text 1: Growth in the use of novel nanohybrids—materials created from the conjugation of multiple distinct nanomaterials, such as iron oxide and gold nanomaterials conjugated for use in magnetic imaging—has outpaced studies of nanohybrids' environmental risks. Unfortunately, risk evaluations based on nanohybrids' constituents are not reliable: conjugation may alter constituents' physiochemical properties such that innocuous nanomaterials form a nanohybrid that is anything but. Text 2: The potential for enhanced toxicity of nanohybrids relative to the toxicity of constituent nanomaterials has drawn deserved attention, but the effects of nanomaterial conjugation vary by case. For instance, it was recently shown that a nanohybrid of silicon dioxide and zinc oxide preserved the desired optical transparency of zinc oxide nanoparticles while mitigating the nanoparticles' potential to damage DNA.

Based on the texts, how would the author of Text 2 most likely respond to the assertion in Text 1 that conjugation may turn innocuous nanomaterials into a harmful nanohybrid?

**A.** By concurring that the risk described in Text 1 should be evaluated but emphasizing that the risk is more than offset by the potential benefits of nanomaterial conjugation 

  *Text 2 never weighs risks against benefits or claims benefits outweigh risks; its silicon dioxide/zinc oxide example shows conjugation reducing a specific harm, not a benefit compensating for a separate harm.*

**B.** By arguing that the situation described in Text 1 may not be representative but conceding that the effects of nanomaterial conjugation are harder to predict than researchers had expected 

  *Text 2 doesn't discuss researchers' prior predictive expectations; its point is that outcomes 'vary by case,' illustrated with an example where conjugation reduced rather than increased harm, not a general claim about difficulty of prediction.*

**C.** By denying that the circumstance described in Text 1 is likely to occur but acknowledging that many aspects of nanomaterial conjugation are still poorly understood 

  *Text 2 grants that enhanced toxicity from conjugation 'has drawn deserved attention' — meaning it is a real, recognized possibility — rather than denying it can occur at all.*

**D.** By agreeing that the possibility described in Text 1 is a cause for concern but pointing out that nanomaterial conjugation does not inevitably produce that result **(Correct)**

  *Correct. Text 2 opens by conceding enhanced toxicity from conjugation 'has drawn deserved attention' (agreeing it's a real concern), then qualifies that 'effects of nanomaterial conjugation vary by case,' backed by an example where conjugation reduced toxicity rather than creating it — the risk is real but not universal.*

*Difficulty: hard*

---

##### Q30
> Text 1: Africa's Sahara region—once a lush ecosystem—began to dry out about 8,000 years ago. A change in Earth's orbit that affected climate has been posited as a cause of desertification, but archaeologist David Wright also attributes the shift to Neolithic peoples. He cites their adoption of pastoralism as a factor in the region drying out: the pastoralists' livestock depleted vegetation, prompting the events that created the Sahara Desert. Text 2: Research by Chris Brierley et al. challenges the idea that Neolithic peoples contributed to the Sahara's desertification. Using a climate-vegetation model, the team concluded that the end of the region's humid period occurred 500 years earlier than previously assumed. The timing suggests that Neolithic peoples didn't exacerbate aridity in the region but, in fact, may have helped delay environmental changes with practices (e.g., selective grazing) that preserved vegetation.

Based on the texts, how would Chris Brierley (Text 2) most likely respond to the discussion in Text 1?

**A.** By pointing out that given the revised timeline for the end of the Sahara's humid period, the Neolithic peoples' mode of subsistence likely didn't cause the region's desertification **(Correct)**

  *Correct. Text 2's revised timeline places the end of the humid period 500 years earlier than previously assumed, and concludes from that timing that Neolithic peoples' practices, including pastoralism, didn't exacerbate the region's aridity — a direct rebuttal of Wright's claim that pastoralism drove the desertification.*

**B.** By claiming that pastoralism was only one of many behaviors the Neolithic peoples took part in that may have contributed to the Sahara's changing climate 

  *Text 2 doesn't broaden the list of contributing Neolithic behaviors; it argues Neolithic peoples in general 'didn't exacerbate aridity' and may have delayed it instead — a rejection of the contribution claim, not an expansion of it.*

**C.** By insisting that pastoralism can have both beneficial and deleterious effects on a region's vegetation and climate 

  *Text 2 credits Neolithic practices like selective grazing specifically with preserving vegetation and delaying change, not with a mixed record of both harm and benefit; no deleterious effect from pastoralism is affirmed in Text 2.*

**D.** By asserting that more research needs to be conducted into factors that likely contributed to the desertification of the Sahara region 

  *Text 2 presents a completed finding with a specific conclusion — revised timeline, Neolithic peoples didn't exacerbate aridity — not a call for further research; this understates the definiteness of Brierley's actual claim.*

*Difficulty: hard*

---

##### Q31
> Text 1: Soy sauce, made from fermented soybeans, is noted for its umami flavor. Umami—one of the five basic tastes along with sweet, bitter, salty, and sour—was formally classified when its taste receptors were discovered in the 2000s. In 2007, to define the pure umami flavor scientists Rie Ishii and Michael O'Mahony used broths made from shiitake mushrooms and kombu seaweed, and two panels of Japanese and US judges closely agreed on a description of the taste. Text 2: A 2022 experiment by Manon Jünger et al. led to a greater understanding of soy sauce's flavor profile. The team initially presented a mixture of compounds with low molecular weights to taste testers who found it was not as salty or bitter as real soy sauce. Further analysis of soy sauce identified proteins, including dipeptides, that enhanced umami flavor and also contributed to saltiness. The team then made a mix of 50 chemical compounds that re-created soy sauce's flavor.

Based on the texts, if Ishii and O'Mahony (Text 1) and Jünger et al. (Text 2) were aware of the findings of both experiments, they would most likely agree with which statement?

**A.** On average, the diets of people in the United States tend to have fewer foods that contain certain dipeptides than the diets of people in Japan have. 

  *National dietary composition is not discussed in either text; Text 1's Japanese and US judges evaluated a taste description, not their countries' typical diets, and Text 2 never compares diets by country.*

**B.** Chemical compounds that activate both the umami and salty taste receptors tend to have a higher molecular weight than those that only activate umami taste receptors. 

  *This reverses Text 2's actual finding — the low-molecular-weight mixture tested first was found lacking in saltiness and bitterness, and it was the dipeptides identified afterward that enhanced both umami and saltiness together, not a claim that dual-activating compounds are heavier than umami-only ones.*

**C.** Fermentation introduces proteins responsible for the increase of umami flavor in soy sauce, and those proteins also increase the perception of saltiness. 

  *Text 2 identifies dipeptide proteins that enhance both umami and saltiness, but neither text attributes their presence specifically to the fermentation process; Text 1 notes soy sauce is fermented, but no causal link between fermentation and dipeptide formation is stated in either text.*

**D.** The broths in the 2007 experiment most likely did not have a substantial amount of the dipeptides that played a key part in the 2022 experiment. **(Correct)**

  *Correct. Ishii and O'Mahony's 2007 broths were designed to isolate 'pure' umami flavor. Jünger's 2022 team found that dipeptides contribute to both umami and saltiness, not umami alone — meaning a broth engineered to represent pure, unmixed umami would plausibly lack the dipeptides whose effect includes saltiness, a taste the 2007 broths weren't meant to capture.*

*Difficulty: sat-hardest*

---

##### Q32
> Text 1: What factors influence the abundance of species in a given ecological community? Some theorists have argued that historical diversity is a major driver of how diverse an ecological community eventually becomes: differences in community diversity across otherwise similar habitats, in this view, are strongly affected by the number of species living in those habitats at earlier times. Text 2: In 2010, a group of researchers including biologist Carla Cáceres created artificial pools in a New York forest. They stocked some pools with a diverse mix of zooplankton and others with a single zooplankton species and allowed the pool communities to develop naturally thereafter. Over the course of four years, Cáceres and colleagues periodically measured the species diversity of the pools, finding—contrary to their expectations—that by the end of the study there was little to no difference in the pools' species diversity.

Based on the texts, how would Cáceres and colleagues (Text 2) most likely describe the view of the theorists presented in Text 1?

**A.** It is largely correct, but it requires a minor refinement in light of the research team's results. 

  *The study found 'little to no difference' in diversity between pools started with very different initial diversity — a result the researchers themselves didn't expect, and one that undermines rather than merely refines the theory that starting diversity drives eventual diversity.*

**B.** It is not compelling as a theory regardless of any experimental data collected by the research team. 

  *This suggests the researchers view the theory as inherently weak independent of evidence, but the study is explicitly framed around testing the theory and finding it unsupported by that specific evidence — the data are what makes the case, not a prior dismissal.*

**C.** It may seem plausible, but it is not supported by the research team's findings. **(Correct)**

  *Correct. The theorists' view — that historical diversity strongly shapes eventual community diversity — predicts pools stocked with diverse versus single-species zooplankton would diverge in diversity over time. Instead, Cáceres and colleagues found 'contrary to their expectations' that diversity converged to be nearly the same regardless of starting point, directly failing to support the theory their experiment was designed to test.*

**D.** It probably holds true only in conditions like those in the research team's study. 

  *The study's finding is that the theory did not hold even under the very conditions tested (the artificial pools), so this choice inverts the result — the theory failed in these conditions, it wasn't confirmed as true specifically within them.*

*Difficulty: medium*

---

##### Q33
> Text 1: Fossils of the hominin Australopithecus africanus have been found in the Sterkfontein Caves in South Africa, but assigning an age to the fossils is challenging because of the unreliability of dating methods in this context. The geology of Sterkfontein has caused soil layers from different periods to mix, impeding stratigraphic dating, and dates cannot be reliably imputed from those of nearby animal bones since the bones may have been relocated by flooding. Text 2: Archaeologists used new cosmogenic nuclide dating techniques to reevaluate the ages of A. africanus fossils found in the Sterkfontein Caves. This technique involves analyzing the cosmogenic nucleotides in the breccia—the matrix of rock fragments immediately surrounding the fossils. The researchers assert that this approach avoids the potential for misdating associated with assigning ages based on Sterkfontein's soil layers or animal bones.

Based on the texts, how would the researchers in Text 2 most likely respond to the claim in Text 1 that dating methods are unreliable in the context of the Sterkfontein Caves?

**A.** They would emphasize the fact that the A. africanus fossils found in the Sterkfontein Caves may have been corrupted in some way over the years. 

  *Text 2's argument is about the reliability of the dating technique — breccia analysis avoids the soil and bone problems — not about the physical condition of the fossils themselves being corrupted.*

**B.** They would contend that if analyses of surrounding layers and bones in the Sterkfontein Caves were combined, then the dating of the fossils there would be more accurate. 

  *Text 2's technique specifically avoids using soil layers and animal bones altogether, analyzing the breccia directly instead; it doesn't propose combining the two unreliable methods Text 1 describes, but bypassing them.*

**C.** They would argue that their techniques are better suited than other methods to the unique challenges posed by the Sterkfontein Caves. **(Correct)**

  *Correct. Text 1's specific challenges are mixed soil layers (defeating stratigraphic dating) and unreliable animal-bone dates (due to flooding relocation). Text 2's cosmogenic nuclide technique analyzes the breccia directly around the fossils and is explicitly said to 'avoid the potential for misdating associated with' both of those exact problems.*

**D.** They would claim that cosmogenic nuclide dating is reliable in the context of the Sterkfontein Caves because it is applied to the fossils directly. 

  *Text 2 states the technique analyzes the breccia — the rock matrix surrounding the fossils — not the fossils themselves directly; this choice misstates what the method actually measures.*

*Difficulty: medium*

---

##### Q34
> Text 1: Films and television shows commonly include a long list of credits naming the people involved in a production. Credit sequences may not be exciting, but they generally ensure that everyone's contributions are duly acknowledged. Because they are highly standardized, film and television credits are also valuable to anyone researching the careers of pioneering cast and crew members who have worked in the mediums. Text 2: Video game scholars face a major challenge in the industry's failure to consistently credit the artists, designers, and other contributors involved in making video games. Without a reliable record of which people worked on which games, questions about the medium's development can be difficult to answer, and the accomplishments of all but its best-known innovators can be difficult to trace.

Based on the texts, how would the author of Text 1 most likely respond to the discussion in Text 2?

**A.** By recommending that the scholars mentioned in Text 2 consider employing the methods regularly used by film and television researchers 

  *Text 1 describes standardized credits as a feature of the film and television industry itself, not a research method scholars could adopt independent of the industry's practices; the fix Text 1 implies is industry-level standardization, not a change in scholarly method.*

**B.** By pointing out that credits have a different intended purpose in film and television than in the medium addressed by the scholars mentioned in Text 2 

  *Text 1 says nothing about credits serving a different purpose across mediums; its point is that film and television credits are useful specifically because they are standardized and reliably present, a difference in practice, not stated purpose.*

**C.** By suggesting that the scholars mentioned in Text 2 rely more heavily on credits as a source of information than film and television researchers do 

  *This reverses the situation — Text 2's scholars face difficulty precisely because reliable video game credits don't exist to rely on, while Text 1 describes film and television credits as a valuable resource researchers do have and can use.*

**D.** By observing that a widespread practice in film and television largely prevents the kind of problem faced by the scholars mentioned in Text 2 **(Correct)**

  *Correct. Text 2's problem is the video game industry's inconsistent crediting, which makes it hard to trace contributors' work. Text 1 establishes that film and television credits are 'highly standardized' and reliably acknowledge contributions, exactly the kind of consistent practice that would prevent the tracing problem Text 2 describes.*

*Difficulty: medium*

---

##### Q35
> Text 1: Like the work of Ralph Ellison before her, Toni Morrison's novels feature scenes in which characters deliver sermons of such length and verbal dexterity that for a time, the text exchanges the formal parameters of fiction for those of oral literature. Given the many other echoes of Ellison in Morrison's novels, both in structure and prose style, these scenes suggest Ellison's direct influence on Morrison. Text 2: In their destabilizing effect on literary form, the sermons in Morrison's works recall those in Ellison's. Yet literature by Black Americans abounds in moments where interpolated speech erodes the division between oral and written forms that literature in English has traditionally observed. Morrison's use of the sermon is attributable not only to the influence of Ellison but also to a community-wide strategy of resistance to externally imposed literary conventions.

Based on the texts, how would the author of Text 2 most likely characterize the claim in Text 1 that Ellison directly influenced Morrison's use of sermon scenes?

**A.** As failing to consider Ellison's and Morrison's equivalent uses of the sermon within the wider cultural context in which they wrote **(Correct)**

  *Correct. Text 2 agrees the sermons 'recall' Ellison's, but locates both writers' use of the device within a broader 'community-wide strategy' found throughout Black American literature, not unique to an Ellison-to-Morrison line of influence. Text 1's claim, resting only on structural and stylistic echoes between the two authors, omits this wider tradition Text 2 says also explains the technique.*

**B.** As misunderstanding the function of sermons in novels by Black American writers other than Ellison and Morrison 

  *Text 2 doesn't claim Text 1 misunderstands sermons' function in other writers' works; it says Text 1 overlooks a broader context that includes other writers, a different criticism (an omission) than a misunderstanding of function elsewhere.*

**C.** As disregarding points of structural and stylistic divergence between the works of Ellison and those of Morrison 

  *Text 2 doesn't argue Text 1 ignored differences between the two authors' works; if anything Text 2 affirms a real similarity — the sermons 'recall' each other — while adding a broader explanation, not identifying overlooked divergences.*

**D.** As being indebted to the tradition of resisting literary conventions that privilege written forms, such as novels, over sermons and other oral forms 

  *This describes Morrison's practice itself, per Text 2's community-wide resistance strategy, not a characterization of Text 1's claim about Ellison's influence; it misapplies a description of the literary tradition to the argument being evaluated.*

*Difficulty: sat-hardest*

---

##### Q36
> Text 1: Virginia Woolf's 1928 novel Orlando is an oddity within her body of work. Her other major novels consist mainly of scenes of everyday life and describe their characters' interior states in great detail, whereas Orlando propels itself through a series of fantastical events and considers its characters' psychology more superficially. Woolf herself sometimes regarded the novel as a minor work, even admitting once that she "began it as a joke." Text 2: Like Woolf's other great novels, Orlando portrays how people's memories inform their experience of the present. Like those works, it examines how people navigate social interactions shaped by gender and social class. Though it is lighter in tone—more entertaining, even—this literary "joke" nonetheless engages seriously with the themes that motivated the four or five other novels by Woolf that have achieved the status of literary classics.

Based on the texts, how would the author of Text 2 most likely respond to the assessment of Orlando presented in Text 1?

**A.** By conceding that Woolf's talents were best suited to serious novels but asserting that the humor in Orlando is often effective 

  *Text 2 doesn't rank Woolf's talents by genre or defend Orlando's humor as effective comedy; its argument is that Orlando engages the same serious themes as her other novels despite its lighter tone, not a defense of its jokes.*

**B.** By agreeing that Orlando is less impressive than certain other novels by Woolf but arguing that it should still be regarded as a classic 

  *Text 2 never ranks Orlando as less impressive than Woolf's other novels; it argues Orlando shares the same thematic seriousness as those novels, a claim of equivalence in substance, not a concession of lesser quality.*

**C.** By acknowledging that Orlando clearly differs from Woolf's other major novels but insisting on its centrality to her body of work nonetheless **(Correct)**

  *Correct. Text 2 grants the stylistic difference Text 1 identifies — 'lighter in tone, more entertaining, even' — but argues Orlando 'nonetheless engages seriously with the themes that motivated' Woolf's other classics: memory, gender, and class. This accepts Text 1's surface observation about tone while rejecting its implication that the novel is minor or peripheral.*

**D.** By concurring that the reputation of Orlando as a minor work has led readers to overlook this novel but maintaining that the reputation is unearned 

  *Text 2 never discusses readers overlooking Orlando or the effects of its reputation on readership; its argument is about the novel's thematic content, not about how its reputation has shaped its reception.*

*Difficulty: hard*

---

##### Q37
> Text 1: Despite its beautiful prose, The Guns of August, Barbara Tuchman's 1962 analysis of the start of World War I, has certain weaknesses as a work of history. It fails to address events in Eastern Europe just before the outbreak of hostilities, thereby giving the impression that Germany was the war's principal instigator. Had Tuchman consulted secondary works available to her by scholars such as Luigi Albertini, she would not have neglected the influence of events in Eastern Europe on Germany's actions. Text 2: Barbara Tuchman's The Guns of August is an engrossing if dated introduction to World War I. Tuchman's analysis of primary documents is laudable, but her main thesis that European powers committed themselves to a catastrophic outcome by refusing to deviate from military plans developed prior to the conflict is implausibly reductive.

Which choice best describes a difference in how the authors of Text 1 and Text 2 view Barbara Tuchman's The Guns of August?

**A.** The author of Text 1 argues that Tuchman should have relied more on the work of other historians, while the author of Text 2 implies that Tuchman's most interesting claims result from her original research. 

  *Text 2 praises Tuchman's 'analysis of primary documents,' her own original research, but never contrasts this with her 'most interesting claims' specifically, nor implies those claims in particular result from it; this overstates a connection Text 2 doesn't draw.*

**B.** The author of Text 1 believes that the scope of Tuchman's research led her to an incorrect interpretation, while the author of Text 2 believes that Tuchman's central argument is overly simplistic. **(Correct)**

  *Correct. Text 1's critique is that Tuchman's failure to consult available secondary sources on Eastern Europe — a scope-of-research problem — caused her to wrongly imply Germany was the principal instigator, an incorrect interpretation. Text 2's critique is different in kind: it doesn't fault her research scope, but calls her actual thesis 'implausibly reductive,' meaning oversimplified.*

**C.** The author of Text 1 asserts that the writing style of The Guns of August makes it worthwhile to read despite any perceived deficiency in Tuchman's research, while the author of Text 2 focuses exclusively on the weakness of Tuchman's interpretation of events. 

  *Text 1 does praise the 'beautiful prose' but doesn't frame that as making the book worthwhile despite its weaknesses — it simply lists both; and Text 2 does not focus exclusively on weakness, since it also calls the book 'engrossing' and calls Tuchman's document analysis 'laudable.'*

**D.** The author of Text 1 claims that Tuchman would agree that World War I was largely due to events in Eastern Europe, while the author of Text 2 maintains that Tuchman would say that Eastern European leaders were not committed to military plans in the same way that other leaders were. 

  *Text 1 argues Tuchman herself neglected Eastern Europe's influence — it doesn't claim Tuchman would agree with that assessment; and Text 2 never discusses what Tuchman would say about Eastern European leaders specifically, only her general thesis about European powers collectively.*

*Difficulty: sat-hardest*

---

##### Q38
> Text 1: The fossil record suggests that mammoths went extinct around 11 thousand years ago (kyr). In a 2021 study of environmental DNA (eDNA)—genetic material shed into the environment by organisms—in the Arctic, Yucheng Wang and colleagues found mammoth eDNA in sedimentary layers formed millennia later, around 4 kyr ago. To account for this discrepancy, Joshua H. Miller and Carl Simpson proposed that arctic temperatures could preserve a mammoth carcass on the surface, allowing it to leach DNA into the environment, for several thousand years. Text 2: Wang and colleagues concede that eDNA contains DNA from both living organisms and carcasses, but for DNA to leach from remains over several millennia requires that the remains be perpetually on the surface. Scavengers and weathering in the Arctic, however, are likely to break down surface remains well before a thousand years have passed.

Which choice best describes how Text 1 and Text 2 relate to each other?

**A.** Text 1 discusses two approaches to studying mammoth extinction without advocating for either, whereas Text 2 advocates for one approach over the other. 

  *Text 1 doesn't present two neutral 'approaches' — it presents a finding (later eDNA) and an explanation for the discrepancy (carcass preservation), not two rival methods; Text 2 doesn't choose between approaches either, it directly challenges the explanation's feasibility.*

**B.** Text 1 presents findings by Wang and colleagues and gives another research team's attempt to explain those findings, whereas Text 2 provides additional detail that calls that explanation into question. **(Correct)**

  *Correct. Text 1 reports Wang's eDNA finding and then Miller and Simpson's proposed explanation — long-term carcass preservation — for the discrepancy. Text 2 adds detail that scavengers and weathering would likely break down surface remains well before the thousands of years the explanation requires, undermining the feasibility of that very explanation.*

**C.** Text 1 describes Wang and colleagues' study and a critique of their methodology, whereas Text 2 offers additional details showing that methodology to be sound. 

  *Miller and Simpson's proposal in Text 1 is not a critique of Wang's methodology — it's an attempt to explain Wang's finding; and Text 2 challenges that proposed explanation rather than vindicating any methodology.*

**D.** Text 1 argues that new research has undermined the standard view of when mammoths went extinct, whereas Text 2 suggests a way to reconcile the standard view with that new research. 

  *This reverses the two texts' roles — it is Text 1's Miller-and-Simpson proposal that attempts reconciliation, explaining away the late eDNA without overturning the 11 kyr extinction date, while Text 2 is the one casting doubt on that reconciliation, not offering one.*

*Difficulty: hard*

---

##### Q39
> Text 1: Dominique Potvin and colleagues captured five Australian magpies (Gymnorhina tibicen) to test a new design for attaching tracking devices to birds. As the researchers fitted each magpie with a tracker attached by a small harness, they noticed some magpies without trackers pecking at another magpie's tracker until it broke off. The researchers suggest that this behavior could be evidence of magpies attempting to help another magpie without benefiting themselves. Text 2: It can be tempting to think that animals are deliberately providing help when we see them removing trackers and other equipment from one another, especially when a species is known to exhibit other cooperative behaviors. At the same time, it can be difficult to exclude the possibility that individuals are simply interested in the equipment because of its novelty, curiously pawing or pecking at it until it detaches.

Based on the texts, how would the author of Text 2 most likely respond to the researchers' perspective in Text 1 on the behavior of the magpies without trackers?

**A.** That behavior might have been due to the novelty of the magpies' captive setting rather than to the novelty of the tracker. 

  *Text 2 specifically attributes the alternative explanation to interest in the equipment's novelty, the tracker itself, not to novelty of the setting the magpies were kept in, which is never mentioned in either text.*

**B.** That behavior likely indicates that the magpies were deliberately attempting to benefit themselves by obtaining the tracker. 

  *Text 2's alternative is curious pecking that causes the tracker to detach, not an attempt to keep or obtain the tracker for the pecking bird's own benefit; nothing in Text 2 suggests the birds wanted to acquire the equipment.*

**C.** That behavior may not be evidence of selflessness in Gymnorhina tibicen because not all the captured magpies demonstrated it. 

  *Text 2's objection is about the alternative explanation for the pecking behavior — novelty-driven curiosity versus deliberate helping — not about the fact that only some magpies exhibited it; participation rate across birds is never raised in Text 2.*

**D.** That behavior might be adequately explained without suggesting that the magpies were attempting to assist the other magpie. **(Correct)**

  *Correct. Text 2 grants that helping behavior is tempting to infer, especially in a cooperative species, but insists it 'can be difficult to exclude the possibility' that the pecking is simply curiosity-driven interest in a novel object. This withholds endorsement of Text 1's 'attempting to help' interpretation without denying it outright.*

*Difficulty: medium*

---

##### Q40
> Text 1: In 2007, a team led by Alice Storey analyzed a chicken bone found in El Arenal, Chile, dating it to 1321–1407 CE—over a century before Europeans invaded the region, bringing their own chickens. Storey also found that the El Arenal chicken shared a unique genetic mutation with the ancient chicken breeds of the Polynesian Islands in the Pacific. Thus, Polynesian peoples, not later Europeans, probably first introduced chickens to South America. Text 2: An Australian research team weakened the case for a Polynesian origin for the El Arenal chicken by confirming that the mutation identified by Storey has occurred in breeds from around the world. More recently, though, a team led by Agusto Luzuriaga-Neira found that South American chicken breeds and Polynesian breeds share other genetic markers that European breeds lack. Thus, the preponderance of evidence now favors a Polynesian origin.

Based on the texts, how would the author of Text 2 most likely respond to the claim in Text 1 that Polynesian peoples probably first introduced chickens to South America?

**A.** By broadly agreeing with the claim but objecting that the timeline it presupposes conflicts with the findings of the genetic analysis conducted by Storey's team 

  *Text 2 doesn't dispute Storey's dating (1321–1407 CE); its critique of Storey's genetic evidence is that the specific mutation she cited turned out to be a poor discriminator, found in breeds worldwide, not that the timeline conflicts with the genetics.*

**B.** By faulting the claim for implying that domestic animals couldn't have been transferred from South America to the Polynesian islands as well 

  *Direction of animal transfer, South America to Polynesia versus the reverse, is never discussed in either text; Text 2's argument is entirely about which genetic evidence better supports Polynesian origin for the El Arenal chicken.*

**C.** By critiquing the claim for being based on an assumption that before the European invasion of South America, the chickens of Europe were genetically uniform 

  *Text 2's objection to Storey's original mutation evidence is that the mutation appears in breeds 'from around the world,' not specifically that Storey assumed genetic uniformity among European chickens; this misstates what made the original mutation evidence weak.*

**D.** By noting that while the claim is persuasive, the findings of Luzuriaga-Neira's team provide stronger evidence for it than the findings of the genetic analysis conducted by Storey do **(Correct)**

  *Correct. Text 2 first reports that the Australian team weakened Storey's original mutation evidence — it wasn't unique to Polynesian or South American breeds — then reports that Luzuriaga-Neira's team found other genetic markers shared specifically between South American and Polynesian breeds but absent in European ones, evidence the text says makes 'the preponderance of evidence' now favor Polynesian origin more strongly than Storey's original, since-weakened, finding did.*

*Difficulty: sat-hardest*

---

##### Q41
> Text 1: Conventional wisdom long held that human social systems evolved in stages, beginning with hunter-gatherers forming small bands of members with roughly equal status. The shift to agriculture about 12,000 years ago sparked population growth that led to the emergence of groups with hierarchical structures: associations of clans first, then chiefdoms, and finally, bureaucratic states. Text 2: In a 2021 book, anthropologist David Graeber and archaeologist David Wengrow maintain that humans have always been socially flexible, alternately forming systems based on hierarchy and collective ones with decentralized leadership. The authors point to evidence that as far back as 50,000 years ago some hunter-gatherers adjusted their social structures seasonally, at times dispersing into small groups but also assembling into communities that included esteemed individuals.

Based on the texts, how would Graeber and Wengrow (Text 2) most likely respond to the "conventional wisdom" presented in Text 1?

**A.** By conceding the importance of hierarchical systems but asserting the greater significance of decentralized collective societies 

  *Graeber and Wengrow don't rank hierarchical systems as important but secondary to decentralized ones; their claim is that humans alternated flexibly between both kinds of systems, not that one was more significant than the other.*

**B.** By disputing the idea that developments in social structures have followed a linear progression through distinct stages **(Correct)**

  *Correct. Text 1's conventional wisdom describes a fixed, linear sequence: equal-status bands, then clans, then chiefdoms, then bureaucratic states, tied to the rise of agriculture. Text 2 directly contradicts the linearity itself, citing hunter-gatherers 50,000 years ago — long before agriculture — already moving flexibly between hierarchical and decentralized structures on a seasonal basis, not a one-way staged progression.*

**C.** By acknowledging that hierarchical roles likely weren't a part of social systems before the rise of agriculture 

  *Text 2's evidence is that hunter-gatherer communities 50,000 years ago, long before agriculture, already assembled into groups 'that included esteemed individuals' — a form of hierarchy predating agriculture, the opposite of what this choice claims Graeber and Wengrow would acknowledge.*

**D.** By challenging the assumption that groupings of hunter-gatherers were among the earliest forms of social structure 

  *Text 2 doesn't dispute that hunter-gatherer groupings were among the earliest social structures — it uses hunter-gatherer behavior 50,000 years ago as its own evidence; the challenge is to the claimed linear progression from those groupings onward, not to their status as an early social structure.*

*Difficulty: medium*

---

#### Text Structure & Purpose (66 items)

##### Q1
> The following text is from Srimati Svarna Kumari Devi's 1894 novel The Fatal Garland (translated by A. Christina Albers in 1910). Shakti is walking near a riverbank that she visited frequently during her childhood.
> 
> She crossed the woods she knew so well. The trees seemed to extend their branches like welcoming arms. They greeted her as an old friend. Soon she reached the river-side.

Which choice best describes the function of the underlined portion "The trees seemed to extend their branches like welcoming arms." in the text as a whole?

**A.** It suggests that Shakti feels uncomfortable near the river. 

  *The image is warm and welcoming — branches extended "like welcoming arms" — not threatening or uncomfortable. This reads the valence of the simile backward.*

**B.** It indicates that Shakti has lost her sense of direction in the woods. 

  *The opening sentence directly rules this out: she "crossed the woods she knew so well." A student picking this has ignored a stated fact one clause earlier that contradicts it.*

**C.** It emphasizes Shakti's sense of belonging in the landscape. **(Correct)**

  *Correct. The woods she knows well seem to welcome her like an old friend — the personification builds a sense that she belongs in this landscape, not that she is a stranger to it.*

**D.** It conveys Shakti's appreciation for her long-term friendships. 

  *"Greeted her as an old friend" personifies the trees; it is a figure of speech about the landscape, not a literal statement about Shakti's actual human friendships, which are never mentioned.*

*Difficulty: medium*

---

##### Q2
> Researchers have found a nearly 164,000-year-old molar from a member of the archaic human species known as Denisovans in a cave in Laos, suggesting that Denisovans lived in a wider range of environments than indicated by earlier evidence. Before the discovery, Denisovans were thought to have lived only at high altitudes in relatively cold climates in what are now Russia and China, but the discovery of the tooth in Laos suggests that they may have lived at low altitudes in relatively warm climates in Southeast Asia as well.

Which choice best states the function of the underlined portion "Before the discovery, Denisovans were thought to have lived only at high altitudes in relatively cold climates in what are now Russia and China," in the text as a whole?

**A.** It dismisses as untrue the research presented in the previous sentence. 

  *The molar finding doesn't dismiss the earlier research as untrue — it expands the known range beyond it. Turning "the range is now known to be wider" into "the earlier finding was false" overstates the relationship.*

**B.** It defines a term used in the description that follows in the rest of the sentence. 

  *No term is being defined here; this is a statement of prior belief, not a definition. There's no unfamiliar word being glossed.*

**C.** It emphasizes the main goal of the research introduced in the previous sentence. 

  *This sentence states what was previously believed, not what any research set out to achieve. There is no stated research "goal" here at all.*

**D.** It provides context that clarifies the significance of the information that follows in the rest of the sentence. **(Correct)**

  *Correct. Knowing the prior belief (high altitude, cold climate) is exactly what makes the new discovery (low altitude, warm climate) significant — the contrast is the point.*

*Difficulty: medium*

---

##### Q3
> Historians Tiya Miles and Roy E. Finkenbine have both documented the assistance Indigenous peoples gave to Black freedom seekers leaving the South before the US Civil War. Much of the historical evidence of this help comes from Indigenous oral traditions and from autobiographies written by the freedom seekers. One such narrative is Jermain Loguen's autobiography, which tells about how Neshnabé (Potawatomi) villagers offered him food, lodging, and directions during his 1835 journey from Tennessee to Canada.

Which choice best describes the function of the underlined sentence "One such narrative is Jermain Loguen's autobiography, which tells about how Neshnabé (Potawatomi) villagers offered him food, lodging, and directions during his 1835 journey from Tennessee to Canada." in the text?

**A.** It provides an example of an autobiography that describes help given by an Indigenous people to a Black freedom seeker. **(Correct)**

  *Correct. "One such narrative" flags it as an example, and its content matches exactly: Neshnabé villagers assisting Loguen, a Black freedom seeker.*

**B.** It shows why Loguen decided to write in great detail about his experiences traveling from Tennessee to Canada. 

  *No motive for why Loguen wrote his autobiography is ever given — the text uses the narrative as evidence of assistance, not as a case study in an author's motives.*

**C.** It argues that autobiographies are particularly important sources of information about geography in the United States before the Civil War. 

  *The text is about autobiographies as evidence of Indigenous assistance, not about geography. This swaps the actual topic for an unrelated one the passage never raises.*

**D.** It suggests that most historians believe that Neshnabé villagers were more successful in assisting freedom seekers than other people were. 

  *No comparison between different groups' success at assisting freedom seekers ever appears — this invents a comparative claim the text doesn't make.*

*Difficulty: medium*

---

##### Q4
> Composer Florence Price won first place for her score Symphony in E Minor at the 1932 Wanamaker Foundation Awards. The piece was performed the following year by the Chicago Symphony Orchestra, a significant recognition of its quality. Price continued to compose many musical pieces throughout her career, blending traditional Black spirituals with classical European Romantic musical traditions. In recent years, Price's concertos and symphonies have been performed and recorded by several major orchestras, further preserving her work for others to enjoy.

Which choice best states the main purpose of the text?

**A.** To provide examples of Price's importance as a composer **(Correct)**

  *Correct. The award win, the Chicago Symphony performance, the blended style, and the ongoing recordings are all offered as a string of examples establishing her importance.*

**B.** To argue that more major orchestras should perform Price's compositions 

  *The text is descriptive, not a call to action — it reports that major orchestras have already performed and recorded her work, not that more of them should.*

**C.** To describe the musical styles that inspired many of Price's symphonies 

  *The text says Price blended Black spirituals with European Romantic tradition in her OWN work — that's her style, not a claim about what "inspired" her, and it's a single supporting detail, not the whole purpose.*

**D.** To compare Price's scores with those of classical European composers 

  *No comparative evaluation of Price's scores against European composers' scores ever appears — the text only says her style blends the two traditions, which is not the same as comparing them.*

*Difficulty: medium*

---

##### Q5
> The following text is adapted from Louisa May Alcott's 1869 novel An Old-Fashioned Girl. Polly, a teenager, is visiting her friend Fanny.
> 
> Fanny's friends did not interest Polly much; she was rather afraid of them [because] they seemed so much older and wiser than herself, even those younger in years. They talked about things of which she knew nothing, and when Fanny tried to explain, she didn't find them interesting; indeed, some of them rather shocked and puzzled her.

Which choice best states the main purpose of the text?

**A.** To portray Polly's reaction to Fanny's friends **(Correct)**

  *Correct. Afraid, uninterested, shocked, puzzled — the whole passage catalogs Polly's feelings toward Fanny's friends.*

**B.** To identify the topics Polly talks about with Fanny's friends 

  *The text says the opposite — Polly "knew nothing" of what was discussed and didn't find the explanations interesting. No actual topics are ever named.*

**C.** To explain how Fanny met some of her friends 

  *No origin story for how Fanny met her friends appears anywhere; only Polly's visit and her reaction to the friends already present are described.*

**D.** To illustrate how Fanny's friends feel about Polly 

  *The text is entirely from Polly's perspective on the friends, not the friends' perspective on Polly — no evidence for how the friends regard her is given.*

*Difficulty: medium*

---

##### Q6
> San Francisco is known for the colorful murals painted on many of its buildings. The densest collection of murals is found on Balmy Alley in the Mission District neighborhood. In the 1970s, Latina artists painted vivid scenes of community life on walls along this block. As the original murals have faded, later generations of artists have painted new ones over them. As a result, Balmy Alley has become a living showcase of San Francisco's artistic spirit, with its murals reflecting changes in the cultural life of the city.

Which choice best states the main purpose of the text?

**A.** To compare the Balmy Alley murals to other murals in San Francisco 

  *The "densest collection" phrase is a superlative, not an actual comparative analysis — no other specific mural site is ever described or evaluated against Balmy Alley.*

**B.** To offer an overview of the history and importance of the Balmy Alley murals **(Correct)**

  *Correct. The text moves from origin (1970s Latina artists) through ongoing repainting to present-day cultural significance — history plus importance.*

**C.** To urge people to protect the murals of San Francisco from decay 

  *The text is descriptive, not persuasive — it treats fading and repainting as a natural, ongoing, even positive process, never asking readers to act.*

**D.** To describe the rise of mural painting in San Francisco beginning in the 1970s 

  *This narrows the citywide, decades-spanning overview to a single origin point and drops the closing claim about present-day cultural significance — it describes only the setup, not the upshot.*

*Difficulty: hard*

---

##### Q7
> The following text is adapted from Oscar Wilde's 1897 nonfiction work De Profundis.
> 
> People whose desire is solely for self-realisation never know where they are going. They can't know. In one sense of the word it is of course necessary to know oneself: that is the first achievement of knowledge. But to recognise that the soul of a man is unknowable, is the ultimate achievement of wisdom. The final mystery is oneself. When one has weighed the sun in the balance, and measured the steps of the moon, and mapped out the seven heavens star by star, there still remains oneself. Who can calculate the orbit of his own soul?

Which choice best describes the function of the underlined question "Who can calculate the orbit of his own soul?" in the text as a whole?

**A.** It reinforces the text's skepticism about the possibility of truly achieving self-knowledge. **(Correct)**

  *Correct. The passage builds toward "the soul of a man is unknowable" and "the final mystery is oneself," and the closing rhetorical question — implying no one can — reinforces that skepticism with a final flourish.*

**B.** It speculates that some readers will share the doubts expressed in the text about the value of self-knowledge. 

  *The question is rhetorical, about whether self-knowledge is achievable at all — it is not a prediction about how particular readers will personally react.*

**C.** It cautions readers that the text's directions for how to achieve self-knowledge are hard to follow. 

  *The text gives no "directions" for achieving self-knowledge — it argues the opposite, that the soul cannot be measured or known, so there is no method here to call hard to follow.*

**D.** It concedes that the definition of self-knowledge advanced in the text is unpopular. 

  *Nowhere does the text call its own definition unpopular — this invents a concession about popularity that never appears.*

*Difficulty: hard*

---

##### Q8
> In most building demolitions, the building materials are destroyed and sent to landfills. City officials in Portland, Oregon wanted to reduce this waste. The officials passed a law requiring demolition companies to deconstruct some buildings instead. Deconstruction involves carefully taking buildings apart piece by piece. Damage to the materials is avoided so that they can be reused in new constructions. A 2019 study found that 27 percent of materials from deconstructions in Portland were able to be reused. The remaining materials were processed for recycling instead of going to a landfill.

Which choice best states the main purpose of the text?

**A.** To explain an effort made by the city of Portland to reduce demolition waste and some results of that effort **(Correct)**

  *Correct. Covers both halves: the effort (the deconstruction law) and the results (the 2019 study's reuse and recycling figures).*

**B.** To show that popular support for measures that reduce demolition waste has increased since 2019 

  *Public opinion is never mentioned — only officials passing a law and a study's material-recovery statistics are discussed.*

**C.** To argue that building deconstruction is not as effective as other measures at reducing demolition waste 

  *The text presents deconstruction's results neutrally to positively and never compares it against any other waste-reduction method, so there's no basis for calling it less effective.*

**D.** To discuss laws aimed to reduce demolition waste in Portland and compare them to similar laws in other cities 

  *No other cities' laws are mentioned anywhere — this is a single-city account with no comparative element.*

*Difficulty: medium*

---

##### Q9
> The following text is from Holly Goldberg Sloan's 2017 novel Short.
> 
> More than two years ago my parents bought a piano from some people who were moving to Utah. Mom and Dad gave it to my brothers and me for Christmas. I had to act really happy because it was such a big present, but I pretty much hated the thing from the second it was carried into the hallway upstairs, which is right next to my bedroom. The piano glared at me. It was like a songbird in a cage. It wanted to be set free.

Which choice best states the main purpose of the text?

**A.** It explains why the narrator always wanted a piano close to her bedroom. 

  *The text says the opposite — she "hated the thing" being right next to her bedroom. There is no expressed wish for a piano nearby.*

**B.** It establishes how the narrator feels about the piano. **(Correct)**

  *Correct. "Hated the thing," "glared at me," and the caged-songbird image all establish her negative feelings toward the piano.*

**C.** It suggests that the narrator's brothers are talented piano players. 

  *The brothers are mentioned only as co-recipients of the gift; nothing about their skill or talent appears anywhere in the text.*

**D.** It describes the event that led the narrator's parents to buy a piano. 

  *The text states the parents bought it from people moving to Utah, but never says what motivated the purchase — no triggering event for the decision is given.*

*Difficulty: medium*

---

##### Q10
> Jackie Ormes's Torchy Brown in Dixie to Harlem (1937-38) was the first comic strip by a Black woman to appear in a widely read newspaper. The strip tells the story of Torchy, a young woman who leaves Mississippi to become a performer in New York City. Torchy's story reflects the experience of the Great Migration (1910-1970), when millions of Black Americans left the South in search of opportunities in other parts of the United States. Torchy Brown thus shows how Ormes used comics to comment humorously on issues affecting Black Americans, which she continued to do throughout her career.

Which choice best states the main purpose of the text?

**A.** To show how Ormes's Torchy Brown inspired other Black women to write comic strips in the 1930s 

  *No claim about Ormes inspiring other Black women cartoonists appears — the text is about the content and significance of her own strip.*

**B.** To illustrate how the subjects Ormes addressed in her comic strips changed over the course of her career 

  *The text says Ormes "continued to" comment on these issues "throughout her career" — that's stated continuity, not change, and this choice mistakes one for the other.*

**C.** To give an example of how Ormes presented the experiences of Black Americans in her comic strips **(Correct)**

  *Correct. Torchy Brown, via the Great Migration parallel, is used specifically as an example of how Ormes addressed Black Americans' experiences in her work.*

**D.** To claim that several characters in Torchy Brown were based on people that Ormes knew personally 

  *No claim about any character being based on a real acquaintance ever appears — Torchy's story reflects a broad historical experience, not a specific biographical connection.*

*Difficulty: medium*

---

##### Q11
> Streams and rivers carry soil and rocks from one location to another. But there is another way for these geological materials to move. Scientists call this process "aeolian transport." In aeolian transport, winds move small particles of soil or rock over potentially great distances. Geologist Melisa Diaz and her team studied dust in Antarctica to find out if it was moved by aeolian transport. They discovered that the dust matched geological material in Australia. Aeolian transport had carried it from one continent to another, across thousands of miles of open ocean.

Which choice best describes the function of the underlined portion "Scientists call this process 'aeolian transport.'" in the text as a whole?

**A.** It presents Melisa Diaz's remarks about difficulties that her team encountered. 

  *This sentence is the author naming the general phenomenon before Diaz's study is even introduced — it is not a quote from Diaz, and it says nothing about any difficulties.*

**B.** It introduces a scientific term that is used in the discussion that follows. **(Correct)**

  *Correct. The sentence names "aeolian transport," a term the rest of the text — Diaz's study, the Antarctica-to-Australia finding — goes on to use repeatedly.*

**C.** It emphasizes the surprising nature of the findings that are presented. 

  *The sentence is a neutral naming, not an evaluative statement — the surprising finding (dust matching Australia across an ocean) comes later, in a different sentence.*

**D.** It explains the difference between two kinds of geological material. 

  *No second kind of geological material is ever contrasted with the first; the text discusses one process moving one kind of material, not a distinction between two kinds.*

*Difficulty: easy*

---

##### Q12
> Many films from the early 1900s have been lost. These losses include several films by the first wave of Black women filmmakers. We know about these lost movies only from small pieces of evidence. For example, an advertisement for Jennie Louise Touissant Welcome's documentary Doing Their Bit still exists. There's a reference in a magazine to Tressie Souders's film A Woman's Error. And Maria P. Williams's The Flames of Wrath is mentioned in a letter and a newspaper article, and one image from the movie was discovered in the 1990s.

Which choice best describes the overall structure of the text?

**A.** The text identifies a complex problem, then presents examples of unsuccessful attempts to solve that problem. 

  *Nothing about "attempts to solve" the loss of these films is discussed — the text describes a situation (lost films, fragmentary evidence) and gives examples of that fragmentary evidence, not attempted solutions.*

**B.** The text summarizes a debate among researchers, then gives reasons for supporting one side in that debate. 

  *No debate or competing positions ever appear — this is a straightforward informational account, not an argument with sides.*

**C.** The text describes a general situation, then illustrates that situation with specific examples. **(Correct)**

  *Correct. A general situation (early films lost, evidence fragmentary) is followed by three specific examples — the advertisement, the magazine reference, and the letter/article/image.*

**D.** The text discusses several notable individuals, then explains commonly overlooked differences between those individuals. 

  *The three filmmakers illustrate the SAME situation in parallel, not contrasted differences — the text never compares them against one another.*

*Difficulty: medium*

---

##### Q13
> Hiroshi Senju is known worldwide for his paintings of waterfalls. These paintings are large and tend not to show the entire waterfall. Instead, Senju focuses on just the point where the falling water reaches the pool below, keeping the top of the waterfall out of view. While Senju's paintings are rooted in art movements originating in the United States, the artist uses traditional Japanese techniques and materials that make his work instantly recognizable.

Which choice best describes the overall structure of the text?

**A.** It introduces an artist and then explains some common characteristics of well-known paintings by that artist. **(Correct)**

  *Correct. Introduces Senju, then describes shared characteristics of his paintings: the composition choice (cropped top), stylistic roots, and materials.*

**B.** It explains a specific painting technique and then provides examples of artists who use the technique. 

  *The text describes one artist's paintings, not a technique shared across multiple named artists — no other artists appear anywhere.*

**C.** It describes a famous painting and then compares it to a lesser-known painting from the same time period. 

  *No single painting is singled out and compared to any other specific painting — Senju's paintings are discussed as a category, not one work versus another.*

**D.** It gives an opinion on an artist and then suggests multiple reasons why the artist's work has been largely overlooked. 

  *Senju is described as "known worldwide" — the opposite of overlooked — and no reasons for neglect are given anywhere.*

*Difficulty: medium*

---

##### Q14
> In 1801, a Blackfoot chief named Ac Ko Mok Ki drew a finely detailed map of the Upper Missouri region. This work demonstrates a vast amount of topographic knowledge, as the map features specific names of mountains and rivers, as well as the first-known sketch of the drainage network of the Missouri River. The map is especially notable because Ac Ko Mok Ki also included details about the numerous tribes that lived in the area.

Which choice best describes the function of the underlined sentence "This work demonstrates a vast amount of topographic knowledge, as the map features specific names of mountains and rivers, as well as the first-known sketch of the drainage network of the Missouri River." in the text as a whole?

**A.** It emphasizes Ac Ko Mok Ki's desire to represent other tribes on the map. 

  *The desire to represent tribes is the content of the NEXT sentence, not this one — this sentence is entirely about topographic knowledge.*

**B.** It explains how Ac Ko Mok Ki developed an interest in mapmaking. 

  *Nothing about how his interest developed is stated anywhere — the text describes the finished map's contents, not the chief's personal history with mapmaking.*

**C.** It identifies some reasons why the map is impressive. **(Correct)**

  *Correct. "Demonstrates a vast amount of topographic knowledge" is exactly a reason to be impressed, backed by two pieces of evidence: named features and the first-known river sketch.*

**D.** It details how the map was used for hunting and trading purposes. 

  *No use of the map — hunting, trading, or otherwise — is ever mentioned; the text discusses only what the map depicts, not how it was used.*

*Difficulty: medium*

---

##### Q15
> In many agricultural environments, the banks of streams are kept forested to protect water quality, but it's been unclear what effects these forests may have on stream biodiversity. To investigate the issue, biologist Xingli Giam and colleagues studied an Indonesian oil palm plantation, comparing the species richness of forested streams with that of nonforested streams. Giam and colleagues found that species richness was significantly higher in forested streams, a finding the researchers attribute to the role leaf litter plays in sheltering fish from predators and providing food resources.

Which choice best states the main purpose of the text?

**A.** It discusses research intended to settle a debate about how agricultural yields can be increased without negative effects on water quality. 

  *"Agricultural yields" is never mentioned anywhere — the unresolved question is about biodiversity effects of forested streams, not crop yield.*

**B.** It explains the differences between stream-protection strategies used in oil palm plantations and stream-protection strategies used in other kinds of agricultural environments. 

  *The study compares forested versus nonforested streams within ONE plantation — no comparison across different types of agricultural environments ever appears.*

**C.** It describes findings that challenge a previously held view about how fish that inhabit streams in agricultural environments attempt to avoid predators. 

  *The finding explains a mechanism — leaf litter shelters fish from predators — it doesn't challenge any prior view of fish behavior, which is never stated as contested.*

**D.** It presents a study that addresses an unresolved question about the presence of forests along streams in agricultural environments. **(Correct)**

  *Correct. The opening sentence names the exact unresolved question — the biodiversity effect of streamside forests — and the rest of the text presents Giam's study addressing it.*

*Difficulty: hard*

---

##### Q16
> Genetic studies have led researchers to suggest that turtles are most closely related to the group that includes modern crocodiles. But studies of fossils have suggested instead that turtles are most closely related to other groups, such as the one that contains modern snakes. However, many of the fossil studies have relied on incomplete data sets. For a 2022 investigation, biologist Tiago R. Simões and colleagues examined more than 1,000 reptile fossils collected worldwide. From this large data set, they found clear agreement with the results of the genetic studies.

Which choice best describes the function of the underlined sentence "However, many of the fossil studies have relied on incomplete data sets." in the text?

**A.** It offers an overview of the tools scientists use to examine fossils. 

  *The sentence identifies a flaw — incomplete data — not any tools or methods used to examine fossils in general.*

**B.** It describes a limitation of some studies about the origin of turtles. **(Correct)**

  *Correct. It directly names a limitation — incomplete data sets — affecting the fossil-based studies just discussed, setting up why Simões's larger data set matters.*

**C.** It summarizes previous research on the evolution of crocodiles. 

  *The sentence is about data-set completeness in fossil studies of turtle relationships broadly — crocodiles are mentioned only as the group genetics links turtles to, not as the subject of this sentence.*

**D.** It criticizes a widely held belief about genetic studies of reptiles. 

  *It's the fossil-based conclusion that's undermined here, not the genetic studies — those are later confirmed, not criticized. This attacks the wrong side of the two lines of evidence.*

*Difficulty: medium*

---

##### Q17
> The following text is adapted from Jason Reynolds's 2016 novel Ghost. The narrator, who is in middle school, is at a bus stop.
> 
> I just go there [to the bus stop] to look at the people working out. See, the gym across the street has this big window-like the whole wall is a window-and they have those machines that make you feel like you're walking up steps and so everybody looks all crazy like they're about to pass out. And trust me, there ain't nothing funnier than that. So I check that out for a little while like it's some kind of movie: The About to Pass Out Show, starring stair-stepper person one through ten.

Which choice best states the main purpose of the text?

**A.** To give a reason why the narrator is excited to start middle school 

  *Nothing about starting middle school appears — "in middle school" is only background context; the passage's content never develops that topic.*

**B.** To describe an activity that the narrator finds amusing **(Correct)**

  *Correct. "There ain't nothing funnier than that" and the mock-show framing ("The About to Pass Out Show") both establish that watching the gym-goers is something the narrator finds funny.*

**C.** To explain a problem that the narrator has overcome 

  *No problem or its resolution is described anywhere — the narrator is simply describing a pastime, not recounting overcoming a difficulty.*

**D.** To discuss a movie that the narrator saw in a theater 

  *"Like it's some kind of movie" is a simile comparing the pastime to watching a movie — it is not a literal account of a movie seen in a theater.*

*Difficulty: medium*

---

##### Q18
> Were penguins always flightless? Theresa Cole and her team argue that penguins could fly at some point, but that they lost that ability more than 60 million years ago as they adapted to marine life. After examining various penguin fossils and genetic information, the researchers concluded that over time penguins developed underwater vision, blood oxygenation, and bone density better suited for swimming than flying. Thus, environmental conditions might have driven penguins to change from flyers to swimmers.

Which choice best describes the function of the underlined sentence "Theresa Cole and her team argue that penguins could fly at some point, but that they lost that ability more than 60 million years ago as they adapted to marine life." in the text as a whole?

**A.** It defines a scientific term used in the sentence that follows. 

  *No scientific term is being defined — the sentence states a research claim, and the sentence that follows elaborates with evidence, not a definition.*

**B.** It contradicts a description in the sentence that follows. 

  *The sentence is supported by, not contradicted by, the fossil and genetic evidence that follows — the relationship is agreement, not contradiction.*

**C.** It provides an answer to the question in the previous sentence. **(Correct)**

  *Correct. The opening question — "Were penguins always flightless?" — is directly answered here: no, they could fly and later lost the ability.*

**D.** It notes that the question in the previous sentence has not been researched. 

  *The sentence directly answers the question with named research — the opposite of saying the question hasn't been studied.*

*Difficulty: easy*

---

##### Q19
> Catherine L. Cardelús is a researcher who studies canopy soil. Canopy soil is formed in a tree's branches (its canopy) when dead leaves and other falling things collect. This material breaks down, becoming canopy soil. Canopy soil helps preserve a healthy water cycle (how water moves through the environment) in rainforests. This benefit is one reason Cardelús is interested in the canopy soils in large choibá trees in rainforests in Costa Rica.

Which choice best describes the text's overall structure?

**A.** It explains a disagreement between researchers and how it was resolved. 

  *No disagreement between researchers appears anywhere — this is a single, uncontested explanation of canopy soil and one researcher's interest in it.*

**B.** It presents an idea and mentions a researcher who disagrees with that idea. 

  *Cardelús doesn't disagree with anything — she's interested in canopy soil precisely because of the benefit the text presents as agreed fact.*

**C.** It compares the sizes of two types of trees over several years. 

  *No tree sizes are discussed and no multi-year comparison exists — canopy soil formation and one benefit are described, not tree dimensions.*

**D.** It introduces a researcher and gives information about what she researches. **(Correct)**

  *Correct. Opens by naming Cardelús and her field, then explains what canopy soil is and why she's specifically interested in it.*

*Difficulty: easy*

---

##### Q20
> The following text is from Louise Erdrich's 1986 novel The Beet Queen. The narrator discusses her relationship with her young niece, Dot. Celestine, the narrator's sister-in-law, is Dot's mother.
> 
> Dot was as impatient with babyhood as I. She tried at once to grow out of it. Celestine never saw that, because she, and only she, took pleasure in Dot's helpless softness. Only Celestine was saddened by her daughter's fierce progress. Day by day, Dot grew stronger. In her shopping-cart stroller she exercised to exhaustion, bouncing for hours to develop her leg muscles.

Which choice best describes the function of the underlined sentence "In her shopping-cart stroller she exercised to exhaustion, bouncing for hours to develop her leg muscles." in the text as a whole?

**A.** It offers a detail that shows how Dot is growing stronger. **(Correct)**

  *Correct. It directly follows and illustrates "Day by day, Dot grew stronger" with a concrete example of Dot's vigorous physical activity.*

**B.** It expresses hope that Celestine will mature psychologically. 

  *The sentence is entirely about Dot's physical exercise, not about Celestine, and no expression of "hope" appears anywhere.*

**C.** It explores some of the narrator's psychological characteristics. 

  *The sentence describes Dot's behavior, not the narrator's own psychology — the narrator is only an observer here.*

**D.** It indicates how sad Celestine is by describing a behavior she engages in. 

  *The behavior described (bouncing in a stroller) is Dot's, not Celestine's, and it illustrates Dot's growing strength, not Celestine's sadness (already stated about a different subject two sentences earlier).*

*Difficulty: medium*

---

##### Q21
> The following text is from Reyna Grande's 2012 memoir The Distance Between Us. In the text, Grande reflects on a time when she and her older sister Mago were children. A Barbie is a type of doll.
> 
> I begged Mago to come play with me. She wasn't as interested in my Barbie as she had been just two months before, which made me sad because that was the only thing Mago had envied me for. Usually, it was me doing the envying. After I pestered her relentlessly, she finally put her notebook down and came over to me.

Which choice best describes the function of the underlined portion "which made me sad because that was the only thing Mago had envied me for" in the text as a whole?

**A.** It indicates Grande's unhappiness over Mago's disinterest in Grande's doll. **(Correct)**

  *Correct. "Made me sad" directly states her emotional reaction, tied specifically to Mago's fading interest in the Barbie doll.*

**B.** It expresses Grande's anger over Mago's refusal to spend time with her. 

  *The text specifies "sad," not anger, and the cause is lost interest in a toy, not a refusal to spend time — Mago does come over and play by the end.*

**C.** It presents an example of how Mago and Grande generally played together as children. 

  *This is one specific reaction to a specific change, not a description of their typical play — and it directly follows a moment when they are NOT yet playing together.*

**D.** It provides a reason for why Mago is unwilling to play with Grande. 

  *By the passage's end, Mago is not unwilling — she comes over and joins Grande after being pestered. The underlined portion explains Grande's sadness, not any reluctance on Mago's part.*

*Difficulty: hard*

---

##### Q22
> Animals use many objects as tools to achieve goals more easily. Such goals include grooming, finding food, and protecting themselves. For a long time, people thought tool use was unique to primates. Dolphins and other animals, though, have busted the myth that tool use requires hands. Inventively, dolphins use sponges to protect their noses from scratches when foraging on the seafloor. Palm cockatoos also get creative. They use leaves to pad their beaks when opening nuts.

Which choice best states the main purpose of the text?

**A.** To question the belief that birds are intelligent 

  *Bird intelligence is never questioned or even discussed — the text is about which animals use tools, not about intelligence.*

**B.** To compare tool use in humans with tool use in palm cockatoos 

  *The actual contrast is primates versus non-primates, not humans versus palm cockatoos — humans as tool users are never directly discussed.*

**C.** To establish that tool use doesn't indicate intelligence 

  *The text never claims tool use is unrelated to intelligence — it corrects the assumption that tool use requires hands or is unique to primates, a different claim entirely.*

**D.** To argue that a variety of animals use tools **(Correct)**

  *Correct. Moves from a general statement about animal tool use, through the corrected myth, to two specific examples (dolphins, cockatoos) — all supporting the claim that many kinds of animals use tools.*

*Difficulty: easy*

---

##### Q23
> The following text is from Ameen Rihani's 1921 poem "The Wanderer."
> 
> I wander among the hills of alien lands
> Where Nature her prerogative resigns
> To Man; where Comfort in her shack reclines
> And all the arts and sciences commands.
> But in my soul
> The eastern billows roll—
> I hear the voices of my native strands.

Which choice best describes the function of the underlined lines "But in my soul / The eastern billows roll— / I hear the voices of my native strands." in the text as a whole?

**A.** It establishes that the speaker's enthusiasm about current travels conflicts with the growing urge to return home. 

  *The poem never expresses "enthusiasm" about the current travels — the "alien lands" framing is neutral to distancing, with no textual evidence of excitement that would then conflict with homesickness.*

**B.** It illustrates the speaker's uncertainty about maintaining strong links with relatives in distant places. 

  *The lines express a pull toward home, not uncertainty about relationships — no relatives or "links" to people are ever mentioned.*

**C.** It conveys the speaker's sense of feeling a pull toward home while traveling in an unfamiliar place. **(Correct)**

  *Correct. The speaker is explicitly "among the hills of alien lands" while the "eastern billows roll" in his soul and he "hears the voices" of home — a direct statement of homeward pull amid foreign surroundings.*

**D.** It reveals that upon returning after an extended absence, the speaker longs for the way a location once felt. 

  *The speaker is currently among "alien lands," still traveling — no return is depicted anywhere in the poem, so "upon returning" misstates the speaker's situation.*

*Difficulty: hard*

---

##### Q24
> Archeological excavation of Market Street Chinatown, a nineteenth-century Chinese American community in San Jose, California, provided the first evidence that Asian food products were imported to the United States in the 1800s: bones from a freshwater fish species native to Southeast Asia. Jinshanzhuang—Hong Kong-based import/export firms—likely coordinated the fish's transport from Chinese-operated fisheries in Vietnam and Malaysia to North American markets. This route reveals the (often overlooked) multinational dimensions of the trade networks linking Chinese diaspora communities.

Which choice best describes the function of the underlined sentence "Jinshanzhuang—Hong Kong-based import/export firms—likely coordinated the fish's transport from Chinese-operated fisheries in Vietnam and Malaysia to North American markets." in the text as a whole?

**A.** It explains why efforts to determine the country of origin of the items mentioned in the previous sentence remain inconclusive. 

  *The origin (Southeast Asia, specifically Vietnam and Malaysia) isn't treated as inconclusive — the sentence states the route confidently; the hedge ("likely") is about the coordinating firm, not the origin.*

**B.** It provides information that helps support a claim about a discovery's significance that is presented in the following sentence. **(Correct)**

  *Correct. It explains the multinational trade route by which the fish reached San Jose, directly supporting the following sentence's claim about the discovery's "multinational dimensions."*

**C.** It traces the steps that were taken to locate and recover the objects that are described in the previous sentence. 

  *This sentence describes the historical trade route of the fish, not the archaeologists' excavation or recovery process — no methodology for locating the bones appears here.*

**D.** It outlines a hypothesis that additional evidence discussed in the following sentence casts some doubt on. 

  *The following sentence builds on this claim ("this route reveals..."), affirming it rather than casting doubt on it.*

*Difficulty: hard*

---

##### Q25
> Using NASA's powerful James Webb Space Telescope (JWST), Mercedes López-Morales and colleagues measured the wavelengths of light traveling through the atmosphere of WASP-39b, an exoplanet, or planet outside our solar system. Different molecules absorb different wavelengths of light, and the wavelength measurements showed the presence of carbon dioxide (CO2) in WASP-39b's atmosphere. This finding not only offers the first decisive evidence of CO2 in the atmosphere of an exoplanet but also illustrates the potential for future scientific breakthroughs held by the JWST.

Which choice best describes the overall structure of the text?

**A.** It discusses a method used by some researchers, then states why an alternative method is superior to it. 

  *No alternative method is ever mentioned or compared against the JWST measurement approach — the text describes only one method and its result.*

**B.** It describes how researchers made a scientific discovery, then explains the importance of that discovery. **(Correct)**

  *Correct. First describes how the team made the discovery (measuring light wavelengths to detect CO2), then explains its importance — first decisive evidence, and a signal for future JWST discoveries.*

**C.** It outlines the steps taken in a scientific study, then presents a hypothesis based on that study. 

  *The "finding" is a completed result, not a new hypothesis proposed afterward — the text states what was found, not a hypothesis still to be tested.*

**D.** It examines how a group of scientists reached a conclusion, then shows how other scientists have challenged that conclusion. 

  *No challenge from other scientists appears anywhere — the CO2 finding is presented as settled ("first decisive evidence"), not contested.*

*Difficulty: medium*

---

##### Q26
> Yawn contagion occurs when one individual yawns in response to another's yawn. Studies of this behavior in primates have focused on populations in captivity, but biologist Elisabetta Palagi and her colleagues have shown that it can occur in wild primate populations as well. In their study, which focused on a wild population of gelada monkeys (Theropithecus gelada) in Ethiopia, the researchers further reported that yawn contagion most commonly occurred in males and across different social groups instead of within a single social group.

Which choice best describes the function of the first sentence "Yawn contagion occurs when one individual yawns in response to another's yawn." in the text as a whole?

**A.** It defines a phenomenon that is discussed in the text. **(Correct)**

  *Correct. The sentence gives a plain definition of yawn contagion, and the rest of the text discusses studies of that phenomenon in different populations.*

**B.** It introduces a problem that is examined in the text. 

  *A definition is not a problem — nothing about yawn contagion is framed as an issue needing to be solved.*

**C.** It makes a claim that is challenged in the text. 

  *The definition of yawn contagion is never disputed — what gets expanded is where it occurs (captive versus wild populations), not what it fundamentally is.*

**D.** It presents a hypothesis that is evaluated in the text. 

  *A definition states what a term means; it doesn't propose an unproven explanation to be tested. Palagi's finding is a reported result, not the evaluation of this sentence's content.*

*Difficulty: easy*

---

##### Q27
> The following text is from Joseph Conrad's 1907 novel The Secret Agent: A Simple Tale. Mr. Verloc is navigating the London streets on his way to a meeting.
> 
> Before reaching Knightsbridge, Mr. Verloc took a turn to the left out of the busy main thoroughfare, uproarious with the traffic of swaying omnibuses and trotting vans, in the almost silent, swift flow of hansoms [horse-drawn carriages]. Under his hat, worn with a slight backward tilt, his hair had been carefully brushed into respectable sleekness; for his business was with an Embassy. And Mr. Verloc, steady like a rock—a soft kind of rock—marched now along a street which could with every propriety be described as private.

Which choice best describes the function of the underlined phrase "a soft kind of rock" in the text as a whole?

**A.** It qualifies an earlier description of Mr. Verloc. **(Correct)**

  *Correct. The phrase immediately narrows "steady like a rock" — a qualification appended right after the initial comparison, softening the hardness implied without abandoning the steadiness image.*

**B.** It emphasizes an internal struggle Mr. Verloc experiences. 

  *The phrase is a narratorial aside about Verloc's character, not a description of any inner conflict — no internal struggle is depicted anywhere in this passage.*

**C.** It contrasts Mr. Verloc with his surroundings. 

  *The phrase modifies the description of Verloc himself, not a comparison to his surroundings — the quiet street and his careful grooming are not being set against this qualifier.*

**D.** It reveals a private opinion Mr. Verloc holds. 

  *This is the narrator's characterization of Verloc, not a private opinion Verloc himself voices — nothing indicates it is his own self-assessment.*

*Difficulty: hard*

---

##### Q28
> In 1973, poet Miguel Algarín started inviting other writers who, like him, were Nuyorican—a term for New Yorkers of Puerto Rican heritage—to gather in his apartment to present their work. The gatherings were so well attended that Algarín soon had to rent space in a cafe to accommodate them. Thus, the Nuyorican Poets Cafe was born. Moving to a permanent location in 1981, the Nuyorican Poets Cafe expanded its original scope beyond the written word, hosting art exhibitions and musical performances as well. Half a century since its inception, it continues to foster emerging Nuyorican talent.

Which choice best describes the overall purpose of the text?

**A.** To explain what motivated Algarín to found the Nuyorican Poets Cafe 

  *The text describes what led to the space's growth (crowded gatherings needing more room), but never states Algarín's personal motivation for starting the gatherings in the first place.*

**B.** To situate the Nuyorican Poets Cafe within the cultural life of New York as a whole 

  *The text stays entirely internal to the Cafe's own history — no wider New York cultural context or comparison ever appears.*

**C.** To discuss why the Nuyorican Poets Cafe expanded its scope to include art and music 

  *The text states THAT the scope expanded, but never gives a reason WHY — the "why" is never addressed.*

**D.** To provide an overview of the founding and mission of the Nuyorican Poets Cafe **(Correct)**

  *Correct. Moves chronologically from founding (1973 gatherings, rented cafe) through growth (1981 permanent location, expanded programming) to present-day mission.*

*Difficulty: medium*

---

##### Q29
> The following text is adapted from Charles Dickens's 1854 novel Hard Times. Coketown is a fictional town in England.
> 
> [Coketown] contained several large streets all very like one another, and many small streets still more like one another, inhabited by people equally like one another, who all went in and out at the same hours, with the same sound upon the same pavements, to do the same work, and to whom every day was the same as yesterday and tomorrow, and every year the counterpart of the last and the next.

Which choice best states the main purpose of the text?

**A.** To emphasize the uniformity of both the town and the people who live there **(Correct)**

  *Correct. The passage is a cascade of "like one another" and "same" repetitions applied to both the streets and the people — uniformity on both fronts.*

**B.** To explain the limited work opportunities available to the town's residents 

  *The text says residents "do the same work," describing routine and sameness, not that work opportunities are limited in number — no claim about job scarcity is made.*

**C.** To reveal how the predictability of the town makes it easy for people lose track of time 

  *The text says every day and year feels the SAME as the last, the opposite of losing track of time — this monotony would make time feel fixed and undifferentiated, not lost.*

**D.** To argue that the simplicity of life in the town makes it a pleasant place to live 

  *The flat, repetitive tone conveys grim monotony, not argued pleasantness, and no evaluative claim that this is a "pleasant place" is made — only a description.*

*Difficulty: medium*

---

##### Q30
> The following text is adapted from Paul Laurence Dunbar's 1902 novel The Sport of the Gods. Joe and some of his family members have recently moved to New York City.
> 
> [Joe] was wild with enthusiasm and with a desire to be a part of all that the metropolis meant. In the evening he saw the young fellows passing by dressed in their spruce clothes, and he wondered with a sort of envy where they could be going. Back home there had been no place much worth going to, except church and one or two people's houses.

Which choice best states the main purpose of the text?

**A.** It illustrates a character's reaction to a new environment. **(Correct)**

  *Correct. Covers Joe's enthusiasm about the city, his envious wondering about the well-dressed young men, and the implicit contrast with limited options "back home" — all his reaction to a new environment.*

**B.** It explains why a character has traveled to a city. 

  *The text never explains WHY Joe's family moved to New York — we're only told they have "recently moved," with no stated reason in the passage itself.*

**C.** It compares a character's thoughts about an event at two different times of day. 

  *There's no comparison of Joe's thoughts "at two different times of day" — the evening scene is the only time referenced, alongside a general memory of home.*

**D.** It presents a character feeling regret over leaving home. 

  *Joe's feelings are enthusiasm and envy toward the city, not regret about leaving home — and the memory of home ("no place much worth going to") is unflattering, the opposite of something to regret losing.*

*Difficulty: medium*

---

##### Q31
> The following text is from Charlotte Perkins Gilman's 1910 poem "The Earth's Entail."
> 
> No matter how we cultivate the land,
> Taming the forest and the prairie free;
> No matter how we irrigate the sand,
> Making the desert blossom at command,
> We must always leave the borders of the sea;
> The immeasureable reaches
> Of the windy wave-wet beaches,
> The million-mile-long margin of the sea.

Which choice best describes the overall structure of the text?

**A.** The speaker argues against interfering with nature and then gives evidence supporting this interference. 

  *This reverses the logic — the poem catalogues humanity's control of land without condemning it, then notes a limit; it never argues against interference and certainly doesn't offer "evidence supporting" interference afterward.*

**B.** The speaker presents an account of efforts to dominate nature and then cautions that such efforts are only temporary. 

  *The poem says the sea's borders can never be crossed — a permanent limit — not that the land-taming efforts themselves are temporary or will be undone. These are different claims.*

**C.** The speaker provides examples of an admirable way of approaching nature and then challenges that approach. 

  *The poem never frames cultivating or irrigating as "admirable," nor does it "challenge" that approach — it simply notes a limit to it, without disapproving of the land-taming itself.*

**D.** The speaker describes attempts to control nature and then offers a reminder that not all nature is controllable. **(Correct)**

  *Correct. The first four lines describe humanity's control over land, and the final lines pivot to the sea as an uncontrollable boundary — control described, then its limit noted.*

*Difficulty: hard*

---

##### Q32
> The following text is adapted from Etsu Inagaki Sugimoto's 1925 memoir A Daughter of the Samurai. As a young woman, Sugimoto moved from feudal Japan to the United States.
> 
> The standards of my own and my adopted country differed so widely in some ways, and my love for both lands was so sincere, that sometimes I had an odd feeling of standing upon a cloud in space, and gazing with measuring eyes upon two separate worlds. At first I was continually trying to explain, by Japanese standards, all the queer things that came every day before my surprised eyes; for no one seemed to know the origin or significance of even the most familiar customs, nor why they existed and were followed.

Which choice best describes the main purpose of the text?

**A.** To convey the narrator's experience of observing and making sense of differences between two cultures she embraces **(Correct)**

  *Correct. "Standards...differed so widely," "love for both lands was so sincere," and "trying to explain...all the queer things" together depict her actively interpreting the gap between two cultures she loves.*

**B.** To establish the narrator's hope of forming connections with new companions by sharing customs she learned as a child 

  *No mention of forming connections with "new companions" appears — the passage is about the narrator's internal process of interpreting cultural differences, not a social outreach goal.*

**C.** To reveal the narrator's recognition that she is hesitant to ask questions about certain aspects of a culture she is newly encountering 

  *The narrator is described as "continually trying to explain" things — actively engaging, not hesitant. The difficulty is others' lack of knowledge, not her own reluctance.*

**D.** To emphasize the narrator's wonder at discovering that the physical distance between two countries is greater than she had expected 

  *"Standing upon a cloud in space" is a metaphor for feeling caught between two worldviews, not a literal claim about physical geographic distance.*

*Difficulty: medium*

---

##### Q33
> In the Here and Now Storybook (1921), educator Lucy Sprague Mitchell advanced the then controversial idea that books for very young children should imitate how they use language, since toddlers, who cannot yet grasp narrative or abstract ideas, seek reassurance in verbal repetition and naming. The most enduring example of this idea is Margaret Wise Brown's 1947 picture book Goodnight Moon, in which a young rabbit names the objects in his room as he drifts off to sleep. Scholars note that the book's emphasis on repetition, rhythm, and nonsense rhyme speaks directly to Mitchell's influence.

Which choice best describes the overall structure of the text?

**A.** The text outlines a debate between two authors of children's literature and then traces how that debate shaped theories on early childhood education. 

  *Mitchell and Brown are not shown debating each other — Brown's book is presented as an example that follows Mitchell's philosophy, not as an opposing position.*

**B.** The text summarizes an argument about how children's literature should be evaluated and then discusses a contrasting view on that subject. 

  *No contrasting view is ever introduced — Goodnight Moon is presented as consistent with and directly influenced by Mitchell's idea, not a competing standard.*

**C.** The text lists the literary characteristics that are common to many classics of children's literature and then indicates the narrative subjects that are most appropriate for young children. 

  *The text doesn't survey characteristics common to many classics — it discusses one specific philosophy and one specific example, not a general list.*

**D.** The text presents a philosophy about what material is most suitable for children's literature and then describes a book influenced by that philosophy. **(Correct)**

  *Correct. First presents Mitchell's philosophy (children's books should imitate toddlers' own language use), then describes Goodnight Moon as "the most enduring example" shaped by exactly that philosophy.*

*Difficulty: medium*

---

##### Q34
> Works of moral philosophy, such as Plato's Republic or Aristotle's Nicomachean Ethics, are partly concerned with how to live a morally good life. But philosopher Jonathan Barnes argues that works that present a method of living such a life without also supplying a motive for it are inherently useful only to those already wishing to be morally good—those with no desire for moral goodness will not choose to follow their rules. However, some works of moral philosophy attempt to describe what constitutes a morally good life while also proposing reasons for living one.

Which choice best describes the overall structure of the text?

**A.** It provides a characterization about a field of thought by noting two works in it and then details a way in which some works in that field are more comprehensive than others. **(Correct)**

  *Correct. Opens with moral philosophy generally, citing two named works, then via Barnes's argument distinguishes method-only works from works that also supply a motive — the latter being more comprehensive.*

**B.** It mentions two renowned works and then claims that despite their popularity it is impossible for these works to serve the purpose their authors intended. 

  *Barnes's argument is that method-only works are "useful only to those already wishing to be morally good," not that it's impossible for them to serve their purpose at all — and popularity is never discussed.*

**C.** It summarizes the history of a field of thought by discussing two works and then proposes a topic of further research for specialists in that field. 

  *The text doesn't recount a history of moral philosophy, nor does it propose a research topic for specialists — it makes a conceptual distinction without any forward-looking research agenda.*

**D.** It describes two influential works and then explains why one is more widely read than the other. 

  *The text never claims one type of work is "more widely read" than another — readership is never at issue; the distinction is about comprehensiveness, not popularity.*

*Difficulty: hard*

---

##### Q35
> Industrial activity is often assumed to be a threat to wildlife, but that isn't always so. Consider the silver-studded blue butterfly (Plebejus argus): as forest growth has reduced grasslands in northern Germany, many of these butterflies have left meadow habitats and are now thriving in active limestone quarries. In a survey of multiple active quarries and patches of maintained grassland, an ecologist found silver-studded blue butterflies in 100% of the quarries but only 57% of the grassland patches. Moreover, butterfly populations in the quarries were four times larger than those in the meadows.

Which choice best describes the function of the underlined portion "Consider the silver-studded blue butterfly (Plebejus argus): as forest growth has reduced grasslands in northern Germany, many of these butterflies have left meadow habitats and are now thriving in active limestone quarries." in the text as a whole?

**A.** It challenges a common assumption about the species under investigation in the research referred to in the text. 

  *The general assumption (industrial activity is a threat to wildlife) is challenged by the OPENING sentence, before this one — this sentence is the supporting example, not a separate challenge, and states no assumption specifically about the species being wrong.*

**B.** It introduces discussion of a specific example that supports the general claim made in the previous sentence. **(Correct)**

  *Correct. The previous sentence makes a general claim (industrial activity isn't always a threat), and this sentence introduces the specific butterfly example that supports it with quarry versus meadow data.*

**C.** It suggests that a certain species should be included in additional studies like the one mentioned later in the text. 

  *No suggestion of further studies including this or any species ever appears — the study already includes the butterfly, and no recommendation for additional research is made.*

**D.** It provides a definition for an unfamiliar term that is central to the main argument in the text. 

  *Naming a species is not defining an unfamiliar term — there's no technical term being explained here.*

*Difficulty: hard*

---

##### Q36
> The following text is from Herman Melville's 1854 novel The Lightning-rod Man.
> 
> The stranger still stood in the exact middle of the cottage, where he had first planted himself. His singularity impelled closer scrutiny. A lean, gloomy figure. Hair dark and lank, mattedly streaked over his brow. His sunken pitfalls of eyes were ringed by indigo halos, and played with an innocuous sort of lightning: the gleam without the bolt. The whole man was dripping. He stood in a puddle on the bare oak floor: his strange walking-stick vertically resting at his side.

Which choice best states the function of the underlined sentence "His singularity impelled closer scrutiny." in the overall structure of the text?

**A.** It elaborates on the previous sentence's description of the character. 

  *The previous sentence describes his position and stillness, not his "singularity" — this sentence pivots to a new focus (his strangeness) that the FOLLOWING sentences then detail.*

**B.** It introduces the setting that is described in the sentences that follow. 

  *What follows is a physical description of the man himself, not the setting — the cottage was already established in the prior sentence.*

**C.** It establishes a contrast with the description in the previous sentence. 

  *There's no contrast between this sentence and the one before it — both continue the narrator's attention to the stranger, building cumulatively rather than opposing each other.*

**D.** It sets up the character description presented in the sentences that follow. **(Correct)**

  *Correct. "His singularity impelled closer scrutiny" announces that a close look is coming, and the sentences that follow deliver exactly that: a detailed physical description.*

*Difficulty: medium*

---

##### Q37
> Horizontal gene transfer occurs when an organism of one species acquires genetic material from an organism of another species through nonreproductive means. The genetic material can then be transferred "vertically" in the second species—that is, through reproductive inheritance. Scientist Atma Ivancevic and her team have hypothesized infection by invertebrate parasites as a mechanism of horizontal gene transfer between vertebrate species: while feeding, a parasite could acquire a gene from one host, then relocate to a host from a different vertebrate species and transfer the gene to it in turn.

Which choice best describes the function of the underlined portion "while feeding, a parasite could acquire a gene from one host, then relocate to a host from a different vertebrate species and transfer the gene to it in turn." in the text as a whole?

**A.** It explains why parasites are less susceptible to horizontal gene transfer than their hosts are. 

  *The sentence doesn't compare parasite versus host susceptibility — it describes the parasite as the AGENT carrying genes between hosts, not as a subject more or less susceptible to receiving genes.*

**B.** It clarifies why some genes are more likely to be transferred horizontally than others. 

  *The text never discusses why some genes specifically would be more likely to transfer than others — the hypothesis is about a mechanism, not differential likelihood among genes.*

**C.** It contrasts how horizontal gene transfer occurs among vertebrates with how it occurs among invertebrates. 

  *The parasites ARE invertebrates, and they're described as the vector for transfer BETWEEN vertebrate hosts — one integrated mechanism, not two processes being contrasted.*

**D.** It describes a means by which horizontal gene transfer might occur among vertebrates. **(Correct)**

  *Correct. The sentence lays out, step by step, exactly how a parasite could move a gene from one vertebrate host to another — the hypothesized mechanism.*

*Difficulty: medium*

---

##### Q38
> Part of the Atacama Desert in Peru has surprisingly rich plant life despite receiving almost no rainfall. Moisture from winter fog sustains plants once they're growing, but the soil's tough crust makes it hard for seeds to germinate in the first place. Local birds that dig nests in the ground seem to be of help: they churn the soil, exposing buried seeds to moisture and nutrients. Indeed, in 2016 Cristina Rengifo Faiffer found that mounds of soil dug up by birds were far more fertile and supported more seedlings than soil in undisturbed areas.

Which choice best describes the function of the underlined portion "they churn the soil, exposing buried seeds to moisture and nutrients." in the text as a whole?

**A.** It elaborates on the idea that the top layer of Atacama Desert soil forms a tough crust. 

  *This sentence describes how birds disrupt the crust, not an elaboration of how the crust itself forms — it's the opposite move, describing the crust's undoing.*

**B.** It describes the process by which seeds are deposited into Atacama Desert soil. 

  *The sentence never describes how seeds get INTO the soil in the first place — it describes what happens to seeds already buried when birds dig, exposing rather than depositing them.*

**C.** It identifies the reason particular bird species dig nests in Atacama Desert soil. 

  *The sentence explains the EFFECT of nest-digging on seeds and soil, not the birds' own motivation for digging nests — no reason for why the birds nest is given anywhere.*

**D.** It explains how certain birds promote seed germination in Atacama Desert soil. **(Correct)**

  *Correct. Directly follows "seem to be of help" and explains the mechanism: churning exposes seeds to moisture and nutrients, addressing the germination problem stated two sentences earlier.*

*Difficulty: medium*

---

##### Q39
> Michelene Pesantubbee, a historian and citizen of the Choctaw Nation, has identified a dilemma inherent to research on the status of women in her tribe during the 1600s and 1700s: the primary sources from that era, travel narratives and other accounts by male European colonizers, underestimate the degree of power conferred on Choctaw women by their traditional roles in political, civic, and ceremonial life. Pesantubbee argues that the Choctaw oral tradition and findings from archaeological sites in the tribe's homeland supplement the written record by providing crucial insights into those roles.

Which choice best describes the overall structure of the text?

**A.** It details the shortcomings of certain historical sources, then argues that research should avoid those sources altogether. 

  *Pesantubbee's approach is to SUPPLEMENT the written sources with oral tradition and archaeology, not to avoid them altogether — the written record remains part of the picture, just corrected.*

**B.** It describes a problem that arises in research on a particular topic, then sketches a historian's approach to addressing that problem. **(Correct)**

  *Correct. First states the dilemma (colonial written sources underestimate Choctaw women's power), then describes Pesantubbee's approach to addressing it via oral tradition and archaeology.*

**C.** It lists the advantages of a particular research method, then acknowledges a historian's criticism of that method. 

  *This inverts who is proposing versus who is criticizing — Pesantubbee is the one proposing the oral-tradition-plus-archaeology approach, not criticizing a method that was praised.*

**D.** It characterizes a particular topic as especially challenging to research, then suggests a related topic for historians to pursue instead. 

  *Pesantubbee doesn't suggest a different topic "instead" — she proposes additional sources for addressing the SAME topic, not a topic switch.*

*Difficulty: hard*

---

##### Q40
> Many archaeologists assume that large-scale engineering projects in ancient societies required an elite class to plan and direct the necessary labor. However, recent discoveries, such as the excavation of an ancient canal near the Gulf Coast of Alabama, have complicated this picture. Using radiocarbon dating, a team of researchers concluded that the 1.39-kilometer-long canal was most likely constructed between 576 and 650 CE by an Indigenous society that was relatively free of social classes.

Which choice best describes the overall structure of the text?

**A.** It describes a common view among archaeologists, then discusses a recent finding that challenges that view. **(Correct)**

  *Correct. Opens with the common assumption (elite class required for large engineering projects), then presents the canal excavation finding that complicates it — a society "relatively free of social classes."*

**B.** It outlines a method used in some archaeological fieldwork, then explains why an alternative method is superior to it. 

  *Radiocarbon dating is mentioned only as the technique used to date the canal, not as one of two competing fieldwork methods being compared — no second method is introduced.*

**C.** It presents contradictory conclusions drawn by archaeologists, then evaluates a study that has apparently resolved that contradiction. 

  *This is a single challenge to a single assumption, not multiple contradictory conclusions being reconciled by a separate resolving study.*

**D.** It identifies a gap in scientific research, then presents a strategy used by some archaeologists to remedy that gap. 

  *This is a challenge to an existing assumption via new evidence, not a previously unstudied gap being addressed by a deliberate research strategy.*

*Difficulty: medium*

---

##### Q41
> Today composer Scott Joplin is mainly celebrated for his catchy ragtime pieces "Maple Leaf Rag" and "The Entertainer." However, by overlooking his less famous works, listeners will miss the full range of Joplin's creativity. For instance, his waltz "Pleasant Moments" and his opera Treemonisha skillfully blend ragtime and classical music. These masterpieces deserve as much fame as Joplin's biggest hits.

Which choice best states the main purpose of the text?

**A.** To describe the similarities and differences between ragtime music and opera 

  *"Pleasant Moments" and Treemonisha are named only as examples of Joplin's overlooked works — the text never systematically compares ragtime and opera as genres.*

**B.** To argue that more attention should be given to Joplin's lesser-known works **(Correct)**

  *Correct. "These masterpieces deserve as much fame as Joplin's biggest hits" is a direct advocacy claim, and the whole passage builds the case for the overlooked works.*

**C.** To encourage music lovers to listen to music by many different composers 

  *The text is entirely about one composer, Joplin, and his own underappreciated works — it never urges listeners toward other composers broadly.*

**D.** To explain how Joplin learned to compose and perform ragtime music 

  *Nothing about how Joplin "learned to compose" is discussed — the text is about which of his finished works deserve more recognition, not his training.*

*Difficulty: medium*

---

##### Q42
> The following text is adapted from Louise Erdrich's 2020 novel The Night Watchman. Louis Pipestone is collecting signatures for a petition from fellow members of the Turtle Mountain Band of Chippewa on the tribe's reservation in North Dakota.
> 
> Louis Pipestone tended the petition like a garden. He kept it with him at all times. In town, his eyes sharpened when he noticed a tribal member who hadn't yet signed. Wherever they were—at the gas pump, mercantile [general store], at Henry's [Café], on the road, or outside the clinic and hospital—Louis cornered them. If they were waiting for a baby to be born, he'd have them sign. If they were laughing, if they were arguing. If they were taking a child home from school, they signed.

Which choice best states the main purpose of the text?

**A.** To suggest that some tribal members refuse to sign the petition because they dislike Louis Pipestone 

  *No one refusing to sign or disliking Pipestone is ever mentioned — every listed encounter ends with people signing, regardless of what they were doing.*

**B.** To show that attitudes toward the petition within the tribal community change over time 

  *No change over time in attitudes is described — the pattern shown is Pipestone's constant, unwavering pursuit of signatures, not an evolving community sentiment.*

**C.** To demonstrate that most tribal members are enthusiastic about signing the petition 

  *The passage focuses on Pipestone's actions and persistence, not the tribal members' own enthusiasm — their compliance doesn't establish their internal attitude.*

**D.** To portray Louis Pipestone's strong commitment to collecting signatures for the petition **(Correct)**

  *Correct. The "tended the petition like a garden" metaphor, his constant vigilance, and the list of situations in which he pursues signatures all portray his relentless commitment.*

*Difficulty: medium*

---

##### Q43
> Very little is known about the role nocturnal insects, such as moths, play in flower pollination because it is difficult to monitor insects at night. To address this problem, a team of scientists used time-lapse cameras to record pollinator visits to red clover all day and night. The recordings showed that while most pollinator visits were by bumblebees, one-third of visits were by moths. Additionally, flowers that were visited by both moths and bees produced more seeds than flowers that were only visited by bees.

Which choice best states the function of the underlined sentence "To address this problem, a team of scientists used time-lapse cameras to record pollinator visits to red clover all day and night." in the text?

**A.** To describe an approach a team of scientists used to study pollinators **(Correct)**

  *Correct. Directly describes the scientists' method — time-lapse cameras, day-and-night recording — used to study pollinator visits.*

**B.** To question a claim scientists make about pollinators 

  *The sentence responds to a stated DIFFICULTY (monitoring insects at night), not a disputed claim, and it does so constructively, not skeptically.*

**C.** To explain why moths prefer red clover to other flowers 

  *This sentence describes the study's method, not any explanation of moth flower preference — the preference-related findings come in later sentences.*

**D.** To announce an unexpected research finding about red clover 

  *This sentence describes the methodology, not a finding — the actual findings (moth visitation rate, seed production) are reported in the sentences after it.*

*Difficulty: easy*

---

##### Q44
> The following text is from Walt Whitman's 1860 poem "Calamus 24."
> 
> I HEAR it is charged against me that I seek to destroy institutions;
> But really I am neither for nor against institutions,
> (What indeed have I in common with them?—Or what with the destruction of them?),
> Only I will establish in the Mannahatta [Manhattan] and in every city of These States, inland and seaboard,
> And in the fields and woods, and above every keel [ship] little or large, that dents the water,
> Without edifices, or rules, or trustees, or any argument,
> The institution of the dear love of comrades.

Which choice best describes the overall structure of the text?

**A.** The speaker questions an increasingly prevalent attitude, then summarizes his worldview. 

  *The speaker responds to a specific charge made against him personally, not to an "increasingly prevalent attitude" — there's no claim about the charge becoming more common over time.*

**B.** The speaker regrets his isolation from others, then predicts a profound change in society. 

  *No regret about isolation appears anywhere, nor does the speaker predict a change in society — he announces his own intention to establish something, a personal ambition.*

**C.** The speaker concedes his personal shortcomings, then boasts of his many achievements. 

  *The speaker doesn't concede any shortcomings — he explicitly denies the charge against him rather than admitting fault, and what follows is a stated intention, not a boast about past achievements.*

**D.** The speaker addresses a criticism leveled against him, then announces a grand ambition of his. **(Correct)**

  *Correct. Opens by addressing the accusation ("charged against me"), denies it, then pivots to announcing his own aim: establishing "the institution of the dear love of comrades" everywhere.*

*Difficulty: hard*

---

##### Q45
> The following text is adapted from George Eliot's 1857 short story "The Sad Fortunes of the Rev. Amos Barton." Mr. Ely is a clergyman in the town of Milby.
> 
> By the laity of Milby and its neighbourhood [Mr. Ely] was regarded as a man of quite remarkable powers and learning, who must make a considerable sensation in London pulpits and drawing-rooms on his occasional visit to the metropolis; and by his brother clergy he was regarded as a discreet and agreeable fellow. Mr. Ely never got into a warm discussion; he suggested what might be thought, but rarely said what he thought himself; he never let other men see that he was laughing at them, and he never gave any one an opportunity of laughing at him.

Which choice best describes the overall structure of the text?

**A.** It shows that Mr. Ely had originally been held in high regard by his friends and then details the events that caused their regard for him to subside. 

  *No mention of anyone's regard "subsiding" or of events causing a decline — the text presents an ongoing, stable favorable view followed by an ongoing description of his guarded behavior, not a before-and-after decline.*

**B.** It implies that Mr. Ely's neighbors are more naive in their estimation of him than people in London are and then explains why his neighbors have been so easily misled. 

  *The text doesn't compare Milby neighbors' opinion to Londoners' — it only speculates about what WOULD happen in London as a measure of his reputation, not an actual contrast between two audiences' naivety.*

**C.** It stresses the discrepancy between Mr. Ely's public and private conduct and then alludes to his motivation for hiding his true personality. 

  *The text doesn't establish a discrepancy between public and private "conduct" (no glimpse of a hidden private self is shown) nor a stated motivation for hiding anything — his guarded behavior is presented directly, not contrasted with an unseen inner truth.*

**D.** It presents the favorable opinion of Mr. Ely that other people hold and then describes the behaviors of Mr. Ely that enable him to maintain that favorable opinion. **(Correct)**

  *Correct. First sentence gives others' favorable view of Ely (laity and clergy both regard him well); second sentence explains the careful, guarded behaviors that sustain that favorable view.*

*Difficulty: sat-hardest*

---

##### Q46
> The following text is from Virginia Woolf's 1919 novel Night and Day. The text describes a gathering of young artists and intellectuals.
> 
> One person after another rose, and, as with an ill-balanced axe, attempted to hew out his conception of art a little more clearly, and sat down with the feeling that for some reason which he could not grasp, his strokes had gone awry. As they sat down they turned almost invariably to the person sitting next them, and rectified and continued what they had just said in public.

Which choice best describes the function of the underlined portions "an ill-balanced axe, attempted to hew out" and "strokes had gone awry" in the text as a whole?

**A.** To demonstrate individuals' puzzlement over the reputation of a certain artwork 

  *Nothing in the passage concerns puzzlement over an artwork's reputation — the axe/hewing imagery is metaphorical for struggling to express ideas verbally, not about assessing any particular piece's reception.*

**B.** To highlight the physical effort involved in individuals' construction of large-scale works of art 

  *"Hew out" and "strokes" are a figurative carving metaphor for the difficulty of speaking clearly about art, not a literal description of physically constructing artworks — no actual artmaking occurs in this scene of people talking.*

**C.** To draw attention to individuals' discontent with the group's conversation about art 

  *The passage is about individuals' difficulty articulating their OWN ideas, not about being unhappy with the group's conversation as a whole — the frustration shown is personal and expressive, not interpersonal.*

**D.** To emphasize the extent of individuals' struggles to articulate thoughts on art **(Correct)**

  *Correct. "Ill-balanced axe" clumsily hewing and "strokes had gone awry" both figuratively convey how difficult and imprecise each speaker found it to express ideas about art clearly.*

*Difficulty: hard*

---

##### Q47
> Why do sand cats purr but lions roar? Researchers hypothesize that this difference between the two feline species may be partly due to a U-shaped bone in their throats called the hyoid. Sand cats, which are much smaller than lions, have a rigid hyoid bone that rumbles when the cat's larynx vibrates, resulting in a purr. By contrast, lions have a somewhat flexible hyoid, and the bone is attached to the skull with a stretchy ligament that sand cats lack. These traits allow lions and most other species of big cats to produce powerful roars. The same traits may also prevent most big cats from purring.

Which choice best describes the overall structure of the text?

**A.** The text presents a theory about two species, then discusses facts that weaken it. 

  *The facts that follow — the hyoid bone structure differences — support the hypothesis, they don't weaken it; the rest of the text builds the case rather than undermining it.*

**B.** The text compares the habitats of two species, then explains how those habitats are changing. 

  *No habitats are discussed anywhere — the entire passage concerns anatomy (the hyoid bone) and vocalization, not where the cats live.*

**C.** The text describes a behavior shared by two species, then discusses other behaviors shared by them. 

  *Purring and roaring are not a shared behavior — the whole point is that sand cats purr and lions roar, i.e., they differ, and the text explains that difference rather than any shared behavior.*

**D.** The text poses a question about two species, then presents a possible answer. **(Correct)**

  *Correct. Opens with "Why do sand cats purr but lions roar?" and then presents the hyoid-bone hypothesis as an answer, with supporting anatomical detail.*

*Difficulty: easy*

---

##### Q48
> The field of study called affective neuroscience seeks instinctive, physiological causes for feelings such as pleasure or displeasure. Because these sensations are linked to a chemical component (for example, the release of the neurotransmitter dopamine in the brain when one receives or expects a reward), they can be said to have a partly physiological basis. These processes have been described in mammals, but Jingnan Huang and his colleagues have recently observed that some behaviors of honeybees (such as foraging) are also motivated by a dopamine-based signaling process.

Which choice best describes the main purpose of the text?

**A.** It describes an experimental method of measuring the strength of physiological responses in humans. 

  *No experimental method for measuring physiological response strength is described, and the discussion isn't limited to humans — it's about mammals generally and honeybees.*

**B.** It illustrates processes by which certain insects can express how they are feeling. 

  *The text is about the physiological mechanism underlying certain behaviors, not about insects "expressing" feelings — foraging is a behavior driven by dopamine signaling, not an outward emotional expression.*

**C.** It summarizes a finding suggesting that some mechanisms in the brains of certain insects resemble mechanisms in mammalian brains. **(Correct)**

  *Correct. The text establishes the mammalian dopamine-based mechanism, then reports Huang's finding that a similar mechanism appears in honeybee brains — a cross-species mechanism resemblance.*

**D.** It presents research showing that certain insects and mammals behave similarly when there is a possibility of a reward for their actions. 

  *The text's actual focus is on the shared underlying mechanism (dopamine signaling), not simply that the behaviors themselves look alike — this describes the wrong level of similarity.*

*Difficulty: medium*

---

##### Q49
> Studying late nineteenth- and early twentieth-century artifacts from an agricultural and domestic site in Texas, archaeologist Ayana O. Flewellen found that Black women employed as farm workers utilized hook-and-eye closures to fasten their clothes at the waist, giving themselves a silhouette similar to the one that was popular in contemporary fashion and typically achieved through more restrictive garments such as corsets. Flewellen argues that this sartorial practice shows that these women balanced hegemonic ideals of femininity with the requirements of their physically demanding occupation.

Which choice best states the main purpose of the text?

**A.** To describe an unexpected discovery that altered a researcher's view of how rapidly fashions among Black female farmworkers in late nineteenth- and early twentieth-century Texas changed during the period 

  *The text never claims the discovery "altered a researcher's view" about how rapidly fashions changed — no prior belief about the pace of change is stated or revised.*

**B.** To discuss research that investigated the ways in which Black female farmworkers in late nineteenth- and early twentieth-century Texas used fashion practices to resist traditional gender ideals 

  *Flewellen's argument is that the women BALANCED hegemonic femininity ideals WITH occupational needs, not that they resisted gender ideals — achieving a fashionable silhouette is conforming, the opposite of resistance.*

**C.** To evaluate a scholarly work that offers explanations for the impact of urban fashion ideals on Black female farmworkers 

  *The text doesn't discuss "urban" fashion ideals specifically, nor does it "evaluate" the scholarly work critically — it reports Flewellen's finding and interpretation straightforwardly.*

**D.** To summarize the findings of a study that explored factors influencing a fashion practice among Black female farmworkers in late nineteenth- and early twentieth-century Texas **(Correct)**

  *Correct. The text reports what Flewellen found and her interpretation of what motivated it — precisely a summary of a study's findings about factors influencing a fashion practice.*

*Difficulty: hard*

---

##### Q50
> The following text is adapted from Herman Melville's 1857 novel The Confidence-Man. Humphry Davy was a prominent British chemist and inventor.
> 
> Years ago, a grave American savant, being in London, observed at an evening party, a certain coxcombical fellow, as he thought, an absurd ribbon in his lapel, and full of smart [banter], whisking about to the admiration of as many as were disposed to admire. Great was the savant's disdain; but, chancing ere long to find himself in a corner with the jackanapes, got into conversation with him, when he was somewhat ill-prepared for the good sense of the jackanapes, but was altogether thrown aback, upon subsequently being [informed that he was] no less a personage than Sir Humphry Davy.

Which choice best states the main purpose of the text?

**A.** It portrays the thoughts of a character who is embarrassed about his own behavior. 

  *The American savant is not shown reflecting on or being embarrassed about his OWN behavior — the text shows him misjudging Davy, but no internal reflection or embarrassment is actually depicted.*

**B.** It presents an account of a misunderstanding. **(Correct)**

  *Correct. The savant dismisses a stranger as a "coxcombical fellow" based on appearance, then is "thrown aback" to learn the stranger was actually the eminent Sir Humphry Davy — a misjudgment based on first impressions.*

**C.** It offers a short history of how a person came to be famous. 

  *The text is not a biographical history of how Davy became famous — his fame is a given fact the savant simply didn't recognize; no account of Davy's path to fame is given.*

**D.** It explains why one character dislikes another. 

  *The point of the passage is the misjudgment and its reveal, not an explanation of ongoing interpersonal dislike — the savant's initial disdain is based on a superficial impression, not a sustained reason to dislike Davy.*

*Difficulty: medium*

---

##### Q51
> Some studies have suggested that posture can influence cognition, but we should not overstate this phenomenon. A case in point: In a 2014 study, Megan O'Brien and Alaa Ahmed had subjects stand or sit while making risky simulated economic decisions. Standing is more physically unstable and cognitively demanding than sitting; accordingly, O'Brien and Ahmed hypothesized that standing subjects would display more risk aversion during the decision-making tasks than sitting subjects did, since they would want to avoid further feelings of discomfort and complicated risk evaluations. But O'Brien and Ahmed actually found no difference between the groups' performance.

Which choice best states the main purpose of the text?

**A.** It argues that research findings about the effects of posture on cognition are often misunderstood, as in the case of O'Brien and Ahmed's study. 

  *The text doesn't claim findings are "often misunderstood" by readers; it says the phenomenon itself "should not [be] overstate[d]" — a caution about claim strength, not a claim about reader misunderstanding.*

**B.** It presents the study by O'Brien and Ahmed to critique the methods and results reported in previous studies of the effects of posture on cognition. 

  *No methodological critique of prior work appears — O'Brien and Ahmed's own hypothesis simply wasn't confirmed by their own results.*

**C.** It explains a significant problem in the emerging understanding of posture's effects on cognition and how O'Brien and Ahmed tried to solve that problem. 

  *There's no "problem" being "solved" here — O'Brien and Ahmed's hypothesis was NOT confirmed; their study is a cautionary example, not a successful solution to a research problem.*

**D.** It discusses the study by O'Brien and Ahmed to illustrate why caution is needed when making claims about the effects of posture on cognition. **(Correct)**

  *Correct. "We should not overstate this phenomenon" is the guiding claim, and O'Brien and Ahmed's null result — despite a plausible, well-reasoned hypothesis — is the case in point illustrating why caution is warranted.*

*Difficulty: hard*

---

##### Q52
> In Jane Austen's novel Mansfield Park, an almost imperceptible smile from potential suitor Henry Crawford causes the protagonist Fanny Price to blush; her embarrassment grows when she suspects that he is aware of it. This moment—in which Fanny not only infers Henry's mental state through his gestures, but also infers that he is drawing inferences about her mental state—illustrates what literary scholar George Butte calls "deep intersubjectivity," a technique for representing interactions between consciousnesses through which Austen's novels derive much of their social and psychological drama.

Which choice best describes the function of the underlined sentence "In Jane Austen's novel Mansfield Park, an almost imperceptible smile from potential suitor Henry Crawford causes the protagonist Fanny Price to blush; her embarrassment grows when she suspects that he is aware of it." in the text as a whole?

**A.** It states a claim about Austen's skill at representing psychological complexity that is reinforced by an example presented in the following sentence. 

  *This reverses the order — this sentence IS the example, while the claim about Austen's technique ("deep intersubjectivity") comes in the following sentence.*

**B.** It advances an interpretation of an Austen protagonist that is contrasted with protagonists from other Austen novels cited in the following sentence. 

  *No other Austen novels or protagonists are ever mentioned for comparison — only Mansfield Park and Fanny Price are discussed.*

**C.** It describes a recurring theme in Austen's novels that is the focus of literary scholar's analysis summarized in the following sentence. 

  *This specific scene is a single illustration of a narrative TECHNIQUE (deep intersubjectivity), not a "recurring theme" being independently identified and then analyzed.*

**D.** It provides a synopsis of an interaction in an Austen novel that illustrates a literary concept discussed in the following sentence. **(Correct)**

  *Correct. The sentence narrates a specific scene, and the following sentence explicitly names this as an illustration of "deep intersubjectivity," a concept it then explains.*

*Difficulty: sat-hardest*

---

##### Q53
> Mathematician Claude Shannon is widely regarded as a foundational figure in information theory. His most important paper, "A Mathematical Theory of Communication," published in 1948 when he was employed at Bell Labs, utilized a concept called a "binary digit" (shortened to "bit") to measure the amount of information in any signal and determine the fastest rate at which information could be transmitted while still being reliably decipherable. Robert Gallagher, one of Shannon's colleagues, said that the bit was "[Shannon's] discovery, and from it the whole communications revolution has sprung."

Which choice best describes the overall structure of the text?

**A.** It presents a theoretical concept, illustrates how the name of the concept has changed, and shows how the name has entered common usage. 

  *"Binary digit (shortened to 'bit')" is an abbreviation detail within describing the concept, not a claim that the name has changed over time or that its adoption into everyday language is tracked historically.*

**B.** It introduces a respected researcher, describes an aspect of his work, and suggests why the work is historically significant. **(Correct)**

  *Correct. Introduces Shannon ("widely regarded as a foundational figure"), describes his key work, and closes with Gallagher's quote suggesting its historical significance.*

**C.** It names the company where an important mathematician worked, details the mathematician's career at the company, and provides an example of the recognition he received there. 

  *Bell Labs is mentioned only in passing as his employer when the paper was published — the text doesn't detail his career there more broadly, nor company-specific recognition.*

**D.** It mentions a paper, offers a summary of the paper's findings, and presents a researcher's commentary on the paper. 

  *Gallagher's quote is about the significance of the bit itself and its broader impact on the whole communications field, not commentary specifically reviewing the paper as a document.*

*Difficulty: medium*

---

##### Q54
> According to Indian economist and sociologist Radhakamal Mukerjee (1889-1968), the Eurocentric concepts that informed early twentieth-century social scientific methods—for example, the idea that all social relations are reducible to struggles between individuals—had little relevance for India. Making the social sciences more responsive to Indians' needs, Mukerjee argued, required constructing analytical categories informed by India's cultural and ecological circumstances. Mukerjee thus proposed the communalist "Indian village" as the ideal model on which to base Indian economic and social policy.

Which choice best describes the overall structure of the text?

**A.** The text recounts Mukerjee's early training in the social scientific disciplines and then lists social policies whose implementation Mukerjee oversaw. 

  *No biographical account of Mukerjee's training is given, and there's no list of social policies he "oversaw" — the text describes his intellectual critique and proposed model, not an administrative record.*

**B.** The text mentions some of Mukerjee's economic theories and then traces their impact on other Indian social scientists of the twentieth century. 

  *The text doesn't trace impact on other social scientists — it stays entirely within Mukerjee's own critique and his own proposed solution, the "Indian village" model.*

**C.** The text presents Mukerjee's critique of the social sciences and then provides an example of his attempts to address issues he identified in his critique. **(Correct)**

  *Correct. First presents Mukerjee's critique (Eurocentric concepts had "little relevance for India"), then provides his proposed remedy — the "Indian village" model — as an example of addressing the issue.*

**D.** The text explains an influential economic theory and then demonstrates how that theory was more important to Mukerjee's work than other social scientists have acknowledged. 

  *The text doesn't compare how other social scientists have assessed Mukerjee's work — no such comparative claim about others' acknowledgment appears anywhere.*

*Difficulty: medium*

---

##### Q55
> Space scientists Anna-Lisa Paul, Stephen M. Elardo, and Robert Ferl planted seeds of Arabidopsis thaliana in samples of lunar regolith—the surface material of the Moon—and, serving as a control group, in terrestrial soil. They found that while all the seeds germinated, the roots of the regolith-grown plants were stunted compared with those in the control group. Moreover, unlike the plants in the control group, the regolith-grown plants exhibited red pigmentation, reduced leaf size, and inhibited growth rates—indicators of stress that were corroborated by postharvest molecular analysis.

Which choice best states the main purpose of the text?

**A.** It describes an experiment that addressed an unresolved question about the extent to which lunar regolith resembles terrestrial soils. 

  *The study isn't investigating whether lunar regolith "resembles" terrestrial soil chemically — it's growing plants in each to compare plant outcomes, a different research question.*

**B.** It compares two distinct methods of assessing indicators of stress in plants grown in a simulated lunar environment. 

  *The text describes one experiment whose stress indicators — pigmentation, leaf size, growth rate, molecular analysis — are all used together cumulatively, not as competing assessment methods.*

**C.** It presents evidence in support of the hypothesis that seed germination in lunar habitats is an unattainable goal. 

  *The text states plainly that "all the seeds germinated" in the regolith, directly contradicting a claim that germination is unattainable — what was impaired was subsequent growth, a different finding.*

**D.** It discusses the findings of a study that evaluated the effects of exposing a plant species to lunar soil conditions. **(Correct)**

  *Correct. The text reports a controlled experiment (regolith versus terrestrial soil) and its findings — germination occurred, but growth was stunted and stress indicators appeared.*

*Difficulty: medium*

---

##### Q56
> Raymond Antrobus, an accomplished poet and writer of prose, recently released his debut spoken word poetry album, The First Time I Wore Hearing Aids, in collaboration with producer Ian Brennan. The album contains both autobiographical and reflective pieces combining Antrobus's spoken words with Brennan's fragmented audio elements and pieces of music to convey how people who are deaf may experience sound, both its presence and absence. Some critics suggest that the album questions the function of sound in the world, highlighting that the experience of sound is multifaceted.

Which choice best describes the overall structure of the text?

**A.** It introduces a collaborative spoken word poetry project, details the approach taken to produce the work, and then provides an example of critique the album received upon release. **(Correct)**

  *Correct. Introduces the album as a collaboration, details the production approach — spoken words combined with fragmented audio and music to convey deaf experience of sound — then closes with critics' interpretive response.*

**B.** It mentions a collection of spoken word poems, distinguishes one poem as being an exemplar on the album, and then offers a summary of the subject matter of the whole collection. 

  *No single poem is singled out as an exemplar — the text discusses the album as a whole, not one representative poem distinguished from the rest.*

**C.** It summarizes the efforts to produce a collection of spoken word poems, presents biographies of two people who worked on the album, and speculates about the meaning behind the poetry. 

  *The text doesn't give biographies of Antrobus and Brennan (only brief professional descriptors), and "speculates about the meaning" overstates what is a reported critical view, not the author's own speculation.*

**D.** It connects two artists to the same spoken word poetry project, explains the extent of their collaboration on each poem, and then provides an overview of the technique used to produce the work. 

  *The text doesn't explain their collaboration poem-by-poem, and it doesn't end with a technique overview — it ends with critical reception instead.*

*Difficulty: hard*

---

##### Q57
> The 1967 release of Harold Cruse's book The Crisis of the Negro Intellectual isolated him from almost all other scholars and activists of the American Civil Rights Movement—though many of those thinkers disagreed with each other, he nonetheless found ways to disagree with them all. He thought that activists who believed that Black people such as himself should culturally assimilate were naïve. But he also sharply criticized Black nationalists such as Marcus Garvey who wanted to establish independent, self-contained Black economies and societies, even though Cruse himself identified as a Black nationalist.

Which choice best describes the function of the underlined sentence "But he also sharply criticized Black nationalists such as Marcus Garvey who wanted to establish independent, self-contained Black economies and societies, even though Cruse himself identified as a Black nationalist." in the text as a whole?

**A.** It describes a direction that Cruse felt the Civil Rights Movement ought to take. 

  *The sentence describes Cruse CRITICIZING a specific group, not proposing any direction he thought the movement should take — no positive prescriptive claim appears here.*

**B.** It indicates that Cruse's reputation as a persistent antagonist of other scholars is undeserved. 

  *The sentence provides EVIDENCE supporting the earlier claim that Cruse found "ways to disagree with them all," reinforcing rather than undermining that reputation.*

**C.** It describes a controversy that Cruse's work caused within the Black nationalist movement. 

  *The sentence doesn't describe a controversy Cruse's work caused among nationalists — it simply states that Cruse, despite self-identifying as a nationalist, criticized fellow nationalists like Garvey; no depicted backlash appears.*

**D.** It helps explain a position with respect to the community of civil rights thinkers. **(Correct)**

  *Correct. The sentence, with its "even though Cruse himself identified as a Black nationalist" twist, is exactly what fleshes out the opening claim about his isolated, all-sides-disagreeing position.*

*Difficulty: hard*

---

##### Q58
> Asteroid 6478 Gault has experienced intermittent mass loss since at least 2013, but in contrast to some asteroids with repeated mass-loss episodes, 6478 Gault has not lost mass at its perihelion (the closest point of its orbit to the Sun), and thus the loss is not attributable to solar energy-driven ice vaporization. And as Jane X. Luu et al. point out, the singular nature of impact ejection makes it untenable as an account of multiple loss episodes of similar duration over several years. Instead, Luu et al. are likely correct that 6478 Gault is shedding mass due to rotational instability.

Which choice best describes the overall structure of the text?

**A.** It presents a scientific observation, describes a contrast between that observation and other observations, and then explains why those other observations should not be considered credible. 

  *The text doesn't say other observations "should not be considered credible" — it rules out two potential explanatory mechanisms for the observed mass loss, not the credibility of any observational data.*

**B.** It describes an astronomical finding, discusses competing theories about that finding that the author regards as flawed, and then describes new evidence that supports an alternative theory. 

  *No "new evidence" is introduced to support the rotational-instability explanation — the text reasons through why the other two explanations don't fit the existing evidence, then names the remaining explanation, without presenting a new dataset.*

**C.** It introduces a natural phenomenon, refutes two potential explanations for that phenomenon, and then presents a third explanation for that phenomenon that the author regards as plausible. **(Correct)**

  *Correct. Introduces the phenomenon, rules out solar-driven vaporization and impact ejection, then presents rotational instability as the explanation Luu et al. — and the author — regard as likely correct.*

**D.** It discusses a physical process, evaluates possible causes of that process, and then states that a persuasive account of the process has yet to be put forward. 

  *The text does NOT conclude that a persuasive account is still missing — it explicitly endorses rotational instability as the likely correct explanation, the opposite of leaving the question open.*

*Difficulty: sat-hardest*

---

##### Q59
> Historians have argued that a crucial component of the Civil Rights Movement's success in the 1960s was the Southern Christian Leadership Conference's Citizen Education Program (CEP), which invited promising activists from across the South to its one-week training sessions in Dorchester, Georgia. Led by experienced organizers such as Dorothy Cotton and Septima Clark, CEP attendees—more than 7,000 in all—participated in workshops on topics ranging from public speaking to legal doctrine before returning home to spearhead local civil rights initiatives.

Which choice best describes the function of the underlined portion "more than 7,000 in all" in the text as a whole?

**A.** It underscores the extent of the CEP's impact on the Civil Rights Movement of the 1960s. **(Correct)**

  *Correct. The large number of attendees who went on to "spearhead local civil rights initiatives" quantifies and reinforces the claim that CEP was "a crucial component" of the movement's success.*

**B.** It illustrates the CEP organizers' efforts to educate participants on a wide variety of topics. 

  *The attendee count doesn't illustrate the variety of topics taught — the range of workshop topics is a separate detail from the headcount, which speaks to scale, not curriculum breadth.*

**C.** It suggests that CEP attendees held a diverse array of opinions about the Southern Christian Leadership Conference's political philosophy. 

  *Nothing about attendees' opinion diversity is stated or implied by a headcount — the number measures participation, not opinion, which is never discussed anywhere in the text.*

**D.** It establishes that criticism of the CEP was limited to a few individuals in the Southern Christian Leadership Conference. 

  *No criticism of the CEP is mentioned anywhere in the text — this invents a controversy dimension that doesn't exist in the passage.*

*Difficulty: easy*

---

##### Q60
> In 2020, rap artist and professor A.D. Carson published the first peer-reviewed rap album about his experiences with Black masculinity called "i used to love to dream." Typically in peer review, experts evaluate scholarly articles prior to publication. For Carson's album, dubbed a "mixtape/e/ssay," peer review involved both scholars and rap artists. In combining elements of a mixtape album with scholarly essays that connect Carson's lyrics to historical and contemporary contexts for listeners both inside and outside academia, Carson's album helped redefine how scholarship is created and shared.

Which choice best states the main purpose of the text?

**A.** To compare the relative public impact of scholarly articles and albums 

  *The text doesn't compare the relative public impact of scholarly articles and albums as general categories — it's specifically about one album's novel hybrid format, not a broad impact comparison.*

**B.** To capture one scholar's opinion of a new rap album 

  *The text isn't framed as one scholar's opinion — it's a general descriptive account of what Carson's album is and did, not an attributed subjective opinion from a named individual.*

**C.** To explain why a certain rap album is particularly innovative **(Correct)**

  *Correct. The text builds the case for the album's innovation at every step: first peer-reviewed rap album, an unusual review process, and helping "redefine how scholarship is created and shared."*

**D.** To describe how each step of the peer review process unfolds 

  *The text describes peer review only generally, in contrast to how it's typically done — it doesn't walk through each step of the process in sequence.*

*Difficulty: medium*

---

##### Q61
> The mimosa tree evolved in East Asia, where the beetle Bruchidius terrenus preys on its seeds. In 1785, mimosa trees were introduced to North America, far from any B. terrenus. But evolutionary links between predators and their prey can persist across centuries and continents. Around 2001, B. terrenus was introduced in southeastern North America near where botanist Shu-Mei Chang and colleagues had been monitoring mimosa trees. Within a year, 93 percent of the trees had been attacked by the beetles.

Which choice best describes the function of the third sentence "But evolutionary links between predators and their prey can persist across centuries and continents." in the overall structure of the text?

**A.** It states the hypothesis that Chang and colleagues had set out to investigate using mimosa trees and B. terrenus. 

  *The sentence is a general statement about predator-prey links, not a specific hypothesis attributed to Chang and colleagues — no research question or intent is stated for their team here.*

**B.** It presents a generalization that is exemplified by the discussion of the mimosa trees and B. terrenus. **(Correct)**

  *Correct. The sentence states a general principle, and the rest of the passage — mimosa trees separated from B. terrenus for over two centuries and a continent, then rapidly attacked once reunited — is exactly a concrete example of that generalization.*

**C.** It provides context that clarifies why the species mentioned spread to new locations. 

  *The sentence explains why the predator-prey relationship persisted or reactivated, not why the trees or beetles "spread to new locations" in the first place — the introductions are historical facts stated elsewhere.*

**D.** It offers an alternative explanation for the findings of Chang and colleagues. 

  *This sentence comes BEFORE Chang and colleagues' findings are even introduced, so it can't be offering an alternative explanation for findings not yet presented — it sets up the principle those findings will exemplify.*

*Difficulty: hard*

---

##### Q62
> The following text is from John Dryden's 1697 translation of Virgil's poem the Aeneid, written in the first century BCE. Queen Dido has just heard the Trojan hero Aeneas recount a sad tale.
> 
> But anxious cares already seiz'd the queen:
> She fed within her veins a flame unseen;
> The hero's valor, acts, and birth inspire
> Her soul with love, and fan the secret fire.
> His words, his looks, imprinted in her heart,
> Improve the passion, and increase the smart.

Which choice best states the main purpose of the text?

**A.** To indicate that Dido is hiding her skepticism of Aeneas's account 

  *Nothing about skepticism of the account appears — the imagery is entirely about love and passion being kindled, not doubt about the truth of Aeneas's tale.*

**B.** To emphasize that Dido has been deeply affected by Aeneas's story **(Correct)**

  *Correct. "Anxious cares already seiz'd the queen," "flame unseen," "fan the secret fire," and "increase the smart" all build a cumulative picture of Dido overwhelmed by strong emotion as a result of Aeneas's story.*

**C.** To imply that Dido engages both emotionally and intellectually with Aeneas 

  *The passage describes an entirely emotional response — "flame," "fire," "smart" (pain) — with no depiction of intellectual engagement or reasoning about Aeneas's account.*

**D.** To suggest that Dido is worried that Aeneas might discover a secret she is keeping from him 

  *The "secret fire" is a metaphor for hidden, kindling passion, not a literal secret she's worried Aeneas will discover — there's no plot content about Dido concealing information from him.*

*Difficulty: medium*

---

##### Q63
> During Rome's republican period, which ended in the first century BCE, libraries were predominantly owned by wealthy individuals who tightly controlled access to their book collections. The first public library became available in Rome in 28 BCE and was soon followed by one commissioned by Emperor Augustus. As modern scholar Fabio Fernandes notes, however, these two traditions aren't as distinct as they seem, as both the emperor and the private library owners viewed their libraries as extensions of their personal patronage, just on vastly differing scales.

Which choice best states the main purpose of the text?

**A.** To give a brief overview of public access to libraries throughout Rome's republican period 

  *The text isn't a brief overview of public access throughout the entire republican period — it focuses on the transition into and comparison with early imperial public libraries via Fernandes's point, going beyond a republic-era access overview.*

**B.** To contend that early imperial leaders in Rome wielded too much influence over libraries 

  *The text never argues that imperial leaders "wielded too much influence" — that critical claim about excess isn't made; Fernandes's point is about a shared underlying logic, not a criticism of overreach.*

**C.** To assert that private and early public libraries in ancient Rome had an essential similarity **(Correct)**

  *Correct. Fernandes's point is exactly this: private and early public libraries "aren't as distinct as they seem" because both were extensions of personal patronage — an essential similarity.*

**D.** To call into question the notion that private Roman libraries disappeared during the first century BCE 

  *The text never claims private libraries "disappeared," nor does it call such a claim into question — private libraries are simply described as continuing to exist alongside the new public ones.*

*Difficulty: hard*

---

##### Q64
> Vadamalai Elangovan and Ganapathi Marimuthu showed that high moonlight intensity inhibits the activity of the greater short-nosed fruit bat (Cynopterus sphinx), a result explicable in terms of benefits and costs: greater lunar intensity may not enable the bats to increase foraging success enough to offset the higher chance of detection by predatory owls or hawks. Most other nocturnal mammals respond to lunar intensity variations similarly to greater short-nosed fruit bats, but mongoose lemurs (Eulemur mongoz) display the opposite pattern, as their heavy reliance on visual foraging results in a different balance of reward and risk.

Which choice best describes the overall structure of the text?

**A.** It discusses two different responses to the same natural phenomenon, explains why one of those responses occurs, and then suggests that the other response still needs to be explained. 

  *The text DOES explain the second response too — "their heavy reliance on visual foraging results in a different balance of reward and risk" is an explanation, not something left unexplained.*

**B.** It describes and accounts for a finding, characterizes the finding as representative of a general pattern, and then describes and accounts for an exception to that pattern. **(Correct)**

  *Correct. Describes and explains the fruit bat finding, generalizes it ("most other nocturnal mammals respond...similarly"), then describes and explains the mongoose lemur exception via a different foraging strategy.*

**C.** It presents and explains a study result, indicates that the result is similar to the results of many other studies, and then attributes a conflicting study result to a difference in that study's methods. 

  *The text doesn't say the fruit bat result matches many OTHER STUDIES — it says most nocturnal mammals behave similarly, a behavioral claim, not a research-replication one; and the lemur exception is explained by biology (visual foraging), not by differing study methods.*

**D.** It introduces an observation of a behavioral pattern, presents an explanation for the pattern, and then describes an exception to the pattern that casts doubt on that explanation. 

  *The mongoose lemur exception doesn't cast doubt on the fruit bat explanation — it's explained by a different factor (visual foraging) fully consistent with the same cost-benefit framework, not one that undermines it.*

*Difficulty: sat-hardest*

---

##### Q65
> Dubautia carrii is a species in a family of plants known collectively as the silversword alliance, all of which grow only on the Hawaiian Islands. Members of this alliance exhibit an extraordinary range of phenotypes, with some species maturing into vines and others into shrubs and trees. All species in the alliance descended from a single ancestral tarweed plant that arrived on the islands around 5 million years ago. The tarweed's descendants diversified into distinct species as they adapted to live in the wide variety of habitats found on the Hawaiian Islands.

Which choice best states the main purpose of the text?

**A.** To indicate the specific tarweed ancestor of all plants that grow on the Hawaiian Islands and explain why the plants have such varied physical characteristics 

  *The ancestral tarweed is the ancestor of the silversword ALLIANCE specifically, not of all plants on the Hawaiian Islands — the text never claims this ancestry applies to every Hawaiian plant.*

**B.** To describe the specific habitat where Dubautia carrii are found and identify other plants that share a common ancestor with them 

  *No specific habitat is named for Dubautia carrii alone — it's introduced as an example species representing the alliance's range, and the habitat discussion is about the alliance broadly.*

**C.** To describe the silversword alliance and explain how the plant family became so varied **(Correct)**

  *Correct. Introduces the silversword alliance via the example of Dubautia carrii, describes its extraordinary phenotypic range, and explains how that diversity arose from one ancestral tarweed.*

**D.** To advance the claim that all plants on the Hawaiian Islands are part of the silversword alliance and list possible ancestors of the plants that make up the alliance 

  *The text doesn't claim all Hawaiian plants belong to the alliance — only that alliance members grow only on Hawaii — and it names one ancestral tarweed, not multiple candidate ancestors.*

*Difficulty: medium*

---

##### Q66
> The following text is from George Marion McClellan's 1895 poem "Eternity."
> 
> My spirit swoons, and all my senses cry
> For Ocean's breast and covering of the sky.
> Rock me to sleep, ye waves, and outward bound,
> Just let me drift far out from toil and care,
> Where lapping of the waves shall be the sound,
> Which mingled with the winds that gently bear
> Me on between a peaceful sea and sky,
> To make my soothing slumberous lullaby.

Which choice best states the main purpose of the text?

**A.** To illustrate the increasing intensity of the speaker's desire to escape ongoing hardship by gliding on the ocean 

  *The poem doesn't show "increasing intensity" building over the lines — it opens already at a peak of longing ("my spirit swoons") and sustains a single steady wish throughout, rather than escalating.*

**B.** To contrast the demands of the speaker's everyday life with the serenity of being rocked to sleep by the ocean 

  *The poem doesn't actually detail the "demands" of the speaker's everyday life to contrast with the ocean — "toil and care" is a brief, general phrase, not a developed contrasting picture.*

**C.** To convey the speaker's longing for the ocean to impart a sense of inner tranquility **(Correct)**

  *Correct. "My spirit swoons," "rock me to sleep," "drift far out from toil and care," and "soothing slumberous lullaby" all express a longing for the ocean to provide calm, peace, and rest.*

**D.** To justify the speaker's qualms about being transported by the ocean to a quiet destination 

  *The speaker has no "qualms" about being carried by the ocean — the whole poem is an eager invitation ("rock me to sleep, ye waves...just let me drift"), the opposite of reluctance needing justification.*

*Difficulty: medium*

---

#### Words in Context (112 items)

##### Q1
> Although the intern had no formal training in graphic design, her poster for the school play was so ______ that the drama teacher asked her to design every future production’s marketing.

Which choice completes the text with the most logical and precise word or phrase?

**A.** amateurish 

  *This reverses the logic. If the poster had looked amateurish, the teacher would have no reason to hand her every future production — the outcome only makes sense if the poster was impressive despite the lack of training.*

**B.** polished **(Correct)**

  *Correct. "Although...no formal training" sets up a contrast between her lack of credentials and the outcome, and the outcome itself — being asked to design every future production — is strong evidence the poster looked professional despite that. "Polished" names exactly that quality.*

**C.** colorful 

  *The sentence never mentions the poster's palette — it describes a level of quality strong enough to earn repeated work. This answers a question about color that the text never raises.*

**D.** adequate 

  *"Adequate" points the right direction (positive) but is far too weak — merely adequate work doesn't explain why a teacher would hand a student every future production's marketing. The sentence's own evidence sets a bar well above "adequate."*

*Difficulty: medium*

---

##### Q2
> The following text is from Bram Stoker's 1897 novel Dracula. The narrator is being driven in a carriage through a remote region at night. The baying of the wolves sounded nearer and nearer, as though they were closing round on us from every side. I grew dreadfully afraid, and the horses shared my fear. The driver, however, was not in the least disturbed; he kept turning his head to left and right, but I could not see anything through the darkness.

As used in the text, what does the word "disturbed" most nearly mean?

**A.** Disorganized 

  *This is 'disturbed' in the sense of rearranged or messed up (like disturbed papers), not the emotional sense the sentence needs. The passage is about the driver's calm reaction to danger, not the state of any objects.*

**B.** Alarmed **(Correct)**

  *Correct. The narrator and horses are both afraid, but 'however' signals a contrast: the driver was 'not in the least disturbed,' meaning he showed none of that fear — he was not alarmed.*

**C.** Offended 

  *The sentence is about fear in response to danger (baying wolves closing in), not about taking insult at something. This swaps the emotional register the passage establishes.*

**D.** Interrupted 

  *This treats 'disturbed' as in 'do not disturb' (interrupting an activity), but the passage describes an emotional reaction to danger, not an activity being broken off.*

*Difficulty: medium*

---

##### Q3
> Dance choreographer Jawole Willa Jo Zollar aims to give people the opportunity to be ______ her creative process. For example, live performances of her dance HairStories, which debuted in 2001, featured videos of people across the United States talking about their hair and audience members sharing pictures of their interesting hairstyles.

Which choice completes the text with the most logical and precise word or phrase?

**A.** nervous about 

  *Nothing in the sentence suggests audience members felt anxious — they contributed videos and photos willingly. This answers an emotional question the text never raises.*

**B.** completed by 

  *The audience contributes material to an ongoing performance; nothing suggests they finish or complete the process. This misreads contribution as completion.*

**C.** delayed by 

  *There is no mention of any delay — the examples describe active audience participation, not something slowing the process down.*

**D.** involved in **(Correct)**

  *Correct. People sharing videos and pictures that become part of the performance is direct evidence of them being involved in — participating in — Zollar's creative process.*

*Difficulty: easy*

---

##### Q4
> A musician and member of the Quechua of Peru, Renata Flores Rivera was eager to promote the Quechua language in her music, but she was ______ speaking it. She met this challenge by asking her grandmother, a native speaker of Quechua, to help her pronounce words in her song lyrics and also by taking classes in the language.

Which choice completes the text with the most logical and precise word or phrase?

**A.** prepared for 

  *If she were already prepared to speak Quechua, she would not need her grandmother's help or language classes. This reverses what the rest of the sentence shows.*

**B.** inexperienced with **(Correct)**

  *Correct. 'But' signals a contrast with her eagerness, and needing a native speaker's help plus taking classes are both direct evidence that she lacked experience speaking the language.*

**C.** skilled in 

  *Directly contradicted by the evidence: someone skilled in speaking a language would not need a relative's help pronouncing words or need to take classes in it.*

**D.** excited about 

  *'Eager to promote' already establishes her enthusiasm; 'but' signals the blank must contrast with that eagerness, describing an obstacle, not a restatement of her excitement.*

*Difficulty: easy*

---

##### Q5
> The following text is from Yann Martel's 2001 novel Life of Pi. The narrator's family owned a zoo when he was a child. It was a huge zoo, spread over numberless acres, big enough to require a train to explore it, though it seemed to get smaller as I grew older, train included.

As used in the text, what does the word "spread" most nearly mean?

**A.** Hidden 

  *A zoo described as 'huge' and requiring a train to explore cannot simultaneously be described as hidden — the two ideas directly conflict.*

**B.** Discussed 

  *This is 'spread' as in spreading a rumor or story, a completely different sense from describing a zoo's physical extent across acres of land.*

**C.** Extended **(Correct)**

  *Correct. 'Spread over numberless acres' describes the zoo's physical extent — how far it reached across the land — which is exactly what 'extended' captures.*

**D.** Coated 

  *This is 'spread' as in spreading butter or jam (applying a coating), a different sense entirely from describing land area.*

*Difficulty: medium*

---

##### Q6
> Charles "Teenie" Harris was a photographer for the Pittsburgh Courier from 1936 to 1975. During his career he took over 70,000 photographs documenting everyday life in Pittsburgh's Black communities. The Carnegie Museum of Art maintains thousands of his photographs, carefully ______ them so that audiences can continue to view them well into the future.

Which choice completes the text with the most logical and precise word or phrase?

**A.** replacing 

  *Replacing the original photographs would work against letting future audiences view them — it contradicts the idea of maintaining the originals for continued viewing.*

**B.** inventing 

  *The photographs already exist — Harris took them decades ago. A museum cannot 'invent' photographs that were already taken.*

**C.** preserving **(Correct)**

  *Correct. 'So that audiences can continue to view them well into the future' is a direct statement of purpose that matches preservation — carefully maintaining the photographs for long-term access.*

**D.** counting 

  *Counting the photographs would not, by itself, ensure that future audiences can view them — it addresses tallying them, not conserving them for viewing.*

*Difficulty: easy*

---

##### Q7
> In the 1970s, video cameras became increasingly affordable for ordinary consumers and gave Ulysses Jenkins and other artists capabilities that were previously unavailable except to television broadcasters. Jenkins recognized and took full advantage of this ______ access to powerful technology to create groundbreaking works of video art, such as Mass of Images (1978).

Which choice completes the text with the most logical and precise word or phrase?

**A.** newfound **(Correct)**

  *Correct. The access described was 'previously unavailable' and only became possible once cameras 'became increasingly affordable' — that is, it was newly gained access, exactly what 'newfound' names.*

**B.** delicate 

  *Nothing in the sentence describes the access as fragile or easily lost — this introduces an attribute the text never raises.*

**C.** inevitable 

  *The sentence emphasizes that this access was newly gained due to falling prices, not that it was destined to happen regardless of circumstance — a different claim than the text supports.*

**D.** habitual 

  *This directly contradicts 'previously unavailable': habitual implies long-standing routine access, the opposite of access that was newly gained.*

*Difficulty: medium*

---

##### Q8
> A brief book review cannot fully convey the ______ of Olga Tokarczuk's novel The Books of Jacob, with its enormous cast of characters, its complicated, wandering plot, and its page numbers that count backward (beginning at 965 and ending at 1).

Which choice completes the text with the most logical and precise word or phrase?

**A.** accuracy 

  *None of the listed features (cast size, plot structure, page numbering) describe how correct or precise the novel is — this answers a question the sentence never asks.*

**B.** inactivity 

  *An 'enormous cast' and a 'wandering plot' describe elaborate, busy structure, not a lack of activity — this reverses what the listed details actually suggest.*

**C.** complexity **(Correct)**

  *Correct. The enormous cast, the complicated and wandering plot, and the backward-counting pages are three separate pieces of evidence for a single quality: the novel's complexity.*

**D.** restraint 

  *An enormous cast, a wandering plot, and an unusual numbering scheme all suggest excess and elaboration, the opposite of restraint.*

*Difficulty: easy*

---

##### Q9
> The following text is from Nella Larsen's 1928 novel Quicksand. The trees in their spring beauty sent through her restive mind a sharp thrill of pleasure. Seductive, charming, and beckoning as cities were, they had not this easy unhuman loveliness.

As used in the text, what does the word "beckoning" most nearly means?

**A.** Demanding 

  *'Demanding' implies force or obligation, a harsher tone than the pleasurable allure ('seductive, charming') the sentence is building toward.*

**B.** Signaling 

  *This is the literal, physical sense of 'beckon' (a gesture calling someone over). Paired with 'seductive' and 'charming,' the sentence needs the figurative sense — alluring — not a literal hand gesture.*

**C.** Inviting **(Correct)**

  *Correct. 'Beckoning' is grouped with 'seductive' and 'charming' as qualities of cities' allure, so it takes the figurative meaning of drawing someone in — inviting.*

**D.** Shifting 

  *Nothing in the sentence describes cities as changing or moving — this introduces an idea absent from the passage.*

*Difficulty: medium*

---

##### Q10
> Biologist Jane Edgeloe and colleagues have located what is believed to be the largest individual plant in the world in the Shark Bay area of Australia. The plant is a type of seagrass called Posidonia australis, and it ______ approximately 200 square kilometers.

Which choice completes the text with the most logical and precise word or phrase?

**A.** acknowledges 

  *A plant cannot 'acknowledge' an area of land — this verb requires an agent capable of recognizing something, which does not fit describing physical size.*

**B.** produces 

  *The sentence describes the plant's physical extent, not something it manufactures or generates — this confuses area covered with an output the plant creates.*

**C.** spans **(Correct)**

  *Correct. Describing the 'largest individual plant in the world' by its area (200 square kilometers) calls for a verb of extent, and 'spans' is exactly that.*

**D.** advances 

  *'Advances' suggests forward movement or progress over time, not a static measurement of area — the wrong category of verb for describing size.*

*Difficulty: easy*

---

##### Q11
> Bioluminescent beetles called fireflies may seem to create flashes of light randomly, but each species of firefly actually has its own special series of repeated flashes and pauses. These unique ______ allow fireflies of the same species to find each other.

Which choice completes the text with the most logical and precise word or phrase?

**A.** quantities 

  *The sentence describes a 'series of repeated flashes and pauses' — a sequence — not an amount. This swaps the described attribute (sequence) for a different one (quantity).*

**B.** decorations 

  *The flashes are described functionally, as a way fireflies find each other, not as ornamental — this misreads a functional signal as a decorative one.*

**C.** patterns **(Correct)**

  *Correct. A 'series of repeated flashes and pauses' is, by definition, a pattern — and that pattern is what lets fireflies of the same species recognize each other.*

**D.** agreements 

  *Fireflies cannot form 'agreements' — this personifies an instinctive biological signal as a deliberate social arrangement, which the sentence never suggests.*

*Difficulty: easy*

---

##### Q12
> Visual artist Gabriela Alemán states that the bold colors of comics, pop art, and Latinx culture have always fascinated her. This passion for the rich history and colors of her Latinx community translates into the ______ artworks she produces.

Which choice completes the text with the most logical and precise word or phrase?

**A.** vivid **(Correct)**

  *Correct. Her fascination with 'bold colors' translating into her own art logically produces artwork that is itself vivid — bright and richly colored.*

**B.** unknown 

  *A described, ongoing passion producing a recognizable artistic style is the opposite of art that is unrecognized or obscure.*

**C.** definite 

  *The sentence is about vividness of color, not certainty or clarity of meaning — this swaps in an unrelated attribute.*

**D.** reserved 

  *'Reserved' (restrained, subdued) directly contradicts a stated fascination with bold colors — the opposite quality the sentence sets up.*

*Difficulty: easy*

---

##### Q13
> In recommending Bao Phi's collection Sông I Sing, a librarian noted that pieces by the spoken-word poet don't lose their ______ nature when printed: the language has the same pleasant musical quality on the page as it does when performed by Phi.

Which choice completes the text with the most logical and precise word or phrase?

**A.** scholarly 

  *The sentence praises a musical quality in the language, not an academic one — this introduces an attribute the text never mentions.*

**B.** melodic **(Correct)**

  *Correct. The colon explains the blank directly: the poems keep 'the same pleasant musical quality' on the page, and 'melodic' names that musical quality precisely.*

**C.** jarring 

  *'Pleasant musical quality' directly contradicts 'jarring,' which describes something harsh or discordant — the opposite of what the sentence states.*

**D.** personal 

  *The sentence's evidence is about musicality of language, not about personal or intimate subject matter — a different attribute than what's described.*

*Difficulty: easy*

---

##### Q14
> The Appalachian Trail is a hiking path in the eastern United States. Much of the 2,000 mile trail passes through wilderness areas. In order to ______ those areas, the United States Congress passed the National Trails System Act in 1968, ensuring that the trail would not be sold or commercially developed.

Which choice completes the text with the most logical and precise word or phrase?

**A.** borrow 

  *Legislation ensuring land is not sold or developed is about safeguarding it permanently, not about borrowing it temporarily — the wrong category of action.*

**B.** postpone 

  *The Act is described as ensuring long-term protection against sale or development, not as merely delaying something for a later date.*

**C.** protect **(Correct)**

  *Correct. 'Ensuring that the trail would not be sold or commercially developed' is a direct restatement of the purpose of the blank — to protect the wilderness areas.*

**D.** decorate 

  *Federal legislation preventing sale or commercial development has nothing to do with ornamenting the trail — this is an unrelated action entirely.*

*Difficulty: easy*

---

##### Q15
> The following text is adapted from Sui Sin Far's 1912 short story "Mrs. Spring Fragrance." Mr. and Mrs. Spring Fragrance immigrated to the United States from China. Mrs. Spring Fragrance was unaware that Mr. Spring Fragrance, tired with the day's business, had thrown himself down on the bamboo settee on the veranda, and that although his eyes were engaged in scanning the pages of the Chinese World, his ears could not help receiving the words which were borne to him through the open window.

As used in the text, what does the word "receiving" most nearly mean?

**A.** Denying 

  *'Could not help' signals an involuntary action his ears performed despite his eyes being elsewhere — the opposite of refusing or denying the words.*

**B.** Entering 

  *This confuses what his ears did (take in the words) with the words themselves moving into the space — a mismatch between the subject performing the action and the action described.*

**C.** Carrying 

  *The sentence already says the words 'were borne to him' — that is the carrying. 'Receiving' describes what his ears did with those words once they arrived, a separate action from the transport itself.*

**D.** Hearing **(Correct)**

  *Correct. His eyes were on the newspaper, but his ears 'could not help' taking in the words carried through the window — that is, hearing them involuntarily.*

*Difficulty: medium*

---

##### Q16
> In 1877, 85% of California's railways were already controlled by the Southern Pacific Railroad. The company further solidified its ______ in rail access to the state's Pacific coast when it completed the Sunset Route in 1883: running from Louisiana to Southern California, the route established the first transcontinental rail line across the southern United States.

Which choice completes the text with the most logical and precise word or phrase?

**A.** dominance **(Correct)**

  *Correct. Controlling 85% of railways and then 'further solidifying' that position with a new transcontinental route is direct evidence of dominance in rail access.*

**B.** creativity 

  *The sentence describes market control being reinforced, not any innovative or inventive quality — an attribute the text never raises.*

**C.** insignificance 

  *Directly contradicts controlling 85% of railways and 'further solidifying' that position — the opposite of insignificant.*

**D.** neutrality 

  *A company consolidating market control through a major new route is the opposite of remaining neutral or uninvolved.*

*Difficulty: easy*

---

##### Q17
> Cucurbits, a group of plants that includes squash and melons, relied on mastodons to spread their seeds in the Ice Age. When these animals died out, cucurbits faced extinction in turn, having lost their means of seed dispersal. Around this time, however, the ancestors of Indigenous peoples in North America began raising cucurbits as crops, thus ______ the plants' survival.

Which choice completes the text with the most logical and precise word or phrase?

**A.** verifying 

  *'Verifying' means confirming something is already true, but growing crops is an action that causes an outcome (survival), not one that confirms a prior fact.*

**B.** multiplying 

  *'Multiplying survival' does not logically follow — survival is not a quantity that gets multiplied; this misapplies a verb of increase to an abstract state.*

**C.** comforting 

  *Plants cannot be emotionally comforted — this personifies the cucurbits in a way the factual, biological register of the sentence does not support.*

**D.** ensuring **(Correct)**

  *Correct. Humans raising cucurbits as crops replaced the lost mastodon-based seed dispersal — the direct cause that kept the plants from going extinct, which is exactly what 'ensuring' their survival names.*

*Difficulty: medium*

---

##### Q18
> According to statistician Nassim Nicholas Taleb, the best way to predict the amount of time a nonperishable entity (such as a building or a technology) will continue to exist is to examine how long it has survived so far. In this view, an item's age is the strongest ______ how much longer it will last.

Which choice completes the text with the most logical and precise word or phrase?

**A.** uncertainty about 

  *The sentence describes 'the best way to predict' — a confident, predictive relationship — which directly contradicts framing age as a source of uncertainty.*

**B.** indicator of **(Correct)**

  *Correct. If examining an item's age is 'the best way to predict' its remaining lifespan, then age functions as the strongest indicator — the clue used to make that prediction.*

**C.** motivation for 

  *This confuses age as a predictive clue with age as a cause that drives or motivates continued existence — a different, causal relationship than the epistemic one the sentence describes.*

**D.** criticism of 

  *Nothing in the sentence evaluates age negatively — it simply describes a predictive relationship, not a judgment.*

*Difficulty: medium*

---

##### Q19
> In the mid-nineteenth century, some abolitionist newspapers ______ westward migration in the United States; by printing a letter that described the easy fortunes and high salaries miners could make in California during the Gold Rush, Frederick Douglass's newspaper North Star was one such publication that inspired readers to relocate.

Which choice completes the text with the most logical and precise word or phrase?

**A.** stimulated **(Correct)**

  *Correct. The example shows North Star printing a letter that 'inspired readers to relocate' — direct evidence that the newspapers actively stimulated migration.*

**B.** assigned 

  *Newspapers cannot 'assign' migration to their readers — this is the wrong category of verb for describing persuasive influence through print.*

**C.** opposed 

  *The example describes a newspaper actively encouraging relocation through an inspiring letter, the opposite of opposing migration.*

**D.** disregarded 

  *Printing content specifically designed to inspire readers to relocate is active engagement with the topic, not disregard of it.*

*Difficulty: easy*

---

##### Q20
> The following text is from Claude McKay's 1922 poem "Morning Joy." The speaker is looking out a window and observing a wold, or large area of land. At night the wide and level stretch of wold, Which at high noon had basked in quiet gold, Far as the eye could see was ghostly white; Dark was the night save for the snow's weird light. I drew the shades far down, crept into bed; Hearing the cold wind moaning overhead Through the sad pines, my soul, catching its pain, Went sorrowing with it across the plain.

As used in the text, what does the word "drew" most nearly mean?

**A.** Pulled **(Correct)**

  *Correct. 'Drew the shades far down' describes a physical action on window shades — pulling them down — right before the speaker crept into bed.*

**B.** Drained 

  *This is 'drew' in the sense of drawing out or exhausting something, which does not fit a physical object like window shades being lowered.*

**C.** Inspired 

  *This is 'drew' as in 'drew inspiration,' an abstract sense that has nothing to do with physically operating window shades.*

**D.** Sketched 

  *This is 'drew' as in drawing a picture, a completely different sense from lowering physical shades before bed.*

*Difficulty: medium*

---

##### Q21
> Osage Nation citizen Randy Tinker-Smith produced and directed the ballet Wahzhazhe, which vividly chronicles Osage history and culture. Telling Osage stories through ballet is ______ choice because two of the foremost ballet dancers of the twentieth century were Osage: sisters Maria and Marjorie Tallchief.

Which choice completes the text with the most logical and precise word or phrase?

**A.** a suitable **(Correct)**

  *Correct. The sentence gives a specific reason — two of the century's foremost ballet dancers were Osage — that directly explains why ballet is a fitting medium for telling Osage stories.*

**B.** a determined 

  *'Determined' describes the resolve of the person making a choice, not whether the choice itself fits the subject matter — the wrong attribute for what the sentence explains.*

**C.** an arbitrary 

  *The sentence gives a specific, substantive reason (renowned Osage ballet dancers) for the choice — the opposite of arbitrary, which means made without reason.*

**D.** an unpredictable 

  *Nothing in the sentence is about surprise or unpredictability — it's about appropriateness given a documented history, an unrelated attribute.*

*Difficulty: medium*

---

##### Q22
> The printing of Virginia Woolf's novels featured a creative ______ between Woolf and her sister Vanessa Bell: a talented painter, Bell worked closely with Woolf to create original cover art for most of the novels.

Which choice completes the text with the most logical and precise word or phrase?

**A.** rebellion 

  *Nothing in the sentence suggests resistance or defiance — the description is of two people working closely together, not rebelling against anything.*

**B.** partnership **(Correct)**

  *Correct. 'Worked closely with Woolf to create original cover art' describes two people collaborating toward a shared creative goal — a partnership.*

**C.** discovery 

  *The sentence describes sustained collaborative work, not a single act of finding or uncovering something.*

**D.** disagreement 

  *'Worked closely' indicates cooperation, the opposite of disagreement or conflict.*

*Difficulty: easy*

---

##### Q23
> Sumerian civilization (which lasted from around 3300 to 2000 BCE) ______ many concepts that persist into present-day civilizations: for example, the first description of the seven-day week appears in the Sumerian Epic of Gilgamesh.

Which choice completes the text with the most logical and precise word or phrase?

**A.** transformed 

  *'Transformed' implies changing something that already existed, but 'first description' indicates the concept originated with the Sumerians rather than being altered from a prior version.*

**B.** introduced **(Correct)**

  *Correct. 'The first description ... appears in the Sumerian Epic of Gilgamesh' is direct evidence that the Sumerians originated — introduced — this concept.*

**C.** inherited 

  *This reverses the direction of origination: 'the first description' means Sumerians created the concept, not that they received it from an earlier source.*

**D.** overlooked 

  *The sentence describes an idea that originated with and persisted from Sumerian civilization — active origination, not neglect.*

*Difficulty: medium*

---

##### Q24
> Physicist Joseph Weber performed ______ work in gravitational wave research in the 1960s and 1970s, conducting key experiments that scientists later used as the basis for their own investigations that led to the first verified detection of a gravitational wave in 2015.

Which choice completes the text with the most logical and precise word or phrase?

**A.** foundational **(Correct)**

  *Correct. 'Later used as the basis for their own investigations' is a direct description of work that later research was built on — exactly what 'foundational' means.*

**B.** supplementary 

  *'Supplementary' implies an add-on to existing work, but 'the basis for' indicates Weber's research came first and others built on it — a primary, not secondary, role.*

**C.** repetitive 

  *Nothing suggests Weber repeated earlier work — the sentence describes his experiments as the origin others later built upon, not a repetition of anything prior.*

**D.** ineffective 

  *Work later used as the basis for a successful 2015 detection was clearly effective, the opposite of ineffective.*

*Difficulty: medium*

---

##### Q25
> As an architect in Los Angeles in the 1950s, Helen Liu Fong became known for avoiding ______ designs in her buildings. Instead of using standard shapes and colors, she typically explored innovative forms and daring hues.

Which choice completes the text with the most logical and precise word or phrase?

**A.** creative 

  *The sentence describes Fong herself as innovative ('innovative forms and daring hues'); a designer known for avoiding creative designs would contradict the very quality attributed to her.*

**B.** bold 

  *'Daring hues' describes what she did use, not what she avoided — this mistakes the described outcome for the avoided quality, reversing the sentence's own contrast.*

**C.** traditional **(Correct)**

  *Correct. 'Instead of using standard shapes and colors' contrasts directly with the blank — 'standard' is what she avoided, and 'traditional' names that quality precisely.*

**D.** understandable 

  *Nothing in the sentence is about clarity or comprehensibility — this introduces an attribute the text never addresses.*

*Difficulty: medium*

---

##### Q26
> Sueño de Familia is an exhibition of drawings, paintings, and ceramics that explores the artistic heritage of US-based artist Yolanda González. The exhibition ______ five generations, featuring works by González's great-grandfather, grandmother, mother, and niece as well as González herself.

Which choice completes the text with the most logical and precise word or phrase?

**A.** borrows 

  *An exhibition does not 'borrow' generations — this is the wrong category of verb for describing what a collection of artworks covers.*

**B.** spans **(Correct)**

  *Correct. Featuring works from great-grandfather to niece — five named generations — is exactly what 'spans' describes: covering that full range.*

**C.** judges 

  *The sentence describes what generations are included, not an evaluative judgment being made about them.*

**D.** neglects 

  *The exhibition actively features all five generations named — the opposite of neglecting them.*

*Difficulty: easy*

---

##### Q27
> US traffic signals didn't always contain the familiar three lights (red, yellow, and green). Traffic lights only ______ red and green lights until the three-light traffic signal was developed in the 1920s.

Which choice completes the text with the most logical and precise word or phrase?

**A.** avoided 

  *The lights did contain red and green — the sentence says they lacked a third color (yellow), not that they avoided the two they had.*

**B.** featured **(Correct)**

  *Correct. Before the three-light signal, traffic lights had only red and green — 'featured' names exactly which two colors made up the earlier signal.*

**C.** appreciated 

  *This is about emotional appreciation, not the literal composition of the signal — the wrong register for a factual description of what colors a light contained.*

**D.** disregarded 

  *The sentence states the lights did contain red and green ('only [these]'), not that they were ignored — this contradicts the given fact.*

*Difficulty: easy*

---

##### Q28
> Scientists previously thought that all electric eels belong to a single species, but a team of researchers led by zoologist C. David de Santana proved this idea wrong by ______ that there are in fact three distinct species of electric eels.

Which choice completes the text with the most logical and precise word or phrase?

**A.** pretending 

  *'Proved this idea wrong' means the researchers established a fact, the opposite of pretending, which implies falseness.*

**B.** complaining 

  *Voicing a complaint is not the same as proving a scientific claim wrong through evidence — an unrelated action.*

**C.** requiring 

  *'Proved this idea wrong by requiring that there are three species' does not logically make sense — requiring is not an action that establishes a fact.*

**D.** demonstrating **(Correct)**

  *Correct. 'Proved this idea wrong by ______ that there are in fact three distinct species' calls for a verb of showing evidence — demonstrating is exactly that.*

*Difficulty: easy*

---

##### Q29
> Studying how workload affects productivity, Maryam Kouchaki and colleagues found that people who chose to do relatively easy tasks first were less ______ compared to those who did hard tasks first. Finishing easy tasks gave participants a sense of accomplishment, but those who tackled hard tasks first actually became more skilled and productive workers over time.

Which choice completes the text with the most logical and precise word or phrase?

**A.** secretive 

  *Nothing in the sentence involves keeping information hidden — this introduces an attribute unrelated to the productivity comparison being described.*

**B.** efficient **(Correct)**

  *Correct. Workers who tackled hard tasks first 'became more skilled and productive,' meaning the easy-first group, by contrast, was less efficient.*

**C.** outgoing 

  *The comparison is about productivity and skill, not sociability — an attribute the sentence never addresses.*

**D.** unsympathetic 

  *Nothing in the sentence is about empathy or attitude toward others — it is strictly about productivity and skill development.*

*Difficulty: medium*

---

##### Q30
> Arturo A. Schomburg was dedicated to preserving books, art, and other materials from peoples of African descent around the world. To get these items, Schomburg ______ friends and colleagues, whom he asked to bring back rare and valuable objects from their international travels. Now, Schomburg's collection is a valuable resource for scholars of Black history and culture.

Which choice completes the text with the most logical and precise word or phrase?

**A.** admired 

  *Admiration is a feeling, not the functional relationship of relying on people to acquire objects for him — the sentence describes an action, not an emotion.*

**B.** disagreed with 

  *Asking friends to bring back objects for him is collaboration, not conflict — the opposite of disagreement.*

**C.** warned 

  *Nothing in the sentence involves cautioning anyone about danger — an unrelated action to asking people to collect objects.*

**D.** depended on **(Correct)**

  *Correct. 'Whom he asked to bring back rare and valuable objects' describes Schomburg relying on friends and colleagues to acquire items for his collection.*

*Difficulty: medium*

---

##### Q31
> The following text is adapted from Mohsin Hamid's 2017 novel Exit West. Saeed lives with his mother and father. On cloudless nights after a daytime rain, Saeed's father would sometimes bring out the telescope, and the family would sip green tea on their balcony, enjoying a breeze, and take turns to look up at objects whose light, often, had been emitted before any of these three viewers had been born—light from other centuries, only now reaching Earth.

As used in the text, what does the word "reaching" most nearly mean?

**A.** Arriving at **(Correct)**

  *Correct. Light 'emitted before any of these three viewers had been born' and 'only now reaching Earth' describes centuries-old starlight finally arriving at Earth.*

**B.** Consulting with 

  *This is 'reaching out' in the sense of contacting someone for advice, a completely different sense that makes no sense applied to light traveling to a planet.*

**C.** Running to 

  *This treats 'reaching' as a physical action of running toward something, but light does not run — the wrong sense for describing light's arrival.*

**D.** Clinging to 

  *Nothing in the sentence describes light holding onto or attaching to Earth — an unrelated sense of the word.*

*Difficulty: medium*

---

##### Q32
> Some people have speculated that two helmets with attached horns discovered in Denmark in 1942 belonged to Vikings, but scholars have long been skeptical. Archaeologist Helle Vandkilde and colleagues recently provided radiocarbon dates for the helmets, and their findings ______ scholars' skepticism: the helmets date to the Nordic Bronze Age, centuries before the Vikings existed.

Which choice completes the text with the most logical and precise word or phrase?

**A.** anticipate 

  *The skepticism already existed before the radiocarbon dating; 'anticipate' would mean predicting something not yet known, but the findings confirm a stance that predates them, not foresee it.*

**B.** inspect 

  *Findings are the output of an inspection, not something that itself 'inspects' an abstract attitude like skepticism — a category mismatch.*

**C.** reveal 

  *The findings reveal the helmets' true age, not the pre-existing skepticism itself, which scholars already held — this misidentifies what the new evidence actually discloses.*

**D.** justify **(Correct)**

  *Correct. The dates show the helmets predate the Vikings, confirming that scholars were right to be skeptical of the Viking attribution — the findings justify that pre-existing skepticism.*

*Difficulty: hard*

---

##### Q33
> The following text is from Booth Tarkington's 1921 novel Alice Adams. Mrs. Adams had always been fond of vases, she said, and every year her husband's Christmas present to her was a vase of one sort or another—whatever the clerk showed him, marked at about twelve or fourteen dollars.

As used in the text, what does the word "marked" most nearly mean?

**A.** Staged 

  *This is unrelated to indicating a dollar value — 'staged' describes arranging something for presentation, not pricing it.*

**B.** Priced **(Correct)**

  *Correct. 'Marked at about twelve or fourteen dollars' describes a vase's price tag — 'priced' names exactly that.*

**C.** Stained 

  *This is 'marked' as in blemished or discolored, an entirely different sense that doesn't fit a dollar figure following the word.*

**D.** Watched 

  *This is 'marked' as in closely observed, which does not fit being followed immediately by a dollar amount describing the vase.*

*Difficulty: medium*

---

##### Q34
> As a young photographer in the 1950s, William Klein ______ the conventions of photography by creating images that were high contrast and included blurred and distorted elements—features generally seen as flaws. So unorthodox was Klein's work that he had difficulty finding a publisher for his now-iconic 1956 photo book Life is Good & Good for You in New York.

Which choice completes the text with the most logical and precise word or phrase?

**A.** reviewed 

  *Evaluating conventions is a different action from violating them — the sentence describes flaw-embracing images and difficulty finding a publisher, evidence of breaking norms, not assessing them.*

**B.** defied **(Correct)**

  *Correct. Creating images with 'features generally seen as flaws' and being called 'unorthodox' is direct evidence that Klein violated — defied — established photographic conventions.*

**C.** respected 

  *'Unorthodox' and difficulty finding a publisher both indicate Klein broke with convention — the opposite of respecting it.*

**D.** prevented 

  *Klein did not stop conventions from existing for others — he personally worked outside them, a different claim than preventing them.*

*Difficulty: medium*

---

##### Q35
> Ronyoung Kim creatively captures the Korean American immigrant experience in her novel Clay Walls by writing about a family from three ______ perspectives. The first section of the novel is from the mother Haesu's perspective, the second is from the father Chun's perspective, and the last is from the daughter Faye's perspective.

Which choice completes the text with the most logical and precise word or phrase?

**A.** distinct **(Correct)**

  *Correct. Three different named characters — mother, father, daughter — each given their own section is direct evidence of three distinct perspectives.*

**B.** required 

  *Nothing indicates any perspective was mandated or necessary — the sentence simply describes the novel's structure, not an obligation.*

**C.** unintended 

  *'Creatively captures' describes a deliberate authorial choice, the opposite of an unintended or accidental structure.*

**D.** unknown 

  *The sentence explicitly names and describes each of the three perspectives, so they are known, not unknown.*

*Difficulty: easy*

---

##### Q36
> Latro, the main character of Gene Wolfe's novel Soldier of the Mist, is a man in ancient Greece. He completely loses his memory whenever he sleeps. So, before sleeping, Latro records the important experiences of each day on a scroll, carefully choosing which ones to ______.

Which choice completes the text with the most logical and precise word or phrase?

**A.** suspect 

  *Latro is recording his own real experiences for later reference, not treating them with suspicion — an emotional reaction the sentence never describes.*

**B.** preserve **(Correct)**

  *Correct. Since Latro loses his memory whenever he sleeps, recording experiences on a scroll beforehand is precisely an act of preserving them against that loss.*

**C.** suggest 

  *'Suggest' implies proposing an idea to someone else, but Latro is writing for his own future benefit, not communicating a proposal.*

**D.** imagine 

  *The scroll records his actual daily experiences, not invented or imagined ones — the sentence describes memory, not fiction.*

*Difficulty: easy*

---

##### Q37
> The following text is from Mark Oshiro's 2018 novel Anger Is a Gift. In the novel, Moss and his friends are on a subway train in Northern California. Lights from the outside world then filled the train car as it rose out of the ground and climbed the elevated track. As long as Moss had lived in West Oakland, he'd never tired of this specific view, so he pointed toward the windows. "Check it," he said, and the Port of Oakland began to pass by them.

As used in the text, what does the word "specific" most nearly mean?

**A.** Imaginary 

  *The view is real — the Port of Oakland is described as actually passing by — which contradicts describing it as imaginary.*

**B.** Energetic 

  *The sentence describes which view Moss never tired of, not how lively or energetic it was — an unrelated attribute.*

**C.** Correct 

  *This is 'specific' in the sense of being precise or accurate, which does not fit 'this ______ view' referring to one particular, singled-out view among others.*

**D.** Particular **(Correct)**

  *Correct. 'This specific view' singles out one view — the one from the elevated track toward the Port of Oakland — that Moss has grown attached to, exactly what 'particular' names.*

*Difficulty: medium*

---

##### Q38
> It would be a mistake to ______ the exhibit that artist and curator Joe Baker, who is a member of the Lenape (Delaware) people, has organized at the Brooklyn Public Library. The exhibit, which includes Lenape beadwork from the 1850s as well as modern works that use traditional patterns, is essential viewing.

Which choice completes the text with the most logical and precise word or phrase?

**A.** complicate 

  *A visitor cannot 'complicate' an already-organized exhibit — this describes an action that doesn't logically apply to viewing it.*

**B.** amplify 

  *Nothing about visiting or discussing the exhibit involves making it louder or more prominent — this doesn't fit the framing of 'a mistake to ______' something described as essential.*

**C.** overlook **(Correct)**

  *Correct. Calling the exhibit 'essential viewing' directly supports that missing — overlooking — it would be a mistake.*

**D.** assemble 

  *Baker has already organized the exhibit; assembling it isn't an action a visitor mistakenly avoids — this misattributes the curator's role to the reader.*

*Difficulty: medium*

---

##### Q39
> The following text is from Darcie Little Badger's 2021 novel A Snake Falls to Earth. Nina is looking at old family photographs. Nina couldn't stop looking at the sepia-toned photograph in an oak frame. Propped on the window ledge, it featured a portrait of Great-Great-Grandmother Rosita as a young woman.

As used in the text, what does the word "featured" most nearly mean?

**A.** Displayed **(Correct)**

  *Correct. The photograph 'featured a portrait' — that is, it displayed or showed an image of Rosita as a young woman.*

**B.** Questioned 

  *A photograph cannot 'question' a portrait — this is not an action a still image can perform.*

**C.** Approved 

  *Nothing in the sentence involves the photograph endorsing or sanctioning the portrait — an unrelated action.*

**D.** Ignored 

  *Nina 'couldn't stop looking' at the photograph, which implies it prominently showed the portrait — the opposite of ignoring it.*

*Difficulty: easy*

---

##### Q40
> Researcher Lucy Salazar is using radiocarbon dating to study Machu Picchu, an ancient Incan fortress in the Andes Mountains. She and her colleagues have found that the site's age differs from the ______ estimate: it is approximately 20 years older than scholars thought when first encountering Machu Picchu in 1911.

Which choice completes the text with the most logical and precise word or phrase?

**A.** genuine 

  *The point is not that the earlier estimate was fake versus authentic, but that it was made earlier and has now been revised — 'genuine' answers a different question than the sentence raises.*

**B.** intentional 

  *Nothing in the sentence describes estimates as deliberate versus accidental — an unrelated attribute to the age discrepancy being discussed.*

**C.** independent 

  *The sentence is not comparing the new dating to an independent versus dependent estimate — this introduces a distinction the text never makes.*

**D.** original **(Correct)**

  *Correct. 'When first encountering Machu Picchu in 1911' identifies the estimate being revised as the original, earlier one scholars first made.*

*Difficulty: medium*

---

##### Q41
> The following text is adapted from Lewis Carroll's 1871 novel Through the Looking-Glass, and What Alice Found There. Alice, a child, is talking to her cat. "Do you hear the snow against the window-panes, Kitty? How nice and soft it sounds! Just as if someone was kissing the window all over outside."

As used in the text, what does the word "soft" most nearly mean?

**A.** Gentle **(Correct)**

  *Correct. Describing the sound of snow against the window as 'nice and soft,' compared to a gentle kissing sound, calls for the sense of gentle or mild.*

**B.** Sensitive 

  *This is 'soft' as in emotionally sensitive, which does not fit describing the quality of a sound.*

**C.** Shapeless 

  *This is 'soft' as in pliable or lacking firm form, a physical-texture sense that doesn't apply to describing a sound.*

**D.** Bland 

  *This is 'soft' as in mild-flavored, a taste-related sense that doesn't fit describing a pleasant sound Alice is enjoying.*

*Difficulty: medium*

---

##### Q42
> The following text is adapted from Charles Chesnutt's 1899 story "The Wife of His Youth." Mr. Ryder is hosting a formal gathering where he will propose marriage to the woman he has been courting. [A] younger and less cautious man would long since have spoken. But he had made up his mind, and had only to determine the time when he would ask her to be his wife. He decided to give a ball in her honor, and at some time during the evening of the ball to offer her his heart and hand.

As used in the text, what does the word "determine" most nearly mean?

**A.** Choose **(Correct)**

  *Correct. 'Had only to determine the time' describes Mr. Ryder deciding on a specific moment to propose — exactly what 'choose' captures.*

**B.** Influence 

  *He is deciding a personal timing for himself, not affecting or influencing an outside factor — the wrong relationship between subject and action.*

**C.** Demonstrate 

  *Demonstrating means showing something to others, which does not fit privately deciding on a time to propose.*

**D.** Measure 

  *This is 'determine' as in calculating a quantity, which doesn't fit selecting a moment in time to act.*

*Difficulty: medium*

---

##### Q43
> When marine biologist Brittany Williams played different ocean recordings to groups of oyster larvae, groups that heard sounds of a healthy oyster reef were the most ______. They were twice as likely as other groups to show signs of making a permanent home. This suggests that playing recordings of a healthy ocean reef may encourage oysters to create such a reef.

Which choice completes the text with the most logical and precise word or phrase?

**A.** responsive **(Correct)**

  *Correct. Being 'twice as likely as other groups ... to show signs of making a permanent home' after hearing the healthy-reef recording is a direct behavioral response — exactly what 'responsive' names.*

**B.** inactive 

  *Showing behavioral signs of settling is an active response, the opposite of inactivity.*

**C.** liked 

  *'Groups ... were the most liked' does not logically match measuring larvae's own behavior — this confuses being favored by an outside party with the larvae's own responsiveness.*

**D.** distressed 

  *Settling and making a permanent home is a positive, encouraged behavior in the study, not a sign of distress.*

*Difficulty: medium*

---

##### Q44
> Manul cats are small, shy felines. They live mostly alone in out-of-the-way parts of Asia, such as on Mount Everest. These cats have been difficult to research because their habitats are so ______ large populations of humans.

Which choice completes the text with the most logical and precise word or phrase?

**A.** full of 

  *Remote, 'out-of-the-way' habitats like Mount Everest would have few humans, not be full of them — this contradicts the described remoteness.*

**B.** drawn to 

  *Shy cats living alone in remote areas would not have habitats described as attracted to large human populations — this contradicts the remoteness the sentence establishes.*

**C.** responsible for 

  *A habitat cannot be causally 'responsible for' a human population — this is the wrong category of relationship between a place and the people near it.*

**D.** distant from **(Correct)**

  *Correct. 'Out-of-the-way' locations and difficulty researching the cats both point to habitats that are distant from large human populations.*

*Difficulty: medium*

---

##### Q45
> Archaeologist Erika Karuzas works with the Confederated Salish and Kootenai Tribes of Montana to preserve culturally significant sites. In 2015 they decided that creating a new national trail connecting many of these sites would ______ their preservation efforts, because the US government provides some protections to national trails that aren't given to other areas.

Which choice completes the text with the most logical and precise word or phrase?

**A.** inspire 

  *The reason given is a concrete legal benefit (government protections), not mere motivational effect on the preservation efforts themselves — a subtle mismatch with the sentence's actual explanation.*

**B.** ignore 

  *The sentence describes an action expected to actively help preservation efforts through legal protections, the opposite of ignoring them.*

**C.** promote **(Correct)**

  *Correct. Government protections given to national trails 'that aren't given to other areas' directly explains how designating a trail would help — promote — the tribes' preservation efforts.*

**D.** reduce 

  *Gaining additional legal protections would strengthen, not reduce, the effectiveness of preservation efforts.*

*Difficulty: medium*

---

##### Q46
> The following text is adapted from José Martí's 1891 poem "At the Salon" (translated by Cecil Charles in 1898). The speaker describes a painting featuring a female figure. From the sterile soil no ray Of hope in a blade of green, Nor sheltering roof is seen— Though the skies are heavy and gray. Ah, this is the woman fair Who stole away my heart In the splendid halls of art Yester-e'en as I wandered there!

As used in the text, what does the word "sheltering" most nearly mean?

**A.** Protective **(Correct)**

  *Correct. A 'sheltering roof' is one that provides cover or protection from the heavy, gray skies described in the same lines.*

**B.** Restrictive 

  *Shelter is about providing cover and protection, not about limiting freedom — a different, negative connotation than what the poem's bleak, unprotected imagery calls for.*

**C.** Affectionate 

  *A roof cannot display affection — this introduces an emotional quality that doesn't apply to a physical structure.*

**D.** Suspicious 

  *This attributes a wary, distrustful quality to a roof, which is an unrelated attribute to whether it provides physical cover.*

*Difficulty: medium*

---

##### Q47
> Following the principles of community-based participatory research, tribal nations and research institutions are equal partners in health studies conducted on reservations. A collaboration between the Crow Tribe and Montana State University ______ this model: tribal citizens worked alongside scientists to design the methodology and continue to assist in data collection.

Which choice completes the text with the most logical and precise word or phrase?

**A.** circumvents 

  *Circumventing means getting around something, but the described collaboration directly follows — rather than avoids — the equal-partnership model.*

**B.** eclipses 

  *Eclipsing means overshadowing or surpassing, but the collaboration is being offered as a case that matches the model, not one that outdoes it.*

**C.** fabricates 

  *Fabricating means inventing falsely, but this is a real, described example that genuinely follows the model — the opposite of a fabrication.*

**D.** exemplifies **(Correct)**

  *Correct. Tribal citizens 'worked alongside scientists to design the methodology' is a concrete instance of the equal-partnership model just described — the collaboration exemplifies it.*

*Difficulty: medium*

---

##### Q48
> Artificially delivering biomolecules to plant cells is an important component of protecting plants from pathogens, but it is difficult to transmit biomolecules through the layers of the plant cell wall. Markita del Carpio Landry and her colleagues have shown that it may be possible to ______ this problem by transmitting molecules through carbon nanotubes, which can cross cell walls.

Which choice completes the text with the most logical and precise word or phrase?

**A.** conceptualize 

  *The researchers have shown an actual physical solution (nanotubes crossing cell walls), not merely formed an idea about the problem — 'conceptualize' understates a demonstrated technical result.*

**B.** neglect 

  *Showing a way to transmit molecules through cell walls is directly addressing the problem, the opposite of neglecting it.*

**C.** illustrate 

  *The researchers are solving the transmission difficulty, not merely depicting or explaining it — illustrate is too weak an action for what nanotubes crossing cell walls accomplishes.*

**D.** overcome **(Correct)**

  *Correct. Carbon nanotubes 'can cross cell walls,' directly solving the stated transmission difficulty — that is, overcoming the problem.*

*Difficulty: medium*

---

##### Q49
> Research conducted by planetary scientist Katarina Miljkovic suggests that the Moon's surface may not accurately ______ early impact events. When the Moon was still forming, its surface was softer, and asteroid or meteoroid impacts would have left less of an impression; thus, evidence of early impacts may no longer be present.

Which choice completes the text with the most logical and precise word or phrase?

**A.** reflect **(Correct)**

  *Correct. 'Evidence of early impacts may no longer be present' describes the surface failing to show — reflect — an accurate record of those early events.*

**B.** receive 

  *This describes the initial moment of impact (a softer surface receiving impacts differently), but the sentence is about whether the surface still shows that history now, a later-stage claim distinct from the impact event itself.*

**C.** evaluate 

  *A surface cannot 'evaluate' events — evaluation requires a thinking agent, which is a category error for a physical surface.*

**D.** mimic 

  *'Mimic' implies artificial imitation, but the sentence is about whether the surface accurately preserves a genuine historical record, not whether it copies something.*

*Difficulty: hard*

---

##### Q50
> Anthropologist Kristian J. Carlson and colleagues examined the fossilized clavicle and shoulder bones of a 3.6-million-year-old early hominin known as "Little Foot." They found that these bones were ______ the clavicle and shoulder bones of modern apes that are frequent climbers, such as gorillas and chimpanzees, suggesting that Little Foot had adapted to life in the trees.

Which choice completes the text with the most logical and precise word or phrase?

**A.** surpassed by 

  *This implies a ranked comparison where one is exceeded by the other, but the conclusion drawn (adaptation to tree life) rests on similarity between the bones, not one being outdone by the other.*

**B.** comparable to **(Correct)**

  *Correct. Similarity to the bones of frequent-climbing apes is what supports the conclusion that Little Foot 'had adapted to life in the trees' — the bones were comparable to those of tree-dwelling apes.*

**C.** independent of 

  *The conclusion about tree adaptation depends on a resemblance between the bone structures, the opposite of the bones being independent of each other.*

**D.** obtained from 

  *Little Foot's bones were not literally sourced from modern apes — this is a category error confusing a comparison with an origin.*

*Difficulty: medium*

---

##### Q51
> The Cambrian explosion gets its name from the sudden appearance and rapid diversification of animal remains in the fossil record about 541 million years ago, during the Cambrian period. Some scientists argue that this ______ change in the fossil record might be because of a shift in many organisms to body types that were more likely to be preserved.

Which choice completes the text with the most logical and precise word or phrase?

**A.** catastrophic 

  *This overreaches: the sentence describes a rapid change in the fossil record itself, not necessarily a disaster for the organisms involved — 'catastrophic' conflates suddenness with calamity the text never claims.*

**B.** elusive 

  *'Elusive' means hard to detect, but the change is described as a clear 'sudden appearance' in the fossil record — the opposite of something hard to find.*

**C.** abrupt **(Correct)**

  *Correct. 'Sudden appearance and rapid diversification' directly describes a change that happened quickly — precisely what 'abrupt' names.*

**D.** imminent 

  *'Imminent' means about to happen in the future, but the event described occurred 541 million years ago — a timing mismatch with the past-tense description.*

*Difficulty: hard*

---

##### Q52
> Particle physicists like Ayana Holloway Arce and Aida El-Khadra spend much of their time ______ what is invisible to the naked eye: using sophisticated technology, they closely examine the behavior of subatomic particles, the smallest detectable parts of matter.

Which choice completes the text with the most logical and precise word or phrase?

**A.** selecting 

  *The sentence describes examining and studying particle behavior, not choosing among a set of options — a different action.*

**B.** inspecting **(Correct)**

  *Correct. 'Closely examine the behavior of subatomic particles' is a direct restatement of what the blank describes — physicists inspecting what's invisible to the naked eye.*

**C.** creating 

  *The sentence describes physicists observing existing subatomic particles' behavior, not manufacturing new particles — a different action than what's described.*

**D.** deciding 

  *'Deciding' is a judgment or choice verb, which doesn't match closely examining and observing behavior over time.*

*Difficulty: easy*

---

##### Q53
> British painter Peter Edwards has a ______ painting portraits of notable figures from a variety of different fields. These characteristic works include his esteemed portraits of poet Wendy Cope and soccer player and coach Ryan Griggs.

Which choice completes the text with the most logical and precise word or phrase?

**A.** complaint about 

  *'Esteemed' and 'characteristic works' both convey a positive, established body of work — the opposite of a complaint, which is negative.*

**B.** reputation for **(Correct)**

  *Correct. 'Esteemed' portraits described as 'characteristic works' across a variety of notable figures is exactly what having a reputation for painting such portraits means.*

**C.** question about 

  *Nothing in the sentence expresses doubt or uncertainty — it describes an established, esteemed body of work, not an open question.*

**D.** requirement for 

  *Painting portraits is not described as an obligation imposed on Edwards — this is the wrong category of relationship between the painter and his characteristic work.*

*Difficulty: easy*

---

##### Q54
> The National Heritage Fellowship was created to publicly ______ exceptional folk and traditional artists in the United States. In 2015, the fellowship was given to the circus aerialist (mid-air acrobat) Dolly Jacobs to celebrate her lifetime contributions to the arts.

Which choice completes the text with the most logical and precise word or phrase?

**A.** startle 

  *Startling someone is unrelated to honoring their artistic achievements — an unrelated action to what a fellowship does.*

**B.** recognize **(Correct)**

  *Correct. 'To celebrate her lifetime contributions' directly restates the purpose of the blank — the fellowship exists to publicly recognize exceptional artists.*

**C.** familiarize 

  *'Familiarize' typically needs an object being introduced to something new, which doesn't match honoring already-established artists for lifetime achievement.*

**D.** convey 

  *'Convey' means to communicate or transmit something, too vague and the wrong category to capture the specific honoring and celebratory purpose described.*

*Difficulty: medium*

---

##### Q55
> The following text is adapted from Mary Seacole's 1857 autobiography Wonderful Adventures of Mrs. Seacole in Many Lands. That journey across the Isthmus [of Panama], insignificant in distance as it was, was by no means an easy one. It seemed as if nature had determined to throw every conceivable obstacle in the way of those who should seek to join the two great oceans of the world.

As used in the text, what does the word "conceivable" most nearly means?

**A.** Obvious 

  *'Conceivable' means able to be imagined, not clear or apparent — a different sense from 'obvious,' which describes ease of perception rather than possibility.*

**B.** Imaginable **(Correct)**

  *Correct. 'Every conceivable obstacle' describes the full range of obstacles one could imagine nature throwing in the way — exactly what 'imaginable' names.*

**C.** Straightforward 

  *The passage describes a journey that was 'by no means easy,' so obstacles being 'straightforward' contradicts the difficulty the sentence establishes.*

**D.** Uninterrupted 

  *'Every conceivable obstacle' describes many kinds of interruption, not a journey free of them — the opposite of uninterrupted.*

*Difficulty: medium*

---

##### Q56
> The following text is from Jhumpa Lahiri's 2003 novel The Namesake. Gogol, a child, is at a beach in Massachusetts with his father. On the beach Gogol collects rocks, digs tunnels in the sand. He and his father wander barefoot, their pant legs rolled halfway up their calves.

As used in the text, what does the word "collects" most nearly mean?

**A.** Increases 

  *Gathering existing rocks does not increase their overall number — this confuses picking rocks up with adding to a total.*

**B.** Makes 

  *Gogol is picking up rocks that already exist on the beach, not creating new ones — a different action than what 'makes' implies.*

**C.** Ignores 

  *Collecting implies actively gathering the rocks, the opposite of ignoring them.*

**D.** Gathers **(Correct)**

  *Correct. 'Collects rocks' on the beach describes Gogol picking up and gathering rocks as he plays.*

*Difficulty: easy*

---

##### Q57
> The following text is adapted from John Matheus's 1925 short story "Fog." The fog extended its tentacles over city and river, gradually obliterating traces of familiar landscapes. At five-thirty the old Panhandle bridge, supported by massive sandstone pillars, stalwart, as when erected fifty years before to serve a generation now passed behind the portals of life, had become a spectral outline against the sky.

As used in the text, what does the word "supported" most nearly mean?

**A.** Held up **(Correct)**

  *Correct. A bridge 'supported by massive sandstone pillars' describes the physical structure holding the bridge up.*

**B.** Encouraged 

  *This is 'support' in the emotional sense of encouragement, which doesn't fit a physical bridge structure held by pillars.*

**C.** Improved on 

  *Nothing in the sentence describes the pillars enhancing or upgrading the bridge — an unrelated sense of the word to physical support.*

**D.** Defended 

  *This is 'support' as in defending an argument or position, which doesn't fit physical pillars holding up a bridge's weight.*

*Difficulty: medium*

---

##### Q58
> The equipment from the Apollo Moon landings (1969-1972), such as radiation detectors and temperature probes, remains there to this day, but the data from these missions were mostly inaccessible until a recent data-transfer project made them ______. This project has allowed researcher Seiichi Nagihara to make use of the information in investigating temperature changes on the Moon.

Which choice completes the text with the most logical and precise word or phrase?

**A.** predictable 

  *The data-transfer project made the data usable, not more foreseeable — an unrelated attribute to the accessibility problem described.*

**B.** complicated 

  *A project designed to make data usable would reduce, not add, complication — and this contradicts the researcher then easily using the data.*

**C.** representative 

  *The issue described is whether the data could be accessed and used, not whether it was typical or representative of anything — a different attribute.*

**D.** available **(Correct)**

  *Correct. 'Mostly inaccessible until' the project, followed by a researcher being able 'to make use of the information,' shows the data became available.*

*Difficulty: medium*

---

##### Q59
> Cat and Plum Blossoms is an important work of Nihonga, or classical Japanese painting. Unlike Kuroda Seiki, who adopted traditional European methods such as painting with oil on canvas, Hishida Shunso ______ traditional Japanese approaches. For instance, Hishida produced Cat and Plum Blossoms by applying color pigments to a silk scroll.

Which choice completes the text with the most logical and precise word or phrase?

**A.** distrusted 

  *Hishida's actual practice — applying pigments to a silk scroll, a traditional method — shows adoption of the approach, not distrust of it.*

**B.** embraced **(Correct)**

  *Correct. 'Unlike Kuroda ... who adopted [European methods],' Hishida used a traditional Japanese technique (silk scroll, pigments) — direct evidence he embraced those approaches.*

**C.** released 

  *'Released traditional approaches' doesn't fit adopting and using a technique — the wrong verb category for actively working within a tradition.*

**D.** overlooked 

  *Producing a painting using a traditional Japanese method is active use of that approach, the opposite of overlooking it.*

*Difficulty: medium*

---

##### Q60
> The following text is adapted from Nathaniel Hawthorne's 1837 story "Dr. Heidegger's Experiment." The main character, a physician, is experimenting with rehydrating a dried flower. At first [the rose] lay lightly on the surface of the fluid, appearing to imbibe none of its moisture. Soon, however, a singular change began to be visible. The crushed and dried petals stirred and assumed a deepening tinge of crimson, as if the flower were reviving from a deathlike slumber.

As used in the text, what does the phrase "a singular" most nearly mean?

**A.** A lonely 

  *This is 'singular' in the sense of 'one, alone,' which does not fit describing a remarkable transformation happening to the flower.*

**B.** A disagreeable 

  *The change described — a dried flower reviving and regaining color — is not depicted as unpleasant; nothing supports a negative connotation.*

**C.** An acceptable 

  *A flower reviving 'from a deathlike slumber' is remarkable, not merely 'acceptable' — this understates the degree of the transformation the sentence describes.*

**D.** An extraordinary **(Correct)**

  *Correct. A crushed, dried flower stirring and reviving 'as if... from a deathlike slumber' is a remarkable event — exactly what 'extraordinary' captures.*

*Difficulty: hard*

---

##### Q61
> The work of molecular biophysicist Enrique M. De La Cruz is known for ______ traditional boundaries between academic disciplines. The university laboratory that De La Cruz runs includes engineers, biologists, chemists, and physicists, and the research the lab produces makes use of insights and techniques from all those fields.

Which choice completes the text with the most logical and precise word or phrase?

**A.** epitomizing 

  *Epitomizing boundaries would mean being a perfect example of maintaining them, but the lab's multidisciplinary makeup does the opposite — it crosses them.*

**B.** transcending **(Correct)**

  *Correct. A lab combining engineers, biologists, chemists, and physicists, drawing on insights from all those fields, is direct evidence of the work crossing — transcending — traditional disciplinary boundaries.*

**C.** anticipating 

  *'Anticipating' means foreseeing something not yet happened, but the lab is actively working across fields now, described as an ongoing reality, not a future prediction.*

**D.** reinforcing 

  *Reinforcing boundaries means strengthening them, but combining multiple fields' techniques does the opposite — it weakens the separation between disciplines.*

*Difficulty: medium*

---

##### Q62
> The following text is from F. Scott Fitzgerald's 1925 novel The Great Gatsby. [Jay Gatsby] was balancing himself on the dashboard of his car with that resourcefulness of movement that is so peculiarly American—that comes, I suppose, with the absence of lifting work in youth and, even more, with the formless grace of our nervous, sporadic games. This quality was continually breaking through his punctilious manner in the shape of restlessness.

As used in the text, what does the word "quality" most nearly mean?

**A.** Standard 

  *This is 'quality' as a level of excellence, which doesn't fit 'this quality was breaking through,' where the word refers back to a described personal trait.*

**B.** Prestige 

  *This is 'quality' as social status, an unrelated sense to a trait (resourcefulness of movement) surfacing through someone's formal manner.*

**C.** Characteristic **(Correct)**

  *Correct. 'This quality' refers back to the 'resourcefulness of movement' just described — a personal trait or characteristic breaking through Gatsby's formal manner.*

**D.** Accomplishment 

  *'Quality' here refers to an inherent trait Gatsby has, not something he achieved or earned — a mismatch with the reflexive reference back to a described trait.*

*Difficulty: hard*

---

##### Q63
> To develop a method for measuring snow depth with laser beams, NASA physicist Yongxiang Hu relied on ______; identifying broad similarities between two seemingly different phenomena, Hu used information about how ants move inside colonies to calculate how the particles of light that make up laser beams travel through snow.

Which choice completes the text with the most logical and precise word or phrase?

**A.** a collaboration 

  *The sentence describes drawing a conceptual comparison between two phenomena, not working jointly with another person or team — a category mismatch.*

**B.** an accessory 

  *An accessory is a supplementary tool or object, not a method of reasoning by comparison — the wrong category for what the colon defines.*

**C.** a contradiction 

  *The definition given after the semicolon is about finding similarities between phenomena, the opposite of a contradiction, which involves conflicting ideas.*

**D.** an analogy **(Correct)**

  *Correct. 'Identifying broad similarities between two seemingly different phenomena' — ants in colonies and light particles in snow — is precisely what an analogy is.*

*Difficulty: medium*

---

##### Q64
> A journalist and well-respected art critic of nineteenth-century Britain, Lady Elizabeth Rigby Eastlake did not hesitate to publish reviews that went against popular opinion. One of her most divisive works was an essay questioning the idea of photography as an emerging medium for fine art: in the essay, Eastlake ______ that the value of photographs was informational rather than creative.

Which choice completes the text with the most logical and precise word or phrase?

**A.** exposed 

  *'Exposed' implies revealing hidden wrongdoing or facts, but this is Eastlake's own stated opinion in an essay, not an uncovering of a hidden truth.*

**B.** asserted **(Correct)**

  *Correct. Publishing a divisive essay stating her view (photography's value was informational, not creative) is exactly what 'asserted' describes — confidently stating a claim.*

**C.** discovered 

  *This is a stated opinion presented in an essay, not an empirical finding — 'discovered' misapplies scientific-style verification to an argued position.*

**D.** doubted 

  *She is described as confidently publishing views that 'did not hesitate' to go against popular opinion — the opposite of tentatively doubting her own claim.*

*Difficulty: medium*

---

##### Q65
> Stephen Hannock's luminous landscape paintings are appealing to viewers but have elicited little commentary from contemporary critics, a phenomenon that may be due to the very fact that the paintings seem so ______. Many critics focus their attention on art that is cryptic or overtly challenging.

Which choice completes the text with the most logical and precise word or phrase?

**A.** innovative 

  *Innovative art would likely draw more critical commentary, not less, so this does not explain the described lack of attention from critics.*

**B.** subversive 

  *Subversive, challenging art is exactly what critics are said to focus on, so this would predict more critical attention, not the 'little commentary' the sentence describes.*

**C.** profound 

  *Profound art also tends to draw critical attention, similar to 'cryptic or overtly challenging' work — this doesn't explain the described lack of commentary either.*

**D.** accessible **(Correct)**

  *Correct. Critics are said to focus on 'cryptic or overtly challenging' art, so paintings that are easy to understand — accessible — would logically draw less critical commentary, explaining the phenomenon described.*

*Difficulty: hard*

---

##### Q66
> In 2008 a complete set of ancient pessoi (glass game pieces) was uncovered from beneath a paving stone in modern-day Israel. Due to their small size, pessoi were easily misplaced, making a whole set a rare find. This has led some experts to suggest that the set may have been buried intentionally; however, without clear evidence, archaeologists are left to ______ what happened.

Which choice completes the text with the most logical and precise word or phrase?

**A.** speculate about **(Correct)**

  *Correct. 'Without clear evidence' directly explains why archaeologists can only guess — speculate about — what happened, rather than know for certain.*

**B.** dismiss 

  *Archaeologists are described as still considering possibilities ('some experts suggest ... may have been buried intentionally'), not dismissing the question outright.*

**C.** expand on 

  *'Expand on' implies building on established facts, but the sentence's point is the lack of clear evidence, not extending known information.*

**D.** catalog 

  *Cataloging is a recording or inventory action, unrelated to interpreting an unknown cause in the absence of evidence.*

*Difficulty: medium*

---

##### Q67
> The following text is adapted from Zora Neale Hurston's 1921 short story "John Redding Goes to Sea." John wants to travel far beyond the village where he lives near his mother, Matty. [John] had on several occasions attempted to reconcile his mother to the notion, but found it a difficult task. Matty always took refuge in self-pity and tears. Her son's desires were incomprehensible to her, that was all.

As used in the text, what does the phrase "reconcile his mother to" most nearly mean?

**A.** Get his mother to accept **(Correct)**

  *Correct. John repeatedly tries to make his mother accept his desire to travel, but she resists with 'self-pity and tears' — 'reconcile his mother to the notion' describes this attempt at winning her acceptance.*

**B.** Get his mother to apologize for 

  *Nothing suggests Matty did something wrong requiring an apology — the difficulty described is her resistance to John's plan, not a wrongdoing on her part.*

**C.** Get his mother to match 

  *This confuses 'reconcile to' with a different sense of 'reconcile' (making two things consistent with each other), rather than making a person accept an idea.*

**D.** Get his mother to reunite with 

  *This is 'reconcile with' someone after a conflict — a different phrase and meaning from 'reconcile [someone] to' an idea they resist.*

*Difficulty: hard*

---

##### Q68
> Business researcher Melanie Brucks and colleagues found that remote video conference meetings may be less conducive to brainstorming than in-person meetings are. The researchers suspect that video meeting participants are focused on staring at the speaker on the screen and don't allow their eyes or mind to wander as much, which may ultimately ______ creativity.

Which choice completes the text with the most logical and precise word or phrase?

**A.** recommend 

  *'Recommend creativity' does not logically follow from meetings being 'less conducive to brainstorming' — this doesn't fit a factor that hinders an outcome.*

**B.** criticize 

  *'Criticize' means to judge negatively, but the sentence describes a causal effect on a mental process, not an evaluative act of criticism.*

**C.** impede **(Correct)**

  *Correct. Meetings being 'less conducive to brainstorming' because participants' minds don't wander as much is a direct explanation of how this may ultimately impede — hinder — creativity.*

**D.** construct 

  *'Less conducive to brainstorming' indicates hindering, the opposite of building or constructing creativity.*

*Difficulty: medium*

---

##### Q69
> Mineralogical differences are detectable in samples collected from two locations on the near-Earth asteroid Ryugu, but such differences may not indicate substantial compositional variations in the asteroid. Cosmochemist Kazuhide Nagashima and colleagues note that at the small scale of the samples, the distribution of minerals is unlikely to be ______.

Which choice completes the text with the most logical and precise word or phrase?

**A.** neglected 

  *'Neglected' describes a lack of attention, which doesn't fit describing a physical mineral pattern across an asteroid's surface.*

**B.** redundant 

  *Minerals being 'redundant' is not a coherent description of how they are physically spread across a sample area.*

**C.** ongoing 

  *'Ongoing' describes a process happening over time, not the spatial evenness of a mineral distribution at a given moment — a category mismatch.*

**D.** uniform **(Correct)**

  *Correct. Small-scale samples naturally show patchy, uneven mineral distribution, which is why the detected differences 'may not indicate substantial compositional variations' in the whole asteroid — the distribution is unlikely to be uniform.*

*Difficulty: hard*

---

##### Q70
> The percentage of US forest land that a 2023 federal report identified as being either mature or old growth exceeds other recent estimates. Given how little ______ there is among scientists regarding the scope of these categories, this discrepancy shouldn't be surprising: forest researchers regularly dispute one another's classifications.

Which choice completes the text with the most logical and precise word or phrase?

**A.** deliberation 

  *Researchers disputing classifications may involve plenty of discussion — the missing element is agreement, not the amount of deliberation happening.*

**B.** vigilance 

  *'Vigilance' means watchfulness or alertness, which is unrelated to whether scientists agree on how categories are defined.*

**C.** interest 

  *Researchers actively disputing classifications clearly have interest in the topic — the issue is disagreement, not a lack of interest.*

**D.** consensus **(Correct)**

  *Correct. 'Forest researchers regularly dispute one another's classifications' is direct evidence of little agreement — consensus — about the scope of these categories.*

*Difficulty: hard*

---

##### Q71
> Economist Jingting Fan argues that the effects of international trade may display spatial variation at sub-national levels. For instance, imported goods may reduce expenses for a country's average consumer, but for consumers living far from ports, high intranational transport costs could ______ the price advantages associated with imports.

Which choice completes the text with the most logical and precise word or phrase?

**A.** nullify **(Correct)**

  *Correct. High transport costs for consumers far from ports would cancel out the savings from cheap imports — exactly what 'nullify' describes.*

**B.** denigrate 

  *'Denigrate' means to criticize or disparage, which doesn't fit describing a real economic force offsetting a financial benefit.*

**C.** underestimate 

  *'Underestimate' is a cognitive verb describing a misjudgment, but transport costs are a real economic force actually reducing the price advantage, not merely a miscalculation of it.*

**D.** misconstrue 

  *'Misconstrue' means to misinterpret, an epistemic error — but the sentence describes an actual physical and economic effect on price advantages, not a misunderstanding of them.*

*Difficulty: hard*

---

##### Q72
> Stars form in cloudlike swirls of gas and dust that cannot be touched, but astrophysicist Nia Imara believes these formations need not remain completely ______ to researchers: she uses simulation data and sophisticated 3D printers to produce interactive models of these stellar nurseries.

Which choice completes the text with the most logical and precise word or phrase?

**A.** repeatable 

  *The contrast set up is between being untouchable and being made physically interactive — this is unrelated to whether the formations can be reproduced.*

**B.** explicable 

  *This is about being explainable, but Imara is described as making physical, touchable models, not producing explanations — the wrong attribute.*

**C.** regrettable 

  *This introduces an unrelated evaluative judgment; the sentence is about physical touchability, not whether the formations are unfortunate.*

**D.** intangible **(Correct)**

  *Correct. 'Cannot be touched' sets up a contrast with 'need not remain completely ______,' and Imara's 3D-printed interactive models directly address making these formations touchable — overcoming their intangibility.*

*Difficulty: medium*

---

##### Q73
> Handedness, a preferential use of either the right or left hand, typically is easy to observe in humans. Because this trait is present but less ______ in many other animals, animal-behavior researchers often employ tasks specially designed to reveal individual animals' preferences for a certain hand or paw.

Which choice completes the text with the most logical and precise word or phrase?

**A.** recognizable **(Correct)**

  *Correct. Contrasted with being 'easy to observe in humans,' and explaining why researchers need 'tasks specially designed to reveal' the trait in animals, the blank must mean less observable — recognizable.*

**B.** intriguing 

  *This is about how interesting the trait is, not about how easy it is to observe — it doesn't explain why special tasks are needed to detect it.*

**C.** significant 

  *This is about the trait's importance, but the issue described is detectability, not how significant handedness is in animals.*

**D.** useful 

  *This is about usefulness, unrelated to why special tasks would be needed to observe a trait that is present but harder to see.*

*Difficulty: medium*

---

##### Q74
> In Nature Poem (2017), Kumeyaay poet Tommy Pico portrays his ______ the natural world by honoring the centrality of nature within his tribe's traditional beliefs while simultaneously expressing his distaste for being in wilderness settings himself.

Which choice completes the text with the most logical and precise word or phrase?

**A.** responsiveness to 

  *This is too one-directional — it doesn't capture the conflicting, simultaneous positive and negative feelings ('honoring ... while simultaneously expressing his distaste') the sentence describes.*

**B.** ambivalence toward **(Correct)**

  *Correct. 'Honoring the centrality of nature ... while simultaneously expressing his distaste' describes conflicted, mixed feelings toward nature — exactly what 'ambivalence' names.*

**C.** renunciation of 

  *'Renunciation' means rejecting something entirely, but Pico also honors nature's centrality to his tribe's beliefs — this ignores half of the described contrast.*

**D.** mastery over 

  *Nothing in the sentence is about controlling or being skilled with the natural world — an unrelated attribute to the described emotional conflict.*

*Difficulty: medium*

---

##### Q75
> Like the 1945 play it reimagines—Federico García Lorca's The House of Bernarda Alba—Marcus Gardley's 2014 play The House That Will Not Stand prominently features women. In both plays, the all-female cast ______ an array of female characters, including a strong mother and several daughters dealing with individual struggles.

Which choice completes the text with the most logical and precise word or phrase?

**A.** engulfs 

  *'Engulf' means to overwhelm or swallow, which doesn't describe a cast's makeup or composition of characters.*

**B.** encourages 

  *'Encourages' implies motivating an action, which doesn't describe what a cast consists of — a mismatch of category.*

**C.** comprises **(Correct)**

  *Correct. 'The all-female cast ______ an array of female characters' describes what the cast consists of — exactly what 'comprises' names.*

**D.** provokes 

  *'Provoke' means to incite a reaction, which doesn't describe the composition of a cast of characters.*

*Difficulty: medium*

---

##### Q76
> During a 2014 archaeological dig in Spain, Vicente Lull and his team uncovered the skeleton of a woman from El Algar, an Early Bronze Age society, buried with valuable objects signaling a high position of power. This finding may persuade researchers who have argued that Bronze Age societies were ruled by men to ______ that women may have also held leadership roles.

Which choice completes the text with the most logical and precise word or phrase?

**A.** waive 

  *'Waive' means to give up a right or claim, which doesn't fit admitting a new possibility based on evidence.*

**B.** concede **(Correct)**

  *Correct. A finding that 'may persuade' researchers who held the opposing view toward a new conclusion describes them admitting — conceding — that this new possibility may be true.*

**C.** refute 

  *'Refute' means to disprove, but the evidence is persuading researchers toward accepting the new idea, not toward disproving it.*

**D.** require 

  *'Persuaded ... to require that women may have also held leadership roles' doesn't logically follow — this doesn't fit the process of being convinced by evidence.*

*Difficulty: medium*

---

##### Q77
> In addition to being an accomplished psychologist himself, Francis Cecil Sumner was a ______ increasing the opportunity for Black students to study psychology, helping to found the psychology department at Howard University, a historically Black university, in 1930.

Which choice completes the text with the most logical and precise word or phrase?

**A.** proponent of **(Correct)**

  *Correct. 'Helping to found the psychology department' to increase opportunity for Black students is direct evidence that Sumner actively advocated for — was a proponent of — that goal.*

**B.** supplement to 

  *'Supplement' means an addition to something else, which doesn't capture actively advocating for and founding an initiative himself.*

**C.** beneficiary of 

  *'Beneficiary' means one who receives a benefit, but Sumner is the one actively creating opportunity for others, not receiving it himself — the wrong direction.*

**D.** distraction for 

  *His founding work directly furthered this goal, the opposite of distracting from it.*

*Difficulty: medium*

---

##### Q78
> The following text is adapted from Nathaniel Hawthorne's 1844 short story "Drowne's Wooden Image." Drowne, a young man, is carving a wooden figure to decorate the front of a ship. Day by day, the work assumed greater precision, and settled its irregular and misty outline into distincter grace and beauty. The general design was now obvious to the common eye.

As used in the text, what does the word "assumed" most nearly mean?

**A.** Acquired **(Correct)**

  *Correct. 'Assumed greater precision' describes the carving gradually taking on — acquiring — more precision as Drowne worked on it day by day.*

**B.** Acknowledged 

  *This is 'assumed' as in accepting something as true, which doesn't fit a carving gradually taking on a physical quality over time.*

**C.** Imitated 

  *The work is gaining a quality itself, not copying something else — imitation is a different, unrelated sense of the word here.*

**D.** Speculated 

  *An inanimate wood carving cannot speculate — this sense of the word requires a thinking agent, a category error here.*

*Difficulty: medium*

---

##### Q79
> Novelist N. K. Jemisin declines to ______ the conventions of the science fiction genre in which she writes, and she has suggested that her readers appreciate her work precisely because of this willingness to thwart expectations and avoid formulaic plots and themes.

Which choice completes the text with the most logical and precise word or phrase?

**A.** question 

  *Questioning conventions is a different stance from following them — this doesn't match 'declines to ______' being explained by a willingness to thwart and avoid formulaic elements.*

**B.** react to 

  *Too vague — 'react to' doesn't capture the specific idea of following established genre rules, which is what 'thwart expectations' implies she avoids doing.*

**C.** perceive 

  *Perceiving is a cognitive, observational verb; 'declines to perceive conventions' doesn't logically pair with 'thwart expectations and avoid formulaic plots.'*

**D.** conform to **(Correct)**

  *Correct. 'Thwart expectations and avoid formulaic plots and themes' is a direct explanation of what Jemisin declines to do — conform to genre conventions.*

*Difficulty: medium*

---

##### Q80
> Interruptions in the supply chain for microchips used in personal electronics have challenged an economist's assertion that retailers can expect robust growth in sales of those devices in the coming months. The delays are unlikely to ______ her projection entirely but will almost certainly extend its time frame.

Which choice completes the text with the most logical and precise word or phrase?

**A.** dispute 

  *Delays are an external event, not an agent capable of 'disputing' a claim — that action typically belongs to a person arguing against something, a category mismatch here.*

**B.** withdraw 

  *Delays cannot 'withdraw' someone else's projection — withdrawal implies the economist herself retracting her own claim, a mismatch of who performs the action.*

**C.** underscore 

  *'Underscore' means to emphasize or reinforce, but the sentence's contrast ('unlikely to ______ entirely but will ... extend its time frame') suggests a negative effect on the projection, not reinforcement of it.*

**D.** invalidate **(Correct)**

  *Correct. 'Unlikely to ______ entirely but will almost certainly extend its time frame' describes delays that won't completely disprove the projection, just delay it — invalidate is exactly what's being ruled out except partially.*

*Difficulty: hard*

---

##### Q81
> Domesticated thousands of years ago by Indigenous people in South America, cacao, the plant from which chocolate is made, deviates structurally from the wild plant it is descended from. Maize (corn), another crop domesticated by Indigenous Americans, shows so little resemblance to any wild plant that genetic research was necessary to ______ teosinte grass as its ancestor.

Which choice completes the text with the most logical and precise word or phrase?

**A.** acquire 

  *'Acquire teosinte grass as its ancestor' is nonsensical — ancestry is not something obtained through research, a category error.*

**B.** develop 

  *Genetic research does not 'develop' an ancestor — ancestry already exists and isn't created by the act of researching it.*

**C.** attract 

  *This verb doesn't fit the verification purpose of the genetic research described — an unrelated action to establishing ancestry.*

**D.** confirm **(Correct)**

  *Correct. Since maize 'shows so little resemblance to any wild plant,' visual inspection alone couldn't establish its ancestor, so genetic research was needed to confirm teosinte grass as that ancestor.*

*Difficulty: medium*

---

##### Q82
> Austin McCoy has argued that historians have tended to ______ rank-and-file workers in analyses of changes in organized labor in the United States in the decades following the Second World War, presenting political, business, and labor leaders as the major actors and ordinary workers as nearly devoid of agency.

Which choice completes the text with the most logical and precise word or phrase?

**A.** epitomize 

  *'Epitomize' means to be a perfect example of something, which doesn't logically pair with historians downplaying workers' agency in their analyses.*

**B.** marginalize **(Correct)**

  *Correct. 'Presenting ... ordinary workers as nearly devoid of agency' is direct evidence that historians have marginalized — downplayed the importance of — rank-and-file workers.*

**C.** extol 

  *'Extol' means to praise highly, but historians are described as downplaying workers' agency, not praising their role.*

**D.** substantiate 

  *'Substantiate' means to provide evidence supporting something's importance, but the sentence describes workers being minimized in analyses, not their importance being supported.*

*Difficulty: medium*

---

##### Q83
> The discoverers of the minor planet 1227 Geranium named it after the plant genus that includes cranesbills. Most of the recently discovered minor planets, however, are given only an identification number, largely due to there being over 500,000 such bodies known at present, which makes the already challenging task of finding a unique name for each nearly ______.

Which choice completes the text with the most logical and precise word or phrase?

**A.** insurmountable **(Correct)**

  *Correct. With 'over 500,000' bodies known and 'most ... given only an identification number' rather than a unique name, the already challenging task has become nearly insurmountable — nearly impossible.*

**B.** feasible 

  *If naming each planet were feasible, more would receive unique names, but most only get numbers — the opposite of what feasible would predict.*

**C.** substantial 

  *'Substantial' (large or significant) doesn't capture the extreme degree implied by 'already challenging ... nearly ______' being the reason nearly all planets go unnamed.*

**D.** unnecessary 

  *The task isn't described as pointless — it's described as too difficult to accomplish for most planets, a different claim than being unnecessary.*

*Difficulty: medium*

---

##### Q84
> The Illustrated History of San Mateo County, published in 1878, features several illustrations by Grafton Tyler Brown showing the California county's farms, residences, and businesses. It was ______ for a business to be featured, since being included suggested that a business was an important part of the community.

Which choice completes the text with the most logical and precise word or phrase?

**A.** risky 

  *No downside or danger is described — the sentence only describes a positive implication (importance) of being included, not any risk.*

**B.** misleading 

  *The suggestion that a featured business was important is presented as an accurate implication of inclusion, not a deceptive one.*

**C.** advantageous **(Correct)**

  *Correct. 'Being included suggested that a business was an important part of the community' describes a clear benefit to being featured — exactly what 'advantageous' names.*

**D.** unremarkable 

  *Being featured is described as carrying a meaningful, notable implication (community importance), the opposite of unremarkable.*

*Difficulty: medium*

---

##### Q85
> The following text is adapted from Upton Sinclair's 1906 novel The Jungle. Marija is helping to manage her sister's wedding. It was [Marija's] task to see that all things went in due form, and after the best home traditions; and, flying wildly hither and thither, bowling every one out of the way, and scolding and exhorting all day with her tremendous voice, Marija was too eager to see that others conformed to the proprieties to consider them herself.

As used in the text, what does the word "consider" most nearly mean?

**A.** Take into account and follow **(Correct)**

  *Correct. Marija makes others 'conform to the proprieties' but is 'too eager' to do the same herself — 'consider them' describes taking the proprieties into account and following them herself, which she fails to do.*

**B.** Admire steadily and praise 

  *Nothing in the sentence is about admiring or praising the proprieties — the passage is about actually following rules of behavior, not appreciating them.*

**C.** Come to a decision about 

  *This is 'consider' in the sense of deliberating or deciding, which doesn't fit 'too eager ... to consider them herself' describing observing or following established proprieties.*

**D.** Have an opinion on 

  *Having a view about the proprieties is different from personally following them, which is what the sentence contrasts with her making everyone else conform.*

*Difficulty: hard*

---

##### Q86
> The fossil remains of the individual known as Oase 1, discovered in Romania in 2002, can help paleoanthropologists not only ______ steps in the evolution of hominids but also illuminate the Pleistocene epoch generally, revealing important details about the time in which Oase 1 lived.

Which choice completes the text with the most logical and precise word or phrase?

**A.** exploit 

  *'Exploit' means to make use of for gain, which doesn't match the epistemic action of understanding evolutionary steps described alongside 'illuminate' and 'revealing.'*

**B.** discern **(Correct)**

  *Correct. Paired with 'illuminate ... revealing important details,' the fossils help paleoanthropologists perceive — discern — steps in hominid evolution.*

**C.** prioritize 

  *'Prioritize' means ranking importance, which doesn't fit gaining understanding of evolutionary steps from fossil evidence.*

**D.** yield 

  *'Yield steps' would mean producing or generating steps, but the fossils help scientists perceive already-existing evolutionary steps, not create them.*

*Difficulty: medium*

---

##### Q87
> Drivers who strongly believe that the toll they must pay to use the Lewis and Clark Bridge, which spans the Ohio River to connect Indiana and Kentucky, is currently too high are unlikely to be ______ a proposal to increase the toll. Advocates for a higher toll are likely to have more success if they instead direct their arguments toward a more persuasive segment of the population.

Which choice completes the text with the most logical and precise word or phrase?

**A.** receptive to **(Correct)**

  *Correct. Drivers who already think the toll is too high would not welcome a proposal to raise it further — they are unlikely to be receptive, or open, to such a proposal.*

**B.** apprised of 

  *'Apprised of' means informed about, but the sentence is about attitude toward a proposal, not whether drivers have been told about it.*

**C.** incensed by 

  *This inverts the sentence's logic: drivers who think the toll is too high would actually likely BE incensed by a proposal to raise it, so 'unlikely to be incensed' contradicts the passage's own setup rather than completing it.*

**D.** cited in 

  *Drivers being 'cited in a proposal' doesn't fit describing their reaction to or openness toward a proposal aimed at persuading them.*

*Difficulty: hard*

---

##### Q88
> Rejecting the premise that the literary magazine Ebony and Topaz (1927) should present a unified vision of Black American identity, editor Charles S. Johnson fostered his contributors' diverse perspectives by promoting their authorial autonomy. Johnson's self-effacement diverged from the editorial stances of W.E.B. Du Bois and Alain Locke, whose decisions for their publications were more ______.

Which choice completes the text with the most logical and precise word or phrase?

**A.** proficient 

  *The contrast being drawn is about editorial control versus authorial autonomy, not about skill level — an unrelated attribute to what 'diverged' is comparing.*

**B.** dogmatic **(Correct)**

  *Correct. Johnson's approach — self-effacement, promoting contributors' autonomy — 'diverged from' Du Bois and Locke's editorial stances, implying theirs were more controlling and rigid in imposing their own vision, which is exactly what 'dogmatic' names.*

**C.** ambiguous 

  *The contrast is about being controlling versus permissive as editors, not about clarity or vagueness of their editorial decisions.*

**D.** unpretentious 

  *This describes Johnson's own self-effacing approach, not a contrast to him — this reverses which editor the sentence is attributing the trait to.*

*Difficulty: hard*

---

##### Q89
> Economist Marco Castillo and colleagues showed that nuisance costs—the time and effort people must spend to make donations—reduce charitable giving. Charities can mitigate this effect by compensating donors for nuisance costs, but those costs, though variable, are largely ______ donation size, so charities that compensate donors will likely favor attracting a few large donors over many small donors.

Which choice completes the text with the most logical and precise word or phrase?

**A.** supplemental to 

  *This doesn't capture the lack of relationship between cost and donation size that explains why charities would prefer large donors over many small ones.*

**B.** predictive of 

  *If costs were predictive of donation size, there would be a meaningful relationship between them, but the logic (a fixed compensation cost applying regardless of donation size) requires no such correlation.*

**C.** independent of **(Correct)**

  *Correct. Since compensating a donor costs roughly the same 'largely' regardless of how much they give, charities favor large donors — the costs don't scale with, and are therefore independent of, donation size.*

**D.** subsumed in 

  *Costs being 'subsumed in' donation size doesn't logically describe the relationship — this misapplies a containment relationship to what is actually a lack of correlation.*

*Difficulty: hard*

---

##### Q90
> The following text is adapted from George Eliot's 1871-72 novel Middlemarch. [Mr. Brooke] had travelled in his younger years, and was held in this part of the country to have contracted a too rambling habit of mind. Mr. Brooke's conclusions were as difficult to predict as the weather.

As used in the text, what does the word "contracted" most nearly mean?

**A.** Restricted 

  *This is 'contract' as in shrink or narrow, which is ironically the opposite of what's described — a 'rambling' habit of mind suggests expansiveness, and 'contracted' here means acquired, not narrowed.*

**B.** Described 

  *This is unrelated to acquiring a trait — 'contracted a habit of mind' is about gaining a characteristic, not being described.*

**C.** Developed **(Correct)**

  *Correct. 'Contracted a too rambling habit of mind' describes Mr. Brooke acquiring a mental habit over his years of travel, much like one 'contracts' an illness — that is, developed it.*

**D.** Settled 

  *'Contracted' here means acquiring a trait during his travels, not becoming fixed or settled — the opposite of the restless, rambling quality described.*

*Difficulty: hard*

---

##### Q91
> The güiro, a musical instrument traditionally made from a dried and hollowed gourd, is thought to have originated with the Taíno people of Puerto Rico. Players use a wooden stick to scrape along ridges cut into the side of the gourd, creating sounds that are highly ______: the sounds produced by güiros can differ based on the distance between the ridges, the types of strokes the player uses, and the thickness of the gourd.

Which choice completes the text with the most logical and precise word or phrase?

**A.** overlooked 

  *This is unrelated to how the sounds differ based on multiple factors — the sentence describes variation, not neglect.*

**B.** powerful 

  *This describes intensity or volume, not variation based on the listed factors (ridge distance, stroke type, gourd thickness) — the wrong attribute.*

**C.** routine 

  *'Routine' implies consistency and predictability, but the sentence emphasizes how sounds differ depending on multiple factors — the opposite of routine.*

**D.** variable **(Correct)**

  *Correct. 'Can differ based on' three separate factors — ridge distance, stroke type, gourd thickness — directly supports the sounds being highly variable.*

*Difficulty: medium*

---

##### Q92
> While scholars believe many Mesoamerican cities influenced each other, direct evidence of such influence is difficult to ascertain. However, recent excavations in a sector of Tikal (Guatemala) unearthed a citadel that shows ______ Teotihuacán (Mexico) architecture—including a near replica of a famed Teotihuacán temple—providing tangible evidence of outside influence in portions of Tikal.

Which choice completes the text with the most logical and precise word or phrase?

**A.** refinements of 

  *'Refinements' implies improving upon something, but a 'near replica' suggests direct similarity or imitation, not an improved version of Teotihuacán architecture.*

**B.** precursors of 

  *'Precursor' means coming before and influencing something later, but the citadel is described as showing Teotihuacán's influence on Tikal, meaning Tikal came after, not before.*

**C.** commonalities with **(Correct)**

  *Correct. A 'near replica of a famed Teotihuacán temple' is direct evidence of architectural similarity — commonalities — between the two cities, providing tangible evidence of outside influence.*

**D.** animosities toward 

  *A 'near replica' evidences architectural similarity and connection, not hostility between the two cities.*

*Difficulty: hard*

---

##### Q93
> Close analysis of the painting Girl with a Flute, long attributed to the seventeenth-century Dutch painter Johannes Vermeer, has revealed subtle deviations from the artist's signature techniques. These variations suggest that the work may be that of a student under Vermeer's tutelage—potentially ______ our understanding of Vermeer as a solitary artist.

Which choice completes the text with the most logical and precise word or phrase?

**A.** negating **(Correct)**

  *Correct. If the painting was actually made by a student rather than Vermeer working alone, this directly undermines — negates — the existing view of Vermeer as a solitary artist.*

**B.** prefiguring 

  *'Prefiguring' means foreshadowing something yet to come, which doesn't fit challenging an existing, already-held understanding.*

**C.** entrenching 

  *'Entrenching' means strengthening a belief, but finding evidence of a student's likely involvement would undermine, not reinforce, the 'solitary artist' view.*

**D.** substantiating 

  *'Substantiating' means confirming or supporting, but the evidence (likely student involvement) contradicts, rather than confirms, the solitary-artist understanding.*

*Difficulty: hard*

---

##### Q94
> While most animals are incapable of passing somatic mutations—genetic alterations that arise in an organism's nonreproductive cells—on to their offspring, elkhorn coral (Acropora palmata) presents an intriguing ______: in a 2022 study, researchers found that elkhorn coral produced offspring that inherited somatic mutations from a parent.

Which choice completes the text with the most logical and precise word or phrase?

**A.** hypothesis 

  *A hypothesis is a proposed, untested explanation, but the sentence describes an observed, confirmed exception (offspring that did inherit somatic mutations), not an untested idea.*

**B.** affinity 

  *'Affinity' means a natural liking or similarity, which doesn't fit describing an exception to a general biological rule.*

**C.** anomaly **(Correct)**

  *Correct. Elkhorn coral doing what 'most animals are incapable of' — passing somatic mutations to offspring — is exactly what an anomaly is: an exception to the general rule.*

**D.** corroboration 

  *'Corroboration' means confirming an existing claim, but the coral's behavior contradicts, rather than supports, the general rule about most animals.*

*Difficulty: medium*

---

##### Q95
> Some foraging models predict that the distance bees travel when foraging will decline as floral density increases, but biologists Shalene Jha and Claire Kremen showed that bees' behavior is inconsistent with this prediction if flowers in dense patches are ______: bees will forage beyond patches of low species richness to acquire multiple resource types.

Which choice completes the text with the most logical and precise word or phrase?

**A.** depleted 

  *This is about quantity or exhaustion of resources, not about species diversity or uniformity within a patch — a different attribute than what 'low species richness' describes.*

**B.** homogeneous **(Correct)**

  *Correct. 'Patches of low species richness' means patches with mostly one type of flower — homogeneous — which explains why bees travel further despite high density, contradicting the density-only model.*

**C.** immature 

  *This is about developmental stage, which is unrelated to species diversity within dense flower patches.*

**D.** dispersed 

  *This directly contradicts 'dense patches' — the sentence already establishes high floral density, so 'dispersed' (spread out, sparse) conflicts with the given premise.*

*Difficulty: hard*

---

##### Q96
> Investigating whether shared false visual memories—specific but inaccurate and widely held recollections of images such as product logos—are caused by people's previous ______ incorrect renditions of the images, researchers Deepasri Prasad and Wilma Bainbridge found that, in fact, such memories are often not explained by familiarity with erroneous versions of the images.

Which choice completes the text with the most logical and precise word or phrase?

**A.** compliance with 

  *'Compliance' implies obeying a rule, which doesn't fit having previously encountered or seen incorrect images.*

**B.** exposure to **(Correct)**

  *Correct. The researchers' conclusion — memories are 'not explained by familiarity with erroneous versions' — restates the hypothesis being tested, that prior exposure to incorrect images caused the false memories.*

**C.** criteria for 

  *'Criteria' means standards for judgment, unrelated to whether people had previously seen incorrect images.*

**D.** forfeiture of 

  *'Forfeiture' means giving something up, which is unrelated to having encountered incorrect renditions of an image.*

*Difficulty: medium*

---

##### Q97
> As an undergraduate researcher in anthropology, Jennifer C. Chen contributed to a groundbreaking study challenging the accepted view that among prehistoric peoples, female participation in hunting was ______. The research team's review of data from late Pleistocene and early Holocene burials in the Americas revealed that, in fact, as many as half of the hunters in those populations were female.

Which choice completes the text with the most logical and precise word or phrase?

**A.** inevitable 

  *If the old view held participation was inevitable (certain to occur), the new finding of higher-than-expected participation wouldn't be surprising or challenge that view — the opposite of what the sentence describes.*

**B.** satisfactory 

  *This is about approval or adequacy, unrelated to the described degree or amount of female participation being challenged.*

**C.** negligible **(Correct)**

  *Correct. The 'accepted view' being overturned by evidence that 'as many as half ... were female' must have held that female participation was minimal or insignificant — negligible.*

**D.** commonplace 

  *This describes what the NEW finding suggests (half the hunters were female), not the OLD accepted view being challenged — this reverses which view holds which value.*

*Difficulty: hard*

---

##### Q98
> The following text is from the 1989 novel The Ancient Child by Kiowa writer N. Scott Momaday. The main character has achieved tremendous commercial success as a painter. More and more often he was asked to compromise his art or himself in one way or another, and more often than not he did so, for he was inclined to be passive and naïve; it was difficult for him to say no. Those who exhibited his work, who praised and purchased it, and who demanded its proliferation began to determine it.

As used in the text, what does the word "determine" most nearly mean?

**A.** Conclude 

  *This is 'determine' as in reaching a conclusion, which doesn't fit describing others controlling an artist's output — a different sense of the word entirely.*

**B.** Dictate **(Correct)**

  *Correct. Given his passivity and tendency to compromise, those who 'demanded its proliferation' are described as beginning to control — dictate — his art, rather than him directing it himself.*

**C.** Evaluate 

  *Evaluating is judging something, which is a weaker and different action than controlling or dictating someone's artistic output.*

**D.** Select 

  *Selecting implies choosing among existing options, but the passage describes those who demanded proliferation actively controlling the direction of his art — a stronger claim than mere selection.*

*Difficulty: hard*

---

##### Q99
> Given that the conditions in binary star systems should make planetary formation nearly impossible, it's not surprising that the existence of planets in such systems has lacked ______ explanation. Roman Rafikov and Kedron Silsbee shed light on the subject when they used modeling to determine a complex set of factors that could support planets' development.

Which choice completes the text with the most logical and precise word or phrase?

**A.** a discernible 

  *The issue isn't that no explanation could be perceived at all — a discernible explanation could still be complex. This doesn't match how the researchers 'shed light' through careful modeling rather than through mere perceptibility.*

**B.** a straightforward **(Correct)**

  *Correct. That researchers needed 'a complex set of factors' via modeling to explain planet formation in binary systems shows the phenomenon lacked a simple — straightforward — explanation.*

**C.** an inconclusive 

  *'Shed light on the subject' implies the researchers DID find a valid, conclusive explanation through modeling — so the phenomenon can't have 'lacked an inconclusive explanation,' which is a double negative that contradicts the resolution described.*

**D.** an unbiased 

  *Nothing in the sentence is about bias or objectivity in existing explanations — an unrelated attribute to the described complexity.*

*Difficulty: hard*

---

##### Q100
> It is by no means ______ to recognize the influence of Dutch painter Hieronymus Bosch on Ali Banisadr's paintings; indeed, Banisadr himself cites Bosch as an inspiration. However, some scholars have suggested that the ancient Mesopotamian poem Epic of Gilgamesh may have had a far greater impact on Banisadr's work.

Which choice completes the text with the most logical and precise word or phrase?

**A.** substantial 

  *'By no means substantial' would mean the influence isn't substantial, but 'indeed, Banisadr himself cites Bosch as an inspiration' confirms the influence is real — negating 'substantial' would incorrectly downplay a confirmed influence the sentence just affirmed.*

**B.** satisfying 

  *This is about emotional satisfaction, an unrelated category for describing whether recognizing an artistic influence is significant.*

**C.** unimportant **(Correct)**

  *Correct. 'By no means unimportant to recognize the influence' means it IS important to recognize it, which matches 'indeed, Banisadr himself cites Bosch as an inspiration' — even though Gilgamesh may have had a greater impact, Bosch's influence still matters.*

**D.** appropriate 

  *This is about whether recognizing the influence is proper or fitting, not about the significance of the influence itself, which is what the sentence's logic turns on.*

*Difficulty: sat-hardest*

---

##### Q101
> Some scientists have suggested that mammals in the Mesozoic era were not a very ______ group, but paleontologist Zhe-Xi Luo's research suggests that early mammals living in the shadow of dinosaurs weren't all ground-dwelling insectivores. Fossils of various plant-eating mammals have been found in China, including species like Vilevolodon diplomylos, which Luo says could glide like a flying squirrel.

Which choice completes the text with the most logical and precise word or phrase?

**A.** predatory 

  *The evidence is about variety in diet and lifestyle (plant-eaters, gliders, not just ground-dwelling insectivores), not specifically about predatory behavior — the challenged old view should be about diversity, not predation.*

**B.** obscure 

  *'Obscure' means poorly known or documented, but the sentence is about the actual variety within the group's diet and lifestyle, not how well-studied Mesozoic mammals were.*

**C.** diverse **(Correct)**

  *Correct. Evidence of plant-eaters, gliders, and non-ground-dwelling mammals directly challenges an old view that Mesozoic mammals were 'not a very' diverse group — this new evidence establishes real variety in diet and lifestyle.*

**D.** localized 

  *Nothing about geographic range is being challenged — the evidence concerns diet and lifestyle diversity, not where these mammals lived.*

*Difficulty: hard*

---

##### Q102
> The following text is adapted from Oscar Wilde's 1895 play The Importance of Being Earnest. CECILY: Have we got to part? ALGERNON: I am afraid so. It's a very painful parting. CECILY: It is always painful to part from people whom one has known for a very brief space of time. The absence of old friends one can endure with equanimity. But even a momentary separation from anyone to whom one has just been introduced is almost unbearable.

As used in the text, what does the word "endure" most nearly mean?

**A.** Regret 

  *'Endure' is not about feeling sorry over something — it describes bearing or withstanding an absence calmly, not an emotion of regret.*

**B.** Persist 

  *This is 'endure' as in continuing over time, which doesn't fit 'endure [an absence] with equanimity,' describing an emotional bearing of difficulty rather than a continuation.*

**C.** Tolerate **(Correct)**

  *Correct. 'The absence of old friends one can endure with equanimity' contrasted with 'almost unbearable' for new acquaintances shows 'endure' means to calmly bear or tolerate.*

**D.** Encourage 

  *This is unrelated to tolerating a difficult experience — encouraging something is a different, unrelated action from bearing an absence.*

*Difficulty: medium*

---

##### Q103
> Scholarly discussions of gender in Shakespeare's comedies often celebrate the rebellion of the playwright's characters against the rigid expectations ______ by Elizabethan society. Most of the comedies end in marriage, with characters returning to their socially dictated gender roles after previously defying them, but there are some notable exceptions.

Which choice completes the text with the most logical and precise word or phrase?

**A.** interjected 

  *'Interjected' means inserted abruptly, like an interruption, which doesn't fit describing established societal norms and expectations.*

**B.** committed 

  *'Committed by society' would suggest a wrongdoing, like a crime, not the imposition of social expectations that characters later return to.*

**C.** illustrated 

  *'Illustrated' means depicted or shown, which doesn't capture expectations actively imposed or mandated by society, later restated as 'socially dictated gender roles.'*

**D.** prescribed **(Correct)**

  *Correct. 'Rigid expectations ... by Elizabethan society' and later 'socially dictated gender roles' both describe expectations mandated by society — exactly what 'prescribed' names.*

*Difficulty: medium*

---

##### Q104
> According to a US policy expert, state taxes are ______ other factors when considering an interstate move. Even significant differences in state taxation have almost no effect on most people's decisions, while differences in employment opportunities, housing availability, and climate are strong influences.

Which choice completes the text with the most logical and precise word or phrase?

**A.** consistent with 

  *This doesn't capture the comparative weighting between taxes and other factors that the sentence describes — a mismatch of relationship.*

**B.** representative of 

  *Taxes are not described as exemplifying other factors — this is the wrong relationship between the two categories of influence.*

**C.** overshadowed by **(Correct)**

  *Correct. Taxes having 'almost no effect' while other factors are 'strong influences' describes taxes being outweighed — overshadowed — by those factors, though not eliminated entirely.*

**D.** irrelevant to 

  *'Almost no effect' is not the same as zero effect or complete irrelevance — this overstates the claim beyond what the text actually supports.*

*Difficulty: hard*

---

##### Q105
> Environmental engineer Florentino De la Cruz has shown that it is misleading to treat municipal solid waste (MSW) as ______ when determining MSW decay rates. Grass in MSW decays at a rate more than 10 times that of corrugated containers, for example, making compositional specification a crucial precondition for determining MSW decay rates.

Which choice completes the text with the most logical and precise word or phrase?

**A.** inviolable 

  *'Inviolable' means must not be violated or sacred, which is unrelated to whether waste is uniform in composition or decay rate.*

**B.** innocuous 

  *'Innocuous' means harmless, which is unrelated to whether different components of waste decay at different rates.*

**C.** undifferentiated **(Correct)**

  *Correct. Grass decaying '10 times' faster than corrugated containers, with 'compositional specification' called 'crucial,' shows that treating MSW as a single undifferentiated mass — ignoring these compositional differences — is misleading.*

**D.** ubiquitous 

  *'Ubiquitous' means present everywhere, which doesn't capture treating waste as uniform in composition — a different, unrelated attribute.*

*Difficulty: hard*

---

##### Q106
> In the 2010s, the price of pop music cassette tapes from the 1980s and 1990s rose dramatically, which had the counterintuitive effect of ______ demand: buyers who hadn't previously wanted to purchase vintage cassettes thronged the market, believing prices would continue to rise and the tapes could be resold at a profit.

Which choice completes the text with the most logical and precise word or phrase?

**A.** exploiting 

  *'Exploiting' means taking advantage of something that already exists, which doesn't fit describing an effect that creates entirely new buyer demand.*

**B.** monetizing 

  *'Monetizing' means converting something into money, which doesn't fit describing the generation of new buyer demand itself.*

**C.** appraising 

  *'Appraising' means evaluating value, which doesn't describe an effect that causes new demand among previously uninterested buyers.*

**D.** engendering **(Correct)**

  *Correct. Rising prices causing new buyers to want tapes — 'counterintuitive' since higher prices normally reduce demand — is exactly what 'engendering,' or generating, new demand describes.*

*Difficulty: medium*

---

##### Q107
> Despite how ______ they may seem at first glance, the works of the philosopher Georg Hegel have proven to be quite influential. Readers who manage to penetrate Hegel's frustratingly dense prose often find that his thrillingly original and profound ideas wind up shaping their own thinking.

Which choice completes the text with the most logical and precise word or phrase?

**A.** authoritative 

  *This doesn't create the needed contrast with 'influential' (both are positive, related qualities), and it doesn't match the difficulty theme in 'frustratingly dense prose ... penetrate.'*

**B.** opaque **(Correct)**

  *Correct. 'Despite how ______ ... quite influential' sets up a contrast, and 'frustratingly dense prose' that readers must 'penetrate' directly matches 'opaque' — hard to see through or understand.*

**C.** empirical 

  *This is about being based on observation or experiment, unrelated to the described difficulty and density of Hegel's prose.*

**D.** facile 

  *'Facile' means easy or simplistic, which directly contradicts 'frustratingly dense prose ... penetrate' — the opposite of the difficulty being described.*

*Difficulty: hard*

---

##### Q108
> Containing over 160 billion base pairs of DNA resulting from polyploidy (whole genome duplication) and accumulation of noncoding DNA without significant deletion, the genome of Tmesipteris oblanceolata (New Caledonian fork fern) is the largest known among eukaryotes—and, given the high biological costs of extremely large genomes, is unlikely to be ______.

Which choice completes the text with the most logical and precise word or phrase?

**A.** protracted 

  *'Protracted' means extended in duration and typically describes processes or events over time, not the size ranking of a physical genome — a category mismatch.*

**B.** superseded **(Correct)**

  *Correct. Given the 'high biological costs of extremely large genomes,' few organisms would evolve an even larger genome — so this record-holding genome is unlikely to be exceeded, or superseded, by another.*

**C.** curtailed 

  *'Curtailed' would mean this genome itself getting cut down, but the sentence is about whether another organism's genome will surpass it in size, not about this genome shrinking.*

**D.** obviated 

  *'Obviate' means to make something unnecessary, which doesn't logically apply to a genome's size or ranking among eukaryotes — a category error.*

*Difficulty: sat-hardest*

---

##### Q109
> Text corpora such as the Bank of English are enormous collections of electronically stored texts that can be used for empirical testing of hypotheses regarding the frequency of typical word usage. If one has a ______ that the word "get" has a high incidence in English, for example, an analysis of a corpus can support that hypothesis by showing that "get" is the fifth most commonly used verb.

Which choice completes the text with the most logical and precise word or phrase?

**A.** recognition 

  *'Recognition' implies already-confirmed knowledge, but the sentence frames this as something to be tested and supported by evidence — not yet confirmed — contradicting the 'hypothesis' framing.*

**B.** scheme 

  *'Scheme' implies a plan or plot, which doesn't fit having an untested belief about word frequency.*

**C.** supposition **(Correct)**

  *Correct. The sentence explicitly refers back to 'that hypothesis,' and 'supposition' — an unproven guess or belief — is exactly what a hypothesis is before it's tested against corpus data.*

**D.** synopsis 

  *'Synopsis' means a summary, which doesn't fit having an unproven belief that then gets tested by data.*

*Difficulty: medium*

---

##### Q110
> In a study of residential mobility in Washington, DC, LaTanya Brown-Robertson et al. found that increases in household spending power (via tax credits) had mixed effects on mobility decisions, possibly because residential location choices are not fully reducible to economic factors but are also ______ noneconomic factors such as access to strong local social networks.

Which choice completes the text with the most logical and precise word or phrase?

**A.** transposed with 

  *'Transposed' means swapped in position or order, which doesn't describe how noneconomic factors might shape a decision alongside economic ones.*

**B.** mediated by **(Correct)**

  *Correct. 'Not fully reducible to economic factors but are also ______ noneconomic factors' means location choices are also shaped — mediated — by noneconomic influences like social networks.*

**C.** decoupled from 

  *'Decoupled' means separated or unrelated, but the sentence claims noneconomic factors DO influence choices, meaning the two are linked, not decoupled.*

**D.** antecedent to 

  *'Antecedent' means coming before in time or sequence, which doesn't capture an ongoing influence or mediation of a decision.*

*Difficulty: hard*

---

##### Q111
> Businesses typically try to promote themselves, but research by Michael Luca, Abhishek Nagaraj, and Gauri Subramani suggests that some do not ______ their marketing. The researchers studied restaurants in Texas and found that those listed on a popular review website (which can be done at no cost) had revenue increases of 5 percent on average, but 33 percent of restaurants studied never listed on the site.

Which choice completes the text with the most logical and precise word or phrase?

**A.** adorn 

  *'Adorn' means to decorate, which is unrelated to whether a business takes advantage of an effective, free marketing opportunity.*

**B.** optimize **(Correct)**

  *Correct. That '33 percent ... never listed' despite the free, revenue-boosting option shows some businesses fail to fully take advantage of — optimize — their marketing.*

**C.** endorse 

  *'Endorse' means to publicly support or approve, which doesn't capture failing to maximize the effectiveness of one's own marketing strategy.*

**D.** counteract 

  *'Counteract' means to oppose or neutralize, which doesn't fit describing businesses simply not maximizing their own marketing efforts.*

*Difficulty: medium*

---

##### Q112
> Despite stated claims of global relevance, much major research on income inequality performed in the 2010s suffered from a myopic focus on a few countries in North America and Western Europe, partly due to limited data availability. Researchers would later ______ this shortcoming after gaining new access to banking records located in nations in Africa, such as Tunisia, and Eastern Europe, such as Hungary.

Which choice completes the text with the most logical and precise word or phrase?

**A.** presuppose 

  *'Presuppose' means to assume beforehand, which doesn't fit actively addressing a described flaw once new data became available.*

**B.** categorize 

  *'Categorize' means to classify, which doesn't fit addressing or fixing a research limitation through new access to data.*

**C.** mitigate **(Correct)**

  *Correct. 'Gaining new access to' more geographically diverse banking records directly addresses the earlier 'myopic focus' — that is, it mitigates, or lessens, this shortcoming.*

**D.** validate 

  *'Validate' means to confirm as correct, but the 'shortcoming' is a flaw being fixed with new data, not something being confirmed as legitimate.*

*Difficulty: medium*

---

### Information & Ideas

#### Central Ideas & Details (67 items)

##### Q1
> The following text is adapted from Johanna Spyri's 1881 novel Heidi (translated by Elisabeth Stork in 1915). Eight-year-old Heidi and her friend's grandmother are looking at some illustrated books. Heidi had come and was looking with wondering eyes at the splendid pictures in the large books, that Grandmama was showing her. Suddenly she screamed aloud, for there on the picture she saw a peaceful flock grazing on a green pasture. In the middle a shepherd was standing, leaning on his crook. The setting sun was shedding a golden light over everything. With glowing eyes Heidi devoured the scene.

Which choice best states the main idea of the text?

**A.** Heidi is upset until she sees a serene image of a pasture in one of Grandmama's books. 

  *Reads "screamed aloud" as evidence Heidi was upset beforehand, but nothing earlier in the passage shows distress — she is already looking with "wondering eyes" before the scream, and every word describing her reaction to the picture itself ("glowing eyes," "devoured the scene") is positive. The scream is excitement, not the end of upset.*

**B.** Heidi is delighted and fascinated by an image she sees in one of Grandmama's books. **(Correct)**

  *Correct. "Wondering eyes," a scream that the surrounding description marks as delight rather than fear, and "with glowing eyes Heidi devoured the scene" all point the same direction: absorbed, delighted fascination with the picture.*

**C.** Heidi is initially frightened by an image in one of Grandmama's books but quickly comes to appreciate its beauty. 

  *Invents a fear-to-appreciation arc the text never depicts. There is one reaction described — the scream immediately followed by glowing eyes and devouring the scene — not two successive emotional states. Nothing marks the scream as fright.*

**D.** Heidi is inspecting an image in one of Grandmama's books because she has never seen a shepherd with his sheep before. 

  *The passage never says why Heidi hasn't seen this before, or that she hasn't. It gives her reaction to the picture, not a biographical reason for her unfamiliarity with shepherds — that causal claim is manufactured, not stated.*

*Difficulty: medium*

---

##### Q2
> Scent is tightly interwoven with our daily lives, often evoking significant memories and important social events. This connection is of growing interest to archaeologists who hope to use it to better understand ancient rituals, trade, social hierarchies, and medicine. Although the speed at which odor molecules dissipate makes identifying ancient scents challenging, advancements in biomolecular technologies show promise in unlocking ancient aromas from preserved artifacts. Archaeological studies making use of these advancements may provide new insights into past societies.

According to the text, what is one reason some archaeologists are interested in recovering scents from ancient artifacts?

**A.** They are investigating whether people's sense of smell has declined in recent centuries. 

  *No sentence in the passage discusses the human sense of smell changing over time. This reason has no textual anchor at all.*

**B.** They believe the scents could illuminate important aspects of ancient life. **(Correct)**

  *Correct. The passage states archaeologists hope to use scent "to better understand ancient rituals, trade, social hierarchies, and medicine" — a direct match for illuminating important aspects of ancient life.*

**C.** They think that ancient scents would be enjoyable to people today. 

  *Fabricates a motive of enjoyment. The passage's interest is scholarly — understanding rituals, trade, hierarchies, medicine — never whether the smells would be pleasant to a modern audience.*

**D.** They hope to develop new medicines using ancient scent molecules. 

  *Converts "medicine" as a subject archaeologists hope to understand into "develop new medicines" as a practical goal. The passage lists ancient medicine among the things scent evidence could illuminate, not something researchers intend to manufacture from it.*

*Difficulty: medium*

---

##### Q3
> Bicycles were first mass-produced in the late nineteenth century throughout Europe and North America, allowing individuals remarkable freedom to travel longer distances quickly and comfortably. This freedom, coupled with the affordability of the vehicle, made the bicycle immensely popular. Individuals were able to live farther from their workplaces, easily visit neighboring towns, and participate in new leisure and sport activities. Bicycling quickly became a popular social endeavor, with enthusiasts forming local cycling clubs to enjoy these newfound activities with others.

Which choice best states the main idea of the text?

**A.** The widespread adoption of the bicycle in the late nineteenth century provided new opportunities for people. **(Correct)**

  *Correct. Living farther from work, visiting nearby towns, new leisure and sport activities, and forming clubs are all instances of one claim: the bicycle opened up new opportunities. This is the sentence the rest of the passage is an example of.*

**B.** The affordability of the bicycle in the late nineteenth century made it the preferred way to travel. 

  *Overclaims a comparison the text never makes. Affordability is named as one contributing factor alongside the freedom to travel, not evidence that the bicycle became travelers' preferred mode over any alternative.*

**C.** The popularity of the bicycle in the late nineteenth century gave rise to the first cycling clubs. 

  *True and it is the passage's last, most specific detail — cycling clubs are one example of the new opportunities, not the whole point. It also smuggles in "first," a claim of priority the passage never makes about these particular clubs.*

**D.** The mass production of the bicycle in the late nineteenth century made it safer for people to use. 

  *Safety is never mentioned. The passage's subject is access and freedom of movement, not a change in the bicycle's mechanical safety.*

*Difficulty: medium*

---

##### Q4
> Artist Justin Favela explained that he wanted to reclaim the importance of the piñata as a symbol in Latinx culture. To do so, he created numerous sculptures from strips of tissue paper, which is similar to the material used to create piñatas. In 2017, Favela created an impressive life-size piñata-like sculpture of the Gypsy Rose lowrider car, which was displayed at the Petersen Automotive Museum in Los Angeles, California. The Gypsy Rose lowrider was famously driven by Jesse Valadez, an early president of the Los Angeles Imperials Car Club.

According to the text, which piece of Favela's art was on display in the Petersen Automotive Museum in 2017?

**A.** A painting of Los Angeles 

  *No painting of Los Angeles is mentioned anywhere. This choice mistakes the museum's location for a subject of the artwork.*

**B.** A sculpture of a lowrider car **(Correct)**

  *Correct. The text names the piece directly: "an impressive life-size piñata-like sculpture of the Gypsy Rose lowrider car," displayed at the Petersen Automotive Museum in 2017.*

**C.** A painting of a piñata 

  *Inverts medium and subject. The sculpture is piñata-like in material and style, but its actual subject is the lowrider car, not a piñata — and it is a sculpture, not a painting.*

**D.** A sculpture of Jesse Valadez 

  *Jesse Valadez is named only as the man who drove the Gypsy Rose lowrider, not as the subject of Favela's sculpture. The sculpture depicts the car itself.*

*Difficulty: easy*

---

##### Q5
> In 2022, researchers rediscovered ancient indigenous glyphs, or drawings, on the walls of a cave in Alabama. The cave's ceiling was only a few feet high, affording no position from which the glyphs, being as wide as ten feet, could be viewed or photographed in their entirety. However, the researchers used a technique called photogrammetry to assemble numerous photos of the walls into a 3D model. They then worked with representatives of tribes originally from the region, including the Chickasaw Nation, to understand the significance of the animal and humanoid figures adorning the cave.

According to the text, what challenge did the researchers have to overcome to examine the glyphs?

**A.** The cave was so remote that the researchers couldn't easily reach it. 

  *Remoteness is never discussed. The stated obstacle concerns the cave's dimensions, not the difficulty of getting to it.*

**B.** Some of the glyphs were so faint that they couldn't be photographed. 

  *The passage never mentions faintness or contrast. The photographing problem it describes is positional — no vantage point could capture the whole glyph — not a matter of visibility.*

**C.** The researchers were unable to create a 3D model of the cave. 

  *Reverses the passage's own resolution. The text says the researchers succeeded in assembling photos into a 3D model using photogrammetry — the opposite of being unable to.*

**D.** The cave's dimensions prevented the researchers from fully viewing the glyphs. **(Correct)**

  *Correct. The low ceiling combined with glyphs up to ten feet wide meant "no position" allowed viewing or photographing them "in their entirety" — a dimensions problem, exactly as stated.*

*Difficulty: medium*

---

##### Q6
> The following text is from Shyam Selvadurai's 1994 novel Funny Boy. The seven-year-old narrator lives with his family in Sri Lanka. Radha Aunty is the narrator's aunt. Radha Aunty, who was the youngest in my father's family, had left for America four years ago when I was three, and I could not remember what she looked like. I went into the corridor to look at the family photographs that were hung there. But all the pictures were old ones, taken when Radha Aunty was a baby or young girl. Try as I might, I couldn't get an idea of what she looked like now. My imagination, however, was quick to fill in this void. ©1994 by Shyam Selvadurai.

According to the text, why does the narrator consult some family photographs?

**A.** He wants to use the photographs as inspiration for a story he is writing. 

  *No story-writing is mentioned anywhere in the passage. This motive is invented.*

**B.** He is curious about how his father dressed a long time ago. 

  *The father's family is mentioned only to establish Radha Aunty's place in it; nothing concerns his clothing or appearance. This substitutes an adjacent, unmentioned detail for the actual subject, Radha Aunty.*

**C.** He hopes the photographs will help him recall what his aunt looked like. **(Correct)**

  *Correct. "I could not remember what she looked like... I went into the corridor to look at the family photographs" states this directly as his reason for looking.*

**D.** He wants to remind his aunt of an event that is shown in an old photograph. 

  *Reverses the direction of the act. The narrator is trying to remember something himself, alone, in a corridor — not communicating anything to his aunt, who is not present and is never being reminded of anything.*

*Difficulty: easy*

---

##### Q7
> NASA's Cassini probe has detected an unusual wobble in the rotation of Mimas, Saturn's smallest moon. Using a computer model to study Mimas's gravitational interactions with Saturn and tidal forces, geophysicist Alyssa Rhoden and colleagues have proposed that this wobble could be due to a liquid ocean moving beneath the moon's icy surface. The researchers believe other moons should be examined to see if they too might have oceans hidden beneath their surfaces.

Which choice best states the main idea of the text?

**A.** Rhoden and colleagues were the first to confirm that several of Saturn's moons contain hidden oceans. 

  *Strips the passage's hedge and inflates its scope at once. The text says the ocean explanation was "proposed," for one moon, and that other moons merely "should be examined" — a suggestion for future work, not a confirmed finding about several moons.*

**B.** Research has failed to identify signs that there is an ocean hidden beneath the surface of Mimas. 

  *Says the opposite of what the passage reports. The wobble is presented as a positive sign consistent with a hidden ocean, not a failure to find one.*

**C.** Rhoden and colleagues created a new computer model that identifies moons with hidden oceans without needing to analyze the moons' rotation. 

  *Inverts the method. The wobble — an anomaly in rotation — is precisely what triggered the investigation, and the model was used to study gravitational interactions and tidal forces via that rotation, not to bypass analyzing it.*

**D.** Research has revealed that an oddity in the rotation of Mimas could be explained by an ocean hidden beneath its surface. **(Correct)**

  *Correct. This tracks the passage's structure exactly: an unusual wobble was detected, and a hidden liquid ocean has been proposed as its explanation — with the hedge ("could be due to") intact.*

*Difficulty: hard*

---

##### Q8
> Shimmering is a collective defense behavior that researchers have observed in giant honeybee colonies. When shimmering, different groups of bees flip their bodies up and down in what looks like waves. This defense is initiated when hornets hover near a colony, serving to deter the hornets from approaching the bees. Researchers hypothesize that this behavior is a specialized defense response to hornets, as it is not observed when other, larger predators approach the colony.

Which choice best states the main idea of the text?

**A.** Researchers are unsure how giant honeybees defend against predators larger than hornets. 

  *The passage never expresses uncertainty about how bees defend against larger predators — only that shimmering specifically is not observed against them. No claim about a different, unclear defense mechanism is made.*

**B.** Researchers think that shimmering in giant honeybees is a specific defense against hornets. **(Correct)**

  *Correct. Matches the passage's hypothesis directly: shimmering is "a specialized defense response to hornets," supported by its absence when other, larger predators approach.*

**C.** Hornets are known to be the main predator of giant honeybees. 

  *Hornets are identified as the trigger for shimmering, not ranked as the colony's "main predator" against all others — that superlative is never made.*

**D.** Several different species of insects use shimmering to defend against hornets. 

  *Expands scope beyond the text, which discusses only giant honeybees. No other insect species are mentioned as also using shimmering.*

*Difficulty: medium*

---

##### Q9
> Oluwaseyi Moejoh cofounded U-recycle Initiative Africa when she was only a teenager. Moejoh and her team founded the organization to teach young people how their actions affect the environment and why recycling is important. For example, the organization put on an exhibit of art made using recycled materials.

According to the text, what is one reason Moejoh and others founded U-recycle Initiative Africa?

**A.** To bring attention to overlooked African artists 

  *The art exhibit is one example of what the organization does, not a stated reason for founding it, and nothing about "overlooked African artists" appears in the text at all.*

**B.** To teach young people why recycling is important **(Correct)**

  *Correct. Stated directly: the team "founded the organization to teach young people how their actions affect the environment and why recycling is important."*

**C.** To help adults gain important outdoor skills 

  *Wrong audience and wrong content — the organization's stated audience is young people, not adults, and outdoor skills are never mentioned.*

**D.** To give teenagers advice about starting businesses 

  *Nothing in the passage concerns business advice. This reason has no basis in the text.*

*Difficulty: easy*

---

##### Q10
> Microplastics are pieces of plastic that are smaller than a grain of rice. These small plastics can be found in large quantities in ocean waters. Ecologist Jessica Reichert and her team are studying the role reef-building corals have in capturing microplastics from ocean waters. Through research, her team has found that these corals may be storing up to 20 million kilograms of microplastics each year in their skeletons and tissues.

Which choice best states the main idea of the text?

**A.** Ecologists are interested in learning more about how certain corals build large reefs. 

  *Mistakes the descriptor "reef-building corals" for the passage's actual topic. The research described is about how these corals capture and store microplastics, not about reef construction.*

**B.** Questions remain around the impact certain corals have on ocean ecosystems. 

  *Fabricates an open question. The passage reports a specific finding — an estimated storage amount — not unresolved uncertainty about ecosystem impact.*

**C.** Microplastics are small pieces of plastic that can be found in ocean waters. 

  *True and it is the passage's opening definition — the setup the rest of the text builds on, not the finding itself. A summary that stops at the definition never reaches Reichert's team's actual result.*

**D.** Ecologists predict that corals store large amounts of microplastics from ocean waters. **(Correct)**

  *Correct. Matches the passage's finding: the team "found that these corals may be storing up to 20 million kilograms of microplastics each year."*

*Difficulty: medium*

---

##### Q11
> Psychologists wanted to test how young children think about rewards and fairness. In an experiment, two teachers handed out rewards while children (ages four to six) watched. The teachers gave out the same number of rewards, but one of them counted the rewards out loud. The children were then asked who was fairer. 73% chose the teacher who counted. The psychologists think that counting showed the children that the teacher wanted to be fair. The children may have believed that the teacher who did not count did not care about fairness.

Which choice best states the main idea of the text?

**A.** Psychologists think children cannot understand the concept of fairness until they are six years old. 

  *No age threshold is proposed. The study includes children ages four to six all forming fairness judgments; there is no claim that understanding begins only at six.*

**B.** An experiment found that counting out loud is the best way to teach mathematical concepts to children. 

  *The study is about fairness perception, not mathematics instruction. Counting out loud is used here as a manipulation that signals fair intent, not as a teaching method — this repurposes a real detail into an unrelated claim.*

**C.** Psychologists think young children expect to be rewarded when the children show that they care about fairness. 

  *Swaps subject and object. It's the teacher's counting that signals the teacher cares about fairness, and it's the teacher the children then judge as fairer — not a claim about children expecting rewards for their own fairness-caring.*

**D.** An experiment showed that the way rewards are given out may affect whether young children think the situation is fair. **(Correct)**

  *Correct. Same number of rewards, different manner of distribution (counted aloud or not), and a large majority judged fairness differently as a result — exactly this claim.*

*Difficulty: hard*

---

##### Q12
> Scrapbooks of saved fabric pieces were commonly kept by women in the nineteenth-century United States, but few are as meticulously detailed as Hannah Ditzler Alspaugh's work. Alongside each piece of fabric, Alspaugh recorded intimate memories, such as dressmaking with her sister. Additionally, she listed the prices and how she used the fabric. Historians note that by representing fifty years of changing textures, patterns, and dress styles, the scrapbook is a record of nineteenth-century textiles and dressmaking as well as Alspaugh's life.

Which choice best states the main idea of the text?

**A.** Alspaugh inspired other women to save pieces of fabric in scrapbooks and provide historical records of nineteenth-century fashions in the United States. 

  *Invents a causal claim. The passage says fabric scrapbooks were "commonly kept" by women generally — implying the practice predates or is independent of Alspaugh — not that she inspired it.*

**B.** Historians rely on fabric scrapbooks to understand how fashions changed throughout the nineteenth-century United States. 

  *Generalizes one exceptional case into a field-wide methodology claim. The passage is about Alspaugh's unusually detailed scrapbook specifically, not a general statement about how historians as a group work.*

**C.** Fabric scrapbooks were a popular hobby for many women in the nineteenth-century United States. 

  *True and it is the opening background sentence — the setup the passage immediately turns away from with "but few are as meticulously detailed as" Alspaugh's. What distinguishes her scrapbook, not the general popularity of the hobby, is the point.*

**D.** Alspaugh's scrapbook provides a detailed account of her life and historical record of fashion trends in the nineteenth-century United States. **(Correct)**

  *Correct. Matches the closing claim directly: the scrapbook "is a record of nineteenth-century textiles and dressmaking as well as Alspaugh's life."*

*Difficulty: hard*

---

##### Q13
> To make her art more widely available, graphic artist Elizabeth Catlett turned to linocuts. In linocut printing, an artist carves an image into a sheet of linoleum to create a stamp that is used to mass-produce prints. In the linocut series The Black Woman (1946–1947), Catlett depicts the everyday experiences of Black women alongside the achievements of well-known Black women. This pairing invites the viewer to draw connections among the women. The linocut process enabled Catlett's work to reach a wide audience and supported her aim to unite Black women through her art.

According to the text, what is significant about Catlett's use of linocut printing?

**A.** Linocut printing involved using materials that were readily available to Catlett. 

  *Material availability is never discussed. The passage's stated significance is about audience reach and connection, not access to supplies.*

**B.** Linocut printing helped Catlett use art to connect people, especially Black women. **(Correct)**

  *Correct. Matches the closing claim: the process "enabled Catlett's work to reach a wide audience and supported her aim to unite Black women through her art."*

**C.** Catlett became commercially successful once she started using linocut printing. 

  *No claim about commercial success appears anywhere in the passage.*

**D.** Catlett was one of the first Black artists to use linocut printing. 

  *Invents a priority claim. The passage never ranks Catlett against other artists as first, early, or otherwise, in her use of the technique.*

*Difficulty: easy*

---

##### Q14
> The following text is from Edith Nesbit's 1902 novel Five Children and It. Five young siblings have just moved with their parents from London to a house in the countryside that they call the White House. It was not really a pretty house at all. It was quite ordinary, and mother thought it was rather inconvenient, and was quite annoyed at there being no shelves, to speak of, and hardly a cupboard in the place. Father used to say that the ironwork on the roof and coping was like an architect's nightmare. But the house was deep in the country, with no other house in sight, and the children had been in London for two years, without so much as once going to the seaside even for a day by an excursion train, and so the White House seemed to them a sort of Fairy Palace set down in an Earthly Paradise.

Which choice best states the main idea of the text?

**A.** Although their parents believe the house has several drawbacks, the children are enchanted by it. **(Correct)**

  *Correct. Matches the passage's structure exactly: the parents' complaints (no shelves, an "architect's nightmare") give way at "But" to the children's view of the house as a "Fairy Palace set down in an Earthly Paradise."*

**B.** The children don't like the house nearly as much as their parents do. 

  *Reverses the passage's actual relationship. It is the parents who complain — mother finds it inconvenient, father calls it a nightmare — while the children are the ones enchanted.*

**C.** Each member of the family admires a different characteristic of the house. 

  *Invents a structure the passage doesn't have. The parents criticize as a pair and the children are enchanted as a group; there is no itemized list of each family member admiring something distinct.*

**D.** The house is beautiful and well built, but the children miss their old home in London. 

  *Contradicts the text on both counts. The house is explicitly "not really a pretty house at all" and an "architect's nightmare," and nothing suggests the children miss London — after two years there without so much as a day at the seaside, the countryside reads as relief, not loss.*

*Difficulty: medium*

---

##### Q15
> The following text is from Beatrice Harraden's 1894 novel Ships that Pass in the Night. In an old second-hand bookshop in London, an old man sat reading Gibbon's History of Rome. He did not put down his book when the postman brought him a letter. He just glanced indifferently at the letter, and impatiently at the postman. Zerviah Holme did not like to be interrupted when he was reading Gibbon; and as he was always reading Gibbon, an interruption was always regarded by him as an insult.

Based on the text, how did Zerviah Holme most likely feel when the letter was delivered?

**A.** He felt relieved because he had been expecting an important letter. 

  *Contradicts the text. He "glanced indifferently at the letter" — the opposite of the anticipation relief would require.*

**B.** He felt excited because the letter was from a good friend. 

  *The letter's sender is never identified, and excitement contradicts the described indifference and impatience.*

**C.** He felt sad because the postman did not stop to talk with him before leaving. 

  *Invents a cause the text never gives. Nothing is said about the postman talking or not talking — his annoyance is tied to the interruption of his reading, not to any social exchange with the postman.*

**D.** He felt annoyed because he was interrupted while reading his favorite author. **(Correct)**

  *Correct. He glances "impatiently at the postman," dislikes being interrupted while reading Gibbon, and since he is "always reading Gibbon," any interruption is "regarded by him as an insult."*

*Difficulty: medium*

---

##### Q16
> The following text is adapted from Frances Hodgson Burnett's 1911 novel The Secret Garden. Mary, a young girl, recently found an overgrown hidden garden. Mary was an odd, determined little person, and now she had something interesting to be determined about, she was very much absorbed, indeed. She worked and dug and pulled up weeds steadily, only becoming more pleased with her work every hour instead of tiring of it. It seemed to her like a fascinating sort of play.

Which choice best states the main idea of the text?

**A.** Mary hides in the garden to avoid doing her chores. 

  *Nothing about hiding or avoiding chores appears in the passage. The gardening is presented as something Mary is drawn to, not an escape from obligation.*

**B.** Mary is getting bored with pulling up so many weeds in the garden. 

  *Says the opposite of the text: she becomes "more pleased with her work every hour instead of tiring of it."*

**C.** Mary is clearing out the garden to create a space to play. 

  *Takes the simile "a fascinating sort of play" — which describes how the gardening feels to her — and turns it into a literal goal of creating a play space, which the passage never states.*

**D.** Mary feels very satisfied when she's taking care of the garden. **(Correct)**

  *Correct. Matches "only becoming more pleased with her work every hour" and finding it "a fascinating sort of play" — sustained satisfaction in the task.*

*Difficulty: medium*

---

##### Q17
> The following text is adapted from Edith Nesbit's 1906 novel The Railway Children. Mother did not spend all her time in paying dull [visits] to dull ladies, and sitting dully at home waiting for dull ladies to pay [visits] to her. She was almost always there, ready to play with the children, and read to them, and help them to do their home-lessons, Besides this she used to write stories for them while they were at school, and read them aloud after tea, and she always made up funny pieces of poetry for their birthdays and for other great occasions.

According to the text, what is true about Mother?

**A.** She wishes that more ladies would visit her. 

  *Contradicts the passage, which opens by saying she did not spend her time on dull visits or waiting for ladies to call on her.*

**B.** Birthdays are her favorite special occasion. 

  *Birthdays are one occasion among "other great occasions" listed; no ranking of favorites is given.*

**C.** She creates stories and poems for her children. **(Correct)**

  *Correct. Directly stated: she "used to write stories for them" and "made up funny pieces of poetry for their birthdays and for other great occasions."*

**D.** Reading to her children is her favorite activity. 

  *The passage lists several activities — playing, reading, helping with lessons, writing stories — without ranking any of them as a favorite.*

*Difficulty: easy*

---

##### Q18
> Arthropods—brine shrimp, hawk moths, and many other invertebrate animals—have a nervous system made up of a brain, nerve cord, and other nerves. Researchers have gained insights about this system in ancient arthropods from traces found in various fossils. For example, in a study of two fossils of the extinct arthropod species Mollisonia symmetrica, Javier Ortega-Hernández, James Weaver, and team observed clear signs of a nerve cord. They also saw possible indications of a syngangalion, a brain-like mass of nerves. Researchers hope to identify more features of the nervous systems of prehistoric arthropods as additional fossils are found.

Which choice best states the main idea of the text?

**A.** There are several similarities between the brains of hawk moths and the brains of brine shrimp. 

  *Fabricates a comparison. Hawk moths and brine shrimp are named only as living examples of arthropods in general, not compared to one another at all.*

**B.** Fossil evidence can contribute to the understanding of the nervous system in ancient arthropods. **(Correct)**

  *Correct. Matches the passage's core claim: researchers "have gained insights about this system in ancient arthropods from traces found in various fossils," illustrated by the Mollisonia symmetrica study.*

**C.** Newly discovered fossils suggest that ancient hawk moths and ancient brine shrimp had spines. 

  *Substitutes the wrong subject and the wrong feature. The fossil study concerns Mollisonia symmetrica, an extinct species — not hawk moths or brine shrimp, which appear only as modern examples — and it describes a nerve cord, not spines.*

**D.** Researchers need to focus on finding more fossils of ancient arthropods. 

  *Converts a description into a prescription. The passage says researchers "hope to identify more features... as additional fossils are found" — an expressed hope contingent on future discovery, not an imperative about what they need to prioritize.*

*Difficulty: hard*

---

##### Q19
> Archaeologist Veronica Waweru visited the Lewa Wildlife Conservancy in Kenya. While exploring there, Waweru noticed many rows of shallow pits carved into stone. Waweru believed the pits could have been used as game boards to play ancient versions of mancala, a two-person strategy game that is still popular today. Some of the more recent pits were carved on top of older pits. This led Waweru to think that the game was played at the site for a long time.

According to the text, why does Waweru think that mancala was played at the site for a long time?

**A.** Some of the newer pits were carved on top of the older pits. **(Correct)**

  *Correct. Stated directly: "Some of the more recent pits were carved on top of older pits. This led Waweru to think that the game was played at the site for a long time."*

**B.** She noticed many rows of shallow pits carved into stone. 

  *This is what led Waweru to think the pits were mancala boards at all, not what led her to conclude the game was played there for a long time — the right observation, but it answers a different question than the one asked.*

**C.** She discovered the pits at the Lewa Wildlife Conservancy. 

  *Location has nothing to do with the duration claim; this detail is real but irrelevant to the stem's specific interrogative.*

**D.** Some of the pits were shallow and others were quite deep. 

  *Contradicts the text, which describes the pits uniformly as "shallow" — it never distinguishes some as deep.*

*Difficulty: medium*

---

##### Q20
> A common assumption among art historians is that the invention of photography in the mid-nineteenth century displaced the painted portrait in the public consciousness. The diminishing popularity of the portrait miniature, which coincided with the rise of photography, seems to support this claim. However, photography's impact on the portrait miniature may be overstated. Although records from art exhibitions in the Netherlands from 1820 to 1892 show a decrease in the number of both full-sized and miniature portraits submitted, this trend was established before the invention of photography.

Based on the text, what can be concluded about the diminishing popularity of the portrait miniature in the nineteenth century?

**A.** Factors other than the rise of photography may be more directly responsible for the portrait miniature's decline. **(Correct)**

  *Correct. Matches the passage's turn: photography's impact "may be overstated," since the exhibition-submission decline "was established before the invention of photography" — pointing toward some other cause.*

**B.** Although portrait miniatures became less common than photographs, they were widely regarded as having more artistic merit. 

  *No comparison of artistic merit is made anywhere in the passage. This value judgment is invented.*

**C.** The popularity of the portrait miniature likely persisted for longer than art historians have assumed. 

  *Misreads a challenge to the cause as a challenge to the fact. The passage confirms the decline happened — records show a decrease — and questions only what caused it, not whether or when it occurred.*

**D.** As demand for portrait miniatures decreased, portrait artists likely shifted their creative focus to photography. 

  *Invents a claim about artists changing mediums. The passage discusses exhibition submission records, not the career choices of individual portrait artists.*

*Difficulty: hard*

---

##### Q21
> Biologists have predicted that birds' feather structures vary with habitat temperature, but this hadn't been tested in mountain environments. Ornithologist Sahas Barve studied feathers from 249 songbird species inhabiting different elevations—and thus experiencing different temperatures—in the Himalaya Mountains. He found that feathers of high-elevation species not only have a greater proportion of warming downy sections to flat and smooth sections than do feathers of low-elevation species, but high-elevation species' feathers also tend to be longer, providing a thicker layer of insulation.

Which choice best states the main idea of the text?

**A.** Barve's investigation shows that some species of Himalayan songbirds have evolved feathers that better regulate body temperature than do the feathers of other species, contradicting previous predictions. 

  *Reverses confirm and contradict. Barve's study is the first test of an existing prediction in mountain environments, and it supports that prediction — it does not contradict it.*

**B.** Barve found an association between habitat temperature and feather structure among Himalayan songbirds, lending new support to a general prediction. **(Correct)**

  *Correct. Biologists had predicted feather structure varies with habitat temperature but hadn't tested it in mountains; Barve's study tests it there and finds the pattern holds — new support for an existing prediction.*

**C.** Barve discovered that songbirds have adapted to their environment by growing feathers without flat and smooth sections, complicating an earlier hypothesis. 

  *Distorts a proportion into an absence, and reverses support into complication. High-elevation feathers have a greater proportion of downy to flat/smooth sections, not zero flat and smooth sections — and the finding supports the hypothesis rather than complicating it.*

**D.** The results of Barve's study suggest that the ability of birds to withstand cold temperatures is determined more strongly by feather length than feather structure, distorting an established belief. 

  *Invents a competition between two findings the passage presents as complementary — greater downy proportion and greater length are both cited as contributing to insulation, not weighed against each other — and again reverses support into distortion of belief.*

*Difficulty: sat-hardest*

---

##### Q22
> Paleontologists searching for signs of ancient life have found many fossilized specimens of prehistoric human ancestors, including several from the Pleistocene era discovered in a geological formation in the Minatogawa quarry in Japan. However, to study the emergence of the earliest multicellular organisms to appear on Earth, researchers must turn elsewhere, such as to the Ediacaran geological formation at Mistaken Point in Canada. A UNESCO World Heritage Site, the 146-hectare reserve contains more than 10,000 fossils that together document a critical moment in evolutionary history.

What does the text indicate about the geological formation at Mistaken Point?

**A.** It holds a greater number of fossils but from a smaller variety of species than the formation in the Minatogawa quarry does. 

  *Fabricates a comparison. A fossil count is given for Mistaken Point alone; no comparable count or species-variety figure is given for Minatogawa, so no such comparison is supported.*

**B.** It has provided evidence that the earliest human species may have emerged before the Pleistocene era. 

  *Substitutes the wrong subject. Mistaken Point documents the emergence of the earliest multicellular organisms, in the Ediacaran era — long before humans existed — not the emergence of human species.*

**C.** It is widely considered by paleontologists to be the most valuable source of information about prehistoric life forms. 

  *Invents a superlative consensus. The passage describes the site factually — UNESCO status, hectare count, fossil count — without ranking its value against other sites.*

**D.** It contains specimens from an older time period than those found in the formation in the Minatogawa quarry. **(Correct)**

  *Correct. Mistaken Point's Ediacaran formation documents the earliest multicellular organisms on Earth, while Minatogawa's Pleistocene formation holds far more recent human-ancestor fossils — Mistaken Point's specimens are older.*

*Difficulty: hard*

---

##### Q23
> The following text is adapted from Edgar Allan Poe's 1849 story "Landor's Cottage." During a pedestrian trip last summer, through one or two of the river counties of New York, I found myself, as the day declined, somewhat embarrassed about the road I was pursuing. The land undulated very remarkably; and my path, for the last hour, had wound about and about so confusedly, in its effort to keep in the valleys, that I no longer knew in what direction lay the sweet village of B——, where I had determined to stop for the night.

Which choice best states the main idea of the text?

**A.** The narrator remembers a trip he took and admits to getting lost. **(Correct)**

  *Correct. "Somewhat embarrassed about the road," a path that "wound about and about so confusedly," and no longer knowing the way to the village he intended to reach all describe getting lost, recalled as a past trip ("last summer").*

**B.** The narrator recalls fond memories of a journey that he took through some beautiful river counties. 

  *Misreads the tone. "Embarrassed," "confusedly," and not knowing which way to go are not fond memories, and the passage never dwells on the counties' beauty — "sweet village" names a destination, not a landscape description.*

**C.** The narrator describes what he saw during a long trip through a frequently visited location. 

  *Nothing suggests the narrator visits this area often, and the passage centers his disorientation about direction, not a catalog of sights.*

**D.** The narrator explains the difficulties he encountered on a trip and how he overcame them. 

  *Overclaims resolution. The excerpt ends with the narrator still lost, not knowing which direction to take — no overcoming of the difficulty is shown.*

*Difficulty: medium*

---

##### Q24
> Philadelphia's Black Pearl Chamber Orchestra, founded by Jeri Lynne Johnson, performs classical music, from well-known compositions by Beethoven to contemporary works by Jessie Montgomery. For the orchestra's iConduct! program, Johnson invites community members to learn some basic elements of conducting and then experience conducting the Black Pearl orchestra themselves.

Which choice best states the main idea of the text?

**A.** The Black Pearl orchestra performs music from all over the world but mostly performs music composed by Philadelphians. 

  *Fabricates both claims. No geographic range of music "from all over the world" is mentioned, and no claim ties most performed music to composers from Philadelphia — the range given is only well-known to contemporary, via Beethoven and Montgomery.*

**B.** Johnson founded the Black Pearl orchestra to perform classical music by contemporary artist Jessie Montgomery. 

  *Narrows a broad founding purpose to a single example. The orchestra performs classical music spanning Beethoven to contemporary composers; Montgomery is one named example of that range, not the stated reason for founding it.*

**C.** The Black Pearl orchestra gives community members the chance to both listen to and participate in classical music performance. **(Correct)**

  *Correct. Covers both halves of the passage: the orchestra performs classical music for audiences, and its iConduct! program lets community members participate by conducting it themselves.*

**D.** Johnson has community members conduct an orchestra to demonstrate how difficult the task is. 

  *Inverts the program's stated purpose. iConduct! is framed as an invitation and an experience for community members, not a demonstration designed to show that conducting is hard.*

*Difficulty: medium*

---

##### Q25
> To dye wool, Navajo (Diné) weaver Lillie Taylor uses plants and vegetables from Arizona, where she lives. For example, she achieved the deep reds and browns featured in her 2003 rug In the Path of the Four Seasons by using Arizona dock roots, drying and grinding them before mixing the powder with water to create a dye bath. To intensify the appearance of certain colors, Taylor also sometimes mixes in clay obtained from nearby soil.

Which choice best states the main idea of the text?

**A.** Reds and browns are not commonly featured in most of Taylor's rugs. 

  *Contradicts the one example given — deep reds and browns are exactly what her 2003 rug featured — and no claim about "most" of her rugs is supported by a single named example.*

**B.** Taylor draws on local resources in the approach she uses to dye wool. **(Correct)**

  *Correct. Matches the passage directly: plants and vegetables "from Arizona, where she lives," Arizona dock roots, and clay "obtained from nearby soil" are all local resources used in her dyeing process.*

**C.** Taylor finds it difficult to locate Arizona dock root in the desert. 

  *No difficulty of any kind is mentioned. The passage describes her process without commenting on how easy or hard it is to find materials.*

**D.** In the Path of the Four Seasons is widely acclaimed for its many colors and innovative weaving techniques. 

  *Invents critical acclaim and confuses dyeing with weaving. The passage discusses her dyeing methods, never her weaving technique, and makes no claim about the rug's reception.*

*Difficulty: medium*

---

##### Q26
> The painter María Izquierdo played an important role in the development of twentieth-century Mexican art, but her work has never been well-known in the United States except among art historians. One reason for Izquierdo's relative obscurity is the enormous popularity of some of her peers. In particular, the painters Frida Kahlo and Diego Rivera have so captivated the interest of US audiences that Izquierdo and other Mexican artists from the period often get overlooked, despite the high quality of their work.

Which choice best states the main idea of the text?

**A.** Izquierdo's work is not as well-known in the United States as it should be because Kahlo and Rivera draw so much of the public's attention. **(Correct)**

  *Correct. Matches the passage's stated reason directly: Kahlo and Rivera's popularity has "so captivated the interest of US audiences" that Izquierdo is "often overlooked, despite the high quality" of her work.*

**B.** During Izquierdo's lifetime, her paintings were displayed in galleries in the United States much more frequently than paintings by Kahlo and Rivera were. 

  *Says the opposite of the text, which describes Izquierdo as relatively obscure in the US precisely because Kahlo and Rivera attract far more attention there.*

**C.** Izquierdo painted some of the same subjects that Kahlo and Rivera painted but used different techniques than they used. 

  *No comparison of subject matter or technique is made anywhere in the passage — only a comparison of relative fame and public attention.*

**D.** Few of Izquierdo's works are in galleries today because she produced only a small number of paintings. 

  *Invents a cause the text doesn't give. The passage attributes her obscurity to her peers' popularity capturing attention, not to a small output on her part.*

*Difficulty: medium*

---

##### Q27
> Many intellectual histories of the Black Power movement of the 1960s and 1970s rely heavily on essays and other explicitly ideological works as primary sources, a tendency that can overrepresent the perspectives of a small number of thinkers, most of whom were male. Historian Ashley D. Farmer has shown that expanding the array of primary sources to encompass more types of print material—including political cartoons, advertisements, and artwork—leads to a much better understanding of the movement and the crucial and diverse roles that Black women played in shaping it.

Which choice best describes the main idea of the text?

**A.** Farmer's methods and research have enriched the historical understanding of the Black Power movement and Black women's contributions to it. **(Correct)**

  *Correct. Matches the passage's claim directly: expanding the range of primary sources, as Farmer has shown, "leads to a much better understanding of the movement" and of Black women's "crucial and diverse roles" in it.*

**B.** Before Farmer's research, historians had largely ignored the intellectual dimensions of the Black Power movement. 

  *Overstates the prior problem. The critique is that histories over-relied on a narrow set of ideological sources dominated by a few male thinkers, not that intellectual history of the movement had been ignored entirely.*

**C.** Other historians of the Black Power movement have criticized Farmer's use of unconventional primary sources. 

  *No reaction from other historians to Farmer's work is mentioned anywhere in the passage.*

**D.** The figures in the Black Power movement whom historians tend to cite would have agreed with Farmer's conclusions about women's roles. 

  *The passage never speculates about how the traditionally cited thinkers would react to Farmer's conclusions.*

*Difficulty: medium*

---

##### Q28
> In many of his sculptures, artist Richard Hunt uses broad forms rather than extreme accuracy to hint at specific people or ideas. In his first major work, Arachne (1956), Hunt constructed the mythical character Arachne, a weaver who was changed into a spider, by welding bits of steel together into something that, although vaguely human, is strange and machine-like. And his large bronze sculpture The Light of Truth (2021) commemorates activist and journalist Ida B. Wells using mainly flowing, curved pieces of metal that create stylized flame.

Which choice best states the text's main idea about Hunt?

**A.** He often depicts the subjects of his sculptures using an unrealistic style. **(Correct)**

  *Correct. Matches the opening claim — "broad forms rather than extreme accuracy" — and both examples: Arachne is "vaguely human... strange and machine-like," and The Light of Truth uses "stylized flame" rather than a literal likeness.*

**B.** He uses different kinds of materials depending on what kind of sculpture he plans to create. 

  *Both named works use metal — welded steel and bronze — and no claim links material choice to sculpture type; this detail is invented.*

**C.** He tends to base his art on important historical figures rather than fictional characters. 

  *Contradicted by the passage's own two examples: Arachne is explicitly a mythical, fictional character, while Ida B. Wells is a historical figure — one of each, not a stated preference for one over the other.*

**D.** He has altered his approach to sculpture over time, and his works have become increasingly abstract. 

  *Invents a trend. The two examples span 1956 to 2021, but the passage frames unrealistic, broad-form depiction as something Hunt "often" does consistently, not as a progression toward increasing abstraction.*

*Difficulty: hard*

---

##### Q29
> The following text is adapted from Robert Louis Stevenson's 1883 novel Treasure Island. Bill is a sailor staying at the Admiral Benbow, an inn run by the narrator's parents. Every day when [Bill] came back from his stroll he would ask if any seafaring men had gone by along the road. At first we thought it was the want of company of his own kind that made him ask this question, but at last we began to see he was desirous to avoid them. When a seaman did [stay] at the Admiral Benbow (as now and then some did) he would look in at him through the curtained door before he entered the parlour; and he was always sure to be as silent as a mouse when any such was present.

According to the text, why does Bill regularly ask about "seafaring men"?

**A.** He's hoping to find an old friend and fellow sailor. 

  *This is the explanation the passage explicitly raises and then discards: "At first we thought it was the want of company of his own kind... but at last we began to see he was desirous to avoid them."*

**B.** He's trying to secure a job as part of the crew on a new ship. 

  *No job or new ship is mentioned anywhere in the passage.*

**C.** He isn't sure that other guests at the inn will be welcoming of sailors. 

  *Substitutes the wrong subject. Bill's own wariness of encountering seafaring men is what's described, not a worry about other guests' attitudes toward sailors.*

**D.** He doesn't want to encounter any other sailor unexpectedly. **(Correct)**

  *Correct. Matches "he was desirous to avoid them" plus his cautious behavior — peering through the curtained door and staying "silent as a mouse" whenever a seaman is present.*

*Difficulty: medium*

---

##### Q30
> The following text is adapted from Guy de Maupassant's nineteenth-century short story "The Trip of Le Horla" (translated by Albert M. C. McMaster, A. E. Henderson, Mme. Quesada, et al.). The narrator is part of a group traveling in a hot-air balloon at night. The earth no longer seems to exist, it is buried in milky vapors that resemble a sea. We are now alone in space with the moon, which looks like another balloon travelling opposite us; and our balloon, which shines in the air, appears like another, larger moon, and a world wandering in the sky amid the stars, through infinity. We no longer speak, think nor live; we float along through space in delicious inertia. The air which is bearing us up has made of us all beings which resemble itself, silent, joyous, irresponsible beings, peculiarly alert, although motionless.

Which choice best states the main idea of the text?

**A.** The narrator feels a growing sense of isolation even though his companions are nearby during the balloon ride. 

  *Misreads the tone as negative and misplaces the companions. The described state is pleasurable ("delicious," "joyous") and explicitly shared — "made of us all beings which resemble itself" — not an isolation felt apart from the companions.*

**B.** The narrator and his companions are completely absorbed in the change in perspective they gain while riding in the balloon. **(Correct)**

  *Correct. The earth "no longer seems to exist," the moon looks like another balloon, and the group floats in "delicious inertia," transformed into "silent, joyous... beings" — a shared, complete absorption in the transformed perspective the flight offers.*

**C.** The narrator and his companions are troubled by the disorienting effects of the altitude while riding in the balloon. 

  *Contradicts the tone throughout: "delicious inertia" and "joyous" describe a pleasant, serene state, not distress or trouble.*

**D.** The narrator is pleasantly surprised by his companions' unrestrained enthusiasm about the sensation of riding in the balloon. 

  *Invents enthusiasm and surprise the text doesn't describe. The companions are said to share the narrator's own silent, still state ("we no longer speak"), not to display enthusiasm he then reacts to.*

*Difficulty: hard*

---

##### Q31
> The recovery of a 1,000-year-old Chinese shipwreck in the Java Sea near present-day Indonesia has yielded a treasure trove of artifacts, including thousands of small ceramic bowls. Using a portable X-ray fluorescence analyzer tool, Lisa Niziolek and her team were able to detect the chemical composition of these bowls without damaging them. By comparing the chemical signatures of the bowls with those of the materials still at old Chinese kiln sites, Niziolek and her team can pinpoint which Chinese kilns likely produced the ceramic bowls.

Which choice best states the main idea of the text?

**A.** Because of a new technology, researchers can locate and recover more shipwrecks than they could in the past. 

  *Misattributes the tool's function. The X-ray fluorescence analyzer is used to study the chemical composition of already-recovered bowls, not to locate or recover shipwrecks.*

**B.** Researchers have been able to identify the location of a number of Chinese kilns in operation 1,000 years ago. 

  *Reverses what's known and unknown. The kiln sites are the known reference point ("materials still at old Chinese kiln sites"); what the researchers are determining is which kiln produced the bowls, not where the kilns are located.*

**C.** With the help of a special tool, researchers have determined the likely origin of bowls recovered from a shipwreck. **(Correct)**

  *Correct. The portable analyzer lets researchers compare the bowls' chemical signatures to kiln-site materials and "pinpoint which Chinese kilns likely produced the ceramic bowls" — determining their likely origin.*

**D.** Before the invention of portable X-ray fluorescence, researchers needed to take a small piece out of an artifact to analyze its components. 

  *The passage states this tool works "without damaging" the bowls but never claims researchers previously had to remove a piece of the artifact — that prior practice is inferred and asserted as fact, not stated.*

*Difficulty: hard*

---

##### Q32
> The following text is adapted from Christina Rossetti's 1881 poem "Monna Innominata 2." I wish I could remember that first day, First hour, first moment of your meeting me, If bright or dim the season, it might be Summer or Winter for [all] I can say; So unrecorded did it slip away, So blind was I to see and to foresee, So dull to mark the budding of my tree That would not blossom yet for many a May.

Which choice best states the main idea of the text?

**A.** The speaker celebrates how the passage of time has strengthened a relationship that once seemed unimportant. 

  *Misreads the tone as celebration when it is regret. The speaker mourns not remembering the relationship's start, and never describes it as once seeming "unimportant" — only that she was too "blind" to foresee its future significance.*

**B.** Because the speaker did not anticipate how important a relationship would become, she cannot recall how the relationship began, which she regrets. **(Correct)**

  *Correct. "I wish I could remember that first day... So unrecorded did it slip away, so blind was I to see and to foresee" states exactly this: unanticipated importance, an unremembered beginning, and regret.*

**C.** As the anniversary of the beginning of an important relationship approaches, the speaker feels conflicted about how best to commemorate it. 

  *Invents plot details absent from the poem — no approaching anniversary and no act of commemoration are mentioned. The poem is about failing to remember the past, not planning for a present-day event.*

**D.** After years of neglecting a once valuable relationship, the speaker worries it may be too late for her to salvage the relationship. 

  *Invents both neglect and a present fear of loss. The speaker's regret concerns not having noticed or remembered the relationship's importance at its start — nothing suggests she is currently neglecting it or fears losing it.*

*Difficulty: hard*

---

##### Q33
> The ice melted on a Norwegian mountain during a particularly warm summer in 2019, revealing a 1,700-year-old sandal to a mountaineer looking for artifacts. The sandal would normally have degraded quickly, but it was instead well preserved for centuries by the surrounding ice. According to archaeologist Espen Finstad and his team, the sandal, like those worn by imperial Romans, wouldn't have offered any protection from the cold in the mountains, so some kind of insulation, like fabric or animal skin, would have needed to be worn on the feet with the sandal.

What does the text indicate about the discovery of the sandal?

**A.** Temperatures contributed to both protecting and revealing the sandal. **(Correct)**

  *Correct. Cold preserved the sandal for centuries in the ice, and a "particularly warm summer" then melted that ice, revealing it — temperature drives both effects.*

**B.** The discovery revealed that the Roman Empire had more influence on Norway than archaeologists previously assumed. 

  *Mistakes a stylistic comparison for a historical claim. The sandal is compared to Roman sandals only in design ("like those worn by imperial Romans"), never presented as evidence of Roman cultural or political influence on Norway.*

**C.** Archaeologists would have found the sandal eventually without help from the general public. 

  *This counterfactual is never addressed. The passage doesn't discuss whether archaeologists would have found the sandal without the mountaineer's discovery.*

**D.** The sandal would have degraded if it hadn't been removed from the ice. 

  *Reverses the actual causation. The sandal was preserved specifically because it stayed in the ice; remaining in the ice prevented degradation, it didn't cause it.*

*Difficulty: hard*

---

##### Q34
> To protect themselves when attacked, hagfish—jawless marine animals that resemble eels—will release large quantities of slimy, mucus-like threads. Because these threads are unusually strong and elastic, scientist Atsuko Negishi and her colleagues have been trying to recreate them in a lab as an eco-friendly alternative to petroleum-based fibers that are often used in fabrics. The researchers want to reproduce the threads in the lab because farming hagfish for their slime would be expensive and potentially harmful to the hagfish.

Which choice best states the text's main idea?

**A.** The slimy threads that hagfish release might help researchers create a new kind of fabric. **(Correct)**

  *Correct. Matches the passage's stated goal directly: recreating the threads in a lab "as an eco-friendly alternative to petroleum-based fibers that are often used in fabrics."*

**B.** Hagfish have inspired researchers to develop a new petroleum-based fabric. 

  *Says the opposite of the text. The threads are being developed as an alternative to petroleum-based fibers, not as a new petroleum-based fabric.*

**C.** Hagfish are not well suited to being raised in captivity. 

  *Overgeneralizes a specific, narrower point. The passage says farming hagfish for slime specifically would be expensive and potentially harmful — not a general claim about hagfish and captivity.*

**D.** The ability of hagfish to slime their attackers compensates for their being jawless. 

  *Invents a causal link. Hagfish being jawless is mentioned only as a descriptive detail, never framed as something the sliming defense compensates for.*

*Difficulty: medium*

---

##### Q35
> Using the Stratospheric Observatory for Infrared Astronomy (SOFIA), a team of astronomers mapped out the magnetic field of G47, one of the Milky Way's galactic bones (dense clouds of gas and dust that run through the middle of the arm of a spiral galaxy). Surprisingly, the map revealed a magnetic field with no clear pattern or direction. The researchers had expected the magnetic field to be similar to the more uniform fields seen in galactic bones in other arms of the Milky Way.

According to the text, what was surprising about the researchers' mapping of the magnetic field of galactic bone G47?

**A.** It showed a weaker magnetic field than expected. 

  *Substitutes the wrong attribute. The surprise concerns the field's lack of pattern or direction, not its strength — strength is never discussed.*

**B.** It implied that previous mappings of the magnetic field were inaccurate. 

  *Invents a claim about prior mappings. The researchers expected G47 to resemble the uniform fields seen in galactic bones "in other arms" — this is a comparison of expectation to a new result, not a re-evaluation of any earlier measurement.*

**C.** It produced magnetic field measurements similar to those for other galactic bones. 

  *Contradicts the passage: the whole point marked "surprisingly" is that G47's field was unlike the uniform fields seen in other galactic bones.*

**D.** It revealed a magnetic field that wasn't uniform. **(Correct)**

  *Correct. Matches directly: the map showed "no clear pattern or direction," against an expectation of uniformity like other galactic bones.*

*Difficulty: medium*

---

##### Q36
> The following text is from Ahmet Hamdi Tanpinar's 1961 novel The Time Regulation Institute (translated from the Turkish in 2014 by Maureen Freely and Alexander Dawe). The narrator was once involved with the Time Regulation Institute, a fictional bureaucracy that regulates the time of Turkey's clocks. I may be the most humble and absurd man in the world and, as my wife says, before the founding of our institute—but I did come to know a truly great man who possessed a natural genius for invention. I spent years at his side. I watched the way he worked. I witnessed how an idea would suddenly catch fire in his mind and take shape, like a tree sprouting shoots and branches, before coming into being. ©2014 by Maureen Freely and Alexander Dawe.

Which choice best states the main idea of the text?

**A.** A person was fortunate enough to have found love despite his obvious shortcomings. 

  *Substitutes the wrong subject. The wife appears only as the source of a self-deprecating remark about the narrator; the passage's actual focus is his admiration for the inventive man, not a love story.*

**B.** An exceptionally talented person professes humility to avoid intimidating others. 

  *Swaps which character has which trait. It is the narrator, quoting his wife, who calls himself "humble and absurd" — not the "truly great man" he admires, who is never described as professing humility.*

**C.** A person appreciates the extensive time he passed in the company of someone he deeply admired. **(Correct)**

  *Correct. "I did come to know a truly great man... I spent years at his side. I watched the way he worked" is the narrator's own appreciative account of time spent with someone he admires.*

**D.** A truly great person lets ideas mature in his mind before expressing them aloud. 

  *Distorts the described process and shifts the focus from the narrator's admiration to a general maxim. The passage describes ideas "suddenly" catching fire and growing organically, closer to spontaneous emergence than deliberate, patient maturation — and the point of the passage is the narrator's appreciation, not a claim about how great people operate in general.*

*Difficulty: sat-hardest*

---

##### Q37
> In present-day Chiapas, Mexico, archaeologist Robert Rosenswig, remote-sensing specialist Ricardo López-Torrijos, and colleagues have located 41 smaller settlements surrounding the ancient Mesoamerican city of Izapa. The researchers have concluded that these settlements were culturally linked to Izapa because each of the settlements is the same age and configured in the same manner as Izapa, with a pyramid to the north and a plaza to the south. Their shared structural orientation suggests that residents of the settlements likely performed some of the same cultural ceremonies as residents in Izapa did.

Which choice best states the main idea of the text?

**A.** Researchers have determined that the arrangement of Izapa's structures was based on those of other nearby settlements. 

  *Reverses the direction of influence. The passage never states which came first or which was modeled on which — it describes the settlements as configured "in the same manner as Izapa," using Izapa as the reference point, not the other way around.*

**B.** Cultural ceremonies in Izapa seem to have played a more important role for its residents than those in smaller, surrounding settlements did. 

  *Fabricates a ranking of importance. The passage claims similarity — settlement residents "likely performed some of the same cultural ceremonies" as Izapa's — not a hierarchy of how important those ceremonies were in each place.*

**C.** Although archaeologists have learned much about Izapa over years of research, they have only recently found the smaller settlements that surrounded it. 

  *Invents a timeline the passage doesn't establish. Nothing frames this find as recent relative to a longer history of Izapa research, or as any kind of narrative surprise.*

**D.** Researchers have inferred that Izapa was related to the smaller settlements that surrounded it based in part on their similarity of construction. **(Correct)**

  *Correct. Matches the passage's stated basis for the conclusion: the settlements were judged "culturally linked to Izapa because" of matching age and configuration — a shared structural orientation used as evidence of connection.*

*Difficulty: hard*

---

##### Q38
> Paleontologist Alan Tennyson and colleagues studied fossil bones found in New Zealand that are more than 55 million years old. The researchers determined that the fossil bones belonged to two previously unknown species of prehistoric penguins. Moreover, they estimated that one of the two penguin species was more than three times the size of the emperor penguin, which is the largest penguin species that exists today.

Based on the text, which choice best describes the two previously unknown penguin species?

**A.** They are frequently studied by paleontologists. 

  *Contradicts the text: these are newly identified species from a single study — described as "previously unknown" — not species with a history of frequent study.*

**B.** They are no longer living species. **(Correct)**

  *Correct. "Prehistoric penguins" whose fossil bones are "more than 55 million years old" are, by definition, extinct — no longer living.*

**C.** They were smaller than penguin species that exist today. 

  *Directly contradicts the text: one species is estimated to have been "more than three times the size of the emperor penguin, which is the largest penguin species that exists today" — larger, not smaller, than any living species.*

**D.** They spent little of their lives in water. 

  *Aquatic behavior is never discussed anywhere in the passage.*

*Difficulty: easy*

---

##### Q39
> A contraction of "you all," the pronoun "y'all" has long been used as a plural version of "you" in the South and in Black communities around the US. In recent decades, most other English-speaking communities in the US have begun to use "y'all." What explains its rise in popularity? Many varieties of English have no pronoun that specifically addresses more than one person and instead must use "you" to address both one person and more than one. But "y'all" always refers to two or more people. As a result, it conveys the speaker's meaning more precisely than "you" can.

Which question does the text most directly attempt to answer?

**A.** How many other plural versions of the pronoun "you" are there in English, besides "y'all"? 

  *Distorts the point into a counting question. The text explains that most varieties of English have no other plural "you" pronoun at all — the absence of alternatives, not a tally of how many exist.*

**B.** Why has the pronoun "y'all" become more widely used in the US? **(Correct)**

  *Correct. The text poses this exact question — "What explains its rise in popularity?" — and then answers it with the explanation about unambiguous plurality.*

**C.** When was the first recorded use of the pronoun "y'all" in the English language? 

  *No historical dating is given. The passage says "y'all" has "long been used," not when it first appeared.*

**D.** Is "y'all" commonly used in English-speaking regions of the world besides the US? 

  *The passage discusses only US English-speaking communities; usage elsewhere in the world is never addressed.*

*Difficulty: medium*

---

##### Q40
> During the World War II era, some Mexican American women adopted a striking new look called pachuca style. They wore altered men's jackets or zoot suits (wide-legged, long-coated suits) and dramatic makeup, and they combed their hair into high, rounded shapes. Some people criticized pachuca style, saying it was dangerous and women should dress traditionally. But historians see things differently. They see pachuca style as a form of rebellion against the era's rigid social expectations for women. They say that it showed a desire for self-expression and freedom on the part of women who adopted the style.

According to the text, how do historians view pachuca style?

**A.** They think that pachuca style was such a popular trend that it continues to influence fashion in the United States to the present day. 

  *No claim about lasting influence on present-day fashion appears in the text, which is bounded to the historians' retrospective view of the WWII era.*

**B.** They think that pachuca style was a way for some Mexican American women to express themselves and resist strict social expectations. **(Correct)**

  *Correct. Matches directly: historians see it "as a form of rebellion against the era's rigid social expectations for women," showing "a desire for self-expression and freedom."*

**C.** They think that pachuca style was celebrated because it enabled some Mexican American women to show their support for the United States during World War II. 

  *Invents a link to wartime patriotism. Historians' described view connects the style to resisting social expectations, not to expressing support for the war effort.*

**D.** They think that pachuca style was similar to other fashion trends that different groups of women adopted in the same period. 

  *No such comparison to other trends is made. Historians' view described in the text is specific to what pachuca style meant, not how it compares to other styles.*

*Difficulty: medium*

---

##### Q41
> In 1934 physicist Eugene Wigner posited the existence of a crystal consisting entirely of electrons in a honeycomb-like structure. The so-called Wigner crystal remained largely conjecture, however, until Feng Wang and colleagues announced in 2021 that they had captured an image of one. The researchers trapped electrons between two semiconductors and then cooled the apparatus, causing the electrons to settle into a crystalline structure. By inserting an ultrathin sheet of graphene above the crystalline structure, the researchers obtained an impression—the first visual confirmation of the Wigner crystal.

Which choice best states the main idea of the text?

**A.** Researchers have obtained the most definitive evidence to date of the existence of the Wigner crystal. **(Correct)**

  *Correct. After decades of remaining "largely conjecture," Wang and colleagues obtained "the first visual confirmation of the Wigner crystal" — the strongest evidence yet.*

**B.** Researchers have identified an innovative new method for working with unusual crystalline structures. 

  *Overgeneralizes a specific imaging technique into a general-purpose method. Trapping electrons, cooling the apparatus, and inserting graphene is described as the method for imaging this particular crystal, not a broadly applicable technique for crystalline structures.*

**C.** Graphene is the most important of the components required to capture an image of a Wigner crystal. 

  *Invents a ranking of importance among the process's components. Graphene is one element in a multi-step process alongside semiconductors and cooling; no component is ranked as most important.*

**D.** It's difficult to acquire an image of a Wigner crystal because of the crystal's honeycomb structure. 

  *Fabricates a cause for the difficulty and drops the passage's actual point. The passage's focus is the achievement of imaging the crystal, not a claim that its honeycomb structure specifically was what made imaging hard.*

*Difficulty: hard*

---

##### Q42
> Cats can judge unseen people's positions in space by the sound of their voices and thus react with surprise when the same person calls to them from two different locations in a short span of time. Saho Takagi and colleagues reached this conclusion by measuring cats' levels of surprise based on their ear and head movements while the cats heard recordings of their owners' voices from two speakers spaced far apart. Cats exhibited a low level of surprise when owners' voices were played twice from the same speaker, but they showed a high level of surprise when the voice was played once each from the two different speakers.

According to the text, how did the researchers determine the level of surprise displayed by the cats in the study?

**A.** They watched how each cat moved its ears and head. **(Correct)**

  *Correct. Stated directly: researchers measured "cats' levels of surprise based on their ear and head movements."*

**B.** They examined how each cat reacted to the voice of a stranger. 

  *Contradicts the setup: the recordings played were of the cats' own owners' voices, not a stranger's.*

**C.** They studied how each cat physically interacted with its owner. 

  *No physical interaction with the owner is described — the owner isn't even physically present, since the voice is played through speakers.*

**D.** They tracked how each cat moved around the room. 

  *No tracking of movement around the room is mentioned; the measure described is specifically ear and head movement, not locomotion.*

*Difficulty: easy*

---

##### Q43
> The following text is from Ezra Pound's 1909 poem "Hymn III," based on the work of Marcantonio Flaminio. As a fragile and lovely flower unfolds its gleaming foliage on the breast of the fostering earth, if the dew and the rain draw it forth; So doth my tender mind flourish, if it be fed with the sweet dew of the fostering spirit, Lacking this, it beginneth straightway to languish, even as a floweret born upon dry earth, if the dew and the rain tend it not.

Based on the text, in what way is the human mind like a flower?

**A.** It becomes increasingly vigorous with the passage of time. 

  *The poem describes conditional flourishing based on nourishment (if fed, lacking this), not a claim about growth accumulating over time.*

**B.** It draws strength from changes in the weather. 

  *Distorts the mechanism. "Dew and rain" function as nourishment or sustenance in the poem, not as variability in weather — the point is presence or absence of a sustaining element, not weather changing.*

**C.** It requires proper nourishment in order to thrive. **(Correct)**

  *Correct. The extended simile is explicit: a flower needs dew and rain to flourish or it languishes, and the mind likewise needs to be "fed with the sweet dew of the fostering spirit" or it "beginneth straightway to languish."*

**D.** It perseveres despite challenging circumstances. 

  *Says the opposite of the poem: without nourishment, the mind (like the flower) "languishes" — fails to persevere — rather than persisting despite the lack.*

*Difficulty: medium*

---

##### Q44
> Businesses selling clothing and other fashion items face obstacles in trying to forecast how much product to order: tastes and styles change quickly, while manufacturing clothing takes a significant amount of time. Researchers Youran Fu and Marshall Fisher have found that combining sellers' own data with information gathered from social media can dramatically improve the accuracy of such forecasts—by 24 to 57 percent in the cases they directly studied. Better predictions mean demand is easier to meet without retailers becoming overstocked.

Which choice best states the main idea of the text?

**A.** Using multiple data sources can enhance the ability of sellers in the fashion industry to anticipate demand. **(Correct)**

  *Correct. Matches the passage's finding directly: combining sellers' own data with social media information "can dramatically improve the accuracy" of demand forecasts.*

**B.** Social media is revolutionizing how both sellers and researchers view the fashion industry. 

  *Inflates a specific forecasting improvement into a sweeping claim about revolutionizing perspective across an industry. The passage reports a measured accuracy gain in forecasting, not a claim about how researchers or sellers view the industry as a whole.*

**C.** Becoming overstocked is the main preoccupation of sellers trying to forecast demand for fashion items. 

  *Elevates a downstream benefit into the passage's central concern. Avoiding overstock is mentioned as an outcome of better forecasting, not stated as sellers' "main preoccupation" — the passage's actual focus is the forecasting difficulty and its solution.*

**D.** Retailers can use their own data to accurately predict how tastes and styles are evolving. 

  *Drops half the finding. The accuracy improvement comes from combining sellers' own data WITH social media data — not from sellers' own data alone, which this choice misattributes the entire gain to.*

*Difficulty: hard*

---

##### Q45
> Historians point to the rule of the Piast dynasty as crucial to the formation of the Polish state. However, some differentiate between members of the dynasty like Mieszko II Lambert, who ruled as king from 1025 to 1031 CE, and less-well-documented figures like Siemomysł, who is said to have ruled in the 10th century but whose historical actuality is disputed. Siemomysł appears in the Gesta principum Polonorum, a chronicle of medieval Polish history written between 1112 and 1118. However, the chronicle's documentation of Siemomysł relies on oral tradition, unlike its records of later rulers.

According to the text, what is a difference between how historians view Siemomysł and how they view Mieszko II Lambert?

**A.** Historians agree that Mieszko II Lambert existed, but disagree about whether Siemomysł existed. **(Correct)**

  *Correct. Mieszko is documented with a defined reign (1025–1031 CE), while Siemomysł's "historical actuality is disputed" — matching exactly this difference in how firmly each is accepted as historical.*

**B.** Historians believe that the Gesta principum Polonorum provides more evidence for Siemomysł's existence than it does for Mieszko II Lambert's existence. 

  *Reverses the evidentiary relationship. The chronicle's account of Siemomysł "relies on oral tradition, unlike its records of later rulers" such as Mieszko — implying Mieszko's documentation is the stronger one, not Siemomysł's.*

**C.** Historians agree that Siemomysł ruled Poland much later than Mieszko II Lambert. 

  *Reverses the chronology. Siemomysł is said to have ruled in the 10th century, earlier than Mieszko's 1025–1031 CE reign in the 11th century — not later.*

**D.** Historians find the orally transmitted stories affirming the existence of Mieszko II Lambert to be more convincing than stories about Siemomysł. 

  *Invents a claim about oral tradition specifically affirming Mieszko. It is Siemomysł's account, not Mieszko's, that the text says relies on oral tradition — and no comparison of persuasiveness between oral stories about the two figures is made.*

*Difficulty: hard*

---

##### Q46
> In a study by Mika R. Moran, Daniel A. Rodriguez, and colleagues, residents of Quito, Ecuador, and Lima, Peru, were surveyed about parks in their cities. Of the 618 respondents from Quito, 82.9% indicated that they use the city's parks, and of the 663 respondents from Lima, 72.7% indicated using city parks. Given that the percentage of Quito respondents who reported living within a 10-minute walk of a park was much lower than that reported by Lima respondents, greater proximity alone can't explain the difference.

The text makes which point about the difference between the proportions of Quito residents and Lima residents using parks?

**A.** It was much larger than the researchers conducting the study expected. 

  *No researcher expectations are mentioned anywhere; the passage reports findings without comparing them to any prior expectation.*

**B.** It is caused by something other than the parks' proximity to city residents. **(Correct)**

  *Correct. Matches the passage's conclusion directly: since Quito respondents reported living near a park less often than Lima respondents did (yet used parks more), "greater proximity alone can't explain the difference" — implying some other factor is responsible.*

**C.** It could be due to inaccuracies in the survey results. 

  *No doubt about survey reliability is raised; the passage treats the reported percentages as given and reasons from them directly.*

**D.** It was calculated using sources that predate the survey. 

  *Nothing about timing or outside sources predating the survey is mentioned — this is invented and irrelevant to the stated point about proximity.*

*Difficulty: hard*

---

##### Q47
> The most recent iteration of the immersive theater experience Sleep No More, which premiered in New York City in 2011, transforms its performance space—a five-story warehouse—into a 1930s-era hotel. Audience members, who wander through the labyrinthine venue at their own pace and follow the actors as they play out simultaneous, interweaving narrative loops, confront the impossibility of experiencing the production in its entirety. The play's refusal of narrative coherence thus hinges on the sense of spatial fragmentation that the venue's immense and intricate layout generates.

What does the text most strongly suggest about Sleep No More's use of its performance space?

**A.** The choice of a New York City venue likely enabled the play's creators to experiment with the use of theatrical space in a way that venues from earlier productions could not. 

  *Conflates location with layout. The passage attributes the play's effect to the venue's size and intricacy — five stories, immense and intricate — not to its being in New York City, and it never compares this venue to those of earlier productions.*

**B.** Audience members likely find the experience of the play disappointing because they generally cannot make their way through the entire venue. 

  *Misreads a deliberate artistic effect as a flaw. The passage frames the impossibility of experiencing the production in its entirety as central to the show's intended narrative refusal ("thus hinges on"), not as a source of audience disappointment.*

**C.** The production's dependence on a particular performance environment would likely make it difficult to reproduce exactly in a different theatrical space. **(Correct)**

  *Correct. The play's core effect — narrative incoherence generated by spatial fragmentation — is described as hinging on this specific venue's "immense and intricate layout," implying the effect is tied to this particular space.*

**D.** Audience members who navigate the space according to a recommended itinerary will likely have a better grasp of the play's narrative than audience members who depart from that itinerary. 

  *No recommended itinerary is mentioned anywhere. Audience members "wander... at their own pace," with no guided path referenced at all.*

*Difficulty: sat-hardest*

---

##### Q48
> The following text is adapted from María Cristina Mena's 1914 short story "The Vine-Leaf." It is a saying in the capital of Mexico that Dr. Malsufrido carries more family secrets under his hat than any archbishop. The doctor's hat is, appropriately enough, uncommonly capacious, rising very high, and sinking so low that it seems to be supported by his ears and eyebrows, and it has a furry look, as if it had been brushed the wrong way, which is perhaps what happens to it if it is ever brushed at all. When the doctor takes it off, the family secrets do not fly out like a flock of parrots, but remain nicely bottled up beneath a dome of old and highly polished ivory.

Based on the text, how do people in the capital of Mexico most likely regard Dr. Malsufrido?

**A.** Many have come to tolerate him despite his disheveled appearance. 

  *Invents an attitude of grudging tolerance. His hat is described humorously, but nothing states people dislike his appearance or merely tolerate him because of it — the passage's actual focus is his reputation for discretion.*

**B.** Few feel concerned that he will divulge their confidences. **(Correct)**

  *Correct. "The family secrets do not fly out like a flock of parrots, but remain nicely bottled up" describes a man trusted to keep secrets — people would have little concern about him revealing confidences.*

**C.** Some dislike how freely he discusses his own family. 

  *Reverses both subject and behavior. The secrets he keeps belong to other families ("more family secrets under his hat than any archbishop"), not his own, and he's described as keeping them bottled up, not discussing them freely.*

**D.** Most would be unimpressed by him were it not for his professional expertise. 

  *No mention of professional skill or a conditional respect based on it. The passage is about his reputation for discretion, not his competence as a doctor.*

*Difficulty: hard*

---

##### Q49
> The following text is adapted from Countee Cullen's 1926 poem "Thoughts in a Zoo." They in their cruel traps, and we in ours, Survey each other's rage, and pass the hours Commiserating each the other's woe, To mitigate his own pain's fiery glow. Man could but little proffer in exchange Save that his cages have a larger range. That lion with his lordly, untamed heart Has in some man his human counterpart, Some lofty soul in dreams and visions wrapped, But in the stifling flesh securely trapped.

Based on the text, what challenge do humans sometimes experience?

**A.** They cannot effectively tame certain wild animals because of a lack of compassion. 

  *Substitutes the wrong relationship. The lion and the human are presented as parallel counterparts sharing a condition of entrapment, not as a taming relationship, and lack of compassion is never mentioned.*

**B.** They cannot focus on setting attainable goals because of a lack of motivation. 

  *Invents goal-setting and motivation as the subject. The poem's image is aspiration trapped by physical constraint — "stifling flesh" — not a psychological failure to set or pursue goals.*

**C.** They quickly become frustrated when faced with difficult tasks because of a lack of self-control. 

  *Invents frustration and self-control as the theme. The poem describes a soul confined by the body, a structural or existential limitation, not a self-control problem with completing tasks.*

**D.** They have aspirations that cannot be fulfilled because of certain limitations. **(Correct)**

  *Correct. "Some lofty soul in dreams and visions wrapped, but in the stifling flesh securely trapped" describes exactly this: aspiration confined by physical limitation.*

*Difficulty: sat-hardest*

---

##### Q50
> For centuries, the widespread acknowledgment of the involvement of the cerebellum—a dense brain structure in vertebrates—in coordinating motor control in humans has hindered recognition of other possible functions of the structure. Neuroscience research from the last two decades now suggests that the cerebellum regulates emotion and social behavior, and recent research by Ilaria Carta and colleagues has identified a pathway connecting the cerebellum to a center for motivation and reward processing known as the ventral tegmental area (VTA).

Which choice best states the main idea of the text?

**A.** The recent verification of a pathway between the VTA and the cerebellum confirms the cerebellum's long-suspected role in motor coordination. 

  *Attaches the new finding to the wrong function. The VTA pathway is evidence for a newly recognized function (motivation and reward), not confirmation of the already well-established motor coordination role.*

**B.** Recent advances in the field of neuroscience have challenged widely accepted claims about the function of a pathway connecting the VTA and the cerebellum. 

  *Misidentifies what's being challenged. The traditional view being complicated is that the cerebellum ONLY governs motor control; the VTA pathway itself is the new finding, not a prior belief being overturned.*

**C.** The cerebellum has primarily been thought to regulate motor functioning, but in recent years neuroscience researchers have been uncovering additional functions. **(Correct)**

  *Correct. Matches the passage's structure: long-standing focus on motor coordination "has hindered recognition of other possible functions," and recent research reveals emotion, social behavior, and motivation-reward pathways as additional roles.*

**D.** Technological limitations have historically hindered the study of the cerebellum, but the recent development of new technologies has led to greater insights into its functions. 

  *Invents a technological cause. The passage attributes the narrow historical focus to widespread conceptual acknowledgment of the motor-control role hindering recognition of other functions — not to any stated technological limitation or breakthrough.*

*Difficulty: hard*

---

##### Q51
> Algae living within the tissues of corals play a critical role in keeping corals, and the marine ecosystems they are part of, thriving. Some coral species appear brown in color when healthy due to the algae colonies living in their tissues. In the event of an environmental stressor, the algae can die or be expelled, causing the corals to appear white. To recover the algae, the bleached corals then begin to produce bright colors, which block intense sunlight, encouraging the light-sensitive algae to recolonize the corals.

What does the text most strongly suggest about corals that produce bright colors?

**A.** These corals have likely been subjected to stressful environmental conditions. **(Correct)**

  *Correct. Bright colors are produced only after bleaching — an environmental stressor kills or expels the algae, turning the coral white, and only then does it produce bright colors to help recolonize — so bright-colored corals have been through such a stressor.*

**B.** These corals are likely more vulnerable to exposure from intense sunlight than white corals are. 

  *Reverses the causal relationship. Bright colors are produced specifically to block intense sunlight, a protective response — making bright corals less, not more, vulnerable to sunlight exposure.*

**C.** These corals have likely recovered from an environmental event without the assistance of algae colonies. 

  *Contradicts the text: bright colors are produced specifically "to recover the algae" by encouraging it to recolonize — meaning the coral hasn't recovered yet and depends on the algae's return, not the opposite.*

**D.** These corals are more likely to survive without algae colonies than brown corals are. 

  *Fabricates a survival comparison. Algae are described as playing "a critical role in keeping corals... thriving" generally, which argues against, not for, corals surviving better without them.*

*Difficulty: hard*

---

##### Q52
> Having written the impassioned call to arms "Letter to the Spanish Americans" in 1791, Peruvian intellectual Juan Pablo Viscardo y Guzmán is often considered a forerunner for the independence movements in Latin America. But Viscardo's role in history would have remained insignificant were it not for Venezuelan revolutionary Francisco de Miranda, who was handed the unpublished letter after Viscardo's death. Miranda not only helped circulate the letter, but his edits and footnotes to the text position Miranda as a central figure in the text's creation.

Which choice best states the main idea of the text?

**A.** The original authorship of "Letter to the Spanish Americans" is disputed by contemporary historians. 

  *No dispute over who originally wrote the letter is mentioned; the passage discusses Miranda's editorial and circulation role, not a controversy over Viscardo's original authorship.*

**B.** The majority of the most eloquently stated arguments in "Letter to the Spanish Americans" were written by Miranda. 

  *Overstates Miranda's contribution. The passage credits him with "edits and footnotes," not with writing the majority of the letter's substantive arguments — this exaggerates an editorial role into primary authorship.*

**C.** Miranda played a crucial role in influencing the content and distribution of "Letter to the Spanish Americans." **(Correct)**

  *Correct. Matches both stated contributions: Miranda "helped circulate the letter" (distribution) and his "edits and footnotes... position Miranda as a central figure in the text's creation" (content).*

**D.** "Letter to the Spanish Americans" persuaded many people in Latin America to pursue national independence. 

  *No claim about the letter's effect on readers or on independence movements' outcomes appears anywhere; the passage discusses only its creation and circulation.*

*Difficulty: hard*

---

##### Q53
> In a paper about p-i-n planar perovskite solar cells (one of several perovskite cell architectures designed to collect and store solar power), Lyndsey McMillon-Brown et al. describe a method for fabricating the cell's electronic transport layer (ETL) using a spray coating. Conventional ETL fabrication is accomplished using a solution of nanoparticles. The process can result in a loss of up to 80% of the solution, increasing the cost of manufacturing at scale—an issue that may be obviated by spray coating fabrication, which the researchers describe as "highly reproducible, concise, and practical."

What does the text most strongly suggest about conventional ETL fabrication?

**A.** It is less suitable for manufacturing large volumes of planar p-i-n perovskite solar cells than an alternative fabrication method may be. **(Correct)**

  *Correct. Conventional fabrication loses up to 80% of the nanoparticle solution, "increasing the cost of manufacturing at scale" — an issue the new spray-coating alternative "may... obviate," implying conventional fabrication is less suited to large-scale manufacturing than the alternative.*

**B.** It is more expensive when manufacturing at scale than are processes for fabricating ETLs used in other perovskite solar cell architectures. 

  *Fabricates a comparison across architectures. The passage compares conventional versus spray-coating fabrication within the same p-i-n architecture, never against ETL fabrication used in other perovskite cell architectures.*

**C.** It typically entails a greater loss of nanoparticle solution than do other established approaches for ETL fabrication. 

  *Fabricates a comparison to a third method. Only two methods are discussed — conventional nanoparticle-solution fabrication and the new spray-coating method — with no other "established approach" named for comparison.*

**D.** It is somewhat imprecise and therefore limits the potential effectiveness of p-i-n planar perovskite solar cells at capturing and storing solar power. 

  *Substitutes the wrong mechanism. The described problem with conventional ETL fabrication is manufacturing cost from solution loss, not precision of the resulting cell or its power-capturing performance.*

*Difficulty: sat-hardest*

---

##### Q54
> Disco remains one of the most ridiculed popular music genres of the late twentieth century. But as scholars have argued, the genre is far less superficial than many people believe. Take the case of disco icon Donna Summer: she may have been associated with popular songs about love and heartbreak (subjects hardly unique to disco, by the way), but like many Black women singers before her, much of her music also reflects concerns about community and identity. These concerns are present in many of the genre's greatest songs, and they generally don't require much digging to reveal.

What does the text most strongly suggest about the disco genre?

**A.** It has been unjustly ignored by most scholars despite the importance of the themes addressed by many of the genre's songs. 

  *Misattributes the dismissive view. The passage says disco is ridiculed popularly — "many people believe" it superficial — while scholars are the ones arguing against that view, not the ones ignoring or dismissing it.*

**B.** It evolved over time from a superficial genre focused on romance to a genre focused on more serious concerns. 

  *Invents a two-phase evolution. The passage says deeper concerns about community and identity are present alongside romance themes in the SAME songs by the SAME artist (Donna Summer), not that the genre shifted from one focus to another over time.*

**C.** It has been unfairly dismissed for the inclusion of subject matter that is also found in other musical genres. **(Correct)**

  *Correct. Disco is widely ridiculed as superficial for songs about "love and heartbreak," subjects the passage explicitly notes are "hardly unique to disco" — the dismissal is unfair partly because what it's mocked for isn't even distinctive to the genre, and deeper concerns sit alongside it.*

**D.** It gave rise to a Black women's musical tradition that has endured even though the genre itself faded in the late twentieth century. 

  *Reverses the stated lineage and invents fading. Donna Summer is described as following "many Black women singers before her" — the tradition precedes and continues through disco, rather than disco giving rise to it — and no claim about the genre fading appears in the text.*

*Difficulty: sat-hardest*

---

##### Q55
> In a study of new technology adoption, Davit Marikyan et al. examined negative disconfirmation (which occurs when experiences fall short of one's expectations) to determine whether it could lead to positive outcomes for users. The team focused on established users of "smart home" technology, which presents inherent utilization challenges but tends to attract users with high expectations, often leading to feelings of dissonance. The researchers found that many users employed cognitive mechanisms to mitigate those feelings, ultimately reversing their initial sense of disappointment.

Which choice best states the main idea of the text?

**A.** Research suggests that most users of smart home technology will not achieve a feeling of satisfaction given the utilization challenges of such technology. 

  *Says the opposite of the finding. The study reports that many users DID reverse their initial disappointment through cognitive mechanisms — the point of examining whether negative disconfirmation "could lead to positive outcomes" — not that most will fail to achieve satisfaction.*

**B.** Although most smart home technology is aimed at meeting or exceeding users' high expectations, those expectations in general remain poorly understood. 

  *Invents a claim about product design intent and misstates what's uncertain. The passage never discusses design goals, and it's the outcomes of negative disconfirmation being studied, not a general claim that expectations are poorly understood.*

**C.** Research suggests that users with high expectations for a new technology can feel content with that technology even after experiencing negative disconfirmation. **(Correct)**

  *Correct. High-expectation users experienced dissonance from utilization challenges (negative disconfirmation), but "many users employed cognitive mechanisms to mitigate those feelings, ultimately reversing their initial sense of disappointment" — ending up content despite the initial shortfall.*

**D.** Although negative disconfirmation has often been studied, little is known about the cognitive mechanisms shaping users' reactions to it in the context of new technology adoption. 

  *Inverts a reported finding into a stated gap. The passage reports a specific result about these cognitive mechanisms ("researchers found that many users employed cognitive mechanisms...") — a finding, not an acknowledged unknown.*

*Difficulty: sat-hardest*

---

##### Q56
> Optical tweezers are specialized scientific tools—particularly useful in biology and medicine—that use high-powered beams of light to trap and manipulate minuscule particles for study. Use of the tool has led to several scientific and medical breakthroughs over the last few decades, but the particles are often under prolonged exposure to the intense heat of the light beams. To overcome the risk of overheating, and thereby damage, researchers sometimes attach nano-sized glass beads to particles, allowing the light to focus on the beads instead of the particles.

Based on the text, what is one advantage of attaching glass beads to particles when using optical tweezers?

**A.** It decreases the time it takes for the optical tweezers to locate and capture the particles. 

  *No timing claim is made. The described benefit concerns avoiding overheating damage, not the speed of locating or capturing particles.*

**B.** It facilitates the maneuvering of particles without directly heating the particles themselves. **(Correct)**

  *Correct. The beads let "the light... focus on the beads instead of the particles," avoiding direct heating of the particles while still allowing them to be manipulated via the optical tweezer.*

**C.** It allows researchers to use weaker light beams to manipulate particles. 

  *The passage never states that beam intensity is reduced — the beads redirect where the still high-powered light focuses, rather than reducing the beam's strength.*

**D.** It adds a material to which particles can transfer any heat absorbed from the optical tweezers' light beam. 

  *Inverts the mechanism. The beads are attached so the light focuses on them INSTEAD OF the particles, avoiding heating the particles in the first place — not so that already-heated particles can transfer heat to the beads afterward.*

*Difficulty: hard*

---

##### Q57
> Some animal-behavior studies involve observing wild animals in their natural habitat, and some involve capturing wild animals and observing them in a laboratory. Each approach has advantages over the other. In wild studies, researchers can more easily presume that the animals are behaving normally, and in lab studies, researchers can more easily control factors that might affect the results. But if, for example, the results from a wild study and a lab study of Western scrub-jays (Aphelocoma californica) contradict each other, one or both of the studies must have failed to account for some factor that was relevant to the birds' behavior.

Which choice best states the main idea of the text?

**A.** When the results of a natural-habitat study and those from a lab study of a wild animal such as the Western scrub-jay conflict, the study in the natural habitat is more likely than the lab study to have accurate results. 

  *Fabricates a hierarchy between the two methods. The passage never favors wild studies over lab studies when results conflict — it says only that a discrepancy means one or both studies missed a relevant factor, without ranking their reliability.*

**B.** Studying wild animals such as the Western scrub-jay in both their natural habitat and lab settings is likely to yield conflicting results that researchers cannot fully resolve. 

  *Treats a hypothetical as a general expectation. The scrub-jay appears only as an "if, for example" illustration of what a contradiction would mean, not a claim that studying them this way typically produces conflict — and the text implies resolution is possible by identifying the missed factor.*

**C.** Wild animals such as the Western scrub-jay can be effectively studied in their natural habitat and in the lab, but each approach has drawbacks that could affect the accuracy of the findings. **(Correct)**

  *Correct. "Each approach has advantages over the other" — wild studies allow presuming normal behavior, lab studies allow controlling factors — and a conflict between them signals a factor either approach's drawbacks could have caused to be missed.*

**D.** Differing results between natural-habitat and lab studies of wild animals such as the Western scrub-jay are a strong indication that both of the studies had design flaws that affected the accuracy of their results. 

  *Overstates a conditional as a general finding. The passage's claim is conditional (if results contradict, a relevant factor was missed by one or both studies) — that is more specific than, and different from, a general claim that conflicting studies always reveal design flaws in both.*

*Difficulty: sat-hardest*

---

##### Q58
> Artificial leaves are a developing renewable energy technology that mimics the process of photosynthesis in plants. These devices are silicon-based solar cells coated in chemical catalysts that activate reactions that split water molecules into hydrogen and oxygen gas. The technology, while generating lots of interest, is not yet commercially viable as a large-scale energy source. To meet this challenge, scientists from many fields are researching ways to store, transport, and distribute the energy the devices produce while other scientists are working to improve the cost and efficiency of the devices.

Which choice best states the main idea of the text?

**A.** Continued research and development in artificial-leaf technology is needed before the devices can be widely used as an energy source. **(Correct)**

  *Correct. The technology "is not yet commercially viable as a large-scale energy source"; to meet that challenge, scientists are actively researching storage, transport, distribution, cost, and efficiency — ongoing, needed work before widespread use.*

**B.** The recent increase in the commercial use of artificial leaves as an energy source has encouraged many scientists to research ways to store, transport, and distribute the technology. 

  *Contradicts the passage and reverses cause and effect. The text says the technology is "not yet commercially viable," the opposite of a recent increase in commercial use — and it is the LACK of viability driving the research, not commercial success encouraging it.*

**C.** Artificial leaves split water molecules into oxygen and hydrogen gas using catalysts more efficiently than plants do using the process of photosynthesis. 

  *Fabricates an efficiency comparison to plants. The passage says artificial leaves "mimic" photosynthesis, never that they outperform it — and efficiency is explicitly something scientists are still trying to improve, implying it isn't yet superior.*

**D.** Artificial leaves were developed to mimic the natural process of photosynthesis in plants in order to store energy for long-term commercial use. 

  *Mistakes an unmet challenge for an achieved design goal. Storage, transport, and distribution are described as problems researchers are CURRENTLY working to solve, not as the technology's already-realized purpose.*

*Difficulty: hard*

---

##### Q59
> Electronic music pioneer Wendy Carlos is credited with the music for three feature films: A Clockwork Orange (1971), The Shining (1980), and Tron (1982). However, her musical score for A Clockwork Orange is mostly made up of her arrangements of Ludwig van Beethoven's work. Also, almost all the music that she and Rachel Elkind composed for The Shining was unused by director Stanley Kubrick. It did not appear in the film. Of the three films, Tron is the one in which audiences can hear the most of Carlos's original compositions.

Which choice best states the main idea of the text?

**A.** Of the three films for which Carlos is credited, Tron features the most original music from her. **(Correct)**

  *Correct. Stated directly in the final sentence: "Of the three films, Tron is the one in which audiences can hear the most of Carlos's original compositions."*

**B.** The director of The Shining used most of the music that Carlos composed for it. 

  *Contradicts the text: "almost all the music... composed for The Shining was unused by director Stanley Kubrick" — the opposite of the director using most of it.*

**C.** Beethoven is widely considered to be a more important composer than Carlos. 

  *Fabricates a value judgment. The passage only notes that Carlos's Clockwork Orange score consists mostly of arrangements of Beethoven's work — a fact about the score's composition, not a ranking of the composers' importance.*

**D.** Carlos is a notable innovator among film composers in the 1970s and 1980s. 

  *Inflates a specific comparison across her three scores into a broad claim about her standing among film composers generally, which the passage never makes — it calls her an "electronic music pioneer," not specifically a leading film composer of the era.*

*Difficulty: hard*

---

##### Q60
> The following text is adapted from William Shakespeare's 1609 poem "Sonnet 27." The poem is addressed to a close friend as if he were physically present. Weary with toil, I [hurry] to my bed, The dear repose for limbs with travel tired; But then begins a journey in my head, To work my mind, when body's work's expired: For then my thoughts—from far where I abide— [Begin] a zealous pilgrimage to thee, And keep my drooping eyelids open wide.

What is the main idea of the text?

**A.** The speaker is asleep and dreaming about traveling to see the friend. 

  *Contradicts the text: his "drooping eyelids" are kept "open wide," meaning he is not asleep. The "journey" and "pilgrimage" are metaphors for his thoughts, not a literal dream.*

**B.** The speaker is planning an upcoming trip to the friend's house. 

  *Takes "a zealous pilgrimage to thee" literally. This describes his thoughts traveling to the friend mentally while he lies awake, not a literal trip he is planning.*

**C.** The speaker is too fatigued to continue discussion with the friend. 

  *No discussion with the friend is depicted in the passage at all — the friend is not present, and the speaker's weariness refers to physical toil, not an inability to keep talking.*

**D.** The speaker is thinking about the friend instead of immediately falling asleep. **(Correct)**

  *Correct. Despite being "weary with toil" and hurrying to bed for "repose," a "journey" begins in his head — his thoughts make "a zealous pilgrimage" to the friend and keep his "drooping eyelids open wide" instead of letting him sleep.*

*Difficulty: hard*

---

##### Q61
> The following text is from Maggie Pogue Johnson's 1910 poem "Poet of Our Race." In this poem, the speaker is addressing Paul Laurence Dunbar, a Black author. Thou, with stroke of mighty pen, Hast told of joy and mirth, And read the hearts and souls of men As cradled from their birth. The language of the flowers, Thou hast read them all, And e'en the little brook Responded to thy call.

Which choice best states the main purpose of the text?

**A.** To praise a certain writer for being especially perceptive regarding people and nature **(Correct)**

  *Correct. The poem praises Dunbar for reading "the hearts and souls of men," the "language of the flowers," and even a brook responding to his call — perceptiveness about both people and nature.*

**B.** To establish that a certain writer has read extensively about a variety of topics 

  *Literalizes the figurative "read." "Hast read them all" (of flowers) and "read the hearts and souls" are metaphors for deep understanding, not a claim that the writer has literally read books on many subjects.*

**C.** To call attention to a certain writer's careful and elaborately detailed writing process 

  *The poem praises the results of his perceptiveness — deep understanding of people and nature — never his writing process, which is not described at all.*

**D.** To recount fond memories of an afternoon spent in nature with a certain writer 

  *Invents a shared narrative event. The poem is addressed to the writer in praise of his abilities, not a recollection of a specific afternoon the speaker spent with him.*

*Difficulty: hard*

---

##### Q62
> In eighteenth-century Britain, the aesthetic concept of the picturesque set a new standard for the appreciation of nature: in contrast with formal gardens, which were explicitly artificial, picturesque scenery—whose hallmarks were rugged terrains and medieval ruins—was prized for its appearance of untamed wilderness. Yet the experience of the picturesque was highly mediated: landscapes were admirable insofar as they adhered to depictions of nature in art and poetry, and tourists seeking the picturesque used optical devices, such as tinted mirrors, to transform views into painterly images.

Which choice best states the main idea of the text?

**A.** Although the picturesque gained currency as an aesthetic ideal in eighteenth-century Britain, the self-evident contradictions inherent in the concept drew much contemporary criticism. 

  *No criticism from contemporaries is mentioned. The passage analyzes an internal tension in the concept itself, not a historical backlash against it.*

**B.** Admirers of picturesque scenery in the eighteenth century were often unmindful of the extent to which their appreciation of nature was shaped by rapidly developing optical technologies. 

  *Contradicts the described behavior and invents a pace of technological change. Tourists actively "used optical devices... to transform views" — a deliberate, known practice, not something they were unaware was shaping their view — and no claim about the devices being "rapidly developing" appears.*

**C.** The defining features of the picturesque landscape, including rugged terrains and medieval ruins, were highly valued by tourists primarily because of their relative prevalence in Britain. 

  *Substitutes the wrong reason. These features were valued for their "appearance of untamed wilderness" and adherence to artistic depictions, not for how common or rare they were in Britain — prevalence is never discussed.*

**D.** Although the idea of the picturesque in nature was premised on the rejection of overt artifice, judgments about the picturesque were nevertheless deeply informed by principles derived from art. **(Correct)**

  *Correct. The picturesque was prized as untamed wilderness in contrast to "explicitly artificial" formal gardens (rejecting artifice), yet landscapes were judged admirable only "insofar as they adhered to depictions of nature in art and poetry," and viewed through devices that made them look painterly — artifice reentering through artistic standards.*

*Difficulty: sat-hardest*

---

##### Q63
> The following text is Vita Sackville-West's circa 1920 poem "Evening." Spars are ships' masts, moorings are ropes that hold docked ships in place, and a riding-light is a light that a ship shines when it is anchored. When little lights in little ports come out, Quivering down through water with the stars, And all the fishing fleet of slender spars Range at their moorings, veer with tide about; When race of wind is stilled and sails are furled, And underneath our single riding-light The curve of black-ribbed deck gleams palely white, And slumbrous waters pool a slumbrous world; —Then, and then only, have I thought how sweet Old age might sink upon a windy youth, Quiet beneath the riding-light of truth, Weathered through storms, and gracious in retreat.

Which choice best states the main idea of the text?

**A.** The tranquility of a port in the evening can incline a person to appreciate the stillness of old age. **(Correct)**

  *Correct. The calm evening scene — "slumbrous waters pool a slumbrous world" — leads the speaker to think "how sweet old age might sink upon a windy youth, quiet beneath the riding-light of truth": the tranquil setting inspires an appreciation for the peacefulness of old age.*

**B.** The difficulty of bringing a ship into port is apt training for dealing with the types of struggles encountered in old age. 

  *Invents a difficult docking process the poem never depicts — the scene is already still and moored, wind stilled, sails furled — and old age is described as "sweet," "quiet," and "gracious," not as a struggle to train for.*

**C.** A person who leads a long life that is varied and active may find it difficult to stay in a calm place. 

  *Contradicts the poem's tone, which models the ease and desirability of stillness ("how sweet... quiet... gracious") with no suggestion that an active life makes calm hard to reach.*

**D.** The contrast between the peacefulness of a port at night and its activity during the day reflects the contrast between the calm of old age and the vibrancy of youth. 

  *Invents a daytime scene to contrast against. The poem describes only the still evening/night port — no depiction of daytime activity exists for this comparison to draw on.*

*Difficulty: sat-hardest*

---

##### Q64
> The fynbos shrubland is a diverse habitat found only in South Africa. It is adjacent to the Afro-temperate forest, with almost no transition space between the two distinct habitats. Plants in the fynbos have uniquely thin and long root systems that spread out over large distances to absorb nutrients from the soil. Ecologists transplanted tree seedlings from the forest into plots in the fynbos. Seedlings isolated from the roots of fynbos plants exhibited a growth rate five times greater than that of the seedlings in plots in close proximity to the roots of fynbos plants.

Based on the text, what role do fynbos roots most likely have in maintaining the border between the fynbos shrubland and the Afro-temperate forest habitats?

**A.** Fynbos roots damage the root systems of forest plants, leaving those plants unable to acquire sufficient nutrients. 

  *Substitutes physical damage for the described mechanism. The experiment shows a growth-rate difference tied to proximity and nutrient competition, not any stated damage to the forest seedlings' root systems.*

**B.** Fynbos roots extend close enough to the forest plants' roots that they constitute a physical barrier that forest plants' roots cannot pass. 

  *Invents a physical-barrier mechanism. The described effect is nutrient absorption over large distances by thin, long roots — a competition for resources, not roots forming an impassable blockade.*

**C.** The root systems of fynbos plants allow the plants to take in so many soil nutrients that forest plants are prevented from flourishing in the fynbos. **(Correct)**

  *Correct. Fynbos roots are "thin and long," spreading "over large distances to absorb nutrients," and forest seedlings grown near them grew at only one-fifth the rate of isolated seedlings — fynbos roots outcompete forest plants for soil nutrients, keeping forest plants from establishing in fynbos territory.*

**D.** The root systems of fynbos plants enhance the soil immediately surrounding the plants, allowing them to thrive in an otherwise harsh habitat. 

  *Shifts the causal target from the forest seedlings to the fynbos plants themselves. The experiment measures the growth of transplanted forest seedlings near versus away from fynbos roots, not any benefit fynbos roots confer on fynbos plants' own soil.*

*Difficulty: sat-hardest*

---

##### Q65
> Jürgen Kocka and other historians of capitalism rarely discuss domestic capitalism in Africa before the period of European colonization, implicitly presenting capitalism as external to and imposed on Africa. Crislayne Alfagali and other Africanist scholars have shown, however, that in parts of Africa, returns-focused investment, the establishment of open markets for wage labor, and other features of capitalism predated colonization. One reason for this discrepancy is that historians of capitalism tend to focus on longitudinal economic data drawn from archival records, which do not exist for much of precolonial Africa.

Which statement about Alfagali and other Africanist scholars is best supported by information in the text?

**A.** They likely make use of different types of evidence than historians of capitalism typically rely on. **(Correct)**

  *Correct. Historians of capitalism rely on "longitudinal economic data drawn from archival records, which do not exist for much of precolonial Africa" — since Alfagali's group found evidence of precolonial capitalism anyway, they must have drawn on different kinds of evidence altogether.*

**B.** They likely differ from historians of capitalism in the methods they use to derive longitudinal economic data from archival records. 

  *Wrongly assumes the same source. The passage says the relevant archival records "do not exist" for precolonial Africa — Alfagali's group must be drawing on different kinds of evidence entirely, not deriving data differently from the same nonexistent archives.*

**C.** They likely have a different view about which activities should be considered capitalist in nature than historians of capitalism do. 

  *Invents a definitional disagreement. The passage's stated reason for the discrepancy is evidence availability, not a difference in what counts as capitalism.*

**D.** They likely view capitalism as having been more beneficial for Africa than historians of capitalism do. 

  *Invents a value judgment. The passage is about historical existence and documentation of capitalist activity, not an evaluation of capitalism's benefits or harms.*

*Difficulty: sat-hardest*

---

##### Q66
> Philosophers note that many people have an intuitive sense that while we ought not to lie, there may be circumstances in which lying is permissible. If this intuition is correct and we lack an inviolable duty to speak truthfully, what grounds opposition to lying in the first place? Japa Pallikkathayil has advanced one answer by appealing to a duty to respect others' agential interests: the possession of false beliefs constrains agency, and thus we ought not to impede the formation of true beliefs unless doing so prevents a greater constraint on someone's agency or an otherwise impermissible end.

Which choice best states the main idea of the text?

**A.** One potential means of justifying opposition to lying is Pallikkathayil's argument that we have an obligation to respect other people's agency that entails a commitment to truthfulness except in certain circumstances. **(Correct)**

  *Correct. The passage's driving question is "what grounds opposition to lying in the first place"; Pallikkathayil answers it with a duty to respect agency that yields a commitment to truthfulness, but one that is explicitly qualified ("unless doing so prevents a greater constraint... or an otherwise impermissible end").*

**B.** Many people have an intuitive sense that lying is permissible in some circumstances but lack a principled way to identify those circumstances, and Pallikkathayil's argument may provide a means of resolving that problem. 

  *Restates the philosophical problem incorrectly. The text's driving question is what grounds opposition to lying at all, not how to identify which specific circumstances make lying permissible — that reframes the problem Pallikkathayil is actually answering.*

**C.** Pallikkathayil's argument suggests that if we have a duty to respect other people's agential interests and if possession of false beliefs constrains agency, then we have an inviolable duty to speak truthfully. 

  *Converts an explicitly qualified duty into an absolute one. Pallikkathayil's argument includes an explicit exception ("unless doing so prevents a greater constraint... or an otherwise impermissible end"), and the passage opens by noting we may lack an inviolable duty in the first place — the opposite of this choice's conclusion.*

**D.** Pallikkathayil's argument shows that if our intuition that circumstances may make lying permissible is correct, then it is unclear whether there are any grounds for an opposition to lying in the first place. 

  *Inverts the argument's purpose. Pallikkathayil's account is offered as a positive answer that DOES provide grounds for opposing lying by appeal to respecting agency — not as an argument that leaves the question unanswered or the grounds unclear.*

*Difficulty: sat-hardest*

---

##### Q67
> In their 2022 paper, Christos Dimopoulos et al., having granted that the existence of antigravity—in which antimatter and matter repel rather than attract each other—lacked affirmative experimental support, rightly argued that such antigravity was worth considering on theoretical grounds given that evidence against it was similarly lacking. But a 2023 report by an international team of researchers details the first direct ballistic observations of antihydrogen atoms under gravity inside a CERN particle accelerator. Corresponding most closely to predictions under gravitational attraction, these observations were thoroughly inconsistent with antigravity.

Which choice best states the main idea of the text?

**A.** Antihydrogen ballistics observations were conducted at CERN to test specific conclusions about antigravity presented in the 2022 paper by Dimopoulos et al. 

  *Fabricates a motive for the 2023 study. The passage presents the observations as a separate, later development — the first direct observations of their kind — not as an experiment designed specifically to test Dimopoulos et al.'s conclusions.*

**B.** Although theoreticians were justified in studying antigravity before the release of the 2023 report, the report's findings suggest that the rationale for theoretical consideration offered in the 2022 paper by Dimopoulos et al. is no longer applicable. **(Correct)**

  *Correct. Dimopoulos et al. "rightly argued" antigravity was worth theoretical consideration BECAUSE evidence against it was "similarly lacking" at the time; the 2023 report now supplies direct evidence "thoroughly inconsistent with antigravity," removing the very absence of contrary evidence that had justified the theoretical openness.*

**C.** The theoretical approach represented in the 2022 paper by Dimopoulos et al. assumed that unambiguous proof of antigravity would not be achievable, but the results in the 2023 report undermine that assumption. 

  *Misstates the 2022 paper's claim. Dimopoulos et al. argued antigravity was worth considering because evidence against it was currently lacking — a claim about the state of evidence at the time, not an assumption that unambiguous proof would never be achievable in the future.*

**D.** Before 2023, researchers' inordinate focus on theoretical considerations hindered the development of the experimental regimen for direct antihydrogen ballistics observations. 

  *Invents a hindrance relationship the text doesn't support. The passage explicitly endorses the 2022 theoretical argument as having "rightly argued" its case, not as an obstacle that delayed the 2023 experimental observations, which are presented as a separate later achievement.*

*Difficulty: sat-hardest*

---

#### Command of Evidence — Quantitative (66 items)

##### Q1
> FIGURE. Bar graph, "Amount of Additional Electricity Wind Turbines Could Generate When Winds Were Stronger Than Forecast." The vertical axis is labeled "Electricity (in thousands of MWh)," marked every 25 units from 0 to 200. West: about 150. Midwest: about 175. TEXT. Electric companies that use wind turbines rely on weather forecasts to predict the maximum amount of power, in megawatt-hours (MWh), they can generate using wind so that they can determine how much they'll need to generate from other sources. When winds are stronger than they were forecast to be, however, the predicted maximum amount of electricity wind turbines could generate will be too low. For example, the graph shows that for the West region, the winds were ______

Which choice most effectively uses data from the graph to complete the example?

**A.** strong enough to generate about 150 thousand more MWh of electricity from wind turbines. **(Correct)**

  *Correct. The West bar sits at about 150, and this is the extra electricity turbines could generate because the wind ran stronger than forecast — the direction ("strong enough," "more") matches the graph's title, and the value matches the bar.*

**B.** so weak that the electricity from wind turbines was about 175 thousand MWh less than predicted. 

  *This gets the direction backward — the graph is titled around winds being stronger than forecast, not weaker — and it also reads the Midwest bar's value (about 175), not the West bar's.*

**C.** so weak that the electricity from wind turbines was about 150 thousand MWh less than predicted. 

  *The value is right — 150 is the West bar — but "so weak... less than predicted" flips the sense of the graph, which shows additional electricity available because winds were stronger, not electricity lost because they were weaker.*

**D.** strong enough to generate about 175 thousand more MWh of electricity from wind turbines. 

  *The direction is right, but 175 is the Midwest bar's value, not the West bar's. The sentence asks specifically about the West region.*

*Difficulty: medium*

---

##### Q2
> TABLE. "Results of Footprint Analysis for Two Sets of Theropod Tracks." Columns: tracks; estimated footprint length (centimeters); average stride length (meters); estimated mean speed (meters per second). La Torre 6A: 32.8 cm; 5.23 m; 6.5–10.3 m/s. La Torre 6B: 28.9 cm; 5.57 m; 8.8–12.4 m/s. TEXT. The table shows data from paleontologist Angélica Torices and colleagues' 2021 study of two sets of dinosaur tracks preserved in a fossilized lake bed in Spain. The tracks, referred to as La Torre 6A and La Torre 6B, were left by two individual theropods (dinosaurs that walked on two legs). The team's findings suggest that of the two theropods, the one that left the La Torre 6B tracks had a higher maximum mean speed, ______

Which choice most effectively uses data from the table to complete the claim?

**A.** a longer footprint, and a longer average stride. 

  *The stride comparison is right — 5.57 m exceeds 5.23 m — but the footprint comparison is flipped. La Torre 6B's footprint (28.9 cm) is shorter than La Torre 6A's (32.8 cm), not longer.*

**B.** a longer footprint, and a shorter average stride. 

  *Both comparisons are inverted here. La Torre 6B's footprint (28.9 cm) is shorter than 6A's (32.8 cm), and its stride (5.57 m) is longer than 6A's (5.23 m) — the exact opposite of what this choice claims on both counts.*

**C.** a shorter footprint, and a longer average stride. **(Correct)**

  *Correct. La Torre 6B's footprint, 28.9 cm, is shorter than 6A's 32.8 cm, and its stride, 5.57 m, is longer than 6A's 5.23 m. Both comparisons match the table.*

**D.** a shorter footprint, and a shorter average stride. 

  *The footprint comparison is correct — 28.9 cm is shorter than 32.8 cm — but the stride comparison is flipped. La Torre 6B's stride (5.57 m) is longer than 6A's (5.23 m), not shorter.*

*Difficulty: medium*

---

##### Q3
> TABLE. "Average Temperatures in July in Four Locations in the Navajo Nation." Columns: location; average highest temperature (Fahrenheit); average lowest temperature (Fahrenheit). Teec Nos Pos: 94°; 65°. Cameron: 99°; 65°. Ramah: 83°; 50°. Tuba City: 83°; 50°. TEXT. The Navajo Nation has the largest land area of any tribal nation in the United States: over 27,000 square miles in the Southwest. Because this area is so huge and its communities are located at various elevations, the people of the Navajo Nation can experience different climate conditions depending on where they live. For example, in July, ______

Which choice most effectively uses data from the table to complete the statement?

**A.** the lowest temperature for both Cameron and Teec Nos Pos was 65°. 

  *This is accurate — both locations do show 65° — but it demonstrates two locations matching each other, not differing. The sentence is illustrating that climate conditions can differ across the Navajo Nation, and a matching pair does the opposite.*

**B.** Tuba City's average highest temperature was 94°, while Teec Nos Pos's was 93°. 

  *Both values are wrong. Tuba City's average highest temperature is 83°, not 94° — 94° belongs to Teec Nos Pos — and Teec Nos Pos's own average highest is 94°, not 93°. This misstates the table on both halves.*

**C.** Ramah's average highest temperature was 83°, while Cameron's was 99°. **(Correct)**

  *Correct. Ramah's average highest, 83°, and Cameron's, 99°, are both accurate, and the 16-degree gap between them is exactly the kind of different climate condition the sentence is illustrating.*

**D.** the lowest temperature for both Ramah and Tuba City was 50°. 

  *This is accurate — both are 50° — but again it shows two locations agreeing, not differing, which does not illustrate a claim about varied climate conditions across the nation.*

*Difficulty: medium*

---

##### Q4
> FIGURE. Line graph, "Copper Production for Three States, 1889–1909," in millions of pounds. Montana (solid, triangle markers): about 100 in 1889, about 270 in 1902, about 310 in 1909. Arizona (dashed, square markers): under 25 in 1889, about 110 in 1902, about 310 in 1909. Michigan (dotted, circle markers): about 95 in 1889, about 165 in 1902, about 230 in 1909. TEXT. Copper had been mined in the US for thousands of years, but large-scale commercial mining of copper took off starting in the late 1800s. This was due to several factors. Technological advancements in the mining industry led to improvements in the production of copper. This helped the country keep up with the growing number of people wanting to buy copper starting in the 1890s. At the same time, the growth of the railroad system made the transportation of copper in large batches much easier. Several states saw rapid growth in the production of this resource, for example, ______

Which choice most effectively uses data in the graph to complete the example?

**A.** The rise in copper production in Michigan slowed from 1902 to 1909. 

  *Even taken at face value, a slowdown in Michigan's rate of increase runs against, not toward, the sentence's point — it is illustrating rapid growth, and a deceleration is the wrong pattern to cite as that example.*

**B.** Montana and Arizona produced more copper than Michigan did in 1909. 

  *This is accurate — both lines sit above Michigan's by 1909 — but it is a single-year ranking, not a picture of growth across 1889 to 1909. The sentence needs an example of rapid growth over the period, and an endpoint comparison doesn't show any change over time at all.*

**C.** Fewer than 100 million pounds of copper were produced in Arizona in 1889. 

  *This is accurate — Arizona's 1889 point sits under 25 — but it is a single data point from a single year. "Rapid growth" is a comparison across time, and one number alone cannot show a rise.*

**D.** Copper production rose significantly from 1889 to 1909 for Arizona, Michigan, and Montana. **(Correct)**

  *Correct. All three lines climb substantially across the two decades — Arizona from under 25 to about 310, Michigan from about 95 to about 230, Montana from about 100 to about 310 — which is exactly the rapid growth the sentence is illustrating.*

*Difficulty: sat-hardest*

---

##### Q5
> TABLE. "Comfort Ratings and Temperature-Adjustment Preferences from One Survey." Columns: participant; comfort rating; preferred temperature adjustment. Participant 20: −2; cooler. Participant 1: 1; cooler. Participant 21: 1; cooler. TEXT. Nan Gao and her team conducted multiple surveys to determine participants' levels of comfort in a room where the temperature was regulated by a commercial climate control system. Participants filled out surveys several times a day to indicate their level of comfort on a scale from −3 (very cold) to +3 (very hot), with 0 indicating neutral (neither warm nor cool), and to indicate how they would prefer the temperature to be adjusted. The table shows three participants' responses in one of the surveys. According to the table, all three participants wanted the room to be cooler, ______

Which choice most effectively uses data from the table to complete the statement?

**A.** and they each reported the same level of comfort. 

  *This contradicts the table directly. The comfort ratings are −2, 1, and 1 — participant 20's rating is not the same as the other two.*

**B.** even though each participant's ratings varied throughout the day. 

  *The table shows one survey — a single snapshot in time — not multiple surveys across the day for these three participants. Whether their ratings varied over the day is not something this table can show.*

**C.** but participant 20 reported feeling significantly colder than the other two participants did. **(Correct)**

  *Correct. Participant 20's rating, −2, is well below participant 1's and participant 21's, both at 1 — a real contrast within the group that the table supports directly.*

**D.** but participant 1 reported feeling warmer than the other two participants did. 

  *Participant 1's rating (1) is not warmer than both of the others — it ties participant 21's rating (also 1) and is warmer only than participant 20's. "The other two" requires beating both, and this choice only beats one.*

*Difficulty: hard*

---

##### Q6
> FIGURE. Bar graph, "Area of Three Glaciers in the 2016 Swiss Glacier Inventory," in square kilometers. Gorner: about 42. Fiescher: about 30. Unteraar: about 23. TEXT. To monitor changes to glaciers in Switzerland, the government periodically measures them for features like total area of ice and mean ice thickness, which are then reported in the Swiss Glacier Inventory. These measurements can be used to compare the glaciers. For example, the Gorner glacier had ______

Which choice most effectively uses data from the graph to complete the example?

**A.** a larger area than either the Fiescher glacier or the Unteraar glacier. **(Correct)**

  *Correct. Gorner's bar, about 42, stands above both Fiescher's (about 30) and Unteraar's (about 23).*

**B.** a smaller area than the Fiescher glacier but a larger area than the Unteraar glacier. 

  *The first half is backward. Gorner (about 42) is larger than Fiescher (about 30), not smaller — Gorner is the tallest bar on the graph, not a middle one.*

**C.** a smaller area than either the Fiescher glacier or the Unteraar glacier. 

  *Both comparisons are inverted. Gorner's bar is the tallest of the three, not the shortest against either other glacier.*

**D.** a larger area than the Fiescher glacier but a smaller area than the Unteraar glacier. 

  *The Fiescher comparison is right, but the Unteraar comparison is flipped. Gorner (about 42) is larger than Unteraar (about 23), not smaller — Unteraar is the smallest of the three glaciers, not the largest.*

*Difficulty: medium*

---

##### Q7
> FIGURE. Line graph, "Singer Sewing Machine Sales in Four Countries, 1903–1918," in machines sold. New Zealand (solid triangle): stays low, roughly 3,000–7,000, across all four years. Australia (dashed square): about 22,000 in 1903, about 30,000 in 1908, about 25,000 in 1913, about 20,000 in 1918. The Philippines (dotted circle): about 5,000 in 1903, about 10,000 in 1908, about 25,000 in 1913, about 45,000 in 1918. Turkey (dashed diamond): about 22,000 in 1903, about 33,000 in 1908, about 50,000 in 1913, about 15,000 in 1918. TEXT. By the early 1900s, the Singer Corporation, a US sewing machine manufacturer founded in 1851, began to see rapidly increasing sales abroad, particularly in Russia, Germany, and the United Kingdom. These markets were responsible for the bulk of Singer's overseas sales, but demand for the company's machines in other countries also grew significantly in the early twentieth century. For instance, sales of their sewing machines in ______

Which choice most effectively uses data from the graph to complete the example?

**A.** the Philippines increased dramatically from 1908 to 1918. **(Correct)**

  *Correct. The Philippines line climbs from about 10,000 in 1908 to about 45,000 in 1918 — a dramatic rise that matches the sentence's claim that demand "grew significantly."*

**B.** New Zealand were largely consistent from 1903 to 1918. 

  *This is an accurate read of the flat New Zealand line, but the sentence needs an example of demand that "grew significantly." A largely consistent, unchanging line is the opposite of growth, however true the description is.*

**C.** Australia increased steadily from 1903 to 1918. 

  *This misreads the shape of the line. Australia rises from 1903 to 1908, then declines through 1913 and 1918 — it is not a steady increase across the whole period.*

**D.** Turkey declined substantially from 1913 to 1918. 

  *This is an accurate read — Turkey's line does fall sharply after its 1913 peak — but a decline is the opposite of the growth in demand the sentence is illustrating.*

*Difficulty: sat-hardest*

---

##### Q8
> TABLE. "Moons of Dwarf Planets." Columns: dwarf planet name; number of moons; name of moons. Haumea: 2; Hi'iaka, Namaka. Ceres: 0; N/A. Makemake: 1; MK 2. Eris: 1; Dysnomia. Pluto: 5; Charon, Nix, Kerberos, Styx, Hydra. TEXT. Like Earth, some dwarf planets in the solar system have exactly one moon. Two examples of such dwarf planets are ______

Which choice most effectively uses data from the table to complete the statement?

**A.** Eris and Makemake. **(Correct)**

  *Correct. Both Eris and Makemake are listed with exactly one moon apiece — Dysnomia and MK 2.*

**B.** Haumea and Eris. 

  *Eris does have exactly one moon, but Haumea has two, Hi'iaka and Namaka — it doesn't meet the "exactly one" requirement the statement asks for.*

**C.** Pluto and Haumea. 

  *Neither planet qualifies. Pluto has five moons and Haumea has two — both well past "exactly one."*

**D.** Makemake and Ceres. 

  *Makemake does have exactly one moon, but Ceres has zero, listed as N/A — zero does not satisfy "exactly one" any more than five or two does.*

*Difficulty: medium*

---

##### Q9
> FIGURE. Line graph, "Investigative Articles Published in the Albuquerque Journal from 2010 to 2019," in number of articles. Approximate values: 2010, 1,100; 2011, 1,300; 2012, 1,500; 2013, 1,600 (the highest point); 2014, 1,000; 2015, 900; 2016, 800 (the lowest point before 2019); 2017, 1,150; 2018, 950; 2019, 500 (the lowest point overall). TEXT. Investigative journalists research and report about fraud, corruption, public hazards, and more. The graph shows the number of investigative articles published in the Albuquerque Journal newspaper from 2010 to 2019. According to an analyst, although the number of investigative articles published in this newspaper has varied significantly over the period shown, the number overall has fallen since 2010.

Which choice most effectively uses data from the graph to justify the underlined claim?

**A.** The newspaper published approximately 1,000 investigative articles in 2010 and approximately 500 in 2019. **(Correct)**

  *Correct. Comparing the first year to the last year of the period shown — the two points that "since 2010" actually spans — shows a drop from about 1,000 to about 500, which is exactly what "has fallen since 2010" claims.*

**B.** The smallest annual number of investigative articles published in the newspaper during the period shown is approximately 1,600 in 2013. 

  *This has the graph's extremes backward. About 1,600 in 2013 is close to the highest point on the line, not the smallest — the actual smallest value, around 500, falls in 2019.*

**C.** The greatest annual number of investigative articles published in the newspaper during the period shown is approximately 1,000 in 2017. 

  *This misidentifies the peak twice over: about 1,000 is not the graph's greatest value (2013's roughly 1,600 is far higher), and 2017 is a minor uptick partway through the decline, not the high point of the line.*

**D.** The newspaper published approximately 1,000 investigative articles in 2010 and approximately 1,600 in 2013. 

  *Both values are accurate, but comparing 2010 to 2013 — an interior peak year — shows a rise, not a fall, and it never reaches the endpoint the claim is actually about. "Since 2010" needs 2010 set against the most recent year, not against the high point in between.*

*Difficulty: sat-hardest*

---

##### Q10
> FIGURE. Line graph, "Number of Young Fish Collected at Mangrove Sites in the Egyptian Red Sea During Three Seasons of 2010." Common silver-biddy (solid triangle): winter about 35, spring about 17, fall about 10. Red Sea goatfish (dashed square): winter about 2, spring about 7, fall 0. Milkfish (dotted circle): winter about 12, spring about 7, fall 0. TEXT. Mangroves are trees or bushes that grow on the coastlines of seas and rivers. Areas with mangroves are great places for young fish since they help keep these fish fed and protected while they grow. To study the importance of mangroves to young fish, researchers Mohamed A. Abu El-Regal and Nesreen K. Ibrahim collected and identified young fish from three different mangrove sites in the Egyptian Red Sea. They collected fish in the winter, spring, and autumn of 2010, collecting a total of 269 fish from 21 different species. For some species, more fish were collected in the winter than the other two seasons, for instance: ______

Which choice most effectively uses the data in the graph to complete the example?

**A.** more common silver-biddy and milkfish were collected in the winter than in either of the other two seasons. **(Correct)**

  *Correct. For the common silver-biddy, winter (about 35) exceeds spring (about 17) and fall (about 10); for milkfish, winter (about 12) exceeds spring (about 7) and fall (0). Both species peak in winter compared with their own spring and fall counts, which is exactly the within-species, cross-season pattern the sentence describes.*

**B.** the common silver-biddy was collected more frequently than the other two species in all three seasons. 

  *This may well be true, but it compares species to each other within each season, not one species' winter count to its own spring and fall counts. The sentence needs winter set against the other seasons for a species, not species set against each other.*

**C.** in the spring, researchers collected more Red Sea goatfish than they collected from the other two species. 

  *This also compares species to each other rather than seasons to each other, and it is confined to a single season (spring), so it cannot show anything about winter counts at all.*

**D.** in the fall, researchers collected 10 common silver-biddy but collected no milkfish or Red Sea goatfish. 

  *This is an accurate snapshot of the fall season alone, but it makes no comparison to winter or spring at all — the sentence is about winter standing out from the other two seasons, and this choice never leaves one season.*

*Difficulty: sat-hardest*

---

##### Q11
> FIGURE. Bar graph, "Deformation Rate of Five Volcanoes," in centimeters per month. Alcedo: about 0.3. Maule: about 1.9. Fernandina: about 0.6. Pacaya: about 3.3. Sierra Negra: about 2.8. TEXT. When magma moves underneath a volcano, it causes the surface of the volcano to change. This is known as deformation. Researchers recently calculated the amount of deformation occurring each month for five volcanoes in Latin America. Although Sierra Negra experienced a lot of deformation, its deformation rate was still lower than that of ______

Which choice most effectively uses data from the graph to complete the statement?

**A.** Alcedo. 

  *Alcedo's rate, about 0.3, is the lowest of the five — far below Sierra Negra's 2.8, not above it. The sentence needs a volcano Sierra Negra trails, and Alcedo is the opposite end of the graph.*

**B.** Pacaya. **(Correct)**

  *Correct. Pacaya's rate, about 3.3, is the only bar higher than Sierra Negra's 2.8 — the one volcano whose deformation rate Sierra Negra's still falls short of.*

**C.** Fernandina. 

  *Fernandina's rate, about 0.6, sits well below Sierra Negra's 2.8, not above it — the same directional error as choosing Alcedo.*

**D.** Maule. 

  *Maule's rate, about 1.9, is the closest value to Sierra Negra's on the graph, which is what makes it tempting, but it is still below 2.8 — Maule is not the volcano Sierra Negra's rate trails.*

*Difficulty: medium*

---

##### Q12
> TABLE. "Effect of Paywall Introduction on Newspaper Companies' Revenues." Columns: newspaper; total revenue change ($ in thousands); percentage change (%); newspaper size. Los Angeles Times: 93,966; 12.5; large. The New York Times: 235,788; 20; large. The Denver Post: −3,765; −1; small. Sun Sentinel: −24,899; −11.9; small. Chicago Tribune: 94,492; 19; large. TEXT. Digital paywalls restrict access to online content to those with a paid subscription. In an investigation of the effect of paywalls on newspaper company revenues for print and digital subscriptions and advertising, Doug J. Chung and colleagues compared actual outcomes (with a paywall) to control estimates (without a paywall). The researchers concluded that introducing a paywall is generally more beneficial for larger newspapers, which have high circulation and tend to offer a substantial amount of unique online content.

Which choice best describes data from the table that support Chung and colleagues' conclusion?

**A.** The Chicago Tribune and the Los Angeles Times had similar total revenue changes, but the Los Angeles Times had a smaller percentage change. 

  *This compares two large newspapers to each other. The conclusion is about large newspapers doing better than small ones, and a comparison that never includes a small newspaper cannot demonstrate that size made the difference.*

**B.** The Los Angeles Times had a 12.5% revenue change, while Chicago Tribune had a 19% revenue change. 

  *Again, both papers here are large. Without a small paper in the comparison, this cannot show that being large — rather than something else — is what predicted the outcome.*

**C.** The New York Times had a 20% revenue change, while Denver Post had a –1% revenue change. **(Correct)**

  *Correct. This sets a large newspaper (The New York Times, up 20%) directly against a small one (The Denver Post, down 1%) — the large-versus-small contrast the conclusion is actually about.*

**D.** The Denver Post had only a –1% revenue change, which was the smallest percentage change of the selected companies. 

  *This is accurate but describes one small newspaper in isolation, with no large newspaper set against it. A single data point cannot establish that size predicted the outcome.*

*Difficulty: sat-hardest*

---

##### Q13
> TABLE. "Daily Distance Traveled by Adult Mountain Lions in Three Seasons." Columns: season; kilometers per day traveled by adult females; kilometers per day traveled by adult males. Cold-dry: 9.28; 15.81. Monsoon: 12.64; 18.93. Hot-dry: 12.48; 18.87. TEXT. Wildlife researcher Dana L. Karelus and her colleagues tracked the movements of female and male adult mountain lions over three seasons: the cold-dry season, the hot-dry season, and the monsoon season. They found that the least amount of travel per day occurred in ______

Which choice most effectively uses data from the table to complete the statement?

**A.** the cold-dry season for both females and males. **(Correct)**

  *Correct. Cold-dry is the lowest value in both columns — 9.28 km/day for females (below 12.64 and 12.48) and 15.81 km/day for males (below 18.93 and 18.87).*

**B.** the cold-dry season for females and the hot-dry season for males. 

  *The female half is right, but the male half checks only one alternative. Hot-dry males travel 18.87 km/day, which is still more than cold-dry males' 15.81 — cold-dry is the male minimum too, not hot-dry.*

**C.** the hot-dry season for females and the monsoon season for males. 

  *Neither half matches the table's actual minimum. Hot-dry females (12.48) exceed cold-dry females (9.28), and monsoon males (18.93) are in fact the highest male value, not the lowest.*

**D.** the monsoon season for both females and males. 

  *Monsoon is the highest value in both columns, not the lowest — 12.64 for females and 18.93 for males are each the largest number in their column. This picks the maximum where the statement asks for the minimum.*

*Difficulty: hard*

---

##### Q14
> TABLE. "Percent of Residents of City Areas in Favor of Adding More Bike Paths." City area; percent of area's residents in favor. North East: 12%. North Central: 26%. North West: 46%. South West: 88%. South Central: 33%. TEXT. A city's Parks and Recreation department is interested in providing residents with more opportunities for bicycling in their neighborhoods. They're considering adding more bike paths and conducted a survey to understand where demand for more bike paths is highest. The survey indicated the highest level of demand, with 88 percent of the residents interested in adding more bike paths, is in the city's ______

Which choice most effectively uses data from the table to complete the statement?

**A.** South West area. **(Correct)**

  *Correct. The South West row shows 88%, matching the figure named in the sentence exactly.*

**B.** South Central area. 

  *South Central's value is 33%, not 88% — a different row entirely.*

**C.** North East area. 

  *North East's value is 12%, the lowest in the table — the opposite end from the 88% the sentence names.*

**D.** North Central area. 

  *North Central's value is 26%, not 88% — a different row from the one the sentence describes.*

*Difficulty: easy*

---

##### Q15
> TABLE. "Guilds in French Cities in the Late Eighteenth Century." Columns: city; date; inhabitants; number of guilds; inhabitants per guild. Paris: 1766; 600,000; 133; 4,511. Bordeaux: 1762; 80,000; 49; 1,633. Rouen: 1775; 74,000; 112; 661. Lyon: 1789; 143,000; 72; 1,986. TEXT. Guilds — local associations of artisans and merchants in the same industry — were widespread in France from the medieval period until the late eighteenth century. But guilds were much more numerous relative to the population in some cities than in others: for example, ______

Which choice most effectively uses data from the table to complete the statement?

**A.** there were 49 guilds in Bordeaux but 72 guilds in Lyon despite the two cities having nearly equal numbers of inhabitants. 

  *The premise is false. Bordeaux (80,000 inhabitants) and Lyon (143,000) are not nearly equal — Lyon's population is nearly double Bordeaux's — so the guild-count comparison here doesn't actually isolate a density difference the way the statement implies.*

**B.** Lyon had far fewer inhabitants than Paris did but had many more guilds. 

  *This reverses the guild count. Lyon has 72 guilds, fewer than Paris's 133 — not many more.*

**C.** there was one guild for every 661 inhabitants in Rouen but one guild for every 4,511 inhabitants in Paris. **(Correct)**

  *Correct. This uses the rate column — inhabitants per guild — which is the size-independent measure the sentence needs to show guilds were "more numerous relative to the population" in one city than another: one guild per 661 people in Rouen against one per 4,511 in Paris is a real and large difference in density.*

**D.** Paris had 133 guilds and 600,000 inhabitants, or one guild for every 4,511 inhabitants. 

  *Every figure here is accurate, but it describes only Paris. The statement requires guild density in "some cities" set against "others," and a single city's numbers, however correct, make no comparison at all.*

*Difficulty: hard*

---

##### Q16
> TABLE. "Time Participants Spent Reading about Five London Museums." Columns: museum name; ranking; percentage of total time spent reading about museum by participants provided with ranking; percentage of total time spent reading about museum by participants not provided with ranking. British Museum: 1; 36; 18. National Gallery: 2; 21; 20. Tate Modern: 4; 16; 17. Victoria and Albert Museum: 5; 14; 23. Natural History Museum: 3; 13; 22. TEXT. Researchers recently conducted an experiment to understand how we use rankings to make decisions. They created a fictitious travel website describing five museums in London. Then, they invited two groups of participants, who had never visited the museums, to review the site and select the museum they would be most likely to visit. Meanwhile, the researchers tracked the amount of time each participant spent reading about each museum. For one group, the website ranked each museum, titling the page "The Top 5 Museums in London." For the other group, the museums and their descriptions were not ranked. The researchers concluded that when reviewing ranked lists, we tend to focus on the top-ranked option.

Which choice best describes data in the table that support the researchers' conclusion?

**A.** Participants who were not provided with a ranking of the museums spent roughly equal amounts of time reading about each museum. 

  *This is an accurate read of the unranked column, but it describes the group that never saw a ranking at all. The conclusion is about what happens when a ranking is present, and this choice stays entirely with the control condition.*

**B.** Participants who were provided with a ranking of the museums spent disproportionately more time reading about the British Museum. **(Correct)**

  *Correct. The British Museum, ranked first, drew 36% of reading time from the ranked group versus only 18% from the unranked group looking at the identical description — a clear, disproportionate pull toward the top-ranked option once a ranking existed.*

**C.** Participants who were provided with a ranking of the museums spent the least amount of time reading about the Natural History Museum. 

  *This is accurate — 13% is the lowest figure in the ranked column — but it identifies the museum that got the least attention, not the top-ranked museum getting extra attention. The conclusion is specifically about a pull toward the top, and this choice describes the opposite end of the list.*

**D.** Participants who were not provided with a ranking of the museums spent the most time reading about the Victoria and Albert Museum. 

  *This is accurate — 23% is the highest figure in the unranked column — but the Victoria and Albert Museum was ranked fifth, and this describes the control group, which never saw any ranking. It cannot show a bias toward top-ranked options when no ranking was shown.*

*Difficulty: sat-hardest*

---

##### Q17
> TABLE. "Estimated Impacts of Invasive Predator Species on Threatened Birds, Mammals, and Reptiles." Columns: invasive predator species; estimated impact on threatened birds; estimated impact on threatened mammals; estimated impact on threatened reptiles. Mongooses: 0.66; 0.75; 0.44. Dogs: 0.67; 0.57; 0.44. Cats: 0.74; 0.61; 0.52. TEXT. How harmful are invasive predators to threatened species? To find out, researchers assigned values from 0.25 to 1.00 to various harms caused by invasive predators. The researchers then used these values to estimate the extent to which several invasive predator species have harmfully impacted threatened birds, mammals, and reptiles. In the table, higher numbers represent greater impacts. The estimated impact of invasive mongooses on threatened mammals is ______

Which choice most effectively uses data from the table to complete the example?

**A.** 0.35. 

  *This value does not appear anywhere in the table for any species or category — it is not a misread cell, just a figure the table never reports.*

**B.** 0.61. 

  *0.61 is cats' impact on mammals, not mongooses'. The column is right; the row is wrong.*

**C.** 0.75. **(Correct)**

  *Correct. The mongooses row and the threatened-mammals column intersect at 0.75.*

**D.** 0.44. 

  *0.44 is mongooses' impact on reptiles, not mammals. The row is right; the column is wrong.*

*Difficulty: easy*

---

##### Q18
> FIGURE. Bar graph, "Test Results for Two New Battery Recycling Processes," showing lithium recovered (%). Type A: recycling process 1 about 30, recycling process 2 about 55. Type B: recycling process 1 about 35, recycling process 2 about 75 (the tallest bar). TEXT. A team of scientists wants to improve the recycling of two of the most common types of lithium-ion batteries used in electronic devices. The team tested two new processes that involve grinding battery materials and aluminum foil together. The highest percentage of lithium recovered in the tests was closest to ______

Which choice most effectively uses data from the graph to complete the statement?

**A.** 75%. **(Correct)**

  *Correct. The tallest bar on the graph — Type B, recycling process 2 — reaches about 75%, the highest recovery rate among all four bars shown.*

**B.** 10%. 

  *No bar on the graph comes anywhere close to this low. Even the shortest bar, Type A under recycling process 1, reaches about 30%.*

**C.** 45%. 

  *This falls between the shorter bars and the taller ones, but no bar actually stops at this height — it reads like a plausible middle guess rather than a value taken from the chart.*

**D.** 20%. 

  *Like 10%, this sits below every bar on the graph, including the shortest one.*

*Difficulty: easy*

---

##### Q19
> TABLE. "Total Electoral College Votes and Popular Votes in the 15th US Presidential Election." Columns: candidate; total electoral college votes; total popular votes. James K. Polk: 170; 1,339,494. Henry Clay: 105; 1,300,004. James Gillespie Birney: 0; 62,103. TEXT. A student is writing a paper on the history of the 15th presidential election in the United States, which was held in 1844. The student needs to determine how many electoral college votes were cast for the winning candidate, James K. Polk. According to the table, James K. Polk received ______

Which choice most effectively uses data from the table to complete the statement?

**A.** 170 electoral college votes. **(Correct)**

  *Correct. Polk's row lists 170 electoral college votes.*

**B.** 103 electoral college votes. 

  *This figure does not match Polk's row at all — the closest real number in the table is Henry Clay's 105 electoral votes, and Clay is a different, losing candidate.*

**C.** 62 electoral college votes. 

  *This is the leading digits of Birney's popular vote total, 62,103 — the wrong column (popular votes, not electoral votes) for the wrong candidate.*

**D.** 44 electoral college votes. 

  *This number appears nowhere in the table, for any candidate, in either column.*

*Difficulty: easy*

---

##### Q20
> TABLE. "Number of Museum Visits (in Millions) from 2016 to 2019." Columns: museum; 2016; 2017; 2018; 2019. National Museum of the American Indian: 1.1; 1.2; 1.1; 0.96. National Museum of African American History and Culture: 0.73; 2.4; 1.9; 2.0. TEXT. A student is researching the number of visits each year to two museums, the National Museum of the American Indian and the National Museum of African American History and Culture. Of the four years included in the table, the year when both museums had the highest number of visits was ______

Which choice most effectively uses data from the table to complete the statement?

**A.** 2016. 

  *2016 is actually the low point for the National Museum of African American History and Culture (0.73, its smallest value in the table), and the American Indian museum's 2016 figure, 1.1, ties 2018 rather than reaching its own peak of 1.2.*

**B.** 2018. 

  *Neither museum peaks in 2018 — the American Indian museum sits at 1.1 (below its 1.2 high) and the African American History museum at 1.9 (below its 2.4 high). It's a plausible middle year, not the peak for either.*

**C.** 2019. 

  *2019 is the American Indian museum's lowest year in the table (0.96), and the African American History museum's 2.0 that year is still below its own 2017 high of 2.4.*

**D.** 2017. **(Correct)**

  *Correct. 2017 is the American Indian museum's own high point (1.2) and the African American History museum's own high point (2.4) at the same time — the one year both rows peak together.*

*Difficulty: medium*

---

##### Q21
> TABLE. "Millions of Metric Tons of Copper Mined in 1995 and 2020." Columns: country; 1995; 2020. Canada: 0.73; 0.59. Indonesia: 0.44; 0.51. Kazakhstan: 0.26; 0.55. Chile: 2.49; 5.73. TEXT. While doing research for a paper about copper mining, a student finds a table with information about four different countries. The student notes that the country that mined 0.55 million metric tons of copper in 2020 had mined ______

Which choice most effectively uses data from the table to complete the statement?

**A.** 0.59 million metric tons of copper in 1995. 

  *0.59 is Canada's 2020 figure, not its 1995 one — a value pulled from an adjacent cell in the wrong country's row, close to 0.55 but not it.*

**B.** 0.44 million metric tons of copper in 1995. 

  *Indonesia's 2020 figure is 0.51, not 0.55, so Indonesia is the wrong country to begin with — this reports Indonesia's own 1995 value as if it answered the question.*

**C.** 0.26 million metric tons of copper in 1995. **(Correct)**

  *Correct. Kazakhstan's 2020 value is 0.55, matching the country identified in the statement, and its 1995 value is 0.26.*

**D.** 2.49 million metric tons of copper in 1995. 

  *Chile's 2020 figure is 5.73, nowhere near 0.55 — the wrong country by a wide margin, with its 1995 value substituted in regardless.*

*Difficulty: medium*

---

##### Q22
> TABLE. "Total Areas of Five Tribal Nations in California." Columns: tribal nation; location; area (square miles). Hoopa Valley Tribe: Northern California; 141.68. La Jolla Band of Luiseño Indians: Southern California; 13.50. Pauma Band of Luiseño Mission Indians: Southern California; 9.36. Agua Caliente Band of Cahuilla Indians: Northern California; 53.68. Los Coyotes Band of Cahuilla and Cupeño Indians: Southern California; 39.21. TEXT. In what is now the state of California, there are over 100 tribal nations. One of the largest, the Hoopa Valley Tribe, covers 141.68 square miles in the northern part of the state. However, most tribal nations in California are less than 50 square miles in total area. For example, the total area of the Los Coyotes Band of Cahuilla and Cupeño Indians in Southern California is ______

Which choice most effectively uses data from the table to support the statement?

**A.** 13.50 square miles. 

  *13.50 is the La Jolla Band of Luiseño Indians' area, not the Los Coyotes Band's.*

**B.** 53.68 square miles. 

  *53.68 belongs to the Agua Caliente Band, not the Los Coyotes Band — and it doesn't even fit the sentence's own point, since it's above the "less than 50 square miles" pattern being illustrated.*

**C.** 9.36 square miles. 

  *9.36 is the Pauma Band of Luiseño Mission Indians' area, not the Los Coyotes Band's.*

**D.** 39.21 square miles. **(Correct)**

  *Correct. The Los Coyotes Band of Cahuilla and Cupeño Indians' row lists 39.21 square miles.*

*Difficulty: easy*

---

##### Q23
> TABLE. "Effect of Neighboring Species on Pollinator Visits to Target Species." Columns: neighboring species; target species; effect value. Virginia spring beauty; star chickweed; 0.4853. Himalayan balsam; marsh woundwort; 0.7905. common dandelion; cat's ear; −0.6254. TEXT. Researchers Carolina Laura Morales and Anna Traveset gathered data about flowering plants growing alongside each other in various locations. In each case, the researchers identified one plant as a "target species" and a nearby plant as a "neighboring species." The researchers then calculated a positive or negative value to show how the neighboring species affected pollinator visits to the target species. One example of a neighboring species with a negative effect value is the ______

Which choice most effectively uses data from the table to complete the example?

**A.** Himalayan balsam. 

  *Himalayan balsam is correctly a neighboring species, but its effect value, 0.7905, is positive, not negative.*

**B.** common dandelion. **(Correct)**

  *Correct. Common dandelion is listed as a neighboring species with an effect value of −0.6254, a negative number.*

**C.** star chickweed. 

  *Star chickweed appears in the table as a target species, not a neighboring species — this answer comes from the wrong column entirely.*

**D.** Virginia spring beauty. 

  *Virginia spring beauty is a neighboring species, the right category, but its effect value, 0.4853, is positive, not negative.*

*Difficulty: medium*

---

##### Q24
> TABLE. "Pyramids in Egypt and the Americas." Columns: pyramid; country; height (meters); age (years before present). The Great Pyramid: Mexico; 33; 2,050 to 2,400. The Pyramid of Djoser: Egypt; 60; 4,600 to 4,700. The Pyramid of Sahure: Egypt; 47; 4,400 to 4,500. El Castillo: Belize; 40; 1,100 to 1,400. TEXT. A student is writing an essay about four pyramids for a history class and wants to note how long ago each pyramid was built and how tall each pyramid is. Consulting the table, the student finds that el Castillo was built 1,100 to 1,400 years ago and is ______

Which choice most effectively uses data from the table to complete the text?

**A.** 33 meters tall. 

  *33 meters is the Great Pyramid's height, not El Castillo's.*

**B.** 47 meters tall. 

  *47 meters is the Pyramid of Sahure's height, not El Castillo's.*

**C.** 40 meters tall. **(Correct)**

  *Correct. El Castillo's row lists a height of 40 meters, matching the 1,100-to-1,400-year age already given.*

**D.** 60 meters tall. 

  *60 meters is the Pyramid of Djoser's height, not El Castillo's.*

*Difficulty: easy*

---

##### Q25
> TABLE. "Total Areas of Five Pueblo Nations in New Mexico." Columns: tribal nation; area (square miles). Pueblo de San Ildefonso: 47.3. Santa Clara Pueblo: 77.1. Taos Pueblo: 156.2. Nambé Pueblo: 32.4. Pueblo of Acoma: 595.7. TEXT. There are nineteen Pueblo tribal nations in New Mexico. A student in a geography class is a citizen of Taos Pueblo in the northern part of the state. The student wants to compare the total area covered by Taos Pueblo with the total areas of various other Pueblo nations in the state. Looking at the table, the student finds that the total area of Taos Pueblo is 156.2 square miles, while the total area of Nambé Pueblo is ______

Which choice most effectively uses data from the table to complete the comparison?

**A.** 47.3 square miles. 

  *47.3 square miles is Pueblo de San Ildefonso's area, not Nambé Pueblo's.*

**B.** 77.1 square miles. 

  *77.1 square miles is Santa Clara Pueblo's area, not Nambé Pueblo's.*

**C.** 32.4 square miles. **(Correct)**

  *Correct. Nambé Pueblo's row lists a total area of 32.4 square miles.*

**D.** 595.7 square miles. 

  *595.7 square miles is the Pueblo of Acoma's area — the largest nation in the table, and a dramatic mismatch for Nambé Pueblo.*

*Difficulty: easy*

---

##### Q26
> FIGURE. Bar graph, "Characteristics of the Banks of the Provo River Downstream of the Jordanelle Dam," in area (square meters), 0 to 140,000. Three series across 1987, 1993, and 2006: grass cover, bare soil, forest cover. 1987: grass cover about 58,000; bare soil about 68,000; forest cover about 75,000. 1993: grass cover about 93,000; bare soil about 10,000; forest cover about 58,000. 2006: grass cover about 130,000; bare soil about 10,000; forest cover about 48,000. TEXT. The Jordanelle Dam was built on the Provo River in Utah in 1992. Earth scientist Adriana E. Martinez and colleagues tracked changes to the environment on the banks of the river downstream of the dam, including how much grass and forest cover were present. They concluded that the dam changed the flow of the river in ways that benefited grass plants but didn't benefit trees.

Which choice best describes data from the graph that support Martinez and colleagues' conclusion?

**A.** The lowest amount of grass cover was approximately 58,000 square meters, and the highest amount of forest cover was approximately 75,000 square meters. 

  *Both figures are accurate, but they're two isolated extreme values, not a comparison over time. The conclusion is about a trend — grass gaining ground while forest doesn't — and this choice never traces either series across the three years.*

**B.** There was more grass cover than forest cover in 1987, and this difference increased dramatically in 1993 and again in 2006. 

  *In 1987 forest cover (about 75,000) actually exceeded grass cover (about 58,000), not the other way around, so the starting premise of this choice is false before the trend claim even begins.*

**C.** There was less grass cover than bare soil in 1987 but more grass cover than bare soil in 1993 and 2006, whereas there was more forest cover than bare soil in all three years. 

  *This is an accurate read of the graph, but every comparison in it is to bare soil, not between grass and forest cover over time. It never shows the trend the conclusion is actually about — grass increasing while forest declines.*

**D.** Grass cover increased from 1987 to 1993 and from 1993 to 2006, whereas forest cover decreased in those periods. **(Correct)**

  *Correct. Grass cover rises at every step (58,000 → 93,000 → 130,000) while forest cover falls at every step (75,000 → 58,000 → 48,000) — the exact opposite trends the conclusion describes as benefiting grass and not benefiting trees.*

*Difficulty: hard*

---

##### Q27
> FIGURE. Bar graph, "Participants' Responses to Three Review Conditions," mean rating on a scale where higher values are more positive, 0 to 7. Two categories: "Helpfulness of review" and "Attitude toward reviewed product." Three series: no anger (control), high anger, low anger. Helpfulness of review: no anger 6.7; high anger 6.1; low anger 6.8. Attitude toward reviewed product: no anger 2.3; high anger 1.9; low anger 2.2. TEXT. To understand how expressions of anger in reviews of products affect readers of those reviews, business scholar Dezhi Yin and colleagues measured study participants' responses to three versions of the same negative review—a control review expressing no anger, a review expressing a high degree of anger, and a review expressing a low degree of anger. Reviewing the data, a student concludes that the mere presence of anger in a review may not negatively affect readers' perceptions of the review, but a high degree of anger in a review does worsen readers' perceptions of the review.

Which choice best describes data from the graph that support the students' conclusion?

**A.** On average, participants' ratings of the helpfulness of the review were substantially higher than were participants' ratings of the reviewed product regardless of which type of review participants had seen. 

  *This is true for all three conditions, but it compares the two rated categories to each other, not the three review conditions to each other. The conclusion is about how anger level changes perception, and this choice never varies the review condition at all.*

**B.** Compared with participants who saw the control review, participants who saw the low-anger review rated the review as slightly more helpful, whereas participants who saw the high-anger review rated the review as less helpful. **(Correct)**

  *Correct. On the same measure, helpfulness, low anger (6.8) edges past the control (6.7) — no negative effect from the mere presence of anger — while high anger (6.1) drops below it — the worsening a high degree of anger produces. Both halves of the conclusion, read off one consistent axis.*

**C.** Participants who saw the low-anger review rated the review as slightly more helpful than participants who saw the control review did, but participants' attitude toward the reviewed product was slightly worse when participants saw the low-anger review than when they saw the no-anger review. 

  *The first clause checks out (6.8 versus 6.7), which is what makes the second clause easy to wave through. But attitude for the low-anger review (2.2) is not worse than the control's (2.3) — it's about the same — and even if it were, a worse outcome from a low-anger review would undercut the conclusion's first half rather than support it.*

**D.** Compared with participants who saw the low-anger review, participants who saw the high-anger review rated the review as less helpful and had a less positive attitude toward the reviewed product. 

  *Both comparisons here are accurate (6.1 versus 6.8, and 1.9 versus 2.2), but they compare high anger to low anger. The conclusion is about comparing each condition to the no-anger control, and this choice never brings the control into the comparison at all.*

*Difficulty: sat-hardest*

---

##### Q28
> FIGURE. Line graph, "Seed Germination with and without H2S Treatment," percent of seeds germinated, 0 to 100, at 24, 48, 72, and 168 hours. Three series: 500 micromoles per liter, 10 micromoles per liter, untreated. 24 hours: untreated 5%; 10 micromoles/L 8%; 500 micromoles/L 0%. 48 hours: untreated 50%; 10 micromoles/L 72%; 500 micromoles/L 35%. 72 hours: untreated 72%; 10 micromoles/L 90%; 500 micromoles/L 80%. 168 hours: untreated 78%; 10 micromoles/L 98%; 500 micromoles/L 92%. TEXT. In high concentrations, hydrogen sulfide (H2S) is typically toxic to many plants. Frederick D. Dooley and colleagues wanted to understand what effects low doses of H2S might have on plant growth. They treated bean, corn, wheat, and pea seeds with various concentrations (measured in micromoles per liter) of H2S and tracked the germination of those seeds along with the germination of untreated seeds. Treatment with particular concentrations of H2S was associated with accelerated germination: for example, ______

Which choice most effectively uses data from the graph to complete the statement?

**A.** at 24 hours, less than 10% of seeds treated with H2S at a concentration of 10 micromoles per liter had germinated, whereas more than 90% of those seeds had germinated at 168 hours. 

  *Both figures are accurate for the 10-micromole series (8% at 24 hours, 98% at 168 hours), but this traces one treated group's own change over time without ever mentioning the untreated seeds. It can't show the treatment accelerated germination relative to no treatment when no comparison to no treatment is made.*

**B.** at 48 hours, more than 70% of seeds treated with H2S at a concentration of 10 micromoles per liter had germinated, whereas only approximately 50% of untreated seeds had germinated. **(Correct)**

  *Correct. At the same 48-hour mark, the treated seeds (72%) are well ahead of the untreated seeds (50%) — a direct, same-time comparison showing the treatment accelerated germination.*

**C.** at 168 hours, more than 90% of seeds treated with H2S at concentrations of 10 or 500 micromoles per liter had germinated, whereas less than 70% of untreated seeds had germinated. 

  *The two treated figures check out (98% and 92%), but by 168 hours the untreated seeds had reached about 78%, not under 70% — this is the point where the treated and untreated lines have converged the most, and the specific number claimed for untreated seeds is wrong.*

**D.** at 48 hours, approximately 50% of seeds treated with H2S at a concentration of 10 micromoles per liter had germinated, whereas only approximately 30% of untreated seeds had germinated. 

  *This makes the right comparison at the right time, but with the wrong numbers — at 48 hours the treated line is close to 72%, not 50%, and the untreated line is close to 50%, not 30%. These values sit closer to the 24-hour reading than the 48-hour one.*

*Difficulty: hard*

---

##### Q29
> FIGURE. Bar graph, "Estimated Temperatures to which Evron Quarry Artifacts Were Exposed," temperature (°C), 0 to 700. Four artifacts: L5_239 about 550; K5_106 about 150; K3_18 about 650; K3_9 about 190. TEXT. Flint artifacts dating to 800,000 to 1,000,000 years ago have been recovered from the Evron Quarry in Israel. Likely created by the hominin Homo erectus, the artifacts have no visual features suggesting that they were exposed to fire, leading some scholars to conclude that these hominins had not acquired control of fire. But Zane Stepka and colleagues recently used a new method to determine whether these artifacts had been exposed to temperatures above 400°C (the typical temperature campfires reach) and concluded that the hominins who inhabited the site may have had control of fire.

Which choice best describes data in the graph that support the team's conclusion?

**A.** Artifacts K5_106 and K3_9 were exposed to temperatures above 400°C. 

  *Neither figure clears the threshold: K5_106 sits at about 150°C and K3_9 at about 190°C, both well below 400°C. This is false of the graph in both halves.*

**B.** Artifacts L5_239 and K3_18 were exposed to temperatures of approximately 550°C and 650°C, respectively. **(Correct)**

  *Correct. Both values match the graph, and both clear the 400°C threshold the team set as the mark of campfire-level heat — exactly the evidence needed to support the conclusion that these hominins had fire.*

**C.** All of the artifacts were exposed to temperatures above 100°C. 

  *This is true of every bar, but 100°C is not the threshold the conclusion depends on — 400°C is, because that's the temperature campfires typically reach. A true statement about a far lower, irrelevant threshold doesn't establish that any artifact was exposed to actual fire.*

**D.** Artifact K3_9 was exposed to a higher temperature than was artifact K5_106. 

  *This comparison is accurate (about 190°C against about 150°C), but neither artifact crosses the 400°C threshold that matters. Comparing two artifacts that were both below fire-level heat says nothing about whether these hominins controlled fire.*

*Difficulty: medium*

---

##### Q30
> FIGURE. Line graph, "Monthly Hours of Sunshine from April to September in Anchorage and Fairbanks, Alaska," hours of sunshine, 0 to 350. Two series: Anchorage, Fairbanks. April: Anchorage 260, Fairbanks 310. May: Anchorage 275, Fairbanks 320. June: Anchorage 290, Fairbanks 330. July: Anchorage 260, Fairbanks 280. August: Anchorage 175, Fairbanks 195. September: Anchorage 110, Fairbanks 130. TEXT. A student is researching monthly hours of sunshine in different cities in Alaska. When comparing trends in Anchorage and Fairbanks, the student concludes that the two cities show a similar pattern in the monthly hours of sunshine from April to September.

Which choice best describes data from the graph that support the student's conclusion?

**A.** The monthly hours of sunshine in both Anchorage and Fairbanks hold steady in June and July before beginning to decline in August. 

  *Both cities already drop from June to July (Anchorage 290 to 260, Fairbanks 330 to 280), so the decline starts a month earlier than this choice describes. "Hold steady" through July misstates the shape of both lines.*

**B.** The monthly hours of sunshine in both Anchorage and Fairbanks increase from April to June and then decrease from June to September. **(Correct)**

  *Correct. Both cities rise from April to June (260 to 290, and 310 to 330) and then fall from June to September (290 to 110, and 330 to 130) — the same rise-then-fall shape in both series, which is exactly what "similar pattern" requires.*

**C.** Anchorage and Fairbanks both have less than 200 monthly hours of sunshine from April to September. 

  *This is false for most of the period — both cities sit well above 200 from April through July, only dropping under 200 in August and September.*

**D.** Anchorage and Fairbanks both have more than 300 monthly hours of sunshine from April to June and less than 200 hours from July to September. 

  *Anchorage never reaches 300 in April, May, or June (its highest is 290), so the first half of this claim fails for one of the two cities before the second half is even checked.*

*Difficulty: medium*

---

##### Q31
> TABLE. "Average Nitrate and Phosphate Concentrations in Seawater after Volcanic Eruption." Columns: nutrient; seawater in lava-affected area, 5–45 meters below surface; seawater in lava-affected area, 75–125 meters below surface; seawater outside of lava-affected area, 5–45 meters below surface; seawater outside of lava-affected area, 75–125 meters below surface. Nitrate (micromoles per liter): 3.1; 0.4; ≤0.03; ≤0.01. Phosphate (micromoles per liter): 0.17; 0.09; 0.14; 0.06. TEXT. After a volcanic eruption spilled lava into North Pacific Ocean waters, a dramatic increase of diatoms (a kind of phytoplankton) near the surface occurred. Scientists assumed the diatoms were thriving on nutrients such as phosphate from the lava, but analysis showed these nutrients weren't present near the surface in forms diatoms can consume. However, there was an abundance of usable nitrate, a nutrient usually found in much deeper water and almost never found in lava. Microbial oceanographer Sonya Dyhrman and colleagues believe that as the lava plunged nearly 300 meters below the surface it dislodged pockets of this nutrient, releasing it to float upward, given that ______

Which choice most effectively uses data from the table to complete the statement?

**A.** at 5–45 meters below the surface, the average concentration of phosphate was about the same in the seawater in the lava-affected area as in the seawater outside of the lava-affected area. 

  *0.17 and 0.14 are close but not the point of the hypothesis, which is about nitrate being dislodged from depth, not about phosphate levels matching between areas. This describes the wrong nutrient for the claim being made.*

**B.** for both depth ranges measured, the average concentrations of nitrate were substantially higher in the seawater in the lava-affected area than in the seawater outside of the lava-affected area. **(Correct)**

  *Correct. At 5–45 meters, 3.1 dwarfs ≤0.03, and at 75–125 meters, 0.4 dwarfs ≤0.01 — nitrate is elevated in the lava-affected area at both depths, exactly what would result if the eruption dislodged deep nitrate and sent it upward through the water column.*

**C.** for both depth ranges measured in the seawater in the lava-affected area, the average concentrations of nitrate were substantially higher than the average concentrations of phosphate. 

  *This is true (3.1 versus 0.17, and 0.4 versus 0.09), but it compares two different nutrients within the same water rather than comparing lava-affected water to unaffected water. The hypothesis is about where the nitrate came from, not about nitrate versus phosphate levels.*

**D.** in the seawater outside of the lava-affected area, there was little change in the average concentration of nitrate from 75–125 meters below the surface to 5–45 meters below the surface. 

  *This is true (≤0.01 to ≤0.03 is a negligible change) but describes only the unaffected water, which is the control condition, not the lava-affected water the hypothesis is actually about. It never shows the dramatic near-surface spike the hypothesis needs.*

*Difficulty: medium*

---

##### Q32
> FIGURE. Line graph, "Urban Population of Algeria, France, Japan, and Nigeria," percent of population living in cities, 0 to 100, from 1970 to 2020. Four series: Algeria, France, Japan, Nigeria. 1970: France about 75, Japan about 72, Algeria about 40, Nigeria about 18. 2020: France about 88, Japan about 92, Algeria about 72, Nigeria about 50. Algeria rises steadily across the period from about 40 in 1970 to about 72 in 2020. TEXT. The share of the world's population living in cities has increased dramatically since 1970, but this change has not been uniform. France and Japan, for example, were already heavily urbanized in 1970, with 70% or more of the population living in cities. The main contributors to the world's urbanization since 1970 have been countries like Algeria, whose population went from ______

Which choice most effectively uses data from the graph to complete the assertion?

**A.** around 50% urban in 1970 to around 90% urban in 2020. 

  *Neither figure matches Algeria's line, which starts near 40% and ends near 72%. These numbers are closer to France's or Japan's trajectory than to Algeria's.*

**B.** less than 40% urban in 1970 to around 90% urban in 2020. 

  *Algeria's 1970 value is close to 40%, and its 2020 value is close to 72%, not 90%. The endpoint here belongs to France or Japan's line, not Algeria's.*

**C.** less than 20% urban in 1970 to more than 50% urban in 2020. 

  *This matches Nigeria's trajectory (about 18% to about 50%), not Algeria's. It's an accurate reading of the graph, just for the wrong country.*

**D.** around 40% urban in 1970 to more than 70% urban in 2020. **(Correct)**

  *Correct. This matches Algeria's own line: about 40% in 1970, climbing to about 72% in 2020 — the steady, decades-long rise that makes Algeria one of the countries driving global urbanization since 1970.*

*Difficulty: hard*

---

##### Q33
> TABLE. "Body Length, Filter Time, and Lunges per Dive for Four Whale Species." Columns: whale species; typical adult body length (meters); average time to filter all engulfed water (seconds); average number of lunges per dive deeper than 50 meters. fin: 18–22; 31.30; 3.95. humpback: 11–17; 17.12; 6.28. minke: 7–10; 8.88; 7.48. blue: 24–34; 60.27; 4.02. TEXT. Some whale species practice lunge feeding, in which they lunge toward prey with their mouths open at wide angles, collect the prey and the surrounding water, and then filter out the water through baleen plates in their mouths. Although the volume of water engulfed increases with whales' body length, the surface area of whales' baleen plates, which influences the rate at which water can be filtered, does not increase with body length to the same degree, which helps explain why ______

Which choice most effectively uses data from the table to complete the statement?

**A.** minke whales and humpback whales show similar average filter times. 

  *8.88 seconds and 17.12 seconds are not similar — humpback's filter time is roughly double minke's. This misreads the table's own numbers.*

**B.** humpback whales show an average of 6.28 lunges per dive. 

  *This is an accurate single value from the table, but it doesn't relate body length to filter time at all — the statement it's completing is specifically about why bigger whales, with proportionally smaller baleen surface area, might filter more slowly.*

**C.** fin whales show a longer average filter time than minke whales do. **(Correct)**

  *Correct. Fin whales (18–22 meters, 31.30 seconds) are far larger and take much longer to filter their engulfed water than minke whales (7–10 meters, 8.88 seconds) — exactly the pattern that body length outpacing baleen surface area would produce.*

**D.** blue whales show the longest average filter time and the highest average number of lunges per dive. 

  *The first half is accurate (60.27 seconds is the longest), but the second half isn't — minke whales have the highest average lunges per dive (7.48), not blue whales (4.02).*

*Difficulty: easy*

---

##### Q34
> FIGURE. Line graph, "Number of Infrared Beam Breaks by Mice Treated with CNO or Saline, by Sex," number of beam breaks, 0 to 1,500, from −4 to 150 minutes from treatment. Four series: females with saline, males with saline, males with CNO, females with CNO. Females with saline stay near 400–500 throughout, dipping toward 100–200 by mid-monitoring. Males with saline and males with CNO both stay roughly flat, fluctuating around 400–600 across the whole period. Females with CNO rise sharply to a peak near 1,400 around minute 38, then decline steadily to about 100–200 by minute 150. TEXT. To investigate the influence of certain estrogen-responsive neurons on energy expenditure, biologist Stephanie Correa et al. treated female and male mice with either saline solution or clozapine-N-oxide (CNO), which activates the neurons. Monitoring the activity levels of the mice by measuring how frequently the animals broke infrared beams crossing their enclosures, Correa et al. found that the mice in their study showed sex-specific differences in response to neuron activation: ______

Which choice most effectively uses data from the graph to complete the assertion?

**A.** the four groups of mice differed greatly in their activity levels before treatment but showed identical activity levels at the end of the monitoring period. 

  *Before treatment, all four groups sit in a similar 400–500 range rather than differing greatly, and none of the groups end at literally identical values — this overstates both the starting spread and the ending convergence.*

**B.** saline-treated females showed substantially more activity at certain points in the monitoring period than saline-treated males did. 

  *Saline is the control condition — it doesn't activate the neurons the study is about. A comparison between the two saline groups can't demonstrate a sex-specific response to neuron activation, because neither group's neurons were activated.*

**C.** CNO-treated females showed more activity relative to saline-treated females than CNO-treated males showed relative to saline-treated males. **(Correct)**

  *Correct. CNO-treated females spike far above saline-treated females (roughly 1,400 versus 400–500), while CNO-treated males track close to saline-treated males (both around 400–600) — a much larger CNO-versus-saline gap in females than in males, which is precisely a sex-specific response to activating the neurons.*

**D.** CNO-treated females showed a substantial increase and then decline in activity over the monitoring period, whereas CNO-treated males showed a substantial decline in activity followed by a steep increase. 

  *The female half is accurate — rise to a peak, then decline. But CNO-treated males stay roughly flat throughout rather than showing a substantial decline followed by a steep increase; that shape belongs to no line on this graph.*

*Difficulty: sat-hardest*

---

##### Q35
> FIGURE. Line graph, "Rotor Diameters of Newly Installed Wind Turbines in the United States, 2011–2021," percent of newly installed turbines, 0 to 90. Four series: >130 meters, <100 meters, 100–115 meters, 115–130 meters. 2011: <100 meters 75%; 100–115 meters 25%; 115–130 meters 0%; >130 meters 0%. The >130-meters series stays at 0% from 2011 through 2015, then climbs from 2016 onward to about 25% by 2021. 2021: <100 meters 5%; 100–115 meters 10%; 115–130 meters 65%; >130 meters 25%. TEXT. All other things being equal, the larger a wind turbine's rotor diameter (the diameter of the imaginary circle swept by the turbine's rotating blades), the greater amount of energy the turbine can generate. In a research paper on wind power, a student claims that in the United States, the amount of energy generated per newly installed turbine increased substantially between 2011 and 2021.

Which choice best describes data in the graph that support the student's claim?

**A.** The percentage of newly installed turbines with rotor diameters greater than 130 meters increased every year between 2011 and 2021. 

  *The >130-meters line sits flat at 0% from 2011 through 2015 before it starts climbing — several years in a row with no increase at all. "Increased every year" misreads that flat stretch as continuous growth.*

**B.** In 2011, nearly 80% of turbines installed had rotor diameters of less than 100 meters, whereas only a little more than 20% of turbines installed that year had rotor diameters of 100–115 meters. 

  *This is an accurate snapshot of 2011 alone (75% and 25%), but it never reaches 2021. The claim is about a change across the full decade, and a single year's breakdown can't show that change.*

**C.** No turbines installed in 2011 had rotor diameters greater than 115 meters, whereas the majority of turbines installed in 2021 had rotor diameters greater than 130 meters. 

  *The 2011 half is accurate, but in 2021 the majority of turbines fall in the 115–130-meter band (65%), not above 130 meters (25%) — combining the two upper bands to call it "greater than 130 meters" misreads which category holds the majority.*

**D.** Most turbines installed in 2011 had rotor diameters of less than 100 meters, whereas most turbines installed in 2021 had rotor diameters of at least 115 meters. **(Correct)**

  *Correct. In 2011, 75% of turbines were under 100 meters — the majority. In 2021, the 115–130-meter and >130-meter bands together make up 90% — also the majority, and at a rotor size that generates far more energy. That shift is exactly the substantial increase in energy per turbine the student claims.*

*Difficulty: sat-hardest*

---

##### Q36
> TABLE. "Participants' Evaluation of the Likelihood That Robots Can Work Effectively in Different Occupations." Columns: occupation; somewhat or very unlikely (%); neutral (%); somewhat or very likely (%). Rows may not add to 100 due to rounding. Television news anchor: 24; 9; 67. Teacher: 37; 16; 47. Firefighter: 62; 9; 30. Surgeon: 74; 9; 16. Tour guide: 10; 8; 82. TEXT. Georgia Tech roboticists De'Aira Bryant and Ayanna Howard, along with ethicist Jason Borenstein, were interested in people's perceptions of robots' competence. They recruited participants and asked them how likely they think it is that a robot could do the work required in various occupations. Participants' evaluations varied widely depending on which occupation was being considered; for example, ______

Which choice most effectively uses data from the table to complete the example?

**A.** 47% of participants believe that it is somewhat or very likely that a robot could work effectively as a teacher, but 37% of respondents believe that it is somewhat or very unlikely that a robot could do so. 

  *Both numbers are pulled from the teacher row, but they don't show variation across occupations — they show two different response options within a single occupation, which isn't the "varied widely depending on which occupation" contrast the text calls for.*

**B.** 9% of participants were neutral about whether a robot could work effectively as a television news anchor, which is the same percent of participants who were neutral when asked about a robot working as a surgeon. 

  *This is accurate (9% and 9%), but it demonstrates two occupations matching, not varying. The example is meant to illustrate how widely opinions differ by occupation, and a tie does the opposite.*

**C.** 82% of participants believe that it is somewhat or very likely that a robot could work effectively as a tour guide, but only 16% believe that it is somewhat or very likely that a robot could work as a surgeon. **(Correct)**

  *Correct. Both figures come from the same response category — "somewhat or very likely" — applied to two different occupations, and the 82%-to-16% gap is exactly the wide variation across occupations the text describes.*

**D.** 62% of participants believe that it is somewhat or very unlikely that a robot could work effectively as a firefighter. 

  *This is a real, accurate figure, but it's a single value for a single occupation. Showing that opinions "varied widely depending on which occupation" requires comparing at least two occupations, and this choice never leaves firefighter.*

*Difficulty: easy*

---

##### Q37
> FIGURE. Bar graph, "Cantaloupe Yield," yield (pounds per acre), 0 to 45, for 2017, 2018, and 2019. Two series: control, nitrogen fertilizer. 2017: control 24, nitrogen fertilizer 34. 2018: control 31, nitrogen fertilizer 42. 2019: control 19, nitrogen fertilizer 28. TEXT. To test the effects of a nitrogen fertilizer on cantaloupe production, researchers grew cantaloupe plants and harvested their fruit over three years. In each year, half the plants were grown using a nitrogen fertilizer, and the other half were grown using a control fertilizer that contained no nitrogen. The researchers concluded that the nitrogen fertilizer increases cantaloupe yield.

Which choice best describes data in the graph that support the researchers' conclusion?

**A.** In every year of the experiment, plants treated with the nitrogen fertilizer had a yield of at least 30 pounds per acre. 

  *In 2019 the nitrogen-fertilizer yield is 28 pounds per acre, under 30 — this threshold fails in one of the three years, and it never compares nitrogen to the control fertilizer at all, which is what the conclusion is actually about.*

**B.** In every year of the experiment, plants treated with the nitrogen fertilizer had a greater yield than did plants treated with the control fertilizer. **(Correct)**

  *Correct. Nitrogen beats the control in every single year — 34 to 24 in 2017, 42 to 31 in 2018, 28 to 19 in 2019 — a consistent same-year, same-condition comparison that directly supports the conclusion that nitrogen fertilizer increases yield.*

**C.** The 2018 yield for plants treated with the control fertilizer was greater than was the 2019 yield for plants treated with the nitrogen fertilizer. 

  *This is accurate (31 versus 28), but it compares the control in one year to nitrogen fertilizer in a different year. The conclusion needs a same-year comparison between the two fertilizers, and this mixes both the fertilizer and the year.*

**D.** The yield for plants treated with the nitrogen fertilizer increased from 2017 to 2018. 

  *This is true (34 to 42) but tracks nitrogen fertilizer against itself across two years, never setting it against the control. A rise in nitrogen's own yield doesn't show nitrogen outperforms the control, which is what the conclusion claims.*

*Difficulty: medium*

---

##### Q38
> TABLE. "Five of the Responses to Survey about Actions to Conserve Energy." Columns: action; action category; percentage of respondents selecting action (%). Use efficient cars/hybrids: efficiency; 2.8. Change thermostat setting: curtailment; 6.3. Use bike or public transportation instead of car: curtailment; 12.9. Use efficient light bulbs: efficiency; 3.6. Turn off lights: curtailment; 19.6. TEXT. In a survey of public perceptions of energy use, researcher Shahzeen Attari and her team asked respondents to name the most effective action ordinary people can take to conserve energy. The team categorized each action as either an efficiency or a curtailment and found that respondents tended to name curtailments more often than they did efficiencies. For example, 19.6% of respondents stated that the most effective way to conserve energy is to turn off the lights, while only ______

Which choice most effectively uses data from the table to complete the text?

**A.** 6.3% of respondents said it was most effective to use efficient cars or hybrids. 

  *6.3% belongs to "change thermostat setting," not "use efficient cars/hybrids" — that row is at 2.8%. The action named and the percentage cited come from different rows.*

**B.** 2.8% of respondents said it was most effective to change the thermostat setting. 

  *2.8% belongs to "use efficient cars/hybrids," not "change thermostat setting" — that row is at 6.3%. This pairs the right kind of figure with the wrong action.*

**C.** 12.9% of respondents said it was most effective to use a bike or public transportation. 

  *12.9% is accurate for that action, but it's a curtailment, the same category as turning off the lights. The sentence is contrasting curtailment against efficiency, so the completion needs to name an efficiency action, and this one doesn't.*

**D.** 3.6% of respondents said it was most effective to use efficient light bulbs. **(Correct)**

  *Correct. "Use efficient light bulbs" is categorized as an efficiency, and its 3.6% sits far below turning off the lights' 19.6% — exactly the curtailment-named-more-often-than-efficiency pattern the sentence is illustrating.*

*Difficulty: easy*

---

##### Q39
> FIGURE. Bar graph, "Suggestions for Improving a University," number of suggestions, 0 to 600. Four categories: additive, neither additive nor subtractive, subtractive, invalid. Additive: about 575. Neither additive nor subtractive: about 175. Subtractive: about 65. Invalid: about 370. TEXT. Gabrielle Adams and colleagues reviewed suggestions for improving a university that had been submitted to the university's president. They coded each suggestion as additive (the idea suggested adding something new to the university), subtractive (the idea suggested removing something from the university), neither additive nor subtractive, or invalid (the idea was not comprehensible). The data illustrated people's tendency to overlook the possibility of removing things to achieve improvements: ______

Which choice most effectively uses data in the graph to complete the statement?

**A.** around 175 suggestions were coded as neither additive nor subtractive, whereas around 575 suggestions were coded as additive. 

  *Both figures are accurate, but the claim is specifically about people overlooking the subtractive option, and this choice never mentions the subtractive category at all.*

**B.** more than 350 suggestions were coded as invalid, whereas fewer than 100 suggestions were coded as subtractive. 

  *Both numbers check out, but "invalid" has nothing to do with whether people thought to suggest removing something — it's a separate category for incomprehensible ideas, not a comparison that bears on the additive-versus-subtractive claim.*

**C.** fewer than 100 suggestions were coded as subtractive, whereas more than 550 suggestions were coded as additive. **(Correct)**

  *Correct. Subtractive suggestions (about 65) are a small fraction of additive ones (about 575) — few people proposed removing anything while many proposed adding, exactly the tendency to overlook subtraction the statement describes.*

**D.** around 575 suggestions were coded as additive, whereas around 175 suggestions were coded as subtractive. 

  *The additive figure is right, but 175 is the count for "neither additive nor subtractive," not for subtractive — subtractive is about 65. This swaps in the wrong category's number.*

*Difficulty: medium*

---

##### Q40
> FIGURE. Bar graph, "Employment in Technology in Hawaii in 2010 and 2019," approximate number of jobs (in thousands), 0 to 7. Three series: engineering services, technical consulting services, computer services. 2010: engineering services 6, technical consulting services 4, computer services 6. 2019: engineering services 6, technical consulting services 5, computer services 5. TEXT. A student in Hawaii is interested in pursuing a career in technology and decides to do some research on local trends. The student notices that the number of jobs in computer services in 2010 was ______

Which choice most effectively uses data from the graph to complete the statement?

**A.** higher than the number of jobs in technical consulting services, and in 2019 was about the same as the number of jobs in engineering services. 

  *The first clause checks out (6 versus 4), but in 2019 computer services (5) sits below engineering services (6), not about the same. The second clause is where this one fails.*

**B.** about the same as the number of jobs in engineering services, and in 2019 was about the same as the number of jobs in technical consulting services. **(Correct)**

  *Correct. In 2010, computer services and engineering services are tied at 6. In 2019, computer services and technical consulting services are tied at 5. Both clauses hold.*

**C.** lower than the number of jobs in engineering services, but in 2019 was higher than the number of jobs in engineering services. 

  *In 2010, computer services and engineering services are equal at 6, not one lower than the other — the first clause is already false.*

**D.** about the same as the number of jobs in technical consulting services, but in 2019 was lower than the number of jobs in technical consulting services. 

  *In 2010, computer services (6) and technical consulting services (4) are two thousand jobs apart, not about the same — the first clause misreads the starting comparison.*

*Difficulty: medium*

---

##### Q41
> FIGURE. Line graph, "Percentage of Maize Exported by Three Countries for Marketing Years 2009/2010–2013/2014," percent, 0 to 90. Three series: Argentina, Brazil, United States. 2009/2010: Argentina 65, Brazil 18, United States 13. 2010/2011: Argentina 65, Brazil 15, United States 10. 2011/2012: Argentina 80, Brazil 33, United States 10. 2012/2013: Argentina 72, Brazil 30, United States 8. 2013/2014: Argentina 65, Brazil 22, United States 13. TEXT. Argentina, Brazil, and the United States are among the world's leading producers of maize (corn), and each country exports a certain percentage of maize each marketing year, which runs from March to February in Argentina and Brazil and from September to August in the United States. A student is researching those percentages and finds that for the marketing year 2012/2013, the percentage of maize exported by ______

Which choice most effectively uses data from the graph to complete the text?

**A.** Brazil increased from the previous marketing year but remained lower than the percentage exported by the United States. 

  *Both halves are wrong. Brazil actually fell from 2011/2012 to 2012/2013 (33 to 30), not increased, and at 30% Brazil remained far above the United States' 8%, not below it.*

**B.** Brazil exceeded the percentage exported by Argentina for the first time. 

  *In 2012/2013, Brazil sits at 30% and Argentina at 72% — Argentina remains well ahead, and Brazil has never exceeded Argentina at any point on the graph.*

**C.** Argentina decreased from the previous marketing year but remained the highest among the three countries. **(Correct)**

  *Correct. Argentina falls from 80% in 2011/2012 to 72% in 2012/2013, a real decrease, and 72% still sits above Brazil's 30% and the United States' 8% — the highest of the three that year.*

**D.** the United States reached its highest point during the five marketing years. 

  *The United States is at 8% in 2012/2013, actually its lowest point on the graph — its highest points, 13%, occur in 2009/2010 and 2013/2014. This is the opposite of what the graph shows.*

*Difficulty: hard*

---

##### Q42
> FIGURE. Bar graph, "Average Ratings of Urban Agriculture's Contribution to Various Social or Ecological Services," rating (0 = no contribution, 5 = high contribution). Three groups: project leaders, stakeholders, general public. Three rated services: provision of medicinal plants, improvement of neighborhood attachment, improvement of local microclimate. Project leaders: medicinal plants 2.0, neighborhood attachment 3.0, local microclimate 3.0. Stakeholders: medicinal plants 3.6, neighborhood attachment 4.1, local microclimate 4.1. General public: medicinal plants 4.6, neighborhood attachment 4.3, local microclimate 3.8. TEXT. Urban agriculture is the practice of growing plant- or animal-based products in urban settings such as community gardens and rooftop farms. Esther Sanyé-Mengual, Kathrin Specht, and their team surveyed three groups of people in Bologna, Italy—leaders of urban agriculture projects, stakeholders in urban agriculture (e.g., food researchers and urban farming associations), and the general public—to compare their views about the extent to which urban agriculture contributes to 25 social or ecological services that the team identified. The survey results show that, on average, project leaders rated urban agriculture as contributing less to ______

Which choice most effectively uses data from the graph to complete the assertion?

**A.** providing medicinal plants than to improving the local microclimate. **(Correct)**

  *Correct. Among project leaders, medicinal plants (2.0) rates lower than local microclimate (3.0) — a real, direct comparison within the one group the sentence is about.*

**B.** improving community members' sense of attachment to the neighborhood than to offering educational opportunities. 

  *The team identified 25 services in total, but this graph shows ratings for only three of them, and "educational opportunities" isn't one of the three plotted here. This choice cites a service the figure never measures.*

**C.** improving the local microclimate than to providing medicinal plants. 

  *This reverses the actual comparison: among project leaders, local microclimate (3.0) rates higher than medicinal plants (2.0), not lower. The two categories are right; the direction is backward.*

**D.** improving the local microclimate than to providing tourist attractions. 

  *"Tourist attractions" is not one of the three services this graph plots — like educational opportunities, it may be among the 25 services the study covered, but it isn't shown here.*

*Difficulty: hard*

---

##### Q43
> FIGURE. Bar graph, "Days per Winter That Lakes Have Surface Ice," days, 0 to 200, for the winters of 1980–81 and 2005–06. Three lakes: Oulujärvi, Mirror Lake, Lake Neusiedl. 1980–81: Oulujärvi 195, Mirror Lake 120, Lake Neusiedl 78. 2005–06: Oulujärvi 157, Mirror Lake 120, Lake Neusiedl 103. TEXT. It is common for freshwater lakes near or above a latitude of 45° north of the equator, like Lake Mjøsa in Norway, to accumulate surface ice in winter. The amount and duration of ice depends on many factors, including local weather conditions as well as the lake's depth, volume, and surface area, but a climate researcher claims that some lakes in these latitudes have seen a decline in the duration of ice between the early 1980s and the mid-2000s. She cites as a typical example ______

Which choice most effectively uses data from the graph to complete the researcher's example?

**A.** both Lake Neusiedl and Oulujärvi, which had fewer than 195 days of ice in the winter of 1980–81. 

  *Oulujärvi's own 1980–81 value is 195 days, not fewer than 195, so this is false for one of the two lakes named — and even where it holds, it's a single-year snapshot with no comparison to 2005–06, so it can't show a decline either way.*

**B.** Lake Neusiedl, which had more days of ice in the winter of 2005–06 than it did in the winter of 1980–81. 

  *This is accurate (103 versus 78) but points the wrong way — Lake Neusiedl gained ice days over the period, which is the opposite of the decline the researcher is citing as her example.*

**C.** Oulujärvi, which had fewer days of ice in the winter of 2005–06 than it did in the winter of 1980–81. **(Correct)**

  *Correct. Oulujärvi drops from 195 days in 1980–81 to 157 days in 2005–06 — a real decline in ice duration between the two winters, exactly the pattern the researcher is illustrating.*

**D.** both Lake Neusiedl and Oulujärvi, which had more than 105 days of ice in the winter of 2005–06. 

  *Lake Neusiedl's 2005–06 value is 103 days, not more than 105 — this fails for one of the two lakes, and like choice A, it's a single-winter snapshot that never compares to 1980–81, so it can't demonstrate a decline regardless.*

*Difficulty: hard*

---

##### Q44
> TABLE. "Survey Results for Two Online Account Sign-in Methods." Columns: sign-in method; percent of participants in the UK who chose method; percent of participants in Japan who chose method; percent of participants in India who chose method. Biometrics (for example, a face scan): 33; 29; 22. Onetime passcodes: 16; 8; 25. TEXT. A survey listed methods for signing into online accounts. Participants in different countries were asked to choose the sign-in method they view as most secure. The table presents data for two of the methods. According to the table, onetime passcodes were viewed as most secure by ______

Which choice most effectively uses data from the table to complete the text?

**A.** 33 percent of survey participants in the UK. 

  *33% is the UK's biometrics figure, not its onetime-passcodes figure — the UK's onetime-passcodes value is 16%. This pulls a number from the wrong row.*

**B.** 22 percent of survey participants in India. 

  *22% is India's biometrics figure, not its onetime-passcodes figure — India's onetime-passcodes value is 25%. Right column, wrong row.*

**C.** 8 percent of survey participants in Japan. **(Correct)**

  *Correct. The onetime-passcodes row and the Japan column intersect at 8%.*

**D.** 16 percent of survey participants in India. 

  *16% is the UK's onetime-passcodes figure, not India's — India's onetime-passcodes value is 25%. Right row, wrong country.*

*Difficulty: easy*

---

##### Q45
> TABLE. "North American Thrasher Mean Bill Size and Habitat Temperature Range." Columns: species; mean bill surface area (cm²); mean maximum temperature of warmest month (°C); mean minimum temperature of coldest month (°C). Brown thrasher: 1.86; 30.40; −4.29. Bendire's thrasher: 1.98; 36.57; 0.24. Long-billed thrasher: 2.24; 35.27; 8.82. Cozumel thrasher: 2.28; 33.27; 18.21. Ocellated thrasher: 3.26; 27.56; 5.45. TEXT. It has been hypothesized that since birds can dissipate excess heat through their bills, bill size should increase with habitat temperature. To evaluate this hypothesis for a 2021 study, Charlotte Probst and colleagues gathered data on mean bill surface area of species of North American thrashers (genus Toxostoma) as well as on climate conditions of the birds' native habitats. Based on their data, Probst and colleagues concluded that the hypothesis was not fully supported.

Which choice most effectively uses data from the table to support Probst and colleagues' conclusion?

**A.** Although the Bendire's thrasher has one of the smallest mean bill surface areas of the birds included in the table, its habitat has one of the lowest mean maximum temperatures in the warmest month and one of the lowest mean minimum temperatures in the coldest month. 

  *Small bill paired with a cool habitat is exactly what the hypothesis predicts — bill size tracking temperature in the expected direction. A case that fits the hypothesis can't be the evidence that the hypothesis wasn't fully supported.*

**B.** Although the Cozumel thrasher has the second greatest mean bill surface area of the birds included in the table, its habitat's mean temperature in the warmest month is significantly higher than that of the other birds' habitats. 

  *A large bill in a hot habitat is again the hypothesis working as predicted — bill size and temperature moving together. This describes agreement between bill size and heat, not a mismatch that would undercut the hypothesis.*

**C.** Of the birds included in the table, the brown thrasher has the smallest mean bill surface area and the habitat with the lowest mean minimum temperature in the coldest month, while the long-billed thrasher has the second-largest mean bill surface area and the habitat with the second-highest mean minimum temperature in the coldest month. 

  *Both pairings here move in the same direction the hypothesis predicts — smallest bill with coldest habitat, second-largest bill with second-warmest habitat. Two more matching cases support the hypothesis; they don't show where it breaks down.*

**D.** Of the birds included in the table, the ocellated thrasher has the largest mean bill surface area and the habitat with the lowest mean maximum temperature in the warmest month, while the Bendire's thrasher has the second smallest mean bill surface area and the habitat with the highest mean maximum temperature in the warmest month. **(Correct)**

  *Correct. This is the mismatch: the ocellated thrasher carries the largest bill despite living where the warmest month is coolest, and the Bendire's thrasher carries a small bill despite living where the warmest month is hottest — bill size and temperature moving in opposite directions, exactly the pattern that keeps the hypothesis from being fully supported.*

*Difficulty: sat-hardest*

---

##### Q46
> FIGURE. Bar graph, “Municipalities’ Responses to Inquiries about Potential Incentives for Firm.” The vertical axis is labeled “Number of municipalities,” marked every 100 from 0 to 1,300. Two bars per category — announcement before election (light gray) and announcement after election (black). No response: about 1,250 before, about 1,230 after. Responded to inquiry: about 180 before, about 190 after. Offered incentive: about 110 before, about 100 after. TEXT. In the United States, firms often seek incentives from municipal governments to expand to those municipalities. A team of political scientists hypothesized that municipalities are much more likely to respond to firms and offer incentives if expansions can be announced in time to benefit local elected officials than if they can’t. The team contacted officials in thousands of municipalities, inquiring about incentives for a firm looking to expand and indicating that the firm would announce its expansion on a date either just before or just after the next election.

Which choice best describes data from the graph that weaken the team’s hypothesis?

**A.** A large majority of the municipalities that received an inquiry mentioning plans for an announcement before the next election didn’t respond to the inquiry. 

  *True of the graph — about 1,250 of the roughly 1,540 before-election municipalities fall in the no-response bar — but it reports only the before-election condition. The hypothesis is a claim about a difference between the before and after conditions, and a number from one bar, however accurate, can’t establish that the two conditions produced different outcomes.*

**B.** The proportion of municipalities that responded to the inquiry or offered incentives didn’t substantially differ across the announcement timing conditions. **(Correct)**

  *Correct. Read across both bars in each responsive category: about 180 versus about 190 responded to the inquiry, and about 110 versus about 100 offered incentives — nearly identical in both pairs. The hypothesis predicts a real gap between the before-election and after-election conditions, and this is the one choice that puts both conditions side by side and reports that the gap isn’t there.*

**C.** Only around half the municipalities that responded to inquiries mentioning plans for an announcement before the next election offered incentives. 

  *This is the kind of number that sounds plausible without being checked. Of the roughly 290 municipalities that engaged at all before the election (about 180 that responded to the inquiry plus about 110 that offered incentives), the 110 that offered incentives make up closer to 38 percent than half. A choice built on a miscalculated proportion fails the graph before the question of relevance is even reached.*

**D.** Of the municipalities that received an inquiry mentioning plans for an announcement date after the next election, more than 1,200 didn’t respond and only around 100 offered incentives. 

  *Both figures are accurate reads of the after-election bars, which is what makes this the most convincing wrong answer on the item. It reports only the after-election condition, though, and weakening the hypothesis requires setting that condition against the before-election one — without the comparison, a true number is just a true number.*

*Difficulty: hard*

---

##### Q47
> TABLE. “Nucleobase Concentrations from Murchison Meteorite and Soil Samples in Parts per Billion.” Columns: nucleobase; Murchison meteorite sample 1; Murchison meteorite sample 2; Murchison soil sample. Isoguanine: 0.5; 0.04; not detected. Purine: 0.2; 0.02; not detected. Xanthine: 39; 3; 1. Adenine: 15; 1; 40. Hypoxanthine: 24; 1; 2. TEXT. Employing high-performance liquid chromatography—a process that uses pressurized water to separate material into its component molecules—astrochemist Yashiro Oba and colleagues analyzed two samples of the Murchison meteorite that landed in Australia as well as soil from the landing zone of the meteorite to determine the concentrations of various organic molecules. By comparing the relative concentrations of types of molecules known as nucleobases in the Murchison meteorite with those in the soil, the team concluded that there is evidence that the nucleobases in the Murchison meteorite formed in space and are not the result of contamination on Earth.

Which choice best describes data from the table that support the team’s conclusion?

**A.** Isoguanine and purine were detected in both meteorite samples but not in the soil sample. **(Correct)**

  *Correct. Isoguanine (0.5 and 0.04 across the two meteorite samples, not detected in soil) and purine (0.2 and 0.02, not detected in soil) are the only nucleobases in the table present in the meteorite and absent from the paired soil sample entirely. If Earth soil doesn’t contain a molecule at all, contamination from that soil can’t be the source of it in the meteorite — the strongest pattern in the table for an extraterrestrial origin.*

**B.** Adenine and xanthine were detected in both of the meteorite samples and in the soil sample. 

  *Both are indeed present in all three columns, but a nucleobase that shows up in the meteorite AND in the paired soil is exactly the kind of overlap that raises a contamination concern rather than ruling one out. This finding points against an extraterrestrial-only origin, not toward one.*

**C.** Hypoxanthine and purine were detected in both the Murchison meteorite sample 2 and the soil sample. 

  *Hypoxanthine does appear in both (1 in sample 2, 2 in soil), but purine does not — the soil column reads “not detected” for purine. A choice that misreads one of its two named values off the table can’t be the credited answer.*

**D.** Isoguanine and hypoxanthine were detected in Murchison meteorite sample 1 but not in sample 2. 

  *Both nucleobases were detected in sample 2 too — isoguanine at 0.04 and hypoxanthine at 1 — just at lower concentrations than in sample 1. A low nonzero value is still a detection; this choice mistakes “present in a smaller amount” for “absent.”*

*Difficulty: hard*

---

##### Q48
> FIGURE. Bar graph, “Fur Seal REM Sleep on Land after an Extended Period in Water.” The vertical axis is labeled “REM sleep as % of baseline (mean difference from baseline was not statistically significant),” marked every 20 from 0 to 180. Two days on land, three seals per day. Day 1: Seal B about 160, Seal A about 165, Seal C about 100. Day 2: Seal B about 90, Seal A about 160, Seal C about 110. TEXT. Research suggests that REM sleep in animals is homeostatically regulated: animals compensate for periods of REM sleep deprivation by increasing subsequent REM sleep. When on land, fur seals get enough REM sleep, but during the weeks they’re in the water, they get almost none. In a study of fur seals’ sleep habits, researchers recorded the REM sleep (as a percentage of baseline) of fur seals once they had returned to land. They concluded that REM sleep may not be homeostatically regulated in fur seals, citing as evidence the fact that the seals in the study ______

Which choice most effectively uses data from the graph to complete the text?

**A.** didn’t show significantly less REM sleep during the second day after returning to land than they did during the first day. 

  *The homeostatic-regulation question is about whether REM sleep rose significantly above baseline after deprivation, not about how Day 1 compares with Day 2. Comparing the two days to each other sets up the wrong axis of contrast — the one the conclusion needs is each seal against its own baseline.*

**B.** showed no significant differences from one another in baseline levels of REM sleep. 

  *Baseline is, by the graph’s own definition, the 100% mark every seal is measured against — comparing seals to each other at that fixed point says nothing about whether any of them slept significantly more than baseline after their time in the water. It’s off-topic for a conclusion about catching up on lost sleep.*

**C.** didn’t consistently demonstrate a significant increase in REM sleep after their period of deprivation in the water. **(Correct)**

  *Correct. The axis label notes that the mean differences from baseline shown — even values well above 100%, like Seal A and Seal B on Day 1 — were not statistically significant. If seals who had just been deprived of REM sleep in the water didn’t reliably show a significant rise above their own baseline once back on land, that’s the direct evidence that homeostatic regulation, which predicts exactly that rise, isn’t occurring.*

**D.** showed no significant difference between REM sleep after returning to land and REM sleep while in the water. 

  *REM sleep while the seals were still in the water was never measured on this graph — only REM sleep after returning to land, on Day 1 and Day 2, is plotted. A comparison to an unplotted value can’t be read off this figure, whether or not it happens to be true.*

*Difficulty: sat-hardest*

---

##### Q49
> FIGURE. Bar graph, “Home Heating Needs Met with Subsurface Thermal Pollution for Two Temperature Conditions, by Percentage of Sites.” The vertical axis is labeled “Percentage of all sites analyzed,” marked every 10 from 0 to 90. Two bars per category — current surface temperature (light gray) and maximum plausible surface temperature (black). 0% local heating needs met: about 82% current, about 13% maximum plausible. Up to 25%: about 5% current, about 8% maximum plausible. More than 25%: about 13% current, about 78% maximum plausible. TEXT. Urbanization, industrialization, and the warming climate create thermal pollution (excess heat) in the shallow subsurface soil. Susanne A. Benz and colleagues analyzed thousands of sites on three continents under one scenario in which surface temperature remains at the current level and under another in which the surface reaches the maximum plausible level. They then categorized each site according to the percentage of local home heating needs that could be met using this excess subsurface heat. The team concluded that if surface temperature approaches the maximum plausible level, the percentage of sites where thermal pollution could feasibly contribute to meeting home heating needs will increase.

Which choice best describes data in the graph that support Benz and colleagues’ conclusion?

**A.** Under both temperature conditions, less than 10% of sites were in the up-to-25% group, but at the maximum plausible surface temperature, almost 80% of sites could have all their local heating needs met by thermal pollution. 

  *The first clause checks out — both bars in the up-to-25% group sit under 10%. The second clause overreaches: the “more than 25%” category, at about 78% of sites at maximum plausible temperature, means those sites get more than a quarter of their needs met, not that thermal pollution supplies ALL of their heating. Treating “more than 25%” as “100%” misstates what the category covers.*

**B.** At current surface temperatures, more than 80% of the sites have no need for supplemental local heating from subsurface thermal pollution, but at the maximum plausible surface temperature, more than 70% of sites exhibit significantly greater home heating needs. 

  *The 0% category means thermal pollution meets none of a site’s heating needs — it doesn’t mean the site has no heating needs at all, which is a different claim entirely. The second clause compounds the error: the graph tracks how much of existing heating needs thermal pollution can meet, not whether heating needs themselves grew, and no category on this figure measures that.*

**C.** At current surface temperatures, more than 80% of sites can meet, at most, 25% of local home heating needs with subsurface thermal pollution, but at the maximum plausible surface temperature, more than 80% of sites can meet greater than 25% of local home heating needs. 

  *The first half is solid: 82% plus 5% is roughly 87%, comfortably more than 80% of sites at “at most 25%.” The second half pushes the more-than-25% bar at maximum plausible temperature — about 78% — past a threshold it doesn’t clear. Rounding a value that sits just under 80% up to “more than 80%” misstates the figure by exactly the margin that makes this choice tempting.*

**D.** At current surface temperatures, more than 80% of the sites cannot use subsurface thermal pollution to meet any portion of local home heating needs, but at the maximum plausible surface temperature, that percentage drops below 20%. **(Correct)**

  *Correct. The 0% category — sites where thermal pollution meets none of local heating needs — sits at about 82% under current temperatures and falls to about 13% at the maximum plausible temperature, which is below 20%. Tracking the same category across both conditions is exactly what shows the share of unhelped sites shrinking as temperature rises, which is the increase in feasible contribution the conclusion describes.*

*Difficulty: sat-hardest*

---

##### Q50
> FIGURE. Line graph, “Median Ages of First Marriage for Men and Women in the United States and in England and Wales, 1900–2000.” Four lines, each dipping somewhat around 1950–1970 before rising sharply toward 2000: Women (England and Wales, triangle markers) rises to about 34 by 2000. Men (United States, dashed square markers) rises to a more moderate value by 2000. Women (United States, dotted circle markers) stays lowest throughout, near 20–23. Men (England and Wales, diamond markers) rises the most sharply after 1970, reaching the highest value on the graph by 2000, about 35. TEXT. A sociology student is reading an essay on the median age of first marriage in Western countries throughout the twentieth century. The author of the essay cites factors common to these countries that the author believes caused an increase in the median age of first marriage, such as new technologies that shortened the time needed for domestic chores, making two-person households less necessary and living alone more viable. The student asserts that beyond these factors there must be additional ones specific to particular Western countries that influenced the increase of age at first marriage.

Which choice most effectively uses data from the graph that support the student’s assertion?

**A.** Between 1970 and 2000, the median age of first marriage rose more sharply for men in England and Wales than it did for men in the United States. **(Correct)**

  *Correct. Both countries were subject to the same technology-driven factors the essay describes, so if those shared factors were the whole story, men in both countries should have risen at similar rates. Instead, men in England and Wales rose noticeably more sharply than men in the United States over the same two decades — a country-to-country gap in the rate of increase that shared factors alone can’t explain, which is exactly the additional, country-specific influence the student is asserting.*

**B.** In England and Wales, the median age of first marriage was consistently higher for men than for women between 1900 and 2000, but this was not always the case in the United States. 

  *This compares men against women within each country rather than comparing the same group across countries. The student’s assertion is about factors specific to particular countries driving the increase, which requires a country-to-country comparison — a gender gap inside one country is the wrong axis entirely.*

**C.** The median age of first marriage for men in England and Wales was lower in 1970 than in 1950 or 1990. 

  *This stays entirely within one country and one line on the graph. Establishing that country-specific factors are at work requires setting one country against another, and a fact about England and Wales alone, however accurately read, can’t do that on its own.*

**D.** Between 1900 and 2000, the median age of first marriage for women in England and Wales was consistently higher than for women in the United States, as was the case for men. 

  *This is a real, sustained gap between the two countries, but it’s a level difference present across the whole century — it doesn’t show a change in that gap over time, or a difference in HOW SHARPLY the age rose. A constant offset is compatible with both countries responding to the same shared factors in parallel; it doesn’t isolate a country-specific influence on the increase itself.*

*Difficulty: sat-hardest*

---

##### Q51
> FIGURE. Bar graph, “Weight of Three Aerial Robots.” The vertical axis is labeled “Weight (grams),” marked every 50 from 0 to 550. Ultra-Fast Robot Hand: about 505. Permanent Magnet Hand: about 295. Yale Model T: about 490. TEXT. Aerial robots vary considerably in their holding force; the Ultra-Fast Robot Hand, for example, has a holding force of 56 newtons, more than twice that of the Permanent Magnet Hand and more than four times that of the Yale Model T. Since an aerial robot must lift its own weight along with its cargo, engineer Jiawei Meng and colleagues used a ratio of each robot’s holding force to the robot’s weight to calculate payload capacity, with higher ratios corresponding to greater capacity, concluding that the Ultra-Fast Robot Hand has a higher payload capacity than the Yale Model T.

Which choice best describes data in the graph that support Meng and colleagues’ conclusion?

**A.** The Ultra-Fast Robot Hand and the Yale Model T each weigh more than 450 grams. 

  *Both robots do weigh over 450 grams, but the conclusion rests on a RATIO of holding force to weight, not on either robot’s absolute weight. Two large weight values on their own say nothing about which robot carries more capacity per gram.*

**B.** The Ultra-Fast Robot Hand and the Yale Model T each weigh more than the Permanent Magnet Hand does. 

  *This is accurate but brings in a third robot that the conclusion isn’t about. Meng and colleagues’ claim compares the Ultra-Fast Robot Hand against the Yale Model T specifically, and neither robot’s weight relative to the Permanent Magnet Hand bears on that comparison.*

**C.** The Yale Model T has a lower holding force than the Permanent Magnet Hand despite weighing more. 

  *This is the right kind of force-versus-weight tradeoff, applied to the wrong pair of robots. The conclusion is about the Ultra-Fast Robot Hand against the Yale Model T, and a comparison between the Yale Model T and the Permanent Magnet Hand doesn’t touch that specific pair.*

**D.** The Ultra-Fast Robot Hand weighs only slightly more than the Yale Model T does. **(Correct)**

  *Correct. The two robots weigh about the same (roughly 505 grams against roughly 490), which is what makes the comparison clean: since the text already establishes that the Ultra-Fast Robot Hand’s holding force is more than four times the Yale Model T’s, a nearly equal weight means that huge force advantage carries almost entirely into the ratio — directly supporting the greater payload capacity Meng and colleagues concluded.*

*Difficulty: sat-hardest*

---

##### Q52
> TABLE. “Tadpole Body Mass and Toxin Production after Three Weeks in Ponds.” Columns: population density; average tadpole body mass (milligrams); average number of distinct bufadienolide toxins per tadpole; average amount of bufadienolide per tadpole (nanograms); average bufadienolide concentration (nanograms per milligram of tadpole body mass). High: 193.87; 22.69; 5,815.51; 374.22. Medium: 254.56; 21.65; 5,525.72; 230.10. Low: 258.97; 22.08; 4,664.69; 171.43. TEXT. Ecologist Veronika Bókony and colleagues investigated within-species competition among common toads (Bufo bufo), a species that secretes various unpleasant-tasting toxins called bufadienolides in response to threats. The researchers tested B. bufo tadpoles’ responses to different levels of competition by creating tadpole population densities but a fixed amount of food. Based on analysis of the tadpoles after three weeks, the researchers concluded that increased competition drove bufadienolide production at the expense of growth.

Which choice uses data from the table to most effectively support the researchers’ conclusion?

**A.** The difference in average tadpole body mass was small between the low and medium population density conditions and substantially larger between the low and high population density conditions. 

  *This is an accurate read of the body-mass column — the low-to-medium gap is small (258.97 to 254.56) and the low-to-high gap is much larger (258.97 to 193.87) — but the conclusion is a trade-off between toxin production AND growth. This choice never mentions toxin data at all, so it supports only the growth half of the claim, not the toxin half.*

**B.** Tadpoles in the low and medium population density conditions had substantially lower average bufadienolide concentrations but had greater average body masses than those in the high population density condition. **(Correct)**

  *Correct. Concentration is far lower at low and medium density (171.43 and 230.10) than at high density (374.22), while body mass is greater at low and medium density (258.97 and 254.56) than at high density (193.87). This is the only choice that ties both halves of the trade-off together in one comparison — higher density means more toxin concentration and less growth, at once.*

**C.** Tadpoles in the high population density condition displayed a relatively modest increase in the average amount of bufadienolide but roughly double the average bufadienolide concentration compared to those in the low population density condition. 

  *The numbers check out — the amount rises modestly (4,664.69 to 5,815.51, about 25%) while the concentration roughly doubles (171.43 to 374.22) — but every value cited here comes from the toxin columns. The conclusion is a trade-off with growth, and a choice that never mentions body mass can’t demonstrate that the toxin gain came “at the expense of” anything.*

**D.** Tadpoles produced approximately the same number of different bufadienolide toxins across the population density conditions, but average tadpole body mass decreased as population density increased. 

  *The body-mass half is accurate — mass does fall as density rises. But “number of distinct toxins” is a count of toxin variety (about 22 across all three conditions, essentially flat), not the amount or concentration of toxin produced. A flat measure can’t demonstrate the increased toxin PRODUCTION the conclusion claims; the choice needed the concentration or amount column instead.*

*Difficulty: sat-hardest*

---

##### Q53
> TABLE. “Swahili Speakers in Three African Countries.” Columns: country; approximate number of speakers (in millions); estimated % of population. Democratic Republic of the Congo: 22; 25. Kenya: 55; 100. Tanzania: 61; 100. TEXT. Swahili is estimated to be the first language of up to 15 million people worldwide. It’s also an officially recognized language in Tanzania, Kenya, and the Democratic Republic of the Congo, which means these countries use Swahili in government documents and proceedings. But even in countries where almost everyone speaks Swahili, for many it isn’t their first language but is instead their second, third, or even fourth language.

Which choice most effectively uses data from the table to support the underlined claim?

**A.** Tanzania has approximately 61 million Swahili speakers, which is much more than the estimated total number of people worldwide for whom Swahili is their first language. **(Correct)**

  *Correct. Since Swahili is the first language of at most about 15 million people on the entire planet, but Tanzania alone has about 61 million speakers, the great majority of Tanzania’s speakers can’t possibly be speaking it as a first language — directly demonstrating that even where almost everyone speaks Swahili, most are speaking it as an additional language.*

**B.** Tanzania is estimated to have at most 15 million Swahili speakers, while the country’s total population is approximately 61 million people. 

  *This swaps the two numbers: the table gives Tanzania about 61 million Swahili SPEAKERS, not a population of 61 million with only 15 million speaking Swahili. The 15 million figure is the worldwide count of first-language speakers from the text, not a value from Tanzania’s row at all.*

**C.** Approximately 100 percent of the people who speak Swahili as their first language live in Kenya, which has a total population of approximately 55 million people. 

  *The table’s “estimated % of population” column reports what share of Kenya’s population speaks Swahili at all, not what share of the world’s first-language speakers live there. Reading a population-coverage percentage as a first-language-speaker percentage confuses two different quantities the table never links.*

**D.** Approximately 100 percent of Kenya’s population speaks Swahili, while only about 25 percent of the Democratic Republic of the Congo’s population speaks Swahili. 

  *Both figures are accurate, but the comparison is between two countries’ overall Swahili-speaking rates — it says nothing about whether those speakers learned Swahili first, second, or third. The underlined claim is specifically about first-language status, which this choice never addresses.*

*Difficulty: hard*

---

##### Q54
> TABLE. “Correlations Between Congestion Ratings and Features of the Crowd in Raters’ Immediate Vicinity.” Columns: crowd feature; before obstacle; after obstacle; overall. Density: 0.8592; 0.7308; 0.7447. Velocity: −0.9357; −0.9518; −0.8587. TEXT. Researcher Xiaolu Jia and colleagues monitored individuals’ velocity and the surrounding crowd density as a group of study participants walked through a space and navigated around an obstacle. Participants rated how congested it seemed before the obstacle, after the obstacle, and overall, and the researchers correlated those ratings with velocity and density. (Correlations range from −1 to 1, with greater distance from 0 indicating greater strength.) The researchers concluded that the correlations with velocity are stronger than those with density.

Which choice best describes data from the table that support the researchers’ conclusion?

**A.** The correlation between congestion ratings before the obstacle and density is further from 0 than the correlation between overall congestion rating and velocity is. 

  *This is accurate as read (0.8592 is further from 0 than −0.8587) but it crosses categories — before-obstacle density against overall velocity — rather than comparing density to velocity within the same rating. Within that mismatched pairing, density actually comes out slightly stronger, which runs against the conclusion rather than for it.*

**B.** The correlation between congestion ratings before the obstacle and velocity is further from 0 than the correlation between overall congestion and velocity is. 

  *Both values are velocity correlations (−0.9357 and −0.8587) — this compares velocity to velocity across two different rating times, never bringing density into the comparison at all. A conclusion about velocity being stronger than density needs both variables in the same comparison.*

**C.** For each of the three ratings, the correlation with velocity is negative while the correlation with density is positive. 

  *The signs are read correctly — velocity is negative and density is positive in all three rows — but sign only indicates direction, not strength. “Further from 0” is about magnitude, and a negative correlation isn’t automatically stronger than a positive one just because the signs differ.*

**D.** For each of the three ratings, correlations with velocity are further from 0 than the corresponding correlations with density are. **(Correct)**

  *Correct. Checked row by row: before obstacle, 0.9357 versus 0.8592; after obstacle, 0.9518 versus 0.7308; overall, 0.8587 versus 0.7447. Velocity’s correlation is further from 0 than density’s in every matched pair, which is exactly what “correlations with velocity are stronger than those with density” requires — and it’s the only choice that keeps each comparison within its own rating category.*

*Difficulty: sat-hardest*

---

##### Q55
> TABLE. “Corn-Related Vocabulary in Various Southeastern Languages.” Columns: language family; word (language); English translation; proposed origin in vocabulary of the Totozoquean language family. Muskogean: tanchi’ (Chickasaw); tanchi (Choctaw); vce (Muscogee, pronounced “uh-chi”) — corn — no. Iroquoian: se-lu (Cherokee) — corn — no. Caddoan: -k’as- (Caddo) — dried corn — yes. Chitimacha: k’asma (Chitimacha) — corn — yes. TEXT. In Caddo, a language from what is now the US Southeast, vocabulary pertaining to corn cultivation resembles equivalent vocabulary in the Totozoquean language family in Mexico. This resemblance is perhaps attributable to cultural contact: such words could have entered Caddo through the intermediary of the neighboring but unrelated Chitimacha language, concurrent with the dissemination of corn itself from Mexico into the Southeast after 700 CE. That the vocabulary pertaining to domestic crops accompanies them as they diffuse into new regions is an established phenomenon globally. Corn cultivation became ubiquitous among the Southeastern tribes, yet ______

Which choice most effectively uses data from the table to complete the statement?

**A.** the origins of vocabulary pertaining to the crop vary across languages in the region, with the words for corn in Cherokee and the Muskogean languages showing no demonstrable relationship to Totozoquean vocabulary. **(Correct)**

  *Correct. The table marks Caddoan and Chitimacha “yes” for a Totozoquean connection but marks Cherokee (Iroquoian) and the Muskogean words “no.” That split completes the “yet”: corn cultivation spread everywhere, but the vocabulary that traveled with it from Mexico did not — Cherokee and the Muskogean languages built their own words instead.*

**B.** the region is linguistically diverse, being home not only to Chitimacha and Caddo, but also to the Muskogean language family (including Chickasaw, Choctaw, and Muscogee) and to one Iroquoian language (Cherokee). 

  *This is an accurate list of the language families in the table, but it’s purely descriptive — it never engages the “yet” contrast between the crop’s universal spread and the vocabulary’s uneven spread. Naming the languages present isn’t the same as showing which ones do or don’t share the Totozoquean-derived words.*

**C.** corn-related vocabulary underwent changes when entering other, unrelated languages, as can be seen by the divergence of the Caddo word from the Chitimacha word it originated in. 

  *Caddo’s -k’as- and Chitimacha’s k’asma are similar but not identical, so there is some divergence between them — but both are marked “yes” for the Totozoquean connection, and the sentence’s contrast is about vocabulary NOT following the crop into languages like Cherokee and the Muskogean family. Comparing two words that share the same origin is the wrong pair for that contrast.*

**D.** words for corn in the languages of the Muskogean family evolved from a common root, with the Muscogee word having lost certain consonant sounds still present in the Chickasaw and Choctaw words. 

  *This is a claim about sound change within the Muskogean family alone, and it doesn’t touch the sentence’s actual point — the contrast between corn’s universal spread and the Totozoquean-linked vocabulary’s uneven spread. Internal Muskogean phonology is a different topic from the one the “yet” sets up.*

*Difficulty: hard*

---

##### Q56
> TABLE. “Percentage Point Changes in US Federal Outlays Relative to GDP by Congressional Status.” Columns: period; congressional status; change in total outlays; change in nondefense outlays; change in defense outlays. 1981–1988, divided: −0.4; −1.3; 0.9. 1975–1976, divided: 2.7; 3.0; −0.3. 1977–1980, undivided: 0.3; 0.6; −0.3. 1964–1968, undivided: 1.9; 1.4; 0.5. 1969–1974, divided: −1.8; 2.1; −3.9. TEXT. Economist Steve H. Hanke has shown that divided US Congresses—which occur when one party holds the majority in the House of Representatives and another party holds the majority in the Senate—tend to accompany reductions in total federal outlays (spending) relative to gross domestic product (GDP), which Hanke interprets to reflect decreases in government size. Hanke calculated the percentage point change in total outlays (encompassing nondefense and defense outlays) for consecutive US Congresses. Hanke has pointed to his calculations as evidence that a divided Congress may be a “necessary but not sufficient condition” for a decrease in government size to occur.

Which choice best describes data from the table that support the underlined claim?

**A.** The periods of undivided Congresses were associated with increases in nondefense outlays, whereas all the periods of divided Congresses except one were associated with reductions in defense outlays. 

  *Both readings are accurate, but a “necessary but not sufficient condition” claim is about TOTAL outlays — whether a decrease in overall spending happens only during, but not always during, divided Congresses. Nondefense and defense outlays are sub-components, and neither one is the column the claim is actually about.*

**B.** All the periods of divided Congresses were associated with reductions in total outlays, although two were also associated with increases in nondefense outlays. 

  *This misstates the total-outlays column: 1975–1976, a divided period, shows a change of +2.7, an increase, not a reduction. “All the periods of divided Congresses” reduced total outlays is false on its face — one of the three did the opposite.*

**C.** The periods of undivided Congresses were associated with increases in total outlays, whereas all the periods of divided Congresses were associated with reductions in either nondefense outlays or defense outlays. 

  *The undivided-Congress half is right — both undivided periods increased total outlays. But “reductions in either nondefense or defense outlays” swaps in a sub-component measure for the divided-Congress half instead of checking what happened to TOTAL outlays, which is the quantity the necessary-but-not-sufficient claim is actually about.*

**D.** All the periods of divided Congresses except one were associated with reductions in total outlays, whereas the periods of undivided Congresses were associated with increases in total outlays. **(Correct)**

  *Correct. In the total-outlays column, both undivided periods increased (+0.3, +1.9) — a decrease never once occurred without a divided Congress, which is the “necessary” half. Two of the three divided periods decreased (−0.4, −1.8) while one increased (+2.7) — a divided Congress didn’t always produce a decrease, which is the “not sufficient” half. This is the only choice that checks both halves of the claim against the column the claim is actually about.*

*Difficulty: sat-hardest*

---

##### Q57
> TABLE. “Distribution of Ecosystem Services Affected by Invasive Species by Service Type.” Columns: region (overall); provisioning (75%); regulating (21%); cultural (4%). West: 73%; 27%; 0%. North: 88%; 12%; 0%. South: 79%; 14%; 7%. East: 83%; 6%; 11%. Central: 33%; 67%; 0%. TEXT. To assess the impact of invasive species on ecosystems in Africa, Benis N. Egoh and colleagues reviewed government reports about how invasive species are undermining ecosystem services (aspects of the ecosystem on which residents depend). The services were sorted into three categories: provisioning (material resources from the ecosystem), regulating (natural processes such as cleaning the air or water), and cultural (nonmaterial benefits of ecosystems). Egoh and her team assert that countries in each region reported effects on provisioning services and that provisioning services represent the majority of the reported services.

Which choice best describes data from the table that support Egoh and colleagues’ assertion?

**A.** Provisioning services represent 73% of the services reported for the West region and 33% of those for the Central region, but they represent 75% of the services reported overall. 

  *All three values are accurate, but citing Central’s 33% as an example works against the “majority” half of the assertion rather than for it — 33% is well under half. Choosing the region where provisioning is weakest as an illustration undercuts the claim it’s meant to support.*

**B.** None of the percentages shown for provisioning services are lower than 33%, and the overall percentage shown for provisioning services is 75%. **(Correct)**

  *Correct. Framing 33% as a floor — “none...lower than” — rather than citing it as a standalone figure shows that even the weakest region still reported a substantial, clearly nonzero share of provisioning services, supporting that every region reported effects on provisioning. Pairing that with the overall 75% establishes the majority half in the same breath.*

**C.** Provisioning services are shown for each region, while no cultural services are shown for some regions. 

  *This confirms provisioning was reported everywhere but never addresses whether provisioning represents a majority of the reported services — the second half of the assertion is left untouched. The detail about cultural services being absent in some regions isn’t part of the claim at all.*

**D.** The greatest percentage shown for provisioning services is 88% for the North region, and the least shown for provisioning services is 33% for the Central region. 

  *These are the two most visually extreme values in the provisioning column, which is exactly why they’re tempting, but reporting a maximum and a minimum doesn’t by itself establish that provisioning is a majority everywhere or overall — the overall 75% figure that actually proves the majority claim is never cited.*

*Difficulty: hard*

---

##### Q58
> TABLE. “Mean Time (in Seconds) Spent per Flower for Four Pollinator Genera.” Columns: pollinator genus; seconds per intact pin flower; seconds per damaged pin flower; seconds per intact thrum flower; seconds per damaged thrum flower. Habropoda: 2.7; 5.4; 4.1; 9.5. Osmia: 5.2; 8.2; 7.1; 8.3. Pierid: 2.6; 4.0; 2.4; 1.9. Xylocopa: 2.3; 2.8; 2.5; 2.2. TEXT. To study how floral damage affects the behavior of pollinators, such as bees, a team of researchers punched holes in the floral tissue of flowers from the vine yellow jessamine (Gelsemium sempervirens), a plant that produces flowers that have either a long pistil and a short stamen (pin morphs) or a short pistil and a long stamen (thrum morphs). The researchers then compared the time different insect pollinators spent visiting intact pin and thrum flowers to the time such pollinators spent visiting the artificially damaged pin and thrum flowers. The researchers concluded that the effect of floral damage on time spent per flower varied by both floral morph and the genus of the pollinator.

Which choice best describes data from the table that support the researchers’ conclusion?

**A.** For pin flowers, damage led to longer times per flower in all pollinator genera, whereas for thrum flowers, damage led to longer times per flower only in Habropoda and Osmia. **(Correct)**

  *Correct. Every genus took longer on damaged pin flowers (2.7→5.4, 5.2→8.2, 2.6→4.0, 2.3→2.8) — one uniform pattern by morph. But for thrum flowers, damage lengthened time only for Habropoda and Osmia (4.1→9.5, 7.1→8.3) while it shortened time for Pierid and Xylocopa (2.4→1.9, 2.5→2.2) — the same intervention producing different effects by genus. Together, that’s an effect that varies by BOTH morph and genus, exactly as the researchers concluded.*

**B.** Compared with pollinators belonging to the genus Osmia, pollinators belonging to the genus Xylocopa spent less time on damaged pin flowers but more time on damaged thrum flowers. 

  *The pin-flower half is right (Xylocopa’s 2.8 is less than Osmia’s 8.2), but the thrum-flower half misreads the table: Xylocopa’s damaged-thrum time is 2.2 seconds, less than Osmia’s 8.3, not more.*

**C.** Damage led to shorter times per thrum flower in three pollinator genera (Osmia, Pierid, and Xylocopa), whereas it led to longer times per thrum flower in one pollinator genus (Habropoda). 

  *Pierid and Xylocopa did get shorter times on damaged thrum flowers, but Osmia’s went from 7.1 to 8.3 seconds — longer, not shorter. Grouping Osmia with the “shorter” genera misreads that cell of the table.*

**D.** Pollinators belonging to the genus Habropoda spent 2.7 seconds on intact pin flowers and 4.1 seconds on intact thrum flowers. 

  *Both figures are accurate, but they’re both intact-flower values — no damaged-flower figure appears at all, so this choice never shows what effect damage had, let alone that the effect varies by morph and genus.*

*Difficulty: sat-hardest*

---

##### Q59
> TABLE. “Three Studies’ Estimated Average Velocity of LMC.” Columns: researchers; study year; estimated average velocity. Murai and Fujimoto: 1980; 344 km/s. Kallivayalil and colleagues: 2006; 378 km/s. Gardiner and colleagues: 1994; 297 km/s. TEXT. In 2006, Nitya Kallivayalil and colleagues calculated the most accurate estimate yet of the average velocity (in kilometers per second) of the Large Magellanic Cloud (LMC) galaxy. Before the 2006 study, estimates of the average velocity were low enough for the LMC to maintain an orbit around the Milky Way galaxy, but according to an analysis by Gurtina Besla and colleagues, the estimated velocity from the 2006 study is too high for the LMC to maintain such an orbit. Therefore, if Besla and colleagues are correct, the maximum average velocity for the LMC that would allow it to maintain orbit around the Milky Way is likely ______

Which choice most effectively uses data from the table to complete the statement?

**A.** above 344 km/s but below 378 km/s. **(Correct)**

  *Correct. Both pre-2006 estimates — 344 km/s (1980) and 297 km/s (1994) — were “low enough to maintain orbit,” so the true maximum must be above the HIGHER of the two, 344 km/s, not just above the lower one. The 2006 estimate, 378 km/s, was “too high to maintain orbit,” so the maximum must fall below that. Only the range between 344 and 378 km/s satisfies both constraints.*

**B.** above 297 km/s but below 344 km/s. 

  *This treats 297 km/s as the highest pre-2006 estimate and stops there, but 344 km/s (1980) was also before 2006 and also low enough to maintain orbit. Ignoring the higher of the two pre-2006 values sets the floor of the range too low.*

**C.** above 378 km/s. 

  *378 km/s is the 2006 estimate that Besla and colleagues found too high to maintain orbit. Placing the maximum above that value would mean even a velocity too high to maintain orbit still counts as within it — the reverse of what the passage states.*

**D.** below 297 km/s. 

  *297 km/s is the lower of the two pre-2006 estimates, both of which were low enough to maintain orbit. Placing the maximum below 297 km/s would mean even a velocity already established as low enough is somehow too high — the reverse of what the passage states.*

*Difficulty: sat-hardest*

---

##### Q60
> TABLE. “Ablation Rates for Three Elements in Cosmic Dust, by Dust Source.” Columns: element; SPC; AST; HTC; OCC. Iron: 20%; 28%; 90%; 98%. Potassium: 44%; 74%; 97%; 100%. Sodium: 45%; 75%; 99%; 100%. TEXT. Earth’s atmosphere is bombarded by cosmic dust originating from several sources: short-period comets (SPCs), particles from the asteroid belt (ASTs), Halley-type comets (HTCs), and Oort cloud comets (OCCs). Some of the dust’s material vaporizes in the atmosphere in a process called ablation, and the faster the particles move, the higher the rate of ablation. Astrophysicist Juan Diego Carrillo-Sánchez led a team that calculated average ablation rates for elements in the dust (such as iron and potassium) and showed that material in slower-moving SPC or AST dust has a lower rate than the same material in faster-moving HTC or OCC dust. For example, whereas the average ablation rate for iron from AST dust is 28%, the average rate for ______

Which choice most effectively uses data from the table to complete the example?

**A.** iron from SPC dust is 20%. 

  *SPC is a slower-moving source, same as AST — pairing two slow sources doesn’t illustrate “slower-moving...has a lower rate than the same material in faster-moving” dust. The example needs iron from a FAST source (HTC or OCC), not another slow one.*

**B.** sodium from OCC dust is 100%. 

  *OCC is a fast-moving source, which is the right kind of source, but the example set up iron as the element under discussion (“the average ablation rate for iron from AST dust is 28%”), and this choice switches to sodium — a different element than the one being compared.*

**C.** iron from HTC dust is 90%. **(Correct)**

  *Correct. HTC is a faster-moving source than AST, and iron is the same element cited in the first half of the sentence. 90% (HTC) is higher than 28% (AST), which is exactly the slower-source/lower-rate versus faster-source/higher-rate pattern the sentence is illustrating.*

**D.** sodium from AST dust is 75%. 

  *This changes both variables at once: sodium instead of iron, and AST — the same slow source already named — instead of a faster one. It neither keeps the element constant nor supplies the faster-moving comparison the example needs.*

*Difficulty: medium*

---

##### Q61
> GRAPH. “Economic Policy Uncertainty in the United Kingdom, 2005–2010.” Bar graph, y-axis: uncertainty (larger values = more uncertainty), 0 to 200. Three series per year — tax and public spending policy, trade policy, general economic policy. 2005: tax about 100; trade about 160; general about 90. 2006: tax about 65; trade about 105; general about 70. 2007: tax about 60; trade about 75; general about 75. 2008: tax about 90; trade about 70; general about 75. 2009: tax about 75; trade about 70; general about 80. 2010: tax about 165; trade about 70; general about 120. TEXT. High levels of public uncertainty about which economic policies a country will adopt can make planning difficult for businesses, but measures of such uncertainty have not tended to be very detailed. Recently, however, economist Sandile Hlatshwayo analyzed trends in news reports to derive measures not only for general economic policy uncertainty but also for uncertainty related to specific areas of economic policy, like tax or trade policy. One revelation of her work is that a general measure may not fully reflect uncertainty about specific areas of policy, as in the case of the United Kingdom, where general economic policy uncertainty ______

Which choice most effectively uses data from the graph to illustrate the claim?

**A.** aligned closely with uncertainty about tax and public spending policy in 2005 but differed from uncertainty about tax and public spending policy by a large amount in 2009. 

  *In 2005 general (about 90) and tax (about 100) are indeed close, but in 2009 they’re close too — about 80 versus about 75 — not a large difference. The second half of this choice misreads the graph, so it can’t be the pair of years that illustrates the claim.*

**B.** was substantially lower than uncertainty about tax and public spending policy each year from 2005 to 2010. 

  *This breaks in 2006, where general (about 70) is actually higher than tax (about 65), not lower. “Each year” is a claim about every bar in the series, and one contrary year is enough to disqualify it.*

**C.** reached its highest level between 2005 and 2010 in the same year that uncertainty about trade policy and tax and public spending policy reached their lowest levels. 

  *General uncertainty peaks in 2010, but trade policy’s lowest point is closer to 2009 and tax and public spending’s lowest point is 2007 — neither low point lines up with general’s 2010 peak. The three series don’t hit their extremes in the same year.*

**D.** was substantially lower than uncertainty about trade policy in 2005 and substantially higher than uncertainty about trade policy in 2010. **(Correct)**

  *Correct. In 2005, general (about 90) sits well below trade (about 160); by 2010, general (about 120) sits well above trade (about 70) — a reversal. A general measure that trails a specific-policy measure one year and outpaces it another year is precisely a general measure failing to “fully reflect” uncertainty about that specific area.*

*Difficulty: sat-hardest*

---

##### Q62
> TABLE. “Effects of Mycorrhizal Fungi on 3 Plant Species.” Columns: plant species; mycorrhizal host; average mass of plants grown in soil containing mycorrhizal fungi (in grams); average mass of plants grown in soil treated to kill fungi (in grams). Corn: yes; 15.1; 3.8. Marigold: yes; 10.2; 2.4. Broccoli: no; 7.5; 7. TEXT. Mycorrhizal fungi in soil benefits many plants, substantially increasing the mass of some. A student conducted an experiment to illustrate this effect. The student chose three plant species for the experiment, including two that are mycorrhizal hosts (species known to benefit from mycorrhizal fungi) and one nonmycorrhizal species (a species that doesn’t benefit from and may even be harmed by mycorrhizal fungi). The student then grew several plants from each species both in soil containing mycorrhizal fungi and in soil that had been treated to kill mycorrhizal and other fungi. After several weeks, the student measured the plants’ average mass and was surprised to discover that ______

Which choice most effectively uses data from the table to complete the statement?

**A.** broccoli grown in soil containing mycorrhizal fungi had a slightly higher average mass than broccoli grown in soil that had been treated to kill fungi. **(Correct)**

  *Correct. Broccoli is the nonmycorrhizal species — one that “doesn’t benefit from and may even be harmed by” the fungi. Finding it still came out slightly ahead with fungi present (7.5 versus 7) is the surprising result: the one species predicted not to benefit showed a benefit anyway, however small.*

**B.** corn grown in soil containing mycorrhizal fungi had a higher average mass than broccoli grown in soil containing mycorrhizal fungi. 

  *This is true (15.1 versus 7.5) but entirely expected — corn is a mycorrhizal host predicted to benefit, so of course it outperforms broccoli under the same fungi-present condition. There’s nothing here that a reader wouldn’t already predict from the setup.*

**C.** marigolds grown in soil containing mycorrhizal fungi had a much higher average mass than marigolds grown in soil that had been treated to kill fungi. 

  *This is also true (10.2 versus 2.4) and also exactly what the setup predicts — marigold is a mycorrhizal host, so a much higher mass with fungi present than without is the expected outcome, not a surprising one.*

**D.** corn had the highest average mass of all three species grown in soil that had been treated to kill fungi, while marigolds had the lowest. 

  *In the fungi-killed condition, broccoli’s mass (7) is actually the highest of the three species, not corn’s (3.8) — corn comes in second. The marigold-lowest half is accurate, but the corn-highest half misreads the column, and neither half touches why the result was surprising.*

*Difficulty: medium*

---

##### Q63
> TABLE. "Delta 15-N Values in Seagrass Samples from Four Sites on the Yucatan, 2016–2017." Columns: site; February 2016; October 2016; February 2017; October 2017. Akumal Bay: no data available; 3.3; 2.0; 6.3. Mahahual: 0.7; no data available; 2.5; 3.4. Tulum: 6.1; 5.9; 2.3; 5.5. Xahuayxol: 0.9; 0.3; −0.9; 1.4. TEXT. Because water from natural, uncontaminated sources is less enriched with the stable nitrogen isotope 15N than wastewater from human activities is, the presence of such wastewater in nature can be detected by examining delta 15-N values (a measure of the ratio of 15N to 14N) in plants. Karla A. Camacho-Cruz and colleagues assessed delta 15-N values in the seagrass Thalassia testudinum from sites on Mexico's Yucatan peninsula with intermediate tourism development, including Akumal Bay and Tulum, and low tourism development, including Mahahual and Xahuayxol, throughout 2016 and 2017. The data suggest that the intermediate-tourism sites experienced influxes of human wastewater. However, the researchers concluded that this happened intermittently.

Which choice best describes data from the table that support the underlined conclusion?

**A.** Although delta 15-N values were generally higher in Akumal Bay and Tulum than in Mahahual and Xahuayxol, the values were lower in Akumal Bay than in Mahahual and Xahuayxol in February 2017. 

  *The first clause is accurate, but the second is not: in February 2017, Akumal Bay's value (2.0) is indeed lower than Mahahual's (2.5), but it is far higher than Xahuayxol's (−0.9), so it is not lower than "Mahahual and Xahuayxol" as a pair. And even if the arithmetic held, a single month's ranking across sites shows nothing about whether an influx happened intermittently — that requires tracking one site's own values over time, not comparing sites to each other at one moment.*

**B.** Delta 15-N values reached their lowest level in February 2017 in both Akumal Bay and Tulum, but no data were available for Akumal Bay in February 2016, when the values reached their highest level in Tulum. 

  *Both halves are individually accurate — 2.0 and 2.3 are each site's lowest recorded value, and Tulum's February 2016 value, 6.1, is indeed its highest, in a month Akumal Bay has no data for. But stitching a missing-data note about one site to an unrelated superlative about a different site doesn't trace a rise-and-fall pattern over time — it names two disconnected extremes rather than showing values moving up and down, which is what "intermittently" requires.*

**C.** Although all sites showed considerable variation in delta 15-N values, the values remained relatively constant in Akumal Bay from October 2016 to February 2017 and in Tulum from February 2016 to October 2016. 

  *The Tulum half checks out — 6.1 to 5.9 is nearly flat. The Akumal Bay half does not: 3.3 to 2.0 is a drop of roughly a third, a real change, not "relatively constant." And even where the description is accurate, "remained constant" is the opposite of what the conclusion needs — an intermittent influx shows up as values that move, not values that hold steady.*

**D.** In Akumal Bay and Tulum, delta 15-N values fluctuated considerably across the three measurements made from October 2016 to October 2017. **(Correct)**

  *Correct. Restrict to the three dates both sites actually have data for — October 2016, February 2017, October 2017 — since Akumal Bay has no February 2016 reading. Akumal Bay: 3.3 → 2.0 → 6.3, down then sharply up. Tulum: 5.9 → 2.3 → 5.5, the same down-then-up shape. That non-monotonic swing at both intermediate-tourism sites is exactly what "intermittently" means: the wastewater signal comes and goes rather than climbing steadily or holding steady.*

*Difficulty: sat-hardest*

---

##### Q64
> FIGURE. Bar graph, "Jasmonic and Salicylic Acid Levels in Tomato Plants," in nanograms of acid per gram of dry weight. Three bars per acid type: control plants; plants exposed to air from whitefly-free plants and then infested; plants exposed to air from whitefly-infested plants and then infested. Jasmonic acid: control about 140, whitefly-free-exposed about 205, whitefly-infested-exposed about 100. Salicylic acid: control about 120, whitefly-free-exposed about 130, whitefly-infested-exposed about 175. TEXT. In tomato plants, herbivory induces defensive production of jasmonic acid, while microbial infection induces defensive production of salicylic acid; plants also emit airborne chemicals to initiate the appropriate defense in nearby tomato plants. Researchers investigated the poor resistance tomato plants show to whitefly herbivory by exposing some plants to airborne chemicals from whitefly-free plants and others to airborne chemicals from whitefly-infested plants, then infesting both groups of plants with whiteflies. The researchers concluded that whiteflies induce tomato plants to emit chemicals that cause other tomato plants to preferentially defend against microbial infection even when under herbivorous attack.

Which choice best describes data from the graph that support the researchers' conclusion?

**A.** When plants exposed to air from whitefly-free plants were infested, they produced more jasmonic acid than did control plants, whereas when plants exposed to air from whitefly-infested plants were infested, they produced less jasmonic acid and more salicylic acid than did control plants. **(Correct)**

  *Correct. Check every clause against the graph: whitefly-free-exposed jasmonic acid (about 205) exceeds control jasmonic acid (about 140). Whitefly-infested-exposed jasmonic acid (about 100) is lower than control jasmonic acid (about 140), and that same group's salicylic acid (about 175) is higher than control salicylic acid (about 120). The pair in the second half — less jasmonic, more salicylic, in the one group exposed to signals from whitefly-infested plants — is exactly "preferentially defend against microbial infection even when under herbivorous attack": the herbivory defense drops while the infection defense rises, in the same plants.*

**B.** When plants exposed to air from whitefly-infested plants were infested, they produced less jasmonic acid than salicylic acid, whereas when plants exposed to air from whitefly-free plants were infested, they produced about the same amount of jasmonic acid and salicylic acid. 

  *The first half checks out — about 100 versus about 175. The second does not: the whitefly-free-exposed group's jasmonic acid (about 205) sits far above its salicylic acid (about 130), not "about the same." A choice this specific still has to clear the arithmetic on both of its halves.*

**C.** When plants exposed to air from whitefly-free plants were infested, they produced both jasmonic acid and salicylic acid, whereas when plants exposed to air from whitefly-infested plants were infested, they exclusively produced salicylic acid. 

  *"Exclusively produced salicylic acid" misreads the graph — the whitefly-infested-exposed group's jasmonic acid bar sits at about 100, not zero. They produced less jasmonic acid than the other groups, not none at all, and "produced both" for the first group is true of essentially every bar on the chart, which is why it feels safe without actually establishing anything.*

**D.** When plants exposed to air from whitefly-infested plants were infested, they produced less jasmonic acid than did control plants, whereas when plants exposed to air from whitefly-free plants were infested, they produced more jasmonic acid and salicylic acid than did control plants. 

  *Every number checks out — whitefly-infested-exposed jasmonic acid (about 100) sits below control (about 140); whitefly-free-exposed jasmonic acid (about 205) and salicylic acid (about 130) both exceed control (about 140 and about 120). But the salicylic acid boost is pinned to the wrong group: the conclusion is about plants exposed to signals from whitefly-infested plants defending preferentially against infection, and this choice never reports that group's salicylic acid rising above control at all — it only reports the whitefly-free-exposed group producing more of both acids, a different, weaker pattern that doesn't show the herbivory-defense-down / infection-defense-up trade-off the conclusion needs.*

*Difficulty: sat-hardest*

---

##### Q65
> TABLE. "Data Sources for Neptune Temperature Analysis." Columns: instrument; observatory; data type; observation years. TEXES (Texas Echelon Cross Echelle Spectrograph): Gemini Observatory; spectroscopy; 2007, 2019. T-ReCS (Thermal-Region Camera Spectrograph): Gemini Observatory; infrared imaging; 2007, 2010. LWS (Long Wavelength Spectrometer): Keck Observatory; infrared imaging; 2003. VISIR (VLT Imager and Spectrometer for mid-InfraRed): European Southern Observatory; spectroscopy; 2006. TEXT. Julianne I. Moses and colleagues have reported that Neptune may have cooled significantly between 2003 and 2020. The team reached this conclusion by analyzing existing infrared imaging and spectroscopy data about the planet obtained from various instruments in different years. Of the team's sources listed in the table, the earliest example of spectroscopy data included in the analysis was obtained in ______

Which choice most effectively uses data from the table to complete the text?

**A.** 2007 using TEXES at the Gemini Observatory. 

  *TEXES is genuinely a spectroscopy instrument, and 2007 is genuinely one of its observation years — but the table lists an earlier spectroscopy year elsewhere. Confirming that a choice is internally consistent with one row is not the same as checking it against every row that shares its data type.*

**B.** 2007 using T-ReCS at the Gemini Observatory. 

  *T-ReCS is an infrared imaging instrument, not a spectroscopy one — the data-type column rules it out before the year is even worth checking. The blank asks specifically for spectroscopy data, and this row never qualifies to compete for it.*

**C.** 2006 using VISIR at the European Southern Observatory. **(Correct)**

  *Correct. Two instruments in the table are marked "spectroscopy": TEXES, observed in 2007 and 2019, and VISIR, observed in 2006. Comparing across only the rows that share that data type, 2006 is earlier than 2007, so VISIR at the European Southern Observatory is the earliest spectroscopy source.*

**D.** 2003 using LWS at the W.M. Keck Observatory. 

  *2003 is the earliest year anywhere in the table, and LWS's row is otherwise read correctly — which is exactly why this choice is tempting. But LWS's data type is infrared imaging, not spectroscopy, so its early date is irrelevant to a blank that asks for the earliest spectroscopy source specifically.*

*Difficulty: hard*

---

##### Q66
> FIGURE. Bar graph, "Banana Ripening Time at Different Temperatures with and without Ethylene Treatment," in days to ripen. Ethylene-treated bars and untreated ("no ethylene") bars at four temperatures. 14°C: ethylene 8, no ethylene 11. 16°C: ethylene 6, no ethylene 9.5. 18°C: ethylene 5.5, no ethylene 8.5. 20°C: ethylene 4, no ethylene 5.5. TEXT. A student is conducting an experiment to test the effect of temperature and ethylene treatment on the ripening speed of bananas. The student treated some bananas with ethylene while leaving others untreated, then allowed both types of bananas to ripen at one of four different temperatures. Comparing the data for bananas with and without ethylene, the student concluded that ______

Which choice most effectively uses data from the graph to complete the student's conclusion?

**A.** 20°C is the ideal temperature at which to store bananas to slow ripening time. 

  *This has the whole experiment backward. Time-to-ripen is shortest at 20°C in both conditions (4 days with ethylene, 5.5 without) — the fastest ripening on the graph, not the slowest. A choice that wants to slow ripening would need the longest times, which sit at 14°C. The graph also never addresses storage as a goal at all; it only reports ripening time under the treatments actually tested.*

**B.** for those bananas that were not treated with ethylene, differences in temperature were not associated with absolute differences in ripening time. 

  *The no-ethylene bars move from 11 days at 14°C down to 5.5 days at 20°C — a difference of more than five and a half days across the temperature range, not the absence of a difference this choice claims. Temperature is doing plenty of work in the untreated bananas; the graph shows the opposite of "not associated."*

**C.** bananas treated with ethylene ripen faster at 14°C and 16°C than at 18°C and 20°C. 

  *This reverses which end of the graph is "faster." Fewer days means faster ripening, and the ethylene bars at 14°C and 16°C (8 and 6 days) are taller — slower — than the bars at 18°C and 20°C (5.5 and 4 days). Ripening is faster at the higher temperatures, the opposite of what this choice states.*

**D.** ethylene was associated with a greater absolute change in ripening time at 14°C, 16°C, and 18°C than at 20°C. **(Correct)**

  *Correct. Compute the ethylene-versus-no-ethylene gap at each temperature: 14°C, 11 − 8 = 3 days; 16°C, 9.5 − 6 = 3.5 days; 18°C, 8.5 − 5.5 = 3 days; 20°C, 5.5 − 4 = 1.5 days. The gap at 20°C is roughly half the size of the gap at any of the other three temperatures, which is exactly the pattern this choice reports.*

*Difficulty: hard*

---

#### Command of Evidence — Textual (70 items)

##### Q1
> Roasted green chiles are a popular ingredient in Southwestern cuisine, but the traditional roasting method of burning propane is not environmentally friendly. To see if solar power could provide a better alternative, engineer Kenneth Armijo and his team roasted batches of green chiles using between 38 and 42 heliostats, which are devices that concentrate sunlight. The team was successful in reaching the same roasting temperature used in traditional propane roasting, but they found that propane yielded faster results. While the fastest solar-roasted green chiles took six minutes, batches using propane took only four. Armijo hypothesizes that they can reduce the roasting time for solar-roasted green chiles by using more heliostats.

Which finding, if true, would most directly support Armijo's hypothesis?

**A.** The temperature inside the roasting drum is distributed more evenly when roasting green chiles with solar power than with propane. 

  *Even temperature distribution is a claim about heat uniformity, not roasting speed. Armijo's hypothesis is specifically that adding more heliostats would cut the time down — a finding about evenness, however true, says nothing about whether six minutes could become five.*

**B.** Attempts to roast green chiles using 50 heliostats yields results in fewer than six minutes. **(Correct)**

  *Correct. Fifty heliostats is more than the 38 to 42 the team already tested, and "fewer than six minutes" beats the fastest time solar roasting had achieved. That is the hypothesis in miniature: more heliostats, less time.*

**C.** Green chile connoisseurs prefer the flavor of solar-roasted green chiles over the flavor of propane-roasted green chiles. 

  *Flavor preference is a real finding about the chiles and entirely beside the point. The hypothesis concerns roasting time, and a taste-test result cannot confirm or deny that more heliostats roast chiles faster.*

**D.** The skins of solar-roasted green chiles are easier to peel than the skins of propane-roasted green chiles. 

  *Peel-ability is another genuine property of the chiles that has nothing to do with roasting speed. The hypothesis is about heliostat count and time, and this finding, however useful in a kitchen, does not touch either variable.*

*Difficulty: hard*

---

##### Q2
> As a monthly newsletter formed in 1969 by a group of Asian American students at the University of California, Los Angeles, Gidra helped raise awareness about social and political issues concerning the Asian American community on campus and at large. The newsletter had an expansive reach for a publication of its kind: around 4,000 copies were published each month. A student writing a history paper, however, hypothesizes that Gidra's influence cannot be measured by the number of newsletters published monthly alone.

Which finding, if true, would most directly support the student's hypothesis?

**A.** The students who initially formed Gidra each contributed financially to its creation. 

  *Financial contribution explains how Gidra got started, not how far its influence spread once it existed. The hypothesis is about whether the print run undercounts the newsletter's reach, and funding its founding is a different question entirely.*

**B.** In addition to covering current events, Gidra also featured works of art and literature. 

  *A richer table of contents is not a wider readership. The hypothesis needs a reason to think Gidra reached more people than the 4,000-copy figure implies, and what was printed inside each copy does not bear on how many people read it.*

**C.** Gidra was initially based out of the Asian American Studies Center at UCLA. 

  *This is a fact about where Gidra operated from, not about how many people its ideas reached. Origin and influence are different claims, and knowing the address does not tell you the readership.*

**D.** People would often give their copies of Gidra to others once they had finished reading an issue. **(Correct)**

  *Correct. If one printed copy was read by several people in turn, the number of readers exceeds the number of copies published — exactly the gap the hypothesis claims the monthly print figure misses.*

*Difficulty: hard*

---

##### Q3
> Many scientists have believed that giraffes are solitary creatures, preferring to spend their time alone instead of with others. But observations of giraffes and their behavior in recent years has suggested that these animals may be more social than we once thought. For example, scientists Zoe Muller and Stephen Harris claim that giraffes may even help each other care for one another's newborns.

Which finding, if true, would most directly support Muller and Harris's conclusion?

**A.** Female giraffes have been observed feeding young giraffes that aren't their direct offspring. **(Correct)**

  *Correct. Feeding a calf that is not your own is exactly what "helping each other care for one another's newborns" describes — cooperative care extended across mothers, not just within one mother's own family.*

**B.** Confrontations between a younger and an older male giraffe are frequently observed. 

  *This is social contact, but the wrong kind — a confrontation is adversarial, not cooperative, and it involves males rather than newborn care. It matches the general topic of giraffe sociality while missing the specific claim.*

**C.** Some female giraffes have been observed sniffing and licking their newborn offspring. 

  *A mother tending her own calf is ordinary maternal behavior, not the cooperative, other-directed care Muller and Harris describe. The claim is about helping raise somebody else's newborn, and this finding never leaves the mother-and-own-calf pair.*

**D.** Giraffes are able to make sounds but are rarely observed communicating with others. 

  *Rare communication points toward giraffes being less social, which runs against a claim that they cooperate to raise young. A finding that argues the opposite of increased sociality cannot be the one that supports it.*

*Difficulty: hard*

---

##### Q4
> "Valia" is a 1907 short story by Leonid Andreyev. In the story, the author emphasizes that the setting where the character Valia is reading is nearly silent: ______

Which quotation from "Valia" most effectively illustrates the claim?

**A.** "The hand in which he carried his book was getting stiff with cold, but he would not ask his mother to take the book from him." 

  *A book and a cold hand are on the same general subject — reading — but neither word says anything about how loud or quiet the room is. The claim is about silence, and this line never reaches it.*

**B.** "Valia was reading a huge, very huge book, almost half as large as himself." 

  *This describes the book's size, which is a detail about the object Valia holds, not about the sound level of the room he is reading in. Size is not silence.*

**C.** "Valia approached the window and examined the toys." 

  *This reports an action and a visual detail — where Valia went, what he looked at — with nothing said about what could or could not be heard. A scene can be described in full and still never mention its sound.*

**D.** "Everything in the room was quiet, so quiet that the only thing to be heard was the rustling of the pages he turned." **(Correct)**

  *Correct. "So quiet that the only thing to be heard" states the near-silence directly, and naming the one sound that does carry — a turned page — is what makes the quiet vivid rather than merely asserted.*

*Difficulty: medium*

---

##### Q5
> A researcher conducted an experiment inspired by studies suggesting that people may benefit from feeling frightened in certain circumstances, such as when watching scary movies or visiting haunted attractions. The researcher recruited several participants and had them walk through a local haunted house attraction. Immediately after exiting the attraction, each participant completed a survey about their experience. Based on the survey responses, the researcher claims that feeling frightened in controlled situations can boost a person's mood and confidence.

Which quotation from a participant would best illustrate the researcher's claim?

**A.** "After I came out of the haunted house, I felt very accomplished and less stressed." **(Correct)**

  *Correct. "Accomplished" is the confidence half of the claim and "less stressed" is the mood half — both parts land in one sentence, tied to a controlled fear experience the participant has just left.*

**B.** "My friends kept laughing as we were walking through the haunted house." 

  *This describes what the participant's friends did, not what the participant felt afterward. The claim is about a boost to a person's own mood and confidence, and this sentence never gets to the speaker's internal state.*

**C.** "The haunted house was scary at first, but I knew everyone was just acting, so I felt less scared after a few minutes." 

  *This explains why the fear faded, not that anything positive followed it. Reporting reduced fear during the walk-through is a different observation from reporting a mood or confidence boost afterward, which is what the claim requires.*

**D.** "The sense of relief I felt at the end of the haunted house was similar to the feelings I have when I finish a scary movie." 

  *Relief is mood-adjacent, but the claim needs both mood and confidence, and this line never mentions confidence at all — it only compares one feeling to a feeling from an unrelated activity.*

*Difficulty: hard*

---

##### Q6
> A museum curator is writing a biographical statement about Trinidadian-born Chinese dancer, choreographer, and teacher Dai Ailian for a new exhibit on Chinese dance. The curator claims that some of the pieces Dai created shortly after arriving in mainland China in 1941, such as the solo dance Yao Drum, reflect a desire to represent the dances of local communities Dai visited during her travels through China.

Which quotation from a work by a dance historian would be the most effective evidence for the curator to include in support of this claim?

**A.** "There is no sound or music accompanying Dai's movements in Yao Drum, aside from the sounds of drumsticks beating against a drum and against each other." 

  *This describes the piece's sound design — what accompanies the movement — which has nothing to do with where the choreography came from. The claim is about the dance's origin in a community Dai visited, not about its score.*

**B.** "Unlike some of the works Dai created in the early 1940s, Yao Drum does not feature a narrative structure, humorous elements, or references to real-life events." 

  *This is the sharpest distractor because it is genuinely about Yao Drum in the early 1940s. But it says the piece contains no references to real-life events — which, read carefully, cuts against a claim that the dance represents a specific community's real dances, rather than supporting it.*

**C.** "Yao Drum was inspired by a ceremonial dance Dai witnessed during her time performing field research among the Yao people in the province of Guizhou in 1941 or 1942." **(Correct)**

  *Correct. This ties Yao Drum directly to a dance Dai observed among a specific community — the Yao people — during her travels, which is exactly the source the curator's claim describes.*

**D.** "Yao Drum is notable for its intense physicality, with Dai performing sharp jumps, swift turns, and dramatic sweeps of her legs through the air as she moves in circles on the stage." 

  *This describes the choreography's movement vocabulary — jumps, turns, sweeps — which is a fact about how the dance looks, not about where its content came from. Style is not origin.*

*Difficulty: sat-hardest*

---

##### Q7
> "The Rock and the Sea" is an 1893 poem by Charlotte Perkins Gilman. In the poem, a rock is portrayed as intending to confront and restrain the sea: ______

Which quotation from "The Rock and the Sea" most effectively illustrates the claim?

**A.** "I am the Rock. Black midnight falls; / The terrible breakers rise like walls / With curling lips and gleaming teeth / They plunge and tear at my bones beneath." 

  *The speaker here is correctly the Rock, but the lines describe the Rock enduring an assault, not confronting or restraining anything — it is the sea doing the tearing while the rock is torn at. Endurance is not intent.*

**B.** "I am the Sea. I hold the land / As one holds an apple in his hand, / Hold it fast with sleepless eyes, / Watching the continents sink and rise." 

  *This is the Sea speaking, not the Rock. Whatever the Sea claims about itself cannot illustrate a claim about what the Rock intends.*

**C.** "I am the Rock, presumptuous Sea! / I am set to encounter thee. / Angry and loud or gentle and still, / I am set here to limit thy power, and I will!" **(Correct)**

  *Correct. "I am set to encounter thee" is the confrontation and "I am set here to limit thy power" is the restraint — both halves of the claim, spoken by the Rock itself as a declared intention.*

**D.** "I am the Sea. The earth I sway; / Granite to me is potter's clay; / Under the touch of my careless waves / It rises in turrets and sinks in caves." 

  *Again the Sea is speaking, not the Rock. The claim is specifically about the Rock's intention toward the sea, and a boast from the sea about its own power over stone cannot illustrate it.*

*Difficulty: hard*

---

##### Q8
> Hip-hop pedagogy is a form of teaching that's gaining popularity across school subjects. It involves incorporating hip-hop and rap music into lessons as well as using hip-hop elements when teaching other subject matters. For example, Quan Neloms's students look for college-level vocabulary and historical events in rap songs. Researchers claim that in addition to developing students' social justice awareness, hip-hop pedagogy encourages student success by raising students' interest and engagement.

Which finding, if true, would most strongly support the underlined claim?

**A.** Students tend to be more enthusiastic about rap music than they are about hip-hop music. 

  *This compares enthusiasm for two music genres to each other, not students' interest or engagement in a course that uses either one. It is a finding about taste in music, not about classroom outcomes.*

**B.** Students who are highly interested in social justice issues typically don't sign up for courses that incorporate hip-hop and rap music. 

  *This describes a group of students avoiding these courses, which points away from the claim that the pedagogy raises interest and engagement rather than toward it.*

**C.** Educators report that they enjoy teaching courses that involve hip-hop and rap music more than teaching courses that don't. 

  *This is about teachers' enjoyment, not students'. The claim is specifically about student success, interest, and engagement, and a finding about how instructors feel does not speak to any of those.*

**D.** Courses that incorporate hip-hop and rap music are among the courses with the highest enrollment and attendance rates. **(Correct)**

  *Correct. High enrollment and attendance are direct, measurable signs of student interest and engagement, and the claim says raised interest and engagement is exactly the mechanism behind the success these courses encourage.*

*Difficulty: sat-hardest*

---

##### Q9
> American fashion designer Patrick Kelly was known for his love of colorful buttons. Many of his signature dresses feature bold assortments of buttons throughout the garment. In a paper, a fashion design student claims that Kelly's use of buttons as decoration was inspired by childhood observations of the styles and actions of the women in his family.

Which quotation from a work by a historian would be the most effective evidence for the student to include in support of this claim?

**A.** "Although some of the assortments of buttons appear to be mismatched pieces scattered randomly throughout Kelly's dresses, his most famous designs feature carefully crafted patterns of matching buttons." 

  *This describes what the buttons look like in his adult designs — random or carefully patterned — not where the idea of using buttons at all came from. The claim is about the source of the inspiration, and this quotation stays with the finished dresses.*

**B.** "Many of Kelly's contemporaries were inspired by his designs to incorporate buttons, as well as zippers and snaps, as decorative items in their work." 

  *This runs the influence the wrong way — other designers being inspired by Kelly, not Kelly being inspired by his family. The claim is about what shaped Kelly as a child, and this quotation is about what Kelly later shaped in others.*

**C.** "Kelly's grandmother, who would repair clothing when he was a child, frequently added mismatched buttons to the clothes to draw attention away from any flaws in the garments." **(Correct)**

  *Correct. This is a specific childhood memory of a woman in Kelly's family — his grandmother — using buttons decoratively on clothing, which is exactly the observation the claim says later shaped his own design choices.*

**D.** "Kelly was destined to be a designer from a young age: he learned how to sew clothing from his aunt Bertha, and his love of drawing was developed by his mother." 

  *This shows Kelly's family shaped his path into design generally — sewing from his aunt, drawing from his mother — but neither detail mentions buttons or a family member's use of them. It supports the family-influence half of the claim while leaving the buttons half untouched.*

*Difficulty: hard*

---

##### Q10
> In addition to her technical skill and daring feats, American stunt pilot Bessie Coleman was also known for dazzling the crowds that came to watch her air shows in the 1920s with her exuberant personality. During her career, she was careful and purposeful about how she crafted her public persona. An aviation researcher has claimed that Coleman intentionally defied social norms of the time by how she chose to present herself to the public.

Which quotation from an article about Coleman would most directly support the aviation researcher's claim?

**A.** "For her air shows, Coleman frequently used the Curtiss JN-4, or 'Jenny,' which at that time was one of the most well-known types of planes." 

  *This is about the equipment Coleman flew, not about how she presented herself to the public. The claim concerns her chosen image, and a common plane model says nothing about that.*

**B.** "While Coleman was beloved by spectators for her charisma, she had a more complicated relationship with her managers and staff, who at times found her behavior too impulsive and demanding." 

  *This describes friction with the people who worked for her, which is a relationship dynamic, not a public self-presentation choice. It never touches how she defied — or conformed to — social norms in how she showed herself to audiences.*

**C.** "Coleman once considered leaving her career as a stunt pilot to focus her efforts on giving speeches, which she felt would better support her public image." 

  *This describes a career change Coleman merely considered, not one she carried out, and it is about a shift in activity rather than a norm-defying choice in appearance or persona. A path she thought about cannot illustrate how she actually presented herself.*

**D.** "Although female pilots were typically expected to wear traditional but impractical attire that included dresses or skirts, photographs of Coleman show her wearing pants and leather jackets." **(Correct)**

  *Correct. This states the norm — dresses or skirts expected of female pilots — and then shows Coleman's actual, photographed choice breaking it, which is intentional self-presentation defying a social norm exactly as the researcher claims.*

*Difficulty: hard*

---

##### Q11
> The Milky Way galaxy is composed of millions of stars in a relatively flat structure containing a thin disk and a thick disk. Based on computer simulations and analysis of data on the brightness, position, and chemical composition of about 250,000 stars in the thick disk (collected from two telescopes, one in China and one orbiting in space), astrophysicists Maosheng Xiang and Hans-Walter Rix claim that the thick disk of the Milky Way formed in two distinct phases rather than a single one.

Which finding, if true, would most directly support the researchers' claim?

**A.** The telescopes used by the researchers have detected stars of similar ages in galaxies other than the Milky Way. 

  *This is about a different set of galaxies entirely, not about the formation history of the Milky Way's own thick disk. The claim is confined to one structure in one galaxy, and this finding never gets there.*

**B.** There's an age difference of about 2 billion years between certain stars in the thick disk. **(Correct)**

  *Correct. A gap in ages among thick-disk stars is exactly what a two-phase formation would produce — one population from an earlier episode, one from a later one — rather than the smooth, continuous spread a single formation phase would leave behind.*

**C.** The thin disk contains about twice as many stars that can be seen from Earth as the thick disk does. 

  *This compares star counts between the thin disk and the thick disk, which is a fact about visibility and structure size, not about how many phases the thick disk took to form.*

**D.** The stars in the Milky Way tend to have very similar chemical compositions. 

  *Similar chemical compositions across the board points toward uniformity, which is closer to what a single continuous formation process would produce than what two distinct phases would. This finding leans against the claim rather than for it.*

*Difficulty: hard*

---

##### Q12
> Some residents in a neighborhood in Atlanta recently founded a community garden inside a local park. The residents agreed to volunteer to take care of the garden together. Students at a local high school surveyed some of the volunteers as part of a project to understand the impact of the new garden. The students concluded that the new garden benefited the community overall by fostering connections and relationships between the volunteers and other residents of the neighborhood who weren't volunteering at the garden.

Which quotation from a survey respondent would best illustrate the students' conclusion?

**A.** "Our first challenge was deciding what plants would be most suitable to the climate and soil here in Atlanta. We needed plants that could survive the hot and humid summers." 

  *This is about a gardening logistics problem — choosing plants for the climate — with no mention of other residents or any relationship formed with them. It is on topic for the garden and off topic for the conclusion.*

**B.** "We're lucky to have a few expert gardeners living in the neighborhood. Some volunteers and I have gone to them a few times with questions, and they've been eager to help us and to learn more about the project." **(Correct)**

  *Correct. This shows volunteers reaching out to neighborhood residents — not identified as fellow volunteers — and a relationship forming in both directions, which is precisely the connection between volunteers and non-volunteering residents the conclusion describes.*

**C.** "I love getting the opportunity to be outside and around nature, especially on days when the weather is nice." 

  *This describes a personal benefit to the speaker — enjoying nature — with no other person in the sentence at all. The conclusion is about relationships between people, and this quotation never leaves one person's own experience.*

**D.** "My favorite thing about the garden is the feeling of pride I get when I walk by each day. As I see the plants growing, I feel good knowing I had a small part in creating this beautiful space in the neighborhood." 

  *Like the previous choice, this is a personal feeling — pride in one's own contribution — with no other resident mentioned. It illustrates an individual benefit of the garden, not a fostered relationship.*

*Difficulty: medium*

---

##### Q13
> Scientists have long believed that giraffes are mostly silent and communicate only visually with one another. But biologist Angela Stöger and her team analyzed hundreds of hours of recordings of giraffes in three European zoos and found that giraffes make a very low-pitched humming sound. The researchers claim that the giraffes use these sounds to communicate when it's not possible for them to signal one another visually.

Which finding, if true, would most directly support Stöger and her team's claim?

**A.** Giraffes have an excellent sense of vision and can see in color. 

  *This establishes that giraffes rely heavily on vision in general, which is useful background for why humming would matter when vision fails — but it is background, not the pattern the claim needs. It never shows the humming actually occurring when visual signaling is blocked.*

**B.** The giraffes only produced the humming sounds at night when they couldn't see one another. **(Correct)**

  *Correct. Night is precisely a condition where visual signaling is impossible, and tying the humming to exactly that condition is the pattern the claim predicts: sound used when sight can't be.*

**C.** Wild giraffes have never been recorded making humming sounds. 

  *If the humming has never been recorded outside zoos, that raises doubt about whether it is a natural communication behavior at all, rather than confirming its use as a substitute for visual signaling. This finding weakens the claim's generality more than it supports the claim itself.*

**D.** Researchers observed other animals in European zoos humming. 

  *This is about other species entirely, not about giraffes using humming to communicate when they can't see each other. The claim is specific to giraffes, and this finding never gets back to them.*

*Difficulty: hard*

---

##### Q14
> Researchers Narelle Haworth and Amy Schramm studied bicycling behavior in Queensland, Australia. Haworth and Schramm asked adult bike riders questions about their level of experience, reasons for riding a bike, and route preferences. The researchers claim that experienced riders who mainly bike to work tend to prefer routes that reduce their travel time.

Which survey response from a bike rider in Queensland would best support the underlined claim?

**A.** "I have a bike, but I don't ride it very often. When the weather is nice, I sometimes use my bike to go into town to do some shopping." 

  *This rider bikes occasionally and for shopping, not as an experienced commuter who mainly bikes to work. The claim is about a specific population, and this respondent is not in it.*

**B.** "I just got a new bike, and I'm looking forward to going on rides with my friends soon." 

  *This is a brand-new rider planning social rides, which is neither "experienced" nor "mainly bike to work." It is a real bike rider's response, just not the one the claim is about.*

**C.** "I bike to my job every day. There's a nice bike path that goes through a park, but I use the bike lane on the main road because it's faster." **(Correct)**

  *Correct. Biking to work every day makes this rider experienced and work-commuting, and choosing the faster route over the nicer one is exactly the travel-time preference the claim describes.*

**D.** "I usually bike to work, but I'm taking the bus now because my bike has a broken part that needs to be fixed." 

  *This rider fits the population — an experienced work commuter — but is not currently biking at all, so no route choice is on display. A claim about route preference needs a rider actually choosing a route.*

*Difficulty: hard*

---

##### Q15
> Biologists have generally believed that the diet of jaguars consists mostly of land-based mammals, but researchers studying a population of jaguars living in the Brazilian Pantanal, a tropical wetland, claim that jaguars can survive on a diet of more fish and aquatic reptiles than mammals.

Which finding, if true, would most directly support the researchers' claim?

**A.** Aquatic reptile and fish remains were detected more often than mammal remains in an analysis of jaguar waste matter found in the area. **(Correct)**

  *Correct. Waste analysis measures what was actually eaten, and finding more aquatic-reptile-and-fish remains than mammal remains is a direct read of diet composition — exactly the comparison the claim makes.*

**B.** Exceptionally high numbers of yacare caiman, an aquatic reptile, were found living in the area. 

  *This shows the prey is available in large numbers, not that jaguars are actually eating more of it than mammals. A high population of potential prey is not the same measurement as a diet composition, however tempting the connection feels.*

**C.** Aquatic prey like the reptiles and fish in the area provide a source of omega-3 fatty acids that aren't often found in land mammals. 

  *This supplies a reason jaguars might favor aquatic prey nutritionally, but a motive is not a measurement of what they actually ate. The claim needs evidence of the diet itself, not an explanation for why a diet shift would make sense.*

**D.** When jaguars in the area preyed on mammals, they tended to prefer semiaquatic ones like capybaras. 

  *This describes which mammals jaguars favor when they do eat mammals — it stays entirely within mammal-eating and never sets that against how much aquatic prey they eat, so it cannot establish the balance the claim depends on.*

*Difficulty: sat-hardest*

---

##### Q16
> "To You" is an 1856 poem by Walt Whitman. In the poem, Whitman suggests that readers, whom he addresses directly, have not fully understood themselves, writing, ______

Which quotation from "To You" most effectively illustrates the claim?

**A.** "You have not known what you are, you have slumber'd upon yourself / all your life, / Your eyelids have been the same as closed most of the time." **(Correct)**

  *Correct. "You have not known what you are" says, to the reader directly, exactly what the claim describes — a lack of self-understanding — and the sleep imagery that follows extends it.*

**B.** "These immense meadows, these interminable rivers, you are immense / and interminable as they." 

  *This does address the reader directly, but it praises the reader's scale rather than pointing out any lack of self-knowledge. The pronoun is right; the content is a compliment, not a diagnosis.*

**C.** "I should have made my way straight to you long ago, / I should have blabb'd nothing but you, I should have / chanted nothing but you." 

  *The subject of these lines is the speaker's own regretted inaction — "I should have" — not a statement about whether the reader understands themselves. The claim is about "you," and this quotation is about "I."*

**D.** "I will leave all and come and make the hymns of you, / None has understood you, but I understand you." 

  *This is a close read: "none has understood you" is about how others perceive the reader, not about whether the reader understands themselves. The claim is specifically about self-understanding, and this line is about being understood by someone else.*

*Difficulty: sat-hardest*

---

##### Q17
> Just Patty is a 1911 novel by Jean Webster. Patty and her friends have just been informed that they will no longer be roommates while at school. Patty talks to Mrs. Trent, the head of the school, about the situation. The narrator presents Patty as trying hard to convince Mrs. Trent to allow the group to continue sharing a room: ______

Which quotation from Just Patty most effectively illustrates the claim?

**A.** "[Mrs. Trent's] lips twitched. It was a fact, deplored by her assistants, that her sense of humour frequently ran away with her sense of justice." 

  *This describes Mrs. Trent's personality — a tendency toward humor over strictness — not anything Patty is doing to persuade her. The claim is about Patty's effort, and this sentence is entirely about the other character.*

**B.** "[Mrs. Trent] nodded dismissal, and the three of them found themselves in the hall again. They looked at one another for a moment of blank silence." 

  *This is the scene's aftermath — the girls dismissed, standing in silence — which shows the conversation is over, not that Patty is actively working to persuade Mrs. Trent during it.*

**C.** "Patty's eyes suddenly brightened. She seized [her friends] by [the] elbow and shoved them into the empty schoolroom." 

  *This shows Patty acting toward her friends, not toward Mrs. Trent, and it happens around the persuasion rather than being the persuasion itself. Excitement before a conversation is not the same as making an argument during one.*

**D.** "Patty did use all the diplomacy at her command. Having dwelt touchingly upon their long friendship, and their sorrow at being separated, she passed lightly to the matter of their new roommates." **(Correct)**

  *Correct. "All the diplomacy at her command" states the effort directly, and dwelling on friendship and sorrow before raising the actual request is the persuasive strategy in action — exactly what "trying hard to convince" looks like.*

*Difficulty: hard*

---

##### Q18
> The Minneapolis Institute of Art in Minneapolis, Minnesota, has over 90,000 works of art. Digital images of thousands of those works have been put online through the museum's website and the Google Arts & Culture project. One of the images is of Mississippi Delta, a drawing by Siah Armajani. In a paper, a student claims that putting a work from the museum online increases the number of people who experience that work.

Which finding, if true, would most directly support the underlined claim?

**A.** The Minneapolis Institute of Art has several works by Siah Armajani. 

  *This is about how many of Armajani's works the museum holds, not about how many people experience any of them online versus in person. Quantity of holdings and size of audience are different facts.*

**B.** Many people who have been to Minneapolis say that the Minneapolis Institute of Art is worth visiting. 

  *This is a general reputation for the museum as a whole, not a measurement of how many people experience one specific work through its online image. Praise for a visit is not a count of viewers.*

**C.** Mississippi Delta has been praised by some critics. 

  *Critical praise speaks to the work's quality, not to how many people have seen it or whether putting it online expanded that number. The claim is about reach, and this finding is about reception.*

**D.** Each year, more people access the online image of Mississippi Delta than visit the Minneapolis Institute of Art in person. **(Correct)**

  *Correct. This directly compares the online audience to the in-person audience and shows the online version reaching more people — exactly the increase in experience the claim describes.*

*Difficulty: medium*

---

##### Q19
> "We Are Marching" is a 1921 poem by Carrie Law Morgan Figgs. In the poem, the speaker predicts future success: ______

Which quotation from "We Are Marching" most effectively illustrates the claim?

**A.** "Can't you hear the sound of feet?" 

  *This is a present-tense sensory question about marching feet, describing what is happening now rather than predicting anything about the future.*

**B.** "You who are out just get in line." 

  *This is an instruction directed at bystanders, telling them to join in — a call to action, not a statement predicting an outcome.*

**C.** "We have answered duty's call." 

  *"Have answered" describes something already completed, in the past, not a claim about what will happen going forward. A prediction points ahead; this line looks back.*

**D.** "We shall never know defeat." **(Correct)**

  *Correct. "Shall never know defeat" is a future-tense assertion of victory — a prediction of success stated outright.*

*Difficulty: medium*

---

##### Q20
> Many trees produce growth rings as they age, with each ring in a tree's trunk representing one year in the tree's life. This often makes it fairly easy to determine how old a tree was when it was cut down: you look at the tree stump and count the dark rings you see. But a researcher claims that this method often can't be used to identify the age of olive trees.

Which detail, if true, would most directly support the researcher's claim?

**A.** The oldest olive tree in the world is likely over 1,100 years old. 

  *This is a record about how old one particular olive tree may be, not a fact about whether the ring-counting method itself can be applied to olive trees in general.*

**B.** Narrow growth rings can suggest that an olive tree experienced harsh conditions. 

  *This describes what to conclude once rings can already be seen and counted — it assumes the rings are visible, which is the opposite of the problem the claim describes. It explains ring interpretation, not ring illegibility.*

**C.** Many olive trees have growth rings that are difficult to see. **(Correct)**

  *Correct. If the rings themselves are often hard to see, counting them to determine age becomes unreliable — which is exactly why the method "often can't be used" for olive trees.*

**D.** Olive trees thrive in areas with hot, dry summers. 

  *This describes the climate olive trees prefer, which has nothing to do with whether their growth rings can be counted to determine age.*

*Difficulty: hard*

---

##### Q21
> Although many transposons, DNA sequences that move within an organism's genome through shuffling or duplication, have become corrupted and inactive over time, those from the long interspersed nuclear elements (LINE) family appear to remain active in the genomes of some species. In humans, they are functionally important within the hippocampus, a brain structure that supports complex cognitive processes. When the results of molecular analysis of two species of octopus—an animal known for its intelligence—were announced in 2022, the confirmation of a LINE transposon in Octopus vulgaris and Octopus bimaculoides genomes prompted researchers to hypothesize that that transposon family is tied to a species' capacity for advanced cognition.

Which finding, if true, would most directly support the researchers' hypothesis?

**A.** The LINE transposon in O. vulgaris and O. bimaculoides genomes is active in an octopus brain structure that functions similarly to the human hippocampus. **(Correct)**

  *Correct. The hypothesis rests on an analogy to humans, where the transposon is active in the hippocampus, a structure that supports cognition. Finding the same transposon active in an octopus brain structure that plays a similar role completes the parallel the hypothesis depends on.*

**B.** The human genome contains multiple transposons from the LINE family that are all primarily active in the hippocampus. 

  *This restates a fact about humans the stimulus has already given — it says nothing new about the octopus genomes the hypothesis is actually about, and a hypothesis cannot be supported by re-reporting its own premise.*

**C.** A consistent number of copies of LINE transposons is present across the genomes of most octopus species, with few known corruptions. 

  *This is a fact about how widespread and intact the transposon family is, not about where it is active or what it does. Prevalence across species is a different question from a tie to cognition, and this finding never reaches the second one.*

**D.** O. vulgaris and O. bimaculoides have smaller brains than humans do relative to body size, but their genomes contain sequences from a wider variety of transposon families. 

  *If a smaller relative brain size comes paired with a wider variety of transposon families, that pulls apart rather than ties together transposon activity and cognitive capacity — more transposon diversity accompanying less brain, not more. This runs against the hypothesis, not for it.*

*Difficulty: hard*

---

##### Q22
> Sandra Cisneros's 1984 novella The House on Mango Street made a lasting impact on US literature. Its depiction of Mexican American culture inspired later authors to examine their own heritage within their fictional works. Also influential was the book's portrayal of the main character, Esperanza, during a pivotal year of her youth. This insightful depiction of a preteen girl encouraged authors who, like Cisneros herself, are Latina to use fictional works to examine experiences from their own youth.

Which statement, if true, would most strongly support the claim in the underlined sentence?

**A.** In interviews, a number of Latina authors say that The House on Mango Street inspired them to write about their own adolescence in their novels. **(Correct)**

  *Correct. This hits every part of the underlined claim at once: the authors are Latina, they name The House on Mango Street as the inspiration, and what it inspired was writing about their own youth — exactly the mechanism the sentence describes.*

**B.** In published writings, several prominent authors who are not Latina say that reading The House on Mango Street influenced their approach to writing fiction. 

  *The claim is specifically about authors who, "like Cisneros herself, are Latina." Authors who are not Latina being influenced in their approach to fiction generally is a different population experiencing a different effect.*

**C.** The House on Mango Street has sold over six million copies and is one of the most commonly read books among high school and university students in the US. 

  *Sales figures and reading-list ubiquity measure the book's reach, not whether Latina authors were moved to write about their own youth because of it. A popular book and an inspiring one are not the same claim.*

**D.** Since 1984, new novels about young Latina characters by Latina authors have often been compared to The House on Mango Street. 

  *Being compared to a book by critics is a claim about critical reception, not about what motivated the authors to write it. A resemblance noticed after the fact is not the same as an inspiration the authors themselves report.*

*Difficulty: medium*

---

##### Q23
> Rivers rich in sediment appear yellow, while increases in red algae make rivers appear red. To track things like the sediment or algae content of large US rivers, John R. Gardner and colleagues used satellite data to determine the dominant visible wavelengths of light measured for various segments of these rivers. The researchers classified wavelengths of 495 nanometers (nm) and below as red, wavelengths between 495 and 560 nm as blue, and wavelengths of 560 nm and above as yellow. The researchers concluded that for the Missouri River, segments flowing into lakes tend to carry more sediment than those flowing out of lakes.

Which finding, if true, would most directly support the researchers' conclusion?

**A.** The segments of the Missouri River that had higher levels of chlorophyll-a, which contributes to the green color of photosynthetic organisms, have dominant wavelengths of light between 490 and 560 nm. 

  *This ties a wavelength band to algae content, not sediment, and it never distinguishes segments flowing into a lake from segments flowing out of one. It is on topic for the study and off topic for this particular conclusion.*

**B.** In lakes through which segments of the Missouri River pass, the dominant wavelength of light tended to be above 560 nm near the lakes' shores and below 560 nm in the lakes' centers. 

  *This compares shore to center within lakes, not segments flowing into a lake to segments flowing out of one. It is a real contrast, just not the contrast the conclusion is about.*

**C.** The majority of the segments of the Missouri River were found to have dominant wavelengths significantly higher than 560 nm. 

  *A single measure of the river as a whole, with no split between segments flowing into lakes and segments flowing out of them, cannot show that one kind of segment carries more sediment than the other kind. The conclusion is a comparison, and this is one number.*

**D.** Segments of the Missouri River flowing into lakes typically had dominant wavelengths of light above 560 nm, while segments flowing out of lakes typically had dominant wavelengths below 560 nm. **(Correct)**

  *Correct. Under the researchers' own classification, 560 nm and above reads as yellow, and yellow signals sediment. Segments flowing in landing above that line and segments flowing out landing below it is exactly the more-sediment-in pattern the conclusion states.*

*Difficulty: hard*

---

##### Q24
> Plants like potatoes, tomatoes, and soybeans are susceptible to bacterial wilt disease caused by the bacteria Ralstonia solanacearum. A multinational team of scientists led by Zhong Wei studied whether other microbes in the soil might influence the degree to which plants are affected by the disease. The team sampled soil surrounding individual tomato plants over time and compared the results of plants that became diseased with those that remained healthy. They concluded that the presence of certain microbes in the soil might explain the difference between healthy and diseased plants.

Which finding, if true, would most directly support the team's conclusion?

**A.** The soil surrounding healthy plants contained significantly higher concentrations of microbes known to inhibit Ralstonia solanacearum than the soil surrounding diseased plants did. **(Correct)**

  *Correct. This names the mechanism the conclusion proposes — certain microbes, present in different amounts around healthy versus diseased plants — and shows those microbes clustered exactly where the conclusion says they should: higher around the plants that stayed healthy.*

**B.** The soil surrounding the plants contained high concentrations of Ralstonia solanacearum regardless of whether the plants were affected by wilt disease. 

  *The conclusion is about other microbes influencing the outcome, not about how much of the pathogen itself was present. A finding about Ralstonia solanacearum concentrations never touches the "certain microbes" the team's explanation depends on.*

**C.** The soil surrounding healthy plants tended to have significantly higher moisture levels than the soil surrounding diseased plants did. 

  *Moisture is a different explanatory variable than microbe presence, and the conclusion specifically credits microbes. A finding about soil moisture doesn't support a claim about which microbes were there.*

**D.** By the end of the experiment, over half the plants had been affected by wilt disease regardless of differences in the types and concentrations of microbes in the surrounding soil. 

  *This says the outcome held steady no matter what the microbes were doing — which is the opposite of the conclusion, that microbe differences explain the difference between healthy and diseased plants. A finding that erases the pattern the conclusion relies on weakens it rather than supporting it.*

*Difficulty: medium*

---

##### Q25
> Although it's clear that Mars once had liquid water on its surface, astronomers have debated whether the evidence of ancient water reflects a prolonged phase of warm, wet conditions—the so-called wet and warm scenario—or a brief period of melting in an otherwise consistently frozen environment. Researchers Benjamin T. Cardenas and Michael P. Lamb recently added to this debate by using data from NASA and the Mars Orbiter Laser Altimeter to map the topography of what is now a large basin in Mars's northern hemisphere. Cardenas and Lamb concluded that the wet and warm scenario is likely correct.

Which finding about the basin, if true, would most directly support Cardenas and Lamb's conclusion?

**A.** Its dimensions and shape indicate that it is unlikely to have formed as the result of an asteroid or comet impact. 

  *Ruling out an impact origin says nothing about how long any liquid water lasted. The debate is between a prolonged wet phase and a brief melt, and this finding doesn't distinguish between those two possibilities at all.*

**B.** It has features suggesting that it once held an ocean that underwent gradual sea-level changes over an extended time. **(Correct)**

  *Correct. "Gradual" and "over an extended time" are exactly what a prolonged wet-and-warm phase would leave behind, as opposed to the abrupt, short-lived signature a brief period of melting would produce.*

**C.** Its physical characteristics are most consistent with it having formed as a result of a massive but short-lived influx of liquid water. 

  *"Short-lived" is a description of the rival scenario — a brief period of melting — not of the wet and warm one Cardenas and Lamb concluded was correct. This finding fits the losing hypothesis, not the winning one.*

**D.** It is surrounded by channels that could have been formed either by running water or by flowing lava. 

  *A finding compatible with two different causes — water or lava — and with either the prolonged or the brief scenario doesn't discriminate between the two water histories at all. It is consistent with too much to support one side over the other.*

*Difficulty: sat-hardest*

---

##### Q26
> The Land of Enchantment is a 1906 travel book by Lilian Whiting. In the book, which describes the experience of traveling through the southwestern United States by train, Whiting reflects on the escape from everyday life that such a journey provides: ______

Which quotation from The Land of Enchantment most effectively illustrates the claim?

**A.** "The opportunities and advantages already offered and constantly increasing are greater than would at first be considered possible." 

  *This is about growth and opportunity in the region the train passes through, not about escaping the routines of everyday life. The subject is the destination's promise, not the traveler's relief from duty.*

**B.** "The social and the picturesque charm of the long journey is singularly enhanced by the leisurely stops made for refreshment." 

  *This praises the journey's charm, which is adjacent to the claim but not the claim itself. Enjoying a pleasant stop is not the same as feeling detached from ordinary duties — the sentence never names what is being left behind.*

**C.** "The real journey begins, of course, at Chicago, and as these trains leave in the evening the traveller fares forth in the seclusion of his berth." 

  *This is a logistical detail about where the journey starts and when the trains depart. It sets the scene without reflecting on what the journey means to the traveler, which is what the claim requires.*

**D.** "One experiences a certain sense of detachment from ordinary day and daylight duties that is exhilarating." **(Correct)**

  *Correct. "Detachment from ordinary day and daylight duties" is the escape from everyday life named directly, and "exhilarating" is Whiting's reflection on what that escape feels like.*

*Difficulty: medium*

---

##### Q27
> Sense and Sensibility is an 1811 novel by Jane Austen. In the novel, Austen describes Marianne Dashwood's ability to persuade others of the rightness of her artistic judgments, as is evident when Marianne visits with John Willoughby, a potential suitor: ______

Which quotation from Sense and Sensibility most effectively illustrates the claim?

**A.** "Above all, when she heard him declare, that of music and dancing he was passionately fond, she gave him such a look of approbation as secured the largest share of his discourse to herself for the rest of his stay." 

  *This shows Marianne winning Willoughby's attention with a look of approval, not persuading him to adopt any judgment of hers. Securing conversation is not the same as changing someone's mind about a matter of taste.*

**B.** "Their taste was strikingly alike. The same books, the same passages were idolized by each—or if any difference appeared, any objection arose, it lasted no longer than till the force of her arguments and the brightness of her eyes could be displayed." **(Correct)**

  *Correct. "The force of her arguments" is the persuasion itself, and "if any difference appeared, any objection arose, it lasted no longer than" shows that persuasion actually working — his objections dissolving under it.*

**C.** "It was only necessary to mention any favourite amusement to engage her to talk. She could not be silent when such points were introduced, and she had neither shyness nor reserve in their discussion." 

  *This describes Marianne's willingness to talk openly about her interests, a trait about her, not an act of persuading Willoughby of anything. Talkativeness is not the mechanism the claim is about.*

**D.** "They speedily discovered that their enjoyment of dancing and music was mutual, and that it arose from a general conformity of judgment in all that related to either." 

  *This reports an agreement they discover they already share, not one Marianne brings about. The claim is about her ability to persuade, and a preexisting conformity of judgment requires no persuading at all.*

*Difficulty: hard*

---

##### Q28
> "Mr. Cornelius Johnson, Office-Seeker" is a 1900 short story by Paul Laurence Dunbar. In the story, the narrator describes Mr. Cornelius Johnson's appearance as conveying his exaggerated sense of his importance: ______

Which quotation from "Mr. Cornelius Johnson, Office-Seeker" most effectively illustrates the claim?

**A.** "He carried himself always as if he were passing under his own triumphal arch." **(Correct)**

  *Correct. This describes his bearing — how he carries himself, which is appearance in the sense the claim means — and the triumphal-arch comparison conveys exaggerated self-importance directly, in a single image.*

**B.** "The grey Prince Albert was scrupulously buttoned about his form, and a shiny top hat replaced the felt of the afternoon." 

  *This is an accurate, neutral description of his clothing. It shows what he wore without conveying any attitude about his own importance — appearance without the exaggerated self-regard the claim requires.*

**C.** "It was a beautiful day in balmy May and the sun shone pleasantly on Mr. Cornelius Johnson's very spruce Prince Albert suit of grey as he alighted from the train in Washington." 

  *This sets the scene — the weather, the arrival, the suit — without conveying any sense of self-importance on his part. It is a description of the moment, not of his exaggerated regard for himself.*

**D.** "Mr. Cornelius Johnson always spoke in a large and important tone." 

  *This is about how he speaks, not how he appears. The claim specifically concerns his appearance, and a description of his tone of voice is a different mode of characterization entirely.*

*Difficulty: medium*

---

##### Q29
> Matthew D. Rocklage and team examined whether consumer ratings of movies can predict box office success. The team considered both numeric star ratings and written reviews in their research. To analyze the written reviews, the team measured the emotionality—the degree to which a written review expresses an emotional reaction—of user reviews on a movie rating website, assigning each review an emotionality score. After reviewing this research, a student argues that the emotionality of movie reviews is unrelated to a movie's success at the box office.

Which finding, if true, would most directly weaken the student's conclusion?

**A.** Movies that had the highest average emotionality scores received the lowest average star ratings on the movie rating website. 

  *This connects emotionality to star ratings, not to box office success. The student's claim is specifically about box office success, and this finding never reaches that outcome.*

**B.** The average emotionality score of a movie's reviews was a positive predictor of that movie's box office earnings. **(Correct)**

  *Correct. This ties emotionality score directly to box office earnings and reports a real relationship between them — exactly the connection the student's "unrelated" claim says doesn't exist.*

**C.** More than half of the movies that the team examined received an average star rating of 3 out of 5 stars. 

  *This describes the distribution of star ratings across the sample and mentions neither emotionality nor box office success. It doesn't connect the two variables the claim is about at all.*

**D.** The movies that were most successful at the box office tended to have high average star ratings. 

  *This uses the right outcome, box office success, but the wrong predictor: star ratings, not emotionality score. The student's claim is specifically about emotionality, and this finding is silent on it.*

*Difficulty: hard*

---

##### Q30
> "On Virtue" is a 1766 poem by Phillis Wheatley. Wheatley addresses the poem directly to the quality of virtue, imploring it to assist her in reaching a future goal: ______

Which quotation from "On Virtue" most effectively illustrates the claim?

**A.** "Attend me, Virtue, thro' my youthful years! / O leave me not to the false joys of time! / But guide my steps to endless life and bliss." **(Correct)**

  *Correct. "Attend me, Virtue" is direct address, "guide my steps" is the imploring request for assistance, and "endless life and bliss" is the future goal — all three parts of the claim in one passage.*

**B.** "I cease to wonder, and no more attempt / Thine height t'explore, or fathom thy profound." 

  *This is Wheatley giving up on trying to comprehend virtue's greatness, not asking virtue to guide her anywhere. A statement of resignation is not an imploring request for help.*

**C.** "O thou bright jewel in my aim I strive / To comprehend thee. Thine own words declare / Wisdom is higher than a fool can reach." 

  *Wheatley addresses virtue directly here, but what she's striving for is to comprehend virtue, not to be guided by it toward a future goal. Understanding virtue and being led by virtue are two different requests.*

**D.** "But, O my soul, sink not into despair, / Virtue is near thee, and with gentle hand / Would now embrace thee, hovers o'er thine head." 

  *The address here is to "my soul," not to Virtue — Virtue is described in the third person as something near the soul, rather than being spoken to and asked for anything. The claim requires Virtue as the addressee, and here it is the subject instead.*

*Difficulty: hard*

---

##### Q31
> "Odalie" is an 1899 short story by Alice Dunbar-Nelson. In the story, a young woman named Odalie attends the annual Mardi Gras carnival in New Orleans, where she lives with her guardian Tante Louise. Dunbar-Nelson portrays Odalie as eager to escape the monotony of her everyday life: ______

Which quotation from "Odalie" most effectively illustrates the claim?

**A.** "Mardi Gras was a tiresome day, after all, she sighed, and Tante Louise agreed with her for once." 

  *This calls Mardi Gras itself — the very escape Odalie is supposedly eager for — tiresome. That runs against the claim rather than illustrating it; the thing she'd be escaping to is described as dull.*

**B.** "In the old French house on Royal Street, with its quaint windows and Spanish courtyard green and cool, and made musical by the plashing of the fountain and the trill of caged birds, lived Odalie in convent-like seclusion." 

  *This establishes her secluded life but describes it in pleasant, even musical terms — a quaint, cool courtyard with birdsong. It shows the confinement without showing any eagerness to escape it, which is the half of the claim this quotation is missing.*

**C.** "When one is shut up in a great French house with a grim sleepy tante and no companions of one's own age, life becomes a dull thing, and one is ready for any new sensation." **(Correct)**

  *Correct. "Life becomes a dull thing" states the monotony directly, and "one is ready for any new sensation" is the eagerness to escape it — both halves of the claim, in the same sentence.*

**D.** "It was Mardi Gras day at last, and early through her window Odalie could hear the jingle of folly bells on the [participants'] costumes, the tinkle of music, and the echoing strains of songs." 

  *This is a sensory description of Mardi Gras arriving — bells, music, costumes — but it never states that Odalie's everyday life is monotonous or that she is eager to leave it. It is scene, not the attitude the claim describes.*

*Difficulty: medium*

---

##### Q32
> Jan Gimsa, Robert Sleigh, and Ulrike Gimsa have hypothesized that the sail-like structure running down the back of the dinosaur Spinosaurus aegyptiacus improved the animal's success in underwater pursuits of prey species capable of making quick, evasive movements. To evaluate their hypothesis, a second team of researchers constructed two battery-powered mechanical models of S. aegyptiacus, one with a sail and one without, and subjected the models to a series of identical tests in a water-filled tank.

Which finding from the model tests, if true, would most strongly support Gimsa and colleagues' hypothesis?

**A.** The model with a sail took significantly less time to complete a sharp turn while submerged than the model without a sail did. **(Correct)**

  *Correct. A faster sharp turn is a direct measure of maneuverability — the exact quality that would help an underwater predator keep up with prey capable of quick, evasive movements.*

**B.** The model with a sail displaced significantly more water while submerged than the model without a sail did. 

  *Water displacement is a property of the sail's size, not a measure of how well the model pursues agile prey. It says nothing about turning speed, tracking ability, or any pursuit-relevant performance.*

**C.** The model with a sail had significantly less battery power remaining after completing the tests than the model without a sail did. 

  *Battery drain is an artifact of how the mechanical model is powered, not a measure of hunting performance. It has no bearing on whether the sail helped the animal catch quick, evasive prey.*

**D.** The model with a sail took significantly longer to travel a specified distance while submerged than the model without a sail did. 

  *This measures straight-line speed, a different dimension from the sharp-turning agility the hypothesis is about, and it points the wrong way: taking longer to cover a distance suggests a disadvantage, not the improved pursuit success the hypothesis predicts.*

*Difficulty: medium*

---

##### Q33
> Pulitzer Prize–winning writer Héctor Tobar has built a multifaceted career as both a journalist and an author of short stories and novels. In an essay about Tobar's work, a student claims that Tobar blends his areas of expertise by applying journalism techniques to his creation of works of fiction.

Which quotation from a literary critic best supports the student's claim?

**A.** "For one novel, an imagined account of a real person's global travels, Tobar approached his subject like a reporter, interviewing people the man had met along the way and researching the man's own writings." **(Correct)**

  *Correct. This is a novel — fiction — and Tobar's approach to writing it is described as reporter-like: interviewing sources, researching documents. That is journalism technique applied directly to the creation of a work of fiction.*

**B.** "Tobar got his start as a volunteer for El Tecolote, a community newspaper in San Francisco, and wrote for newspapers for years before earning a degree in creative writing and starting to publish works of fiction." 

  *This is a career timeline — journalism first, fiction later — not an account of journalism techniques being used inside a work of fiction. Sequence is not the same as blending.*

**C.** "Many of Tobar's notable nonfiction articles are marked by the writer's use of techniques usually associated with fiction, such as complex narrative structures and the incorporation of symbolism." 

  *This runs in the opposite direction from the claim: fiction techniques appearing in his nonfiction, not journalism techniques appearing in his fiction. The blending is real, but backward.*

**D.** "The protagonist of Tobar's third novel is a man who wants to be a novelist and keeps notes about interesting people he encounters so he can use them when developing characters for his stories." 

  *This describes a fictional character's habits within the plot of a novel, not a technique Tobar himself uses as a writer. A character who takes notes like a reporter is not evidence that Tobar wrote the novel like one.*

*Difficulty: hard*

---

##### Q34
> An Ideal Husband is an 1895 play by Oscar Wilde. In the play, which is a satire, Wilde suggests that a character named Lady Gertrude Chiltern is perceived as both extremely virtuous and unforgiving, as is evident when another character says ______

Which quotation from An Ideal Husband most effectively illustrates the claim?

**A.** "Lady Chiltern is a woman of the very highest principles, I am glad to say. I am a little too old now, myself, to trouble about setting a good example, but I always admire people who do." 

  *This praises her principles, the virtuous half of the claim, but says nothing about her being unforgiving. Half the requirement is met and half is left untouched.*

**B.** "Do you know, [Lady Chiltern], I don't mind your talking morality a bit. Morality is simply the attitude we adopt towards people whom we personally dislike." 

  *This is addressed to Lady Chiltern, but its content is the speaker's own opinion about morality in general. It never actually characterizes her as virtuous or as unforgiving — she is the audience for the line, not its subject.*

**C.** "[Lady Chiltern] does not know what weakness or temptation is. I am of clay like other men. She stands apart as good women do—pitiless in her perfection—cold and stern and without mercy." **(Correct)**

  *Correct. "Good women" and "perfection" state the virtuous half; "pitiless," "cold and stern," and "without mercy" state the unforgiving half. Both qualities land in a single description.*

**D.** "Lady Chiltern, you are a sensible woman, the most sensible woman I know." 

  *"Sensible" is neither virtuous nor unforgiving — it praises a different quality, practicality, that the claim never mentions.*

*Difficulty: medium*

---

##### Q35
> In 1967 the US Congress created the Corporation for Public Broadcasting, which in turn created National Public Radio (NPR). NPR began producing and distributing high-quality news and cultural programming to affiliate stations across the United States in 1971. In a research paper, a student claims that the Corporation for Public Broadcasting and NPR were inspired by the British Broadcasting System (BBC), which had been established in the 1920s.

Which quotation from a work by a historian would be the most effective evidence for the student to include in support of this claim?

**A.** "Although the BBC had begun as a private corporation, politicians successfully argued to make it a public company because they believed a public broadcaster could help build national unity in the aftermath of World War I." 

  *This describes only the BBC's own history — why it became public in Britain. It never mentions US legislators or NPR, so it can't show that the American system was inspired by the British one; it establishes just one side of the comparison.*

**B.** "For many decades, the BBC had no competition since it held Britain's only broadcasting license, whereas in the United States, the Corporation for Public Broadcasting launched NPR in a broadcasting market already filled with competitors." 

  *This contrasts the two systems' market conditions — a difference between them, not a link showing one inspired the other. Highlighting how unlike they were works against a claim of direct inspiration rather than for it.*

**C.** "Congress's embrace of publicly funded broadcasting reflected a common belief among US politicians that the role of government was not only to ensure people's safety and liberty but also to enrich people's lives in other ways." 

  *This describes US politicians' general philosophy of government without ever mentioning the BBC. It establishes only the American side of the claim, with no link back to the British model the student says inspired it.*

**D.** "The goal of the BBC was to support British democracy by promoting an informed citizenry, and US legislators believed that ensuring access to high-quality programming could do the same for democracy in the United States." **(Correct)**

  *Correct. This states the BBC's goal and then shows US legislators adopting the same reasoning for their own system — the direct parallel that demonstrates inspiration, with both sides of the comparison present in one quotation.*

*Difficulty: hard*

---

##### Q36
> In the 1970s, a roughly 60,000-year-old piece of hyena bone marked with nine notches was discovered at a site in western France once inhabited by Neanderthals. Although many believe that only modern humans developed systems for notating numbers, one archaeologist asserts that this artifact may be a sign that Neanderthals also recorded numerical information. The notches on the bone are unevenly spaced but approximately parallel, and microscopic analysis reveals that they were made with a single stone tool; according to the archaeologist, this suggests that the notches were all made at one time by one individual as a means of counting something.

Which finding, if true, would most directly weaken the underlined claim?

**A.** Parallel lines are a common feature in modern humans' early systems for recording numerical information. 

  *If parallel lines are a common feature of genuine numerical-recording systems, that makes the archaeologist's reading of the bone more plausible by analogy, not less. This points toward the claim, not against it.*

**B.** More than nine approximately parallel notches made with a different stone tool are present on another artifact found at a site in western France. 

  *A different artifact, with a different notch count made by a different tool, doesn't say anything about whether this bone's nine notches represent counting. It's a fact about a separate object, not a competing account of this one.*

**C.** It would have taken careful effort to make evenly spaced lines on bone with the stone tools typically used by Neanderthals. 

  *The bone in question has notches that are unevenly spaced, not evenly spaced, so a fact about the effort needed for even spacing doesn't describe this artifact at all — and if it did apply, effortful, deliberate marks would support intentional counting rather than undermine it.*

**D.** Decorative art discovered at another Neanderthal site in western France primarily features patterns of unevenly spaced parallel lines. **(Correct)**

  *Correct. This supplies a competing explanation for the exact pattern on the bone — unevenly spaced, roughly parallel lines — showing Neanderthals produced that pattern for decoration elsewhere, which undercuts the inference that this particular set of notches must have been counting marks.*

*Difficulty: sat-hardest*

---

##### Q37
> "Ghosts of the Old Year" is an early 1900s poem by James Weldon Johnson. In the poem, the speaker describes experiencing an ongoing cycle of anticipation followed by regretful reflection: ______

Which quotation from "Ghosts of the Old Year" most effectively illustrates the claim?

**A.** "What does this brazen tongue declare, / That falling on the midnight air / Brings to my heart a sense of care / Akin to fright?" 

  *This describes a single startled reaction to a sound, not a repeating cycle of hope followed by regret. One moment of fright is not the ongoing pattern the claim describes.*

**B.** "The snow has ceased its fluttering flight, / The wind sunk to a whisper light, / An ominous stillness fills the night, / A pause—a hush." 

  *This is atmospheric description — snow, wind, stillness — with no anticipation and no regret expressed anywhere in it. It sets a mood without illustrating the cycle the claim is about.*

**C.** "It tells of many a squandered day, / Of slighted gems and treasured clay, / Of precious stores not laid away, / Of fields unreaped." 

  *This is regret, entirely — squandered days, slighted opportunities, unreaped fields. It supplies the reflection half of the claim but nothing of the anticipation that is supposed to precede it.*

**D.** "And so the years go swiftly by, / Each, coming, brings ambitions high, / And each, departing, leaves a sigh / Linked to the past." **(Correct)**

  *Correct. "Each, coming, brings ambitions high" is the anticipation, "each, departing, leaves a sigh" is the regretful reflection, and "each...each" makes the pattern explicitly cyclical — everything the claim describes, in one quotation.*

*Difficulty: hard*

---

##### Q38
> East Australian humpback whales migrate up to 10,000 kilometers each year to reach their breeding grounds. Researchers long believed that migrating whales live only on the extra energy they stored up during the feeding season. But marine biologist Vanessa Pirotta and her team aren't so sure. They analyzed 20 years of observations of the migrating whales made by citizen scientists (members of the public who help collect data for scientific research). The team claims that the whales may not live only on their stored energy during migration.

Which finding, if true, would most directly support the team's claim?

**A.** Citizen scientists have observed many different types of marine animals feeding alongside the whales. 

  *This is about other marine animals feeding near the whales, not about the whales feeding themselves. The claim is specifically about whether the whales rely only on stored energy, and this finding is about a different set of animals entirely.*

**B.** Citizen scientists have made many observations of the whales feeding as they migrate to their breeding grounds. **(Correct)**

  *Correct. Feeding during migration is a direct sign that the whales are taking in energy along the way, not living only on what they stored beforehand — exactly what the claim proposes.*

**C.** Citizen scientists have made more observations of the whales migrating to their breeding grounds than of the whales returning to their feeding grounds. 

  *This is a fact about how the observation data was collected — more sightings on the outbound leg than the return leg — not a fact about whether the whales fed during either leg. It's about sampling, not about energy source.*

**D.** Citizen scientists have recently begun to observe the whales migrating to their breeding grounds earlier in the year. 

  *A shift in migration timing says nothing about whether the whales feed during the trip or rely solely on stored energy. It's a finding about when the migration happens, not about what fuels it.*

*Difficulty: medium*

---

##### Q39
> "Often Rebuked, Yet Always Back Returning" is an 1846 poem by Emily Brontë. The poem conveys the speaker's determination to experience the countryside around her: ______

Which quotation from the poem most effectively illustrates the claim?

**A.** "Often rebuked, yet always back returning / To those first feelings that were born with me, / And leaving busy chase of wealth and learning / For idle dreams of things which cannot be." 

  *This is about returning to inward feelings and turning away from "wealth and learning" — it names no outdoor scene, and the claim is specifically about experiencing the countryside, not about inner values in general.*

**B.** "I'll walk, but not in old heroic traces, / And not in paths of high morality, / And not among the half-distinguished faces, / The clouded forms of long-past history." 

  *Every clause here states what she will not do — not heroic traces, not high morality, not the faces of history. It never affirms where she will walk or what countryside she seeks; it's a list of rejections, not a destination.*

**C.** "I'll walk where my own nature would be leading: / It vexes me to choose another guide: / Where the grey flocks in ferny glens are feeding; / Where the wild wind blows on the mountain side." **(Correct)**

  *Correct. "I'll walk where my own nature would be leading" and "it vexes me to choose another guide" state the determination outright, and "grey flocks in ferny glens" and "the wild wind blows on the mountain side" are the countryside itself.*

**D.** "To-day, I will seek not the shadowy region; / Its unsustaining vastness waxes drear; / And visions rising, legion after legion, / Bring the unreal world too strangely near." 

  *This states what she will avoid — a "shadowy region" of visions and an "unreal world" — which is about turning away from imaginative fantasy, not about determination to experience the actual countryside around her.*

*Difficulty: hard*

---

##### Q40
> Hedda Gabler is an 1890 play by Henrik Ibsen. As a woman in the Victorian era, Hedda, the play's central character, is unable to freely determine her own future. Instead, she seeks to influence another person's fate, as is evident when she says to another character, ______

Which quotation from a translation of Hedda Gabler most effectively illustrates the claim?

**A.** "Then what in heaven's name would you have me do with myself?" 

  *This is a question about Hedda's own uncertain situation — it shows her lack of direction over her own future, but it says nothing about her seeking to influence someone else's. Only half the claim is here.*

**B.** "I want for once in my life to have power to mould a human destiny." **(Correct)**

  *Correct. "To mould a human destiny" is, almost word for word, seeking to influence another person's fate — the exact desire the claim describes.*

**C.** "Then I, poor creature, have no sort of power over you?" 

  *This is phrased as a question about lacking power over the other person, the opposite of seeking to exert it. A denial of influence is not the same as a desire to influence.*

**D.** "Faithful to your principles, now and for ever! Ah, that is how a man should be!" 

  *This admires someone else's steadfastness to their own principles. It's a comment on his character, not an attempt by Hedda to shape or influence his fate.*

*Difficulty: medium*

---

##### Q41
> "When Dawn Comes to the City" is a 1922 poem by Claude McKay, who immigrated to the United States from the island nation of Jamaica as an adult. The poem conveys McKay's contrasting feelings about New York City—his adopted home in the US—and his home country: ______

Which quotation from "When Dawn Comes to the City" most effectively illustrates the claim?

**A.** "A lonely newsboy hurries by, / Humming a recent ditty; / Red streaks strike through the gray of the sky, / The dawn comes to the city [New York City]." 

  *This describes only the New York City dawn scene — a newsboy, streaks of light, the city waking. The home country never appears, so there is no contrast here, only one side of it.*

**B.** "Dark figures start for work; / I watch them sadly shuffle on, / 'Tis dawn, dawn in New York. / But I would be on the island of the sea, / In the heart of the island of the sea." **(Correct)**

  *Correct. "Dawn in New York" watched sadly, set directly against "But I would be on the island of the sea" — both places named, feelings pulling in opposite directions, in the same passage.*

**C.** "And the shaggy Nannie goat is calling, calling, calling / From her little trampled corner of the long wide lea / That stretches to the waters of the hill-stream falling / Sheer upon the flat rocks joyously!" 

  *This is a pastoral scene, presumably the home island, described entirely on its own. New York never enters the passage, so it shows one side of the contrast without the other.*

**D.** "The tired cars go grumbling by, / The moaning, groaning cars, / And the old milk carts go rumbling by, / Under the same dull stars." 

  *This is a New York street scene only — grumbling cars, milk carts, dull stars. The home country is absent, so no contrast between the two places is established.*

*Difficulty: hard*

---

##### Q42
> Among the most visited art museums in the world, the Galleria dell'Accademia in Florence had approximately 1.7 million visitors in 2019. The Galleria dell'Accademia also offers virtual tours that art lovers can view for free online. Although there were initial concerns that people who viewed the virtual tours would then consider an in-person visit unnecessary, museum administrators claim that their surveys of in-person visitors show that those concerns are unjustified.

Which statement, if true, would most directly support the administrators' claim?

**A.** Many surveyed visitors to the Galleria dell'Accademia indicated that the virtual tours convinced them to plan an in-person visit. **(Correct)**

  *Correct. If the virtual tours actually drove people to plan an in-person visit, that is the direct opposite of the feared effect — tours making a visit seem unnecessary — and shows the concern was unjustified.*

**B.** Most surveyed visitors to the Galleria dell'Accademia indicated that they were unaware of the virtual tours before their first in-person visit. 

  *Visitors who never saw the virtual tours before visiting can't tell you anything about whether the tours affect the decision to visit in person — the tours had no chance to influence a choice these visitors never made in light of them.*

**C.** Most surveyed visitors to the Galleria dell'Accademia indicated that they lived somewhere other than Florence. 

  *Where visitors live is a demographic fact with no bearing on whether virtual tours make an in-person visit feel unnecessary. It doesn't test the concern at all.*

**D.** Many surveyed visitors to the Galleria dell'Accademia indicated that they would likely view the virtual tours in order to reminisce about their in-person visit. 

  *This is about using the virtual tours after an in-person visit, for nostalgia. The concern the administrators are addressing is about tours discouraging a visit beforehand, and this finding is about a different use case entirely.*

*Difficulty: medium*

---

##### Q43
> Baltimore, Maryland, has installed engineered structures along 71% of its shoreline to protect infrastructure from wave erosion and other hazards, a practice known as shoreline hardening. To evaluate the responses of waterbirds to two types of hardening structures—riprap and bulkheads—Diann Prosser et al. surveyed waterbird communities consisting of the tundra swan, the great blue heron, and 62 other species at different sites in the Chesapeake Bay on the US East Coast. Utilizing the Index of Waterbird Community Integrity (IWCI), on which a high score corresponds to high community integrity, the researchers found that bulkheads are more strongly negatively correlated with waterbird community integrity than is riprap.

Which finding, if true, would most directly illustrate the researchers' finding?

**A.** The difference in average IWCI scores for waterbird communities at Stony and Old Road, two sites with a higher percentage of shoreline consisting of bulkheads than of riprap, was statistically insignificant. 

  *Both sites here lean toward bulkheads, so this compares two bulkhead-heavy sites to each other rather than setting a bulkhead site against a riprap site. It can't show that one structure type is worse than the other when both examples are the same type.*

**B.** Waterbird communities at Old Road, a site with a relatively high percentage of shoreline consisting of bulkheads, had lower average IWCI scores than did waterbird communities at Miles, a site with a relatively high percentage of shoreline consisting of riprap. **(Correct)**

  *Correct. This isolates the comparison the finding is about — a bulkhead-dominant site against a riprap-dominant site — and shows the bulkhead site scoring lower, exactly the stronger negative association the finding describes.*

**C.** Waterbird communities at Curtis, a site with a high percentage of shoreline consisting of bulkheads and riprap, had lower average IWCI scores than did waterbird communities at Onancock, a site with a low percentage of shoreline consisting of bulkheads and riprap. 

  *Both structure types rise together at Curtis and fall together at Onancock, so this varies the total amount of hardening, not which type of hardening is present. It can't isolate bulkheads as the worse structure when riprap moves in lockstep with it.*

**D.** Waterbird communities at Curtis, a site with equal percentages of shoreline consisting of bulkheads and riprap, had higher average IWCI scores than did waterbird communities at Miles, a site with different percentages of shoreline consisting of bulkheads and riprap. 

  *"Different percentages" at Miles doesn't say which structure type is more common there, so it's impossible to tell whether this comparison even points toward bulkheads being worse than riprap. The direction the finding needs is left unspecified.*

*Difficulty: sat-hardest*

---

##### Q44
> In 1534 CE, King Henry VIII of England split with the Catholic Church and declared himself head of the Church of England, in part because Pope Clement VII refused to annul his marriage to Catherine of Aragon. Two years later, Henry VIII introduced a policy titled the Dissolution of the Monasteries that by 1540 had resulted in the closure of all Catholic monasteries in England and the confiscation of their estates. Some historians assert that the enactment of the policy was primarily motivated by perceived financial opportunities.

Which quotation from a scholarly article best supports the assertion of the historians mentioned in the text?

**A.** “At the time of the Dissolution of the Monasteries, about 2 percent of the adult male population of England were monks; by 1690, the proportion of the adult male population who were monks was less than 1 percent.” 

  *This is a real statistic about the monastery, and about monks specifically, which is what makes it feel relevant. It tracks how many men were monks across a century and a half — it says nothing about why Henry enacted the policy in 1536, financial or otherwise.*

**B.** “A contemporary description of the Dissolution of the Monasteries, Michael Sherbrook’s Falle of the Religious Howses, recounts witness testimony that monks were allowed to keep the contents of their cells and that the monastery timber was purchased by local yeomen.” 

  *This describes what happened to monastery property after the closures — some of it sold to local yeomen — which is a detail about the policy’s aftermath, not evidence of the motive behind enacting it. A sale that occurred once monasteries were already being dissolved doesn’t establish why Henry dissolved them in the first place.*

**C.** “In 1535, the year before enacting the Dissolution of the Monasteries, Henry commissioned a survey of the value of church holdings in England—the work, performed by sheriffs, bishops, and magistrates, began that January and was swiftly completed by the summer.” **(Correct)**

  *Correct. Commissioning a nationwide valuation of church property in the year immediately before dissolving the monasteries is exactly the kind of preparatory act a financial motive would predict: it shows the crown pricing the assets before seizing them, which is a much more direct link to perceived financial opportunity than any description of the policy’s religious origins or its aftermath.*

**D.** “The October 1536 revolt known as the Pilgrimage of Grace had several economic motives: high food prices due to a poor harvest the prior year; the Dissolution of the Monasteries, which closed reliable sources of food and shelter for many; and rents and taxes throughout Northern England that were not merely high but predatory.” 

  *This is about the economic motives of the people who rose up against the Dissolution, not about Henry’s motive for enacting it. The claim is about why the king pursued the policy, and a list of grievances held by the policy’s opponents speaks to a different person’s reasoning entirely.*

*Difficulty: sat-hardest*

---

##### Q45
> Neural networks are computer models intended to reflect the organization of human brains and are often used in studies of brain function. According to an analysis of 11,000 such networks, Rylan Schaeffer and colleagues advise caution when drawing conclusions about brains from observations of neural networks. They found that when attempting to mimic grid cells (brain cells used in navigation), while 90% of the networks could accomplish navigation-related tasks, only about 10% of those exhibited any behaviors similar to those of grid cells. But even this approximation of grid-cell activity has less to do with similarity between the neural networks and biological brains than it does with the rules programmed into the networks.

Which finding, if true, would most directly support the claim in the underlined sentence?

**A.** The rules that allow for networks to exhibit behaviors like those of grid cells have no equivalent in the function of biological brains. **(Correct)**

  *Correct. If the specific rules that produce grid-cell-like behavior in a network have nothing corresponding to them in how a real brain works, then the behavior is being generated by the programming, not by any underlying similarity to a biological brain — which is exactly what the underlined sentence claims.*

**B.** The networks that do not exhibit behaviors like those of grid cells were nonetheless programmed with rules that had proven useful in earlier neural-network studies. 

  *The underlined claim is about why the networks that DO show grid-cell-like behavior show it. This finding is about the 90% that showed no such behavior at all, which is the wrong group to explain the approximation the sentence is discussing.*

**C.** Neural networks can often accomplish tasks that biological brains do, but they are typically programmed with rules to model multiple types of brain cells simultaneously. 

  *This is a general fact about how neural networks are built and doesn’t address the specific question the claim raises — whether the grid-cell resemblance found in that 10% traces to programmed rules or to genuine brain-like function. Modeling several cell types at once neither confirms nor denies that.*

**D.** Once a neural network is programmed, it is trained on certain tasks to see if it can independently arrive at processes that are similar to those performed by biological brains. 

  *This restates the general premise of the kind of study being described — training a network and checking whether it converges on brain-like processes — without addressing whether any resulting resemblance is a product of the rules or of real similarity. It describes the method, not the finding the claim needs.*

*Difficulty: hard*

---

##### Q46
> In the 1980s, many musicians and journalists in the English-speaking world began to draw attention to music from around the globe—such as mbaqanga from South Africa and quan họ from Vietnam—that can’t be easily categorized according to British or North American popular music genres, typically referring to such music as “world music.” While some scholars have welcomed this development for bringing diverse musical forms to prominence in countries where they’d previously been overlooked, musicologist Su Zheng claims that the concept of world music homogenizes highly distinct traditions by reducing them all to a single category.

Which finding about mbaqanga and quan họ, if true, would most directly support Zheng’s claim?

**A.** Mbaqanga and quan họ developed independently of each other and have little in common musically. **(Correct)**

  *Correct. If two traditions that developed independently and share little musically are nonetheless lumped into the same “world music” label, that is precisely what it means to homogenize highly distinct traditions by reducing them to a single category — the finding supplies the distinctness the label is accused of erasing.*

**B.** Mbaqanga is significantly more popular in the English-speaking world than quan họ is. 

  *Relative popularity is a fact about audience size, not about whether the two traditions are being flattened into a single category. Zheng’s claim concerns homogenization, and a popularity gap doesn’t speak to that at all.*

**C.** Mbaqanga and quan họ are now performed by a diverse array of musicians with no direct connections to South Africa or Vietnam. 

  *This is about who performs the music today, which is a question about diffusion and adoption, not about whether the traditions themselves are being treated as musically interchangeable under one label. It doesn’t bear on homogenization.*

**D.** Mbaqanga and quan họ are highly distinct from British and North American popular music genres but similar to each other. 

  *This says the two traditions ARE similar to each other, which runs against Zheng’s point rather than for it. Her claim is that “world music” erases real distinctness between traditions; a finding that they are genuinely alike undercuts the idea that grouping them together does any erasing at all.*

*Difficulty: medium*

---

##### Q47
> Archaeologists have held that the Casarabe culture, which emerged in the southwestern Amazon basin in the first millennium CE, was characterized by a sparse, widely distributed population and little intervention in the surrounding wilderness. Recently, however, archaeologist Heiko Prümers and colleagues conducted a study of the region using remote-sensing technology that enabled them to create three-dimensional images of the jungle-covered landscape from above, and the researchers concluded that the Casarabe people developed a form of urbanism in the Amazon basin.

Which finding about the remote-sensing images, if true, would most directly support Prümers and colleagues’ conclusion?

**A.** They show shapes consistent with widely separated settlements of roughly equal small size surrounded by uncultivated jungle. 

  *Widely separated, small, and surrounded by uncultivated jungle is a description of the sparse, low-intervention settlement pattern archaeologists already believed in — it matches the old view, not the new conclusion that the Casarabe people built something urban.*

**B.** They show shapes consistent with long-distance footpaths running from Casarabe territories to large cities outside the region inhabited by the Casarabe people. 

  *This shows the Casarabe connected to large cities somewhere else, not that the Casarabe themselves built urban settlements. The conclusion is about what the Casarabe people developed within their own territory, and a footpath to someone else’s city doesn’t establish that.*

**C.** They show shapes consistent with scattered small farms created by clearing jungle areas near sources of fresh water. 

  *Scattered small farms is still a rural, dispersed pattern — closer to the old view of a sparse population than to urbanism. Farming near water doesn’t show the dense, organized settlement structure the conclusion claims.*

**D.** They show shapes consistent with monumental platforms and dense central settlements linked to smaller settlements by a system of canals and roadways. **(Correct)**

  *Correct. Monumental platforms, dense central settlements, and a connecting system of canals and roadways are the defining features of an urban settlement pattern — exactly the kind of organization the conclusion says the Casarabe people developed.*

*Difficulty: hard*

---

##### Q48
> Many governments that regularly transfer money to individuals—to provide supplemental incomes for senior citizens, for example—have long done so electronically, but other countries typically have distributed physical money and have only recently developed electronic transfer infrastructure. Researchers studied the introduction of an electronic transfer system in one such location and found that recipients of electronic transfers consumed a different array of foods than recipients of physical transfers of the same amount did. One potential explanation for this result is that individuals conceive of and allocate funds in physical money differently than they conceive of and allocate funds in electronic form.

Which finding from the study, if true, would most directly weaken the potential explanation?

**A.** Recipients of electronic transfers typically spent their funds at a slower rate than recipients of physical transfers did. 

  *A difference in spending speed tied to the form the money arrived in is exactly the kind of behavioral gap the explanation predicts, so this points toward the explanation rather than against it. A weakener has to cut against the account, not illustrate it.*

**B.** Nearly every recipient of an electronic transfer withdrew the entire amount in physical money shortly after receiving the transfer. **(Correct)**

  *Correct. If electronic-transfer recipients converted their funds to physical cash almost immediately, then by the time either group actually bought food, both were holding the same kind of money. That removes the very distinction — electronic form versus physical form — that the explanation says drove the difference in what people bought.*

**C.** Recipients of physical transfers tended to purchase food about as frequently as recipients of electronic transfers did. 

  *The study’s result is about which foods were bought, not how often purchases happened. Matching purchase frequency between the two groups says nothing about whether their conception of the money shaped what ended up in the cart.*

**D.** Some recipients of physical transfers received small amounts of money relatively frequently, while others received large amounts relatively infrequently. 

  *This describes variation within the physical-transfer group alone. The explanation is about a difference between physical and electronic recipients, and a finding that never compares the two groups can’t weaken a claim about the gap between them.*

*Difficulty: sat-hardest*

---

##### Q49
> Icebergs generally appear to be mostly white or blue, depending on how the ice reflects sunlight. Ice with air bubbles trapped in it looks white because much of the light reflects off the bubbles. Ice without air bubbles usually looks blue because the light travels deep into the ice and only a little of it is reflected. However, some icebergs in the sea around Antarctica appear to be green. One team of scientists hypothesized that this phenomenon is the result of yellow-tinted dissolved organic carbon in Antarctic waters mixing with blue ice to produce the color green.

Which finding, if true, would most directly weaken the team’s hypothesis?

**A.** White ice doesn’t change color when mixed with dissolved organic carbon due to the air bubbles in the ice. 

  *The hypothesis is specifically about blue ice mixing with organic carbon to make green — it says nothing about white ice. A finding that white ice resists the mixing effect leaves the actual mechanism, involving blue ice, completely untouched.*

**B.** Dissolved organic carbon has a stronger yellow color in Antarctic waters than it does in other places. 

  *A stronger yellow tint specifically in Antarctic waters would help explain why green icebergs turn up there rather than elsewhere — that supports the hypothesis by strengthening the proposed mechanism, not weakens it.*

**C.** Blue icebergs and green icebergs are rarely found near each other. 

  *The hypothesis is about what’s dissolved in the ice, not about where icebergs of different colors happen to drift relative to one another. Geographic proximity doesn’t test whether organic carbon content is what separates a blue iceberg from a green one.*

**D.** Blue icebergs and green icebergs contain similarly small traces of dissolved organic carbon. **(Correct)**

  *Correct. If blue and green icebergs both carry about the same small trace of dissolved organic carbon, then organic carbon content isn’t what’s tracking the color difference between them — which is the exact mechanism the hypothesis proposes.*

*Difficulty: hard*

---

##### Q50
> Barchester Towers is an 1857 novel by Anthony Trollope. In the novel, Trollope’s portrayal of Dr. Proudie underscores the character’s exaggerated sense of his own abilities: ______

Which quotation from Barchester Towers most effectively illustrates the claim?

**A.** “It must not...be taken as proved that Dr. Proudie was a man of great mental powers, or even of much capacity for business, for such qualities had not been required in him.” 

  *This is the narrator directly denying that Dr. Proudie has great abilities — an objective assessment, not Dr. Proudie’s own opinion of himself. The claim is about his exaggerated self-regard, and a line stating he lacks the abilities says nothing about what he believes he has.*

**B.** “[Dr. Proudie] was comparatively young, and had, as he fondly flattered himself, been selected as possessing such gifts, natural and acquired, as must be sure to recommend him to a yet higher notice.” **(Correct)**

  *Correct. “As he fondly flattered himself” marks this as Dr. Proudie’s own self-assessment, and what he believes about himself — that his gifts are certain to earn him still greater notice — is exactly the exaggerated sense of his own abilities the claim describes.*

**C.** “[Dr. Proudie’s] residence in the metropolis, rendered necessary by duties thus entrusted to him, his high connexions, and the peculiar talents and nature of the man, recommended him to persons in power.” 

  *This describes external factors — where he lived, who he knew — recommending him to powerful people. It is about how others and his circumstances elevated him, not about his own inflated view of his abilities.*

**D.** “[Dr. Proudie] was certainly possessed of sufficient tact to answer the purpose for which he was required without making himself troublesome.” 

  *This credits him with a real, modest quality — just enough tact for the job — which is the opposite of an exaggerated self-view. A claim of exaggeration needs him overestimating himself, not the narrator confirming a limited ability.*

*Difficulty: hard*

---

##### Q51
> An archaeological team led by Piotr Bieliński and Sultan al-Bakri found remnants of a 4,000-year-old Bronze Age board game at a site in Oman. Little is left of the game except a stone board, which is carved with a grid and has places to hold game pieces. Some scholars claim that the game was largely played by traders.

Which finding, if true, would most directly support the scholars’ claim?

**A.** Other examples of the game dating to the same period have been found in the remains of several homes in the region, including in one home that may have belonged to a trader. 

  *Only one of several homes may have belonged to a trader — the rest are unaccounted for. A single uncertain link to a trader among many homes of unknown occupation is too thin to establish that the game was LARGELY played by traders.*

**B.** Similar games have been found in other sites dating to the same period that were connected to the site in Oman via trade routes. 

  *This is about the sites being linked by trade routes, which shows the game traveled along paths traders used — but it doesn’t say who was actually playing it. Site connectivity is a different claim from player identity.*

**C.** The other known examples of the game dating to the same period have been found along routes that seem to have been used primarily by traders at the time. **(Correct)**

  *Correct. If every other known example of the game consistently turns up specifically along routes that traders primarily used, that’s a strong and consistent pattern tying the game to the people who traveled those routes — directly supporting the claim that traders were the game’s main players.*

**D.** Remnants of other goods have been found at the site in Oman that probably also reached the location through trade. 

  *This is about other goods at the site, not about the game or who played it. General evidence of trade activity at the site doesn’t establish that the specific people playing this game were traders.*

*Difficulty: medium*

---

##### Q52
> Several studies of sediment (e.g., dirt, pieces of rock, etc.) in streams have shown an inverse correlation between sediment grain size and downstream distance from the primary sediment source, suggesting that stream length has a sorting effect on sediment. In a study of sediment sampled at more than a dozen sites in Alpine streams, however, geologists Camille Litty and Fritz Schlunegger found that cross-site variations in grain size were not associated with differences in downstream distance, though they did not conclude that downstream distance is irrelevant to grain size. Rather, they concluded that sediment influx in these streams may have been sufficiently spatially diffuse to prevent the typical sorting effect from being observed.

Which finding about the streams in the study, if true, would most directly support Litty and Schlunegger’s conclusion?

**A.** The streams regularly experience portions of their banks collapsing into the water at multiple points upstream of the sampling sites. **(Correct)**

  *Correct. Bank collapses at multiple points upstream mean new sediment is entering the stream throughout its length rather than from one primary source — exactly the spatially diffuse influx Litty and Schlunegger propose as what masked the usual downstream sorting effect.*

**B.** The streams contain several types of sediment that are not typically found in streams where the sorting effect has been demonstrated. 

  *This is about what kinds of sediment are present, not about where along the stream new sediment enters. The conclusion turns on the spatial pattern of influx, and sediment composition doesn’t speak to that.*

**C.** The streams mostly originate from the same source, but their lengths vary considerably due to the different courses they take. 

  *A single common source for most of the streams is the opposite of spatially diffuse influx — it points toward one primary source, not sediment entering at many points, which undercuts the conclusion rather than supporting it.*

**D.** The streams are fed by multiple tributaries that carry significant volumes of sediment and that enter the streams downstream of the sampling sites. 

  *Sediment entering downstream of where the samples were taken can’t affect the grain size measured at those sites — it arrives after the point being measured. To matter for this conclusion, the added sediment has to enter upstream of or throughout the sampled reach, not below it.*

*Difficulty: sat-hardest*

---

##### Q53
> In vertical inheritance, parents pass genes to their offspring, but in horizontal transfer (HT), one species, often bacteria, passes genetic material to an unrelated species. In a 2022 study, herpetologist Atsushi Kurabayashi and his team investigated HT in multicellular organisms—namely, snakes and frogs in Madagascar. The team detected BovB—a gene transmitted vertically in snakes—in many frog species. The apparent direction of gene transfer seems counterintuitive because frogs usually don’t survive encounters with snakes and so wouldn’t be able to transmit the newly acquired gene to offspring, but the team concluded that BovB is indeed transmitted from snakes to frogs, either directly or indirectly, via HT.

Which finding, if true, would most directly support the team’s conclusion?

**A.** BovB can be transmitted across frog species through HT. 

  *This is about the gene spreading from frog to frog, not about how it got from a snake into a frog in the first place. It doesn’t establish the snake-to-frog origin the conclusion is about.*

**B.** Parasites known to feed on species of snakes and frogs in which the BovB gene occurs also carry BovB. **(Correct)**

  *Correct. A shared parasite that feeds on BovB-carrying snakes and BovB-carrying frogs and itself carries BovB supplies exactly the indirect pathway the conclusion needs — a vector that could move the gene from snake to frog without the frog ever having to survive a direct encounter.*

**C.** BovB cannot be reliably transmitted from a snake species to bacteria that are usually encountered by frog species. 

  *This rules out one possible indirect route — transmission via bacteria — rather than supplying one. A finding that a proposed vector doesn’t work weakens the case for an indirect pathway; it doesn’t strengthen it.*

**D.** Frog species with BovB show few discernible advantages as compared with frog species that do not carry BovB. 

  *Whether carrying BovB benefits a frog is a question about fitness, not about how the gene got there. The conclusion is about the direction and mechanism of transmission, which this finding doesn’t address.*

*Difficulty: sat-hardest*

---

##### Q54
> Electra is a circa 420–410 BCE play by Sophocles, translated in 1870 by R.C. Jebb. Electra, who is in mourning for her dead father and her long-absent brother, is aware of the intensity of her grief but believes it to be justified: ______

Which quotation from Electra most effectively illustrates the claim?

**A.** “O thou pure sunlight, and thou air, earth’s canopy, how often have ye heard the strains of my lament, the wild blows dealt against this bleeding breast, when dark night fails!” 

  *This vividly shows how intense her grief is — the laments, the blows against her own breast — but nothing in it says she believes that grief is justified. It gives the intensity half of the claim without the belief half.*

**B.** “Send to me my brother; for I have no more the strength to bear up alone against the load of grief that weighs me down.” 

  *This shows the weight of her grief and a plea for help, but it never explains why she thinks that grief is warranted. A statement of how heavy the burden feels is not a statement that the burden is justified.*

**C.** “I know my own passion, it escapes me not; but, seeing that the causes are so dire, will never curb these frenzied plaints, while life is in me.” **(Correct)**

  *Correct. “I know my own passion, it escapes me not” shows her awareness of her grief’s intensity, and “seeing that the causes are so dire, will never curb these frenzied plaints” gives the reason — because the causes are dire, the grief is warranted and she won’t restrain it. Both halves of the claim land in one line.*

**D.** “But never will I cease from dirge and sore lament, while I look on the trembling rays of the bright stars, or on this light of day.” 

  *This shows her grief will persist for as long as she lives, which speaks to duration, not to her awareness of its intensity or her reasoning for why it’s justified. Persistence alone leaves both halves of the claim unaddressed.*

*Difficulty: hard*

---

##### Q55
> A member of the Otomi, an Indigenous people in Central Mexico, Octavio Medellín immigrated to the United States as a child, and his sculpture bears the impress of traditions on both sides of the border: US modernist sculpture, Mexican modernist painting, Otomi art, and ancient sculpture of other Mexican Indigenous peoples, including the Maya. In his 1950 masterpiece History of Mexico, Medellín fuses these influences into a style so idiosyncratic that it resists efforts to view his work through the lens of nationality or cultural identity. Artists, he insisted, should strive for individual expression, even as they draw inspiration from their heritage and the communities where they live and work.

Which quotation from an art critic most directly challenges the underlined claim in the text?

**A.** “Although a number of ancient Indigenous artistic traditions pictured human forms in profile, the forms populating the surface of A History of Mexico suggest a specifically Maya influence.” 

  *This does identify a specific cultural influence in the work, which is in tension with “resists...cultural identity.” But it stops at noting an influence — it never draws the conclusion the underlined claim explicitly denies, that the work therefore invites classification along that cultural line.*

**B.** “In A History of Mexico, the synthesis of ancient and modernist traditions functions as a stylistic parallel to the work’s subject matter: a survey of centuries of Mexican history.” 

  *This elaborates on how the fusion of influences works rather than disputing that a fusion resisting classification exists. It reads as an explanation of the idiosyncratic synthesis, not a challenge to it.*

**C.** “Many critics focus on Indigenous influences in A History of Mexico and other key works by Medellín to the exclusion of influences from non-Indigenous art.” 

  *This critiques how OTHER critics have approached Medellín’s work, not the work itself. It doesn’t assert that A History of Mexico can in fact be classified by nationality or cultural identity — it’s commentary about a pattern in criticism, not a direct challenge to the claim.*

**D.** “While A History of Mexico features modernist motifs, it relies primarily on angular human forms in profile—a staple of Maya sculpture—and thus invites classification as Indigenous art.” **(Correct)**

  *Correct. This explicitly concludes that the work “invites classification as Indigenous art” — directly contradicting the claim that Medellín’s style “resists efforts to view his work through the lens of nationality or cultural identity.” Where the other choices note an influence or discuss criticism, this one draws the exact conclusion the underlined claim denies.*

*Difficulty: sat-hardest*

---

##### Q56
> In countries with right-hand traffic, drivers who want to make a left turn at a traffic intersection with stoplights have to wait for either a gap in oncoming traffic or a designated left-turn signal to turn green. At busy intersections, this often causes a backup of vehicles waiting to turn left or being prevented from proceeding by left-turning vehicles in front of them. Transportation researcher Vikash V. Gayah claims that in urban areas eliminating the option to turn left at busy intersections—both with and without dedicated left-turn signals—would improve traffic flow and, as a result, reduce overall travel times even if such a restriction would require drivers to sometimes travel a slightly longer distance.

Which finding, if true, would most directly support the researcher’s claim?

**A.** In a town that installed left-turn signals at all busy intersections, seven out of ten survey respondents agreed with the statement “the streets in my community are easier to navigate by motor vehicle than before.” 

  *The intervention here is installing left-turn signals, not eliminating the left-turn option — Gayah’s claim is specifically about removing the choice to turn left, both with and without signals. A survey about a town that added signals speaks to a different policy than the one the claim is about.*

**B.** A traffic study of intersections in a large city shows that on average drivers wait longer to make a left turn at intersections without left-turn signals than at intersections with such signals. 

  *This compares two ways of permitting left turns against each other; it says nothing about what happens when the option to turn left is removed entirely, which is the intervention the claim is about. A finding about signals helping left-turners doesn’t bear on eliminating left turns altogether.*

**C.** After a city eliminated left turns at busy intersections, a package-delivery company reports that its drivers have been able to reach more addresses in the city daily, on average, and therefore deliver more packages there annually. **(Correct)**

  *Correct. Reaching more addresses per day is a direct sign that drivers are moving through the city faster — exactly the reduced travel time and improved traffic flow the claim predicts would follow from eliminating left turns at busy intersections.*

**D.** Statistics reveal that school buses in a city that eliminated left turns at most intersections took on average two minutes longer to complete their routes after the restriction took effect than they did before. 

  *This is the opposite of what the claim predicts: routes got slower, not faster, after left turns were eliminated. A finding that undermines the claim can’t be the one that supports it.*

*Difficulty: hard*

---

##### Q57
> Many archaeologists will tell you that categorizing excavated fragments of pottery by style, period, and what objects they belong to relies not only on standard criteria, but also on instinct developed over years of practice. In a recent study, however, researchers trained a deep-learning computer model on thousands of images of pottery fragments and found that it could categorize them as accurately as a team of expert archaeologists. Some archaeologists have expressed concern that they might be replaced by such computer models, but the researchers claim that outcome is highly unlikely.

Which finding, if true, would most directly support the researchers’ claim?

**A.** In the researchers’ study, the model was able to categorize the pottery fragments much more quickly than the archaeologists could. 

  *A model that’s both as accurate and faster than archaeologists is a reason to worry MORE about replacement, not less. This finding feeds the very concern the researchers are trying to dismiss rather than supporting their claim that replacement is unlikely.*

**B.** In the researchers’ study, neither the model nor the archeologists were able to accurately categorize all the pottery fragments that were presented. 

  *This shows the model has limits, but so do the archaeologists — it establishes rough parity in one narrow task, not that archaeologists do something else the model can’t. It doesn’t touch the reason replacement is supposedly unlikely.*

**C.** A survey of archaeologists showed that categorizing pottery fragments limits the amount of time they can dedicate to other important tasks that only human experts can do. **(Correct)**

  *Correct. If categorizing fragments is time that could go to tasks only human experts can do, then a model that takes over categorizing doesn’t make archaeologists redundant — it frees them for the work that still requires them. That’s exactly why replacement would be unlikely.*

**D.** A survey of archaeologists showed that few of them received dedicated training in how to properly categorize pottery fragments. 

  *If archaeologists mostly rely on undeveloped, informal skill at categorizing rather than trained expertise, that makes the case for replacement easier, not harder — it suggests the task doesn’t require the specialized human judgment the researchers’ claim depends on.*

*Difficulty: hard*

---

##### Q58
> Black beans (Phaseolus vulgaris) are a nutritionally dense food, but they are difficult to digest in part because of their high levels of soluble fiber and compounds like raffinose. They also contain antinutrients like tannins and trypsin inhibitors, which interfere with the body’s ability to extract nutrients from foods. In a research article, Marisela Granito and Glenda Álvarez from Simón Bolívar University in Venezuela claim that inducing fermentation of black beans using lactic acid bacteria improves the digestibility of the beans and makes them more nutritious.

Which finding from Granito and Álvarez’s research, if true, would most directly support their claim?

**A.** When cooked, fermented beans contained significantly more trypsin inhibitors and tannins but significantly less soluble fiber and raffinose than nonfermented beans. 

  *More trypsin inhibitors and tannins in the fermented beans would mean fermentation made the beans HARDER to digest on that front, not easier — this is a mixed and partly contrary result, not a clean case for improved digestibility.*

**B.** Fermented beans contained significantly less soluble fiber and raffinose than nonfermented beans, and when cooked, the fermented beans also displayed a significant reduction in trypsin inhibitors and tannins. **(Correct)**

  *Correct. Soluble fiber, raffinose, tannins, and trypsin inhibitors are the specific compounds the passage names as the reasons beans are hard to digest and less nutritious. A finding that fermentation reduces all four is a direct hit on every mechanism the claim depends on.*

**C.** When the fermented beans were analyzed, they were found to contain two microorganisms, Lactobacillus casei and Lactobacillus plantarum, that are theorized to increase the amount of nitrogen absorbed by the gut after eating beans. 

  *This is about nitrogen absorption via specific microorganisms, a mechanism the passage never mentions. It doesn’t touch the soluble fiber, raffinose, tannins, or trypsin inhibitors that the claim is actually built on.*

**D.** Both fermented and nonfermented black beans contained significantly fewer trypsin inhibitors and tannins after being cooked at high pressure. 

  *This credits cooking at high pressure, not fermentation, with the reduction — and it happens in BOTH bean types equally, so it can’t be evidence that fermentation specifically is what improves digestibility.*

*Difficulty: sat-hardest*

---

##### Q59
> Art collectives, like the United States- and Vietnam-based collective The Propeller Group or Cuba’s Los Carpinteros, are groups of artists who agree to work together: perhaps for stylistic reasons, or to advance certain shared political ideals, or to help mitigate the costs of supplies and studio space. Regardless of the reasons, art collectives usually involve some collaboration among the artists. Based on a recent series of interviews with various art collectives, an arts journalist claims that this collaboration can be difficult for artists who are often used to having sole control over their work.

Which quotation from the interviews best illustrates the journalist’s claim?

**A.** “The first collective I joined included many amazingly talented artists, and we enjoyed each other’s company, but because we had a hard time sharing credit and responsibility for our work, the collective didn’t last.” **(Correct)**

  *Correct. “A hard time sharing credit and responsibility for our work” is the collaboration itself proving difficult, and it’s severe enough that the collective dissolved over it — a direct illustration of collaboration being hard for artists used to sole control.*

**B.** “We work together, but that doesn’t mean that individual projects are equally the work of all of us. Many of our projects are primarily the responsibility of whoever originally proposed the work to the group.” 

  *This describes a collective that has arranged things so individual artists mostly retain their own responsibility for projects — a setup that avoids the difficulty of shared control rather than illustrating it.*

**C.** “Having worked as a member of a collective for several years, it’s sometimes hard to recall what it was like to work alone without the collective’s support. But that support encourages my individual expression rather than limits it.” 

  *This explicitly says collaboration ENCOURAGES rather than limits individual expression — the opposite of the claim that shared control is difficult for artists used to working alone.*

**D.** “Sometimes an artist from outside the collective will choose to collaborate with us on a project, but all of those projects fit within the larger themes of the work the collective does on its own.” 

  *This is about outside artists occasionally joining projects that stay on-theme — it doesn’t describe any difficulty collective members have sharing control over their own work.*

*Difficulty: hard*

---

##### Q60
> Boldly mixing elements of poetry, fiction, drama, philosophy, and manifesto, Puerto Rican writer Giannina Braschi creates cross-genre literature that explores themes such as immigration and independence. Her works have inspired responses from individuals across different fields and in a wide range of formats, from musical compositions to a comic book to architecture and furniture design. In an essay, a student asserts that the production of these diverse creations by others is reflective of Braschi’s own approach to crafting literature.

Which quotation from a scholarly review of Braschi’s work best supports the student’s claim?

**A.** “Braschi is the focus of a 2020 collection of essays in which fifteen scholars from seven different countries delved into the linguistic and structural patterns of her writings.” 

  *This is about scholars analyzing her writing, not about other creators producing musical, visual, or architectural works in response to it. It doesn’t touch the diverse-formats point the student’s claim is about.*

**B.** “Braschi’s eagerness to push boundaries and blend genres within literature invites us to consider how other art forms might also engage with literature.” **(Correct)**

  *Correct. This directly links Braschi’s own genre-blending approach to literature with the idea that it invites engagement from other art forms — the same connection the student’s claim makes between how she crafts her work and the diverse creations (music, comics, architecture) it has inspired.*

**C.** “Before settling in New York City, where she would go on to become a college professor, Braschi studied literature and philosophy in several cities around the world.” 

  *This is biographical detail about where Braschi studied and worked. It says nothing about her cross-genre approach or about the range of creative responses her work has inspired.*

**D.** “In addition to her creative literary works, Braschi has produced academic pieces analyzing writings by Miguel de Cervantes, Federico García Lorca, and other authors.” 

  *This describes Braschi as a critic of OTHER authors’ work, not as someone whose own genre-blending inspires diverse creative responses from others. It’s the reverse relationship from the one the claim is about.*

*Difficulty: medium*

---

##### Q61
> “The Young Girl” is a 1920 short story by Katherine Mansfield. In the story, the narrator takes an unnamed seventeen-year-old girl and her younger brother out for a meal. In describing the teenager, Mansfield frequently contrasts the character’s pleasant appearance with her unpleasant attitude, as when Mansfield writes of the teenager, ______

Which quotation from “The Young Girl” most effectively illustrates the claim?

**A.** “I heard her murmur, ‘I can’t bear flowers on a table.’ They had evidently been giving her intense pain, for she positively closed her eyes as I moved them away.” 

  *This shows the teenager’s unpleasant, oversensitive attitude toward flowers, but it says nothing about her appearance — there’s no pleasant-appearance half of the contrast here for the attitude to be set against.*

**B.** “While we waited she took out a little, gold powder-box with a mirror in the lid, shook the poor little puff as though she loathed it, and dabbed her lovely nose.” **(Correct)**

  *Correct. “Lovely nose” gives the pleasant appearance, and “as though she loathed it” — her contempt for her own powder-puff, mid-gesture — gives the unpleasant attitude. Both halves of the contrast land in the same sentence.*

**C.** “I saw, after that, she couldn’t stand this place a moment longer, and, indeed, she jumped up and turned away while I went through the vulgar act of paying for the tea.” 

  *This shows her unpleasant, dismissive attitude toward the narrator and the setting, but nothing here describes her appearance. Without the appearance half, there’s no contrast to illustrate.*

**D.** “She didn’t even take her gloves off. She lowered her eyes and drummed on the table. When a faint violin sounded she winced and bit her lip again. Silence.” 

  *This is a catalog of unpleasant, standoffish behavior — refusing to remove her gloves, wincing, biting her lip — with no mention of her appearance at all. It illustrates the attitude alone, not the contrast with appearance.*

*Difficulty: medium*

---

##### Q62
> O Pioneers! is a 1913 novel by Willa Cather. In the novel, Cather depicts Alexandra Bergson as a person who takes comfort in understanding the world around her: ______

Which quotation from O Pioneers! most effectively illustrates the claim?

**A.** “She looked fixedly up the bleak street as if she were gathering her strength to face something, as if she were trying with all her might to grasp a situation which, no matter how painful, must be met and dealt with somehow.” 

  *This shows her bracing to confront a difficult situation, but the situation is explicitly one she is still struggling to grasp, not one she already understands and takes comfort in. It’s effort toward understanding, not comfort from having it.*

**B.** “She had never known before how much the country meant to her. The chirping of the insects down in the long grass had been like the sweetest music. She had felt as if her heart were hiding down there, somewhere, with the quail and the plover and all the little wild things that crooned or buzzed in the sun.” 

  *This is about emotional attachment and belonging to the land, not about understanding the world around her. Affection for the country is a different claim from taking comfort in comprehending it.*

**C.** “Alexandra drove off alone. The rattle of her wagon was lost in the howling of the wind, but her lantern, held firmly between her feet, made a moving point of light along the highway, going deeper and deeper into the dark country.” 

  *This is physical description of Alexandra driving through the dark — atmospheric detail with no reference to her understanding the world or drawing comfort from it.*

**D.** “Alexandra drew her shawl closer about her and stood leaning against the frame of the mill, looking at the stars which glittered so keenly through the frosty autumn air. She always loved to watch them, to think of their vastness and distance, and of their ordered march. It fortified her to reflect upon the great operations of nature, and when she thought of the law that lay behind them, she felt a sense of personal security.” **(Correct)**

  *Correct. “It fortified her to reflect upon the great operations of nature” and “she felt a sense of personal security” is comfort, stated directly, and it comes specifically from understanding — reflecting on the law behind the stars’ “ordered march.” Both the comfort and its source in comprehension are explicit.*

*Difficulty: hard*

---

##### Q63
> In the “language nest” model of education, Indigenous children learn the language of their people by using it as the medium of instruction and socialization at pre-K or elementary levels. In their 2016 study of a school in an Anishinaabe community in Ontario, Canada, scholars Lindsay Morcom and Stephanie Roy (who are Anishinaabe themselves) found that the model not only imparted fluency in the Anishinaabe language but also enhanced students’ pride in Anishinaabe culture overall. Given these positive effects, Morcom and Roy predict that the model increases the probability that as adults, former students of the school will transmit the language to younger generations in their community.

Which finding, if true, would most strongly support the researchers’ prediction?

**A.** Anishinaabe adults who didn’t attend the school feel roughly the same degree of cultural pride as the former students of the school feel. 

  *If pride ends up about the same whether or not someone attended the school, that weakens the case that the school’s effect on pride matters for anything downstream — including language transmission. It cuts against the prediction rather than supporting it.*

**B.** After transferring to the school, new students experience an increase in both fluency and academic performance overall. 

  *Academic performance is never mentioned in the study’s findings or the prediction — the prediction is specifically about transmitting the language to the next generation, not about grades. This introduces an outcome the claim isn’t about.*

**C.** As adults, former students of the school are just as likely to continue living in their community as individuals who didn’t attend the school. 

  *Staying in the community is a plausible enabling condition for transmitting language locally, but “just as likely” describes no difference between the two groups — it doesn’t show the school produced any effect that would make transmission MORE probable, which is what the prediction claims.*

**D.** As they complete secondary and higher education, former students of the school experience no loss of fluency or cultural pride. **(Correct)**

  *Correct. The prediction depends on the fluency and pride the language-nest model built early on actually persisting into adulthood — if those benefits faded before students had children of their own, there would be nothing left to transmit. Finding that they don’t fade is exactly what the prediction needs to hold.*

*Difficulty: sat-hardest*

---

##### Q64
> King Lear is a circa 1606 play by William Shakespeare. In the play, the character of King Lear attempts to test his three daughters’ devotion to him. He later expresses regret for his actions, as is evident when he ______

Which choice most effectively uses a quotation from King Lear to illustrate the claim?

**A.** says of himself, “I am a man / more sinned against than sinning.” 

  *This is Lear casting himself as more wronged than wrongdoing — the opposite posture from regret. Regret requires owning the fault; this quotation disclaims it.*

**B.** says during a growing storm, “This tempest will not give me leave to ponder / On things would hurt me more.” 

  *This shows the storm distracting Lear from painful thoughts, but it never says what those thoughts are or that they concern regret for his own actions toward his daughters. It gestures at pain without naming its source.*

**C.** says to himself while striking his head, “Beat at this gate that let thy folly in / And thy dear judgement out!” **(Correct)**

  *Correct. Striking his own head while calling his own past decision “folly” and blaming himself for letting his judgment out is regret named and directed at himself — exactly the self-blame for his actions the claim describes.*

**D.** says of himself, “I will do such things— / What they are yet, I know not; but they shall be / The terrors of the earth!” 

  *This is Lear vowing future action, not looking back with regret at what he’s already done. It’s forward-facing threat, not backward-facing self-reproach.*

*Difficulty: medium*

---

##### Q65
> In a series of experiments, Julio Sevilla and Claudia Townsend showed that manipulating the space between products in store displays can influence consumers’ views of those products. Participants in several of the experiments regarded the same products in the same (generic) retail settings as significantly more valuable when the product-to-space ratio was low than when it was high. But in one of the experiments, Sevilla and Townsend arranged the same jewelry with different levels of intervening space at an upscale retailer (Tiffany & Co.) and a relatively inexpensive retailer (Forever 21). The result of this experiment suggests that a store context associated with inexpensive products may moderate the effect Sevilla and Townsend observed in their other experiments.

Which finding from the experiment with Tiffany & Co. and Forever 21, if true, would most directly support the conclusion presented in the text?

**A.** At Tiffany & Co., participants judged jewelry spaced far apart to be substantially more valuable than jewelry spaced close together, but at Forever 21, participants judged jewelry spaced far apart to be only slightly more valuable than jewelry spaced close together. **(Correct)**

  *Correct. The original effect (more space = seen as more valuable) still shows up at upscale Tiffany & Co. but is much weaker at inexpensive Forever 21 — exactly the pattern of the inexpensive-store context dampening, or moderating, the effect rather than eliminating or reversing it.*

**B.** At both Tiffany & Co. and Forever 21, participants judged jewelry spaced far apart to be less valuable than jewelry spaced close together, but the difference in perceived value was significantly greater at Tiffany & Co. than at Forever 21. 

  *This reverses the direction of the original effect at BOTH stores — spacing jewelry farther apart makes it seem LESS valuable, not more, everywhere. That contradicts the effect Sevilla and Townsend’s other experiments established, so it can’t illustrate the inexpensive context merely moderating it.*

**C.** Participants judged jewelry spaced far apart at Tiffany & Co. to be similar in value to jewelry spaced far apart at Forever 21, but participants judged jewelry spaced close together at Tiffany & Co. to be more valuable than jewelry spaced close together at Forever 21. 

  *This compares the two stores against each other rather than comparing far-apart spacing to close-together spacing within each store. It never establishes whether the original space-to-value effect appeared, weakened, or disappeared at either retailer.*

**D.** When jewelry was spaced far apart, participants judged the jewelry at Tiffany & Co. to be more valuable than the jewelry at Forever 21, but when jewelry was spaced close together, participants judged the jewelry at Tiffany & Co. to be less valuable than the jewelry at Forever 21. 

  *Like choice C, this only compares Tiffany & Co. to Forever 21 at each spacing level — it doesn’t compare far-apart to close-together spacing within either store, so it never shows whether the original effect held, weakened, or vanished at the inexpensive retailer.*

*Difficulty: sat-hardest*

---

##### Q66
> Water flowing around an obstruction creates vortices (patterns of swirls) of varying size; by detecting the vortices, fish can determine the size and position of the obstruction. Testing by Yuzo R. Yanagisuru, Otar Akanyeti, and James C. Liao using models of three head shapes—narrow (low ratio of width to length), intermediate, and wide (high ratio of width to length)—showed that for medium-sized vortices, fish with wide heads would be least able to distinguish between vortices and general turbulence in the water. A second research team has therefore hypothesized that in low-visibility conditions, wider-headed fish will be less likely than narrower-headed fish to detect obstructions.

Which finding, if true, would most directly support the second research team's hypothesis?

**A.** A study using obstructions that created medium-sized vortices in low-visibility conditions found that the bristlemouth (Chaetostoma yurubiense), which has a relatively wide head, bumped into more than half of the obstructions. 

  *A high collision rate for one wide-headed species, on its own, says nothing about whether wide heads specifically are the disadvantage — a narrow-headed fish tested under the same conditions might bump into obstructions just as often, or more. The hypothesis is a comparison between wide- and narrow-headed fish, and one species' number, with nothing set against it, can't make that comparison.*

**B.** A study using obstructions that created medium-sized vortices in low-visibility conditions found that some specimens of dusky smooth-hound (Mustelus canis), which has a relatively narrow head, bumped into the obstructions more often than other specimens of the same fish did. 

  *This compares narrow-headed fish to other narrow-headed fish, which can't show anything about wide heads versus narrow heads — head shape isn't even a variable within this comparison, since every specimen involved has the same relatively narrow head.*

**C.** A study using obstructions that created medium-sized vortices in low-visibility conditions found that the wider-headed bristlemouth (Chaetostoma yurubiense) bumped into obstructions more often than the narrower-headed dusky smooth-hound (Mustelus canis) did. **(Correct)**

  *Correct. This sets a wide-headed species directly against a narrow-headed one, under the same medium-vortex, low-visibility conditions, and finds the wide-headed fish colliding more — exactly the pattern "wider-headed fish will be less likely… to detect obstructions" predicts.*

**D.** A study using obstructions that created medium-sized vortices in low-visibility conditions found that the narrower-headed dusky smooth-hound (Mustelus canis) bumped into the obstructions just as often as the wider-headed bristlemouth (Chaetostoma yurubiense) did. 

  *This is the right comparison — narrow-headed against wide-headed, same conditions — reaching the wrong result. "Just as often" means no difference between the two groups, which is precisely what the hypothesis says should not happen if wider heads make obstacle detection harder.*

*Difficulty: hard*

---

##### Q67
> Neurobiologists Laura Cuaya, Raúl Hernández-Pérez, and colleagues investigated the language detection abilities of eighteen dogs. The researchers monitored the brain activity of Joey (an Australian shepherd), Mini (a mixed breed), and other dogs while the animals listened to three recordings: one of The Little Prince being read in Spanish, the second in Hungarian, and a third made up of short, randomly selected fragments of the first two, scrambled so that they didn't resemble human speech. Each dog was familiar with either Spanish or Hungarian, but not both. The team concluded that differences in dogs' anatomical features may affect their ability to distinguish speech from nonspeech.

Which finding from the study, if true, would most directly support the team's conclusion?

**A.** Long-headed dogs accustomed to hearing Spanish tended to show more brain activity when hearing Spanish than long-headed dogs accustomed to hearing Hungarian showed when hearing Hungarian. 

  *Both groups here have the same head shape and are compared on the language they were each raised with — that's a comparison of Spanish-familiar dogs to Hungarian-familiar dogs, not a comparison between anatomical types. Anatomy is held constant, not tested, so nothing here can support a claim about anatomical features mattering.*

**B.** Compared with shorter-headed dogs, longer-headed dogs showed a greater difference in brain activity when hearing either Spanish or Hungarian than when hearing the scrambled recording. **(Correct)**

  *Correct. This ties an anatomical difference (longer- versus shorter-headed) to a difference in the specific skill the conclusion is about — telling speech (Spanish or Hungarian, whichever the dog knew or didn't) apart from nonspeech (the scrambled recording). One head shape showing a bigger speech-versus-nonspeech gap than the other is exactly "differences in dogs' anatomical features may affect their ability to distinguish speech from nonspeech."*

**C.** The pattern of brain activity that long-headed dogs showed when hearing the scrambled recording was different from the pattern of brain activity that short-headed dogs showed when hearing the language they were accustomed to. 

  *This compares two different head shapes, which looks promising, but it also swaps the recording between them — the long-headed dogs' response to nonspeech is set against the short-headed dogs' response to speech. A "different pattern" between two different anatomies hearing two different things could come from either variable, so it can't isolate anatomy as the reason.*

**D.** Compared with shorter-headed dogs, longer-headed dogs showed a greater difference in brain activity when hearing the language they were accustomed to than when hearing the other language. 

  *This is a real anatomical comparison, but the two recordings on both sides of it are speech — the familiar language against the unfamiliar one. The conclusion is about distinguishing speech from nonspeech, and a gap between two kinds of speech never touches the scrambled, nonspeech recording at all.*

*Difficulty: hard*

---

##### Q68
> The variety of species with adaptations to produce toxins is matched by the variety of uses of those toxins: northern stargazers, for example, use toxins for defense, whereas tiger snakes use toxins for predation and skeleton shrimp use toxins for intraspecific competition. In fact, a species may have adaptations enabling it to produce a toxin with multiple uses. Finding that the venom used by the Panamanian scorpion Centruroides granosus to subdue prey also inhibits growth of the pathogenic bacteria Escherichia coli, Dumas Gálvez and colleagues conclude that the particular form of venom production observed in C. granosus may have propagated through the species because it mitigates risk during feeding in addition to enhancing predation success.

Which finding, if true, would most directly support Gálvez and colleagues' conclusion?

**A.** E. coli does not appear to be virulent for C. granosus even when transmitted from prey captured without the use of venom. 

  *If E. coli isn't dangerous to the scorpion even without the venom's antibacterial action, then there was no feeding risk for the venom to mitigate in the first place. This finding removes the risk the conclusion says the venom protects against, rather than supporting the idea that it does.*

**B.** E. coli is frequently found in species preyed on by C. granosus and can survive exposure to the digestive juices of C. granosus. **(Correct)**

  *Correct. This establishes both halves the conclusion needs: E. coli is a real, recurring hazard in what the scorpion actually eats, not a lab curiosity, and it survives the scorpion's own digestion — meaning the gut can't be relied on to neutralize it. That leaves the venom's antibacterial action, delivered at the moment of subduing prey, as the thing standing between the scorpion and infection, which is exactly "mitigates risk during feeding."*

**C.** C. granosus appears to be chemically sensitive to prey infected with E. coli and tends to favor uninfected individuals. 

  *If the scorpion can already detect and avoid infected prey before feeding, that is a separate risk-mitigation strategy that doesn't require the venom to do anything — it competes with the conclusion's explanation rather than supporting it. A species that can smell the danger away needs the venom's antibacterial property less, not more.*

**D.** Exposure to C. granosus venom also inhibits the growth of nonpathogenic bacteria species common in the native environment of C. granosus. 

  *This shows the venom's antibacterial effect is broad rather than targeted, but broad action against harmless bacteria says nothing about whether it protects against the pathogenic risk of feeding specifically. The conclusion is about mitigating a feeding-borne infection risk, and this finding never gets back to that pathogen.*

*Difficulty: sat-hardest*

---

##### Q69
> The ancient Greek concept of "mimesis," a term used in the works of Plato, Aristotle, and other Greek philosophers in discussions of representational art—visual, performance, or literary art that aims to depict the real world—is a foundational concept of the Western philosophy of aesthetics. Mimesis is typically translated as "imitation" in modern editions of ancient Greek texts, but scholar Stephen Halliwell warns that this is overly reductive: "imitation" implies that art merely copies—and is thus by definition entirely derivative of—a reality that exists outside and prior to the work of art, and translating "mimesis" thusly obscures the multifaceted ways in which the ancient Greeks understood the relationship between art and reality.

Which statement, if true, would most directly support the claim by Halliwell presented in the text?

**A.** One of the earliest appearances of mimesis's root word, mimos, can be found in an ancient Greek tragedy in reference to dramatic impersonation, and the mim- root came to be generally associated with the musical and poetic arts by the fifth century BCE. 

  *This traces the word's history and its association with certain art forms, which is a fact about etymology, not about whether the concept meant only "copying" or something richer. Halliwell's claim is about the range of ideas "imitation" flattens, and a timeline of the root word never gets to that range.*

**B.** Both Plato's and Aristotle's theorizations of mimesis examine the psychological effects that works of art induce in the viewer or listener. 

  *This says the two philosophers shared a common focus, which is a similarity between them, not evidence that mimesis covers more than "derivative copying." Halliwell's complaint is about a reductive translation obscuring multiple different relationships between art and reality; a single shared concern the two philosophers both examined doesn't display any of that variety.*

**C.** Although several of Plato's earliest philosophical works discuss aesthetic ideas, the term "mimesis" doesn't appear in Plato's discussions of art until Cratylus, a relatively late work. 

  *This is a fact about when Plato started using a particular word, not about what the word meant once he used it. It bears on the term's textual history, not on whether "imitation" undersells the concept's range of meaning.*

**D.** Although Plato's writings typically characterize representational art as an inferior reflection of the physical world, Aristotle suggests that mimesis can refer to art's capacity to envision hypothetical conditions that could, but don't yet, exist. **(Correct)**

  *Correct. This puts two genuinely different Greek understandings of mimesis side by side — Plato's, which does match "derivative copy," and Aristotle's, which describes art imagining what doesn't yet exist, nothing like mere copying. That contrast is the multifacetedness Halliwell says the single word "imitation" erases.*

*Difficulty: hard*

---

##### Q70
> Jean-Bernard Caron and colleagues recently discovered a cache of jellyfish fossils in the Burgess Shale, a site in the Canadian Rockies that is rich in fossils from the Cambrian period (over 500 million years ago). Caron and colleagues claim that these are the oldest jellyfish fossils ever discovered. In the past twenty years, two sites in China and the United States have yielded fossils of a similar age that some experts believe are most likely jellyfish due to their shapes and the appearance of projecting tentacles. But Caron and colleagues argue that the apparent tentacles are in fact the comb rows of ctenophores, gelatinous animals that are only distantly related to jellyfish.

Which statement, if true, would most directly weaken the claim by Caron and colleagues about the fossils found in China and the United States?

**A.** Sites in the Canadian Rockies from later periods than the Cambrian period have yielded fossils that have been conclusively identified as ctenophore fossils. 

  *This confirms that ctenophore fossils exist and can be conclusively identified somewhere, which if anything supports Caron and colleagues' ability to tell ctenophores from jellyfish — it says nothing about whether the specific China and U.S. fossils were misidentified. Wrong site, wrong period, wrong question.*

**B.** The fossils found in China and the United States are so poorly preserved that though they cannot be conclusively identified as jellyfish, they cannot be conclusively identified as ctenophores either. **(Correct)**

  *Correct. Caron and colleagues' claim rests on a specific, confident reidentification — the apparent tentacles are ctenophore comb rows, not jellyfish tentacles. If the fossils are too poorly preserved to conclusively support either identification, that confidence is unearned, which directly undercuts the claim rather than the fossils' age or origin.*

**C.** While ctenophore fossils have been discovered in China and the United States, they have never been discovered in the Burgess Shale. 

  *This is about where ctenophore fossils have and haven't turned up, not about whether the particular China and U.S. fossils in question are ctenophores rather than jellyfish. It leaves Caron and colleagues' specific reidentification of those fossils completely untouched.*

**D.** The fossils discovered by Caron and colleagues in the Burgess Shale were better preserved than the fossils discovered by other researchers in China and the United States. 

  *This is about the quality of a different set of fossils — Caron and colleagues' own Burgess Shale jellyfish, not the China and U.S. finds their claim is about. A comparison of preservation quality between two unrelated fossil caches doesn't bear on whether the China and U.S. tentacles are jellyfish or ctenophore.*

*Difficulty: hard*

---

#### Inferences (71 items)

##### Q1
> Microbes that live in shallow lakes and ponds produce methane, a harmful greenhouse gas. Ecologist Ralf Aben and his team wanted to see how different types of shallow-water plants might affect the amount of methane that escapes into the atmosphere. Aben's team set up some water tanks with soil and microbes from local ponds. Some tanks had a type of underwater plant that grows in the soil called watermilfoil. Other tanks had either duckweed, a type of plant that floats on the water's surface, or algae. Aben and his team found that tanks with duckweed and algae released higher levels of methane than tanks with watermilfoil did. This finding suggests that ______

Which choice most logically completes the text?

**A.** the presence of some kinds of underwater plants like watermilfoil helps prevent methane from escaping shallow lakes and ponds. **(Correct)**

  *Correct. Tanks with the rooted underwater plant (watermilfoil) released less methane than tanks with the floating plants (duckweed, algae). That is exactly the finding restated: a plant like watermilfoil is associated with less methane escaping.*

**B.** shallow lakes and ponds release more methane than deeper bodies of water because shallow bodies of water usually have more plants than deep bodies of water do. 

  *The experiment never included deep water at all — every tank modeled a shallow-water setup with different plant types. A comparison between shallow and deep bodies of water is invented, not measured.*

**C.** shallow lakes and ponds are more likely to contain algae than to contain either watermilfoil or duckweed. 

  *The tanks were set up by the researchers, who chose which plant went in which tank — the study says nothing about which plants naturally occur more often in real shallow lakes and ponds.*

**D.** having a mix of algae, underwater plants, and floating plants is the best way to reduce the amount of methane in shallow lakes and ponds. 

  *No tank contained a mixture of plant types — each tank had one kind. A claim about mixtures being "best" is invented, and it also ignores that watermilfoil alone, not a combination, was the one linked to lower methane.*

*Difficulty: medium*

---

##### Q2
> In their book Smart Pricing, Jagmohan Raju and Z. John Zhang consider musicians' use of the nontraditional "pay as you wish" pricing model. This model generally offers listeners the choice to pay more or less than a suggested price for a song or album—or even to pay nothing at all. As the authors note, that's the option most listeners chose for an album by the band Harvey Danger. Only about 1% opted to pay for the album, resulting in earnings below the band's expectations. But the authors also discuss musician Jane Siberry, who saw significant earnings from her "pay as you wish" online music store as a result of many listeners choosing to pay more than the store's suggested prices. Hence, the "pay as you wish" model may ______

Which choice most logically completes the text?

**A.** prove financially successful for some musicians but disappointing for others. **(Correct)**

  *Correct. The two examples point in opposite directions — Harvey Danger earned below expectations, Siberry earned significantly — so the model's outcome depends on the musician. "May" is the right hedge for evidence that cuts both ways.*

**B.** hold greater financial appeal for bands than for individual musicians. 

  *This gets the pairing backward: Harvey Danger, a band, is the example that disappointed, while Siberry, an individual musician, is the example that succeeded — the opposite of what this choice claims.*

**C.** cause most musicians who use the model to lower the suggested prices of their songs and albums over time. 

  *Nothing in the passage discusses musicians adjusting suggested prices after seeing results — this is a mechanism invented beyond what the two examples show.*

**D.** more strongly reflect differences in certain musicians' popularity than traditional pricing models do. 

  *The passage never compares "pay as you wish" pricing to traditional pricing models on how well either reflects an artist's popularity — that comparison is not something the text sets up.*

*Difficulty: medium*

---

##### Q3
> Arthur Conan Doyle's stories about detective Sherlock Holmes were published between 1887 and 1927. They have inspired countless successful adaptations, including comic strips, movies, and a television series Sherlock Hound, directed by Hayao Miyazaki, who is celebrated for his animated movies. Until 2014, these stories were copyrighted. The right to adapt was only available to those who could afford the copyright fee and gain approval from the strict copyright holders of Doyle's estate. Some journalists predict that the number of Sherlock Holmes adaptations is likely to increase since the end of copyright means that ______

Which choice most logically completes the text?

**A.** Doyle's original stories will become hard to find. 

  *Copyright ending typically makes a work easier, not harder, to access and reproduce — nothing about the stories becoming scarce follows from the end of copyright.*

**B.** people will become more interested in detective stories than they were in the 1800s. 

  *A shift in genre-wide reader interest is never addressed — the passage is about legal barriers to adaptation, not about how appealing detective fiction is to audiences over time.*

**C.** producing adaptations will become easier and less expensive. **(Correct)**

  *Correct. Before 2014, adapting the stories required paying a copyright fee and winning approval from strict estate holders. Once copyright ends, both of those barriers disappear — directly explaining why more adaptations are predicted.*

**D.** the former copyright holders of Doyle's estate will return fees they collected. 

  *The end of copyright going forward has no bearing on fees already collected in the past — retroactive refunds are not a consequence of copyright expiration and are never mentioned.*

*Difficulty: medium*

---

##### Q4
> One aspect of in-person shopping that online shopping can't replicate is the opportunity to touch a product before buying it. Does this difference matter? In an experiment, researchers asked one group of participants to touch a mug and a toy, while another group was prohibited from touching the two items. The participants were then asked how much money they'd pay for the items. People who got to touch the items were willing to pay much more money for them than were people who weren't allowed to touch the items. This finding suggests that ______

Which choice most logically completes the text?

**A.** people who mainly shop online probably spend more money every month than people who mainly shop in person do. 

  *The experiment measured willingness to pay for two specific touched or untouched items, not total monthly spending across all purchases and shopping habits — that is a different quantity entirely.*

**B.** in-person shopping may make products seem more valuable than they seem if only viewed online. **(Correct)**

  *Correct. Touching raised willingness to pay; not touching (as in viewing online) did not. That is exactly what the experiment measured — perceived value tracks the ability to touch the product.*

**C.** retailers with in-person and online stores should charge the same price for a given product in both places. 

  *The passage reports a finding about perceived value, not a pricing recommendation. If anything, the result suggests differentiated pricing might make sense, not that prices should be equalized.*

**D.** online retailers may be able to raise the prices they charge for products that are only available online. 

  *This reverses the logic. Touch increased perceived value; products that can never be touched (online-only) would be the ones with less basis for a value increase, not more.*

*Difficulty: medium*

---

##### Q5
> Archaeologists have been debating the origin of a rare form of lead found in Shang dynasty (1766-1046 BCE) bronze artifacts since its presence was discovered in China in the 1990s. Different researchers have proposed theories on which regions of the world would have had the raw materials containing the specific lead in these artifacts, but no conclusive evidence has been presented. What is intriguing is that bronze artifacts from China dated after the Shang dynasty do not contain this form of lead, suggesting that ______

Which choice most logically completes the text?

**A.** Shang dynasty bronze pieces are rare and therefore more valuable than those from other time periods. 

  *The disappearance of a lead type says nothing about the rarity or market value of the bronze pieces themselves — value is never measured or discussed.*

**B.** the source of some of the raw materials used to make bronze was exploited only until the end of the Shang dynasty. **(Correct)**

  *Correct. The lead form is present in Shang bronzes and absent afterward. The simplest account of a raw material vanishing from the record at a fixed point is that access to its source stopped — exactly what "exploited only until the end of the Shang dynasty" says.*

**C.** bronze was used for a short time during the Shang dynasty before different metals were used to make artifacts. 

  *This mistakes the disappearance of one lead type for the disappearance of bronze itself — but bronze artifacts continued to be made after the Shang dynasty, just without this particular lead.*

**D.** methods used to analyze bronze artifacts are not useful on pieces that are dated after the Shang dynasty. 

  *Nothing suggests the analysis method itself broke down on later pieces — the far simpler explanation is that the material composition genuinely changed, not that detection failed.*

*Difficulty: hard*

---

##### Q6
> Off-off-Broadway theaters emerged in the late 1950s as a rebellion against mainstream Broadway theaters in New York, freeing artists to create productions that were more experimental than typical Broadway shows. One such artist was playwright María Irene Fornés. Working with off-off Broadway theaters enabled Fornés not only to direct her own plays but also to direct them exactly as she intended them to be staged, regardless of how strange the results might have seemed to audiences accustomed to Broadway shows. In this way, Fornés ______

Which choice most logically completes the text?

**A.** wrote plays that would have been too expensive to produce if someone else had directed the production. 

  *Production cost under a different director is never discussed — this economic claim has no basis in the passage.*

**B.** recognized that staging an off-off-Broadway play was more complicated than staging a Broadway play. 

  *The passage is about creative control and freedom, not relative staging difficulty — complexity of production is a different quantity than the artistic license being described.*

**C.** would have been more famous if she had created plays that were mainstream instead of experimental. 

  *This is pure counterfactual speculation about fame under a different career path — nothing in the passage supports or addresses it.*

**D.** illustrates the artistic opportunity offered by off-off Broadway theaters. **(Correct)**

  *Correct. Off-off-Broadway freed artists to work experimentally and on their own terms; Fornés used exactly that freedom to direct her plays as she intended. She is a direct illustration of the opportunity just described.*

*Difficulty: medium*

---

##### Q7
> North American gray wolves usually have mixed gray and white fur, but some members of the species have a version of a gene, or gene variant, that gives them a mostly black coat instead. Sarah Cubaynes and her team studied twelve populations of North American gray wolves. They found that the black-furred wolves are more common in areas where outbreaks of distemper virus happen regularly. The team also discovered that the black-furred wolves are more likely to be immune to distemper than the gray-furred wolves are. Taken together, these findings suggest that ______

Which choice most logically completes the text?

**A.** North American gray wolves experience more outbreaks of distemper virus than other wolf species do. 

  *No other wolf species is studied or mentioned — a cross-species comparison of outbreak frequency is invented.*

**B.** the gene variant that results in black fur may be linked to immunity to the distemper virus. **(Correct)**

  *Correct. Black-furred wolves cluster in outbreak-prone areas and are more often immune — combining both findings points to a link between the fur-color gene variant and distemper immunity.*

**C.** the average life span of gray wolves is likely to increase over time because of a particular gene variant. 

  *Life span is never measured in this study — the findings concern immunity and geographic distribution of a coat-color gene, not longevity.*

**D.** gray-furred wolves will soon replace black-furred wolves across North America. 

  *This reverses the expected direction: if the black-fur variant carries an immunity advantage in outbreak-prone areas, that variant would be expected to persist or spread there, not be replaced by the gray-furred type.*

*Difficulty: medium*

---

##### Q8
> In many cultures, a handshake can create trust between people. Engineer João Avelino and his team are designing a robot to shake hands with a human in order to improve human-robot interactions. The robot hand adjusts its movements and pressure to better imitate the feel of a human hand. The researchers want the robot's handshake to feel realistic because ______

Which choice most logically completes the text?

**A.** lifelike handshakes may make people more comfortable interacting with robots. **(Correct)**

  *Correct. The passage opens by establishing that handshakes build trust between people, and the stated goal is to improve human-robot interactions — a realistic handshake would carry over that trust-building effect into how people feel about robots.*

**B.** it's easier to program a robot to perform handshakes than it is to program a robot to perform some other types of greetings. 

  *Relative programming difficulty across different types of greetings is never discussed — this is an invented technical claim.*

**C.** people are less likely to interact with robots that don't look like humans. 

  *The passage is about how a handshake feels (touch), not what a robot looks like (sight) — this swaps the sensory channel the researchers were actually working on.*

**D.** the robot in the researchers' study may have uses other than interacting with humans. 

  *This undercuts the stated purpose of the project — improving human-robot interaction — with an unsupported alternative use that the passage never raises.*

*Difficulty: easy*

---

##### Q9
> Martin Dančák, Wewin Tjiasmanto, and colleagues have identified a new carnivorous plant species (Nepenthes pudica) in Indonesia. Like other carnivorous plants, N. pudica has pitfall traps, or pitchers, that capture prey, but unlike others, the pitchers of N. pudica are located underground. The researchers unearthed the new species on fairly dry ridges with surfaces that host few other plants and animals. Therefore, the researchers hypothesize that the N. pudica species likely ______

Which choice most logically completes the text?

**A.** represents one of many undiscovered carnivorous plant species in the region. 

  *The existence of other undiscovered species is not something the ridge habitat evidence speaks to at all — it's an invented claim about how many species remain to be found.*

**B.** formed pitchers early in development to absorb more moisture. 

  *Pitchers are described only as prey-capturing traps; the passage assigns them no moisture-absorbing function, and developmental timing is never mentioned.*

**C.** is buried by nearby animals as they forage along the ridges for food. 

  *This reverses cause and effect, describing the plant as passively buried by animals rather than having evolved underground traps itself — and no animal-burying behavior is mentioned.*

**D.** evolved to have underground traps to access more prey than would surface traps. **(Correct)**

  *Correct. The ridges' surfaces host few plants and animals, meaning little prey is available above ground. Locating the traps underground instead would let the plant reach more prey than surface traps could, explaining the unusual placement.*

*Difficulty: hard*

---

##### Q10
> In the South Pacific, New Caledonian crows use two different kinds of stick tools. One tool is complex. The crows shape a stick from a rare plant into a hook. The other tool is basic. The crows find a stick without a hook on the ground. The hooked tool is harder to get but is much better than the basic tool at removing prey from holes. When studying New Caledonian crows, ecologist Barbara Klump found that they hold the hooked tools in their claws when not using them, or they carefully put them in a safe place. The crows don't do the same with the basic tools. This suggests to Klump that the ______

Which choice most logically completes the text?

**A.** hooked stick tools are more valuable to the crows than the stick tools without hooks. **(Correct)**

  *Correct. The crows treat hooked tools with more care — holding them or storing them safely — while leaving basic tools without such care. That careful handling is exactly what signals greater value, consistent with the hooked tool being harder to obtain and more effective.*

**B.** hooked stick tools are easier for most of the crows to hold than the stick tools without hooks. 

  *Ease of physically gripping the tool is never discussed — the behavior described is about storage and care after use, not grip mechanics.*

**C.** crows prefer to share their hooked stick tools but don't share the stick tools without hooks. 

  *Sharing between crows is never mentioned anywhere in the passage — this is invented social behavior.*

**D.** crows realize that both kinds of stick tools are less effective than their claws are at removing prey from holes. 

  *This contradicts the passage, which says the hooked tool is "much better" at removing prey from holes — implying it outperforms not using a tool, not that tools are inferior to claws.*

*Difficulty: medium*

---

##### Q11
> Georgia Douglas Johnson wrote many plays in the 1920s and 1930s. At the time, professional theater companies rarely put on plays by Black women, so few of Johnson's plays made it to the stage. Only a small number of her plays were published in her lifetime. But that doesn't mean that Johnson never learned what other people thought of her plays. Johnson hosted weekly get-togethers for fellow Black writers and artists in her Washington, D.C., home. Attendees would read and discuss one another's work, including Johnson's own. These gatherings could therefore serve as ______

Which choice most logically completes the text?

**A.** an occasion for professional theater companies to put on plays. 

  *These were informal home gatherings among writers and artists, not staged productions by professional companies — which the passage explicitly says rarely staged Johnson's plays.*

**B.** an opportunity for Johnson to get feedback on her plays. **(Correct)**

  *Correct. The passage sets this up directly: attendees discussed one another's work "including Johnson's own," and this follows the point that Johnson still learned what people thought of her plays despite limited staging and publication.*

**C.** a way for Johnson to learn about plays that were produced in other cities. 

  *Geographic scope of productions in other cities is never discussed — this is an invented detail unrelated to the home gatherings.*

**D.** subject matter for future plays by Johnson. 

  *Nothing indicates the gatherings themselves became content Johnson wrote about — this consequence is invented.*

*Difficulty: medium*

---

##### Q12
> Alice Guy-Blaché directed hundreds of films between 1896 and 1920. She wanted audiences to feel like they were watching real people on screen. She would encourage actors in her films to behave naturally. Guy-Blaché even hung a large sign reading "Be Natural" in the studio where she made her films. At the time, films lacked sound, so actors needed to rely solely on their bodies and facial expressions to convey emotions. As a result, actors tended to highly exaggerate their actions and expressions. The style of acting in Guy-Blaché's films was therefore ______

Which choice most logically completes the text?

**A.** copied by many of Guy-Blaché's peers. 

  *If her natural style broke from the period's norm of exaggeration, nothing supports the further claim that other directors' actors then adopted it — widespread copying is invented.*

**B.** familiar to actors who had worked on other directors' films. 

  *This reverses the contrast the passage sets up: if the period's norm (established by the lack of sound) was exaggerated acting, then Guy-Blaché's demand for natural behavior would be unfamiliar, not familiar, to actors trained in that norm.*

**C.** very unusual for the period. **(Correct)**

  *Correct. The passage establishes that the lack of sound generally led actors to "highly exaggerate their actions and expressions." Guy-Blaché instead demanded natural behavior — a clear departure from that norm, making her films' acting style unusual for the era.*

**D.** better than film acting today. 

  *No comparison to modern film acting is made anywhere in the passage — this evaluative claim is invented.*

*Difficulty: hard*

---

##### Q13
> To create the poems in her 2017 collection One Last Word, poet Nikki Grimes used a writing method called the golden shovel. This method often involves choosing a line from an existing poem and then using each word from that line as the last word of each line in a new poem. Grimes wanted the poems in One Last Word to honor important Black poets of the past, so she chose lines by poets such as Langston Hughes and Georgia Douglas Johnson. Writing in this way can be challenging and might seem as though it would produce awkward poems. However, reviewers praised One Last Word as a beautiful and powerful tribute to the poets who inspired it. This reaction suggests that ______

Which choice most logically completes the text?

**A.** most reviewers didn't understand Grimes's goal for One Last Word. 

  *This reverses the reviewers' judgment: praising the collection as a "powerful tribute" shows reviewers grasped and appreciated Grimes's goal, not that they misunderstood it.*

**B.** Grimes successfully used the golden shovel method to achieve her goal for One Last Word. **(Correct)**

  *Correct. Grimes's goal was to honor past Black poets through the golden shovel method; despite the method's difficulty, reviewers praised the result as a beautiful, powerful tribute — meaning she achieved exactly what she set out to do.*

**C.** Langston Hughes and Georgia Douglas Johnson are two of Grimes's favorite poets. 

  *The passage says she chose these poets' lines to honor important Black poets of the past, not that they are specifically her personal favorites — this imports an unsupported claim about personal preference.*

**D.** Grimes inspired many other writers to create poems using the golden shovel method. 

  *Nothing about Grimes influencing other writers' techniques is discussed — this consequence is invented.*

*Difficulty: medium*

---

##### Q14
> Researchers wanted to study how consumers' reactions to an ad may be affected by other ads. The researchers began by showing study participants an ad for a product, with some seeing a less detailed ad and others seeing a more detailed one. Then, all participants viewed the same second ad for a store and shared their opinion about the store based on this second ad. Participants who had first seen an ad less detailed than the second ad had a higher opinion of the store than the participants who had first seen a more detailed ad. The researchers concluded that reactions to an ad may be affected by ______

Which choice most logically completes the text?

**A.** the number of people who viewed the ad. 

  *Audience size was never manipulated or measured in this study — the variable tested was the level of detail in the first ad.*

**B.** the length of time viewing previous ads. 

  *The study varied how detailed the first ad was, not how long participants spent viewing it — this substitutes a different quantity for the one actually tested.*

**C.** the amount of detail viewed in previous ads. **(Correct)**

  *Correct. The manipulation was the level of detail in the first ad (less detailed vs. more detailed), and it changed opinions of the second ad — directly supporting that reactions are affected by the detail level of prior ads.*

**D.** the time of day that the ad is viewed. 

  *Time of day is never addressed anywhere in the study description — this variable is invented.*

*Difficulty: easy*

---

##### Q15
> In the 1950s and '60s, plant breeders created shorter varieties of wheat and rice plants with improved yields. Kelly Gillespie, Rex Bernardo, and other plant specialists are building on that work by exploring the development of shorter corn varieties. Greater height can allow individual plants to produce more ears of corn. However, greater height also makes the stalks more likely to snap or be uprooted in strong winds before the corn can be harvested. Because of this trade-off, some plant specialists suggest that shorter corn varieties will actually ______

Which choice most logically completes the text?

**A.** help improve yields of harvested corn by being more likely to survive severe winds. **(Correct)**

  *Correct. Taller plants can produce more ears but are more likely to snap or uproot in wind before harvest. Shorter plants, being sturdier against wind, would lose less of their crop to storm damage — improving the yield that actually survives to be harvested.*

**B.** be more likely to be uprooted due to the weight of the corn on the stalks. 

  *This reverses the stated trade-off: greater height, not shorter height, is what the passage links to a higher risk of uprooting in strong winds.*

**C.** require more land for planting than short varieties of wheat and rice typically do. 

  *Land requirements are never discussed for either corn or the earlier wheat and rice work — this comparison is invented.*

**D.** begin developing more ears of corn on each plant than the tallest variety of corn currently does. 

  *This contradicts the stated trade-off, which says greater height allows for more ears per plant — so shorter plants producing fewer ears, not more, is what the passage's logic implies.*

*Difficulty: hard*

---

##### Q16
> In her 2021 article "Throwaway History: Towards a Historiography of Ephemera," scholar Anne Garner discusses John Johnson (1882-1956), a devoted collector of items intended to be discarded, including bus tickets and campaign pamphlets. Johnson recognized that scholarly institutions considered his expansive collection of ephemera to be worthless-indeed, it wasn't until 1968, after Johnson's death, that Oxford University's Bodleian Library acquired the collection, having grasped the items' potential value to historians and other researchers. Hence, the example of Johnson serves to ______

Which choice most logically completes the text?

**A.** demonstrate the difficulties faced by contemporary historians in conducting research at the Bodleian Library without access to ephemera. 

  *This contradicts the passage: the Bodleian Library acquired Johnson's ephemera collection, so historians there have access to it, not the reverse.*

**B.** represent the challenge of incorporating examples of ephemera into the collections of libraries and other scholarly institutions. 

  *No incorporation "challenge" or process is described — the passage says the collection simply wasn't valued and was later acquired, not that acquiring it posed some special difficulty.*

**C.** lend support to arguments by historians and other researchers who continue to assert that ephemera holds no value for scholars. 

  *This directly contradicts the passage, which says the Bodleian "grasped the items' potential value to historians and other researchers" — the opposite of asserting ephemera has no scholarly value.*

**D.** illustrate both the relatively low scholarly regard in which ephemera was once held and the later recognition of ephemera's possible utility. **(Correct)**

  *Correct. Johnson's collection was first dismissed as worthless by institutions, then later acquired by the Bodleian once its value was recognized — exactly the low-regard-then-recognition arc this choice describes.*

*Difficulty: medium*

---

##### Q17
> Some businesses believe that when employees are interrupted while doing their work, they experience a decrease in energy and productivity. However, a team led by Harshad Puranik, who studies management, has found that interruptions by colleagues can have a social component that increases employees' sense of belonging, resulting in greater job satisfaction that benefits employees and employers. Therefore, businesses should recognize that ______

Which choice most logically completes the text?

**A.** the interpersonal benefits of some interruptions in the workplace may offset the perceived negative effects. **(Correct)**

  *Correct. Businesses assume interruptions hurt productivity, but Puranik's team found a social benefit — greater belonging and job satisfaction — from colleague interruptions. "May offset" properly hedges a tension the passage presents without resolving completely.*

**B.** in order to maximize productivity, employers should be willing to interrupt employees frequently throughout the day. 

  *The finding is about a social component of naturally occurring interruptions, not a recommendation to deliberately maximize interruption frequency — this prescribes an action the passage never suggests.*

**C.** most employees avoid interrupting colleagues because they don't appreciate being interrupted themselves. 

  *Employee reluctance to interrupt others is never discussed, and it would contradict the premise that interruptions do occur and even carry benefits.*

**D.** in order to cultivate an ideal workplace environment, interruptions of work should be discouraged. 

  *This directly reverses the point of the "however": the research suggests interruptions may not need to be discouraged, since they carry a social benefit — the opposite of this recommendation.*

*Difficulty: medium*

---

##### Q18
> Songbirds learn to respond to and imitate their species' songs from an early age. With each generation, small differences are introduced that result in distinct variations—called dialects—among geographically isolated populations of the same species. A research study examined whether twelve-day-old Ficedula hypoleuca (pied flycatcher) nestlings prefer local dialects over the unfamiliar dialects of nonlocal F. hypoleuca populations: the more begging calls the nestlings made in response to a song, the stronger their preference. The researchers found that nestlings produced more begging calls in response to their own dialect than nonlocal dialects. Since song preference plays a role in songbird mate selection, the finding suggests that ______

Which choice most logically completes the text?

**A.** F. hypoleuca nestlings' preference for their own dialect likely disappears as they mature to promote socialization between different F. hypoleuca populations. 

  *This contradicts the logical chain the passage sets up, where the preference is tied to later mate selection — it also has no evidence for the preference fading with age.*

**B.** F. hypoleuca nestlings who show an early preference for their own dialect are likely to receive more food from their caretakers than nestlings who show no preferences among any F. hypoleuca dialects. 

  *Feeding and caretaking are never discussed — this consequence is invented and unrelated to the song-preference-and-mate-selection link the passage establishes.*

**C.** F. hypoleuca nestlings' preference for their own dialect likely drives them when they mature to reproduce with other F. hypoleuca from local rather than nonlocal populations. **(Correct)**

  *Correct. Since song preference plays a role in mate selection, and nestlings prefer their local dialect, that preference — if it persists to maturity — would drive them toward mates who sing the local dialect, meaning reproduction with local rather than nonlocal populations.*

**D.** F. hypoleuca nestlings show a preference for both local F. hypoleuca dialects and the songs of other local songbirds over the songs of nonlocal birds of any species. 

  *The study is specifically about F. hypoleuca dialects across different populations of the same species — it never tests or claims a preference involving entirely different songbird species.*

*Difficulty: hard*

---

##### Q19
> Dutch painters in the sixteenth and seventeenth centuries often showed tables filled with large wheels of cheese or carved shards of butter. Some art historians, noting that dairy products were a major component of the Dutch diet, interpret these depictions as reflections of everyday Dutch eating habits. However, a group of researchers recently reviewed hundreds of food-related paintings and found that lemons—which could only be acquired at great cost, since they had to be imported from warmer climates—feature in Dutch paintings of the period more than three times as frequently as dairy products do, thereby casting doubt on the idea that ______

Which choice most logically completes the text?

**A.** dairy products were a more significant component of the Dutch diet of the period than lemons were. 

  *This is likely still true — dairy was a diet staple while lemons were rare imports — so it isn't what the finding casts doubt on; the doubt targets the art historians' painting-as-reflection claim, not the diet fact itself.*

**B.** food was a more popular subject among Dutch painters than it was among painters from other countries at the time. 

  *No comparison to painters from other countries is made anywhere in the passage — this cross-national comparison is invented.*

**C.** depictions of food in Dutch paintings of the period should be taken as realistic representations of Dutch eating habits. **(Correct)**

  *Correct. This is the idea the art historians proposed — that the paintings reflect everyday eating habits. Since expensive, rarely eaten lemons appear far more often than the actual dietary staple (dairy), the paintings clearly are not simply reflecting typical diet, casting doubt on treating them as realistic.*

**D.** Dutch painters of the period may have depicted foods for symbolic reasons rather than to show what Dutch people typically ate. 

  *The blank needs to name the idea being undermined by the finding, not the new interpretation the finding might support — this answers the wrong slot in the sentence, describing a plausible conclusion rather than the doubted claim.*

*Difficulty: hard*

---

##### Q20
> When the Vinland Map, a map of the world purported to date to the mid-1400s, surfaced in 1957, some scholars believed it demonstrated that European knowledge of the eastern coast of present-day North America predated Christopher Columbus's 1492 arrival. In 2021, a team including conservators Marie-France Lemay and Paula Zyats and materials scientist Anikó Bezur performed an extensive analysis of the map and the ink used. They found that the ink contains titanium dioxide, a compound that was first introduced in ink manufacturing in the early 1900s. Therefore, the team concluded that ______

Which choice most logically completes the text?

**A.** mid-1400s Europeans could not have known about the eastern coast of present-day North America. 

  *The finding is about the ink's chemical composition and dating, not about what geographic knowledge Europeans actually had — this substitutes a claim about the map's content for a claim about its authenticity.*

**B.** the Vinland Map could not have been drawn by mid-1400s mapmakers. **(Correct)**

  *Correct. Titanium dioxide wasn't introduced into ink manufacturing until the early 1900s, but the map purports to date to the mid-1400s. Since that ink could not have existed then, the map could not actually have been produced by mid-1400s mapmakers.*

**C.** mapmakers must have used titanium compounds in their ink in the 1400s. 

  *This reverses the logic entirely: since titanium dioxide wasn't introduced until the 1900s, 1400s mapmakers could not have used it, not that they must have.*

**D.** there isn't enough information to determine when the ink was created. 

  *This contradicts the passage, which states the team found titanium dioxide, a compound "first introduced... in the early 1900s" — information that is sufficient to date the ink to no earlier than that period.*

*Difficulty: medium*

---

##### Q21
> It's common for jazz musicians and fans to refer to certain songs as having "swing," indicating that the songs provoke a strong feeling, like the impulse to tap one's foot or dance. The exact acoustic properties that give a song swing, however, have long been thought to be undefinable. To investigate swing, a team led by physicist Corentin Nelias delayed the downbeats and synchronized the offbeats in jazz piano solos and asked jazz musicians to compare the intensity of swing in each modified piece with the intensity of swing in the original piece. They found that participants were more than seven times likelier to characterize the modified songs as having swing than to characterize the original versions as having swing, suggesting that ______

Which choice most logically completes the text?

**A.** synchronized offbeats tend to give a song swing regardless of whether downbeats are delayed. 

  *The study manipulated delayed downbeats and synchronized offbeats together, never in isolation — claiming synchronized offbeats matter "regardless of" the other variable asserts more than a study with both variables changed at once can support.*

**B.** the acoustic properties that give a song swing are not easy for jazz musicians to manipulate. 

  *This contradicts the finding: the researchers successfully manipulated downbeats and offbeats and produced a large, consistent effect on perceived swing — the opposite of showing these properties are hard to manipulate.*

**C.** jazz songs that feature the piano are more likely to have swing than are jazz songs that do not feature the piano. 

  *The study used only piano solos, with no comparison to non-piano jazz songs — this cross-instrument comparison is invented.*

**D.** the timing of downbeats and offbeats may play a crucial role in giving a song swing. **(Correct)**

  *Correct. The researchers manipulated the timing of both downbeats and offbeats together, and modified songs were rated as having swing far more often than the originals — directly suggesting that this timing plays a crucial role in creating swing.*

*Difficulty: hard*

---

##### Q22
> The Indus River valley civilization flourished in South Asia from 3300 BCE to 1300 BCE. Many examples of the civilization's writing system exist, but researchers haven't yet deciphered it or identified which ancient language it represents. Nevertheless, archaeologists have found historical artifacts, such as clay figures and jewelry, that provide information about the civilization's customs and how its communities were organized. The archaeologists' findings therefore suggest that ______

Which choice most logically completes the text?

**A.** investigating an ancient civilization is easier without knowledge of the civilization's language. 

  *The passage shows learning is possible without deciphering the language, not that lacking the language makes investigation easier — that overstates what the finding supports.*

**B.** knowing an ancient civilization's language isn't necessary in order to learn details about the civilization. **(Correct)**

  *Correct. Despite never deciphering the writing system, archaeologists learned about the civilization's customs and social organization through other artifacts — showing language knowledge isn't strictly required to learn about a civilization.*

**C.** archaeological research should focus on finding additional artifacts rather than deciphering ancient languages. 

  *The passage reports what happened, not a recommendation about where future research should focus — this prescribes a priority the text never states.*

**D.** examining the civilization's historical artifacts has resolved the debate about this civilization's language. 

  *This contradicts the passage's explicit statement that researchers "haven't yet deciphered" the writing system — the language question remains unresolved.*

*Difficulty: medium*

---

##### Q23
> To investigate the history of plate subduction—when one of Earth's tectonic plates slides beneath another—Sarah M. Aarons and colleagues compared ancient rocks from the Acasta Gneiss Complex in Canada to modern rocks. Using isotope analysis, the researchers found that Acasta rocks dating to about 4.02 billion years ago (bya) most strongly resemble modern rocks formed in a plume setting (an area in which hot rocks from Earth's mantle flow upward into the crust). By contrast, they found that Acasta rocks dating to about 3.75 bya and 3.6 bya have an isotope composition that is similar to that of modern rocks formed in a subduction setting. Aarons's team therefore concluded that ______

Which choice most logically completes the text?

**A.** subduction-like processes began occurring in some locations no later than 3.75 bya. **(Correct)**

  *Correct. Rocks dated to 3.75 bya and 3.6 bya show a subduction-setting isotope signature, meaning subduction-like processes were occurring by at least 3.75 bya, the older of the two subduction-associated dates. "No later than" captures this without overclaiming an earlier start.*

**B.** subduction replaced mantle plume formation as the most common geological process by about 4.02 bya. 

  *This reverses the timeline: the 4.02 bya rocks show a plume signature, not subduction, meaning subduction had not yet appeared or dominated by that early date.*

**C.** the majority of the rocks in the Acasta Gneiss Complex formed through subduction. 

  *Only a small, dated sample of rocks was analyzed — two of three showing a subduction signature says nothing about the majority of all rocks in the entire Complex.*

**D.** the rocks in the Acasta Gneiss Complex are of a more recent origin than scientists previously thought. 

  *No prior scientific belief about the age of these rocks being revised is mentioned — the passage presents the ages (4.02, 3.75, 3.6 bya) as established facts, not corrections to earlier dating.*

*Difficulty: hard*

---

##### Q24
> The Haitian Declaration of Independence was issued in 1804, bringing to an end the revolution against colonial France that began in 1791. Written in French, which was not the first language of most Haitians but which was used throughout Europe as the language of international diplomacy, the declaration notes that Haiti will not bring rebellion to other Caribbean nations, promises to respect the sovereignty of its neighbors—widely understood as a reassurance to the United States—and sets up Haiti as an example for future struggles against colonizers (an implicit reference to the many colonies then found in the Americas). So even though the declaration is explicitly addressed to the Haitian people, it's reasonable to conclude that ______

Which choice most logically completes the text?

**A.** aspects of the declaration were modeled on similar documents from other countries. 

  *No comparison to other countries' declarations or documents is made anywhere in the passage — this claim about influence is invented.*

**B.** the French government may have been surprised by the declaration. 

  *The French government's emotional reaction is never discussed, and given that the declaration marked the end of a revolution against France, surprise is neither supported nor ruled out by the passage.*

**C.** many Haitian people opposed the revolution and the declaration. 

  *This contradicts the context: Haiti had just won its revolution and declared independence, and nothing in the passage suggests internal opposition to either.*

**D.** the declaration actually had several intended audiences. **(Correct)**

  *Correct. Despite being addressed to the Haitian people, the declaration was written in French (Europe's diplomatic language), includes a reassurance widely understood as directed at the United States, and implicitly addresses other colonies in the Americas — showing it had multiple intended audiences beyond just Haitians.*

*Difficulty: hard*

---

##### Q25
> By running computer simulations of the development of our solar system, André Izidoro, Rajdeep Dasgupta, and colleagues concluded that the Sun may have been surrounded by three giant dust rings before the planets started to form. The researchers suggest that the materials in the innermost ring became the four planets closest to the Sun, the materials in the middle ring produced the rest of the planets, and the materials in the outermost ring created the asteroids and other small bodies in the region beyond Neptune. In one simulation, the researchers delayed the initial formation of the middle ring, causing oversized super-Earths to begin developing from the innermost ring. The researchers therefore hypothesize that ______

Which choice most logically completes the text?

**A.** the middle ring formed earlier in the solar system's development than the initial simulations suggested. 

  *This reverses the manipulation described, which was delaying — not accelerating — the middle ring's formation, and no "initial simulations" baseline for an earlier timing is mentioned.*

**B.** the timing of the initial formation of the middle ring played an important role in determining the eventual size of Earth. **(Correct)**

  *Correct. Delaying the middle ring's formation caused the innermost ring — the source of the four planets closest to the Sun, including Earth — to develop oversized super-Earths instead. That shows the middle ring's formation timing affects the size outcome of inner planets like Earth.*

**C.** if the formation of the outermost ring had occurred earlier in a simulation, all the planets would have become super-Earths. 

  *The experiment manipulated only the middle ring's timing and affected only the innermost ring's output — nothing involves the outermost ring's timing or "all" planets becoming super-Earths.*

**D.** the innermost ring actually formed into all the planets in our solar system, not just the four closest to the Sun. 

  *This directly contradicts the passage's explicit statement that the innermost ring produces only the four planets closest to the Sun, while the middle ring produces the rest.*

*Difficulty: hard*

---

##### Q26
> Astronomers investigated the Arabia Terra region of Mars because it appears to contain irregularly shaped craters that may have been caused by massive volcanic explosions. In their investigations of Arabia Terra, the researchers found remnants of ash deposits in an amount and thickness that would result from a massive volcanic eruption. However, erosion and past resurfacing events could have modified the surface of the planet. Therefore, ______

Which choice most logically completes the text?

**A.** the current makeup of the Arabia Terra region might not accurately reflect the volcanic activity of Mars's past. **(Correct)**

  *Correct. Since erosion and resurfacing "could have modified" the surface, the ash deposits and craters observed today might not fully or accurately reflect the actual extent of past volcanic activity — a properly hedged conclusion matching the passage's own uncertainty.*

**B.** eruptions from Mars's volcanoes were likely not as massive as astronomers previously believed. 

  *This reverses the direction: the ash amount and thickness found is consistent with a massive eruption, and erosion would if anything have removed evidence, making activity seem less extensive than it actually was — not more.*

**C.** ash was most likely expelled from multiple different volcanoes on Mars's surface. 

  *The number or source of volcanoes involved is never discussed — this is an invented claim about volcano count.*

**D.** the craters found in the Arabia Terra region were necessarily created by events other than volcanic eruptions. 

  *This contradicts the setup, which investigates the craters precisely because they may result from volcanic explosions, and the ash evidence supports a volcanic origin — "necessarily" also overclaims a certainty the passage never establishes.*

*Difficulty: hard*

---

##### Q27
> As the name suggests, dramaturges originated in theater, where they continue to serve a variety of functions: conducting historical research for directors, compiling character biographies for actors, and perhaps most importantly, helping writers of plays and musicals to hone the works' stories and characters. Performance scholar Susan Manning observes that many choreographers, like playwrights and musical theater writers, are concerned with storytelling and characterization. In fact, some choreographers describe the dances they create as expressions of narrative through movement; it is therefore unsurprising that ______

Which choice most logically completes the text?

**A.** dramaturges can have a profound impact on the artistic direction of plays and musicals. 

  *This restates a role dramaturges already had in theater rather than drawing the new connection the passage's "therefore" demands — the parallel to choreographers and dance is the actual point being built toward.*

**B.** choreographers developing dances with narrative elements frequently engage dramaturges to assist in refining those elements. **(Correct)**

  *Correct. Dramaturges help playwrights and musical writers hone stories and characters; choreographers are described as similarly concerned with storytelling and characterization, even framing dances as narrative. It follows naturally that choreographers would engage dramaturges the same way writers do.*

**C.** dances by choreographers who incorporate narrative elements are more accessible to audiences than dances by choreographers who do not. 

  *Audience accessibility or reception is never discussed — the passage concerns the creative collaboration process, not how audiences respond to narrative versus non-narrative dance.*

**D.** some directors and actors rely too heavily on dramaturges to complete certain research tasks. 

  *This evaluative claim about over-reliance is never made, and it shifts focus to directors and actors rather than the choreographer connection the passage is building toward.*

*Difficulty: medium*

---

##### Q28
> Ana Castillo's 1986 novel The Mixquiahuala Letters is a story told entirely through expressive letters from the narrator to her friend—letters that Castillo suggests could be read in several different orders. As they began reading it in class, some students remarked that they found the novel's letter format daunting and its treatment of gender relations old-fashioned. The professor, however, pointed out that the novel is written in modern-sounding language and addresses issues that still matter today, suggesting that The Mixquiahuala Letters ______

Which choice most logically completes the text?

**A.** has more to say about gender relations than other novels from the same period. 

  *No comparison to other novels' treatment of gender relations is made — this cross-novel comparison is invented.*

**B.** is more relevant to contemporary audiences than it may seem at first. **(Correct)**

  *Correct. Students initially found the novel's treatment of gender relations "old-fashioned," seeming dated. The professor countered that the language sounds modern and the issues raised still matter today — suggesting the novel is more relevant to today's readers than that first impression indicated.*

**C.** is easier to read than many contemporary novels that focus on friendship. 

  *Students found the format "daunting," which points away from easy reading, and no comparison to friendship-themed contemporary novels is made anywhere.*

**D.** is best understood after multiple readings in different orders. 

  *While the letters could be read in different orders, the professor's actual point was about the novel's modern language and lasting relevance, not about needing repeated readings to be understood — this pulls from an earlier detail rather than the point being made.*

*Difficulty: medium*

---

##### Q29
> Biologist Natacha Bodenhausen and colleagues analyzed the naturally occurring bacterial communities associated with leaves and roots of wild Arabidopsis thaliana, a small flowering plant. The researchers found many of the same bacterial genera in both the plants' leaves and roots. To explain this, the researchers pointed to the general proximity of A. thaliana leaves to the ground and noted that rain splashing off soil could bring soil-based bacteria into contact with the leaves. Alternatively, the researchers noted that wind, which may be a source of bacteria in the aboveground portion of plants, could also bring bacteria to the soil and roots. Either explanation suggests that ______

Which choice most logically completes the text?

**A.** bacteria carried by wind are typically less beneficial to A. thaliana than soil-based bacteria are. 

  *Relative benefit or harm of different bacteria types is never discussed — the passage is about shared bacterial genera and possible transmission routes, not a benefit comparison.*

**B.** some bacteria in A. thaliana leaves and roots may share a common source. **(Correct)**

  *Correct. Both explanations — rain splashing soil bacteria onto leaves, or wind carrying leaf bacteria to soil and roots — point to a shared transmission pathway between leaves and roots. Either way, bacteria appear to move between the two locations from a common source, explaining the shared genera found in both.*

**C.** many bacteria in A. thaliana leaves may have been deposited by means other than rain. 

  *Wind is only one of the two alternative explanations offered — the "either explanation" framing means both remain possibilities, not that non-rain deposition is established as true.*

**D.** A. thaliana leaves and roots are especially vulnerable to harmful bacteria. 

  *Nothing classifies the shared bacteria as harmful, and vulnerability to harm is never discussed — the passage is only about a shared source for the bacteria found.*

*Difficulty: hard*

---

##### Q30
> Zines are small-scale, self-printed magazines. They have been around since the Black literary zine Fire!! was created in the 1920s. Since then, zines have appealed to creators looking for an inexpensive form of expression to share with a select audience. Zine creators often mix art with social commentary and challenge mainstream culture. At first, the internet appeared to replace the zine, but this old form persists. Today, there are enough zines in the United States to support annual zine festivals. This suggests that ______

Which choice most logically completes the text?

**A.** creators can reach a larger audience by posting online. 

  *This contradicts the passage's point that zines persist as a physical, select-audience form despite the internet, rather than because creators moved their work online.*

**B.** zines are still a meaningful form of expression. **(Correct)**

  *Correct. Despite the internet's apparent threat to replace it, the zine persists and remains numerous enough to support annual festivals — suggesting zines still hold real value as a form of expression for their creators.*

**C.** creators can continue to explore new art forms. 

  *Zines are described as an "old form" that persists, not a source of new art forms — this claim about exploring new forms is unsupported.*

**D.** zines are good sources of mainstream culture. 

  *This directly contradicts the passage's statement that zine creators "challenge mainstream culture" — the opposite of being a source of it.*

*Difficulty: medium*

---

##### Q31
> Marine archaeologists have found much of the wooden hull of a sixteenth-century ship in a flooded quarry in southeast England. When it is exposed to air and water, wood rots quickly unless it is protected by sediment that shields it from oxygen. Therefore, the discovered ship was likely ______

Which choice most logically completes the text?

**A.** covered by a protective sediment layer in the quarry. **(Correct)**

  *Correct. Wood rots quickly when exposed to air and water unless sediment shields it from oxygen, and this ship's hull survived largely intact after centuries. It must therefore have been covered and protected by sediment in the quarry — a direct, necessary inference from the stated mechanism.*

**B.** one of several other ships buried in the same quarry. 

  *No other ships are mentioned anywhere in the passage — this claim is invented.*

**C.** a confirmation of previous theories about the type of wood that was used in sixteenth-century ships. 

  *Wood-type theories are never discussed — the passage is about the preservation mechanism (sediment shielding wood from oxygen), not about wood species.*

**D.** first constructed much earlier than previously thought. 

  *No prior dating estimate is mentioned as being revised — the passage simply states it is a "sixteenth-century ship" as a given fact, not something in dispute.*

*Difficulty: medium*

---

##### Q32
> Parthenogenesis is a form of reproduction in which a female reproduces without mating. She produces an egg containing a single offspring whose DNA, or genetic material, comes entirely from its mother. Among birds, parthenogenesis has been found in a handful of species, including pigeons and turkeys. When scientists at the San Diego Zoo analyzed the DNA of the zoo's California condors (a species of vulture), they discovered that two individuals weren't genetically similar enough to any of the males in the condor enclosure to be their offspring. However, both had hatched from eggs laid by females in the enclosure. Thus, the scientists concluded that ______

Which choice most logically completes the text?

**A.** at least one of those individuals' mothers was born as a result of parthenogenesis. 

  *This misplaces which generation reproduced parthenogenetically — the evidence concerns the two individuals themselves being products of parthenogenesis, not their mothers' own birth origin.*

**B.** California condors may reproduce through parthenogenesis in zoos but not in the wild. 

  *No comparison between zoo and wild condor reproduction is made — this setting-dependent claim is invented.*

**C.** the mothers of the two individuals probably reproduced through parthenogenesis. **(Correct)**

  *Correct. The two condors' DNA doesn't match any male in the enclosure, ruling out normal mating with those males, yet both hatched from eggs laid by females in the enclosure. The best explanation is that the mothers reproduced via parthenogenesis, since offspring DNA in that process comes entirely from the mother.*

**D.** California condors reproduce through parthenogenesis only if females lack sufficient access to males. 

  *This contradicts the setup: males were present, since the DNA comparison was made against "males in the condor enclosure" — undermining a "lack of access" explanation.*

*Difficulty: hard*

---

##### Q33
> Several artworks found among the ruins of the ancient Roman city of Pompeii depict a female figure fishing with a cupid nearby. Some scholars have asserted that the figure is the goddess Venus, since she is known to have been linked with cupids in Roman culture, but University of Leicester archaeologist Carla Brain suggests that cupids may have also been associated with fishing generally. The fact that a cupid is shown near the female figure, therefore, ______

Which choice most logically completes the text?

**A.** is not conclusive evidence that the figure is Venus. **(Correct)**

  *Correct. Brain's alternate explanation — that cupids may be linked to fishing generally, not just to Venus — means the cupid's presence doesn't uniquely point to Venus. It could simply be signaling fishing, so it isn't conclusive proof of the figure's identity.*

**B.** suggests that Venus was often depicted fishing. 

  *No general pattern about how frequently Venus was depicted fishing is established — the passage discusses this one ambiguous case, not a broader trend.*

**C.** eliminates the possibility that the figure is Venus. 

  *This overcorrects in the opposite direction: Brain's alternative explanation weakens, but does not eliminate, the Venus interpretation, since it offers an alternative reading rather than proof against Venus.*

**D.** would be difficult to account for if the figure is not Venus. 

  *This reverses the logic: Brain's alternative explanation (cupids linked to fishing generally) makes it easy, not difficult, to account for a non-Venus figure appearing with a cupid nearby.*

*Difficulty: hard*

---

##### Q34
> Over 600 languages are spoken in New York City in addition to English—one can find Amharic spoken in the neighborhood of Norwood, or Ilocano in Woodside. Most speakers of Chinese languages reside in the neighborhood of Flushing (part of New York City's borough of Queens) and in Chinatown, in the borough of Manhattan. New immigrants from north China, where Mandarin is the primary first language, tend to settle in Queens, while new immigrants from south China, where many people speak Cantonese or Fuzhounese as a first language, tend to settle in Manhattan. It can therefore be inferred that ______

Which choice most logically completes the text?

**A.** languages tend to change more rapidly in areas where many languages are spoken than in areas where few languages are spoken. 

  *The rate of language change is never discussed — the passage is about where speakers of different languages settle, not about how languages evolve.*

**B.** languages spoken by immigrant peoples can differ significantly in vocabulary and pronunciation from those same languages in their country of origin. 

  *No comparison between immigrant dialects and home-country versions of the same language is made anywhere in the passage.*

**C.** there is a positive correlation between the physical size of a country and the number of languages spoken in that country. 

  *Country size is never discussed — this variable is entirely invented.*

**D.** correlations in a country between languages and regions where they are spoken can replicate themselves in a new country to which the original country's citizens emigrate. **(Correct)**

  *Correct. In China, north correlates with Mandarin and south with Cantonese or Fuzhounese. When these groups emigrate, north Chinese immigrants (Mandarin) settle in Queens and south Chinese immigrants (Cantonese/Fuzhounese) settle in Manhattan — the origin country's regional language pattern is being replicated onto new neighborhoods in the destination city.*

*Difficulty: hard*

---

##### Q35
> Red velvet cake has been a favorite dessert of many for years, but the recipe's origins are unclear. A bakery in Dallas, Texas, argued that it created the first recipe for the cake when the bakery opened in the 1860s. The Adams Extract Co., which sells baking products, claims to have created the recipe in the 1930s to help market their red dye. A US hotel and a Canadian department store also publicly stated that the red velvet cake sold in each of their establishments in the 1930s was an original creation, each alleging that it was the recipe author. No clear evidence has emerged to favor one of these claims over the others. It thus seems that ______

Which choice most logically completes the text?

**A.** red velvet cake was first baked sometime before the 1860s. 

  *No evidence for a date earlier than the 1860s claim is given anywhere in the passage — this earlier origin is invented.*

**B.** we cannot say at present who actually baked the first red velvet cake. **(Correct)**

  *Correct. Multiple competing claims exist — the Dallas bakery, Adams Extract Co., a US hotel, and a Canadian department store — and "no clear evidence has emerged to favor one of these claims over the others." The only warranted conclusion is that the true inventor currently cannot be determined.*

**C.** none of the supposed inventors of red velvet cake are likely to have invented it. 

  *This overreaches: lack of evidence favoring any one claim doesn't mean all claims are unlikely to be true — one of them probably is the actual inventor, we simply don't know which.*

**D.** the bakery in Dallas, Texas, probably invented red velvet cake. 

  *This directly contradicts the passage's statement that no evidence favors any claim over the others — singling out one claimant as most likely is unsupported.*

*Difficulty: medium*

---

##### Q36
> Scholars are increasingly exploring the communication and preservation of ecological knowledge through Indigenous songs (e.g., Sakha songs about local ecosystems and those of the Kaluli people about rainforest sounds). In one study, ethnobiologist Dana Lepofsky et al. received insight from Kwaxsistalla Wathl'thla, a song keeper for the Kwakwaka'wakw people in Canada, into songs referencing the people's use of terraced gardens in intertidal zones along the Pacific Northwest coast for the cultivation of clams for consumption. Archaeological evidence of significant increases in clam size and abundance in that area concurrent with the documented past implementation of the method described in the songs supports the conclusion that ______

Which choice most logically completes the text?

**A.** the practice used by ancestors of modern Kwakwaka'wakw people not only effectively maintained a food source but also promoted its robustness. **(Correct)**

  *Correct. Archaeological evidence shows clam size and abundance significantly increased alongside implementation of the terraced-garden method described in the songs — directly supporting that the practice not only sustained the food source but also strengthened it.*

**B.** non-Indigenous people around the Pacific Northwest coast adopted the practice developed by the Kwakwaka'wakw people after observing its efficacy. 

  *Adoption of the practice by outside groups is never discussed — this claim is entirely invented.*

**C.** there is greater corroboration in the archaeological record of ecological practices described in Kwakwaka'wakw songs than of those described in Sakha and Kaluli songs. 

  *No archaeological corroboration for Sakha or Kaluli songs is discussed at all — they appear only as introductory examples, so no such comparison can be drawn.*

**D.** although contemporary Kwakwaka'wakw people have a deep understanding of and appreciation for the fishing and farming practices used by their ancestors, they no longer implement these practices themselves. 

  *Current-day practice status is never discussed — the passage concerns historical evidence for past implementation, not whether the practice continues or has stopped today.*

*Difficulty: hard*

---

##### Q37
> The Household, Income and Labour Dynamics in Australia Survey (HILDA) examines trends in economic well-being among 25,000 people in Australia unfolding over many years. As is true of most longitudinal studies, this need for years of data collection results in high costs. By contrast, a relatively straightforward fitness study, such as one that is merely trying to identify the percentage of regular exercisers in a city who do weight training, may not need a large budget because ______

Which choice most logically completes the text?

**A.** longitudinal methods are probably suitable for the fitness study. 

  *This contradicts the "by contrast" framing: the fitness study is explicitly set apart from the longitudinal HILDA study as a simpler, one-time survey, not another longitudinal design.*

**B.** it would be easy for HILDA researchers to add questions to their economic well-being study. 

  *Ease of modifying HILDA's survey questions is never discussed — this is an invented claim about the wrong study.*

**C.** 25,000 people is more than enough for HILDA to find trends in economic well-being. 

  *This misapplies HILDA's sample size to a claim about that study's own sufficiency, when the actual contrast being drawn is about study duration (longitudinal vs. one-time), not sample size adequacy.*

**D.** the fitness study can be done well without years of data collection. **(Correct)**

  *Correct. HILDA is expensive because it is longitudinal, requiring years of data collection. The fitness study is described as straightforward — just identifying a percentage at one point in time — meaning it doesn't need the years-long collection that drives up HILDA's costs, so it can be done well on a smaller budget.*

*Difficulty: medium*

---

##### Q38
> Marta Coll and colleagues' 2010 Mediterranean Sea biodiversity census reported approximately 17,000 species, nearly double the number reported in Carlo Bianchi and Carla Morri's 2000 census—a difference only partly attributable to the description of new invertebrate species in the interim. Another factor is that the morphological variability of microorganisms is poorly understood compared to that of vertebrates, invertebrates, plants, and algae, creating uncertainty about how to evaluate microorganisms as species. Researchers' decisions on such matters therefore can be highly consequential. Indeed, the two censuses reported similar counts of vertebrate, plant, and algal species, suggesting that ______

Which choice most logically completes the text?

**A.** Coll and colleagues reported a much higher number of species than Bianchi and Morri did largely due to the inclusion of invertebrate species that had not been described at the time of Bianchi and Morri's census. 

  *This contradicts the passage, which explicitly says the newly described invertebrates explain the gap "only partly," not largely.*

**B.** some differences observed in microorganisms may have been treated as variations within species by Bianchi and Morri but treated as indicative of distinct species by Coll and colleagues. **(Correct)**

  *Correct. Vertebrate, plant, and algal counts were similar between the censuses, ruling those groups out as the source of the near-doubling. Combined with the passage's point that microorganism classification is uncertain, the large gap is best explained by the two teams making different calls about what counts as a distinct microorganism species.*

**C.** Bianchi and Morri may have been less sensitive to the degree of morphological variation displayed within a typical species of microorganism than Coll and colleagues were. 

  *This asserts a specific direction — which team was more or less sensitive — that the passage's uncertainty framing doesn't support; it's equally possible Coll's team over-split species rather than Bianchi and Morri under-splitting them.*

**D.** the absence of clarity regarding how to differentiate among species of microorganisms may have resulted in Coll and colleagues underestimating the number of microorganism species. 

  *This reverses the likely direction: Coll's count was almost double Bianchi and Morri's, so if classification uncertainty explains the gap, it means Coll's team counted more species, not fewer — an overestimate relative to a stricter standard, not an underestimate.*

*Difficulty: sat-hardest*

---

##### Q39
> Researchers recently found that disruptions to an enjoyable experience, like a short series of advertisements during a television show, often increase viewers' reported enjoyment. Suspecting that disruptions to an unpleasant experience would have the opposite effect, the researchers had participants listen to construction noise for 30 minutes and anticipated that those whose listening experience was frequently interrupted with short breaks of silence would thus ______

Which choice most logically completes the text?

**A.** find the disruptions more irritating as time went on. 

  *This describes a change over time within the disrupted condition, not the comparison between disrupted and uninterrupted groups the researchers were actually predicting.*

**B.** rate the listening experience as more negative than those whose listening experience was uninterrupted. **(Correct)**

  *Correct. Disruptions to enjoyable experiences increase enjoyment; the researchers hypothesized disruptions to unpleasant experiences would have the "opposite effect" — meaning disruptions would make the unpleasant experience even more negative than it would be uninterrupted.*

**C.** rate the experience of listening to construction noise as lasting for less time than it actually lasted. 

  *The prediction concerns reported enjoyment or negativity of the experience, not perceived duration — this substitutes a different quantity than what was being tested.*

**D.** perceive the volume of the construction noise as growing softer over time. 

  *Perceived volume is never discussed — this is an entirely different dimension from the enjoyment or negativity ratings the study was designed to measure.*

*Difficulty: medium*

---

##### Q40
> German theater practitioner Bertolt Brecht (1898-1956) believed that theater should elicit an intellectual rather than an emotional response from audiences, provoking them to consider social and political realities that extend beyond the characters and events depicted onstage. Brecht's influence can be seen in English playwright Caryl Churchill's 1979 play Cloud 9: although the play sometimes invites empathetic reactions, it primarily works to engage audiences in an interrogation of patriarchy and colonialism, which it does by placing audiences at a distance, thereby encouraging them to ______

Which choice most logically completes the text?

**A.** focus on the characters' beliefs about social and political issues as revealed by the characters' actions. 

  *This contradicts Brecht's method: he wanted engagement extending beyond the characters and events onstage, and "placing audiences at a distance" works against close identification with characters' beliefs.*

**B.** reflect on social and political phenomena not directly related to patriarchy and colonialism. 

  *This directly contradicts the passage's statement that the play "primarily works to engage audiences in an interrogation of patriarchy and colonialism" specifically.*

**C.** recognize pertinent social and political parallels between Germany during Brecht's time and England at the time when Churchill was writing Cloud 9. 

  *No historical Germany-England parallel is discussed — the passage is about Brecht's theatrical philosophy influencing Churchill's method, not about a claim the play draws such a parallel.*

**D.** be dispassionate as they think critically about the social and political questions raised by the play. **(Correct)**

  *Correct. Brecht wanted an intellectual, not emotional, response, achieved through audience distance. Churchill's play similarly "places audiences at a distance," which — following Brecht's philosophy — encourages a dispassionate, critical engagement with the social and political questions the play raises.*

*Difficulty: hard*

---

##### Q41
> Archaeologists and historians used to believe that the Maya civilization during its Classic period (roughly 250-900) lacked agricultural marketplaces. One reason for this belief was that these scholars misunderstood the ecology of the regions the Maya inhabited. Marketplaces typically emerge because different individuals or groups want to trade resources they control for resources they don't control. Scholars seriously underestimated the ecological diversity of the Maya landscape and thus assumed that ______

Which choice most logically completes the text?

**A.** marketplaces likely would not have attracted many traders from outside the regions controlled by the Maya. 

  *The passage's mechanism concerns diversity within Maya lands themselves, not traders from beyond Maya-controlled territory — this shifts the scope to the wrong group.*

**B.** farming practices would have been largely the same throughout Maya lands even if the crops people produced varied significantly. 

  *This contradicts the underestimation of ecological diversity: if scholars underestimated diversity, they would have assumed crops did not vary significantly, not that crops varied while practices stayed uniform.*

**C.** marketplaces would not have enabled Maya people to acquire many products different from those they already produced. **(Correct)**

  *Correct. Marketplaces emerge from trading resources one group controls for resources another group controls, which requires ecological diversity across regions. Since scholars underestimated that diversity, they would have assumed there wasn't much different to trade for — that marketplaces wouldn't provide access to products much different from what people already produced.*

**D.** farmers would trade agricultural products only if they had already produced enough to meet their own needs. 

  *A subsistence-surplus condition like this is never discussed — the passage's mechanism concerns ecological diversity enabling complementary trade, not a threshold based on meeting one's own needs first.*

*Difficulty: sat-hardest*

---

##### Q42
> Scientists studying Mars long thought the history of its crust was relatively simple. One reason for this is that geologic and climate data collected by a spacecraft showed that the crust was largely composed of basalt, likely as a result of intense volcanic activity that brought about a magma ocean, which then cooled to form the planet's surface. A study led by Valerie Payré focused on additional information—further analysis of data collected by the spacecraft and infrared wavelengths detected from Mars's surface—that revealed the presence of surprisingly high concentrations of silica in certain regions on Mars. Since a planetary surface that formed in a mostly basaltic environment would be unlikely to contain large amounts of silica, Payré concluded that ______

Which choice most logically completes the text?

**A.** the information about silica concentrations collected by the spacecraft is likely more reliable than the silica information gleaned from infrared wavelengths detected from Mars's surface. 

  *Both types of data were used together in Payré's study, and no claim about the relative reliability of one data source over the other is made anywhere in the passage.*

**B.** high silica concentrations on Mars likely formed from a different process than that which formed the crusts of other planets. 

  *No other planets' crust-formation processes are discussed or compared — this is an invented comparison.*

**C.** having a clearer understanding of the composition of Mars's crust and the processes by which it formed will provide more insight into how Earth's crust formed. 

  *Earth is never mentioned in the passage — this claimed benefit to Earth science is entirely invented.*

**D.** Mars's crust likely formed as a result of other major geological events in addition to the cooling of a magma ocean. **(Correct)**

  *Correct. The crust was thought to be simply basalt from a cooled magma ocean, but a mostly basaltic environment is unlikely to contain large amounts of silica. Since high silica concentrations were found, something else must have contributed to forming the surface — meaning the crust's history involves more than just magma-ocean cooling.*

*Difficulty: hard*

---

##### Q43
> The Hubble Space Telescope (HST) is projected to maintain operation until at least 2030, but it has already revolutionized high-resolution imaging of solar-system bodies in visible and ultraviolet (UV) light wavelengths, notwithstanding that only about 6% of the bodies imaged by the HST are within the solar system. NASA researcher Cindy L. Young and colleagues assert that a new space telescope dedicated exclusively to solar-system observations would permit an extensive survey of minor solar-system bodies and long-term UV observation to discern how solar-system bodies change over time. Young and colleagues' recommendation therefore implies that the HST ______

Which choice most logically completes the text?

**A.** will likely continue to be used primarily to observe objects outside the solar system. **(Correct)**

  *Correct. Only about 6% of bodies imaged by the HST are within the solar system, meaning roughly 94% are outside it — HST is already used primarily for non-solar-system objects. Young's recommendation is for a new, dedicated solar-system telescope to complement it, implying the HST would likely continue on its existing primary track.*

**B.** will no longer be used to observe solar system objects if the telescope recommended by Young and colleagues is deployed. 

  *This overreaches into total exclusion — the recommendation is for a complementary dedicated telescope, not evidence that the HST would stop all solar-system observation.*

**C.** can be modified to observe the features of solar system objects that are of interest to Young and colleagues. 

  *Modifying the HST's own capabilities is never discussed — the recommendation is to build a new telescope, not to retrofit the HST.*

**D.** lacks the sensors to observe the wavelengths of light needed to discern how solar-system bodies change over time. 

  *This contradicts the passage, which states the HST already images objects "in visible and ultraviolet (UV) light wavelengths" — a dedicated telescope would allow more extensive, long-term observation, not compensate for a total lack of the needed sensors.*

*Difficulty: hard*

---

##### Q44
> Geoglyphs are large-scale designs of lines or shapes created in a natural landscape. The Nazca Lines were created in the Nazca Desert in Peru by several Indigenous civilizations over a period of many centuries. Peruvian archaeologist Johny Isla specializes in these geoglyphs. At a German exhibit about the Nazca Lines, he saw an old photograph of a large geoglyph of a whalelike figure and was surprised that he didn't recognize it. Isla returned to Peru and used a drone to search a wide area, looking for the figure from the air. This approach suggests that Isla thought that if he hadn't already seen it, the whalelike geoglyph ______

Which choice most logically completes the text?

**A.** must represent a species of whale that went extinct before there were any people in Peru. 

  *This invented biological claim about an extinct whale species is unrelated to why Isla used a drone to search for the geoglyph's location.*

**B.** is actually located in Germany, not Peru, and isn't part of the Nazca Lines at all. 

  *This contradicts the passage: Isla returned to Peru specifically to search for the geoglyph with a drone, indicating he believed it was located in Peru and was part of the Nazca Lines, which the photograph was explicitly about.*

**C.** is probably in a location Isla hadn't ever come across while on the ground. **(Correct)**

  *Correct. Isla, an expert who specializes in these geoglyphs, didn't recognize the figure despite his expertise, then searched a wide area using an aerial drone rather than doubting the geoglyph's existence. That behavior suggests he suspected it existed somewhere he simply hadn't physically encountered on the ground.*

**D.** was almost certainly created a long time after the other Nazca Lines geoglyphs were created. 

  *Relative dating of this geoglyph compared to others is never discussed — searching by drone for an unseen location says nothing about when it was made.*

*Difficulty: medium*

---

##### Q45
> Indigenous cultures possess unique knowledge of the medicinal uses of plants. According to a 2021 study, 73 percent of the medicinal uses of plants native to North America are reflected in the vocabulary of a single Indigenous language. However, as more and more Indigenous people exclusively speak a globally dominant language, such as English, their ancestral languages fade from daily use. This lends added importance to tribal nations' efforts to preserve their languages. By ensuring the continued use of Cherokee, Ojibwe, and the hundreds of other Indigenous languages in what is now the United States, tribal nations are also ______

Which choice most logically completes the text?

**A.** increasing the number of medicinal plants represented in the vocabularies of Indigenous languages. 

  *This reverses the direction: preserving a language preserves its existing vocabulary and the knowledge already encoded in it — it doesn't add new medicinal-use terms or increase a plant count.*

**B.** transmitting terms for medicinal plants from Indigenous languages to globally dominant languages. 

  *This reverses the passage's actual concern, which is Indigenous languages fading as globally dominant languages take over — not Indigenous vocabulary being transmitted into those dominant languages.*

**C.** preserving knowledge about the medicinal value of plants native to the tribal nations' lands. **(Correct)**

  *Correct. Since a majority of medicinal plant uses are encoded in the vocabulary of Indigenous languages, preserving those languages — Cherokee, Ojibwe, and the rest — simultaneously preserves the medicinal knowledge embedded in that vocabulary.*

**D.** ensuring that citizens of tribal nations have physical access to medicinal plants. 

  *The passage is about linguistic and knowledge preservation, not about physical access to the plants themselves — this substitutes a different kind of access for the one actually discussed.*

*Difficulty: medium*

---

##### Q46
> Laura Mulvey has theorized that in narrative film, shots issuing from a protagonist's point of view compel viewers to identify with the character. Such identification is heightened by "invisible editing," or editing so inconspicuous that it renders cuts between shots almost unnoticeable. Conversely, Mulvey proposes that conspicuous editing or an absence of point-of-view shots would induce a more critical stance toward a protagonist. Consider, for example, the attic scene in Alfred Hitchcock's The Birds, a conspicuously edited sequence of tens of shots, few of which correspond to the protagonist's point of view. According to Mulvey's logic, this scene should affect viewers by ______

Which choice most logically completes the text?

**A.** obscuring their awareness of the high degree of artifice involved in constructing the montage. 

  *This reverses Mulvey's logic: conspicuous editing by definition draws attention to the constructed, artificial nature of the editing rather than hiding it — invisible editing, not conspicuous editing, is what obscures artifice.*

**B.** lessening their identification with the protagonist, if not alienating them from the character altogether. **(Correct)**

  *Correct. Mulvey's theory holds that conspicuous editing and an absence of point-of-view shots induce a more critical stance toward a protagonist. The attic scene is both conspicuously edited and mostly non-point-of-view, matching both conditions that Mulvey says reduce identification.*

**C.** compelling them to identify with the film's director, whose proxy is the camera, and not with the protagonist. 

  *This invented claim about director-identification is not part of Mulvey's theory as described, which contrasts protagonist-identification with critical distance, not director-identification.*

**D.** diverting their attention away from the film's content and toward its stylistic attributes. 

  *Mulvey's stated theory is specifically about identification with versus critical distance from the protagonist, not about attention shifting from content to style — this substitutes a different claim than the one the passage describes.*

*Difficulty: sat-hardest*

---

##### Q47
> Many animals, including humans, must sleep, and sleep is known to have a role in everything from healing injuries to encoding information in long-term memory. But some scientists claim that, from an evolutionary standpoint, deep sleep for hours at a time leaves an animal so vulnerable that the known benefits of sleeping seem insufficient to explain why it became so widespread in the animal kingdom. These scientists therefore imply that ______

Which choice most logically completes the text?

**A.** prolonged deep sleep is likely advantageous in ways that have yet to be discovered. **(Correct)**

  *Correct. These scientists claim the known benefits of sleep (healing, memory) don't seem sufficient to explain its evolutionary persistence despite its vulnerability risk — implying there must be other, not-yet-known benefits that justify sleep's widespread evolutionary success.*

**B.** most traits perform functions that are hard to understand from an evolutionary standpoint. 

  *This expands from a specific claim about sleep to a sweeping claim about most evolutionary traits in general — a scope the passage never supports.*

**C.** it is more important to understand how widespread prolonged deep sleep is than to understand its function. 

  *This prescriptive priority claim is never made, and it's self-contradictory in context — the scientists' entire claim is about function, that known functions are insufficient to explain sleep's spread.*

**D.** many traits that provide significant benefits for an animal also likely pose risks to that animal. 

  *This again expands from the passage's specific claim about sleep to a general biological principle about many traits, which is never stated.*

*Difficulty: hard*

---

##### Q48
> Researchers Suchithra Rajendran and Maximilian Popfinger modeled varying levels of passenger redistribution from short-haul flights (flights of 50 to 210 minutes, from takeoff to landing) to high-speed rail trips. Planes travel faster than trains, but air travel typically requires 3 hours of lead time for security, baggage handling, and boarding that rail travel doesn't, so short-haul routes take similar amounts of time by air and by rail. However, the model suggests that as rail passenger volumes approach current capacity limits, long lead times emerge. Therefore, for rail to remain a viable alternative to short-haul flights, ______

Which choice most logically completes the text?

**A.** rail systems should offer fewer long-haul routes and airlines should offer more long-haul routes. 

  *The passage is entirely about short-haul routes — long-haul routes are never discussed at all.*

**B.** rail systems may need to schedule additional trains for these routes. **(Correct)**

  *Correct. Rail's advantage over short-haul flights depends on avoiding long lead times, but the model shows those lead times emerge as rail approaches capacity limits. To preserve that advantage, rail systems would need to increase capacity — for example, by scheduling additional trains — to avoid hitting those limits.*

**C.** security, baggage handling, and boarding procedures used by airlines may need to be implemented for rail routes. 

  *This is the opposite of what would help: those procedures are exactly what makes air travel require 3 hours of lead time in the first place, so adding them to rail would undermine, not preserve, rail's competitive advantage.*

**D.** passengers who travel by rail for these routes will need to accept that lead times will need to be similar to those for air. 

  *This describes rail losing its advantage and becoming non-viable — the outcome if the capacity problem isn't addressed — which is the opposite of what's needed for rail to remain viable.*

*Difficulty: hard*

---

##### Q49
> Henry Ossawa Tanner's 1893 painting The Banjo Lesson, which depicts an elderly man teaching a boy to play the banjo, is regarded as a landmark in the history of works by Black artists in the United States. Scholars should be cautious when ascribing political or ideological values to the painting, however: beliefs and assumptions that are commonly held now may have been unfamiliar to Tanner and his contemporaries, and vice versa. Scholars who forget this fact when discussing The Banjo Lesson therefore ______

Which choice most logically completes the text?

**A.** risk judging Tanner's painting by standards that may not be historically appropriate. **(Correct)**

  *Correct. The caution given is that present-day beliefs and assumptions may not have been shared by Tanner or his contemporaries, and vice versa. Scholars who forget this risk imposing modern-day standards onto a historical work — anachronistically judging it by standards that may not fit its original context.*

**B.** tend to conflate Tanner's political views with those of his contemporaries. 

  *This describes a different error — mixing up individuals within the same era — rather than the passage's actual concern, which is mixing up beliefs across different eras.*

**C.** forgo analyzing Tanner's painting in favor of analyzing his political activity. 

  *Neglecting the painting in favor of biographical political activity is never discussed — this alternative behavior is invented.*

**D.** wrongly assume that Tanner's painting was intended as a critique of his fellow artists. 

  *This oddly specific claim about a critique of fellow artists has no basis in the passage, which never suggests this particular misreading.*

*Difficulty: medium*

---

##### Q50
> A heliograph is a semaphore device used for sending optical communications—usually in the form of Morse code—by reflecting flashes of sunlight off a mirror. Heliographs were used for rapid communication across expansive distances for military, surveying, and forestry purposes during the late nineteenth and early twentieth centuries, but they were largely effective only during the daytime, and the range of the device depended on factors such as the opacity of the air and line of sight. Therefore, heliographs were eventually replaced by technology that ______

Which choice most logically completes the text?

**A.** worked on similar principles but was easier to produce and maintain. 

  *Ease of production and maintenance is not the limitation discussed — the passage's stated limitations are about environmental and timing constraints on functionality, not manufacturing difficulty.*

**B.** was not so constrained by environmental circumstances. **(Correct)**

  *Correct. Heliographs' limitations were being daytime-only and dependent on environmental factors like air opacity and line of sight. Replacement technology, following logically from those specific limitations, would overcome those environmental constraints.*

**C.** could be used for more than military, surveying, or forestry purposes. 

  *Expanding the range of use cases isn't the limitation being addressed — the passage's issue is environmental and functional constraints, not the range of application domains.*

**D.** enabled communication that didn't require knowledge of Morse code. 

  *Morse code encoding is never described as a limitation — the stated limitations are daytime-only operation and environmental dependency, not the encoding scheme used.*

*Difficulty: medium*

---

##### Q51
> Tides can deposit large quantities of dead vegetation within a salt marsh, smothering healthy plants and leaving a salt panne—a depression devoid of plants that tends to trap standing water—in the marsh's interior. Ecologist Kathryn Beheshti and colleagues found that burrowing crabs living within these pannes improve drainage by loosening the soil, leading the pannes to shrink as marsh plants move back in. At salt marsh edges, however, crab-induced soil loosening can promote marsh loss by accelerating erosion, suggesting that the burrowing action of crabs ______

Which choice most logically completes the text?

**A.** can be beneficial to marshes with small pannes but can be harmful to marshes with large pannes. 

  *This frames the distinction as panne size, but the passage's actual contrast is between the marsh interior (pannes) and the marsh edges — a location distinction, not a size distinction.*

**B.** may promote increases in marsh plants or decreases in marsh plants, depending on the crabs' location. **(Correct)**

  *Correct. In panne interiors, crab burrowing improves drainage, shrinking pannes and letting marsh plants return — an increase. At marsh edges, crab burrowing accelerates erosion, promoting marsh loss — a decrease. This is exactly a location-dependent dual effect.*

**C.** tends to be more heavily concentrated in areas of marsh interiors with standing water than at marsh edges. 

  *Relative crab density or concentration by location is never discussed — the passage describes only the differing effects of crab burrowing at each location.*

**D.** varies in intensity depending on the size of the panne relative to the surrounding marsh. 

  *No comparison of panne size to marsh size, or of intensity varying with such a ratio, is discussed — the actual variable is location (interior panne versus edge), not relative size.*

*Difficulty: hard*

---

##### Q52
> "Gestures" in painting are typically thought of as bold, expressive brushstrokes. In the 1970s, American painter Jack Whitten built a 12-foot (3.7-meter) tool he named the "developer" to apply paint to an entire canvas in one motion, resulting in his series of "slab" paintings from that decade. Whitten described this process as making an entire painting in "one gesture," signaling a clear departure from the prevalence of gestures in his work from the 1960s. Some art historians claim this shift represents "removing gesture" from the process. Therefore, regardless of whether using the developer constitutes a gesture, both Whitten and these art historians likely agree that ______

Which choice most logically completes the text?

**A.** any tool that a painter uses to create an artwork is capable of creating gestures. 

  *This is a sweeping generalization about all tools that neither Whitten nor the historians make — the passage discusses one specific tool and disagreement about whether it counts, not a general claim about every tool.*

**B.** Whitten's work from the 1960s exhibits many more gestures than his work from the 1970s does. **(Correct)**

  *Correct. Whitten himself describes the 1970s developer process as "one gesture," a clear departure from the prevalence of gestures in his 1960s work — implying the 1960s work had many gestures. The art historians go further, saying the shift "removes gesture" entirely. Regardless of who is right about the developer itself, both agree the 1960s work had far more gestures than the 1970s work.*

**C.** Whitten became less interested in exploring the role of gesture in his work as his career progressed. 

  *This contradicts the implication of continued engagement: Whitten explicitly frames the developer process as making "one gesture," suggesting sustained interest in the concept even as its form changed, not diminished interest.*

**D.** Whitten's work from the 1960s is much more realistic than his work from the 1970s is. 

  *Realism or representational quality is never discussed at all — the passage is entirely about the concept of gesture, not visual realism.*

*Difficulty: sat-hardest*

---

##### Q53
> During the Bourbon Restoration in France (1814-1830), the right to vote required in part that a person paid at least 300 francs in direct taxes to the government. The four most common taxes (the quatre vieilles) were levied on real estate (both land and buildings); the doors and windows in taxpayer homes; the rental values of homes; and the businesses of artisans and merchants. (Foreign investments were either exempt from taxation or taxed lightly.) Although relatively few people paid the tax on real estate, it was the main means of voter qualification and accounted for over two-thirds of government receipts during this period, suggesting that during the Bourbon Restoration ______

Which choice most logically completes the text?

**A.** those people who had the right to vote most likely had substantial holdings of French real estate. **(Correct)**

  *Correct. The real estate tax was the "main means of voter qualification" and accounted for most government receipts despite being paid by "relatively few people" — meaning those few taxpayers paid large amounts, implying substantial real estate holdings among those who could vote through this route.*

**B.** the voting habits of French artisans and merchants were effective in reducing tax burdens on businesses. 

  *Voting behavior affecting tax policy is never discussed, and the artisan/merchant tax is a separate, minor category from the real estate tax central to voter qualification.*

**C.** the number of doors and windows in French residences was kept to a minimum but increased after 1830. 

  *1830 marks the end of the Bourbon Restoration period being discussed, and nothing about tax-related behavior after that date is mentioned.*

**D.** French people with significant foreign investments were unlikely to have the right to vote. 

  *Foreign investments were lightly taxed or exempt, meaning wealthy people with other qualifying assets — like real estate — could still meet the voting threshold regardless of foreign holdings; nothing suggests foreign-investment holders specifically lacked real estate.*

*Difficulty: sat-hardest*

---

##### Q54
> Mosses can struggle in harsh desert conditions because these plants require enough sunlight for photosynthesis but not so much that they risk drying out. Researchers Jenna Ekwealor and Kirsten M. Fisher found several species of Syntrichia caninervis, a type of desert moss, growing under quartz crystals in California's Mojave Desert. To evaluate whether these semitransparent rocks benefited the moss, the researchers compared the shoot tissue, a measure of plant growth, of S. caninervis when growing on the soil surface versus when the moss was growing under the quartz rocks. They found that the shoot tissue was 62% longer for moss growing under the quartz as compared to moss on the soil surface, suggesting that ______

Which choice most logically completes the text?

**A.** S. caninervis is one of the few types of moss that can survive under semitransparent rocks. 

  *No comparison to other moss species' ability to survive under rocks is made — the study concerns one species' growth in two conditions, not a cross-species survival comparison.*

**B.** quartz crystals do not transmit the necessary sunlight for photosynthesis in S. caninervis. 

  *This contradicts the growth data: moss under quartz grew 62% more than moss on open soil, meaning photosynthesis clearly still occurred there — evidence of thriving, not light starvation.*

**C.** S. caninervis growing under quartz crystals experience lower light intensity and are thus able to retain more moisture. **(Correct)**

  *Correct. Mosses need some sunlight but not so much that they dry out. Since quartz is semitransparent, it likely filters light while still allowing enough through for photosynthesis, reducing light intensity and helping the moss retain moisture — avoiding the drying-out risk and explaining the better growth observed.*

**D.** quartz crystals are capable of supporting S. caninervis growth if the crystals are not too thin. 

  *No thickness variable or threshold for the crystals is discussed anywhere in the passage — this condition is invented.*

*Difficulty: hard*

---

##### Q55
> To better understand the burrowing habits of Alpheus bellulus (the tiger pistol shrimp), some studies have used resin casting to obtain precise measurements of the shrimps' burrows. Resin casting involves completely filling an empty burrow with a liquid plastic that hardens to create a three-dimensional model; however, recovering the model inevitably requires destroying the burrow. In their 2022 study, Miyu Umehara and colleagues discovered that an x-ray computed tomography (CT) scanner can accurately record a burrow's measurements both at a moment in time and throughout the entire burrow-building process, something that's impossible with resin casting because ______

Which choice most logically completes the text?

**A.** it can only be used on burrows below a certain size. 

  *No size constraint on resin casting is discussed anywhere in the passage — the stated limitation is destruction upon recovery, not a size threshold.*

**B.** it does not allow for multiple castings of the same burrow over time. **(Correct)**

  *Correct. Recovering a resin cast destroys the burrow, meaning it can only be measured once, at that single destructive moment. That makes it impossible to track a burrow throughout its building process, which requires repeated measurements of the same burrow over time — something a non-destructive CT scan can do instead.*

**C.** the casting process takes more time than A. bellulus takes to construct a burrow. 

  *This fabricated comparison of casting speed versus construction speed is never made — the actual limitation is destructiveness, not slowness.*

**D.** the process of recovering the model distorts the resin's shape. 

  *The passage says recovery "requires destroying the burrow," not that it distorts the resin cast itself — this misattributes the destruction to the wrong object.*

*Difficulty: hard*

---

##### Q56
> Conventional theories of rhetoric hold that presenting information as coming from credentialed experts increases that information's credibility. When communications researcher Sungkyoung Lee and her colleagues tested messages seeking volunteers for clinical trials, however, they found that participants in their study judged recruitment messages from former trial volunteers as significantly more credible than messages from doctors (i.e., credentialed experts). One reason for this may be that the doctors' status as credentialed experts wasn't ignored but rather was outweighed by participants' views of the experiential relevance of the two types of messengers; that is, participants may have reacted the way they did because ______

Which choice most logically completes the text?

**A.** messages from former trial volunteers depicted clinical trials as being more positive experiences than did messages from doctors. 

  *This introduces a content or tone difference between the messages that isn't discussed — the passage's explanation concerns experiential relevance of the messenger, not positive versus negative framing of the message.*

**B.** participants did not have enough experience to evaluate the credibility of the doctors' messages but did have experience to evaluate the credibility of former trial volunteers' messages. 

  *This misreads "experiential relevance" as being about participants' own ability to judge each messenger, rather than about which messenger's personal experience is relevant to the trial-volunteering decision.*

**C.** the fact that former trial volunteers went through the same experience that participants were contemplating while doctors did not was more important to participants than the doctors' status as credentialed experts was. **(Correct)**

  *Correct. The passage explains that the doctors' expert status "wasn't ignored but... was outweighed by participants' views of the experiential relevance" of the two messenger types. This choice directly captures that logic: participants weighed the volunteers' lived, relevant experience above the doctors' credentials.*

**D.** participants regarded the experiences of both the doctors and former trial volunteers as relevant to the subject of clinical trials but were skeptical of the doctors' status as credentialed experts. 

  *This contradicts the passage, which explicitly says credentialed status "wasn't ignored" — not that it was doubted or discounted — just that it was outweighed by another factor.*

*Difficulty: sat-hardest*

---

##### Q57
> During their larval phase, numerous species of coral reef fish are drawn toward areas where light is present. To better understand how artificial light at night (ALAN) might affect some coral reef fish, researchers explored the effect of exposure to low levels of ALAN on the reproductive success of the common clownfish (Amphiprion ocellaris). While exposure to low levels of ALAN had no significant effect on spawning frequency and egg fertilization in A. ocellaris, incubation in the presence of ALAN completely inhibited hatching. These findings suggest that ______

Which choice most logically completes the text?

**A.** A. ocellaris that settle in areas with low levels of ALAN have significantly higher rates of successful egg fertilization than A. ocellaris that settle in areas without ALAN do. 

  *This contradicts the passage, which says ALAN had "no significant effect" on egg fertilization — the opposite of a significantly higher fertilization rate due to ALAN.*

**B.** the reproductive success of A. ocellaris would be at risk if they were to selectively settle in regions that are regularly exposed to low levels of ALAN. **(Correct)**

  *Correct. Even though low ALAN doesn't affect spawning frequency or fertilization, it completely inhibits hatching during incubation — a devastating effect on reproduction overall. If clownfish were to settle in and be regularly exposed to ALAN through their reproductive cycle, their reproductive success would be severely compromised.*

**C.** the reproductive success of A. ocellaris is more greatly affected by the presence of low levels of ALAN during incubation than the reproductive success of other species of coral reef fish is. 

  *No other species' reproductive response to ALAN is discussed or compared — this cross-species comparison is invented.*

**D.** the spawning frequency of A. ocellaris was more strongly affected by the presence of low levels of ALAN than egg fertilization was, though both were less affected than incubation. 

  *This contradicts the passage, which says ALAN had no significant effect on both spawning frequency and egg fertilization equally — inventing a distinction between two things stated to be equally unaffected.*

*Difficulty: hard*

---

##### Q58
> Overgrazing by purple sea urchins has caused many kelp forests along North America's west coast to be replaced by urchin barrens—areas stripped of vegetation and covered in purple sea urchins. Urchins in barrens persist in a state of starvation that lessens their nutritional value—and thus their appeal—to many predators. Sarah Gravem and colleagues placed sunflower sea stars, a once-abundant predator species suffering massive population declines in recent years, in aquariums that each contained a nutritionally poor and a nutritionally rich purple sea urchin. The researchers found that the sea stars selected the nutritionally rich urchin in 42.7% of trials and the nutritionally poor urchin in 37.5% of trials, suggesting that ______

Which choice most logically completes the text?

**A.** sunflower sea stars are willing to hunt sea urchins, but if given a choice, they will prey on other more nutritious marine animals instead. 

  *The experiment's choice was between two types of urchins, not between urchins and other prey species — no other prey species are introduced or compared.*

**B.** sunflower sea stars are reluctant to feed on both nutritionally poor and nutritionally rich sea urchins and are therefore unlikely to thrive in kelp forests. 

  *This contradicts the data: sea stars selected one urchin type or the other in over 80% of trials combined, showing meaningful consumption of both types rather than general reluctance to feed on either.*

**C.** sunflower sea stars are less likely to consume sea urchins in barrens than other species of sea stars are, putting sunflower sea stars at high risk of extinction. 

  *No other sea star species' urchin consumption is presented or compared in the passage — this comparison is invented.*

**D.** sunflower sea stars do not avoid foraging on nutritionally poor sea urchins, making sunflower sea star population recovery a potentially important tool for controlling urchin barrens. **(Correct)**

  *Correct. Sea stars selected the nutritionally poor urchin in 37.5% of trials, nearly as often as the nutritionally rich one, showing they don't strongly avoid poor-nutrition urchins — unlike other predators, whom starved urchins lose appeal to. Since sunflower sea stars will still eat the poor-nutrition urchins found in barrens, restoring their declining population could help control those barrens.*

*Difficulty: sat-hardest*

---

##### Q59
> In a three-year study of parasitic infections by Anomotaenia brevis tapeworms in Temnothorax nylanderi ants, entomologist Susanne Foitzik and colleagues found something unexpected: rather than reducing its host's fitness, as is typical of parasites, A. brevis greatly extends the lifespan of a T. nylanderi worker ant and seems to halt the effects of aging. Furthermore, those infected receive special treatment, ceasing their share of labor to sustain the colony and remaining in the nest as uninfected workers feed, groom, and transport them. By contrast, the researchers observed that uninfected workers in parasitized colonies have shortened lifespans, most likely because the ______

Which choice most logically completes the text?

**A.** uninfected workers are at high risk for direct exposure to A. brevis in the course of providing social care to the infected workers in the nest. 

  *The passage never suggests the shortened lifespan comes from catching the parasite through caregiving contact — infected workers are framed as recipients of care, and infection risk to caregivers is never discussed.*

**B.** need to compensate for reduced contributions within the colony while also caring for infected workers is burdensome to the uninfected workers. **(Correct)**

  *Correct. Infected workers stop contributing labor entirely while still needing care — fed, groomed, and transported by uninfected workers. This means uninfected workers must make up for the missing labor and provide extra caretaking, a doubled burden that plausibly explains their shortened lifespans.*

**C.** high level of activity maintained by the uninfected workers makes them better able than infected workers to quickly disperse when the nest is attacked by a predator. 

  *This invented, unrelated claim about predator response has nothing to do with why lifespans would be shortened — if anything it would suggest a survival benefit, not a shortened lifespan.*

**D.** average lifespan of T. nylanderi worker ants in colonies without parasitic activity typically falls well below three years, the range covered by the study. 

  *This reframes the finding as being about a baseline lifespan rather than explaining why lifespan is shortened specifically due to the presence of infected workers, and it invents a specific duration claim never given in the passage.*

*Difficulty: hard*

---

##### Q60
> In the early nineteenth century, some Euro-American farmers in the northeastern United States used agricultural techniques developed by the Haudenosaunee (Iroquois) people centuries earlier, but it seems that few of those farmers had actually seen Haudenosaunee farmers firsthand. Barring the possibility of several farmers of the same era independently developing techniques that the Haudenosaunee people had already invented, these facts most strongly suggest that ______

Which choice most logically completes the text?

**A.** those farmers learned the techniques from other people who were more directly influenced by Haudenosaunee practices. **(Correct)**

  *Correct. Few farmers saw Haudenosaunee farmers firsthand, and independent reinvention is ruled out. The techniques must therefore have spread through some intermediary chain — learned from others who had more direct contact with Haudenosaunee practices, rather than directly from the Haudenosaunee themselves.*

**B.** the crops typically cultivated by Euro-American farmers in the northeastern United States were not well suited to Haudenosaunee farming techniques. 

  *Crop suitability is never discussed — the passage concerns how the techniques were transmitted, not whether they were compatible with particular crops.*

**C.** Haudenosaunee farming techniques were widely used in regions outside the northeastern United States. 

  *No claim about geographic spread beyond the northeastern United States is made anywhere in the passage — this is invented.*

**D.** Euro-American farmers only began to recognize the benefits of Haudenosaunee farming techniques late in the nineteenth century. 

  *This contradicts the passage, which explicitly states this is about the early nineteenth century, not late in the century.*

*Difficulty: hard*

---

##### Q61
> One theory behind human bipedalism speculates that it originated in a mostly ground-based ancestor that practiced four-legged "knuckle-walking," like chimpanzees and gorillas do today, and eventually evolved into moving upright on two legs. But recently, researchers observed orangutans, another relative of humans, standing on two legs on tree branches and using their arms for balance while they reached for fruits. These observations may suggest that ______

Which choice most logically completes the text?

**A.** bipedalism evolved because it was advantageous to a tree-dwelling ancestor. **(Correct)**

  *Correct. The standard theory says bipedalism arose from a ground-based knuckle-walking ancestor. The new observation of tree-dwelling orangutans standing bipedally to reach fruit suggests an alternative: bipedalism could have originated because it was useful to a tree-dwelling ancestor, challenging the ground-based origin story.*

**B.** bipedalism must have evolved simultaneously with knuckle-walking and tree-climbing. 

  *This overreaches into an oddly specific claim about simultaneous co-evolution of three separate behaviors — the orangutan observation suggests an alternative pathway, not a claim about simultaneous development of all three.*

**C.** moving between the ground and the trees would have been difficult without bipedalism. 

  *This reverses the observation: orangutans are shown standing bipedally to reach fruit within a tree, and nothing establishes bipedalism as necessary for moving between ground and trees generally.*

**D.** a knuckle-walking human ancestor could have easily moved bipedally in trees. 

  *This conflates the two competing hypotheses — describing the old theory's ground-based knuckle-walking ancestor as also moving bipedally in trees — rather than drawing out what the new orangutan observation actually suggests.*

*Difficulty: hard*

---

##### Q62
> The increased integration of digital technologies throughout the process of book creation in the late 20th and early 21st centuries lowered the costs of book production, but those decreased costs have been most significant in the manufacturing and distribution process, which occurs after the authoring, editing, and design of the book are complete. This suggests that in the late 20th and early 21st centuries, ______

Which choice most logically completes the text?

**A.** digital technologies made it easier than it had been previously for authors to write very long works and get them published. 

  *Work length and ease of long-form writing are never discussed — this claim is invented and unrelated to the cost-stage comparison the passage draws.*

**B.** customers generally expected the cost of books to decline relative to the cost of other consumer goods. 

  *Customer expectations, and any comparison to the pricing of other consumer goods, are never discussed anywhere in the passage.*

**C.** publishers increased the variety of their offerings by printing more unique titles but also printed fewer copies of each title. 

  *This invented, specific business-strategy claim about title variety and print runs is never addressed by the passage.*

**D.** the costs of writing, editing, and designing a book were less affected than were the costs of manufacturing and distributing a book. **(Correct)**

  *Correct. The passage explicitly states cost decreases from digital technology have been "most significant" in manufacturing and distribution, which occurs after authoring, editing, and design — directly implying those earlier stages were less affected by the cost decreases.*

*Difficulty: medium*

---

##### Q63
> Volunteering, or giving time for a community service for free, is a valuable form of civic engagement because helping in a community is also good for society as a whole. In a survey of youths in the United States, most young people said that they believe volunteering is a way to help people on an individual level. Meanwhile, only 6% of the youths said that they think volunteering is a way to help fix problems in society overall. These replies suggest that ______

Which choice most logically completes the text?

**A.** many young people think they can volunteer only within their own communities. 

  *The geographic scope of volunteering is never discussed — the survey measures perceived type of benefit (individual versus societal), not the geographic location of volunteer work.*

**B.** volunteering may be even more helpful than many young people think it is. **(Correct)**

  *Correct. The passage establishes that volunteering benefits both individuals and society as a whole. The survey shows most youths recognize only the individual-level benefit, with just 6% recognizing the societal-level benefit — meaning young people's perception undersells volunteering's actual, established value.*

**C.** volunteering can help society overall more than it can help individual people. 

  *The passage never ranks the magnitude of individual versus societal benefit — it says volunteering is good for both, without establishing which effect is greater.*

**D.** many young people may not know how to find ways to volunteer their time. 

  *This is about access to volunteering opportunities, not about beliefs regarding volunteering's societal value, which is what the survey actually measured.*

*Difficulty: medium*

---

##### Q64
> Ancestral Puebloans, the civilization from which present-day Pueblo tribes descended, emerged as early as 1500 B.C.E. in an area of what is now the southwestern United States and dispersed suddenly in the late 1200s C.E., abandoning established villages with systems for farming crops and turkeys. Recent analysis comparing turkey remains at Mesa Verde, one such village in southern Colorado, to samples from modern turkey populations in the Rio Grande Valley of north central New Mexico determined that the latter birds descended in part from turkeys cultivated at Mesa Verde, with shared genetic markers appearing only after 1280. Thus, researchers concluded that ______

Which choice most logically completes the text?

**A.** conditions of the terrains in the Rio Grande Valley and Mesa Verde had greater similarities in the past than they do today. 

  *Terrain or geography is never discussed — the evidence used is genetic (turkey DNA), not environmental or geological.*

**B.** some Ancestral Puebloans migrated to the Rio Grande Valley in the late 1200s and carried farming practices with them. **(Correct)**

  *Correct. Mesa Verde was abandoned suddenly in the late 1200s, and modern Rio Grande Valley turkeys share genetic markers with Mesa Verde turkeys appearing only after 1280 — right around the dispersal. This timing match suggests people migrated from Mesa Verde to the Rio Grande Valley around that time, carrying their turkeys and farming practices with them.*

**C.** Indigenous peoples living in the Rio Grande Valley primarily planted crops and did not cultivate turkeys before 1280. 

  *This overreaches: the shared genetic markers appearing "only after 1280" refers specifically to Mesa Verde-descended markers, not to the total absence of any turkey cultivation in the Rio Grande Valley before that date.*

**D.** the modern turkey remains at Mesa Verde likely adopted the farming practices of Indigenous peoples living in the other regions. 

  *This reverses the finding's direction: the passage states Rio Grande Valley turkeys descended in part from turkeys cultivated at Mesa Verde, meaning Mesa Verde is the source, not that Mesa Verde adopted practices from elsewhere.*

*Difficulty: hard*

---

##### Q65
> Ratified by more than 90 countries, the Nagoya Protocol is an international agreement ensuring that Indigenous communities are compensated when their agricultural resources and knowledge of wild plants and animals are utilized by agricultural corporations. However, the protocol has shortcomings. For example, it allows corporations to insist that their agreements with communities to conduct research on the commercial uses of the communities' resources and knowledge remain confidential. Therefore, some Indigenous advocates express concern that the protocol may have the unintended effect of ______

Which choice most logically completes the text?

**A.** diminishing the monetary reward that corporations might derive from their agreements with Indigenous communities. 

  *This reverses whose interest is at stake: the passage's concern is about protecting and verifying compensation for Indigenous communities, not about limiting corporate profit.*

**B.** limiting the research that corporations conduct on the resources of the Indigenous communities with which they have signed agreements. 

  *Confidentiality restricts who can see the agreements or research outcomes, not whether the research itself happens — this conflates secrecy with restricting the actual research activity.*

**C.** preventing independent observers from determining whether the agreements guarantee equitable compensation for Indigenous communities. **(Correct)**

  *Correct. Because corporations can insist agreements remain confidential, that secrecy would prevent independent observers from reviewing the agreements to verify whether communities are receiving fair compensation as the protocol intends — undermining the protocol's own purpose through a lack of transparency.*

**D.** discouraging Indigenous communities from learning new methods for harvesting plants and animals from their corporate partners. 

  *This invented claim about knowledge flowing from corporations to communities reverses the passage's actual concern, which is protecting communities' own existing knowledge from being used by corporations, not communities learning from corporations.*

*Difficulty: hard*

---

##### Q66
> Many of William Shakespeare's tragedies address broad themes that still appeal to today's audiences. For instance, Romeo and Juliet, which is set in the Italy of Shakespeare's time, tackles the themes of parents versus children and love versus hate, and the play continues to be read and produced widely around the world. But understanding Shakespeare's so-called history plays can require a knowledge of several centuries of English history. Consequently, ______

Which choice most logically completes the text?

**A.** many theatergoers and readers today are likely to find Shakespeare's history plays less engaging than the tragedies. **(Correct)**

  *Correct. Tragedies like Romeo and Juliet address broad, universally relatable themes requiring no special background knowledge, hence their continued wide appeal. History plays require specialized historical knowledge — a barrier most contemporary audiences lack — making them likely less engaging by comparison.*

**B.** some of Shakespeare's tragedies are more relevant to today's audiences than twentieth-century plays. 

  *No comparison to twentieth-century plays, or to any specific other era's plays, is made anywhere in the passage — this comparison is invented.*

**C.** Romeo and Juliet is the most thematically accessible of all Shakespeare's tragedies. 

  *This makes an absolute superlative claim ranking Romeo and Juliet against every other Shakespearean tragedy, when the passage only uses it "for instance" as one example of tragedies broadly, without ranking it against the others.*

**D.** history plays require a knowledge of several centuries of English history. 

  *This simply restates a premise already given in the passage rather than drawing the new consequence that "Consequently" demands.*

*Difficulty: medium*

---

##### Q67
> In a 2017 article, historian Jasmine Kilburn-Toppin explains that in early modern London, members of the city's guilds (trade and artisanal associations) were participants in a civic culture in which gift giving both signaled and conferred social status. Research on this phenomenon has tended to focus on philanthropic gifting by London's largest guilds; for her part, Kilburn-Toppin focuses on the gifting of handmade objects and fixtures (such as decorative paneling or plasterwork) within the craft guilds, which were "composed of highly discerning producers and consumers of material cultures." Given this characterization, it can reasonably be inferred that the gifting of such objects may have ______

Which choice most logically completes the text?

**A.** ensured that knowledge of the materials and techniques used by members of the craft guilds stayed within the craft guilds. 

  *Knowledge secrecy or containment is never discussed — the passage is about gift-giving and social status, not about guarding technique or material knowledge.*

**B.** emphasized ostentatious offerings in the case of the largest guilds and prosaic objects in the case of the craft guilds. 

  *This contradicts the passage's characterization: craft guild gifts (decorative paneling, plasterwork) are described as coming from "highly discerning producers and consumers," which undersells them by calling them merely "prosaic."*

**C.** functioned as a way for craft guild members to maintain and enhance their professional reputations among their peers. **(Correct)**

  *Correct. Guild gift-giving "signaled and conferred social status" generally, and craft guilds specifically were "highly discerning producers and consumers of material cultures." Their handmade-object gifts, evaluated by fellow discerning craftspeople, would function as a way to demonstrate skill and maintain professional reputation among peers.*

**D.** conferred greater social status when the recipient belonged to one of London's largest guilds than when the recipient belonged to a craft guild. 

  *No comparison of the magnitude of social status conferred by guild type or size is made in the passage — this comparison is invented.*

*Difficulty: sat-hardest*

---

##### Q68
> With the ongoing expansion of e-commerce, consumers are expecting faster and faster delivery of goods, but delivery companies continue to struggle with last-mile logistics (the final step in delivery to consumers) due to challenges such as complex and inefficient delivery routes. Innovations to mitigate these challenges have been emerging—the use of aerial drones, for example—but these innovations tend to engender their own complications (e.g., regulations on the use of drones in residential airspace), leading researchers to conclude that ______

Which choice most logically completes the text?

**A.** consumers' expectations for reduced delivery times may be outstripping what is viable for delivery companies to provide. **(Correct)**

  *Correct. Consumers want ever-faster delivery, but delivery companies struggle with last-mile logistics, and even innovative solutions like drones create new complications rather than solving the problem. This suggests the trend of consumer expectations may be outpacing what companies can actually achieve given these persistent obstacles.*

**B.** a better understanding of consumers' expectations for delivery is needed so that companies can better plan for fluctuations in delivery volume. 

  *This prescriptive claim about understanding consumer demand isn't supported by the passage's evidence, which is about logistics and regulatory barriers, not about understanding demand better.*

**C.** rapid delivery is a leading factor in consumer satisfaction, and therefore delivery companies would benefit from investing resources in reducing delivery times. 

  *This ignores the passage's core point that ongoing innovation efforts are already hitting new complications, suggesting simple additional investment isn't guaranteed to solve the problem — and it recommends action rather than describing what the evidence shows.*

**D.** there may not be sufficient incentive for delivery companies to attempt to solve the problems associated with last-mile logistics. 

  *This contradicts the passage, which describes companies actively working on the problem through emerging innovations — directly contradicting a claim that there's insufficient incentive to even attempt solutions.*

*Difficulty: hard*

---

##### Q69
> Arthurian legends (tales related to the character of King Arthur) derive from many sources, such as Vita Sancti Cadoci, composed in the 11th century, and Culhwch and Olwen from the second half of the 12th century. One of the most significant sources, Geoffrey of Monmouth's History of the Kings of Britain, was written in the 1130s; some material from it was later adapted by the Norman poet Wace into the Roman de Brut in 1155. But Wace didn't merely adapt History, he added to it as well, introducing the famous Round Table at which Arthur's knights assembled, which suggests that ______

Which choice most logically completes the text?

**A.** Roman de Brut is more historically accurate than History, because Culhwch and Olwen had not been written when Geoffrey of Monmouth was writing his work. 

  *Historical accuracy is never discussed — the passage discusses which sources include which narrative elements and when, not the veracity of any account.*

**B.** Geoffrey of Monmouth was unaware of stories of the Round Table when composing his History, though historians know that works containing such stories were available to him. 

  *This contradicts the passage's clear statement that Wace added the Round Table — implying it wasn't in Geoffrey's earlier History — and there's no claim that Round Table stories existed elsewhere for Geoffrey to have drawn on.*

**C.** Geoffrey of Monmouth's accounts of Arthurian legends in his History are more similar overall in content to the accounts in Culhwch and Olwen than they are to the accounts in Roman de Brut. 

  *No such comparative content analysis between these specific works is made anywhere in the passage — this comparison is invented.*

**D.** the Arthurian legends that the author of Vita Sancti Cadoci drew on would not have featured the Round Table. **(Correct)**

  *Correct. The Round Table was introduced by Wace in 1155, added to Geoffrey's History (written in the 1130s), where it did not previously appear. Since Vita Sancti Cadoci was composed even earlier, in the 11th century, the Arthurian legends available to its author would predate the Round Table's 1155 introduction and thus would not have included it.*

*Difficulty: sat-hardest*

---

##### Q70
> The Mammillaria cactus M. boolii occurs naturally only in the state of Sonora in Mexico, and the smallness of its range makes it especially vulnerable to extinction. The traditional single-species approach to conservation emphasizes the need to focus on individual species most at risk, like M. boolii, but recently, conservationists have argued that an ecosystem-based approach that incorporates the many interactions between the climate, terrain, and various species of a given geographical area may lead to better outcomes for all the species in a given location. If this view is correct, the single-species approach to the conservation of M. boolii could thus ______

Which choice most logically completes the text?

**A.** lead to a better understanding of how the distribution of Mammillaria species throughout Mexico has affected their survival. 

  *This shifts scope to the entire Mammillaria genus across all of Mexico, when the passage is specifically about M. boolii, a single species in Sonora, and its interactions with the broader Sonora ecosystem, not genus-wide distribution.*

**B.** allow conservationists to better consider how climatic changes affecting Sonora may reduce the number of species competing with M. boolii. 

  *This reverses the critique: the single-species approach's flaw, per the ecosystem view, is that it does not adequately consider such broader ecological interactions, not that it enables better consideration of them.*

**C.** erroneously shift the focus of conservation efforts away from M. boolii itself. 

  *This is the opposite of the actual critique: the single-species approach focuses too narrowly and exclusively on M. boolii — that's its defining feature, per "focus on individual species most at risk, like M. boolii" — not away from it.*

**D.** fail to consider the ways in which the survival of M. boolii may be influenced by changes in the populations of other species that inhabit Sonora. **(Correct)**

  *Correct. The ecosystem-based approach argues species' survival depends on interactions with other species, climate, and terrain in the same location. A single-species approach, by focusing only on M. boolii in isolation, would fail to account for how changes in other Sonora species affect M. boolii's own survival — a direct consequence of accepting the ecosystem view's premise.*

*Difficulty: sat-hardest*

---

##### Q71
> One recognized social norm of gift giving is that the time spent obtaining a gift will be viewed as a reflection of the gift's thoughtfulness. Marketing experts Farnoush Reshadi, Julian Givi, and Gopal Das addressed this view in their studies of norms specifically surrounding the giving of gift cards, noting that while recipients tend to view digital gift cards (which can be purchased online from anywhere and often can be redeemed online as well) as superior to physical gift cards (which sometimes must be purchased in person and may only be redeemable in person) in terms of usage, 94.8 percent of participants surveyed indicated that it is more socially acceptable to give a physical gift card to a recipient. This finding suggests that ______

Which choice most logically completes the text?

**A.** gift givers likely overestimate the amount of effort required to use digital gift cards and thus mistakenly assume gift recipients will view them as less desirable than physical gift cards. 

  *This confuses effort to use a gift card with effort to obtain it — the social norm the passage opens with is specifically about time spent obtaining a gift, not effort to use it once received.*

**B.** physical gift cards are likely preferred by gift recipients because the tangible nature of those cards offers a greater psychological sense of ownership than digital gift cards do. 

  *This contradicts the passage, which says recipients view digital cards as superior "in terms of usage," and it misattributes the 94.8% finding — that figure is about givers' judgment of social acceptability, not recipients' own preference.*

**C.** physical gift cards are likely less desirable to gift recipients than digital gift cards are because of the perception that physical cards require unnecessary effort to obtain. 

  *This misattributes the effort-based reasoning to recipients' desirability judgment rather than givers' social-acceptability judgment, and it reverses the norm's direction — more effort to obtain should signal more thoughtfulness, not less desirability.*

**D.** gift givers likely perceive digital gift cards as requiring relatively low effort to obtain and thus wrongly assume gift recipients will appreciate them less than they do physical gift cards. **(Correct)**

  *Correct. The opening norm links effort to obtain a gift to perceived thoughtfulness. Digital cards can be bought online from anywhere (low effort), while physical cards sometimes require an in-person purchase (higher effort). Despite recipients rating digital cards as superior in usage, givers overwhelmingly still favor giving physical cards — consistent with givers assuming, per the norm, that a low-effort digital card will be appreciated less than it actually is.*

*Difficulty: sat-hardest*

---

### Standard English Conventions

#### Boundaries (95 items)

##### Q1
> While one requires oxygen and one does ______ and anaerobic respiration are both forms of cellular respiration—that is, they are processes by which cells break down glucose to use as energy.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** not aerobic 

  *Fuses the dependent clause directly into the independent clause with no mark at all. "While one requires oxygen and one does not" is dependent (subordinator "While" up front), so it cannot simply run into "aerobic and anaerobic respiration are both forms..." without a boundary.*

**B.** not. Aerobic 

  *Ends the sentence with a period after "not," but "While one requires oxygen and one does not" starts with the subordinator "While" and can never stand alone — punctuating it as a full sentence produces a fragment.*

**C.** not, aerobic **(Correct)**

  *Correct. "While one requires oxygen and one does not" is dependent; "aerobic and anaerobic respiration are both forms of cellular respiration" is independent. Dependent clause first takes a comma before the independent clause that follows.*

**D.** not; aerobic 

  *A semicolon requires an independent clause on its left. "While one requires oxygen and one does not" is dependent, so the semicolon fails here exactly as a period would.*

*Difficulty: medium*

---

##### Q2
> Human-made (synthetic) fibers used in clothes and many other consumer products are more durable than most natural plant ______ the manufacture of synthetic fibers requires toxic chemical solvents that can pollute air and water.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** fibers, 

  *Both sides are independent clauses in contrast, and a bare comma cannot join them. This is a comma splice.*

**B.** fibers but 

  *"But" is on the FANBOYS list, but the comma that has to come before it is missing. Independent-but-independent needs comma plus conjunction, not the conjunction alone.*

**C.** fibers 

  *No punctuation at all between two independent clauses is a fused sentence — the most extreme version of the same boundary error.*

**D.** fibers, but **(Correct)**

  *Correct. Two independent clauses in contrast, joined with a comma plus the FANBOYS conjunction "but."*

*Difficulty: medium*

---

##### Q3
> Emperor Ashoka ruled the Maurya Empire in South Asia from roughly 270 to 232 BCE. He is known for enforcing a moral code called the Law of Piety, which established the sanctity of animal ______ the just treatment of the elderly, and the abolition of the slave trade.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** life 

  *This is a three-item series — sanctity of animal life, just treatment of the elderly, abolition of the slave trade — and dropping the comma fuses the first two items into one.*

**B.** life; 

  *A semicolon is only needed in a series when the items themselves contain commas. None of these three items do, so the semicolon over-punctuates a plain series.*

**C.** life: 

  *A colon has no role in the middle of a list it did not introduce — nothing new is being announced at this exact point, just the next item in a series already underway.*

**D.** life, **(Correct)**

  *Correct. An ordinary series comma separating the first item from the second in a three-item list with no internal commas.*

*Difficulty: easy*

---

##### Q4
> A subseasonal weather forecast attempts to predict weather conditions three to four weeks in ______ its predictions are therefore more short-term than those of the seasonal forecast, which attempts to predict the weather more than a month in advance.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** advance, 

  *Both sides are independent clauses, and "therefore" inside the second clause is an adverb, not a conjunction — it cannot license a bare comma at the boundary. Comma splice.*

**B.** advance 

  *No mark at all between two independent clauses is a fused sentence.*

**C.** advance; **(Correct)**

  *Correct. Both sides stand alone as sentences, so the boundary takes a semicolon. "Therefore" sits inside the second clause as an ordinary adverb and needs no comma of its own there.*

**D.** advance and 

  *"And" is a FANBOYS conjunction but still needs a comma in front of it to join two independent clauses; without one, this is the same missing-comma error as joining with a bare "but" or "so."*

*Difficulty: medium*

---

##### Q5
> In her book The Woman Warrior: Memoirs of a Girlhood Among Ghosts, author Maxine Hong Kingston examines themes ______ childhood, womanhood, and Chinese American identity by intertwining autobiography and mythology.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** of: 

  *"Examines themes of childhood, womanhood, and Chinese American identity" is a single verb-plus-object phrase; the colon breaks it apart for no reason, and a colon-introduced list would normally drop the leading "of" rather than keep it dangling right after the mark.*

**B.** of **(Correct)**

  *Correct. No punctuation is needed — "themes of childhood, womanhood, and Chinese American identity" is one continuous object of "examines."*

**C.** of— 

  *A dash mid-phrase serves no function here; nothing is being set off as a supplement, since "of childhood, womanhood, and Chinese American identity" is essential to what "themes" means in this sentence.*

**D.** of, 

  *A comma here would treat "childhood, womanhood, and Chinese American identity" as a removable aside, but the list is the essential object of "examines themes of" — nothing about it can be deleted.*

*Difficulty: medium*

---

##### Q6
> The fine, powdery substance that covers the Moon's surface is called regolith. Because regolith is both readily available and high in oxygen ______ scientists have wondered whether it could be used as a potential source of oxygen for future lunar settlements.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** content and 

  *"And" wrongly coordinates a dependent clause ("Because regolith is...") with an independent one as if they were equal, parallel items, and there is still no comma marking the actual boundary.*

**B.** content, **(Correct)**

  *Correct. "Because regolith is both readily available and high in oxygen content" is dependent; the comma introduces the independent clause "scientists have wondered..." that follows.*

**C.** content 

  *Drops the comma a dependent clause needs before the independent clause that completes it, leaving the boundary unmarked despite the length of the intro clause.*

**D.** content, and 

  *Same problem as choice A — "and" cannot coordinate a subordinate "Because" clause with the main clause; the comma alone (without "and") is what the sentence needs.*

*Difficulty: medium*

---

##### Q7
> Psychophysicist Howard Moskowitz was hired by a soda company to determine how much artificial sweetener ______ After conducting consumer taste tests, he found that no such ideal existed: participants expressed a wide range of preferences for different blends of sweetener, carbonization, and flavoring.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** do most people prefer in a diet drink? 

  *This is an indirect question buried inside a larger statement ("...to determine how much..."), so it needs declarative word order, not the inverted "do most people prefer" order of a direct question — and it should not end in a question mark, since the whole sentence is a statement.*

**B.** do most people prefer in a diet drink. 

  *Keeps the inverted, direct-question word order ("do most people prefer") inside what has to be a declarative embedded question, even though the period at the end is correct.*

**C.** most people prefer in a diet drink? 

  *Fixes the word order to declarative ("most people prefer") but still ends in a question mark, when the containing sentence is a statement about what Moskowitz was hired to determine, not a direct question.*

**D.** most people prefer in a diet drink. **(Correct)**

  *Correct. An indirect question embedded in a statement takes declarative word order ("most people prefer," not "do most people prefer") and ends with a period, since the sentence as a whole is not asking anything.*

*Difficulty: hard*

---

##### Q8
> About 70,000 meteorites have been found on Earth. Although most meteorites are fragments of ______ hundred have been identified as being from the Moon or Mars.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** asteroids. Several 

  *"Although most meteorites are fragments of asteroids" starts with the subordinator "Although" and is dependent — ending it with a period turns it into a fragment.*

**B.** asteroids, several **(Correct)**

  *Correct. "Although most meteorites are fragments of asteroids" is dependent; "several hundred have been identified..." is independent. Dependent-first takes a comma.*

**C.** asteroids; several 

  *A semicolon needs an independent clause on its left, and "Although most meteorites are fragments of asteroids" is dependent.*

**D.** asteroids: several 

  *A colon needs an independent clause on its left for the same reason a semicolon does — the "Although" clause never qualifies.*

*Difficulty: medium*

---

##### Q9
> After the printing press was introduced in 1440, handwritten manuscripts from Europe's medieval period were often destroyed and the paper used for other purposes. In one instance, pages ______ a collection of Norse tales dating to 1270 were discovered lining a bishop's miter (hat).

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** from: 

  *"Pages" alone is not a complete clause, so there is nothing here for a colon to follow — and "from a collection of Norse tales dating to 1270" is the essential phrase identifying which pages, not an addition to a finished statement.*

**B.** from, 

  *Severs the subject "pages" from the prepositional phrase that identifies which pages are meant. "From a collection of Norse tales dating to 1270" is essential, not a removable supplement, so no comma belongs here.*

**C.** from **(Correct)**

  *Correct. "Pages from a collection of Norse tales dating to 1270" is the full subject of "were discovered," with no punctuation needed between the noun and its essential modifying phrase.*

**D.** from— 

  *A dash severs the subject from its essential modifying phrase just as wrongly as a comma would — nothing here is a removable supplement.*

*Difficulty: hard*

---

##### Q10
> When particles are suspended in liquid (like pollen in a water glass), they will zigzag randomly through the liquid and collide with one another in perpetuity. This type of random, continuous ______ is known as Brownian motion, can be observed throughout the natural world.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** movement: which 

  *A colon does not open a nonrestrictive supplement, and it leaves the comma before "can be observed" with nothing matching it — the closing mark is already fixed as a comma in the given text.*

**B.** movement, which **(Correct)**

  *Correct. "Which is known as Brownian motion" is a nonrestrictive supplement about "movement," opened here with a comma to match the comma already closing it before "can be observed."*

**C.** movement which 

  *Drops the opening comma while the closing comma before "can be observed" is already fixed in the sentence — an unmatched, one-sided supplement.*

**D.** movement. Which 

  *"Which is known as Brownian motion" is a relative clause; standing alone after a period, it has no independent subject and is a fragment.*

*Difficulty: hard*

---

##### Q11
> In 1959, the film industry debuted Smell-O-Vision. Theaters were fitted with specialized vents that emitted odors at specific points in a ______ as the scent of roses when roses appeared in a scene. Smell-O-Vision failed to impress, however, with one reviewer declaring it "briefly weird and not very interesting."

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** movie such 

  *"Such as the scent of roses..." is a nonessential example tacked onto the end of a complete clause, and examples introduced this way take a comma before "such as." This choice drops it.*

**B.** movie; such 

  *A semicolon needs an independent clause on both sides. "Such as the scent of roses when roses appeared in a scene" has no subject-verb of its own — it is an example phrase, not a clause.*

**C.** movie. Such 

  *Ending the sentence here leaves "Such as the scent of roses when roses appeared in a scene" standing alone with no main verb — a fragment.*

**D.** movie, such **(Correct)**

  *Correct. A comma introduces the nonessential example "such as the scent of roses..." following a complete independent clause.*

*Difficulty: medium*

---

##### Q12
> Robin Wall Kimmerer of the Citizen Potawatomi Nation is a bryologist, a plant scientist who specializes in mosses. To Kimmerer, mosses are Earth's most adaptable plants: they can clone ______ enter a dormant state in times of drought, and grow in areas that don't have soil.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** themselves; 

  *This is a plain three-item verb series (clone, enter, grow) with no internal commas inside any item, so a semicolon here over-punctuates — semicolons in a series are reserved for items that already contain commas.*

**B.** themselves, **(Correct)**

  *Correct. An ordinary series comma between the first and second items of "clone themselves, enter a dormant state..., and grow in areas..."*

**C.** themselves. And 

  *Ending the sentence here leaves "And enter a dormant state in times of drought, and grow in areas that don't have soil" with no subject of its own — a fragment built from the tail of a verb series.*

**D.** themselves 

  *Drops the comma needed between the first and second items of the series, fusing "clone themselves enter a dormant state" as if it were one action.*

*Difficulty: medium*

---

##### Q13
> In 1976, the Inuit rock group Sikumiut recorded the album People of the Ice. Though only their first record, it shows a band already skilled at the difficult task of making music that sounds easy and fun. On songs like "Utirumavunga," Lucassie Koperqualuk's guitar riffs effortlessly ______ Charlie Adams's delightfully catchy vocal melodies.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** blend, with 

  *"Blend with" is a single verb-plus-preposition unit; a comma between them severs the verb from the preposition it requires.*

**B.** blend. With 

  *Ending the sentence at "blend" leaves "With Charlie Adams's delightfully catchy vocal melodies" as a lone prepositional phrase with no verb — a fragment.*

**C.** blend; with 

  *A semicolon needs an independent clause on its right, and "with Charlie Adams's delightfully catchy vocal melodies" is a prepositional phrase, not a clause.*

**D.** blend with **(Correct)**

  *Correct. No punctuation is needed — "blend with" is one continuous verb phrase taking "Charlie Adams's...vocal melodies" as its object.*

*Difficulty: medium*

---

##### Q14
> In 2000, Nora de Hoyos Comstock, herself an owner of a successful consulting firm, sought to increase Latina representation in corporate ______ founded Las Comadres para las Americas, an international community that for over two decades has served as a resource and information network for Latina business professionals.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** settings she 

  *No mark at all between two independent clauses — a fused sentence.*

**B.** settings, she 

  *Both "...sought to increase Latina representation in corporate settings" and "she founded Las Comadres..." are independent clauses; a bare comma cannot join them. Comma splice.*

**C.** settings and she 

  *"And" is a FANBOYS conjunction but still needs a comma before it to join two independent clauses, which this choice omits.*

**D.** settings. She **(Correct)**

  *Correct. A period ends the first independent clause; "She founded Las Comadres..." begins a new sentence.*

*Difficulty: medium*

---

##### Q15
> Fans of science fiction will ______ multiple references to classic sci-fi stories in Janelle Monáe's song lyrics, including her recurring nods to the plot of the 1927 sci-fi film Metropolis.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** appreciate the **(Correct)**

  *Correct. No punctuation is needed between the verb "appreciate" and its direct object "the multiple references..."*

**B.** appreciate. The 

  *Ending the sentence at "appreciate" leaves "The multiple references to classic sci-fi stories..." with no verb of its own — a fragment, and it also strips the verb "appreciate" of the object it needs.*

**C.** appreciate, the 

  *A comma between a verb and its direct object is never licensed, no matter how natural the pause feels.*

**D.** appreciate: the 

  *A colon here breaks the verb from the object it governs; "the multiple references..." is not a list being introduced after a complete statement, it is the thing being appreciated.*

*Difficulty: medium*

---

##### Q16
> Winding through the ice atop Norway's Jotunheim Mountains is the Lendbreen pass, an ancient route that was used by hunters, farmers, traders, and travelers in the Middle Ages before eventually falling into disuse. Recently, archeologists have ______ knives, horseshoes, wool tunics, and thousands of other artifacts from the icy pass.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** unearthed: 

  *A colon planted right after the verb that governs its own object list is the classic colon-after-a-verb trap — "knives, horseshoes, wool tunics, and thousands of other artifacts" is what was unearthed, not an addition to a finished statement.*

**B.** unearthed, 

  *Severs the verb "have unearthed" from its own direct object list with no justification.*

**C.** unearthed— 

  *A dash does the same wrong thing a comma would — cuts the verb off from the objects it takes.*

**D.** unearthed **(Correct)**

  *Correct. No punctuation is needed; "knives, horseshoes, wool tunics, and thousands of other artifacts" are the direct objects of "have unearthed."*

*Difficulty: medium*

---

##### Q17
> In 1959, marine biologist Dr. Albert Jones founded the Underwater Adventure Seekers, a scuba diving ______ that is the oldest club for Black divers in the United States and that has helped thousands of diving enthusiasts become certified in the field.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** club **(Correct)**

  *Correct. "That is the oldest club...and that has helped thousands..." is an essential relative clause defining which club — essential "that" clauses take no comma.*

**B.** club, 

  *Treats the following "that" clause as a removable nonessential aside, but "that" clauses are essential by convention and are never preceded by a comma.*

**C.** club— 

  *Same error as the comma, in dash form — sets off an essential defining clause as if it were an optional supplement.*

**D.** club, and 

  *Inserts a comma and a spurious "and" before the first "that" clause, which does not coordinate anything — the sentence only has one relative clause structure ("that is...and that has..."), not two separate items joined by "and" at this point.*

*Difficulty: medium*

---

##### Q18
> In the novel Things Fall Apart by Chinua Achebe, Okonkwo is a leader of Umuofia (a fictional Nigerian clan) and takes pride in his culture's traditions. However, when the arrival of European missionaries brings changes to Umuofia, the novel asks a central question: How ______

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Umuofia's traditions will be affected. 

  *The colon introduces a genuine posed question ("the novel asks a central question: How..."), which needs inverted question word order and a question mark. This choice uses statement order and a period on both counts.*

**B.** will Umuofia's traditions be affected. 

  *Gets the inverted question word order right ("will Umuofia's traditions be affected") but ends with a period instead of the question mark a genuine posed question requires.*

**C.** Umuofia's traditions will be affected? 

  *Ends correctly with a question mark but keeps statement word order ("Umuofia's traditions will be affected") instead of the inversion a direct question needs.*

**D.** will Umuofia's traditions be affected? **(Correct)**

  *Correct. "How" here introduces a genuine posed question, so it takes inverted word order ("will Umuofia's traditions be affected") and ends with a question mark.*

*Difficulty: hard*

---

##### Q19
> Dolores Huerta's advocacy on behalf of farmworkers was rooted in her experience as a schoolteacher in Stockton, California, in the early 1950s. Hoping to help her students and their families outside the ______ Huerta left teaching to start the Stockton chapter of the Community Service Organization, a group focused on the needs of local farmworkers.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** classroom. 

  *"Hoping to help her students and their families outside the classroom" has no main verb of its own — "Hoping" is a participle — so ending it with a period turns an introductory phrase into a fragment.*

**B.** classroom; 

  *A semicolon needs an independent clause on its left. "Hoping to help her students and their families outside the classroom" is a participial phrase, not a clause.*

**C.** classroom, **(Correct)**

  *Correct. An introductory participial phrase takes a comma before the main clause "Huerta left teaching..."*

**D.** classroom 

  *Drops the comma an introductory phrase needs before the main clause, leaving "outside the classroom Huerta left teaching" unmarked at the boundary.*

*Difficulty: medium*

---

##### Q20
> In 2009, researchers determined that pottery fragments from a cave in China were close to 18,000 years old. These are some of the oldest ______ of pottery ever found.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** pieces: 

  *"Of pottery ever found" is not a list or explanation being introduced after a finished statement — it is the essential phrase completing what "pieces" means, so the colon has nothing to introduce.*

**B.** pieces, 

  *Severs "pieces" from the essential modifying phrase "of pottery ever found" that identifies what kind of pieces these are.*

**C.** pieces **(Correct)**

  *Correct. No punctuation is needed; "pieces of pottery ever found" is a single noun phrase.*

**D.** pieces— 

  *Same error as the comma, in dash form — nothing here is a removable supplement.*

*Difficulty: easy*

---

##### Q21
> According to the University of Hawai'i at Mānoa, aloha 'āina is "a recognition, commitment, and practice sustaining the ea — or life breath" between the Hawaiian people and their natural environments. The concept has been proudly embodied ______ Native Hawaiians for generations, contributing to the lush flora and renowned beauty of the islands.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** by; 

  *"Embodied by" is a single passive-verb-plus-agent unit; a semicolon after "by" severs the verb from the agent it requires and leaves nothing independent on the right.*

**B.** by: 

  *A colon here breaks the passive construction "embodied by Native Hawaiians" apart with no list or explanation actually being introduced.*

**C.** by, 

  *A comma between the passive verb "embodied" and its required agent phrase "by Native Hawaiians" is unjustified — nothing is being set off.*

**D.** by **(Correct)**

  *Correct. No punctuation is needed; "embodied by Native Hawaiians" is one continuous passive-verb phrase.*

*Difficulty: medium*

---

##### Q22
> The element carbon has the highest melting point ______ all the elements on the periodic table—3,500 degrees Celsius.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** of **(Correct)**

  *Correct. "Highest...of all the elements" is a single superlative construction; "of" is the preposition it requires, with no punctuation before it.*

**B.** of— 

  *A dash mid-phrase breaks "highest melting point of" away from the "all the elements" it needs to complete the comparison.*

**C.** of, 

  *A comma here severs a required preposition from the phrase it introduces, for no reason.*

**D.** of: 

  *A colon has nothing to introduce yet — "the highest melting point of" is not a complete statement on its own, it is still mid-phrase.*

*Difficulty: easy*

---

##### Q23
> Located in the northern United States, the Great Lakes Basin contains roughly 35,000 islands. Lake Superior has Grand Island, for example. Lake Michigan has Belle Isle. Lake Huron, though, is home ______ the largest island of them all: Manitoulin Island.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** to; 

  *"Is home to" is a fixed phrasal construction; a semicolon after "home" strips it of the preposition it needs and leaves an incomplete predicate on the left.*

**B.** to— 

  *A dash mid-phrase breaks "is home to" apart from its object with no supplement being set off.*

**C.** to **(Correct)**

  *Correct. No punctuation is needed; "is home to the largest island of them all" is the complete predicate.*

**D.** to, 

  *A comma between "home" and the "to" it requires severs a fixed phrase for no reason.*

*Difficulty: easy*

---

##### Q24
> In her large-scale sculpture Casa-Isla, artist Edra Soto included references to her childhood in Puerto Rico. For example, the sculpture's steel panels have a crisscrossing pattern inspired by the iron gates ______

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Soto would see in her neighborhood? 

  *"Soto would see in her neighborhood" is declarative word order describing the gates, matching a statement, not a direct question — so the trailing question mark is wrong even though the word order is right.*

**B.** Soto would see in her neighborhood. **(Correct)**

  *Correct. This is an essential relative clause (relative pronoun "that" omitted) describing the iron gates, in ordinary statement word order, ending the larger declarative sentence with a period.*

**C.** would Soto see in her neighborhood. 

  *Inverts to question word order ("would Soto see") inside a sentence that is describing the sculpture, not asking anything — the wrong order despite the correct period.*

**D.** would Soto see in her neighborhood? 

  *Wrong on both counts — inverted question word order and a question mark, in a sentence that is simply describing where the pattern's inspiration came from.*

*Difficulty: hard*

---

##### Q25
> Azulejos, mosaics made of glazed ceramic tiles, can be found throughout Portugal. These mosaics beautify places such as ______ stations, and public squares.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** libraries train 

  *Fuses the first and second items of the series — libraries, train stations, and public squares — by dropping the comma between them.*

**B.** libraries: train 

  *A colon right after the first item of a list it did not introduce has nothing to announce.*

**C.** libraries—train 

  *Same problem as the colon, in dash form — no supplement is being set off mid-list.*

**D.** libraries, train **(Correct)**

  *Correct. An ordinary series comma between the first item (libraries) and the second (train stations).*

*Difficulty: easy*

---

##### Q26
> Many Samoans enjoy a sport called kilikiti. This bat-and-ball game was derived from ______ kilikiti differs from cricket in a few key ways.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** cricket but: 

  *"But" still needs the comma that belongs before it to join the two independent clauses, and a colon has no role tacked onto the end of a coordinating conjunction.*

**B.** cricket but, 

  *Puts the comma after "but" instead of before it — the comma belongs at the clause boundary, ahead of the conjunction, not trailing it as though "but" itself needed to be set off.*

**C.** cricket, but **(Correct)**

  *Correct. Two independent clauses joined with a comma before the FANBOYS conjunction "but."*

**D.** cricket, but, 

  *Adds an extra, unnecessary comma after "but" on top of the correct one before it, isolating the conjunction as if it were parenthetical.*

*Difficulty: medium*

---

##### Q27
> By analyzing ice cores from Greenland and Antarctica, a research team at Sweden's Lund University discovered evidence of a solar storm that occurred 9,200 years ago. Scientists had previously thought the Sun to be in a relatively "quiet" phase at that ______ the Lund team's finding suggests otherwise.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** time but 

  *Missing the comma that has to come before "but" when it joins two independent clauses.*

**B.** time, but **(Correct)**

  *Correct. Two independent clauses in contrast, joined with comma plus "but."*

**C.** time, 

  *A bare comma cannot join two independent clauses. Comma splice.*

**D.** time 

  *No mark at all between two independent clauses — a fused sentence.*

*Difficulty: medium*

---

##### Q28
> The algaita is a double reed wind instrument from West Africa. The reed of a wind instrument is the mouthpiece ______ A double reed contains two pieces of cane that vibrate and produce sound as air passes between them.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** where sound is made? 

  *"Where sound is made" is declarative word order defining the mouthpiece — this is a statement, not a question, so it should not end in a question mark despite the correct word order.*

**B.** where is sound made. 

  *Inverts to question word order ("is sound made") inside a sentence that is simply defining what the mouthpiece is, not asking anything — wrong order despite the correct period.*

**C.** where sound is made. **(Correct)**

  *Correct. "Where sound is made" is declarative word order defining the mouthpiece, ending the statement with a period.*

**D.** where is sound made? 

  *Wrong on both counts — inverted question word order and a question mark, in a sentence that is defining a term, not posing a question.*

*Difficulty: hard*

---

##### Q29
> Both Sona Charaipotra, an Indian American, and Dhonielle Clayton, an African American, grew up frustrated by the lack of diverse characters in books for young people. In 2011, these two writers joined forces to found CAKE Literary, a book packaging ______ specializes in the creation and promotion of stories told from diverse perspectives for children and young adults.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** company, 

  *Sets "company" off with a comma as though a complete statement had just ended, but that strips "specializes" of the relative pronoun it needs and leaves it with no clear subject of its own.*

**B.** company that **(Correct)**

  *Correct. "That specializes in the creation and promotion of stories..." is an essential relative clause identifying which company — essential "that" clauses take no comma.*

**C.** company 

  *Drops the relative pronoun "that" entirely, leaving "specializes" without the connector it needs to attach to "company."*

**D.** company, that 

  *"That" clauses are essential and are never preceded by a comma — that convention belongs to nonrestrictive "which" clauses instead.*

*Difficulty: hard*

---

##### Q30
> Where ______ Interestingly, it was invented by an author. It first appears in the novel Through the Looking Glass by English author Lewis Carroll.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** did the word "chortle" come from. 

  *This is a genuine, standalone direct question — it gets the inverted word order right ("did the word come from") but wrongly ends with a period instead of a question mark.*

**B.** the word "chortle" did come from? 

  *"The word 'chortle' did come from" is not standard question inversion — a real question fronts "did" ("did the word come from"), not buries it mid-clause.*

**C.** did the word "chortle" come from? **(Correct)**

  *Correct. Full question inversion ("did the word come from") plus a question mark, matching a genuine posed question.*

**D.** the word "chortle" come from. 

  *Uses statement word order in what is meant to be a direct question, and ends with a period instead of a question mark — wrong on both counts.*

*Difficulty: hard*

---

##### Q31
> At 1,377 meters, the Tsing Ma Bridge in China is one of the longest suspension bridges in the ______ the Golden Gate Bridge in the United States, at 1,280 meters, is even longer.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** world but 

  *Missing the comma that has to precede "but" when it joins two independent clauses.*

**B.** world, but, 

  *Adds an unnecessary second comma right after "but," isolating the conjunction as though it were parenthetical, on top of the correct comma before it.*

**C.** world, 

  *A bare comma with no conjunction cannot join two independent clauses. Comma splice.*

**D.** world, but **(Correct)**

  *Correct. Two independent clauses in contrast, joined with comma plus the FANBOYS conjunction "but."*

*Difficulty: medium*

---

##### Q32
> In early 1700s England, it was legal for shops to sell prints of artists' engravings without the artists' permission. This changed in 1735 with the passage of the Engravers' Copyright ______ gave engravers control over the distribution and sale of all prints made from their designs.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Act, which **(Correct)**

  *Correct. There was only one Engravers' Copyright Act, so "which gave engravers control..." is a nonrestrictive supplement about it, opened here with a comma.*

**B.** Act; which 

  *A semicolon needs an independent clause on its right, but "which gave engravers control..." is a relative clause and cannot stand alone.*

**C.** Act. Which 

  *"Which gave engravers control over the distribution and sale of all prints made from their designs" standing alone after a period has no independent subject — a fragment.*

**D.** Act 

  *Drops the relative pronoun "which" entirely, so "gave" has no clear connector to "Act" and instead fuses directly onto the prepositional phrase "with the passage of," producing a run-on.*

*Difficulty: hard*

---

##### Q33
> Photosynthesis, the mechanism by which plants use sunlight to turn carbon dioxide and water into ______ is fueled in part by an enzyme called Photosystem II that harvests energy-giving electrons from water molecules.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** nutrients 

  *The supplement "the mechanism by which plants use sunlight to turn carbon dioxide and water into nutrients" was opened with a comma after "Photosynthesis" and never gets a matching comma to close it before "is fueled."*

**B.** nutrients and 

  *Inserting "and" wrongly treats "is fueled in part by..." as a second item coordinated with the supplement, when it is actually the main clause's verb, and the supplement still never closes.*

**C.** nutrients, **(Correct)**

  *Correct. Closes the supplement opened by the comma after "Photosynthesis," matching pair to pair.*

**D.** nutrients— 

  *A dash does not match the comma that opened the supplement after "Photosynthesis" — an unmatched pair.*

*Difficulty: hard*

---

##### Q34
> Po'Pay was a Tewa leader from Ohkay Owingeh, a pueblo located about twenty-five miles north of present-day Santa Fe, New Mexico. He was instrumental in organizing the Pueblo Revolt of ______ as a result of his leadership, the Spanish colonizers were expelled from the region for a time.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** 1680 

  *No mark at all between two independent clauses — a fused sentence.*

**B.** 1680 and 

  *"And" is a FANBOYS conjunction but still needs the comma that belongs before it to join two independent clauses.*

**C.** 1680, 

  *A bare comma cannot join two independent clauses. Comma splice.*

**D.** 1680, and **(Correct)**

  *Correct. Two independent clauses joined with comma plus "and."*

*Difficulty: medium*

---

##### Q35
> In 2008, two years after the death of science fiction writer Octavia Butler, the Huntington Library in ______ received a collection of more than 8,000 items, including Butler's private notes, research materials, manuscripts, photos, and drawings. Today, the Octavia E. Butler Collection is one of the most researched archives at the library.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** California, 

  *Severs the subject "the Huntington Library in California" from its verb "received" — "California" is essential to naming which library, not a removable aside.*

**B.** California: 

  *A colon between the subject and its verb has nothing to introduce — the subject noun phrase is not yet complete as an independent clause.*

**C.** California— 

  *Same subject-verb severing as the comma, in dash form.*

**D.** California **(Correct)**

  *Correct. No punctuation between the subject "the Huntington Library in California" and its verb "received."*

*Difficulty: medium*

---

##### Q36
> Archaeologists have estimated that the pre-Columbian Native American city of Cahokia, located across the Mississippi River from modern-day St. Louis, Missouri, had as many as 20,000 inhabitants in the year 1150 ______ it one of the largest cities in North America at the time.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** CE making 

  *Drops the comma needed before the trailing participial phrase "making it one of the largest cities..."*

**B.** CE. Making 

  *"Making it one of the largest cities in North America at the time" is a participial phrase with no main verb of its own — standing alone after a period, it is a fragment.*

**C.** CE, making **(Correct)**

  *Correct. A comma introduces the trailing participial phrase describing the consequence of Cahokia's population.*

**D.** CE; making 

  *A semicolon needs an independent clause on its right, but "making it one of the largest cities..." is a participial phrase, not a clause.*

*Difficulty: medium*

---

##### Q37
> Detroit natives Timothy Paule and Nicole Lindsey have combined their two passions, Detroit and beekeeping, to improve the health of their city's flowers and other vegetation. In 2017, the couple converted a vacant lot in the city into an ______ in the years that followed they acquired nine additional lots and established more than 35 hives.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** apiary, 

  *A bare comma cannot join two independent clauses. Comma splice.*

**B.** apiary, and **(Correct)**

  *Correct. Two independent clauses joined with comma plus "and."*

**C.** apiary and 

  *Missing the comma that has to come before "and" when it joins two independent clauses.*

**D.** apiary 

  *No mark at all between two independent clauses — a fused sentence.*

*Difficulty: medium*

---

##### Q38
> Santa Clara Pueblo artist Roxanne Swentzell's sculpture Mud Woman Rolls On consists of five human figures made of clay and plant fiber and arranged in descending size; each figure holds the smaller one in front of it. The arrangement of the figures, according to ______ represents her idea that "we all come from the Earth, generation after generation."

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Swentzell 

  *The parenthetical "according to Swentzell" was opened with a comma after "figures" and needs a matching comma to close before "represents" — this choice leaves it one-sided.*

**B.** Swentzell, **(Correct)**

  *Correct. Closes the mid-sentence supplement "according to Swentzell" to match the comma that opened it after "figures."*

**C.** Swentzell: 

  *A colon does not match the comma that opened the supplement, and a colon is not used to close a mid-sentence aside like this in any case.*

**D.** Swentzell— 

  *A dash does not match the comma that opened the supplement — an unmatched pair.*

*Difficulty: medium*

---

##### Q39
> Nine months before Rosa Parks made history by refusing to comply with the segregated seating policy on a Montgomery, Alabama, bus, a fifteen-year-old Montgomery girl named Claudette Colvin was arrested for the same ______ to some historians, Colvin's arrest led to Parks's action and eventually to the desegregation of Montgomery's bus system.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** offense. According **(Correct)**

  *Correct. A period ends the first independent clause; "According to some historians," begins the second sentence's introductory phrase, capitalized.*

**B.** offense, according 

  *A bare comma joining what should be two separate sentences is a comma splice, and "according" is left lowercase as though continuing rather than starting a new sentence.*

**C.** offense according 

  *No punctuation at all — fully fused, with the internal comma after "According to some historians" missing too.*

**D.** offense and according 

  *Inserting "and" without a comma before it still fails to mark a valid boundary, and it flattens what is meant to be two separate sentences into one improperly joined clause.*

*Difficulty: medium*

---

##### Q40
> It is generally true that technological change is a linear process, in which once-useful technologies are replaced by new and better ______ the reawakening of interest in the steam engine (from advocates of carbon-neutral rail travel) reminds us that ostensibly obsolete technologies may be brought back into service to address society's changing needs.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** ones, even so; 

  *Puts a comma at the actual clause boundary (wrong — "even so" is an adverb, not a conjunction, and cannot license one) and moves the semicolon to after "so" instead of before it.*

**B.** ones even so, 

  *Marks nothing at all at the true clause boundary before "even so" and only adds a comma after it — this leaves the two independent clauses essentially fused, with "even so" not properly set off either.*

**C.** ones; even so, **(Correct)**

  *Correct. "Even so" is a conjunctive adverb, so the true clause boundary takes a semicolon before it; the adverb itself is then followed by a comma before the rest of the clause.*

**D.** ones, even so, 

  *"Even so" is an adverb, not a conjunction, and a bare comma at the clause boundary in front of it cannot join two independent clauses — a comma splice, just dressed up with the adverb correctly comma'd on its far side.*

*Difficulty: sat-hardest*

---

##### Q41
> In 2017, artists Isabel and Ruben Toledo redesigned the costumes and sets for The Miami City Ballet's production of The ______ to reviewers, the Toledos' designs helped infuse the production with elements of Miami's Latin American culture.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Nutcracker according, 

  *Leaves the first sentence with no closing mark or capital letter, and misplaces the comma after "according" instead of in the position "According to reviewers," needs.*

**B.** Nutcracker, according 

  *A bare comma joining what should be two separate sentences is a comma splice, with "according" left lowercase.*

**C.** Nutcracker according 

  *No punctuation at all — fully fused.*

**D.** Nutcracker. According **(Correct)**

  *Correct. A period ends the first sentence; "According to reviewers," begins the second, capitalized, with its own internal comma already in place.*

*Difficulty: medium*

---

##### Q42
> Humans were long thought to have begun occupying the Peruvian settlement of Machu Picchu between 1440 and 1450 CE. However, a team led by anthropologist Dr. Richard Burger used accelerator mass spectrometry to uncover evidence that it was occupied ______ 1420 CE, according to Burger, humans were likely inhabiting the area.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** earlier. In **(Correct)**

  *Correct. A period ends the first sentence at "earlier"; "In 1420 CE," begins the second, with its own internal supplement "according to Burger," already bracketed by commas.*

**B.** earlier, in 

  *A bare comma joining what should be two separate sentences is a comma splice, with "in" left lowercase.*

**C.** earlier, which in 

  *"Which" has no clause left to attach to — "humans were likely inhabiting the area" already has its own subject, "humans," leaving the relative pronoun with no grammatical role.*

**D.** earlier in 

  *No punctuation at all, fusing "earlier" directly into "in 1420 CE" as if it were one continuous phrase rather than the start of a new sentence.*

*Difficulty: hard*

---

##### Q43
> According to Naomi Nakayama of the University of Edinburgh, the reason seeds from a dying dandelion appear to float in the air while ______ is that their porous plumes enhance drag, allowing the seeds to stay airborne long enough for the wind to disperse them throughout the surrounding area.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** falling, 

  *Severs the long subject ("the reason seeds...appear to float in the air while falling") from its main verb "is" — no length of subject licenses a comma there.*

**B.** falling: 

  *A colon between the subject and its verb has the same problem as a comma — it breaks a single grammatical unit apart for no reason.*

**C.** falling; 

  *A semicolon needs an independent clause on its left, but everything before it here is still part of the subject of "is" — not yet a complete clause.*

**D.** falling **(Correct)**

  *Correct. No punctuation between the long subject and its verb "is," however far apart the sentence has pushed them.*

*Difficulty: hard*

---

##### Q44
> In 1727, dramatist Lewis Theobald presented a new play, Double Falsehood, at a London theater. Theobald claimed that his drama was based on a little-known play by William Shakespeare, Cardenio. Many, including poet Alexander Pope, were ______ historians have determined that Shakespeare's company did perform a play called Cardenio in 1613.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** skeptical but 

  *Missing the comma that has to precede "but" when it joins two independent clauses.*

**B.** skeptical, but **(Correct)**

  *Correct. Two independent clauses in contrast, joined with comma plus "but."*

**C.** skeptical, 

  *A bare comma cannot join two independent clauses. Comma splice.*

**D.** skeptical 

  *No mark at all between two independent clauses — a fused sentence.*

*Difficulty: medium*

---

##### Q45
> Luci Tapahonso is the inaugural poet laureate of the Navajo Nation. Her book Sáanii Dahataal/The Women Are Singing—a combination of fiction and memoir, poetry and ______ serves as a testament to her versatility as a writer.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** prose; 

  *A semicolon does not match the dash that opened the supplement, and it also wrongly implies "serves as a testament..." starts a new independent clause when it actually needs "her book" — the noun before the supplement — as its subject.*

**B.** prose 

  *Leaves the supplement, opened with a dash before "a combination," with no closing mark at all before "serves."*

**C.** prose, 

  *A comma does not match the dash that opened the supplement — an unmatched pair.*

**D.** prose— **(Correct)**

  *Correct. Closes the supplement with a dash to match the dash that opened it before "a combination of fiction and memoir."*

*Difficulty: hard*

---

##### Q46
> Swedish scientists Eva Engvall and Peter Perlmann developed a method for measuring the concentration of different proteins in a biological sample. Their ______ ELISA (enzyme-linked immunosorbent assay), is used to detect and measure proteins that indicate the presence of certain diseases.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** method (called 

  *Opens the supplement with a parenthesis, but the sentence already closes it with a comma before "is used" — an unmatched pair.*

**B.** method—called 

  *Opens with a dash while the supplement is already fixed to close with a comma — an unmatched pair.*

**C.** method, called **(Correct)**

  *Correct. Opens the supplement "called ELISA..." with a comma to match the comma that already closes it before "is used."*

**D.** method called 

  *Leaves the supplement with no opening mark at all, while a comma already closes it later — one-sided.*

*Difficulty: hard*

---

##### Q47
> How do scientists determine what foods were eaten by extinct hominins such as Neanderthals? In the past, researchers were limited to studying the marks found on the fossilized teeth of skeletons, but in 2017 a team led by Laura Weyrich of the Australian Centre for Ancient DNA tried something ______ the DNA found in Neanderthals' fossilized dental plaque.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** new: sequencing **(Correct)**

  *Correct. "Tried something new" is a complete independent clause; the colon introduces the gerund phrase specifying exactly what that new thing was.*

**B.** new; sequencing 

  *A semicolon needs an independent clause on its right, but "sequencing the DNA found in Neanderthals' fossilized dental plaque" is a gerund phrase, not a clause.*

**C.** new, sequencing: 

  *Places a comma before "sequencing" and moves the colon to the end, where it introduces nothing — the punctuation is scrambled relative to where the actual boundary and explanation belong.*

**D.** new. Sequencing 

  *"Sequencing the DNA found in Neanderthals' fossilized dental plaque" standing alone after a period has no subject-predicate structure of its own — a fragment.*

*Difficulty: hard*

---

##### Q48
> The 2022 Nobel Prize in Chemistry was awarded to three pioneers in the field of click chemistry: two-time Nobel laureate Barry Sharpless, who coined the term "click chemistry" in 1998; Carolyn Bertozzi, founder of the Bertozzi Group at ______ and Morten Meldal, a professor at the University of Copenhagen in Denmark.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Stanford 

  *Missing the semicolon that should separate this item from the next ("and Morten Meldal...") — without it, the second and third people in the list fuse together.*

**B.** Stanford, 

  *The series already committed to semicolons as item separators (one appears right after "in 1998"); switching back to a comma here is inconsistent and reintroduces ambiguity, since these items already contain their own internal commas.*

**C.** Stanford: 

  *A colon has no role between items already inside a series it did not introduce.*

**D.** Stanford; **(Correct)**

  *Correct. Once a series' items contain internal commas, semicolons mark every item boundary — consistently, including this one.*

*Difficulty: sat-hardest*

---

##### Q49
> Customers who are satisfied with how a company resolves a service issue may regard that company more positively than they would if no such issue had occurred. This idea is known as the service recovery ______ research suggests that it has important implications for customer loyalty and retention.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** paradox, 

  *A bare comma cannot join two independent clauses. Comma splice.*

**B.** paradox 

  *No mark at all between two independent clauses — a fused sentence.*

**C.** paradox, and **(Correct)**

  *Correct. Two independent clauses joined with comma plus "and."*

**D.** paradox and, 

  *Puts the comma after "and" instead of before it — the comma belongs at the clause boundary, ahead of the conjunction.*

*Difficulty: medium*

---

##### Q50
> In a 2023 study, researchers documented a fascinating behavior in the aquatic plant Elodea densa. When exposed to low levels of light, the plant's ______ the cellular organs that generate energy from light—reshuffled to form a tightly packed, glass-like surface ideal for collecting more light.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** chloroplasts 

  *The supplement "the cellular organs that generate energy from light" already closes with a dash before "reshuffled" — this choice leaves it with no opening dash, one-sided.*

**B.** chloroplasts; 

  *A semicolon does not match the dash that already closes the supplement, and it wrongly implies the appositive is an independent clause, which it is not.*

**C.** chloroplasts, 

  *A comma does not match the dash that already closes the supplement — an unmatched pair.*

**D.** chloroplasts— **(Correct)**

  *Correct. Opens the supplement with a dash to match the dash that closes it before "reshuffled."*

*Difficulty: hard*

---

##### Q51
> In ancient Greece, an Epicurean was a follower of Epicurus, a philosopher whose beliefs revolved around the pursuit of pleasure. Epicurus defined pleasure as "the absence of pain in the body and of trouble in the ______ that all life's virtues derived from this absence.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** soul," positing **(Correct)**

  *Correct. The comma closing the quotation sits inside the closing quotation mark, per convention, and "positing that all life's virtues derived from this absence" is a participial phrase continuing the sentence outside the quote.*

**B.** soul": positing 

  *Places a colon outside the closing quotation mark where convention calls for a comma inside it, and a colon does not fit grammatically after a quoted noun phrase in this position anyway.*

**C.** soul"; positing 

  *A semicolon after the closing quote is wrong for the same convention reason, and "positing that all life's virtues derived from this absence" is not an independent clause, so the semicolon fails doubly.*

**D.** soul." Positing 

  *Ends the quoted material as its own sentence, leaving "Positing that all life's virtues derived from this absence" to stand alone — a participial phrase with no main verb, a fragment.*

*Difficulty: sat-hardest*

---

##### Q52
> The Lion Light system, developed by Kenyan inventor Richard Turere, consists of LED lights installed around the perimeter of livestock pastures. Powered with ______ the blinking LEDs keep lions away at night, thus protecting the livestock without risking harm to the endangered lions.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** energy collected, by solar panels, during the day 

  *Brackets "by solar panels" as though it were a removable aside, but it is essential — it explains how the energy was collected, and deleting it would strip needed information.*

**B.** energy collected by solar panels during the day 

  *Drops the comma that has to follow the entire introductory participial phrase before the main clause "the blinking LEDs keep lions away..."*

**C.** energy collected by solar panels during the day, **(Correct)**

  *Correct. No internal commas within the essential phrase "collected by solar panels during the day," and one comma after the full introductory phrase, before the main clause.*

**D.** energy, collected by solar panels during the day, 

  *Inserts a comma right after "energy," treating "collected by solar panels during the day" as a nonessential aside about energy in general, when it actually defines which energy is meant.*

*Difficulty: hard*

---

##### Q53
> Materials scientist Marie-Agathe Charpagne and her colleagues believed they could improve on the multicomponent alloy NiCoCr, an equal-proportions mixture of nickel (Ni), cobalt (Co), and chromium (Cr), by replacing chromium with ruthenium ______ the alloy that resulted, NiCoRu, turned out to be an unsuitable replacement for NiCoCr.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** (Ru) 

  *No mark at all between two independent clauses — a fused sentence.*

**B.** (Ru) but 

  *Missing the comma that has to precede "but" when it joins two independent clauses.*

**C.** (Ru), 

  *A bare comma cannot join two independent clauses. Comma splice.*

**D.** (Ru), but **(Correct)**

  *Correct. Two independent clauses in contrast, joined with comma plus "but."*

*Difficulty: medium*

---

##### Q54
> Seneca sculptor Marie Watt's blanket art comes in a range of shapes and sizes. In 2004, Watt sewed strips of blankets together to craft a 10-by-13-inch ______ in 2014, she arranged folded blankets into two large stacks and then cast them in bronze, creating two curving 18-foot-tall blue-bronze pillars.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** sampler later, 

  *Wedges in a redundant "later" beside the sentence's own "in 2014," and the comma at the clause boundary still cannot join two independent clauses on its own. Comma splice.*

**B.** sampler; **(Correct)**

  *Correct. Both sides are independent clauses, so the boundary takes a semicolon.*

**C.** sampler, 

  *A bare comma cannot join two independent clauses. Comma splice.*

**D.** sampler, later, 

  *Same comma-splice problem as choice A, with the same redundant "later" wedged in beside the already-present "in 2014."*

*Difficulty: medium*

---

##### Q55
> Gathering accurate data on water flow in the United States is challenging because of the country's millions of miles of ______ the volume and speed of water at any given location can vary drastically over time.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** waterways and the fact that, 

  *Inserts a comma right after "that," severing the conjunction from the noun clause it is supposed to introduce ("that the volume and speed...can vary").*

**B.** waterways, and the fact that, 

  *"And" here simply joins two noun phrases that are both objects of "because of," not two independent clauses, so no comma belongs before it — and the second comma after "that" is wrong for the same reason as choice A.*

**C.** waterways, and, the fact that 

  *Brackets "and" with commas as though it were a parenthetical aside, but it is a plain coordinating word here with nothing to set off.*

**D.** waterways and the fact that **(Correct)**

  *Correct. "And" simply joins two noun-phrase objects of "because of" — "the country's millions of miles of waterways" and "the fact that the volume and speed...can vary" — with no punctuation needed.*

*Difficulty: hard*

---

##### Q56
> In her analysis of Edith Wharton's The House of Mirth (1905), scholar Candace Waid observes that the novel depicts the upper classes of New York society as "consumed by the appetite of a soulless ______ an apt assessment given that The House of Mirth is set during the Gilded Age, a period marked by rapid industrialization, economic greed, and widening wealth disparities.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** materialism"; and 

  *Places the semicolon outside the closing quotation mark, and "an apt assessment given that..." is an appositive phrase renaming the quotation, not an independent clause a semicolon (or a coordinating "and") could properly join.*

**B.** materialism" and 

  *No punctuation at the quotation boundary at all, and "and" wrongly implies the appositive is a second coordinated item rather than a phrase renaming the whole preceding quotation.*

**C.** materialism," **(Correct)**

  *Correct. The comma sits inside the closing quotation mark, per convention, and the appositive phrase "an apt assessment given that..." follows directly.*

**D.** materialism" 

  *Missing the comma before the appositive phrase entirely, running the quotation directly into "an apt assessment..." with no boundary mark.*

*Difficulty: hard*

---

##### Q57
> A conceptual artist and designer embraced by both the art world and the fashion ______ Mary Ping was chosen to curate the exhibition Front Row: Chinese American Designers for the Museum of Chinese in America.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** world 

  *Drops the comma that has to follow this long introductory appositive phrase before the main clause "Mary Ping was chosen..."*

**B.** world: 

  *A colon needs an independent clause on its left, but "a conceptual artist and designer embraced by both the art world and the fashion world" has no subject-verb of its own — it is a long noun phrase in apposition to "Mary Ping."*

**C.** world; 

  *A semicolon needs an independent clause on its left for the same reason a colon does — the phrase before it is not one.*

**D.** world, **(Correct)**

  *Correct. A comma follows the introductory appositive phrase describing Mary Ping, before the main clause.*

*Difficulty: hard*

---

##### Q58
> Beatrix Potter is perhaps best known for writing and illustrating children's books such as The Tale of Peter Rabbit (1902), but she also dedicated herself to mycology, the study of ______ more than 350 paintings of the fungal species she observed in nature and submitting her research on spore germination to the Linnean Society of London.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** fungi; producing 

  *A semicolon needs an independent clause on its right, but "producing more than 350 paintings...and submitting her research..." is a participial phrase, not a clause.*

**B.** fungi. Producing 

  *"Producing more than 350 paintings of the fungal species she observed in nature..." standing alone after a period has no main verb of its own — a fragment.*

**C.** fungi producing 

  *Drops the comma needed before the trailing participial phrase, fusing "fungi" directly into "producing."*

**D.** fungi, producing **(Correct)**

  *Correct. A comma introduces the trailing participial phrase describing what she did as part of her dedication to mycology.*

*Difficulty: medium*

---

##### Q59
> The first computerized spreadsheet, Dan Bricklin's VisiCalc, improved financial recordkeeping not only by providing users with an easy means of adjusting data in spreadsheets but also by automatically updating all calculations that were dependent on these ______ to VisiCalc's release, changing a paper spreadsheet often required redoing the entire sheet by hand, a process that could take days.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** adjustments prior 

  *No punctuation at all, fully fused, and missing the internal comma that "Prior to VisiCalc's release" needs before the main clause of the new sentence.*

**B.** adjustments, prior 

  *A bare comma joining what should be two separate sentences is a comma splice, with "prior" left lowercase.*

**C.** adjustments. Prior **(Correct)**

  *Correct. A period ends the first sentence; "Prior to VisiCalc's release," begins the second, capitalized, with its own internal comma before the main clause.*

**D.** adjustments and prior 

  *Inserting "and" without the comma it needs still fails to mark a valid boundary, and this coordination does not fit the intended two-sentence structure.*

*Difficulty: medium*

---

##### Q60
> The Mesoamerican city of Teotihuacan featured a uniquely egalitarian urban housing infrastructure. Built between the first and seventh centuries CE, Teotihuacan housed its residents (as many as 200,000, by some ______ in a complex of comfortable apartments of comparable size.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** estimates) **(Correct)**

  *Correct. Closes the parenthetical aside "(as many as 200,000, by some estimates)" to match the parenthesis that opened it after "residents."*

**B.** estimates), 

  *Adds an unnecessary comma right after the closing parenthesis; the sentence continues directly into "in a complex of comfortable apartments" with nothing left to set off.*

**C.** estimates— 

  *A dash does not match the opening parenthesis — a parenthetical opened with "(" has to close with ")", not a dash.*

**D.** estimates 

  *Leaves the parenthetical aside with no closing mark at all, unclosed.*

*Difficulty: medium*

---

##### Q61
> A recent study tracked the number of bee species present in twenty-seven New York apple orchards over a ten-year period. ______ found that when wild growth near an orchard was cleared, the number of different bee species visiting the orchard decreased.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Entomologist Heather Grab: 

  *A colon between the subject and its verb "found" has nothing to introduce — the subject is a tightly bound title-plus-name unit, not a completed independent clause.*

**B.** Entomologist, Heather Grab, 

  *Treats "Entomologist" as a complete noun being renamed by an appositive, but "Entomologist Heather Grab" functions as a single tightly bound title-plus-name unit — like "Dr. Smith" — that takes no internal commas.*

**C.** Entomologist Heather Grab **(Correct)**

  *Correct. No punctuation is needed; the title and name form a single subject, followed directly by the verb "found."*

**D.** Entomologist Heather Grab, 

  *A trailing comma wrongly severs the complete subject from its verb "found."*

*Difficulty: medium*

---

##### Q62
> In a 2016 study, Eastern Washington University psychologist Amani El-Alayli found that, among the study participants who experienced frisson (a physiological response akin to goosebumps or getting the chills) while listening to music, there was one personality trait that they scored particularly ______ openness to experience.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** high. On 

  *Severs "high" from the preposition "on" that "scored...on" requires, leaving "On openness to experience" to stand alone as a fragment — a lone prepositional phrase.*

**B.** high on; 

  *A semicolon needs an independent clause on its right, but "openness to experience" is just a noun phrase.*

**C.** high on 

  *Drops the colon that should introduce the specific trait being named, leaving no signal for what "openness to experience" refers to.*

**D.** high on: **(Correct)**

  *Correct. "They scored particularly high on" is a complete independent clause, and the colon introduces the trait it names: openness to experience.*

*Difficulty: hard*

---

##### Q63
> In 2018, a team of researchers led by Dr. Caitlin Whalen compiled every available measurement of ocean mixing rates from the past two decades. With this novel data set, the team was able to determine how current-driven mixing varies across ______ and what impact it has on the distribution of heat and nutrients in the ocean.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** regions, 

  *"And" here coordinates two noun clauses that are both objects of "determine" ("how current-driven mixing varies across regions" and "what impact it has on..."), not two independent clauses, so no comma belongs before it.*

**B.** regions: 

  *"Determine how current-driven mixing varies across regions" is not yet a complete independent clause — it is still mid-object — so a colon has nothing finished to follow.*

**C.** regions; 

  *A semicolon needs an independent clause on both sides, and neither side qualifies here — both are noun clauses serving as objects of "determine."*

**D.** regions **(Correct)**

  *Correct. No punctuation is needed; "and" simply joins two noun clauses that are both objects of "determine."*

*Difficulty: hard*

---

##### Q64
> Researcher Lin Zhi developed a process for increasing the tensile strength—measured in gigapascals, or GPa—of silkworm ______ dissolving and reweaving the silk in a solution of iron metal ions, zinc, and sugar, Zhi increased the amount of force required to stretch it from approximately 0.5 GPa to 2 GPa.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** silk, by 

  *A bare comma joining what should be two separate sentences is a comma splice, with "by" left lowercase.*

**B.** silk by 

  *No punctuation at all — fully fused.*

**C.** silk and by 

  *Inserting "and" does not fit — "By dissolving and reweaving the silk..." is meant to be the introductory phrase of a new sentence, not something coordinated onto the first.*

**D.** silk. By **(Correct)**

  *Correct. A period ends the first sentence; "By dissolving and reweaving the silk..." begins the second sentence's introductory participial phrase, capitalized.*

*Difficulty: medium*

---

##### Q65
> In discussing Mary Shelley's 1818 epistolary novel Frankenstein, literary theorist Gayatri Spivak directs the reader's attention to the character of Margaret Saville. As Spivak points out, Saville is not the protagonist of Shelley's ______ as the recipient of the letters that frame the book's narrative, she's the "occasion" of it.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** novel 

  *Fuses two independent clauses with no punctuation at all and drops the corrective adverb "rather" that the sentence needs to signal the contrast.*

**B.** novel, 

  *A bare comma cannot join two independent clauses, and "rather" is still missing. Comma splice.*

**C.** novel; rather, **(Correct)**

  *Correct. A semicolon at the true clause boundary, with "rather" as the conjunctive adverb correcting the prior statement, followed by its own comma.*

**D.** novel, rather, 

  *"Rather" is an adverb, not a coordinating conjunction, so a bare comma before it cannot join two independent clauses — a comma splice, even with "rather" correctly bracketed by commas.*

*Difficulty: sat-hardest*

---

##### Q66
> Using satellite remote sensing, Dr. Catherine Nakalembe, director of NASA's Harvest Africa initiative, gathers important data on crop health. Nakalembe doesn't just compile the ______ she also shares her findings with African farmers, enabling them to make data-driven decisions about managing critical food crops.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** information, though; **(Correct)**

  *Correct. "Though" trails the first clause as its own adverb (comma before it), and the semicolon marks the actual boundary between the two independent clauses.*

**B.** information, though, 

  *Gets the comma before the trailing "though" right but then uses only a comma — not a semicolon — at the true clause boundary. Comma splice.*

**C.** information; though 

  *Places the semicolon too early, right before "though," as if "though" opens the second clause — but "though" here trails the first clause as its own modifier, so this misplaces the boundary and leaves the second clause unattached.*

**D.** information though, 

  *Missing the comma before the trailing "though" entirely, and using only a comma (not a semicolon) at the actual clause boundary — wrong twice over.*

*Difficulty: sat-hardest*

---

##### Q67
> In paleontology, the term "Elvis taxon" gets applied to a newly identified living species that was once presumed to be extinct. Like an Elvis impersonator who might bear a striking resemblance to the late musical icon Elvis Presley himself, an Elvis taxon is not the real thing, ______ is a misidentified look-alike.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** however but it 

  *Stacks "however" and "but" together, which does not fit any standard pattern, and still leaves no sentence break before the second independent clause.*

**B.** however it 

  *With only the fixed comma before "however" and nothing else marking a boundary, the two independent clauses run together — a fused reading with no clean break.*

**C.** however, it 

  *Brackets "however" with commas as a mid-sentence parenthetical, but the underlying boundary between "is not the real thing" and "it is a misidentified look-alike" is still marked only by commas — a comma splice disguised by the inserted adverb, exactly the trap this course's own teach block warns about.*

**D.** however. It **(Correct)**

  *Correct. "However" trails the first clause (the fixed comma before it already does that job), the period ends that sentence, and "It is a misidentified look-alike" begins a new one.*

*Difficulty: sat-hardest*

---

##### Q68
> In 1955, Indian Bengali filmmaker Satyajit Ray released his first movie, Pather ______ quiet black-and-white drama about a family in rural India, Ray's film was quite different from the loud, colorful action-romance movies that were popular at the time.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Panchali a 

  *No punctuation at all between the film's title and the new sentence's opening noun phrase — fully fused, with no capital letter marking the new sentence either.*

**B.** Panchali, which was a 

  *Turns "a quiet black-and-white drama..." into a relative clause attached to "Panchali," but once that clause closes, "Ray's film was quite different..." has no grammatical connection to what precedes — the relative clause already used up "Panchali" as its subject, leaving "Ray's film" orphaned.*

**C.** Panchali, a 

  *A bare comma joining what should be two separate sentences is a comma splice.*

**D.** Panchali. A **(Correct)**

  *Correct. A period ends the first sentence; "A quiet black-and-white drama about a family in rural India" begins the second sentence's introductory appositive phrase, capitalized.*

*Difficulty: hard*

---

##### Q69
> The Tantaquidgeon Museum in Uncasville, Connecticut, was founded in 1931 with the goal of showcasing the culture and history of the Mohegan ______ today, nearly a century later, it is the oldest Native-owned and -operated museum in the country.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Tribe, and **(Correct)**

  *Correct. Two independent clauses joined with comma plus "and."*

**B.** Tribe 

  *No mark at all between two independent clauses — a fused sentence.*

**C.** Tribe and 

  *Missing the comma that has to precede "and" when it joins two independent clauses.*

**D.** Tribe, 

  *A bare comma cannot join two independent clauses. Comma splice.*

*Difficulty: medium*

---

##### Q70
> The poem Beowulf begins with the word "hwæt," which is an Old English ______ as "hark!" or "listen!" in some versions, the word was playfully rendered as "bro!" by Maria Dahvana Headley in her 2020 translation of the poem.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** exclamation, translated 

  *The first sentence properly ends at "exclamation"; joining it to the next with a bare comma is a comma splice, and "translated" is left lowercase instead of starting a new sentence.*

**B.** exclamation and translated 

  *Inserting "and" wrongly coordinates within what should be one sentence, without the comma two independent clauses would need in any case.*

**C.** exclamation translated 

  *No punctuation at all — fully fused.*

**D.** exclamation. Translated **(Correct)**

  *Correct. A period ends the first sentence; "Translated as 'hark!' or 'listen!' in some versions," begins the second sentence's introductory participial phrase, capitalized.*

*Difficulty: medium*

---

##### Q71
> The field of geological oceanography owes much to American ______ Marie Tharp, a pioneering oceanographic cartographer whose detailed topographical maps of the ocean floor and its multiple rift valleys helped garner acceptance for the theories of plate tectonics and continental drift.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** geologist, 

  *Severs the title "geologist" from the name "Marie Tharp" it directly precedes — the two form one tightly bound subject unit, like "American geologist Marie Tharp," with nothing between them.*

**B.** geologist **(Correct)**

  *Correct. No punctuation between the bare title and the name it directly precedes.*

**C.** geologist; 

  *A semicolon needs an independent clause on both sides, and neither the title alone nor the name alone qualifies.*

**D.** geologist: 

  *A colon has nothing to introduce here — "owes much to American geologist" is not yet a complete statement.*

*Difficulty: medium*

---

##### Q72
> Quantum particles of light—photons—provide an unhackable means of transmitting encryption keys over networks, as attempts to observe particles in quantum states will invariably alter the particles ______ dismantle any information they transmit.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** and in the process, 

  *Opens the internal supplement "in the process" with no comma right after "and," leaving it one-sided even though a comma correctly closes it after "process."*

**B.** and, in the process, **(Correct)**

  *Correct. A comma opens the parenthetical "in the process" right after "and," matching the comma that closes it after "process."*

**C.** and in the process— 

  *Uses a dash to close a supplement that never opens with any mark at all — an unmatched, one-sided pairing.*

**D.** and, in the process 

  *Opens the parenthetical correctly with a comma after "and" but drops the comma that should close it after "process" — one-sided on the other end.*

*Difficulty: hard*

---

##### Q73
> In 2018, the innovative works of Congolese sculptor and architect Bodys Isek ______ were featured in City Dreams, a solo exhibition at New York's Museum of Modern Art.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Kingelez; 

  *Severs the subject — a person's full name, still incomplete without "Kingelez" — from its verb "were featured."*

**B.** Kingelez, 

  *A comma between the complete subject and its verb is unjustified.*

**C.** Kingelez **(Correct)**

  *Correct. "Kingelez" completes the subject's full name; no punctuation belongs before the verb "were featured."*

**D.** Kingelez: 

  *A colon here has nothing to introduce — the subject is not yet a complete independent clause.*

*Difficulty: easy*

---

##### Q74
> The 1977 play And the Soul Shall Dance depicts two Japanese American farming families in Depression-era Southern California. Critics have noted the way pioneering ______ compares the experiences of issei (Japanese nationals who emigrated to America) and nisei (their American-born children).

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** playwright, Wakako Yamauchi, 

  *Brackets the name as though "playwright" alone already identified a specific, known individual — but the name is essential to say which playwright is meant, not a removable aside.*

**B.** playwright, Wakako Yamauchi 

  *Same wrong opening comma as choice A, with no matching closing comma even under that flawed reading.*

**C.** playwright Wakako Yamauchi, 

  *A stray trailing comma wrongly separates the complete subject "pioneering playwright Wakako Yamauchi" from its verb "compares."*

**D.** playwright Wakako Yamauchi **(Correct)**

  *Correct. No punctuation — the title and name form one tightly bound subject, directly followed by the verb "compares."*

*Difficulty: medium*

---

##### Q75
> With some 16,000 in attendance, the Second World Black and African Festival of Arts and ______ or FESTAC '77, as the event was more commonly known—became the largest pan-African event on record. FESTAC drew people from around the world to Lagos, Nigeria, for a monthlong celebration of Black and African art, scholarship, and activism.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Culture: 

  *A colon does not match the dash that already closes the supplement after "known," and a colon is not the tool used to open a mid-sentence renaming aside like this one.*

**B.** Culture— **(Correct)**

  *Correct. Opens the supplement "or FESTAC '77, as the event was more commonly known" with a dash to match the dash that closes it.*

**C.** Culture, 

  *A comma does not match the dash that already closes the supplement — an unmatched pair.*

**D.** Culture 

  *Leaves the supplement with no opening mark at all, though it already closes with a dash — one-sided.*

*Difficulty: hard*

---

##### Q76
> The relationship between genomes and epigenomes reveals how cells with identical DNA develop different ______ whereas the genome in each cell contains a complete DNA sequence, the epigenome consists of chemical compounds that determine which traits in the sequence will be expressed.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** functions 

  *Drops the colon needed to signal that an explanation follows — without it, "functions whereas the genome..." fuses together with no signal that what comes next explains the claim just made.*

**B.** functions, 

  *A comma does not carry the colon's "what follows explains what precedes" role, and using one here fails to mark that the whereas-construction explains rather than merely continues the first clause.*

**C.** functions and, 

  *Wrongly coordinates with "and" as though adding a second, equal independent clause, when what follows is actually explaining the first claim, not just adding to it.*

**D.** functions: **(Correct)**

  *Correct. The left side is a complete independent clause, and the colon introduces the whole "whereas...the epigenome..." construction as the explanation of how cells develop different functions.*

*Difficulty: sat-hardest*

---

##### Q77
> The city of Amsterdam partnered with consultants to develop Public Eye—an ethical AI-powered crowd-monitoring ______ video streamed from cameras in heavily touristed areas, the AI algorithm determines crowd sizes without, in the interest of protecting individuals' privacy, retaining the footage.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** system—analyzing 

  *Keeps everything as one sprawling sentence: a second dash here would need to pair with the one already opened after "Public Eye" to bracket "an ethical AI-powered crowd-monitoring system," but "analyzing video..." then dangles after that close with no sentence break before "the AI algorithm determines," producing a run-on.*

**B.** system, analyzing 

  *A comma instead of a period still fails to mark the needed sentence boundary, stringing everything into one overlong, improperly joined sentence.*

**C.** system. Analyzing **(Correct)**

  *Correct. The first sentence is complete ("The city of Amsterdam partnered with consultants to develop Public Eye—an ethical AI-powered crowd-monitoring system"), so a period ends it; "Analyzing video streamed from cameras in heavily touristed areas," begins the second sentence's introductory phrase.*

**D.** system analyzing 

  *No punctuation at all — fully fused into one sprawling run-on.*

*Difficulty: sat-hardest*

---

##### Q78
> On November 2, 1772, amid rising tensions with Great Britain, Boston colonists formed the Boston Committee of Correspondence. By 1774, what had started as a local means of mobilizing support for the Patriot cause had grown into something far more ______ network of such committees that, facilitating communication among the colonies, helped lay the groundwork for the Continental Congress.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** extensive: a **(Correct)**

  *Correct. "What had started as...had grown into something far more extensive" is a complete independent clause, and the colon introduces the noun phrase "a network of such committees..." that identifies what that "something" was.*

**B.** extensive; a 

  *"A network of such committees that...helped lay the groundwork" is a single extended noun phrase, not an independent clause — its only verb, "helped," belongs to the relative clause modifying "network," so a semicolon has no independent clause on its right to pair with.*

**C.** extensive, it was a 

  *Inserting "it was" creates a second clause joined to the first by only a comma — a comma splice — and redundantly restates what "had grown into something far more extensive" already said.*

**D.** extensive. A 

  *"A network of such committees that...helped lay the groundwork for the Continental Congress" standing alone after a period is just a noun phrase with no independent top-level verb — a fragment.*

*Difficulty: sat-hardest*

---

##### Q79
> In the 1950s, novel audio technologies allowed the addition of another instrument to jazz and swing ______ relatively quiet instrument, its full range of sound was finally audible alongside the blaring brass instruments of the time, allowing flautists like Bennie Maupin and Bobbi Humphrey to perform with other jazz greats.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** music, the flute, a 

  *A comma instead of a colon fails to cleanly name the instrument, and there is no sentence break before "A relatively quiet instrument" either — everything runs together with no boundary where one is needed.*

**B.** music. The flute, a 

  *Leaves "The flute, a relatively quiet instrument" as an orphaned subject with no verb of its own once "its full range of sound was finally audible" supplies its own separate subject, "its."*

**C.** music; the flute, a 

  *The same orphaned-subject problem as choice B, now introduced with a semicolon instead of a period — "the flute, a relatively quiet instrument" still has no verb before "its full range of sound" takes over as subject.*

**D.** music: the flute. A **(Correct)**

  *Correct. The colon names the instrument ("the flute") that completes the independent clause before it; the period then ends that sentence, and "A relatively quiet instrument" opens the next as an introductory appositive for "its."*

*Difficulty: sat-hardest*

---

##### Q80
> American writer Edwidge Danticat, who emigrated from Haiti in 1981, has won acclaim for her powerful short stories, novels, and ______ her lyrical yet unflinching depictions of her native country's turbulent history, writer Robert Antoni has compared Danticat to Nobel Prize–winning novelist Toni Morrison.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** essays, praising 

  *The first sentence properly ends once the three-item series (stories, novels, essays) is complete; joining it to the next with a bare comma is a comma splice, and "praising" is left lowercase.*

**B.** essays and praising 

  *"And" wrongly treats "praising..." as a fourth series item or a second coordinated action, when it is meant to begin a new sentence with its own subject, "writer Robert Antoni."*

**C.** essays praising 

  *No punctuation at all, fully fused, missing the mark that should end the series and the sentence.*

**D.** essays. Praising **(Correct)**

  *Correct. A period ends the first sentence, with "essays" completing its three-item series; "Praising her lyrical yet unflinching depictions..." begins the second sentence's introductory participial phrase.*

*Difficulty: medium*

---

##### Q81
> Joshua Hinson, director of the language revitalization program of the Chickasaw Nation in Oklahoma, helped produce the world's first Indigenous-language instructional app, Chickasaw ______ Chickasaw TV, in 2010; and a Rosetta Stone language course in Chickasaw, in 2015.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Basic; in 2009, an online television network; 

  *Places the first semicolon too early, right after "Basic" and before "in 2009" — but "in 2009" is part of the first item's own internal date, not a separate item boundary.*

**B.** Basic; in 2009, an online television network, 

  *Same misplaced first semicolon as choice A, and it also ends with a comma rather than a semicolon before the third item — mixing separator types inconsistently within one series.*

**C.** Basic, in 2009; an online television network, **(Correct)**

  *Correct. The comma keeps "Basic, in 2009" together as the first item's own internal date, the semicolon separates the first item from the second, and the series continues consistently with a semicolon before the third item, "and a Rosetta Stone..."*

**D.** Basic, in 2009, an online television network, 

  *Uses only commas throughout a series whose items already contain their own internal commas — exactly the case that requires semicolons as the item-level separators.*

*Difficulty: sat-hardest*

---

##### Q82
> A group of ecologists led by Axel Mithöfer at the Max Planck Institute for Chemical Ecology in Germany examined the defensive responses of two varieties of the sweet potato ______ TN57, which is known for its insect resistance, and TN66, which is much more susceptible to pests.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** plant. 

  *"TN57, which is known for its insect resistance, and TN66, which is much more susceptible to pests" has no independent top-level verb — both "which" clauses are subordinate — so standing alone after a period, it is a fragment.*

**B.** plant; 

  *A semicolon needs an independent clause on its right for the same reason a period fails — the right side is not one.*

**C.** plant 

  *Drops the colon that should introduce the two named varieties the sentence already promised ("two varieties of the sweet potato plant"), leaving "plant TN57" to fuse with no signal.*

**D.** plant: **(Correct)**

  *Correct. The independent clause before it promises two specific varieties, and the colon introduces them by name: TN57 and TN66.*

*Difficulty: hard*

---

##### Q83
> Nigerian author Buchi Emecheta's celebrated literary oeuvre includes The Joys of Motherhood, a novel about the changing roles of women in 1950s ______ a television play about the private struggles of a newlywed couple in Nigeria; and Head Above Water, her autobiography.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** Lagos, A Kind of Marriage, 

  *Uses a comma at the item boundary where the series has already committed to semicolons (one appears later, before "and Head Above Water") — inconsistent once items contain their own internal commas.*

**B.** Lagos; A Kind of Marriage, **(Correct)**

  *Correct. A semicolon separates the first item from the second, consistent with the semicolon used later in the series, and the comma after the second item's title correctly introduces its description.*

**C.** Lagos, A Kind of Marriage: 

  *Uses a comma at the item boundary (the same inconsistency as choice A) and adds a colon after the second item's title that has no naming or introducing role at that spot.*

**D.** Lagos; A Kind of Marriage 

  *Gets the semicolon right at the item boundary but drops the comma that should follow the second item's title before its own description, "a television play about..."*

*Difficulty: sat-hardest*

---

##### Q84
> From afar, African American fiber artist Bisa Butler's portraits look like paintings, their depictions of human faces, bodies, and clothing so intricate that it seems only a fine brush could have rendered them. When viewed up close, however, the portraits reveal themselves to be ______ stitching barely visible among the thousands of pieces of printed, microcut fabric.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** quilts, and the 

  *"And" wrongly treats "the stitching barely visible..." as a second coordinated item, but it has no finite verb of its own ("visible" is an adjective, not a verb) — there is nothing of matching grammatical weight for "and" to join.*

**B.** quilts, the **(Correct)**

  *Correct. A comma introduces the absolute phrase "the stitching barely visible among the thousands of pieces of printed, microcut fabric," which modifies the whole preceding clause.*

**C.** quilts; the 

  *A semicolon needs an independent clause on its right, but "the stitching barely visible..." has no finite verb — it is an absolute phrase, not a clause.*

**D.** quilts. The 

  *"The stitching barely visible among the thousands of pieces of printed, microcut fabric" standing alone after a period has no finite verb — a fragment.*

*Difficulty: hard*

---

##### Q85
> Sociologist Alton Okinaka sits on the review board tasked with adding new sites to the Hawai'i Register of Historic Places, which includes Pi'ilanihale Heiau and the 'Ōpaeka'a Road Bridge. Okinaka doesn't make such decisions ______ all historical designations must be approved by a group of nine other experts from the fields of architecture, archaeology, history, and Hawaiian culture.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** single-handedly, however; **(Correct)**

  *Correct. "However" trails the first clause as its own adverb, comma before it, and the semicolon marks the actual boundary between the two independent clauses.*

**B.** single-handedly; however, 

  *Places the semicolon too early, right before "however," as if it opens the second clause — but "however" here trails the FIRST clause (modifying "doesn't make such decisions single-handedly"), so this misplaces the boundary.*

**C.** single-handedly, however, 

  *Gets the comma before the trailing "however" right but uses only a comma — not a semicolon — at the true clause boundary. Comma splice.*

**D.** single-handedly however 

  *Missing both commas around "however" and the semicolon at the clause boundary — every needed mark is absent.*

*Difficulty: sat-hardest*

---

##### Q86
> A study published by Rice University geoscientist Ming Tang in 2019 offers a new explanation for the origin of Earth's ______ structures called arcs, towering ridges that form when a dense oceanic plate subducts under a less dense continental plate, melts in the mantle below, and then rises and bursts through the continental crust above.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** continents geological 

  *Drops the colon that should signal an explanation is coming, fusing "continents" directly into "geological" with no boundary marked.*

**B.** continents: geological **(Correct)**

  *Correct. The independent clause before it is complete, and the colon introduces the explanatory noun phrase "geological structures called arcs..."*

**C.** continents; geological 

  *"Geological structures called arcs, towering ridges that form when..." is a noun phrase with modifying appositive and relative clause, not an independent clause — a semicolon fails without one on its right.*

**D.** continents. Geological 

  *"Geological structures called arcs, towering ridges that form when a dense oceanic plate subducts..." standing alone after a period has no independent top-level verb — a fragment.*

*Difficulty: hard*

---

##### Q87
> The Organisation for Economic Co-operation and Development (OECD) tracks comparative price list data for its thirty-eight member countries. For instance, in July 2021, a hypothetical basket of goods priced at 100 US dollars (USD) in the United States would have cost 62 USD and 110 USD in fellow OECD ______ and Luxembourg, respectively.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** nations, Chile 

  *Severs "nations" from the essential examples "Chile and Luxembourg" that identify exactly which nations are meant — not a removable aside.*

**B.** nations; Chile 

  *A semicolon needs an independent clause on both sides, and neither "nations" alone nor "Chile and Luxembourg, respectively" qualifies.*

**C.** nations: Chile 

  *A colon treats the country names as a list being introduced after a finished statement, but they are tightly identifying which nations "nations" refers to, and "respectively" needs them sitting directly against "nations" to read naturally.*

**D.** nations Chile **(Correct)**

  *Correct. No punctuation — "Chile and Luxembourg" directly and essentially identifies which OECD nations are meant.*

*Difficulty: hard*

---

##### Q88
> The pedagogy of the Suzuki method is rooted in several central ______ by Japanese violinist Shinichi Suzuki, who sought to parallel the linguistic learning environment, the method emphasizes playing instruments from a very young age and teaches students as young as three to play simple classical pieces such as "March in G."

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** tenets. Developed **(Correct)**

  *Correct. A period ends the first sentence; "Developed by Japanese violinist Shinichi Suzuki, who sought to parallel the linguistic learning environment," begins the second sentence's introductory participial phrase.*

**B.** tenets developed 

  *No punctuation at all — fully fused.*

**C.** tenets that, developed 

  *Turns "developed by...Suzuki" into a clause attached to "tenets" via "that," but it was the METHOD, not the tenets, that Suzuki developed — this garbles the intended meaning and leaves the sentence unable to resume grammatically once "the method emphasizes" arrives.*

**D.** tenets, developed 

  *A comma instead of a period joins what should be two separate sentences — a comma splice.*

*Difficulty: medium*

---

##### Q89
> During the decades-long movement to codify the rights of Latinos in the US, certain events were pivotal: the founding of social justice group the League of United Latin American Citizens in ______ Katzenbach v. Morgan court decision in 1966, which affirmed the rights of Latino voters, is another such event.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** 1929. For one, the 

  *Moves "For one" to open the second sentence, but that same sentence goes on to call its own subject "another such event" — pairing an opening "for one" (signaling a first example) with "another" (signaling an additional one) inside the same sentence contradicts itself. "For one" needs to trail the first example instead.*

**B.** 1929, for one, the 

  *A comma instead of a period fails to separate the two examples into their own sentences at all — a comma splice, with "for one" now sitting mid-splice rather than closing the first example.*

**C.** 1929 for one, the 

  *Missing the comma before "for one" entirely, fusing "1929 for one" together, in addition to failing to mark the sentence boundary with a period.*

**D.** 1929, for one. The **(Correct)**

  *Correct. The comma sets off "for one" as a trailing tag closing the first example ("...in 1929, for one" = as one example), the period ends that sentence, and "The Katzenbach v. Morgan...decision...is another such event" begins its own sentence, with "another" now correctly pairing against the already-established "for one."*

*Difficulty: sat-hardest*

---

##### Q90
> The Austronesian language family includes Tagalog, Malagasy, and some 1,200 other languages throughout the Pacific, making it one of the largest language families in the world and of keen interest to ______ of the University of Toronto.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** linguist, Diane Massam, 

  *Brackets the name as though "linguist" alone already identified a specific, known individual — but the name is essential to say which linguist is meant, not a removable aside.*

**B.** linguist, Diane Massam 

  *Same wrong opening comma as choice A, without even a matching closing comma.*

**C.** linguist Diane Massam **(Correct)**

  *Correct. No punctuation — the title and name form one tightly bound unit, the object of "to."*

**D.** linguist: Diane Massam 

  *"Of keen interest to linguist" is not a complete independent clause — still mid-prepositional-phrase — so a colon has nothing finished to follow, and nothing is being introduced or enumerated here anyway.*

*Difficulty: medium*

---

##### Q91
> Featuring works by the photographers Lola Álvarez Bravo and Else "Yva" Neuländer-Simon, the 2021 exhibition The New Woman Behind the Camera set out to provide a wide-ranging overview of photography by women in the 1920s through the ______ given the collection's breadth of more than 120 photos, its efforts were largely successful.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** 1950s, and **(Correct)**

  *Correct. Two independent clauses joined with comma plus "and."*

**B.** 1950s and 

  *Missing the comma that has to precede "and" when it joins two independent clauses.*

**C.** 1950s 

  *No mark at all between two independent clauses — a fused sentence.*

**D.** 1950s, 

  *A bare comma cannot join two independent clauses. Comma splice.*

*Difficulty: medium*

---

##### Q92
> Philosopher Peter Kivy was a leading figure in musical ______ evidenced by his belief that instead of evoking particular emotions, such as sadness or joy, compositions elicit a listener's emotional response to the structure and artistry of the music itself, Kivy's approach to the study of music was decidedly formalist.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** aesthetics as 

  *No punctuation at all — fully fused, with no sentence break before the introductory phrase that should start the second sentence.*

**B.** aesthetics and as 

  *Inserting "and" does not fit, and there is still no proper sentence-boundary punctuation before what is meant to be a new sentence beginning with "As evidenced by..."*

**C.** aesthetics, as 

  *A comma instead of a period fails to mark the needed sentence boundary — everything from "as evidenced" through "decidedly formalist" gets tacked onto "aesthetics" as one long comma splice.*

**D.** aesthetics. As **(Correct)**

  *Correct. A period ends the first sentence; "As evidenced by his belief that..." begins the second sentence's introductory phrase, capitalized.*

*Difficulty: medium*

---

##### Q93
> Recent analysis of 32532 Thereus—an outer solar system object orbiting the Sun between Jupiter and Saturn—has determined its color to be gray, suggesting an icy composition. Such interpretations are ultimately ______ the object's gray coloration may be an incidental effect of radiation, solar wind, or collisions with other objects rather than evidence of its physical makeup.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** speculative, though 

  *Gets the comma before the trailing "though" right but supplies no further mark at all before "the object's gray coloration..." — fusing the two independent clauses.*

**B.** speculative, though; **(Correct)**

  *Correct. "Though" trails the first clause as its own adverb (comma before it), and the semicolon marks the true boundary between the two independent clauses.*

**C.** speculative; though 

  *Places the semicolon too early, right before "though," treating it as if it opens the second clause — but "though" trails the FIRST clause here, so this misplaces the boundary.*

**D.** speculative, though, 

  *Uses only a comma — not a semicolon — at the true clause boundary, even with "though" correctly bracketed by commas. Comma splice.*

*Difficulty: sat-hardest*

---

##### Q94
> As a behavioral economist, Katy Milkman of the University of Pennsylvania recognizes that people sometimes make irrational economic decisions. Milkman's research can thus address anomalies that neoclassical economic ______ assume that people are consistently rational decision-makers—cannot explain.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** models—which **(Correct)**

  *Correct. Opens the supplement "which assume that people are consistently rational decision-makers" with a dash to match the dash that closes it before "cannot explain."*

**B.** models, which 

  *A comma does not match the dash that already closes the supplement — an unmatched pair.*

**C.** models which 

  *Leaves the nonrestrictive "which" clause with no opening mark at all, though a dash already closes it later — one-sided.*

**D.** models which— 

  *Puts the dash after "which" instead of before it, failing to open the supplement at the correct boundary — right after "models," where the supplement actually begins.*

*Difficulty: hard*

---

##### Q95
> In 2021, Mexican biologist Martha Lydia Macías-Rubalcava led a review of the scientific literature related to endophytic fungi (i.e., fungi that live inside a host ______ researching 120 endophytic fungi–produced compounds, she found that their phytotoxicity can make them viable alternatives to chemical herbicides for controlling weeds.

Which choice completes the text so that it conforms to the conventions of Standard English?

**A.** plant). By **(Correct)**

  *Correct. Closes the parenthetical gloss "(i.e., fungi that live inside a host plant)" to match its opening, a period ends that sentence, and "By researching 120 endophytic fungi–produced compounds," begins the second sentence's introductory phrase.*

**B.** plant), by 

  *A comma instead of a period fails to end the first sentence, creating a run-on as "by researching..." gets improperly attached with only a comma.*

**C.** plant) and by 

  *Inserting "and" does not fit either — "by researching..." is meant to introduce a new sentence's main clause, "she found that...," not to be coordinated onto the end of the first sentence.*

**D.** plant) by 

  *No punctuation at all after the closing parenthesis — fully fusing the two sentences with no boundary mark.*

*Difficulty: medium*

---

### Expression of Ideas

#### Rhetorical Synthesis (92 items)

##### Q1
> NOTES. While researching a topic, a student has taken the following notes: • Oracles of the Pink Universe was a 2021 exhibition at the Denver Museum of Art in Colorado. • It featured eight artworks by South African artist Simphiwe Ndzube. • One of these works is a painting titled Assertion of Will. • Assertion of Will depicts three standing figures. • The figures wear clothing made of fabric pieces stitched to the painting's canvas.

The student wants to describe how fabric is used in Assertion of Will. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** In Assertion of Will, the figures' clothing is made of fabric pieces stitched to the painting's canvas. **(Correct)**

  *Correct. It states exactly how fabric is used — as pieces stitched to the canvas to form the figures' clothing — which is the specific mechanism the goal asked for.*

**B.** The exhibition Oracles of the Pink Universe featured artworks by artist Simphiwe Ndzube. 

  *This places the painting inside its exhibition and names its artist, but it never mentions fabric at all. A sentence cannot describe a use of fabric while never referring to fabric.*

**C.** Depicting three standing, clothed figures, Assertion of Will is a painting by Simphiwe Ndzube. 

  *"Clothed" names that the figures wear something without saying what that clothing is made of or how it was applied to the canvas — the exact detail the goal is asking for is the one word this choice leaves out.*

**D.** Simphiwe Ndzube's Assertion of Will was one of eight artworks exhibited in Oracles of the Pink Universe at the Denver Museum of Art. 

  *Accurate provenance — where the work was shown and how many pieces accompanied it — but provenance is not a description of fabric use, and this choice never gets to the canvas at all.*

*Difficulty: easy*

---

##### Q2
> NOTES. While researching a topic, a student has taken the following notes: • Muslins are woven cotton fabrics with a variety of uses. • Dhaka muslin is a handmade fabric produced in Dhaka, Bangladesh. • It has an extremely fine weave and is primarily used to make luxury clothing. • Sheeting muslin is a machine-made fabric produced in factories. • It has a coarse weave and is primarily used to upholster furniture and create backdrops for theater sets.

The student wants to emphasize a difference between the two muslins. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Dhaka muslin is a handmade fabric with an extremely fine weave, while sheeting muslin is machine made with a coarse weave. **(Correct)**

  *Correct. Both muslins appear, and "while" states an explicit contrast on the two properties — production method and weave — that the notes actually distinguish them by.*

**B.** Dhaka muslin and sheeting muslin are two different types of woven cotton fabrics. 

  *This says a difference exists without stating what it is. "Two different types" is a label, not the content of the contrast the goal asked to be emphasized.*

**C.** Muslins can be used in a variety of ways, from making luxury clothing to upholstering furniture and creating backdrops for theater sets. 

  *This lists uses without naming which muslin does which, so nothing distinguishes Dhaka muslin from sheeting muslin. It reads as if one fabric had all these uses.*

**D.** Sheeting muslin is machine made, has a coarse weave, and is used for furniture and theater sets. 

  *Only sheeting muslin appears; Dhaka muslin is never mentioned. A single fabric described in isolation cannot be a difference between two fabrics.*

*Difficulty: easy*

---

##### Q3
> NOTES. While researching a topic, a student has taken the following notes: • The Azores is a group of islands about 870 miles off the coast of Portugal. • Historians have long believed that in the fifteenth century Portuguese mariners were the first humans to populate the Azores. • A 2015 study coauthored by Sofia Gabriel and Maria da Luz Mathias found that Vikings from Scandinavia may have populated the Azores as early as the ninth century. • The researchers found a genetic connection between house mice in the Azores and house mice in Scandinavia. • House mice may have traveled from Scandinavia to the Azores on Viking ships.

The student wants to specify who may have first populated the Azores, according to the 2015 study. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Historians have long believed that the first humans to populate the Azores, a group of islands about 870 miles off the coast of Portugal, arrived in the fifteenth century. 

  *This is the older, long-held belief the 2015 study revises — it names Portuguese mariners' era without ever citing the study, and it answers a "who traditionally believed" question rather than "who does the 2015 study propose."*

**B.** Portuguese mariners may not have been the first humans to populate the Azores. 

  *This states what the study casts doubt on but never names who the study proposes instead. "Specify who" requires naming the candidate, and this choice names only who has been ruled out.*

**C.** In their 2015 study, the researchers found a genetic connection between house mice in the Azores and those in Scandinavia. 

  *This is the evidence the study used, not its conclusion about human settlers. Reporting the mouse-DNA finding does not specify who the study proposes as the first humans to populate the islands.*

**D.** According to a 2015 study, the first humans to populate the Azores may have been Vikings from Scandinavia, not mariners from Portugal as previously believed. **(Correct)**

  *Correct. It attributes the claim to the 2015 study and names the specific group the study proposes — Vikings from Scandinavia — which is exactly what "specify who" requires.*

*Difficulty: medium*

---

##### Q4
> NOTES. While researching a topic, a student has taken the following notes: • Yellowstone is a national park in the northwest United States. • In 1995, gray wolves were reintroduced into the park. • Since then, the number of gray wolves in the park has stabilized at roughly 100. • This number is believed to be the park's carrying capacity. • Carrying capacity describes the maximum number of a species that a specific environment's resources can sustain over time.

The student wants to specify the number of gray wolves in Yellowstone. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Gray wolves were reintroduced into Yellowstone, a national park in the northwest United States, in 1995. 

  *This gives the reintroduction date and location but never states a number of wolves, which is the one thing "specify the number" requires.*

**B.** As of 1995, there were gray wolves living in Yellowstone, a national park in the northwest United States. 

  *This confirms wolves were present in 1995 but supplies no count. "There were gray wolves" is not a specified number, and 1995 is the reintroduction year, not the year the population stabilized at roughly 100.*

**C.** The carrying capacity of an environment, such as Yellowstone, describes the maximum number of species that the environment can sustain over time. 

  *This defines the general term "carrying capacity" rather than reporting Yellowstone's actual wolf count. It answers a define-the-term goal, not a specify-the-number goal.*

**D.** Yellowstone is a national park that has roughly 100 gray wolves living in it. **(Correct)**

  *Correct. It states the specific figure — roughly 100 — that the notes give for the park's gray wolf population, which is exactly what the goal calls for.*

*Difficulty: easy*

---

##### Q5
> NOTES. While researching a topic, a student has taken the following notes: • Novelist Willa Cather grew up in Nebraska and attended the University of Nebraska-Lincoln. • Some of Cather's best-known novels are set in Nebraska. • Two such novels are O Pioneers! (1913) and My Ántonia (1918). • Cather's novels describe the experiences of immigrants who settled in the Great Plains.

The student wants to identify the setting of Cather's novel My Ántonia. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** My Ántonia is set in Nebraska, where Cather grew up. **(Correct)**

  *Correct. It names the specific setting — Nebraska — that the goal asks for, and adds only the biographical detail the notes offer to explain the connection.*

**B.** Cather, author of My Ántonia, described the experiences of immigrants in her novels. 

  *This describes what Cather's novels are generally about, not where My Ántonia specifically takes place. "Experiences of immigrants" is subject matter, not a setting.*

**C.** Among Cather's best-known novels are O Pioneers! (1913) and My Ántonia (1918). 

  *This only lists the novel among Cather's other works and gives its publication date — neither of which is a setting. The goal asked where the novel takes place, not when it was published.*

**D.** Cather attended the University of Nebraska-Lincoln and set some of her novels in Nebraska. 

  *"Some of her novels" is a vague plural that never confirms My Ántonia specifically is one of them, so the sentence never actually identifies that novel's setting.*

*Difficulty: easy*

---

##### Q6
> NOTES. While researching a topic, a student has taken the following notes: • In 2013, paleontology professor Hesham Sallam and his students from Mansoura University in Egypt made a discovery. • The team found a partial dinosaur skeleton at a site in Egypt's Dakhla Oasis. • The skeleton belonged to a dinosaur species that lived approximately 80 million years ago. • The new species was named Mansourasaurus to recognize the team that discovered it.

The student wants to explain the origin of the species' name. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Mansourasaurus, a new species discovered in Egypt in 2013, lived approximately 80 million years ago. 

  *This gives the species' age and discovery year but says nothing about why it is called Mansourasaurus — the notes' one bullet that actually addresses the name is never used.*

**B.** A partial dinosaur skeleton found in Egypt's Dakhla Oasis belonged to a species named Mansourasaurus. 

  *This reports the discovery site and confirms the name exists, but it does not explain where the name came from. Stating a name is not the same as explaining its origin.*

**C.** Mansourasaurus, a species that lived approximately 80 million years ago, was discovered in 2013 by Egyptian paleontologist Hesham Sallam and a team of university students. 

  *This credits the discovery to Sallam's team accurately but never connects that fact to the name itself — it describes who found the fossil, not why the species is called Mansourasaurus.*

**D.** The new species was named Mansourasaurus to recognize the team that discovered it, a professor and students from Mansoura University. **(Correct)**

  *Correct. It states the actual reason for the name — to recognize the discovering team — and specifies the university the name echoes, which is the origin the goal asks for.*

*Difficulty: medium*

---

##### Q7
> NOTES. While researching a topic, a student has taken the following notes: • The tundra is a type of environment characterized by especially harsh winter conditions. • Winter temperatures in the tundra average a frigid -30 degrees Fahrenheit. • Animals that have adapted to these conditions can survive tundra winters. • During the tundra's short growing season, average temperatures can reach a relatively mild 54 degrees Fahrenheit. • Around 1,700 different kinds of plants are able to grow in the tundra.

The student wants to emphasize how harsh the conditions can be in the tundra. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Winters in the tundra are especially harsh, with temperatures averaging a frigid -30 degrees Fahrenheit. **(Correct)**

  *Correct. It asserts the harshness directly and backs it with the single most extreme figure in the notes — the -30-degree winter average — which is exactly the emphasis the goal calls for.*

**B.** Animals that have adapted to harsh winter conditions can survive tundra winters. 

  *This is about survival strategies, not about how harsh the conditions themselves are. It mentions harshness only in passing while the sentence's real subject is animal adaptation.*

**C.** There are around 1,700 different kinds of plants that can live in the tundra, where average temperatures can reach a mild 54 degrees Fahrenheit. 

  *This uses the growing-season figure, which the notes describe as "relatively mild" — the opposite of harsh. It emphasizes plant diversity under mild conditions, not winter harshness.*

**D.** Along with animals that have adapted to the tundra's conditions, around 1,700 different kinds of plants can live in the tundra. 

  *This combines the adaptation bullet and the plant-count bullet, neither of which states a harsh condition — it emphasizes how much life the tundra supports, which argues against harshness rather than for it.*

*Difficulty: medium*

---

##### Q8
> NOTES. While researching a topic, a student has taken the following notes: • A wok is a cooking pan that originated in China during the Han dynasty (206 BCE-220 CE). • The wok's round, wide base helps cook food evenly. • The wok's high, angled sides help contain oil splatters. • Grace Young is a cook and culinary historian. • Her book The Breath of a Wok (2004) traces the history of the wok.

The student wants to describe the wok's shape. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Grace Young's 2004 book, The Breath of a Wok, traces the history of the cooking pan. 

  *This is about a book on the wok's history, not about the wok's physical shape. Nothing in it describes the base or the sides at all.*

**B.** Able to cook food evenly and contain oil splatters, the wok is the subject of Grace Young's 2004 book. 

  *This states the wok's functions and names the book about it, but never describes the shape that produces those functions — round, wide base and high, angled sides never appear.*

**C.** A wok is a cooking pan with a round, wide base and high, angled sides. **(Correct)**

  *Correct. It states the wok's physical shape directly and completely, using both shape details the notes provide, which is exactly what "describe the wok's shape" requires.*

**D.** The design of a wok, a type of cooking pan that originated in China during the Han dynasty, helps the pan cook food evenly and contain oil splatters. 

  *This explains what the wok's design accomplishes and where the wok originated, but it never states what that design actually looks like — the shape itself is the one thing left unnamed.*

*Difficulty: easy*

---

##### Q9
> NOTES. While researching a topic, a student has taken the following notes: • The Sasanian Empire lasted about 400 years (AD 224 to AD 651). • The Sasanians controlled an area spanning 1.4 million square miles. • This area included present-day Iran and Iraq. • The empire's capital was the ancient city of Ctesiphon. • Ctesiphon was located near present-day Baghdad, Iraq.

The student wants to specify the location of Ctesiphon. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The Sasanian Empire began in AD 224 and ended in AD 651. 

  *This gives the empire's dates, not Ctesiphon's location. Ctesiphon is not even mentioned, so this cannot specify where the city was.*

**B.** The capital of the Sasanian Empire, which spanned 1.4 million square miles, was Ctesiphon. 

  *This confirms Ctesiphon was the capital and gives the empire's total area, but it never states where the city itself was located — the empire's size is not the city's location.*

**C.** The Sasanians controlled an area of 1.4 million square miles, including present-day Iran and Iraq. 

  *This describes the empire's overall territory, not the capital city's specific location. Ctesiphon is never named, so the sentence cannot specify where it was.*

**D.** Ctesiphon, the capital of the Sasanian Empire, was located near present-day Baghdad, Iraq. **(Correct)**

  *Correct. It names Ctesiphon and states exactly where it was — near present-day Baghdad, Iraq — which is precisely the location the goal asks to be specified.*

*Difficulty: easy*

---

##### Q10
> NOTES. While researching a topic, a student has taken the following notes: • Archaeologist Dr. Sada Mire founded the Horn Heritage Foundation to preserve the cultural history of regions in the Horn of Africa. • Horn Heritage has overseen a preservation project to create 3D digital scans of ancient rock art in Somaliland. • Paintings found at the Laas Geel caves are included in the scans. • The Laas Geel paintings feature human figures and animals. • Paintings found at the Dhagah Nabi Galay caves are included in the scans. • The Dhagah Nabi Galay caves feature what are thought to be the earliest examples of writing in East Africa.

The student wants to emphasize a similarity between the Laas Geel paintings and the Dhagah Nabi Galay paintings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The earliest examples of writing in East Africa are thought to be featured in the paintings at the Dhagah Nabi Galay caves in Somaliland. 

  *Only one site's paintings appear here. With nothing said about Laas Geel, there is no second thing to be similar to, so this cannot emphasize a similarity between the two.*

**B.** The paintings at the Dhagah Nabi Galay caves feature examples of writing, while those at the Laas Geel caves feature humans and animals. 

  *This states both sites but uses "while" to contrast what each set of paintings features — that is a difference between the two sites, the opposite relation from the similarity the goal asked for.*

**C.** In Somaliland, the paintings in the Laas Geel caves feature human figures and animals. 

  *Only Laas Geel is described; Dhagah Nabi Galay never appears. A single site cannot be shown to be similar to a site the sentence never mentions.*

**D.** The Laas Geel paintings and the Dhagah Nabi Galay paintings are both examples of ancient rock art found in Somaliland. **(Correct)**

  *Correct. Both sites appear, and "both" states the shared property — ancient rock art in Somaliland — that the goal's similarity is built on.*

*Difficulty: medium*

---

##### Q11
> NOTES. While researching a topic, a student has taken the following notes: • In 1897, African American inventor Andrew Beard invented an automatic coupler. • It improved on the existing design of train car couplers. • It made the job of connecting train cars safer. • In 1938, African American inventor Frederick Jones invented a mobile refrigeration system. • It improved on the existing design of food transport trucks. • It enabled trucks to carry perishable foods farther.

The student wants to emphasize a similarity between Beard's invention and Jones's invention. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Beard's automatic coupler and Jones's mobile refrigeration system both improved on existing designs. **(Correct)**

  *Correct. Both inventions are named, and "both improved on existing designs" states the exact shared property the notes give for each — the similarity the goal is asking for.*

**B.** In 1897, Beard invented an automatic coupler, which made the job of connecting train cars safer. 

  *Only Beard's invention appears; Jones's is never mentioned. A sentence about one invention cannot show a similarity to an invention it does not discuss.*

**C.** Beard's invention made the job of connecting train cars safer, whereas Jones's invention enabled food transport trucks to carry perishables farther. 

  *Both inventions appear, but "whereas" pairs each with its own distinct effect, stating a contrast between what the two inventions did rather than a similarity between them.*

**D.** Jones's mobile refrigeration system, which he invented in 1938, made it possible for food transport trucks to carry perishable foods farther. 

  *Only Jones's invention is described here; Beard's automatic coupler never appears. With one invention missing, there is nothing for this one to be similar to.*

*Difficulty: medium*

---

##### Q12
> NOTES. While researching a topic, a student has taken the following notes: • The painter Frida Kahlo is one of the most influential artists of the twentieth century. • She was born in Coyoacán, Mexico, in 1907. • She is best known for her vivid and richly symbolic self-portraits. • The Two Fridas (1939) features two versions of Kahlo sitting together. • One version wears a European-style dress and the other a traditional Tehuana dress.

The student wants to introduce Kahlo to an audience unfamiliar with the artist. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Known for being vivid and richly symbolic, Frida Kahlo's self-portraits include The Two Fridas (1939). 

  *This assumes the reader already knows who Kahlo is and jumps straight into cataloguing one of her paintings — it never establishes who she is or why she matters, which is what introducing an unfamiliar figure requires.*

**B.** The 1939 painting The Two Fridas is one example of a self-portrait by Frida Kahlo. 

  *This names Kahlo only as the author of one painting rather than introducing her as an artist — it gives a reader who has never heard of her no sense of who she is or why she is significant.*

**C.** One painting by Frida Kahlo features two versions of herself, with one version wearing a European-style dress and the other a traditional Tehuana dress. 

  *This describes a single painting's content in detail without ever introducing Kahlo herself — no birth year, no reputation, no explanation of what she is known for.*

**D.** One of the most influential artists of the twentieth century, Mexican painter Frida Kahlo is best known for her self-portraits, which are vivid and richly symbolic. **(Correct)**

  *Correct. It establishes who Kahlo is, her stature, her nationality, and what she is known for — exactly the biographical grounding an unfamiliar audience needs to be introduced to an artist.*

*Difficulty: medium*

---

##### Q13
> NOTES. While researching a topic, a student has taken the following notes: • Bioluminescence is the emission of light by living organisms. • This light is produced by chemical reactions in organisms' cells. • Jellyfish emit flashes of blue light. • This behavior serves to startle predators. • Black dragonfish emit a steady red light. • This behavior helps them locate prey in deep waters.

The student wants to emphasize a difference between the behavior of jellyfish and that of black dragonfish. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Both jellyfish and black dragonfish are organisms that emit light, which is produced by chemical reactions in these organisms' cells. 

  *"Both" states what jellyfish and black dragonfish share — how their light is produced — which is a similarity, the opposite of the difference the goal asks for.*

**B.** Black dragonfish emit a steady red light, which helps them locate prey in deep waters. 

  *Only black dragonfish appear; jellyfish are never mentioned. A single species' behavior cannot be a difference from a species the sentence never discusses.*

**C.** Bioluminescence, the emission of light by living organisms, results from chemical reactions in organisms' cells. 

  *This defines bioluminescence in general terms and names neither jellyfish nor black dragonfish specifically, so it cannot emphasize any difference between their behaviors.*

**D.** Jellyfish emit light to startle predators, whereas black dragonfish do so to locate prey. **(Correct)**

  *Correct. Both species appear, and "whereas" states the exact functional difference the notes give — startling predators versus locating prey — which is the difference the goal calls for.*

*Difficulty: medium*

---

##### Q14
> NOTES. While researching a topic, a student has taken the following notes: • Annie Wu is a prominent American flutist who graduated from the New England Conservatory. • She has won multiple national flute competitions. • She is best known for a 2011 YouTube video that has been viewed over two million times. • The video shows her performing Three Beats for Beatbox Flute, an original work by composer Greg Pattillo. • Wu combines flute playing and beatboxing in the video.

The student wants to emphasize Wu's most well-known achievement. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Annie Wu, who has won multiple national flute competitions, has also combined flute playing and beatboxing. 

  *This leads with the competition wins, which the notes never call her most well-known accomplishment, and treats the beatbox performance as a secondary add-on rather than the achievement itself.*

**B.** Among her many achievements, prominent American flutist Annie Wu graduated from the New England Conservatory and has won multiple national flute competitions. 

  *This lists credentials — schooling and competitions — but never mentions the 2011 video the notes explicitly identify as what she is best known for.*

**C.** Annie Wu is best known for a 2011 YouTube video performance of Three Beats for Beatbox Flute that has been viewed over two million times. **(Correct)**

  *Correct. It states directly that this video is what Wu is "best known for" and gives its viewership, matching the notes' own language for her most well-known achievement.*

**D.** Composer Greg Pattillo's original work Three Beats for Beatbox Flute combines flute playing and beatboxing. 

  *This makes Pattillo's composition the subject rather than Wu's performance of it — the sentence credits the piece, not the flutist, and Wu is never named as the one being recognized.*

*Difficulty: medium*

---

##### Q15
> NOTES. While researching a topic, a student has taken the following notes: • In 1897, twenty Black US Army infantrymen rode bicycles from Montana to Missouri. • The 1,900-mile journey took forty-one days. • The goal was to test the idea of forming a military bicycle corps. • In 2022, Erick Cedeño, a Black long-distance cyclist, reenacted the journey on its 125th anniversary. • Cedeño wanted to honor the infantrymen on the journey's 125th anniversary.

The student wants to emphasize how far the infantrymen traveled. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The US infantrymen rode their bicycles from Montana to Missouri—traveling a total of 1,900 miles. **(Correct)**

  *Correct. It states the actual distance figure — 1,900 miles — that the notes give, which is exactly the quantity the goal asks to be emphasized.*

**B.** The 125th anniversary of the infantrymen's journey was in 2022. 

  *This gives the anniversary year, not a distance. Nothing in this choice tells a reader how far the infantrymen actually rode.*

**C.** The goal of the 1897 journey was to test the idea of forming a military bicycle corps. 

  *This states the journey's purpose, not its length. A reader is told why the ride happened but never how far it covered.*

**D.** Over a century later, Erick Cedeño honored the infantrymen by reenacting their 1897 journey. 

  *This describes Cedeño's 2022 reenactment and its purpose, never stating the 1,900-mile distance the original infantrymen traveled.*

*Difficulty: easy*

---

##### Q16
> NOTES. While researching a topic, a student has taken the following notes: • Komodo dragons are the largest lizards in the world. • They live on four islands in Komodo National Park, Indonesia. • The park has a total of twenty-nine islands.

The student wants to emphasize how many islands in Komodo National Park have Komodo dragons living on them. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Komodo dragons, the world's largest lizards, live on islands in Komodo National Park, Indonesia. 

  *This says Komodo dragons live on islands but drops the actual count — neither the four islands they inhabit nor the twenty-nine islands in the park appears.*

**B.** The largest lizards in the world are found in Komodo National Park. 

  *This identifies the park but gives no island count at all, so it cannot emphasize how many of the park's islands hold Komodo dragons.*

**C.** Only four of the twenty-nine islands in Komodo National Park have Komodo dragons living on them. **(Correct)**

  *Correct. It states both figures — four of twenty-nine — and "only" frames the smallness of that fraction, which is precisely the emphasis the goal calls for.*

**D.** There are twenty-nine islands in Indonesia's Komodo National Park. 

  *This gives the park's total island count but never mentions how many of those islands actually have Komodo dragons, which is the number the goal asks to be emphasized.*

*Difficulty: medium*

---

##### Q17
> NOTES. While researching a topic, a student has taken the following notes: • Certhidea olivacea is a perching bird that can be found on the Galápagos Island of Pinzón. • Creagrus furcatus is a seabird that can be found on the Galápagos Island of Darwin. • Conservation organizations evaluate the risk that species will become extinct in the near future. • C. olivacea faces a high risk of extinction. • C. furcatus faces little risk of becoming extinct in the near future.

The student wants to compare the extinction risk faced by C. olivacea with that faced by C. furcatus. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** According to conservation organizations, C. olivacea has a higher risk of becoming extinct in the near future than C. furcatus. **(Correct)**

  *Correct. Both species appear, and "higher risk... than" states the exact relative relationship the notes support — a high risk for one species set explicitly against a low risk for the other.*

**B.** C. furcatus faces a high risk of extinction, while C. olivacea faces little risk of becoming extinct in the near future. 

  *This reverses the notes: they state that C. olivacea, not C. furcatus, faces the high risk. The comparison is stated but the risk levels are swapped between the two species.*

**C.** Conservation organizations have evaluated both C. furcatus's and C. olivacea's risk of becoming extinct in the near future. 

  *This confirms both species were evaluated but never states what either species' risk level actually is, so no comparison between them is ever made.*

**D.** C. olivacea is a perching bird that faces a high risk of extinction. 

  *Only C. olivacea appears; C. furcatus is never mentioned. A single species' risk level cannot be compared to a species the sentence leaves out.*

*Difficulty: medium*

---

##### Q18
> NOTES. While researching a topic, a student has taken the following notes: • Miguel Luciano is a multimedia visual artist. • One of his sculptures is Double Phantom/EntroP.R. (2017). • The work consists of two red Schwinn Phantom bicycles that he fused together. • The bicycles face opposite directions. • The bicycles share the same rear wheel.

The student wants to describe how the bicycles in Double Phantom/EntroP.R. are fused together. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** To create the sculpture Double Phantom/EntroP.R., Miguel Luciano fused together two Schwinn Phantom bicycles. 

  *This confirms the bicycles were fused but never describes how — neither the shared rear wheel nor the opposite orientation, the two facts that actually explain the fusion, appears.*

**B.** There are two red Schwinn Phantom bicycles in the sculpture Double Phantom/EntroP.R. 

  *This states that two bicycles exist in the work but says nothing about how they are joined — count is not a description of a fusion technique.*

**C.** The two red bicycles in Double Phantom/EntroP.R. are fused together so that they share the same rear wheel while facing opposite directions. **(Correct)**

  *Correct. It states exactly how the bicycles are joined — sharing one rear wheel while facing opposite directions — which is the mechanism the goal asks to be described.*

**D.** Double Phantom/EntroP.R. is a sculpture created by multimedia visual artist Miguel Luciano. 

  *This identifies the artist and the work's title but never touches on the bicycles or how they are fused at all.*

*Difficulty: easy*

---

##### Q19
> NOTES. While researching a topic, a student has taken the following notes: • The mountain pygmy possum is a mammal species. • Up until 1966, it was believed to be extinct. • That year, a live mountain pygmy possum was identified in the wild in Australia. • The mountain pygmy possum is considered a Lazarus species. • "Lazarus species" is a term for living species of organisms that were once believed to be extinct.

The student wants to define the term "Lazarus species" and provide an example of one. Which choice most effectively uses relevant information from the notes to accomplish these goals?

**A.** The term "Lazarus species" describes a living species of organism, such as the mountain pygmy possum, that was once believed to be extinct. **(Correct)**

  *Correct. It gives the definition in the notes' own terms — a living species once believed extinct — and folds in the mountain pygmy possum as the required example, satisfying both parts of the two-part goal.*

**B.** One example of a Lazarus species is the mountain pygmy possum, a mammal species that was identified in the wild in Australia in 1966. 

  *This supplies the example but never states the general definition of "Lazarus species" — a reader who did not already know the term would still not know what it means after reading this.*

**C.** The mountain pygmy possum, a species of mammal, was identified in the wild in 1966. 

  *This reports the 1966 rediscovery as a fact about the possum but never uses the term "Lazarus species" or defines it — the goal's defining half is missing entirely.*

**D.** Sometimes, a species once believed to be extinct is later found living in the wild. 

  *This paraphrases the definition without ever naming the term "Lazarus species" or citing the mountain pygmy possum as an example — both required elements are missing.*

*Difficulty: hard*

---

##### Q20
> NOTES. While researching a topic, a student has taken the following notes: • The human body requires magnesium for over 300 essential processes. • Magnesium is a mineral present in many foods. • Peanuts contain 49 milligrams per ounce (mg/oz) of magnesium. • Almonds contain 80 mg/oz. • Chia seeds contain 150 mg/oz.

The student wants to identify which of the three foods has the highest magnesium content. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** At 80 mg/oz, almonds contain more magnesium than peanuts (49 mg/oz). 

  *This compares only two of the three foods and leaves out chia seeds, which at 150 mg/oz actually has the highest content — so the comparison it makes does not identify the true highest.*

**B.** Chia seeds contain 150 mg/oz of magnesium, which is more than peanuts and almonds. **(Correct)**

  *Correct. It names chia seeds — the food with the highest figure in the notes — and states explicitly that its content exceeds both of the other two foods.*

**C.** Magnesium is present in many foods, including peanuts, almonds, and chia seeds. 

  *This lists the three foods without giving any of their magnesium figures, so no highest can be identified from it at all.*

**D.** Peanuts contain 49 mg/oz of magnesium, a mineral the human body requires for over 300 essential processes. 

  *Peanuts have the lowest figure of the three, not the highest, and this choice never mentions the other two foods' amounts to establish any ranking at all.*

*Difficulty: easy*

---

##### Q21
> NOTES. While researching a topic, a student has taken the following notes: • The Haber-Bosch process is an industrial process used to manufacture ammonia (NH3). • It was invented by chemists Fritz Haber and Carl Bosch in 1910. • The process's primary reaction combines nitrogen (N2) from the air with hydrogen (H2). • It requires an iron catalyst and high temperatures and pressures. • Most of the ammonia produced by this process is used in fertilizers.

The student wants to provide an overview of the Haber-Bosch process. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The Haber-Bosch process needs nitrogen, hydrogen, and an iron catalyst. 

  *This lists the inputs but leaves out the conditions the reaction actually requires — high temperatures and pressures — and what the process actually produces, giving only a partial picture rather than an overview.*

**B.** The Haber-Bosch process uses an iron catalyst along with high temperatures and pressures to manufacture ammonia from nitrogen and hydrogen. **(Correct)**

  *Correct. It names the reactants, the catalyst, the conditions, and the product in a single sentence — the fullest overview the notes support, matching what "provide an overview" requires.*

**C.** Chemists Fritz Haber and Carl Bosch invented an industrial process to manufacture ammonia to be used in fertilizers. 

  *This covers the process's inventors and its end use, but never describes the process itself — no reactants, catalyst, or conditions appear, so this is history and application, not an overview of the process.*

**D.** In 1910, chemists Fritz Haber and Carl Bosch invented the Haber-Bosch process, which requires high temperatures and pressures. 

  *This gives the invention date and one condition, but omits the reactants and the catalyst — too thin a slice of the notes to count as an overview of the process.*

*Difficulty: medium*

---

##### Q22
> NOTES. While researching a topic, a student has taken the following notes: • Sue is the nickname of a dinosaur fossil specimen housed at the Field Museum of Natural History. • The Field Museum of Natural History is located in Chicago, Illinois. • Sue is a member of the genus Tyrannosaurus. • Big Mike is the nickname of a dinosaur fossil specimen housed at the Museum of the Rockies. • The Museum of the Rockies is located in Bozeman, Montana. • Big Mike is a member of the genus Tyrannosaurus.

The student wants to emphasize a similarity between the two specimens. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The Field Museum of Natural History, where Sue is housed, is located in Chicago, Illinois. 

  *Only Sue appears here, and the fact given is about the museum's city, not about any property shared with Big Mike. Big Mike is never mentioned.*

**B.** Big Mike is the nickname of a Tyrannosaurus fossil specimen housed at the Museum of the Rockies in Bozeman, Montana. 

  *Only Big Mike is described; Sue never appears. A single specimen's details cannot show a similarity to a specimen the sentence leaves out entirely.*

**C.** The dinosaur fossil specimens Sue and Big Mike are both members of the genus Tyrannosaurus. **(Correct)**

  *Correct. Both specimens are named, and "both members of the genus Tyrannosaurus" states the exact property the notes show they share, which is the similarity the goal calls for.*

**D.** While Sue is housed at the Field Museum of Natural History, Big Mike is housed at the Museum of the Rockies. 

  *Both specimens appear, but "while" sets their two different housing museums against each other — a contrast between the two, not a shared trait, which is the opposite of a similarity.*

*Difficulty: easy*

---

##### Q23
> NOTES. While researching a topic, a student has taken the following notes: • Organisms release cellular material into their environment by shedding substances such as hair or skin. • The DNA in these substances is known as environmental DNA, or eDNA. • Researchers collect and analyze eDNA to detect the presence of species that are difficult to observe. • Geneticist Sara Oyler-McCance's research team analyzed eDNA in water samples from the Florida Everglades to detect invasive constrictor snake species in the area. • The study determined a 91% probability of detecting Burmese python eDNA in a given location.

The student wants to present the study to an audience already familiar with environmental DNA. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Sara Oyler-McCance's researchers analyzed eDNA in water samples from the Florida Everglades for evidence of invasive constrictor snakes, which are difficult to observe. **(Correct)**

  *Correct. It uses "eDNA" as an already-known term rather than re-explaining it, and presents the study — who ran it, where, and what it looked for — which is what an audience already versed in eDNA needs.*

**B.** An analysis of eDNA can detect the presence of invasive species that are difficult to observe, such as constrictor snakes. 

  *This describes what eDNA analysis can do in general terms but never presents the actual study — no researcher, no location, no python probability appears.*

**C.** Researchers found Burmese python eDNA, or environmental DNA, in water samples; eDNA is the DNA in released cellular materials, such as shed skin cells. 

  *This spells out what eDNA stands for and defines it from scratch — exactly the explanation an audience "already familiar with environmental DNA" does not need, and it never names the study's researcher.*

**D.** Sara Oyler-McCance's researchers analyzed environmental DNA (eDNA)—that is, DNA from cellular materials released by organisms—in water samples from the Florida Everglades. 

  *This does present the study but pauses to define eDNA in an appositive ("that is, DNA from cellular materials released by organisms") — exactly the kind of explanation the audience clause says is unnecessary for a reader already familiar with the term.*

*Difficulty: hard*

---

##### Q24
> NOTES. While researching a topic, a student has taken the following notes: • Species belonging to the Orchidaceae (orchid) family can be found in both tropical and temperate environments. • Orchidaceae species diversity has not been well studied in temperate forests, such as those in Oaxaca, Mexico. • Arelee Estefanía Muñoz-Hernández led a study to determine how many different Orchidaceae species are present in the forests of Oaxaca. • Muñoz-Hernández and her team collected orchids each month for a year at a site in Oaxaca. • Seventy-four Orchidaceae species were present at the site.

The student wants to present the study and its findings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** A study led by Arelee Estefanía Muñoz-Hernández identified a total of 74 Orchidaceae species in the temperate forests of Oaxaca, Mexico. **(Correct)**

  *Correct. It names the researcher who led the study and states the finding — 74 species — combining both halves of the two-part goal in a single sentence.*

**B.** There are orchids in many environments, but there are 74 Orchidaceae species in Oaxaca, Mexico. 

  *This gives the finding but never presents the study itself — no researcher and no mention that a year-long collection effort produced the number.*

**C.** Oaxaca, Mexico, is home to temperate forests containing 74 Orchidaceae species. 

  *This states the finding as a fact about a place, without ever attributing it to Muñoz-Hernández's study — the study itself, half of what the goal asks to be presented, is missing.*

**D.** Arelee Estefanía Muñoz-Hernández and her team wanted to know how many different Orchidaceae species are present in the forests of Oaxaca, Mexico, so they conducted a study to collect orchids. 

  *This presents the study's purpose and method but stops before reporting what the study actually found — the 74-species finding, the other half of the goal, never appears.*

*Difficulty: medium*

---

##### Q25
> NOTES. While researching a topic, a student has taken the following notes: • Platinum is a rare and expensive metal. • It is used as a catalyst for chemical reactions. • Platinum catalysts typically require a large amount of platinum to be effective. • Researcher Jianbo Tang and his colleagues created a platinum catalyst that combines platinum with liquid gallium. • Their catalyst was highly effective and required only trace amounts of platinum (0.0001% of the atoms in the mixture).

The student wants to explain an advantage of the new platinum catalyst developed by Jianbo Tang and colleagues. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Researcher Jianbo Tang and his colleagues created a platinum catalyst that combines platinum, a rare and expensive metal, with liquid gallium. 

  *This describes what the new catalyst is made of but never says why that composition is an advantage — it never mentions the tiny 0.0001% platinum content that makes it cheaper to produce.*

**B.** Like other platinum catalysts, the new platinum catalyst requires a particular amount of the metal to be effective. 

  *"Like other platinum catalysts" claims a similarity to conventional catalysts, when the notes' whole point is that this one is different — it needs far less platinum, not "a particular amount" comparable to the rest.*

**C.** Platinum is a rare and expensive metal that is used as a catalyst for chemical reactions; however, platinum catalysts typically require a large amount of platinum to be effective. 

  *This states the general drawback of platinum catalysts as a category but never introduces Tang's specific innovation or how it overcomes that drawback — no advantage of the new catalyst is ever stated.*

**D.** While still highly effective, the new platinum catalyst requires far less of the rare and expensive metal than do other platinum catalysts. **(Correct)**

  *Correct. It states the advantage directly — comparable effectiveness with far less of the costly metal — which is exactly the improvement over conventional platinum catalysts that the notes describe.*

*Difficulty: medium*

---

##### Q26
> NOTES. While researching a topic, a student has taken the following notes: • Allan Houser was a Chiricahua Warm Springs Apache sculptor, illustrator, and painter. • Many of his sculptures featured Native American figures. • He depicted this subject matter using abstract, modernist forms, developing a distinctive style that influenced many other artists. • His well-known sculpture Sacred Rain Arrow was pictured on the State of Oklahoma license plate.

The student wants to describe the distinctive style of Houser's sculptures. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** A sculptor, illustrator, and painter, Houser developed a distinctive style for portraying Native American figures. 

  *This confirms a distinctive style exists and names his subject matter and disciplines, but it never states what the style actually consisted of — abstract, modernist forms are never mentioned.*

**B.** Houser's sculptures employ abstract, modernist forms to depict Native American figures. **(Correct)**

  *Correct. It names the specific stylistic features — abstract, modernist forms — that the notes give as what makes Houser's sculptures distinctive.*

**C.** Many other artists have been influenced by the style of Houser's sculptures. 

  *This describes the style's impact on other artists, not what the style itself looks like. A reader learns the style was influential without ever learning what it was.*

**D.** The sculpture Sacred Rain Arrow is a well-known example of Houser's style. 

  *This names one sculpture as an instance of the style without describing any of the style's actual features — abstraction and modernism are never named.*

*Difficulty: medium*

---

##### Q27
> NOTES. While researching a topic, a student has taken the following notes: • In 2018 researchers Adwait Deshpande, Shreejata Gupta, and Anindya Sinha were observing wild macaques in India's Bandipur National Park. • They saw macaques calling out and gesturing at humans who were eating or carrying food. • They designed a study to find out if the macaques were intentionally communicating to try to persuade the humans to share their food. • In the study trials, macaques frequently called out to and gestured at humans holding food. • In the study trials, macaques called out to and gestured at empty-handed humans less frequently.

The student wants to present the study's results. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Macaques in the study called out and gestured more frequently at humans holding food than at empty-handed humans. **(Correct)**

  *Correct. It reports what the trials actually found — the difference in frequency between food-holding and empty-handed humans — which is the study's results, exactly what the goal asks for.*

**B.** In 2018, researchers who had observed macaques in India's Bandipur National Park calling out and gesturing at humans designed a study. 

  *This describes the observation that led to the study and the fact that a study was designed, but stops before any trial result is reported.*

**C.** The researchers hoped to find out if the macaques were intentionally communicating to try to persuade humans to share their food. 

  *This states the study's hypothesis or research question, not what the trials actually found — a hoped-for answer is not a result.*

**D.** The researchers studied how macaques behaved around both humans holding food and empty-handed humans. 

  *This describes the study's design — what conditions were compared — without reporting which condition actually produced more calling and gesturing.*

*Difficulty: easy*

---

##### Q28
> NOTES. While researching a topic, a student has taken the following notes: • Muckrakers were journalists who sought to expose corruption in US institutions during the Progressive Era (1897-1920). • Ida Tarbell was a muckraker who investigated the Standard Oil Company. • She interviewed Standard Oil executives, oil industry workers, and public officials. • She examined thousands of pages of the company's internal communications, including letters and financial records. • Her book The History of the Standard Oil Company (1904) exposed the company's unfair business practices.

The student wants to emphasize the thoroughness of Ida Tarbell's investigation of the Standard Oil Company. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Ida Tarbell not only interviewed Standard Oil executives, oil industry workers, and public officials but also examined thousands of pages of the company's internal communications. **(Correct)**

  *Correct. "Not only... but also" stacks two separate investigative methods — wide-ranging interviews and thousands of pages of documents — which is what actually demonstrates thoroughness, rather than merely stating that the investigation happened.*

**B.** Ida Tarbell, who investigated the Standard Oil Company, was a muckraker (a journalist who sought to expose corruption in US institutions during the Progressive Era, 1897-1920). 

  *This defines what a muckraker is and identifies Tarbell as one, but says nothing about the scope or depth of her actual investigation — no interviews, no documents.*

**C.** As part of her investigation of the Standard Oil Company, muckraker Ida Tarbell conducted interviews. 

  *This mentions only one of Tarbell's two investigative methods and drops the specific detail — who she interviewed and how many pages of documents she reviewed — that shows thoroughness rather than just activity.*

**D.** Published in 1904, muckraker Ida Tarbell's book The History of the Standard Oil Company exposed the company's unfair business practices. 

  *This describes the outcome of the investigation — the published book and what it exposed — without describing the investigation's methods, which is where the thoroughness the goal asks for actually lives.*

*Difficulty: medium*

---

##### Q29
> NOTES. While researching a topic, a student has taken the following notes: • John Carver was one of the 41 signatories of the Mayflower Compact. • The Mayflower Compact was a legal agreement among the pilgrims that immigrated to Plymouth Colony. • It was created in 1620 to establish a common government. • It states that the pilgrims who signed it wanted to "plant the first colony in the northern parts of Virginia" under King James. • Carver became the first governor of Plymouth Colony.

The student wants to specify the reason the Mayflower Compact was created. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Stating that its signatories wanted to "plant the first colony in the northern parts of Virginia," the Mayflower Compact was a legal agreement among the pilgrims that immigrated to Plymouth Colony. 

  *This quotes the compact's colonization intent and identifies it as a legal agreement, but never states the reason it was created — to establish a common government — which the notes give explicitly.*

**B.** Created in 1620, the Mayflower Compact states that the pilgrims wanted to "plant the first colony in the northern parts of Virginia." 

  *This gives the creation date and the colonization goal quoted in the document, but not the compact's own stated purpose — establishing a common government — which is what "reason it was created" is asking for.*

**C.** The Mayflower Compact was created to establish a common government among the pilgrims that immigrated to Plymouth Colony. **(Correct)**

  *Correct. It states the compact's purpose directly, in the notes' own words — to establish a common government — which is exactly the reason for its creation the goal asks to be specified.*

**D.** The Mayflower Compact had 41 signatories, including John Carver, the first governor of Plymouth Colony. 

  *This gives the number of signatories and Carver's later role but never states why the document was created in the first place.*

*Difficulty: easy*

---

##### Q30
> NOTES. While researching a topic, a student has taken the following notes: • Marine biologist Camille Jazmin Gaynus studies coral reefs. • Coral reefs are vital underwater ecosystems that provide habitats to 25% of all marine species. • Reefs can include up to 8,000 species of fish, such as toadfish, seahorses, and clown triggerfish. • The Amazon Reef is a coral reef in Brazil. • It is one of the largest known reefs in the world.

The student wants to introduce the scientist and her field of study to a new audience. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Located in Brazil, the Amazon Reef is one of the largest known coral reefs in the world. 

  *This introduces the Amazon Reef, not Gaynus. Neither the scientist nor her field of study — the two things the goal asks to be introduced — appears anywhere in this sentence.*

**B.** Marine biologist Camille Jazmin Gaynus studies coral reefs, vital underwater ecosystems that provide homes to 25% of all marine species. **(Correct)**

  *Correct. It names Gaynus, identifies her as a marine biologist, and defines her field of study — coral reefs and their significance — introducing both parts the goal requires to a reader who knows neither.*

**C.** Providing homes to 25% of all marine species, including up to 8,000 species of fish, coral reefs are vital underwater ecosystems and thus of great interest to marine biologists. 

  *This describes coral reefs and mentions marine biologists as a general category, but never names Gaynus specifically — the scientist herself is never introduced.*

**D.** As Camille Jazmin Gaynus knows well, coral reefs are vital underwater ecosystems, providing homes to thousands of species of fish. 

  *"As... knows well" treats Gaynus as already familiar background rather than introducing her — it never states that she is a marine biologist or that studying reefs is her field.*

*Difficulty: hard*

---

##### Q31
> NOTES. While researching a topic, a student has taken the following notes: • Some US reformers sought to improve society in the 1800s by building utopias. • A utopia is a community intended to represent a perfect society based on a specific set of principles. • One such community was Brook Farm near Boston, Massachusetts. • It was founded in 1841 by writer George Ripley. • Ripley wrote in a letter that his goal for Brook Farm was "to guarantee the highest mental freedom, by providing all with labor, adapted to their tastes and talents, and securing to them the fruits of their industry."

The student wants to explain the goal of Brook Farm using a quotation from George Ripley. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** In a letter, writer George Ripley explained his goal to "guarantee the highest mental freedom." 

  *This truncates the quotation to its opening clause and never names Brook Farm — a reader would not know which community this goal belongs to.*

**B.** Utopias, such as Brook Farm, founded by George Ripley in 1841, were based on a specific set of principles intended to create a perfect society. 

  *This defines utopias in general and places Brook Farm among them, but never quotes Ripley's own words about the farm's specific goal.*

**C.** Founded by George Ripley near Boston, Massachusetts, Brook Farm was part of a trend in the 1800s, when reformers in the United States built utopias. 

  *This places Brook Farm in its historical context but never quotes Ripley or states his goal for the community at all.*

**D.** Established in 1841, Brook Farm was a utopian community created to "guarantee the highest mental freedom, by providing all with labor... [and] the fruits of their industry," according to founder George Ripley. **(Correct)**

  *Correct. It names Brook Farm, attributes the quotation to Ripley, and uses his own words to state the community's goal — exactly what "explain the goal... using a quotation" requires.*

*Difficulty: medium*

---

##### Q32
> NOTES. While researching a topic, a student has taken the following notes: • Wool is a natural—and economically important—fiber that is obtained from animals like sheep. • Australia is a leading producer of wool. • The thickness of wool fibers varies across sheep breeds. • Merino sheep produce fine wool that is used for apparel. • Rambouillet sheep produce fine wool that is used for apparel. • Romney sheep produce thick wool that is used for rugs and blankets.

The student wants to emphasize how Romney wool differs from Merino and Rambouillet wool. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Romney wool is just one of the many kinds of wools, each originating from a different breed of sheep. 

  *This states that wool varies by breed in general but never names what actually distinguishes Romney wool from the other two breeds — thickness and use are never mentioned.*

**B.** Sheep wool varies from breed to breed, so Romney wool will be different than other kinds of wool. 

  *This asserts that a difference exists as a logical inference ("so... will be different") without ever stating what that difference actually is.*

**C.** The fine wool produced by Merino and Rambouillet sheep is used for apparel, whereas the thicker wool of Romney sheep is used in rugs and blankets. **(Correct)**

  *Correct. It names all three breeds, groups Merino and Rambouillet by their shared property, and contrasts them against Romney on both thickness and use — the exact difference the notes establish.*

**D.** Wool is an economically important fiber—especially in Australia—that can be used to make apparel or even rugs and blankets. 

  *This lists wool's general uses without attributing any of them to a specific breed, so Romney is never actually distinguished from Merino or Rambouillet.*

*Difficulty: medium*

---

##### Q33
> NOTES. While researching a topic, a student has taken the following notes: • Mexican tetras are a fish species with two distinct populations. • Surface-dwelling tetras live on the surface and are able to see. • Cave-dwelling tetras live in total darkness and have lost the ability to see. • Cave-dwelling tetras have asymmetrical skulls with more sensory receptors on one side than the other. • These receptors help cave-dwelling tetras navigate in darkness.

The student wants to emphasize a difference between surface-dwelling and cave-dwelling tetras. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Surface-dwelling and cave-dwelling tetras may belong to the same species, but they are quite different. 

  *This claims a difference exists ("quite different") without stating what it actually is — the vision difference the notes support never appears.*

**B.** Cave-dwelling tetras can no longer see but use sensory receptors on their skulls to navigate. 

  *Only cave-dwelling tetras are described here; surface-dwelling tetras are never mentioned, so nothing is contrasted against them.*

**C.** Mexican tetras are a fish species with two distinct populations: surface-dwelling tetras and cave-dwelling tetras. 

  *This names the two populations but never states how they actually differ — no mention of sight, darkness, or the skull receptors.*

**D.** Surface-dwelling tetras can see, whereas cave-dwelling tetras cannot. **(Correct)**

  *Correct. Both populations appear, and "whereas" states the exact difference the notes establish — one can see, the other cannot — which is the difference the goal asks to be emphasized.*

*Difficulty: easy*

---

##### Q34
> NOTES. While researching a topic, a student has taken the following notes: • A marathon is a long-distance running race that is 26.2 miles long. • An ultramarathon is a long-distance running race of more than 26.2 miles. • The Kepler Challenge is a one-day, 37.3-mile ultramarathon in New Zealand. • The Spreelauf is a six-day, 261-mile ultramarathon in Germany.

The student wants to make a generalization about ultramarathons. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Examples of ultramarathons include the 37.3-mile Kepler Challenge in New Zealand and the 261-mile Spreelauf in Germany. 

  *This lists two specific ultramarathons as examples but never states a general claim that applies to ultramarathons as a category — examples alone are not a generalization.*

**B.** A marathon is 26.2 miles long, but the Spreelauf ultramarathon, at 261 miles, is far longer. 

  *This compares one ultramarathon to a marathon rather than making a claim that covers ultramarathons as a category — it uses only one of the two ultramarathon examples and ignores the Kepler Challenge.*

**C.** Ultramarathons range widely in length, from a few dozen miles to a few hundred. **(Correct)**

  *Correct. It states a general claim — that ultramarathons vary widely in length — supported by the range the two examples actually span (37.3 to 261 miles), which is a genuine generalization.*

**D.** While the Kepler Challenge is a one-day ultramarathon, the Spreelauf is a six-day ultramarathon. 

  *This contrasts the two named races on duration but makes no general claim about ultramarathons as a category — it is a comparison of two instances, not a generalization.*

*Difficulty: medium*

---

##### Q35
> NOTES. While researching a topic, a student has taken the following notes: • From Earth, all the meteors in a meteor shower appear to originate from a single spot in the sky. • This spot is called the meteor shower's radiant. • The Perseid meteor shower is visible in the northern hemisphere in July and August. • Like many meteor showers, it is named for the location of its radiant. • Its radiant is located within the constellation Perseus.

The student wants to explain the origin of the Perseid meteor shower's name. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The Perseid meteor shower is named for the constellation Perseus, the location of the meteor shower's radiant. **(Correct)**

  *Correct. It states directly what the name comes from — the constellation Perseus, where the radiant sits — which is exactly the origin of the name the goal asks to be explained.*

**B.** A meteor shower's name may be linked to a single spot in the sky. 

  *This states the general naming pattern for meteor showers without ever naming the Perseid shower or the constellation Perseus specifically.*

**C.** The Perseid meteor shower, which has a radiant, is visible in the northern hemisphere in July and August. 

  *This gives when and where the shower is visible but never states that its name comes from the constellation Perseus — the actual origin of the name is missing.*

**D.** From Earth, all the meteors in a meteor shower appear to originate from a radiant, such as the one within Perseus. 

  *This explains what a radiant is in general and mentions Perseus only as an example location, without ever stating that this is specifically why the Perseid shower is named as it is.*

*Difficulty: easy*

---

##### Q36
> NOTES. While researching a topic, a student has taken the following notes: • Claude McKay (1889-1948) was a Jamaican American writer. • Songs of Jamaica (1912) and Constab Ballads (1912) are two acclaimed poetry collections that McKay published while living in Jamaica. • McKay moved to Harlem in New York City in 1914. • He is best known as a poet and novelist of the Harlem Renaissance, a literary and cultural movement of the 1920s and 1930s. • His most famous works include the poetry collection Harlem Shadows (1922) and the novel Home to Harlem (1928).

The student wants to emphasize Claude McKay's accomplishments before moving to Harlem. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Jamaican American writer Claude McKay is the author of works such as Songs of Jamaica (1912), Constab Ballads (1912), Harlem Shadows (1922), and Home to Harlem (1928). 

  *This mixes the pre-Harlem poetry collections with the later Harlem Renaissance works (1922 and 1928) without distinguishing them by period, so it never isolates his accomplishments before the move.*

**B.** Although he is best known as a Harlem Renaissance writer, Claude McKay had published two acclaimed poetry collections in 1912 while living in Jamaica: Songs of Jamaica and Constab Ballads. **(Correct)**

  *Correct. The concession ("although he is best known as...") sets aside his later fame, and the main clause isolates exactly the pre-Harlem accomplishment — two 1912 collections published while still in Jamaica.*

**C.** In 1914, Claude McKay moved to Harlem, where he would become known as a poet and novelist of the Harlem Renaissance (a literary and cultural movement of the 1920s and 1930s). 

  *This describes what happened after the move to Harlem, which is the opposite of the timeframe — before the move — that the goal asks to be emphasized.*

**D.** Before moving to Harlem, Claude McKay—author of the poetry collection Harlem Shadows (1922) and the novel Home to Harlem (1928)—lived in Jamaica. 

  *"Before moving to Harlem" points at the right period, but the appositive identifies McKay using his later Harlem Renaissance works (1922, 1928) rather than the Jamaica-era accomplishments the goal calls for.*

*Difficulty: hard*

---

##### Q37
> NOTES. While researching a topic, a student has taken the following notes: • Architect Julian Abele studied Gregorian and neo-Gothic architecture in Europe. • Abele worked for an architecture firm that was hired in 1924 to design buildings for Duke University's new campus. • Most of the buildings on Duke's campus were designed in the Gregorian or neo-Gothic architectural styles. • At the time, Abele was not formally credited with designing the buildings. • Based on the buildings' architectural styles, historians believe Abele designed most of the campus buildings.

The student wants to specify why historians believe Abele designed most of Duke's campus buildings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Given that most of the buildings on Duke's campus feature architectural styles that Abele had studied in Europe, historians believe Abele is the one who designed them. **(Correct)**

  *Correct. "Given that" states the actual reasoning the notes attribute to historians — the buildings' styles match what Abele had specifically studied — which is exactly the reason the goal asks to be specified.*

**B.** Though Abele wasn't formally credited at the time, historians believe he designed most of the buildings on Duke's campus. 

  *This states that historians hold this belief and notes he lacked formal credit, but never says why they believe it — the stylistic evidence connecting Abele to the buildings is never mentioned.*

**C.** Most of Duke's campus buildings, which were designed by a firm Abele worked for, were designed in the Gregorian and neo-Gothic architectural styles. 

  *This states the buildings' styles and the firm's role but never connects that fact to Abele individually or to why historians credit him specifically — his own attribution never appears.*

**D.** Abele, an architect who studied Gregorian and neo-Gothic architecture in Europe, is believed to have designed most of the buildings on Duke's campus. 

  *This states the belief and Abele's training in parallel but never draws the causal connection between the two — it doesn't say historians infer his authorship from the match between his training and the buildings' style.*

*Difficulty: hard*

---

##### Q38
> NOTES. While researching a topic, a student has taken the following notes: • In geology, an Aeolian landform is one that has been created by the wind. • In Greek mythology, Aeolus is the keeper of the winds. • Aeolian landforms are created when the wind erodes, transports, or deposits material. • A mushroom rock is a rock formation in which the top is wider than the base. • A mushroom rock can be formed when the wind erodes the base and the top at different rates.

The student wants to provide an explanation and an example of Aeolian landforms. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Aeolian landforms are created by different wind-based processes; for example, some are created by wind erosion. 

  *This gives the general explanation but its "example" is only a process (erosion), not an actual landform — a mushroom rock, the concrete example the notes supply, never appears.*

**B.** Aeolian landforms—landforms created by the wind—include the mushroom rock, a rock formation in which the wind erodes the base of the rock faster than the top. **(Correct)**

  *Correct. It defines Aeolian landforms and names the mushroom rock as a specific example, explaining how differential erosion produces its shape — both explanation and example are present.*

**C.** Erosion, transportation, and deposition are three examples of how the wind can create Aeolian landforms and mushroom rocks. 

  *These three items are processes, not examples of landforms — the goal calls for an example of an Aeolian landform, and only the mushroom rock (mentioned but not described) would qualify.*

**D.** A mushroom rock is a rock formation that owes its shape to the wind, a natural force associated with Aeolus in Greek mythology. 

  *This gives the example (mushroom rock) but never states the general explanation of what an Aeolian landform is or how wind creates such landforms broadly — only the mythology connection is offered instead.*

*Difficulty: medium*

---

##### Q39
> NOTES. While researching a topic, a student has taken the following notes: • J.R.R. Tolkien's 1937 novel The Hobbit features two maps. • The novel opens with a reproduction of the map that the characters use on their quest. • This map introduces readers to the fictional world they are about to enter. • The novel closes with a map depicting every stop on the characters' journey. • That map allows readers to reconstruct the story they have just read.

The student wants to contrast the purposes of the two maps in The Hobbit. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The Hobbit's opening map introduces readers to the fictional world they are about to enter, while the closing map allows them to reconstruct the story they have just read. **(Correct)**

  *Correct. Both maps appear, and "while" contrasts their distinct purposes — introducing the world versus reconstructing the completed journey — which is exactly the contrast the goal asks for.*

**B.** The Hobbit, a novel published by J.R.R. Tolkien in 1937, features a reproduction of a map that the characters use on their quest, as well as a map that appears at the end of the novel. 

  *This confirms both maps exist and where each appears, but never states what purpose either one serves — the contrast the goal asks for is never made.*

**C.** The Hobbit's two maps, one opening and one closing the novel, each serve a purpose for readers. 

  *This asserts that each map has a purpose without ever naming what those purposes are, so no actual contrast between them is stated.*

**D.** In 1937, author J.R.R. Tolkien published The Hobbit, a novel featuring both an opening and a closing map. 

  *This gives the publication year and confirms two maps exist, but says nothing about what either map does for the reader, so no contrast is stated.*

*Difficulty: medium*

---

##### Q40
> NOTES. While researching a topic, a student has taken the following notes: • Etel Adnan was a Lebanese American poet and artist known for making many leporellos. • A leporello is an artist's book that is folded accordion style. • When the book is expanded, the artist's work is revealed, and its zigzag shape allows it to stand on its own. • Her leporello December from My Window (1993) features a panoramic landscape. • It is painted using ink and watercolor.

The student wants to describe Adnan's December from My Window to an audience already familiar with leporellos. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Featuring a panoramic landscape, the 1993 work is one of Adnan's many leporellos, which are accordion-style folded books that when expanded reveal the artist's work. 

  *This re-explains what a leporello is ("accordion-style folded books that when expanded reveal the artist's work") — exactly the background an audience "already familiar with leporellos" does not need — before ever giving the specific content of this particular work.*

**B.** When expanded, Adnan's 1993 leporello December from My Window reveals a panoramic landscape painted in ink and watercolor. **(Correct)**

  *Correct. It treats "leporello" as already known and moves straight to describing this specific work — panoramic landscape, ink and watercolor — which is what a reader already familiar with the form still needs to learn.*

**C.** Known for making many other accordion-style folded books called leporellos, Adnan created December from My Window in 1993. 

  *This re-defines leporellos as "accordion-style folded books," background the audience clause says is unnecessary, and never describes what December from My Window itself actually depicts.*

**D.** A leporello, such as Adnan's December from My Window, is folded accordion style, and due to its zigzag shape it is able to stand on its own when fully expanded. 

  *This is a general definition of leporellos with Adnan's book cited only as an example — it explains the form the audience already knows rather than describing this specific work's content.*

*Difficulty: hard*

---

##### Q41
> NOTES. While researching a topic, a student has taken the following notes: • In the art world, the term biennial traditionally refers to an art exhibition that takes place every two years in a single location. • Such biennials are held in New York, Berlin, and Venice. • In 2006, artists Ed Gomez and Luis Hernandez founded the unconventional MexiCali Biennial. • The MexiCali Biennial hosts exhibitions in different venues on both sides of the US-Mexico border. • The MexiCali Biennial has taken place on an uneven schedule, with exhibitions in 2006, 2009-10, 2013, and 2018-20.

The student wants to emphasize a difference between the MexiCali Biennial and traditional biennials. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** In 2006, artists Ed Gomez and Luis Hernandez founded the MexiCali Biennial, which has taken place in 2006, 2009-10, 2013, and 2018-20. 

  *This gives the founding and the exhibition years but never mentions traditional biennials at all, so no contrast between the two is ever made.*

**B.** Unlike traditional biennials, the MexiCali Biennial hosts exhibitions in different venues on an uneven schedule. **(Correct)**

  *Correct. "Unlike traditional biennials" names both sides of the comparison, and "different venues on an uneven schedule" states the exact properties — location and timing — that distinguish the MexiCali Biennial.*

**C.** The term biennial traditionally refers to an art exhibition that takes place every two years in a single location, not to exhibitions hosted at a variety of times and venues. 

  *This defines the traditional meaning of "biennial" but never names the MexiCali Biennial specifically — it states what the term usually means, not how this particular biennial departs from it.*

**D.** Biennial exhibitions have been held in New York, Berlin, and Venice but also on both sides of the US-Mexico border. 

  *This lists locations without ever naming the MexiCali Biennial by name or stating what makes it unconventional relative to a traditional biennial — the contrast is implied by geography alone, not stated.*

*Difficulty: medium*

---

##### Q42
> NOTES. While researching a topic, a student has taken the following notes: • The Pueblo of Zuni is located about 150 miles west of Albuquerque, New Mexico. • It is the traditional home of the A:shiwi (Zuni) people. • The A:shiwi A:wan Museum and Heritage Center was established by tribal members in 1992. • Its mission is stated on its website: "As a tribal museum and heritage center for the Zuni people and the Zuni people we work to provide learning experiences that emphasize A:shiwi ways of knowing, as well as exploring modern concepts of knowledge and the transfer of knowledge."

The student wants to emphasize how long the museum has existed. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The Pueblo of Zuni is home to the A:shiwi A:wan Museum and Heritage Center, which was founded by tribal members. 

  *This confirms the museum was founded by tribal members but gives no date or duration at all, so nothing about how long it has existed is emphasized.*

**B.** The A:shiwi A:wan Museum and Heritage Center has served the Pueblo of Zuni since 1992. **(Correct)**

  *Correct. "Since 1992" states the founding year in a form that emphasizes ongoing duration — exactly how long the museum has existed, which is what the goal asks for.*

**C.** According to its website, the A:shiwi A:wan Museum and Heritage Center (founded in the 1990s) works to "emphasize A:shiwi ways of knowing." 

  *"Founded in the 1990s" is vaguer than the exact 1992 date the notes provide, and the sentence's real focus is the mission-statement quotation, not the museum's age.*

**D.** Knowledge has been one of the central themes of the A:shiwi A:wan Museum and Heritage Center from its founding. 

  *"From its founding" gestures at duration without ever stating the actual year, and the sentence's real content is the museum's thematic mission, not its age.*

*Difficulty: medium*

---

##### Q43
> NOTES. While researching a topic, a student has taken the following notes: • Gravitational waves are powerful ripples that originate in deep space and eventually pass through Earth. • The Laser Interferometer Gravitational Wave Observatory (LIGO) is a physics study that began in 2002. • LIGO's goal is to detect and analyze gravitational waves. • LIGO uses a pair of massive gravitational wave detectors called interferometers that are thousands of miles apart. • In 2015, for the first time in history, LIGO researchers detected a gravitational wave passing through Earth.

The student wants to present LIGO's aim and methodology. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** In 2015, LIGO's massive interferometers detected a powerful ripple that originated in deep space and eventually passed through Earth. 

  *This reports the 2015 detection — a result — rather than LIGO's aim (to detect and analyze gravitational waves) or its methodology (paired, widely spaced interferometers) as ongoing features of the study.*

**B.** Though the physics study LIGO began in 2002, its massive interferometers didn't detect a gravitational wave until 2015. 

  *This states the founding date and the delay before the first detection, but never states LIGO's actual goal or explains its detection methodology beyond naming "interferometers."*

**C.** To achieve its aims, LIGO uses a pair of massive interferometers that are thousands of miles apart. 

  *This gives the methodology but not the aim itself — "its aims" is referenced but never stated as detecting and analyzing gravitational waves, so only half of the two-part goal is satisfied.*

**D.** A physics study designed to detect and analyze gravitational waves, LIGO uses a pair of massive interferometers that are thousands of miles apart. **(Correct)**

  *Correct. It states LIGO's aim — to detect and analyze gravitational waves — and its methodology — paired interferometers thousands of miles apart — combining both halves the goal requires.*

*Difficulty: medium*

---

##### Q44
> NOTES. While researching a topic, a student has taken the following notes: • Just like states have state flags, some cities have city flags. • Over one hundred US cities have redesigned their flags since 2015. • The city of Pocatello, Idaho, redesigned its flag after it was named the most poorly designed flag in North America. • Pocatello's new flag better represents the city's mountainous geography and civic priorities. • Residents consider the new flag to be a meaningful symbol of civic pride.

The student wants to make and support a generalization about the effect of redesigning a city flag. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Over one hundred US cities have redesigned their flags, including Pocatello, whose flag had been named the most poorly designed flag in North America. 

  *This reports how many cities redesigned flags and why Pocatello did, but never states any effect that redesigning has — no claim about what a new flag accomplishes for a city or its residents.*

**B.** Pocatello is just one of over one hundred US cities that have redesigned their flags. 

  *This places Pocatello among many redesigning cities but states no general effect of redesigning a flag — nothing here is a claim about what redesigning does.*

**C.** After it was named the most poorly designed flag in North America, the flag of Pocatello was redesigned to better represent the city's geography and civic priorities. 

  *This is a specific account of Pocatello alone, not a generalization about redesigning flags as a practice — it never extends beyond this one case to a broader claim.*

**D.** Redesigning a poorly designed city flag can create a meaningful symbol of civic pride, as was the case when Pocatello redesigned its original flag to better represent its geography and civic priorities. **(Correct)**

  *Correct. It states a general claim — redesigning can create a meaningful symbol of civic pride — and supports it with the specific Pocatello case, satisfying both the "make" and "support" halves of the goal.*

*Difficulty: hard*

---

##### Q45
> NOTES. While researching a topic, a student has taken the following notes: • Minnesota defines a lake as an inland body of water of at least 10 acres. • Wisconsin's definition of a lake doesn't take size into account. • By its own definition, Wisconsin has over 15,000 lakes, many smaller than 10 acres. • By Minnesota's definition, Wisconsin has only about 6,000 lakes.

The student wants to contrast Minnesota's definition of a lake with Wisconsin's. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Wisconsin, which doesn't take size into account in defining a lake, claims that it has over 15,000 lakes. 

  *Only Wisconsin's definition and count appear; Minnesota's definition is never mentioned, so nothing is actually contrasted against it.*

**B.** Because its definition of a lake is different from Minnesota's, it is unclear how many lakes Wisconsin really has. 

  *This says the definitions differ without ever stating what either definition actually is — no size threshold for Minnesota, no size-blindness explained for Wisconsin.*

**C.** According to Minnesota's definition of a lake—an inland body of water of at least 10 acres—Wisconsin has about 6,000 lakes. 

  *This states Minnesota's definition but applies it only to Wisconsin's count under that one standard — it never states Wisconsin's own definition as a point of contrast.*

**D.** Minnesota's definition of a lake—an inland body of water of at least 10 acres—is more restrictive than Wisconsin's, which doesn't take size into account. **(Correct)**

  *Correct. Both definitions appear explicitly, and "more restrictive than" states the exact contrast — a size threshold versus none — that the notes establish between the two states.*

*Difficulty: medium*

---

##### Q46
> NOTES. While researching a topic, a student has taken the following notes: • Maika'i Tubbs is a Native Hawaiian sculptor and installation artist. • His work has been shown in the United States, Canada, Japan, and Germany, among other places. • Many of his sculptures feature discarded objects. • His work Erasure (2008) includes discarded audiocassette tapes and magnets. • His work Home Grown (2009) includes discarded pushpins, plastic plates and forks, and wood.

The student wants to emphasize a similarity between the two works. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Erasure (2008) uses discarded objects such as audiocassette tapes and magnets; Home Grown (2009), however, includes pushpins, plastic plates and forks, and wood. 

  *"However" frames the two works' different materials as a contrast, treating the specific objects as distinguishing rather than as evidence of the underlying similarity — both using discarded objects.*

**B.** Tubbs's work, which often features discarded objects, has been shown both within the United States and abroad. 

  *This states a general pattern across Tubbs's work and where it was shown, but never names Erasure or Home Grown specifically as the two works to be compared.*

**C.** Like many of Tubbs's sculptures, both Erasure and Home Grown include discarded objects: Erasure uses audiocassette tapes, and Home Grown uses plastic forks. **(Correct)**

  *Correct. Both works are named, "both... include discarded objects" states the shared property directly, and a concrete example from each supports it — exactly the similarity the goal asks for.*

**D.** Tubbs completed Erasure in 2008 and Home Grown in 2009. 

  *This states only the completion years of the two works, which are different from each other, and says nothing about the shared use of discarded materials that the goal asks to be emphasized.*

*Difficulty: medium*

---

##### Q47
> NOTES. While researching a topic, a student has taken the following notes: • In meteorology, an air mass is a large body of air with generally uniform humidity and temperature. • Air masses are commonly classified by two-letter names. • The first letter indicates the humidity of the air mass, while the second letter indicates the temperature. • cA (continental arctic) means dry and cold, for example. • mT (maritime tropical) means moist and warm. • This classification system is based on the work of a Swedish meteorologist named Tor Bergeron (1891-1977).

The student wants to provide an example of an air mass. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Air masses are large bodies of air with generally uniform humidity and temperature. 

  *This defines what an air mass is in general terms but never gives a specific instance of one — no cA or mT designation appears.*

**B.** The air mass classification system uses two-letter names and is based on the work of Tor Bergeron, a Swedish meteorologist. 

  *This describes the classification system and its origin, not a concrete example of an actual air mass — cA and mT are never cited.*

**C.** Air masses are commonly classified by a two-letter name that indicates humidity and temperature. 

  *This describes the naming pattern in the abstract without giving a specific two-letter example — neither cA nor mT is actually cited as an instance.*

**D.** One type of air mass is known as a cA, or continental arctic, air mass because it is dry and cold. **(Correct)**

  *Correct. It names a specific, concrete air mass — cA, continental arctic — and explains what the designation means, which is exactly the example the goal asks to be provided.*

*Difficulty: easy*

---

##### Q48
> NOTES. While researching a topic, a student has taken the following notes: • The international Slow Food movement was founded in 1989 with the signing of the "Slow Food Manifesto." • The movement promotes universal access to healthy, high-quality food. • It calls for sustainable food production practices that protect local environments, ecosystems, and biodiversity. • It advocates for fair treatment of and compensation for food production workers. • The Slow Food USA organization was founded in 2000.

The student wants to introduce the Slow Food movement to a new audience. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The international Slow Food movement, founded in 1989, promotes universal access to healthy, high-quality food that is produced sustainably by workers who are treated and compensated fairly. **(Correct)**

  *Correct. It establishes when the movement began and states its core mission — sustainable, fair, high-quality food access — giving a new audience the essential grounding the goal calls for.*

**B.** The signing of the "Slow Food Manifesto" in 1989 marked the founding of the international Slow Food movement, while the Slow Food USA organization was founded in 2000. 

  *This gives two founding dates but never states what the movement actually promotes or stands for — a new audience learns when it started but not what it is.*

**C.** The Slow Food movement advocates for food production workers. 

  *This names only one of the movement's several goals (worker treatment) and omits its founding, its food-access mission, and its environmental focus — far too thin to introduce the movement as a whole.*

**D.** Goals of the movement include universal access to healthy, high-quality food and sustainable food practices. 

  *This lists two of the movement's goals but never names it as the "Slow Food movement," gives no founding date, and provides no context that would introduce it to someone hearing of it for the first time.*

*Difficulty: medium*

---

##### Q49
> NOTES. While researching a topic, a student has taken the following notes: • In the early 1900s, suffragists organized marches for women's voting rights. • Suffragists in the United Kingdom marched from Edinburgh to London. • This march began on October 12, 1912, and ended on November 16, 1912. • Suffragists in the United States marched from New York City to Albany, New York. • This march began on December 16, 1912, and ended on December 28, 1912.

The student wants to emphasize the order in which the two marches occurred. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** After suffragists in the UK marched from Edinburgh to London, suffragists in the US marched from New York City to Albany, New York. **(Correct)**

  *Correct. "After" states the actual sequence the dates establish — the UK march (October-November 1912) preceded the US march (December 1912) — which is the order the goal asks to be emphasized.*

**B.** In the early 1900s, suffragists in the UK and the US marched for women's voting rights. 

  *This mentions both marches happened but states no sequence between them — no word like "before," "after," or a date order appears.*

**C.** A march from New York City to Albany, New York, was followed by one that began in Edinburgh and ended in London. 

  *This reverses the actual order: the notes' dates show the UK march (ending November 16) happened before the US march (beginning December 16), not after it.*

**D.** From October 12 to November 16, 1912, suffragists in the UK marched from Edinburgh to London. 

  *Only the UK march appears here; the US march and any sequencing between the two are never mentioned, so no order is ever emphasized.*

*Difficulty: medium*

---

##### Q50
> NOTES. While researching a topic, a student has taken the following notes: • Mary Kang is a Korean American portrait photographer. • She is based in New York City and in Austin, Texas. • One of Kang's photographs features artist Dominique Fung. • In the portrait, Fung is seated on the floor. • Five of Fung's paintings are resting against the wall behind her.

The student wants to describe where Fung is in the photograph to an audience already familiar with Kang and Fung. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Dominique Fung is in a photograph by Mary Kang, a portrait photographer based in New York City and Austin, Texas. 

  *This reintroduces Kang's profession and locations — exactly the background an audience already familiar with her does not need — and never describes where Fung is positioned within the photograph.*

**B.** Mary Kang is a photographer based in both New York City and Austin, Texas. 

  *This is entirely background about Kang, redundant for an audience already familiar with her, and it never mentions Fung's position in the photograph at all.*

**C.** Five paintings by artist Dominique Fung can be seen in the background of Mary Kang's photograph. 

  *This describes the paintings in the background but never states where Fung herself is positioned — seated on the floor — which is the specific placement the goal asks to be described.*

**D.** In Kang's portrait of her, Fung is seated on the floor, with five of her paintings resting against the wall behind her. **(Correct)**

  *Correct. It treats Kang and Fung as already known and goes straight to the specific detail the goal asks for — Fung's position, seated on the floor with her paintings behind her.*

*Difficulty: hard*

---

##### Q51
> NOTES. While researching a topic, a student has taken the following notes: • Pointillism is a painting technique in which small, distinct dots of color are applied in patterns to form an image. • Betty Acquah is an artist from Ghana who uses pointillism in her work. • "By extending dabs of color in the subject matter into the background and vice-versa, an illusion of movement is created," she says about pointillism. • Her work often portrays Ghanaian women, whom she sees as the "unsung heroines of the Ghanaian Republic." • Her pointillist painting "Exquisite" (2016) features five dancing women twirling their skirts.

The student wants to provide a quotation from Acquah that explains why she used pointillism in "Exquisite." Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** In painting "Exquisite," Acquah applied pointillism to create what she called an "illusion of movement" within the painting's five dancing women and their twirling skirts. **(Correct)**

  *Correct. It names "Exquisite," quotes Acquah's own explanation of what pointillism achieves — an "illusion of movement" — and connects that quoted reasoning specifically to the dancing figures in this painting.*

**B.** Pointillism, the technique used in Acquah's "Exquisite," involves the application of small, distinct dots of color. 

  *This defines pointillism in the notes' general terms rather than quoting Acquah, and it never explains why she chose the technique for this particular painting.*

**C.** In "Exquisite," Acquah uses a technique that she says involves "extending dabs of color in the subject matter into the background and vice-versa." 

  *This quotes Acquah but cuts the quotation off before her stated reason ("an illusion of movement is created") — it describes the technique's mechanics, not why she used it.*

**D.** "Exquisite" portrays Acquah's fellow Ghanaian women as she sees them: the "unsung heroes of the Ghanaian Republic." 

  *This quotes Acquah on her subject matter — how she views Ghanaian women — not on why she used pointillism specifically. It also misquotes "heroines" as "heroes."*

*Difficulty: hard*

---

##### Q52
> NOTES. While researching a topic, a student has taken the following notes: • Thailand's annual Songkran Water Festival is held each April. • It marks Songkran, the traditional Thai New Year. • People splash and spray each other for fun at the festival's community-wide water fights. • In Bangkok, thousands gather along Silom Road for the city's largest water fight. • In Chiang Mai, thousands gather at a historical monument called the Tha Phae Gate for the city's largest water fight.

The student wants to emphasize a similarity in how people in Bangkok and Chiang Mai celebrate Songkran. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The largest water fight in Bangkok takes place along a city street, whereas the largest water fight in Chiang Mai takes place at a historical monument. 

  *Both cities appear, but "whereas" contrasts their different venues — a street versus a monument — which is a difference between the two cities, not a similarity.*

**B.** In both Bangkok and Chiang Mai, thousands gather to celebrate Songkran with water fights. **(Correct)**

  *Correct. "In both" names the shared property directly — thousands gathering for water fights in each city — which is exactly the similarity the goal asks to be emphasized.*

**C.** People in both Bangkok and Chiang Mai celebrate Songkran, but they don't do so in exactly the same way. 

  *"But they don't do so in exactly the same way" explicitly flags a difference between the two cities' celebrations rather than stating what they share.*

**D.** Each April, people in Thailand celebrate Songkran, the traditional Thai New Year. 

  *This describes the holiday generally without naming Bangkok or Chiang Mai specifically, so no similarity between the two cities is ever stated.*

*Difficulty: medium*

---

##### Q53
> NOTES. While researching a topic, a student has taken the following notes: • In 2022, University of Miami researchers discovered brine pools in the Gulf of Aqaba. • A brine pool is an underwater lake that sits on the ocean floor. • The water in brine pools is three to eight times saltier than the surrounding ocean. • The extreme saltiness of this water makes it toxic to most sea life. • Some forms of bacteria are able to survive in brine pools.

The student wants to explain why brine pools are toxic to most sea life. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Though brine pools are toxic to most sea life, some bacteria can survive there. 

  *This concedes the toxicity and notes an exception (bacteria), but never states the mechanism — the extreme saltiness — that actually causes the toxicity.*

**B.** The water in brine pools is toxic to most sea life because it is three to eight times saltier than the surrounding ocean. **(Correct)**

  *Correct. "Because" states the actual cause — the extreme salinity — that the notes give for the toxicity, which is exactly the explanation the goal asks for.*

**C.** The brine pools in the Gulf of Aqaba are toxic to most sea life and were discovered by researchers in 2022. 

  *This states that the pools are toxic and when they were discovered, but never explains what causes the toxicity — the salinity figure never appears.*

**D.** Brine pools are salty underwater lakes that sit on the ocean floor. 

  *This defines what a brine pool is in general terms without stating why that salinity makes it toxic — the causal link the goal asks for is missing.*

*Difficulty: easy*

---

##### Q54
> NOTES. While researching a topic, a student has taken the following notes: • Crown shyness is a phenomenon in which the tops (crowns) of neighboring trees grow close together but don't overlap. • To explain how this happens, Australian forester M.R. Jacobs proposes the mutual abrasion theory. • According to Jacobs's theory, when trees brush against one another, branches break off. • Malaysian scholar Francis S.P. Ng posits the mutual shade avoidance theory. • According to Ng's theory, when tree branches detect shade from nearby trees' branches, they stop growing.

The student wants to compare the causes of crown shyness proposed in the two theories. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** While Jacobs proposes that crown shyness is caused by neighboring tree branches brushing against one another, Ng posits that it occurs when branches detect shade from nearby trees' branches. **(Correct)**

  *Correct. Both theorists' proposed causes appear, correctly matched to each — abrasion for Jacobs, shade detection for Ng — with "while" stating the comparison the goal calls for.*

**B.** Both Jacobs and Ng have proposed theories to explain what causes crown shyness. 

  *This confirms two theories exist without ever stating what either theory's proposed cause actually is, so no comparison of causes is made.*

**C.** Ng posits the mutual shade avoidance theory, whereas Jacobs proposes an alternative theory. 

  *This names Ng's theory but leaves Jacobs's unnamed as merely "an alternative," so only one side of the comparison actually states a cause.*

**D.** Jacobs's mutual abrasion theory proposes that when neighboring trees brush against one another, branches break off, resulting in a phenomenon in which the tops of trees grow close together but don't overlap. 

  *Only Jacobs's theory and its cause are described; Ng's shade avoidance theory never appears, so nothing is compared against it.*

*Difficulty: hard*

---

##### Q55
> NOTES. While researching a topic, a student has taken the following notes: • In the midst of the US Civil War, Susie Taylor escaped slavery and fled to Union-army-occupied St. Simons Island off the Georgia coast. • She began working for an all-Black army regiment as a nurse and teacher. • In 1902, she published a book about the time she spent with the regiment. • Her book was the only Civil War memoir to be published by a Black woman. • It is still available to readers in print and online.

The student wants to emphasize the uniqueness of Taylor's accomplishment. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Taylor fled to St. Simons Island, which was then occupied by the Union army, for whom she began working. 

  *This describes Taylor's flight and early work but says nothing about her book or its distinction as the only such memoir — the accomplishment itself is missing.*

**B.** After escaping slavery, Taylor began working for an all-Black army regiment as a nurse and teacher. 

  *This describes her wartime work but never mentions the book or the "only" distinction that actually makes her accomplishment unique.*

**C.** The book Taylor wrote about the time she spent with the regiment is still available to readers in print and online. 

  *This confirms the book's availability today but never states what made it unique when published — the "only" fact establishing her singular accomplishment is missing.*

**D.** Taylor was the only Black woman to publish a Civil War memoir. **(Correct)**

  *Correct. "The only" is the exact word the notes use to establish uniqueness, and it states the specific accomplishment — the sole Civil War memoir published by a Black woman.*

*Difficulty: medium*

---

##### Q56
> NOTES. While researching a topic, a student has taken the following notes: • Sam Maloof (1916-2009) was an American woodworker and furniture designer. • He was the son of Lebanese immigrants. • He received a "genius grant" from the John D. and Catherine T. MacArthur Foundation in 1985. • The Museum of Fine Arts in Boston, Massachusetts, owns a rocking chair that Maloof made from walnut wood. • The armrests and the seat of the chair are sleek and contoured, and the back consists of seven spindle-like slats.

The student wants to describe the rocking chair to an audience unfamiliar with Sam Maloof. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** With its sleek, contoured armrests and seat, the walnut rocking chair in Boston's Museum of Fine Arts is just one piece of furniture created by American woodworker Sam Maloof. **(Correct)**

  *Correct. It describes the chair's specific physical features — sleek, contoured armrests and seat, walnut material, museum location — while introducing Maloof by profession for a reader who does not yet know him.*

**B.** Sam Maloof was born in 1916 and died in 2009, and during his life, he made a chair that you can see if you visit the Museum of Fine Arts in Boston. 

  *This gives Maloof's lifespan and where to see the chair but never describes what the chair actually looks like — no armrests, seat, or slats are mentioned.*

**C.** Furniture designer Sam Maloof was a recipient of one of the John D. and Catherine T. MacArthur Foundation's "genius grants." 

  *This describes Maloof's award, not the chair itself — the object the goal asks to be described never appears in this sentence.*

**D.** The rocking chair is made from walnut, and it has been shaped such that its armrests and seat are sleek and contoured. 

  *This describes the chair well but never introduces Maloof at all — for an audience unfamiliar with him, the chair is described with no context for who made it.*

*Difficulty: medium*

---

##### Q57
> NOTES. While researching a topic, a student has taken the following notes: • In the early 1960s, the US had a strict national-origins quota system for immigrants. • The number of new immigrants allowed from a country each year was based on how many people from that country lived in the US in 1890. • This system favored immigrants from northern Europe. • Almost 70% of slots were reserved for immigrants from Great Britain, Ireland, and Germany. • The 1965 Hart-Celler Act abolished the national-origins quota system.

The student wants to present the significance of the Hart-Celler Act to an audience unfamiliar with the history of US immigration. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Almost 70% of slots were reserved for immigrants from Great Britain, Ireland, and Germany at the time the Hart-Celler Act was proposed. 

  *This gives a detail about the old quota system but never mentions the Hart-Celler Act's own effect — that it abolished the system — so its significance is never actually stated.*

**B.** Prior to the Hart-Celler Act, new immigration quotas were based on how many people from each country lived in the US in 1890. 

  *This describes the pre-1965 quota formula but never states what the Hart-Celler Act itself did — abolishing that system — so its significance is left unstated.*

**C.** The quota system in place in the early 1960s was abolished by the 1965 Hart-Celler Act. 

  *This correctly states that the act abolished the quota system but never explains what that system was or why abolishing it mattered — too thin for an audience with no prior context.*

**D.** The 1965 Hart-Celler Act abolished the national-origins quota system, which favored immigrants from northern Europe. **(Correct)**

  *Correct. It states what the act did and, in the same sentence, gives an unfamiliar reader enough context about the system it replaced — favoring northern Europe — to grasp why that mattered.*

*Difficulty: medium*

---

##### Q58
> NOTES. While researching a topic, a student has taken the following notes: • Soo Sunny Park is a Korean American artist who uses light as her primary medium of expression. • She created her work Unwoven Light in 2013. • Unwoven Light featured a chain-link fence fitted with iridescent plexiglass tiles. • When light passed through the fence, colorful prisms formed.

The student wants to describe Unwoven Light to an audience unfamiliar with Soo Sunny Park. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Park's 2013 installation Unwoven Light, which included a chain-link fence and iridescent tiles made from plexiglass, featured light as its primary medium of expression. 

  *This describes the materials but drops the work's actual visual effect — the colorful prisms formed as light passed through — which is the detail that makes the piece vivid to a new reader.*

**B.** Korean American light artist Soo Sunny Park created Unwoven Light in 2013. 

  *This introduces Park and dates the work but describes nothing about what Unwoven Light actually is or looks like — no fence, no tiles, no prisms.*

**C.** The chain-link fence in Soo Sunny Park's Unwoven Light was fitted with tiles made from iridescent plexiglass. 

  *This describes the materials but never mentions the prisms formed by light passing through — the visual payoff that actually shows what the work does.*

**D.** In Unwoven Light, a 2013 work by Korean American artist Soo Sunny Park, light formed colorful prisms as it passed through a fence Park had fitted with iridescent tiles. **(Correct)**

  *Correct. It introduces Park, names the work, and describes both its construction and its visual effect — colorful prisms from light passing through the fitted fence — giving an unfamiliar audience the fullest picture.*

*Difficulty: medium*

---

##### Q59
> NOTES. While researching a topic, a student has taken the following notes: • In 1999, astronomer Todd Henry studied the differences in surface temperature between the Sun and nearby stars. • His team mapped all stars within 10 parsecs (approximately 200 trillion miles) of the Sun. • The surface temperature of the Sun is around 9,800°F, which classifies it as a G star. • 327 of the 357 stars in the study were classified as K or M stars, with surface temperatures under 8,900°F (cooler than the Sun). • 11 of the 357 stars in the study were classified as A or F stars, with surface temperatures greater than 10,300°F (hotter than the Sun).

The student wants to emphasize how hot the Sun is relative to nearby stars. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** At around 9,800°F, which classifies it as a G star, the Sun is hotter than most but not all of the stars within 10 parsecs of it. **(Correct)**

  *Correct. It states the Sun's temperature and, using the notes' own figures (327 cooler K/M stars versus 11 hotter A/F stars), correctly qualifies the relative claim as "most but not all" rather than overstating it.*

**B.** Astronomer Todd Henry determined that the Sun, at around 9,800°F, is a G star, and several other stars within a 10-parsec range are A or F stars. 

  *This mentions the hotter A/F stars but never makes the actual relative comparison the goal asks for — it doesn't state that the Sun is hotter than the much larger group of K/M stars.*

**C.** Of the 357 stars within ten parsecs of the Sun, 327 are classified as K or M stars, with surface temperatures under 8,900°F. 

  *This reports the K/M star count and temperature range but never states the Sun's own temperature or makes an explicit relative comparison between the Sun and these stars.*

**D.** While most of the stars within 10 parsecs of the Sun are classified as K, M, A, or F stars, the Sun is classified as a G star due to its surface temperature of 9,800°F. 

  *This lumps the cooler K/M stars and the hotter A/F stars into one undifferentiated "most," which obscures rather than states how the Sun's heat actually compares — it never says the Sun is hotter than the K/M majority.*

*Difficulty: hard*

---

##### Q60
> NOTES. While researching a topic, a student has taken the following notes: • In 2017, a research team led by Mary Caswell Stoddard determined the average lengths of eggs produced by various bird species. • Gygis alba is a species of bird in the order Charadriiformes. • Gygis alba eggs had an average length of 4.46 cm. • Gavia stellata is a species of bird in the order Gaviiformes. • Gavia stellata eggs had an average length of 7.22 cm.

Which choice most effectively uses information from the given sentences to emphasize a difference between the eggs of the two species?

**A.** A 2017 study compared the lengths of eggs produced by an array of different bird species, such as Gygis alba and Gavia stellata. 

  *This confirms both species were part of the study but never states either species' actual egg length, so no difference between them is ever expressed.*

**B.** A 2017 study found that Gygis alba eggs had an average length of 4.46 cm, whereas Gavia stellata eggs were longer, with an average length of 7.22 cm. **(Correct)**

  *Correct. Both species' egg lengths appear, and "whereas... longer" states the exact numerical difference — 4.46 cm versus 7.22 cm — that the goal asks to be emphasized.*

**C.** The bird species Gygis alba, which belongs to the order Charadriiformes, and Gavia stellata, of the order Gaviiformes, were included in a 2017 study that compared the average lengths of their eggs. 

  *This names both species and their taxonomic orders but never actually states either egg length or the numerical gap between them — the difference itself is missing.*

**D.** Mary Caswell Stoddard led a research study that determined the average lengths of eggs, including those of Gygis alba birds (4.46 cm) and Gavia stellata birds (7.22 cm). 

  *Both figures are present, but they are listed as parallel facts rather than framed as a contrast — no word like "whereas" or "longer" ties them together as a stated difference.*

*Difficulty: easy*

---

##### Q61
> NOTES. While researching a topic, a student has taken the following notes: • Chromosomes are cellular structures that contain genes. • Genes carry critical instructions for determining an organism's physical traits. • Members of the same species typically have the same number of chromosomes. • The pineapple (Ananas comosus) and the melon (Cucumis melo) are species of fruits. • The pineapple has fifty chromosomes. • The melon has twenty-four chromosomes.

The student wants to specify how many chromosomes the pineapple has. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The pineapple's chromosomes contain genes, which are critical to determining an organism's physical traits. 

  *This explains what chromosomes do in general but never states the pineapple's actual chromosome count — the number fifty never appears.*

**B.** The pineapple (Ananas comosus) has fifty chromosomes. **(Correct)**

  *Correct. It states the specific number of chromosomes the pineapple has — fifty — which is exactly the figure the goal asks to be specified.*

**C.** The pineapple (Ananas comosus) and the melon (Cucumis melo) both have chromosomes, but the pineapple has more than the melon does. 

  *This states that the pineapple has more chromosomes than the melon without ever giving the pineapple's actual number — a comparison is not the same as the specific figure the goal asks for.*

**D.** The melon, a species of fruit, has twenty-four structures called chromosomes. 

  *This gives the melon's chromosome count, not the pineapple's — the wrong fruit is specified entirely.*

*Difficulty: easy*

---

##### Q62
> NOTES. While researching a topic, a student has taken the following notes: • Tecozautla is a municipality in the state of Hidalgo, Mexico. • Municipalities are governmental regions responsible for providing many public services to their residents. • One service they provide is street lighting. • Tecozautla covers an area of roughly 535 km². • Hidalgo is divided into 84 municipalities.

The student wants to emphasize the size of Tecozautla. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The municipality of Tecozautla in Hidalgo, Mexico, covers an area of roughly 535 km². **(Correct)**

  *Correct. It states the actual area figure — roughly 535 km² — that the notes give for Tecozautla, which is exactly the size the goal asks to be emphasized.*

**B.** Providing street lighting is just one example of the public services that municipalities provide. 

  *This describes municipal services in general and never mentions Tecozautla's area at all.*

**C.** Tecozautla is one of 84 governmental regions, known as municipalities, across Hidalgo. 

  *This gives the total number of municipalities in Hidalgo, not Tecozautla's own area — the figure that would actually emphasize its size never appears.*

**D.** Tecozautla—a governmental region in the state of Hidalgo, Mexico—provides many public services to its residents. 

  *This describes Tecozautla's function as a municipality, not its physical size — the 535 km² figure is never mentioned.*

*Difficulty: easy*

---

##### Q63
> NOTES. While researching a topic, a student has taken the following notes: • Generally, an object will heat up when twisted. • The twisting of an object is known as torsion. • A 2019 study led by Zunfeng Liu and Ray Baughman tested the torsional heating of various fibers. • When a 3-millimeter-thick sample of thermoplastic polyurethane (TPU) fiber was twisted, its average surface temperature increased by 6°C. • When a 4-millimeter-thick sample of styrene-ethylene-butylene-styrene (SEBS) rubber fiber was twisted, its average surface temperature increased by 3.5°C.

The student wants to contrast the two samples. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** When the fibers were twisted as part of the 2019 study, the surface temperature of both samples increased. 

  *"Both" states what the two samples share — a temperature increase — which is a similarity, not the contrast between them the goal asks for.*

**B.** In 2019, researchers studied the effect of torsional heating on various fibers, including samples of SEBS rubber and TPU. 

  *This names both samples but never states any property that distinguishes them from each other — no thickness or temperature-increase figures appear.*

**C.** Twisting an object will generally cause its temperature to increase, a process known as torsional heating. 

  *This states the general phenomenon of torsional heating without naming either the TPU or the SEBS rubber sample specifically, so nothing is contrasted.*

**D.** The SEBS rubber sample used in the 2019 study was thicker than the TPU sample. **(Correct)**

  *Correct. Both samples appear, and "thicker than" states an actual measured difference between them from the notes — the 4 mm SEBS sample versus the 3 mm TPU sample.*

*Difficulty: medium*

---

##### Q64
> NOTES. While researching a topic, a student has taken the following notes: • Pineapple is a fruit that contains ascorbic acid, an essential nutrient for humans. • Every 100 grams (g) of pineapple contains 48 milligrams (mg) of ascorbic acid. • Many animals can make ascorbic acid in their bodies, but humans cannot. • Humans must get ascorbic acid from foods, including fruits and vegetables. • Ascorbic acid is also known as vitamin C.

The student wants to provide an example of a fruit that contains vitamin C. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Humans cannot make ascorbic acid in their bodies, but they can get it from foods, such as fruits, for example. 

  *This mentions fruits only as a vague category ("such as fruits, for example") without naming a specific fruit — pineapple, the actual example the notes provide, never appears.*

**B.** Vitamin C, also known as ascorbic acid, can be found in pineapple as well as other fruits. **(Correct)**

  *Correct. It names pineapple specifically as an example of a fruit containing vitamin C, which is exactly the concrete example the goal asks to be provided.*

**C.** Since humans cannot make vitamin C in their bodies, they must get it from food. 

  *This explains why humans need dietary vitamin C but never names a specific fruit as an example — pineapple is never mentioned.*

**D.** Many animals can make ascorbic acid, which is also known as vitamin C, in their bodies, but humans cannot. 

  *This contrasts animals and humans on ascorbic-acid production but never provides an example of a fruit that contains it — pineapple is never mentioned.*

*Difficulty: easy*

---

##### Q65
> NOTES. While researching a topic, a student has taken the following notes: • Texture analysis and historical analysis are two approaches to art criticism. • Texture analysis examines how surfaces are visually represented in an artwork. • Such an analysis of Giorgione's Youth Holding an Arrow might consider how the painting's blended colors make the subject's skin appear smooth to texture. • Historical analysis considers the historical context in which a work was created. • Such an analysis of Diego Velázquez's Las Meninas might consider how the painting's depiction of the artist with King Philip IV symbolizes art's historical ties to power.

The student wants to present historical analysis to an audience unfamiliar with the concept. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** A texture analysis of Youth Holding an Arrow might consider how the painting's blended colors make the subject's skin appear smooth to texture. 

  *This describes texture analysis, not historical analysis — the wrong one of the two approaches the notes contrast is presented here.*

**B.** Texture analysis differs from historical analysis in that texture analysis examines how surfaces are visually represented in an artwork. 

  *This states what texture analysis does, using historical analysis only as an unexplained point of contrast — a reader unfamiliar with historical analysis is never told what it actually considers.*

**C.** An approach to art criticism, historical analysis considers the historical context in which a work was created. **(Correct)**

  *Correct. It names historical analysis directly and states its defining feature — considering the historical context of a work's creation — giving an unfamiliar audience the concept itself, plainly stated.*

**D.** Las Meninas's depiction of the artist with King Philip IV symbolizes art's historical ties to power. 

  *This gives a specific application of historical analysis to one painting without ever stating what historical analysis, as a general concept, actually is.*

*Difficulty: medium*

---

##### Q66
> NOTES. While researching a topic, a student has taken the following notes: • Lighthouses send out crucial light signals to help ships and other watercraft navigate at night. • Before automation, lighthouses were run by lighthouse keepers. • Maria Younghans was the lighthouse keeper at Biloxi Light in Mississippi. • She held this position from 1867 to 1918. • Flora McNeil was the lighthouse keeper at Bridgeport Breakwater Light in Connecticut. • She held this position from 1904 to 1920.

The student wants to emphasize the order in which the two lighthouse keepers began their careers. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** From 1867 to 1918, the nighttime waters of Mississippi were more navigable thanks to lighthouse keepers Flora McNeil and Maria Younghans. 

  *This misattributes the 1867-1918 dates, which belong to Younghans alone, to both keepers jointly, and it credits McNeil with Mississippi service she never had at Biloxi Light — the notes place her in Connecticut.*

**B.** Before automation, lighthouse keepers like Maria Younghans and Flora McNeil were crucial to ensuring safe navigation for watercraft. 

  *This states their general importance to navigation without ever citing either keeper's start date, so no order between them is established.*

**C.** Flora McNeil began her career as a lighthouse keeper years after Maria Younghans did. **(Correct)**

  *Correct. It states the order directly: Younghans began in 1867, McNeil in 1904 — decades later — which is exactly the sequence the goal asks to be emphasized.*

**D.** Maria Younghans's career as a lighthouse keeper ended in 1918, whereas Flora McNeil's ended in 1920. 

  *This states the order in which their careers ended, not when they began — the goal specifically asks about the start of their careers, which this choice never addresses.*

*Difficulty: medium*

---

##### Q67
> NOTES. While researching a topic, a student has taken the following notes: • Hina Hanta is an online archive curated by the Choctaw Nation of Oklahoma. • Hina Hanta means "bright path" in Choctaw. • It features images of cultural artifacts relevant to the history of the Choctaw people. • It includes a fanner basket (ufko tapushik in Choctaw) made from cane. • It includes a robe (nita anchi) made from bear fur.

The student wants to specify the fanner basket's name in Choctaw. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The Hina Hanta archive features cultural artifacts, such as a fanner basket and a robe, that are relevant to the history of the Choctaw people. 

  *This mentions the fanner basket exists but never gives its Choctaw name — ufko tapushik never appears.*

**B.** The cane fanner basket, which is included in the Hina Hanta online archive, is called an ufko tapushik in Choctaw. **(Correct)**

  *Correct. It names the fanner basket and states its specific Choctaw name — ufko tapushik — which is exactly what the goal asks to be specified.*

**C.** Hina Hanta, which means "bright path" in Choctaw, includes a fanner basket in Choctaw. 

  *This translates the archive's own name, "Hina Hanta," not the fanner basket's — "includes a fanner basket in Choctaw" never states the basket's actual Choctaw term, ufko tapushik.*

**D.** The name of the online archive Hina Hanta means "bright path" in Choctaw. 

  *This gives the translation of the archive's name, not the fanner basket's Choctaw name — the fanner basket is never even mentioned.*

*Difficulty: easy*

---

##### Q68
> NOTES. While researching a topic, a student has taken the following notes: • Grimanesa Amoros is a Peruvian American artist well known for her LED light sculptures. • Her sculpture Uros Island is made of smooth, multicolored LED domes. • It occupies 335 cubic feet of space. • Her sculpture Fortuna is made of entangled blue and white LED tubes. • It occupies 19,950 cubic feet of space.

The student wants to emphasize a similarity between Uros Island and Fortuna. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The smooth LED domes of Grimanesa Amoros's Uros Island stand in contrast to the tangled LED tubes of Fortuna. 

  *"Stand in contrast to" states a difference in form — domes versus tubes — between the two works, the opposite of the similarity the goal asks for.*

**B.** At 19,950 cubic feet in size, Grimanesa Amoros's Fortuna cuts a larger figure than the 335-cubic-foot Uros Island. 

  *This compares the two works' sizes and states that Fortuna is far larger — a difference between them, not a shared property.*

**C.** Grimanesa Amoros is the artist behind Uros Island—a sculpture made of smooth multicolored LED domes. 

  *Only Uros Island is described; Fortuna is never mentioned, so nothing is shown to be similar to it.*

**D.** Uros Island is an LED light sculpture made by Grimanesa Amoros, as is Fortuna. **(Correct)**

  *Correct. Both sculptures are named, and "as is Fortuna" states the shared property — that both are LED light sculptures by Amoros — which is exactly the similarity the goal asks to be emphasized.*

*Difficulty: medium*

---

##### Q69
> NOTES. While researching a topic, a student has taken the following notes: • As engineered structures, many bird nests are uniquely flexible yet cohesive. • A research team led by Yashraj Bhosale wanted to better understand the mechanics behind these structural properties. • Bhosale's team used laboratory models that simulated the arrangement of flexible sticks into nest-like structures. • The researchers analyzed the points where sticks touched one another. • When pressure was applied to the model nests, the number of contact points between the sticks increased, making the structures stiffer.

The student wants to present the primary aim of the research study. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Bhosale's team wanted to better understand the mechanics behind bird nests' uniquely flexible yet cohesive structural properties. **(Correct)**

  *Correct. It states the study's actual purpose — understanding the mechanics behind nests' flexible-yet-cohesive properties — in the notes' own language, which is exactly the aim the goal asks to be presented.*

**B.** The researchers used laboratory models that simulated the arrangement of flexible sticks and analyzed the points where sticks touched one another. 

  *This describes the study's method, not its aim — what the researchers wanted to learn, as opposed to how they went about learning it, is never stated.*

**C.** After analyzing the points where sticks touched, the researchers found that the structures became stiffer when pressure was applied. 

  *This reports a finding of the study, not the purpose that motivated it in the first place — a result is not the same as an aim.*

**D.** As analyzed by Bhosale's team, bird nests are uniquely flexible yet cohesive engineered structures. 

  *This restates the phenomenon under study as a fact about nests, without ever stating that the team's aim was to understand the mechanics behind it.*

*Difficulty: medium*

---

##### Q70
> NOTES. While researching a topic, a student has taken the following notes: • The Million Song Dataset (MSD) includes main audio features and descriptive tags for popular songs. • Audio features include acoustic traits such as loudness and pitch intervals. • Many algorithms use these audio features to predict a new song's popularity. • These algorithms may fail to accurately identify main audio features of a song with varying acoustic traits. • Algorithms based on descriptive tags that describe fixed traits such as genre are more reliable predictors of song popularity.

The student wants to explain a disadvantage of relying on audio features to predict a song's popularity. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Many popularity-predicting algorithms are based on a song's audio features, such as loudness and pitch intervals. 

  *This states that audio-feature-based algorithms exist and names two audio features, but never explains what goes wrong with relying on them — no disadvantage is stated.*

**B.** Algorithms based on audio features may misidentify the main features of a song with varying acoustic traits, making such algorithms less reliable predictors of popularity than those based on fixed traits. **(Correct)**

  *Correct. It states the actual mechanism the notes give for the disadvantage — misidentifying features in songs whose acoustic traits vary — and connects it directly to reduced reliability, which is the explanation the goal asks for.*

**C.** Audio features describe acoustic traits such as pitch intervals, which may vary within a song, whereas descriptive tags describe fixed traits such as genre, which are reliable predictors of popularity. 

  *This contrasts audio features and descriptive tags generally, but never states the specific failure mode — misidentifying a song's main features — that the notes give as the disadvantage.*

**D.** The MSD's descriptive tags are reliable predictors of a song's popularity, as the traits they describe are fixed. 

  *This praises descriptive tags rather than explaining any disadvantage of audio features — the notes' actual complaint about audio features is never stated.*

*Difficulty: hard*

---

##### Q71
> NOTES. While researching a topic, a student has taken the following notes: • Some powerful works of literature have so influenced readers that new legislation has been passed as a result. • The Interesting Narrative of the Life of Olaudah Equiano (1789) is the autobiography of a man who endured slavery on both sides of the Atlantic. • Equiano's book contributed to the passage of the Slave Trade Act of 1807. • The Jungle (1906) is a fictional work by Upton Sinclair that describes unsanitary conditions in US meatpacking plants. • Sinclair's book contributed to the passage of the Pure Food and Drug Act in 1906.

The student wants to emphasize a difference between the two books. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Although both are powerful works of literature that contributed to new legislation, Equiano's book is an autobiography, while Sinclair's is fictional. **(Correct)**

  *Correct. The concession states what the two books share, and the main clause states the specific difference the notes actually give — one is autobiography, the other fiction — which is exactly the contrast the goal asks for.*

**B.** They may have written about different topics, but Equiano and Sinclair both influenced readers. 

  *"Both influenced readers" states a similarity, and the difference gestured at ("different topics") is never specified — what the actual difference is remains unstated.*

**C.** The 1807 Slave Trade Act resulted in part from a book by Equiano, while the 1906 Pure Food and Drug Act resulted in part from a book by Sinclair. 

  *This states that each book led to different legislation, which is a fact about their legislative effects, not about the books themselves — it never states the difference in what kind of book each one is (autobiography versus fiction).*

**D.** The Interesting Narrative of the Life of Olaudah Equiano and The Jungle are two works of literature that contributed to new legislation (concerning the slave trade and food safety, respectively). 

  *This states what the two books have in common — both contributed to legislation — and their different subjects, but never states the difference in form (autobiography versus fiction) that the notes actually establish.*

*Difficulty: medium*

---

##### Q72
> NOTES. While researching a topic, a student has taken the following notes: • In 1971, experimental musician Pauline Oliveros created Sonic Meditations. • Sonic Meditations is not music but rather a series of sound-based exercises called meditations. • Each meditation consists of instructions for participants to make, imagine, listen to, or remember sounds. • The instructions for Meditation V state, "walk so silently that the bottoms of your feet become ears." • Those for Meditation XVIII state, "listen to a sound until you no longer recognize it."

The student wants to provide an explanation and an example of Oliveros's Sonic Meditations. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Sonic Meditations is not music but rather a series of sound-based meditations that consist of instructions; Meditation XVIII, for instance, instructs participants to "listen to a sound until you no longer recognize it." **(Correct)**

  *Correct. It explains what Sonic Meditations actually is — instruction-based exercises, not music — and then gives a concrete example, Meditation XVIII's quoted instruction, satisfying both halves of the two-part goal.*

**B.** In 1971, Oliveros created Sonic Meditations, a series of meditations that consist of instructions for participants to make, imagine, listen to, or remember sounds. 

  *This gives the general explanation of what Sonic Meditations is but never cites a specific meditation's instructions as an example — neither Meditation V nor XVIII is quoted.*

**C.** "Walk so silently that the bottoms of your feet become ears" is one example of the instructions found in Oliveros's Sonic Meditations. 

  *This gives a specific example but never explains what Sonic Meditations actually is — that it is a series of sound-based exercises rather than music is never stated.*

**D.** While both meditations consist of instructions, Meditation XVIII instructs participants to "listen," whereas Meditation V instructs participants to "walk." 

  *This contrasts two specific meditations' instructions but never explains the general nature of Sonic Meditations as a whole — that it is a set of exercises, not music.*

*Difficulty: hard*

---

##### Q73
> NOTES. While researching a topic, a student has taken the following notes: • Freddie Wong (born 1985) is a director and special effects artist from the United States. • He is best known for the action-comedy web series Video Game High School (VGHS). • VGHS premiered in 2012 on RocketJump, a YouTube channel that Wong cocreated. • The series was celebrated for its inventive video game-centric world and high-quality special effects. • VGHS was nominated for a Producers Guild Award for Outstanding Digital Series.

The student wants to begin a narrative about Wong's award-nominated web series. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** In 2012, director and visual effects artist Freddie Wong launched a new action-comedy web series: Video Game High School. **(Correct)**

  *Correct. It opens at the actual starting point of the narrative — the 2012 launch — naming both Wong and the series, which is what "begin a narrative" about the show requires.*

**B.** Video Game High School was celebrated for its inventive video game-centric world and high-quality special effects, and it was nominated for a Producer's Guild Award for Outstanding Digital Series. 

  *This reports the series' later reception and award nomination — events that happen after a series exists — which fits an ending or a middle of the story, not its beginning.*

**C.** Wong, cocreator of the YouTube channel RocketJump, would go on to see his web series be nominated for a Producers Guild Award. 

  *"Would go on to see" is future-looking language that anticipates a later award nomination rather than opening the narrative at its actual starting point, the series' 2012 launch.*

**D.** In 2012, Video Game High School premiered on RocketJump; it would later be nominated for an award. 

  *This begins with the premiere but immediately jumps forward to the later award ("it would later be"), and it also drops Wong himself, whose introduction is central to the narrative the goal asks to begin.*

*Difficulty: medium*

---

##### Q74
> NOTES. While researching a topic, a student has taken the following notes: • The popular wood-wide web theory posits that trees can communicate and exchange resources with one another via common mycorrhizal networks (CMNs) of fungi. • Ecologist Dr. Suzanne Simard first suggested this theory in 1997. • She described trees as "super-cooperators." • In the 2022 study "The Decay of the Wood-Wide Web?," mycologist Dr. Justine Karst and colleagues evaluated dozens of CMN studies. • They write that CMNs "have captured the interest of broad audiences. We are concerned, however, that recent claims about CMNs in forests are disconnected from evidence."

The student wants to use a quotation to emphasize a potential problem with the wood-wide web theory. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Describing trees as "super-cooperators," Simard first suggested that trees can exchange resources with one another in 1997. 

  *This quotes Simard's original, favorable framing of the theory, not a critical assessment — nothing here raises a problem with the theory at all.*

**B.** In "The Decay of the Wood-Wide Web?" Karst and colleagues note that common mycorrhizal networks "have captured the interest of broad audiences." 

  *This quotes Karst's neutral observation about the theory's popularity, not the sentence that follows expressing concern — the actual critical claim is left out.*

**C.** After evaluating dozens of CMN studies, Karst and colleagues expressed concern that recent claims about common mycorrhizal networks are "disconnected from evidence." **(Correct)**

  *Correct. It quotes the actual critical language from Karst's study — "disconnected from evidence" — which is exactly the potential problem with the theory the goal asks to be emphasized.*

**D.** Despite the concerns expressed in the 2022 study "The Decay of the Wood-Wide Web?," the wood-wide web theory remains popular. 

  *This references that concerns exist without quoting them, and its main clause emphasizes the theory's continuing popularity rather than the problem itself — the concession subordinates the very thing the goal asks to be emphasized.*

*Difficulty: hard*

---

##### Q75
> NOTES. While researching a topic, a student has taken the following notes: • A thermal inversion is a phenomenon where a layer of atmosphere is warmer than the layer beneath it. • In 2022, a team of researchers studied the presence of thermal inversions in twenty-five gas giants. • Gas giants are planets largely composed of helium and hydrogen. • The team found that gas giants featuring a thermal inversion were also likely to contain heat-absorbing metals. • One explanation for this relationship is that these metals may reside in a planet's upper atmosphere, where their absorbed heat causes an increase in temperature.

The student wants to present the study's findings to an audience already familiar with thermal inversions. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Heat-absorbing metals may reside in a planet's upper atmosphere. 

  *This states only the proposed explanation for the finding, not the finding itself — that thermal-inversion gas giants were likely to contain heat-absorbing metals in the first place.*

**B.** The team studied thermal inversions in twenty-five gas giants, which are largely composed of helium and hydrogen. 

  *This describes the study's scope and defines what a gas giant is made of — background an audience already familiar with thermal inversions does not especially need — but never reports what the team actually found.*

**C.** Researchers found that gas giants featuring a thermal inversion were likely to contain heat-absorbing metals, which may reside in the planets' upper atmospheres. **(Correct)**

  *Correct. It treats "thermal inversion" as already known and states the actual finding — the link to heat-absorbing metals — plus the proposed explanation, which is what presenting the findings to this audience requires.*

**D.** Gas giants were likely to contain heat-absorbing metals when they featured a layer of atmosphere warmer than the layer beneath it, researchers found; this phenomenon is known as a thermal inversion. 

  *This defines "thermal inversion" from scratch ("a layer of atmosphere warmer than the layer beneath it") — exactly the explanation an audience already familiar with the term does not need.*

*Difficulty: hard*

---

##### Q76
> NOTES. While researching a topic, a student has taken the following notes: • A commodity chain is the series of links connecting the production and purchase of a commodity on the world market. • Chinese American anthropologist Anna Tsing studies the contemporary commodity chain of matsutake mushrooms. • At one end of the matsutake chain are mushroom pickers in Oregon. • At the other end are wealthy consumers who buy the costly matsutake in Japan. • According to Tsing, "Japanese traders began importing matsutake in the 1980s, when the scarcity of matsutake in Japan first became clear."

The student wants to provide an overview of the matsutake commodity chain. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The contemporary matsutake commodity chain has its origins in the 1980s when, according to Tsing, "the scarcity of matsutake in Japan first became clear." 

  *This gives the chain's historical origin but never describes the chain itself — neither end of the chain, the Oregon pickers or the Japanese consumers, is ever mentioned.*

**B.** Commodity chains include the linked production and purchase of commodities, such as the matsutake mushroom, on the world market. 

  *This defines what a commodity chain is in general, using matsutake only as one example among many, without describing the actual matsutake chain's two ends.*

**C.** Decades after the Japanese import of matsutake began, a commodity chain now links matsutake pickers in Oregon with wealthy consumers of the costly mushrooms in Japan. **(Correct)**

  *Correct. It describes the full chain — from Oregon pickers to wealthy Japanese consumers — with enough historical framing to give a genuine overview, which is what the goal asks for.*

**D.** Wealthy consumers who buy the costly mushrooms in Japan are at one end of the matsutake commodity chain. 

  *This describes only one end of the chain — the Japanese consumers — and never mentions the Oregon pickers at the other end, giving a partial rather than an overview picture.*

*Difficulty: medium*

---

##### Q77
> NOTES. While researching a topic, a student has taken the following notes: • Archaeologist Jon Erlandson and colleagues argue that humans first arrived in the Americas by sea. • They propose that humans traveled between Pacific Ocean islands and coastlines from northeast Asia to the Americas. • Many of these islands and coastal zones were later submerged as glaciers melted and sea levels rose. • The researchers think that "a coastal route, including kelp forests and estuaries, would have provided a rich mix of marine, estuarine, riverine, and terrestrial resources" such as seaweeds, fish, and birds. • This proposed scenario is known as the kelp highway hypothesis.

The student wants to summarize the kelp highway hypothesis. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Pacific Ocean islands and coastlines likely contained "a rich mix of marine, estuarine, riverine, and terrestrial resources" such as seaweeds, fish, and birds, according to researchers. 

  *This gives only the resource detail from the hypothesis and never states its central claim — that humans first reached the Americas by traveling this island-and-coastline sea route.*

**B.** One argument about how humans first arrived in the Americas is the kelp highway hypothesis proposed by Jon Erlandson and colleagues. 

  *This names the hypothesis and its proposers but never states what the hypothesis actually claims — the sea route between islands and coastlines is never described.*

**C.** Humans may have first arrived in the Americas by sea, traveling between Pacific Ocean islands and coastlines and subsisting on a variety of resources. **(Correct)**

  *Correct. It states the hypothesis's central claim — a sea route between islands and coastlines, sustained by varied resources — which is a genuine summary of what the kelp highway hypothesis proposes.*

**D.** As glaciers melted and sea levels rose, many Pacific Ocean islands and coastal zones were submerged. 

  *This states a later geological consequence — why the route is hard to trace today — rather than summarizing what the hypothesis itself claims about how humans arrived.*

*Difficulty: medium*

---

##### Q78
> NOTES. While researching a topic, a student has taken the following notes: • Neuroscientists Krishnan Padmanabhan and Zhen Chen sought to better understand the workings of the brain's olfactory system. • They devised a study using mathematical models. • They found that certain fibers allow the brain to toggle from one method of processing smells to another. • In one method, cells in the piriform cortex (where the perception of odor forms) capture olfactory information at a given moment. • In the other, the cells track changes in olfactory information over time.

The student wants to summarize the study's findings. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** To arrive at these findings, which describe dual methods of processing smells in the piriform cortex, Padmanabhan and Chen devised a study using mathematical models. 

  *This gestures at "these findings" and the method used to reach them, but never actually states what the two processing methods are — capturing a moment versus tracking change over time is never described.*

**B.** Padmanabhan and Chen showed that olfactory information is captured by cells in the piriform cortex, where the perception of odor forms. 

  *This reports only one of the two processing methods — capturing information at a given moment — and omits the other, tracking changes over time, so the findings are only half summarized.*

**C.** Using mathematical models, Padmanabhan and Chen devised a study to better understand the workings of the brain's olfactory system. 

  *This describes the study's method and original purpose, not what it actually found — the toggle between the two processing methods, the study's actual finding, never appears.*

**D.** According to Padmanabhan and Chen, the brain can toggle between capturing olfactory information at a given moment and tracking changes in that information over time. **(Correct)**

  *Correct. It states the study's actual finding — that the brain toggles between the two named processing methods — which is exactly the finding the goal asks to be summarized.*

*Difficulty: hard*

---

##### Q79
> NOTES. While researching a topic, a student has taken the following notes: • Nissologists are scientists who study islands. • Some nissologists define an island as any piece of land surrounded by water. • Using that definition, they determined Sweden has 221,000 islands. • Other nissologists define an island as being 1 kilometer square, a certain distance from the mainland, and having at least 50 permanent residents. • Using that definition, they determined Sweden has 24 islands.

The student wants to make and support a generalization about nissologists' definition of an island. Which choice most effectively uses relevant information from the notes to accomplish these goals?

**A.** The definition of an island as any piece of land surrounded by water is supported by some nissologists, scientists who study islands. 

  *This states one specific definition and who holds it, but never makes a general claim about how nissologists' definitions vary or supports that claim with the Sweden comparison.*

**B.** Multiple counts of Sweden's islands have been based on different definitions of an island. 

  *This states that different definitions produce different counts but never generalizes about nissologists' definitions as a category — it stays narrowly about Sweden's counts rather than about the definitions themselves.*

**C.** Based on a recent count, Sweden has a relatively small number of islands with at least 50 permanent residents. 

  *This reports only the 24-island figure under one definition, omitting the 221,000-island figure under the other — with only one definition's result given, no generalization about definitions is supported.*

**D.** Nissologists' different definitions can result in huge disparities in counts of islands, as the example of Sweden shows. **(Correct)**

  *Correct. It states a general claim — that differing definitions produce huge disparities — and supports it with the Sweden example, whose 221,000-versus-24 gap is exactly the disparity the notes provide.*

*Difficulty: hard*

---

##### Q80
> NOTES. While researching a topic, a student has taken the following notes: • In 1978, Sámi activists staged protests to block the construction of a dam on the Alta River in Norway. • The dam would disrupt Sámi fishing and reindeer herding. • The dam was ultimately built, but the Alta conflict had a lasting impact. • It brought international attention to the issue of Sámi rights. • It led to a set of 2005 legal protections establishing Sámi rights to lands, waters, and resources.

The student wants to make and support a generalization about the Alta conflict. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** During the Alta conflict, Sámi activists staged protests to block the construction of a dam on the Alta River in Norway that would disrupt local fishing and reindeer herding. 

  *This is a specific account of what happened during the conflict, not a generalization about its broader significance — no general claim about lasting impact is made or supported.*

**B.** Although the dam that the Sámi activists had protested was ultimately built, the Alta conflict had a lasting impact. 

  *This states that the conflict had a lasting impact, which gestures at a generalization, but never specifies what that impact actually was — neither the international attention nor the 2005 legal protections is mentioned to support the claim.*

**C.** Sámi rights to lands, waters, and resources received international attention and legal protections as a result of the Alta conflict. 

  *This states the specific outcomes accurately but frames them as facts about this one conflict rather than as support for a broader generalization about what such conflicts can accomplish.*

**D.** The Alta conflict had a lasting impact, resulting in international attention and legal protections for Sámi rights to lands, waters, and resources. **(Correct)**

  *Correct. It states the general claim — a lasting impact — and supports it with the specific evidence the notes provide, international attention and the 2005 legal protections, satisfying both halves of the goal.*

*Difficulty: medium*

---

##### Q81
> NOTES. While researching a topic, a student has taken the following notes: • Stars form in a galaxy when gravity causes a massive cloud of dust and gas to collapse. • A galaxy in a phase of rapid star formation is called a starburst galaxy. • Quenching is a process in which a galaxy loses star-forming gas. • A galaxy that no longer forms stars is called a quenched galaxy. • A quenched galaxy has entered the poststarburst phase.

The student wants to explain what a quenched galaxy is. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Before quenching, a starburst galaxy will form stars at a rapid rate. 

  *This describes the starburst galaxy's earlier state, before quenching occurs, not what a quenched galaxy itself is — the very thing the goal asks to be explained.*

**B.** When it becomes quenched, a starburst galaxy enters the poststarburst phase. 

  *This names the phase a quenched galaxy enters without ever stating the defining property of a quenched galaxy — that it no longer forms stars — which the notes give directly.*

**C.** Having entered the poststarburst phase, a quenched galaxy is one that no longer forms stars. **(Correct)**

  *Correct. It states the defining property directly — a quenched galaxy is one that no longer forms stars — while also noting the phase it has entered, which is exactly what "explain what a quenched galaxy is" requires.*

**D.** A starburst galaxy will lose star-forming gas and eventually become quenched. 

  *This describes the process of quenching happening to a starburst galaxy over time, not the definition of what a quenched galaxy actually is once the process is complete.*

*Difficulty: easy*

---

##### Q82
> NOTES. While researching a topic, a student has taken the following notes: • African American women played prominent roles in the Civil Rights Movement, including at the famous 1963 March on Washington. • Civil rights activist Anna Hedgeman, one of the march's organizers, was a political adviser who had worked for President Truman. • Civil rights activist Daisy Bates was a well-known journalist and advocate for school desegregation. • Hedgeman worked behind the scenes to make sure a woman was included in the lineup of speakers at the march. • Bates was the sole woman to speak, delivering a brief but memorable address to the cheering crowd.

The student wants to compare the two women's contributions to the March on Washington. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Hedgeman and Bates contributed to the march in different ways; Bates, for example, delivered a brief but memorable address. 

  *Both women are named and "in different ways" gestures at contrast, but only Bates's contribution is actually specified — Hedgeman's behind-the-scenes advocacy for a woman speaker never appears, so the comparison stays one-sided.*

**B.** Hedgeman worked in politics and helped organize the march, while Bates was a journalist and school desegregation advocate. 

  *This contrasts their general professional backgrounds — politics versus journalism — rather than their actual contributions to the march itself; Hedgeman's specific advocacy for a woman speaker and Bates's speech are never mentioned.*

**C.** Although Hedgeman worked behind the scenes to make sure a woman speaker was included, Bates was the sole woman to speak at the march. **(Correct)**

  *Correct. It names each woman's specific contribution — Hedgeman securing a place for a woman speaker, Bates being that speaker — and "although" ties them together as complementary yet distinct roles in the same event.*

**D.** Many African American women, including Bates and Hedgeman, fought for civil rights, but only one spoke at the march. 

  *This generalizes to "many African American women" and never distinguishes Hedgeman's specific contribution from Bates's — "only one spoke" identifies a fact about Bates without stating what Hedgeman herself contributed.*

*Difficulty: hard*

---

##### Q83
> NOTES. While researching a topic, a student has taken the following notes: • Ulaanbaatar is the capital of Mongolia. • The city's population is 907,802. • Ulaanbaatar contains 31.98 percent of Mongolia's population. • Hanoi is the capital of Vietnam. • The city's population is 7,781,631. • Hanoi contains 8.14 percent of Vietnam's population.

The student wants to emphasize the relative sizes of the two capitals' populations. Which choice most effectively uses relevant information from the given sentences to emphasize the relative sizes of the two capitals' populations?

**A.** Mongolia's capital is Ulaanbaatar, which has 907,802 people, and Vietnam's capital is Hanoi, which has 7,781,631 people. 

  *This gives both raw population figures side by side but treats them as parallel facts rather than making the relative claim the goal asks for — nothing states how the two cities' sizes actually compare to each other or to their countries.*

**B.** Comparing Vietnam and Mongolia, 7,781,631 is 8.14 percent of Vietnam's population, and 907,802 is 31.98 percent of Mongolia's. 

  *This reports both percentage figures accurately but never draws the actual relative point they support — that the smaller-population capital, Ulaanbaatar, accounts for the larger share of its country. The numbers are given without their implication stated.*

**C.** Even though Hanoi (population 7,781,631) is larger than Ulaanbaatar (population 907,802), Ulaanbaatar accounts for more of its country's population. **(Correct)**

  *Correct. It states the counterintuitive relative relationship directly — Hanoi has far more people, yet Ulaanbaatar makes up a larger share of its own country — which is the relative-size emphasis the goal asks for.*

**D.** The populations of the capitals of Mongolia and Vietnam are 907,802 (Ulaanbaatar) and 7,781,631 (Hanoi), respectively. 

  *This lists both raw figures without stating any relationship between them — no comparison word, no percentage, no claim about relative size is made.*

*Difficulty: hard*

---

##### Q84
> NOTES. While researching a topic, a student has taken the following notes: • The Atlantic Monthly magazine was first published in 1857. • The magazine focused on politics, art, and literature. • In 2019, historian Cathryn Halverson published the book Faraway Women and the "Atlantic Monthly." • Its subject is female authors whose autobiographies appeared in the magazine in the early 1900s. • One of the authors discussed is Juanita Harrison.

The student wants to introduce Cathryn Halverson's book to an audience already familiar with the Atlantic Monthly. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Cathryn Halverson's Faraway Women and the "Atlantic Monthly" discusses female authors whose autobiographies appeared in the magazine in the early 1900s. **(Correct)**

  *Correct. It treats the Atlantic Monthly as already known and moves straight to introducing the book — its author, title, and subject — which is what a reader already familiar with the magazine still needs to learn.*

**B.** A magazine called the Atlantic Monthly, referred to in Cathryn Halverson's book title, was first published in 1857. 

  *This re-explains what the Atlantic Monthly is and when it was founded — background an audience already familiar with the magazine does not need — while barely introducing the book itself.*

**C.** Faraway Women and the "Atlantic Monthly" features contributors to the Atlantic Monthly, first published in 1857 as a magazine focusing on politics, art, and literature. 

  *This spends most of the sentence re-defining the magazine (founding year, focus areas) rather than describing the book's own subject — Halverson's actual focus, female authors' autobiographies, is never mentioned.*

**D.** An author discussed by Cathryn Halverson is Juanita Harrison, whose autobiography appeared in the Atlantic Monthly in the early 1900s. 

  *This introduces one specific author from the book rather than the book itself — a reader is never told the book's title or its general subject, only one example from inside it.*

*Difficulty: medium*

---

##### Q85
> NOTES. While researching a topic, a student has taken the following notes: • One of history's greatest libraries was the House of Wisdom in Baghdad, Iraq. • It was founded in the eighth century with the goal of preserving all the world's knowledge. • Scholars at the House of Wisdom collected ancient and contemporary texts from Greece, India, and elsewhere and translated them into Arabic. • Writings included those of the Greek philosopher Aristotle and the Indian mathematician Aryabhata. • The House of Wisdom used Chinese papermaking technology to create paper versions to be studied and shared.

The student wants to explain how the House of Wisdom preserved the world's knowledge. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The House of Wisdom was known for bringing together knowledge from around the world, including from Greece, India, and China. 

  *This states that knowledge was gathered from multiple places but never explains the actual process — translation into Arabic and papermaking — by which that knowledge was preserved.*

**B.** Founded in Iraq in the eighth century, the House of Wisdom employed many scholars as translators. 

  *This mentions translation but never states what was translated, into what language, or how the resulting texts were then preserved and shared — the process is only partially sketched.*

**C.** Writings from the Greek philosopher Aristotle and the Indian mathematician Aryabhata were preserved at the House of Wisdom. 

  *This names two specific authors whose works were preserved but never explains the actual mechanism of preservation — translation into Arabic and the creation of paper copies.*

**D.** The House of Wisdom collected writings from different countries and created paper versions in Arabic to be studied and shared. **(Correct)**

  *Correct. It states the actual two-step process — collecting texts and creating Arabic paper versions — that the notes give as how the House of Wisdom preserved the world's knowledge.*

*Difficulty: medium*

---

##### Q86
> NOTES. While researching a topic, a student has taken the following notes: • The magnificent frigatebird (Fregata magnificens) is a species of seabird that feeds mainly on fish, tuna, squid, and other small sea animals. • It is unusual among seabirds in that it doesn't dive into the water for prey. • One way it acquires food is by using its hook-tipped bill to snatch prey from the surface of the water. • Another way it acquires food is by taking it from weaker birds by force. • This behavior is known as kleptoparasitism.

The student wants to emphasize a similarity between the two ways a magnificent frigatebird acquires food. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** A magnificent frigatebird never dives into the water, instead using its hook-tipped bill to snatch prey from the surface. 

  *This describes only one of the two feeding methods — snatching prey with its bill — and never mentions kleptoparasitism, so no similarity between the two methods is stated.*

**B.** Neither of a magnificent frigatebird's two ways of acquiring food requires the bird to dive into the water. **(Correct)**

  *Correct. Both methods appear, and "neither... requires diving" states the shared property that connects them — the one trait the notes establish as true of both the bill-snatching and the kleptoparasitism.*

**C.** Of the magnificent frigatebird's two ways of acquiring food, only one is known as kleptoparasitism. 

  *"Only one" states a difference between the two methods — that just one carries the kleptoparasitism label — rather than a similarity shared by both.*

**D.** In addition to snatching prey from the water with its hook-tipped bill, a magnificent frigatebird takes food from other birds by force. 

  *This lists both methods but never states what they have in common — "in addition to" only adds one method after the other without naming a shared property between them.*

*Difficulty: medium*

---

##### Q87
> NOTES. While researching a topic, a student has taken the following notes: • The National Congress of American Indians (NCAI) was founded in 1944 by representatives of fifty tribal governments. • The NCAI was created to protect the sovereignty of Indigenous tribes. • Napoleon B. Johnson (Cherokee) was the NCAI's first president. • In 1975, the US Congress passed the Indian Self-Determination and Education Assistance Act (Public Law 96-638). • This legislation formally acknowledged tribes' right to self-governance. • The advocacy of the NCAI was a key factor in the law's passing.

The student wants to identify an accomplishment of the NCAI. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The NCAI, founded by representatives of fifty tribal governments, had Napoleon B. Johnson (Cherokee) as its first president. 

  *This describes the NCAI's founding and its first president — organizational facts, not an accomplishment the organization achieved.*

**B.** Founded in 1944, the NCAI was created by representatives of tribal governments from fifty sovereign Indigenous tribes. 

  *This restates the founding details without ever mentioning what the NCAI actually went on to accomplish — the 1975 law and its own advocacy role in passing it are missing.*

**C.** The NCAI's advocacy was key to the passing of Public Law 96-638, legislation formally acknowledging Indigenous tribes' right to self-governance. **(Correct)**

  *Correct. It states an actual accomplishment — the NCAI's advocacy being key to a specific law's passage — which is exactly what the goal asks to be identified.*

**D.** In 1975, the NCAI passed the Indian Self-Determination and Education Assistance Act, which was created to protect the sovereignty of Indigenous tribes. 

  *This misattributes passing the law directly to the NCAI when the notes state Congress passed it with the NCAI's advocacy as a contributing factor, and it wrongly reuses the NCAI's own founding purpose (protecting sovereignty) to describe the 1975 act's goal (self-governance), which are different things.*

*Difficulty: medium*

---

##### Q88
> NOTES. While researching a topic, a student has taken the following notes: • Phobetor, a name drawn from Greek mythology, is an exoplanet that orbits the star PSR B1257+12, also known as Lich. • Phobetor's mass is 0.01 times that of Jupiter, or 0.01 Jupiter masses. • Mastika, which means "gem" or "jewel" in Malay, is an exoplanet that orbits the star HD 179949, also known as Gumala. • Mastika's mass is 0.92 Jupiter masses.

The student wants to make and support a generalization about exoplanets. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Exoplanets that are named Phobetor orbit Lich, and those that are named Mastika orbit Gumala. 

  *This restates the two specific orbital facts as if they were general rules ("exoplanets that are named Phobetor"), but it never makes a claim that actually generalizes beyond these two specific planets.*

**B.** Even though Phobetor and Mastika are both exoplanets, their masses are different: Phobetor's mass is 0.01 Jupiter masses, and Mastika's is 0.92 Jupiter masses. 

  *This is a specific comparison of the two planets' masses, not a generalization about exoplanets as a category — mass is also not the property the notes actually build toward generalizing (naming origin is).*

**C.** Many stars have both a designation and a proper name; for instance, PSR B1257+12 is also known as Lich, and HD 179949 is also known as Gumala. 

  *This generalizes about stars' dual naming, not about exoplanets — the goal asks for a generalization about exoplanets, and this choice is about the stars the exoplanets orbit instead.*

**D.** Exoplanet names have diverse origins, a fact that can be seen in the cases of Phobetor, a name drawn from Greek mythology, and Mastika, which means "gem" or "jewel" in Malay. **(Correct)**

  *Correct. It states a general claim — that exoplanet names have diverse origins — and supports it with both specific examples the notes provide, one from Greek mythology and one from Malay, satisfying both halves of the goal.*

*Difficulty: hard*

---

##### Q89
> NOTES. While researching a topic, a student has taken the following notes: • In a 2023 study, environmental scientist Jazmin Locke-Rodriguez and colleagues tested the use of floating treatment wetlands (FTWs) in Florida. • FTWs are artificial floating platforms of plants used to remediate polluted or nutrient-imbalanced water. • Finding: FTWs using marigold flowers removed 52% more total phosphorus than the control. • Finding: the test yielded 65 market-quality blooms per square meter. • The authors concluded marigolds showed "promising potential as a commercially viable remediating crop cultivated on FTWs in South Florida."

The student wants to present the findings of the study. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** The authors concluded that marigolds grown on FTWs were "commercially viable," having produced 65 blooms per square meter of market-quality blooms in a 2023 study. 

  *This reports the bloom finding and the authors' conclusion but omits the other stated finding — the 52% greater phosphorus removal — giving only half of what the notes report as "findings."*

**B.** In a 2023 study, Locke-Rodriguez and colleagues found that marigolds cultivated on FTWs produced 52% more market-quality flower blooms than the control. 

  *This misreports the finding: the notes state marigolds removed 52% more phosphorus than the control, not that they produced 52% more blooms — the bloom figure (65 per square meter) is a separate, unrelated finding.*

**C.** Locke-Rodriguez and colleagues found that FTWs using marigolds not only helped remove phosphorus from the water but also yielded market-quality blooms. **(Correct)**

  *Correct. It presents both findings the notes report — the phosphorus removal and the market-quality bloom yield — combined with "not only... but also," which is what "present the findings" (plural) requires.*

**D.** FTWs using marigolds, Locke-Rodriguez and colleagues found, yielded 65 flower blooms and removed 52% of phosphorus from the water. 

  *This distorts both figures: the 65 blooms were per square meter, not a flat total, and the 52% figure describes how much more phosphorus was removed than the control, not 52% of all phosphorus present.*

*Difficulty: hard*

---

##### Q90
> NOTES. While researching a topic, a student has taken the following notes: • Two opposing theories of vision divided scholars for many centuries. • The ancient Greek mathematician Euclid (circa 300 BCE) supported the extramission theory. • This theory held that the eyes emit a form of radiation that illuminates objects in its range. • The ancient Greek philosopher Aristotle (384-322 BCE) supported the intromission theory. • This theory held that objects emit a form of radiation that reaches the eyes. • In the eleventh century, Arab mathematician Ibn al-Haytham (965-1040 CE) largely settled the debate with the first conclusive experiments supporting intromission.

The student wants to provide a historical overview of the two theories. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Scholars were divided between the extramission and intromission theories of vision until Ibn al-Haytham's eleventh-century experiments largely settled the debate in support of intromission. **(Correct)**

  *Correct. It names both theories, frames them as a historical division, and gives the resolution — Ibn al-Haytham's experiments — completing the arc from division to settlement that an overview requires.*

**B.** Through two opposing theories of vision—extramission and intromission—Euclid, Aristotle, and Ibn al-Haytham held that a form of radiation is emitted either from objects or from the eyes. 

  *This blurs the three figures' positions together as if all three simply held one of two views, without noting that Ibn al-Haytham's role was to settle the debate through experiment rather than simply hold a side.*

**C.** While Ibn al-Haytham largely settled the debate in the eleventh century, Aristotle supported the theory of intromission centuries before. 

  *Euclid and the extramission theory are never mentioned — only half of the "two theories" the goal asks to be overviewed actually appears.*

**D.** Before the eleventh century, the ancient Greek philosopher Aristotle supported the intromission theory, which held that objects emit a form of radiation that reaches the eyes. 

  *Only Aristotle and intromission appear; Euclid's extramission theory and Ibn al-Haytham's resolution are both missing, leaving only one theory of the two described.*

*Difficulty: hard*

---

##### Q91
> NOTES. While researching a topic, a student has taken the following notes: • British scholar Robert Plot described fossilized dinosaur bones in his 1676 book The Natural History of Oxfordshire. • Plot earned a reputation for being the first person to have discovered dinosaur remains. • In 1990, archaeologists in Lesotho, southern Africa, discovered a fossilized phalanx of a Massospondylus carinatus dinosaur in a cave once inhabited by humans. • Indigenous Khoesan and Basotho peoples had inhabited the cave beginning around 1100 CE. • According to paleontologist Julien Benoit, these peoples may have found the phalanx and brought it to the cave centuries before Plot's descriptions.

The student wants to emphasize the significance of the 1990 discovery to Plot's reputation. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** Benoit challenged Plot's reputation for being the first person to have discovered M. carinatus remains. 

  *This attributes the challenge to Benoit's own action rather than to the 1990 discovery itself, and it narrows Plot's reputation to "M. carinatus" specifically, when the notes describe his reputation as being for dinosaur remains generally.*

**B.** Evidence that Khoesan and Basotho peoples may have found an M. carinatus phalanx as long ago as 1100 CE suggests that Plot may not have been the first person to have discovered dinosaur remains. **(Correct)**

  *Correct. It states the actual significance the goal asks for — the 1990 evidence casts doubt on the very reputation ("first person") the notes say Plot earned — connecting the discovery directly to the effect on his standing.*

**C.** According to Benoit's analysis of the 1990 discovery, Indigenous peoples in southern Africa may have brought the fossilized phalanx to the cave as long ago as 1100 CE. 

  *This reports Benoit's finding accurately but never connects it back to Plot or his reputation at all — the significance to Plot, which the goal asks for, is left out entirely.*

**D.** In 1990, more than three centuries after Plot claimed in his book that he had found fossilized dinosaur bones, archaeologists uncovered evidence in southern Africa that disproved his claims. 

  *This overstates the notes: Benoit's account says the earlier peoples "may have" found the phalanx first, a hedge — "disproved his claims" asserts a certainty the notes never establish, and it misdescribes Plot as claiming to have found the bones himself rather than describing already-found ones.*

*Difficulty: hard*

---

##### Q92
> NOTES. While researching a topic, a student has taken the following notes: • Digital Light Synthesis (DLS) is a form of additive manufacturing that utilizes light to rapidly cure liquid resin into high-quality 3D objects. • Step 1: Ultraviolet (UV) light images are projected up into a pool of liquid resin, where the object's first layer takes shape. • Step 2: The partially cured resin object is raised, leaving a thin space (a "dead zone") beneath it for oxygen and liquid resin to flow through. • Step 3: The UV light passes through the dead zone—maintaining the flow of resin—and partially cures additional layers of the object. • Step 4: When the resin object is complete, it is baked in an oven to complete the curing.

The student wants to describe how DLS cures 3D objects. Which choice most effectively uses relevant information from the notes to accomplish this goal?

**A.** DLS is a form of additive manufacturing that creates a "dead zone" in which UV light solidifies layer by layer before being baked in an oven, creating a high-quality, 3D object. 

  *This misplaces where curing happens: the notes describe UV light projecting up into the resin pool to shape each layer, with the dead zone existing only to let resin and oxygen flow beneath the rising object — the dead zone is not where the light solidifies the object.*

**B.** DLS cures 3D objects by passing through a "dead zone," adding layers to the object, then curing the object in an oven. 

  *This reverses the notes' order and drops the mechanism entirely: the dead zone lets resin flow so the object can be raised between layers, and the oven bake completes curing only after the object is already substantially cured by UV light, not as the layer-adding step itself.*

**C.** In DLS, UV light images are projected into a liquid resin pool to cure a 3D object layer by layer; once solidified, the object is baked in an oven. **(Correct)**

  *Correct. It states the actual mechanism in the right order — UV light curing successive layers within the resin pool, followed by an oven bake to complete curing — which matches the notes' four steps.*

**D.** In DLS, UV light is projected into layers of liquid resin until the resin solidifies and passes through a "dead zone," wherein the curing is completed. 

  *This has the resin itself passing through the dead zone and being fully cured there, when the notes describe the object being raised out of the resin (leaving the dead zone beneath it) and curing being completed later in the oven, not in the dead zone.*

*Difficulty: medium*

---

## Math

### Algebra

#### Systems of two linear equations (57 items)

##### Q1
Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pairs of pants for $86, and Sofia purchased 3 shirts and 5 pairs of pants for $166. Which of the following systems of linear equations represents the situation, if x represents the price, in dollars, of each shirt and y represents the price, in dollars, of each pair of pants?

**A.** 4x + 2y = 86
3x + 5y = 166 **(Correct)**

  *Correct. Hiro bought 4 shirts and 2 pants for $86: 4x + 2y = 86. Sofia bought 3 shirts and 5 pants for $166: 3x + 5y = 166. Each equation pairs the right count with the right person's total.*

**B.** 4x + 3y = 86
2x + 5y = 166 

  *Takes Hiro's shirt count (4) but pairs it with Sofia's pants count (3) in the first equation, and Sofia's shirt count is mangled into a 2 in the second. The counts have been mixed across the two people rather than kept with the person who actually bought them.*

**C.** 4x + 2y = 166
3x + 5y = 86 

  *Uses Hiro's correct item counts (4 shirts, 2 pants) but attaches Sofia's total ($166) to them, and vice versa. The counts are right; the dollar totals have been swapped between the two people.*

**D.** 4x + 3y = 166
2x + 5y = 86 

  *Combines both errors at once: the item counts are mixed between Hiro and Sofia, and the two dollar totals are also swapped. Every number in this system is real — none of them are paired with the person or purchase they actually belong to.*

*Difficulty: medium*

---

##### Q2
A petting zoo sells two types of tickets. The standard ticket, for admission only, costs $5. The premium ticket, which includes admission and food to give to the animals, costs $12. One Saturday, the petting zoo sold a total of 250 tickets and collected a total of $2,300 from ticket sales. Which of the following systems of equations can be used to find the number of standard tickets, s, and premium tickets, p, sold on that Saturday?

**A.** s + p = 250
5s + 12p = 2,300 **(Correct)**

  *Correct. Total tickets: s + p = 250. Total revenue, standard at $5 and premium at $12: 5s + 12p = 2,300.*

**B.** s + p = 250
12s + 5p = 2,300 

  *Attaches the premium price ($12) to standard tickets and the standard price ($5) to premium tickets — the two prices are swapped relative to the ticket type the stem assigns them to.*

**C.** 5s + 12p = 250
s + p = 2,300 

  *Puts the ticket count (250) where the dollar total belongs and the dollar total (2,300) where the ticket count belongs — the two equations have been assigned to the wrong quantities entirely.*

**D.** 12s + 5p = 250
s + p = 2,300 

  *Combines both errors: the prices are swapped between ticket types, and the count equation is set equal to the revenue total while the revenue equation is set equal to the ticket count.*

*Difficulty: medium*

---

##### Q3
x = 10
y = x + 21
The solution to the given system of equations is (x, y). What is the value of y?

**A.** 2.1 

  *Divides 21 by 10 instead of adding them — the equation says y = x + 21, not y = 21/x or 21/10. Addition and division are not interchangeable just because both numbers appear in the same line.*

**B.** 10 

  *This is x, not y. It's the given value, reported before the second equation was ever used.*

**C.** 21 

  *Reports the constant from y = x + 21 while dropping the x term entirely, as though the equation read y = 21.*

**D.** 31 **(Correct)**

  *Correct. Substitute x = 10 into y = x + 21: y = 10 + 21 = 31.*

*Difficulty: easy*

---

##### Q4
y = 2x + 3
x = 1
What is the solution (x, y) to the given system of equations?

**A.** (1, 2) 

  *Computes 2(1) and stops there, dropping the '+ 3' from the equation entirely — as though y = 2x rather than y = 2x + 3.*

**B.** (1, 5) **(Correct)**

  *Correct. Substitute x = 1: y = 2(1) + 3 = 5.*

**C.** (2, 3) 

  *Reads the equation's own slope and intercept — 2 and 3 — off as though they were the coordinates of the solution point, rather than solving the system using the given x = 1.*

**D.** (2, 7) 

  *Uses the coefficient 2 as if it were the given x-value instead of the actual given value x = 1, then computes y = 2(2) + 3 = 7 from that wrong x.*

*Difficulty: easy*

---

##### Q5
y = 4x - 9
y = 19
What is the solution (x, y) to the given system of equations?

**A.** (4, 19) 

  *Uses the coefficient 4 as x without ever solving the equation, simply pairing it with the given y = 19.*

**B.** (7, 19) **(Correct)**

  *Correct. Set 4x - 9 = 19, so 4x = 28 and x = 7. The pair is (7, 19).*

**C.** (19, 4) 

  *The same unsolved-coefficient error as choice A, with the coordinates additionally written in reversed order.*

**D.** (19, 7) 

  *Solves correctly for x = 7, then writes the ordered pair with y first: (19, 7) instead of (7, 19).*

*Difficulty: medium*

---

##### Q6
Connor has c dollars and Maria has m dollars. Connor has 4 times as many dollars as Maria, and together they have a total of $25.00. Which system of equations represents this situation?

**A.** c = 4m
c + m = 25 **(Correct)**

  *Correct. Connor has 4 times Maria's amount: c = 4m. Together they total $25: c + m = 25.*

**B.** m = 4c
c + m = 25 

  *Reverses who has 4 times as much — this says Maria has 4 times Connor's amount, the opposite of what the sentence states.*

**C.** c = 25m
c + m = 4 

  *Swaps the multiplier and the total: 25 (the combined total) is used as the multiplier, and 4 (the multiplier) is used as the total.*

**D.** m = 25c
c + m = 4 

  *Combines both errors: the multiplier relationship is reversed, and the multiplier and the total have also traded places.*

*Difficulty: medium*

---

##### Q7
A dance teacher ordered outfits for students for a dance recital. Outfits for boys cost $26, and outfits for girls cost $35. The dance teacher ordered a total of 28 outfits and spent $881. If b represents the number of outfits the dance teacher ordered for boys and g represents the number of outfits the dance teacher ordered for girls, which of the following systems of equations can be solved to find b and g?

**A.** 26b + 35g = 28
b + g = 881 

  *Sets the dollar-cost equation equal to the outfit count (28) and the count equation equal to the dollar total (881) — the two equations have been assigned to the wrong quantities.*

**B.** 26b + 35g = 881
b + g = 28 **(Correct)**

  *Correct. Total cost: 26b + 35g = 881. Total outfits: b + g = 28.*

**C.** 26g + 35b = 28
b + g = 881 

  *Attaches the boys' price to g and the girls' price to b, and additionally sets the cost equation equal to the outfit count instead of the dollar total.*

**D.** 26g + 35b = 881
b + g = 28 

  *The outfit count and dollar total are correctly placed, but the two prices are swapped — $35 is attached to boys and $26 to girls, the reverse of what the stem states.*

*Difficulty: medium*

---

##### Q8
x + y = 20
2(x + y) + 3y = 85
If (x, y) is the solution to the given system of equations, what is the value of y?

**A.** 10 

  *Assumes x and y split the total of 20 evenly, since only the first equation was used to produce this: x = y = 10. The second equation — the one that actually distinguishes x from y — was never touched.*

**B.** 15 **(Correct)**

  *Correct. Substitute x + y = 20 into the second equation: 2(20) + 3y = 85, so 40 + 3y = 85, 3y = 45, and y = 15.*

**C.** 60 

  *Substitutes x + y = 20 into the '2(x + y)' term correctly, but then substitutes it a second time into the separate '3y' term as well, computing 3(x + y) = 3(20) = 60 and reporting that product directly as y. The 20 belongs only to the parenthesized term, not to the standalone y.*

**D.** 65 

  *Subtracts the two right-hand sides (85 - 20 = 65) and reports that raw difference as y, without ever expanding 2(x + y) or isolating y algebraically.*

*Difficulty: hard*

---

##### Q9
3x + y = 29
x = 2
If (x, y) is the solution to the given system of equations, what is the value of y?

**A.** 2 

  *This is x, the given value — reported before the first equation was ever used to find y.*

**B.** 35 

  *Adds 3x to 29 instead of subtracting it: 29 + 3(2) = 35, the opposite of the correct move for isolating y.*

**C.** 23 **(Correct)**

  *Correct. Substitute x = 2: 3(2) + y = 29, so 6 + y = 29 and y = 23.*

**D.** 26 

  *Subtracts the coefficient 3 from 29 instead of subtracting the full product 3x = 3(2) = 6 — treating the equation as though x had never been substituted in.*

*Difficulty: medium*

---

##### Q10
An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $20, how many novels did she purchase?

**A.** 2 

  *Divides the difference of the two totals (20 - 11 = 9) by the novel's price (4) instead of by the price difference between a novel and a magazine (4 - 1 = 3): 9/4 = 2.25, rounded down to 2. The elimination step needs the price gap, not either price alone.*

**B.** 3 **(Correct)**

  *Correct. Let n = novels and m = magazines: n + m = 11 and 4n + m = 20. Subtracting gives 3n = 9, so n = 3 (and m = 8, checking: 4(3) + 8 = 20 ✓).*

**C.** 4 

  *Substitutes n in place of m in the price equation — writing 4n + n = 20 instead of 4n + m = 20, as though every item purchased were a novel. That gives 5n = 20, n = 4.*

**D.** 5 

  *Drops the magazine term from the price equation entirely, solving 4n = 20 as though all 11 items were novels priced at $4 each.*

*Difficulty: hard*

---

##### Q11
A discount airline sells a certain number of tickets, x, for a flight for $90 each. It sells the number of remaining tickets, y, for $250 each. For a particular flight, the airline sold 120 tickets and collected a total of $27,600 from the sale of those tickets. Which system of equations represents this relationship between x and y?

**A.** x + y = 120
90x + 250y = 27,600 **(Correct)**

  *Correct. Total tickets: x + y = 120. Total revenue: 90x + 250y = 27,600.*

**B.** x + y = 120
90x + 250y = 120(27,600) 

  *Multiplies the revenue total by the ticket count, as though $27,600 needed to be scaled by 120 before it could appear in the equation. The $27,600 is already the actual total collected — it doesn't get multiplied by anything.*

**C.** x + y = 27,600
90x + 250y = 120(27,600) 

  *Sets the ticket-count equation equal to the dollar total instead of 120, and then also multiplies the revenue side by 120 — the two given numbers have been assigned to the wrong roles and one of them is scaled on top of that.*

**D.** 90x = 250y
120x + 120y = 27,600 

  *Sets the two ticket-price terms equal to each other, as though the revenue from the $90 tickets had to match the revenue from the $250 tickets — nothing in the stem claims that. It also scales the count equation by 120 instead of using the given total directly.*

*Difficulty: medium*

---

##### Q12
A movie theater charges $11 for each full-price ticket and $8.25 for each reduced-price ticket. For one movie showing, the theater sold a total of 214 full-price and reduced-price tickets for $2,145. Which of the following systems of equations could be used to determine the number of full-price tickets, f, and the number of reduced-price tickets, r, sold?

**A.** f + r = 2,145
11f + 8.25r = 214 

  *Sets the ticket-count equation equal to the dollar total and the revenue equation equal to the ticket count — the two totals have been swapped between equations.*

**B.** f + r = 214
11f + 8.25r = 2,145 **(Correct)**

  *Correct. Total tickets: f + r = 214. Total revenue: 11f + 8.25r = 2,145.*

**C.** f + r = 214
8.25f + 11r = 2,145 

  *The count and total are placed correctly, but the two prices are swapped — $8.25 is attached to full-price tickets and $11 to reduced-price tickets, the reverse of what the stem states.*

**D.** f + r = 2,145
8.25f + 11r = 214 

  *Combines both errors: the ticket count and dollar total are swapped between equations, and the two prices are also swapped between ticket types.*

*Difficulty: medium*

---

##### Q13
Angela is playing a video game. In this game, players can score points only by collecting coins and stars. Each coin is worth c points, and each star is worth s points. The first time she played, Angela scored 700 points. She collected 20 coins and 10 stars. The second time she played, Angela scored 850 points. She collected 25 coins and 12 stars. Which system of equations can be used to correctly determine the values of c and s?

**A.** 10c + 20s = 700
12c + 25s = 850 

  *Swaps the coin and star counts within each equation — 20 coins ends up as the coefficient of s, and 10 stars ends up as the coefficient of c, the reverse of the actual play.*

**B.** 20c + 10s = 700
25c + 12s = 850 **(Correct)**

  *Correct. First game: 20 coins and 10 stars scored 700 points, so 20c + 10s = 700. Second game: 25 coins and 12 stars scored 850 points, so 25c + 12s = 850.*

**C.** 20c + 700s = 10
25c + 850s = 12 

  *Puts the point total (700) where a coefficient belongs and the coin count (10) where the point total belongs — the score and the item count have traded places.*

**D.** 700c + 20s = 10
850c + 25s = 12 

  *Makes the same coefficient/total swap as choice C, and additionally reverses the order of the coin and star coefficients within each equation.*

*Difficulty: medium*

---

##### Q14
2x + 7y = 9
8x + 28y = a
In the given system of equations, a is a constant. If the system has infinitely many solutions, what is the value of a?

**A.** 4 

  *This is the multiplier itself (8/2 = 4), reported as the answer instead of applied to the constant. The multiplier is the tool that produces a; it is not a.*

**B.** 9 

  *Reuses the original constant unscaled, as though the second equation's constant had to equal the first's. Every part of the equation — including the constant — takes the same multiplier.*

**C.** 36 **(Correct)**

  *Correct. Infinitely many solutions means the second equation is the first multiplied through by one constant. The x-coefficients give that multiplier: 8/2 = 4 (checked against the y-coefficients: 7 × 4 = 28 ✓). Apply it to the constant: 4(9) = 36.*

**D.** 54 

  *Uses the difference between the x-coefficients (8 - 2 = 6) as the scale factor instead of their ratio (8/2 = 4), giving 9 × 6 = 54. Two equations describe the same line when one is a constant multiple of the other, not a constant amount added to it.*

*Difficulty: sat-hardest*

---

##### Q15
y = 4
x = y + 6
The solution to the given system of equations is (x, y). What is the value of x?

**A.** 10 **(Correct)**

  *Correct. Substitute y = 4: x = 4 + 6 = 10.*

**B.** 6 

  *Reports the constant from x = y + 6 alone, as though the y term weren't there.*

**C.** 4 

  *This is y, not x — the given value, reported without ever using the second equation.*

**D.** 2 

  *Computes 6 - y instead of y + 6, reversing the order of the subtraction: 6 - 4 = 2.*

*Difficulty: easy*

---

##### Q16
5x = 15
-4x + y = -2
The solution to the given system of equations is (x, y). What is the value of x + y?

**A.** -17 

  *Solves the first equation with a sign error, treating 5x = 15 as though it were -5x = 15 and getting x = -3. Carrying that wrong x into y = -2 + 4x = -2 + 4(-3) = -14 gives x + y = -3 + (-14) = -17.*

**B.** -13 

  *Compounds two sign errors: the same x = -3 from the sign slip on 5x = 15, combined with also flipping the constant when isolating y (using y = 2 + 4x instead of y = -2 + 4x): y = 2 + 4(-3) = -10. x + y = -3 + (-10) = -13.*

**C.** 13 **(Correct)**

  *Correct. From 5x = 15, x = 3. Substitute: -4(3) + y = -2, so y = -2 + 12 = 10. x + y = 3 + 10 = 13.*

**D.** 17 

  *Solves x = 3 correctly, but flips the sign of the constant when isolating y — using y = 2 + 4x instead of y = -2 + 4x: y = 2 + 12 = 14. x + y = 3 + 14 = 17.*

*Difficulty: medium*

---

##### Q17
x + y = 18
5y = x
What is the solution (x, y) to the given system of equations?

**A.** (15, 3) **(Correct)**

  *Correct. Substitute x = 5y: 5y + y = 18, so 6y = 18 and y = 3, giving x = 15. Check: 5(3) = 15 ✓.*

**B.** (16, 2) 

  *Satisfies x + y = 18 but not 5y = x — 5(2) = 10, not 16. This is what 6y = 18 gives when divided incorrectly as y = 2 instead of y = 3, with x = 18 - 2 = 16 following from that wrong y. Checking only the first equation would not catch it.*

**C.** (17, 1) 

  *Also satisfies only x + y = 18. This comes from miscounting the combined coefficient in 6y = 18 — treating it as though the coefficient were larger than 6 — which drags y down to 1 and x up to 17.*

**D.** (18, 0) 

  *The x-intercept of x + y = 18 alone — a plausible-looking point on that one line, picked without ever using 5y = x to check it. 5(0) = 0, not 18.*

*Difficulty: medium*

---

##### Q18
4x - 3y = 5
x = 8
What is the solution (x, y) to the given system of equations?

**A.** (8, 9) **(Correct)**

  *Correct. Substitute x = 8: 4(8) - 3y = 5, so 32 - 3y = 5, -3y = -27, and y = 9.*

**B.** (8, -24) 

  *Confuses which variable the coefficient -3 belongs to, computing y = -3x = -3(8) = -24 directly instead of solving 4x - 3y = 5 for y.*

**C.** (8, -9) 

  *Reaches -3y = -27 correctly, then drops the negative sign when dividing — computing -27/3 = -9 instead of -27/-3 = 9.*

**D.** (8, 24) 

  *Misapplies the y-coefficient's magnitude as a direct multiplier on x while dropping the constant term entirely: y = 3x = 3(8) = 24, instead of solving 4x - 3y = 5 for y using both the 4x term and the 5.*

*Difficulty: medium*

---

##### Q19
(1/2)y = 4
x - (1/2)y = 2
The system of equations above has solution (x, y). What is the value of x?

**A.** 3 

  *Solves (1/2)y = 4 by multiplying by the fraction instead of its reciprocal — treating '(1/2)y = 4' as meaning y = 4 × (1/2) = 2 rather than y = 4 × 2 = 8. Substituting that wrong y: x - (1/2)(2) = 2, so x - 1 = 2 and x = 3.*

**B.** 7/2 

  *Solves (1/2)y = 4 by subtracting 1/2 from both sides instead of multiplying both sides by 2, getting y = 4 - 1/2 = 7/2, and reports that value directly without ever using the second equation.*

**C.** 4 

  *Misreads '(1/2)y = 4' as meaning y = 4 outright, ignoring the 1/2 coefficient entirely. Substituting: x - (1/2)(4) = 2, so x - 2 = 2 and x = 4.*

**D.** 6 **(Correct)**

  *Correct. From (1/2)y = 4, y = 8. Substitute: x - (1/2)(8) = 2, so x - 4 = 2 and x = 6.*

*Difficulty: medium*

---

##### Q20
A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?

**A.** 30 

  *Assumes the 60 tents split evenly between the two sizes (30 and 30), which ignores the actual capacity constraint entirely: 2(30) + 4(30) = 180 people, not 202.*

**B.** 20 

  *Solves for the number of 4-person tents using the wrong divisor — dividing the excess capacity (202 - 2(60) = 82) by 4 instead of by the capacity difference (4 - 2 = 2), getting roughly 20.5, and then reports that as the 2-person count instead of the 4-person count it was actually approximating.*

**C.** 19 **(Correct)**

  *Correct. Let a = 2-person tents and b = 4-person tents: a + b = 60 and 2a + 4b = 202. Substituting a = 60 - b: 2(60 - b) + 4b = 202, so 120 + 2b = 202, b = 41, and a = 60 - 41 = 19.*

**D.** 18 

  *Slips in the arithmetic when solving 2b = 82 for the 4-person tent count, landing one off at b = 42 instead of b = 41, then subtracts from 60 to get 18 instead of 19.*

*Difficulty: hard*

---

##### Q21
y = -(1/9)x
y = (1/2)x
The solution to the given system of equations is (x, y). What is the value of x?

**A.** -9 

  *Reads the denominator of the first equation's coefficient off directly as x, without ever setting the two expressions equal to each other and solving.*

**B.** -7 

  *An arithmetic slip while cross-multiplying -(1/9)x = (1/2)x — the two sides are set equal but the resulting equation isn't correctly reduced to 0 = (11/18)x, so a nonzero value gets reported instead of the only value that actually works.*

**C.** 0 **(Correct)**

  *Correct. Both lines pass through the origin (each is of the form y = kx with no constant term), and two distinct lines through the origin intersect only at the origin. Setting -(1/9)x = (1/2)x gives -(1/9)x - (1/2)x = 0, or -(11/18)x = 0, so x = 0.*

**D.** 2 

  *Reads the denominator of the second equation's coefficient off directly as x, the same shortcut as choice A applied to the other line.*

*Difficulty: hard*

---

##### Q22
4x + 5y = 100
5x + 4y = 62
If the system of equations above has solution (x, y), what is the value of x + y?

**A.** 0 

  *Defaults to 0 without solving — this is not what subtracting or adding the two equations produces; it's simply reported without carrying out the combination that actually links x + y to the two totals.*

**B.** 9 

  *Divides 162 by 18 instead of by 9 when finishing 9x + 9y = 162 — an easy slip to make since both 9 and 18 appear in the surrounding arithmetic, but only 9 is the actual coefficient on x + y.*

**C.** 18 **(Correct)**

  *Correct. Add the two equations directly: 9x + 9y = 162, so x + y = 18. (The mirrored coefficients make this the whole solution — no need to find x and y separately.)*

**D.** 38 

  *Subtracts the equations instead of adding them, computing x - y = 62 - 100 = -38, then reports its magnitude — the difference, not the sum, and with the sign dropped besides.*

*Difficulty: hard*

---

##### Q23
In the xy-plane, the graph of y = x + 3 intersects the graph of y = 2x - 6 at the point (a, b). What is the value of a?

**A.** 3 

  *Rearranges x + 3 = 2x - 6 with a sign error — treating it as though the -6 flips to +6 when it moves — reaching x = -3, then reports the number with the sign dropped.*

**B.** 6 

  *Doubles the y-intercept of the first line (3 × 2 = 6) rather than actually setting the two equations equal to each other and solving for the intersection.*

**C.** 9 **(Correct)**

  *Correct. Set x + 3 = 2x - 6: 3 + 6 = 2x - x, so a = x = 9.*

**D.** 12 

  *Solves for a = 9 correctly, then reports b instead — b = a + 3 = 12 — answering the coordinate the stem didn't ask for.*

*Difficulty: medium*

---

##### Q24
The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how many questions did the player answer correctly?

**A.** 10 

  *This is the number of incorrect answers (40 - 30), not the number correct.*

**B.** 25 

  *Averages the score and total questions (50/2 = 25) rather than setting up the actual system — the score isn't half the correct-answer count, it's twice the correct count minus the incorrect count.*

**C.** 30 **(Correct)**

  *Correct. Let c = correct, i = incorrect: c + i = 40 and 2c - i = 50. Adding the equations eliminates i: 3c = 90, so c = 30.*

**D.** 45 

  *Averages the two given totals (40 + 50)/2 = 45 instead of solving the system — a plausible-looking number that never actually combines the equations correctly.*

*Difficulty: medium*

---

##### Q25
x + 2y = 6
x - 2y = 4
The solution to the given system of equations is (x, y). What is the value of x?

**A.** 2.5 

  *Reaches 2x = 10 correctly, but divides by 4 instead of 2 — a slip that borrows the coefficient from the y-elimination step (4y = 2) instead of using the coefficient actually in front of x.*

**B.** 5 **(Correct)**

  *Correct. Add the two equations: 2x = 10, so x = 5.*

**C.** 6 

  *Reads the constant from x + 2y = 6 directly as x, as though y were automatically 0 — it isn't; y = 0.5 here.*

**D.** 10 

  *Reaches 2x = 10 by adding the equations correctly, then reports 10 directly without finishing the division by 2.*

*Difficulty: easy*

---

##### Q26
Which of the following systems of linear equations has no solution?

**A.** y = 6x + 3
y = 6x + 9 **(Correct)**

  *Correct. Both lines have slope 6 (identical), and different y-intercepts (3 and 9) — parallel and distinct, so no pair (x, y) satisfies both.*

**B.** y = 10
y = 10x + 10 

  *A horizontal line (slope 0) and a slanted line (slope 10) are never parallel to each other; they always cross at exactly one point. Different-looking equations don't automatically mean no solution.*

**C.** y = 14x + 14
y = 10x + 14 

  *The slopes differ (14 and 10), so these lines cross at exactly one point — in fact right at their shared y-intercept, (0, 14). A matching intercept doesn't create a conflict; only matching slopes with different intercepts do that.*

**D.** x = 3
y = 10 

  *A vertical line and a horizontal line are never parallel to each other; they always cross at exactly one point — here, (3, 10).*

*Difficulty: hard*

---

##### Q27
y = 2x - 3
3y = 5x
In the solution to the system of equations above, what is the value of y?

**A.** -15 

  *Correctly finds x = 9, but then negates the whole expression by mistake: y = -(2(9) - 3) = -15, instead of y = 2(9) - 3 = 15.*

**B.** -9 

  *Rearranges 6x - 9 = 5x by moving the x-terms to the wrong side, reaching x = -9 (instead of x = 9), and reports that mis-solved value directly as y.*

**C.** 9 

  *This is x, not y — reported before the second half of the solve, y = 2(9) - 3.*

**D.** 15 **(Correct)**

  *Correct. Substitute y = 2x - 3 into 3y = 5x: 3(2x - 3) = 5x, so 6x - 9 = 5x, x = 9, and y = 2(9) - 3 = 15.*

*Difficulty: hard*

---

##### Q28
5x + 3y = 38
x + 3y = 10
In the solution (x, y) to the system of equations above, what is the value of x?

**A.** 1 

  *This is y (from x + 3y = 10 with x = 7: 7 + 3y = 10, y = 1), not x.*

**B.** 14 

  *Reaches 4x = 28 correctly by subtracting the equations, then divides by 2 instead of 4, doubling the correct answer.*

**C.** 7 **(Correct)**

  *Correct. Subtract the second equation from the first: 4x = 28, so x = 7.*

**D.** 28 

  *Reaches 4x = 28 correctly, then reports that un-divided value directly as x.*

*Difficulty: medium*

---

##### Q29
x + 3y = 29
3y = 11
The solution to the given system of equations is (x, y). What is the value of x?

**A.** 11 

  *Mistakes 'x + 3y = 29' for meaning x = 3y, reporting the given value of 3y (11) directly as x without ever using the subtraction.*

**B.** 3.67 

  *Solves for y instead of x — 3y = 11 gives y ≈ 3.67 — and reports that rather than continuing to find x.*

**C.** 18 **(Correct)**

  *Correct. Substitute 3y = 11 into the first equation: x + 11 = 29, so x = 18.*

**D.** 40 

  *Adds 11 to 29 instead of subtracting it: 29 + 11 = 40, the opposite of the move needed to isolate x.*

*Difficulty: medium*

---

##### Q30
8x + y = 5
y = 9x + 1
The solution to the given system of equations is (x, y). What is the value of x?

**A.** -6 

  *Treats the substitution as a subtraction between the two equations rather than a true substitution: 8x - (9x + 1) = 5, giving -x - 1 = 5, so x = -6.*

**B.** 4/17 **(Correct)**

  *Correct. Substitute y = 9x + 1: 8x + (9x + 1) = 5, so 17x + 1 = 5, 17x = 4, and x = 4/17.*

**C.** 6/17 

  *Moves the constant to the wrong side with a sign error: 17x = 5 + 1 = 6 instead of 17x = 5 - 1 = 4, giving x = 6/17.*

**D.** 4 

  *Reaches 17x = 4 correctly, then reports the numerator alone, without dividing by 17.*

*Difficulty: hard*

---

##### Q31
y = -(1/5)x
y = (1/7)x
The solution to the given system of equations is (x, y). What is the value of x?

**A.** -5 

  *Reads the denominator of the first coefficient off directly as x, without solving the system at all.*

**B.** 0 **(Correct)**

  *Correct. Both lines pass through the origin, since neither has a constant term. Two distinct lines through the origin (different slopes -1/5 and 1/7) meet only there: setting -(1/5)x = (1/7)x gives -(12/35)x = 0, so x = 0.*

**C.** 2 

  *Reads the difference between the two denominators (7 - 5 = 2) and reports it as x, treating the denominators as though they were the quantities to combine.*

**D.** 7 

  *Reads the denominator of the second coefficient off directly as x — the same shortcut as choice A, applied to the other equation.*

*Difficulty: hard*

---

##### Q32
y = 3x
2x + y = 12
The solution to the given system of equations is (x, y). What is the value of 5x?

**A.** 24 

  *Doubles the correctly-requested quantity (2 × 12 = 24), computing 10x instead of the 5x the stem actually asks for.*

**B.** 15 

  *Combines 2x and 3x as 4x instead of 5x — a basic addition slip (2 + 3 misread as 4) — getting 4x = 12, x = 3, and 5x = 15.*

**C.** 12 **(Correct)**

  *Correct. Substitute y = 3x into the second equation: 2x + 3x = 12, so 5x = 12 — which is exactly the quantity the stem asks for, with no further division needed.*

**D.** 5 

  *Reads the coefficient '5' from '5x' off directly as the answer, without ever solving for its value.*

*Difficulty: hard*

---

##### Q33
At how many points do the graphs of the equations y = x + 20 and y = 8x intersect in the xy-plane?

**A.** 0 

  *The slopes (1 and 8) are different, so these lines are not parallel — they must cross somewhere.*

**B.** 1 **(Correct)**

  *Correct. The slopes differ (1 ≠ 8), so the lines are not parallel and cross at exactly one point — two straight lines can never cross more than once.*

**C.** 2 

  *Two straight lines cross at most once. Crossing twice is a behavior of curves, not of lines.*

**D.** 8 

  *Reads the coefficient 8 from y = 8x off directly as the answer, confusing a slope with a count of intersection points.*

*Difficulty: medium*

---

##### Q34
6x + 7y = 28
2x + 2y = 10
The solution to the given system of equations is (x, y). What is the value of y?

**A.** -2 **(Correct)**

  *Correct. From the second equation, x + y = 5, so x = 5 - y. Substitute into the first: 6(5 - y) + 7y = 28, so 30 - 6y + 7y = 28, and y = -2.*

**B.** 7 

  *This is x (from x = 5 - y = 5 - (-2) = 7), not y — the system is solved correctly, but the wrong variable is reported.*

**C.** 14 

  *This is 2x (2 × 7 = 14), not y — a further step past the correct x, in the wrong direction.*

**D.** 18 

  *Subtracts the two constants directly (28 - 10 = 18) without ever combining the equations to eliminate a variable.*

*Difficulty: hard*

---

##### Q35
A proposal for a new library was included on an election ballot. A radio show stated that 3 times as many people voted in favor of the proposal as people who voted against it. A social media post reported that 15,000 more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?

**A.** 7,500 **(Correct)**

  *Correct. Let f = in favor, a = against: f = 3a and f = a + 15,000. Setting them equal: 3a = a + 15,000, so 2a = 15,000 and a = 7,500.*

**B.** 15,000 

  *This is the given difference between the two vote totals, reported directly instead of using it to solve for the against-count.*

**C.** 22,500 

  *This is f, the number in favor (3 × 7,500 = 22,500), not the number against.*

**D.** 45,000 

  *Adds the in-favor count, the against count, and the given difference all together (22,500 + 7,500 + 15,000) instead of solving the system for the against-count alone.*

*Difficulty: hard*

---

##### Q36
y = 6x + 16
-7x - y = 36
What is the solution (x, y) to the given system of equations?

**A.** (-4, -8) **(Correct)**

  *Correct. Substitute y = 6x + 16 into the second equation: -7x - (6x + 16) = 36, so -13x - 16 = 36, -13x = 52, and x = -4. Then y = 6(-4) + 16 = -8.*

**B.** (-20/13, -80/13) 

  *Distributes the negative sign incorrectly when substituting — flipping only the constant term's sign rather than the whole parenthetical: -7x + (-6x + 16) = 36 instead of -7x - 6x - 16 = 36. That gives -13x + 16 = 36, so x = -20/13, with y following from the same sign slip.*

**C.** (4, 40) 

  *Reaches -13x = 52 correctly in magnitude, then drops the negative sign, reporting x = 4 instead of x = -4. y = 6(4) + 16 = 40 follows from that wrong x.*

**D.** (20, 136) 

  *Misreads '-7x - y = 36' as '-7x + y = 36' (drops the negative on y), substituting y = 6x + 16 to get -x + 16 = 36, so -x = 20; then drops that negative too, reporting x = 20. y = 6(20) + 16 = 136 follows from that doubly-flawed x.*

*Difficulty: sat-hardest*

---

##### Q37
One of the two equations in a system of linear equations is given: y = (2/7)x + 3. The system has infinitely many solutions. If the second equation in the system is y = mx + b, where m and b are constants, what is the value of b?

**A.** -3 

  *Infinitely many solutions requires the second equation to be identical to the first, so b must match the given intercept exactly — flipping its sign breaks that match.*

**B.** -1/3 

  *Computes the negative reciprocal of the slope, as though the second line needed to be perpendicular to the first rather than identical to it. Infinitely many solutions means the same line twice, not a perpendicular one.*

**C.** 1/3 

  *Confuses the roles of the slope and the intercept, computing a value related to the slope's reciprocal rather than simply reporting the given intercept.*

**D.** 3 **(Correct)**

  *Correct. Infinitely many solutions means the two equations describe the same line, so m = 2/7 and b = 3 — identical to the given equation.*

*Difficulty: sat-hardest*

---

##### Q38
The sum of a number x and 7 is twice as large as a number y. The number y is 3 less than the number x. Which system of equations describes this situation?

**A.** x + 7 = 2y
y = x - 3 **(Correct)**

  *Correct. 'The sum of x and 7 is twice as large as y' means x + 7 = 2y. 'y is 3 less than x' means y = x - 3.*

**B.** x + 7 = 2y
y = 3 - x 

  *Reads '3 less than x' as '3 minus x' instead of 'x minus 3' — reversing the order of the subtraction.*

**C.** 2(x + 7) = y
y = x - 3 

  *Applies the multiplier to the wrong side — making y equal to twice the whole quantity (x + 7), when the sentence says the sum (x + 7) is twice y, not the other way around.*

**D.** 2(x + 7) = y
y = 3 - x 

  *Combines both errors: the multiplier is on the wrong side, and the subtraction order is reversed.*

*Difficulty: medium*

---

##### Q39
y = 3x + 9
3y = 8x - 6
The solution to the given system of equations is (x, y). What is the value of x - y?

**A.** -123 

  *This is x + y (-33 + (-90) = -123), the sum rather than the difference the stem asks for.*

**B.** -33 

  *This is x alone, reported before computing x - y.*

**C.** 3 

  *Drops the coefficient 3 from '3y = 8x - 6', solving y = 8x - 6 directly against y = 3x + 9: 3x + 9 = 8x - 6 gives x = 3, and stops there without going on to compute x - y.*

**D.** 57 **(Correct)**

  *Correct. Substitute y = 3x + 9 into 3y = 8x - 6: 3(3x + 9) = 8x - 6, so 9x + 27 = 8x - 6, and x = -33. Then y = 3(-33) + 9 = -90, and x - y = -33 - (-90) = 57.*

*Difficulty: hard*

---

##### Q40
-x + y = -3.5
x + 3y = 9.5
If (x, y) satisfies the system of equations above, what is the value of y?

**A.** 5 

  *This is x (from -x + 1.5 = -3.5, x = 5), not y.*

**B.** 6 

  *Reaches 4y = 6 correctly by adding the equations, then reports that un-divided value directly as y.*

**C.** 1.5 **(Correct)**

  *Correct. Add the two equations: 4y = 6, so y = 1.5.*

**D.** -3.5 

  *Reports the given constant from the first equation directly, without solving the system at all.*

*Difficulty: medium*

---

##### Q41
During a month, Morgan ran r miles at 5 miles per hour and biked b miles at 10 miles per hour. She ran and biked a total of 200 miles that month, and she biked for twice as many hours as she ran. What is the total number of miles that Morgan biked during the month?

**A.** 80 

  *This is 2r (2 × 40), doubling the running distance instead of finding the biking distance.*

**B.** 100 

  *Assumes the 200 miles split evenly between running and biking (100 each), ignoring the actual hours relationship — running and biking happen at different speeds, so equal time does not mean equal distance, and equal distance isn't what's given here either.*

**C.** 120 

  *Applies 'twice as many hours' directly to the distances instead of first converting through the different speeds, assuming b = 1.5r rather than correctly deriving b = 4r from equal-hours-at-different-speeds. That gives r + 1.5r = 200, r = 80, b = 120.*

**D.** 160 **(Correct)**

  *Correct. Hours running: r/5. Hours biking: b/10. 'Twice as many hours biking' means b/10 = 2(r/5), so b = 4r. With r + b = 200: r + 4r = 200, r = 40, b = 160.*

*Difficulty: hard*

---

##### Q42
In the system of equations below, a and c are constants.
(1/2)x + (1/3)y = 1/6
ax + y = c
If the system of equations has an infinite number of solutions (x, y), what is the value of a?

**A.** -1/2 

  *Reaches the correct magnitude for the multiplier but with the wrong sign — infinitely many solutions needs the second equation to be a positive multiple of the first, not a negated one.*

**B.** 0 

  *Assumes the x-coefficient has to vanish for the system to work out, but a system with a = 0 would make the second equation y = c — a horizontal line, which is not proportional to the first equation at all.*

**C.** 1/2 

  *Reports the original x-coefficient from the first equation directly, without applying the multiplier that scales it into the second equation's form.*

**D.** 3/2 **(Correct)**

  *Correct. Infinitely many solutions means the second equation is the first scaled by one constant. The y-coefficients give that multiplier: 1/(1/3) = 3. Apply it to the x-coefficient: (1/2)(3) = 3/2.*

*Difficulty: sat-hardest*

---

##### Q43
7x - 5y = 4
4x - 8y = 9
If (x, y) is the solution to the system of equations above, what is the value of 3x + 3y?

**A.** -13 

  *Reports the y-coefficient that results from adding the two equations' y-terms (-5 + -8 = -13) directly, rather than actually computing the value of 3x + 3y.*

**B.** -5 **(Correct)**

  *Correct. Subtract the second equation from the first: (7x - 5y) - (4x - 8y) = 4 - 9, so 3x + 3y = -5. The subtraction was built to produce exactly this combination.*

**C.** 5 

  *Reaches the correct combination but drops the negative sign, reporting 5 instead of -5.*

**D.** 13 

  *Adds the two equations' constants (4 + 9 = 13) directly, without actually combining the equations to isolate 3x + 3y.*

*Difficulty: hard*

---

##### Q44
A movie theater sells two types of tickets, adult tickets for $12 and child tickets for $8. If the theater sold 30 tickets for a total of $300, how much, in dollars, was spent on adult tickets? (Disregard the $ sign when gridding your answer.)

**A.** 120 

  *This is the amount spent on child tickets (8 × 15 = 120), not adult tickets.*

**B.** 150 

  *Assumes the tickets split evenly (15 adult, 15 child) and reports half of $300, ignoring that adult and child tickets don't cost the same.*

**C.** 180 **(Correct)**

  *Correct. Let a = adult, c = child: a + c = 30 and 12a + 8c = 300. Substituting c = 30 - a: 12a + 8(30 - a) = 300, so 4a + 240 = 300, a = 15. Adult revenue: 12(15) = 180.*

**D.** 15 

  *This is the number of adult tickets sold, not the dollar amount spent on them.*

*Difficulty: hard*

---

##### Q45
5x + 14y = 45
10x + 7y = 27
The solution to the given system of equations is (x, y). What is the value of xy?

**A.** 3.6 

  *This is x + y (0.6 + 3), the sum rather than the product the stem asks for.*

**B.** 1.8 **(Correct)**

  *Correct. Multiply the first equation by 2 and subtract the second: (10x + 28y) - (10x + 7y) = 90 - 27, so 21y = 63, y = 3. Substitute: 5x + 14(3) = 45, 5x = 3, x = 0.6. xy = (0.6)(3) = 1.8.*

**C.** 0.6 

  *This is x alone, reported without multiplying by y.*

**D.** 3 

  *This is y alone, reported without multiplying by x.*

*Difficulty: hard*

---

##### Q46
y = (1/2)x + 8
y = cx + 10
In the system of equations above, c is a constant. If the system has no solution, what is the value of c?

**A.** 2 

  *Reports the reciprocal of the correct slope (2 instead of 1/2), as though the coefficient needed to be inverted rather than matched directly.*

**B.** 8 

  *Reports the y-intercept from the first equation instead of the slope — the stem asks for c, the coefficient of x, not the constant term.*

**C.** 0.5 **(Correct)**

  *Correct. No solution means the lines are parallel but distinct: same slope, different intercept. The intercepts already differ (8 ≠ 10), so matching the slope is all that's needed: c = 1/2.*

**D.** -0.5 

  *Reaches the correct magnitude for the slope but flips its sign — parallel lines need the same slope, not the opposite one.*

*Difficulty: hard*

---

##### Q47
y = 2x + 1
y = ax - 8
In the system of equations above, a is a constant. If the system of equations has no solution, what is the value of a?

**A.** -1/2 

  *Computes the negative reciprocal of the given slope, as though the second line needed to be perpendicular to the first. No solution requires the same slope, not a perpendicular one.*

**B.** 0 

  *Assumes any value that makes the second line 'look different' — here, a horizontal line — guarantees no solution, without checking that the slopes must actually match to be parallel.*

**C.** 1 

  *Reports half of the correct slope, as though the coefficient needed to be halved rather than matched directly.*

**D.** 2 **(Correct)**

  *Correct. No solution means the lines are parallel but distinct: same slope, different intercept. The intercepts already differ (1 ≠ -8), so matching the slope is all that's needed: a = 2.*

*Difficulty: hard*

---

##### Q48
Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain purchase of raspberries and blackberries would cost $37.00 at Store A or $66.00 at Store B. How many pints of blackberries are in this purchase?

**A.** 4 

  *This is the number of pints of raspberries in the purchase, not blackberries.*

**B.** 5 **(Correct)**

  *Correct. Let r = raspberry pints, b = blackberry pints: 5.5r + 3b = 37 and 6.5r + 8b = 66. Solving: from the first equation, b = (37 - 5.5r)/3; substituting into the second and solving gives r = 4, then b = (37 - 22)/3 = 5.*

**C.** 8 

  *Solves the system with the two stores' price equations swapped — using Store A's prices against Store B's total and vice versa — which produces a blackberry count of 8 instead of the correct 5.*

**D.** 12 

  *Combines the two equations by adding them directly (37 + 66 = 103) rather than solving the system properly, then works backward from that combined total to a distorted pint count.*

*Difficulty: sat-hardest*

---

##### Q49
One of the two equations in a linear system is 2x + 6y = 10. The system has no solution. Which of the following could be the other equation in the system?

**A.** x + 3y = 5 

  *Dividing 2x + 6y = 10 through by 2 gives exactly x + 3y = 5 — this is the same line drawn twice, which produces infinitely many solutions, not none.*

**B.** x + 3y = -20 **(Correct)**

  *Correct. Dividing the given equation by 2 gives x + 3y = 5 — same coefficients as this choice (1 and 3), but a different constant (-20 ≠ 5). Same ratio, different constant: parallel and distinct, so no solution.*

**C.** 6x - 2y = 0 

  *The coefficient ratio here (6 to -2) doesn't match the given equation's ratio (2 to 6) at all — these lines aren't parallel and cross at exactly one point.*

**D.** 6x + 2y = 10 

  *The coefficients (6 and 2) look related to the given equation's (2 and 6) because they're swapped, but swapped coefficients are not proportional coefficients — the ratios 6/2 = 3 and 2/6 = 1/3 are reciprocals, not equal, so these lines cross at exactly one point.*

*Difficulty: sat-hardest*

---

##### Q50
A piece of wire with a length of 32 inches is cut into two parts. One part has a length of x inches, and the other part has a length of y inches. The value of x is 4 more than 3 times the value of y. What is the value of x?

**A.** 24 

  *Drops the '+ 4' from x = 4 + 3y, using x = 3y instead. With x + y = 32: 3y + y = 32, y = 8, x = 24.*

**B.** 7 

  *This is y, not x — the system is solved correctly, but the wrong variable is reported.*

**C.** 25 **(Correct)**

  *Correct. x + y = 32 and x = 4 + 3y. Substitute: 4 + 3y + y = 32, so 4y = 28, y = 7, and x = 4 + 3(7) = 25.*

**D.** 28 

  *Reaches 4y = 28 correctly, then reports that un-divided value directly instead of finishing the solve for x.*

*Difficulty: medium*

---

##### Q51
ax + by = 72
6x + 2by = 56
In the given system of equations, a and b are constants. The graphs of these equations in the xy-plane intersect at the point (4, y). What is the value of a?

**A.** 3 

  *Divides the second equation's x-coefficient (6) by 2 — the multiplier that relates the y-terms — as though a should scale the same way, without actually solving for by and using it in the first equation.*

**B.** 4 

  *Reports the given x-coordinate (4) directly as a, rather than solving for the coefficient.*

**C.** 6 

  *Reports the x-coefficient from the second equation (6) directly, as though both equations had to share the same x-coefficient just because they intersect at the same point.*

**D.** 14 **(Correct)**

  *Correct. At x = 4, the second equation gives 6(4) + 2by = 56, so 2by = 32 and by = 16. Substitute into the first equation: a(4) + 16 = 72, so 4a = 56 and a = 14.*

*Difficulty: sat-hardest*

---

##### Q52
(3/2)y - (1/4)x = (2/3) - (3/2)y
(1/2)x + 3/2 = py + 9/2
In the given system of equations, p is a constant. If the system has no solution, what is the value of p?

**A.** -6 

  *Reaches the correct magnitude for the multiplier but with the sign flipped.*

**B.** 3/2 

  *Reports the coefficient 3/2 straight from the first equation without first combining the two 3/2 y terms on the same side (3y in total), which is what actually sets the multiplier used to find p.*

**C.** 6 **(Correct)**

  *Correct. Combine the first equation's y-terms: (3/2)y + (3/2)y = 3y, giving -(1/4)x + 3y = 2/3. The second equation rearranges to (1/2)x - py = 3. The x-coefficient multiplier is (1/2)/(-1/4) = -2; applying it to the y-coefficient, 3(-2) = -6, which must equal -p, so p = 6.*

**D.** 12 

  *Doubles the correct multiplier, treating the two 3y-like terms as combining to 6y instead of 3y.*

*Difficulty: sat-hardest*

---

##### Q53
4x - 6y = 10y + 2
ty = (1/2) + 2x
In the given system of equations, t is a constant. If the system has no solution, what is the value of t?

**A.** -8 

  *Reaches the correct magnitude but with the sign flipped.*

**B.** 16 

  *Reports the y-coefficient from the first equation's standard form (-16, sign dropped) directly, without applying the multiplier that relates it to the second equation's x-coefficient.*

**C.** 8 **(Correct)**

  *Correct. Rearrange the first equation: 4x - 16y = 2. Rearrange the second: -2x + ty = 1/2. The x-coefficient multiplier is -2/4 = -1/2; applying it to the first equation's y-coefficient, -16(-1/2) = 8, which must equal t.*

**D.** 4 

  *Reports the x-coefficient from the first equation's standard form (4) directly, confusing it with t.*

*Difficulty: sat-hardest*

---

##### Q54
24x + y = 48
6x + y = 72
The solution to the given system of equations is (x, y). What is the value of y?

**A.** 48 

  *Reads the constant from the first equation directly, as though x were automatically 0 — it isn't; x is negative here.*

**B.** 72 

  *Reads the constant from the second equation directly, the same zero-x assumption as choice A applied to the other equation.*

**C.** 80 **(Correct)**

  *Correct. Subtract the second equation from the first: 18x = -24, so x = -4/3. Substitute: 6(-4/3) + y = 72, so -8 + y = 72, and y = 80.*

**D.** -24 

  *Reaches 18x = -24 correctly, then reports that un-divided value directly instead of continuing to solve for y.*

*Difficulty: hard*

---

##### Q55
-x - wy = -337
2x - wy = 47
In the given system of equations, w is a constant. In the xy-plane, the graphs of these equations intersect at the point (q, 19), where q is a constant. What is the value of w?

**A.** -11 

  *Reaches the correct magnitude but with the sign flipped.*

**B.** 18 

  *Solves using only the first equation, assuming x = 0: -19w = -337 gives w ≈ 17.7, rounded to 18 — this ignores the second equation entirely, which is needed to pin down x first.*

**C.** 11 **(Correct)**

  *Correct. At y = 19: from the first equation, x = 337 - 19w. From the second, x = (47 + 19w)/2. Setting equal: 337 - 19w = (47 + 19w)/2, so 674 - 38w = 47 + 19w, 627 = 57w, and w = 11.*

**D.** 2 

  *Solves using only the second equation, assuming x = 0: -19w = 47 gives w ≈ -2.5, and reports the rounded magnitude — again ignoring the first equation entirely.*

*Difficulty: sat-hardest*

---

##### Q56
Which system of linear equations has no solution?

**A.** -2x + 3y = -9
2x - 3y = 9 

  *Multiplying the first equation by -1 gives 2x - 3y = 9 — exactly the second equation. Same line drawn twice means infinitely many solutions, not none.*

**B.** 2x - 3y = 9
3x + 4y = 10 

  *The coefficient ratios (2/3 and 3/4) aren't equal, so these lines aren't even parallel — they cross at exactly one point.*

**C.** 2x - 3y = 9
-6x + 9y = -27 

  *Multiplying the first equation by -3 gives -6x + 9y = -27 — exactly the second equation. Same line twice again, so infinitely many solutions, not none.*

**D.** -2x + 3y = 9
4x - 6y = 18 **(Correct)**

  *Correct. Multiply the first equation by -2: 4x - 6y = -18. Compare to the second equation, 4x - 6y = 18 — same coefficients, different constants (-18 ≠ 18). Parallel and distinct: no solution.*

*Difficulty: hard*

---

##### Q57
8x + 7y = 9
24x + 21y = 27
For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?

**A.** (r, -8r/7 + 9/7) **(Correct)**

  *Correct. The second equation is the first multiplied through by 3, so both describe the same line: 8x + 7y = 9, giving y = -8x/7 + 9/7. Letting x = r gives y = -8r/7 + 9/7 — a point on that line for every real r.*

**B.** (-8r/7 + 9/7, r) 

  *Swaps which coordinate is parametrized by r — this places the correctly-computed y-expression in the x-slot and r in the y-slot, the reverse of the actual line's equation solved for y.*

**C.** (-8r/7 + 9, 8r/7 + 27) 

  *Drops the '/7' from part of the intercept (uses 9 instead of 9/7) and mishandles the sign on the slope term in the second coordinate — neither expression actually satisfies 8x + 7y = 9.*

**D.** (r/3 + 9, -r/3 + 27) 

  *Works from the unsimplified second equation (24x + 21y = 27) without recognizing it reduces to the same line as the first, producing coordinate expressions that don't actually satisfy either original equation.*

*Difficulty: sat-hardest*

---

#### Linear equations in two variables (60 items)

##### Q1
A store sells two different-sized containers of a certain Greek yogurt. The store's sales of this Greek yogurt totaled 1,277.94 dollars last month. The equation 5.48x + 7.30y = 1,277.94 represents this situation, where x is the number of smaller containers sold and y is the number of larger containers sold. According to the equation, which of the following represents the price, in dollars, of each smaller container?

**A.** 5.48 **(Correct)**

  *Correct. Since 5.48x is the revenue from smaller containers (price times quantity sold), the coefficient 5.48 that multiplies x is the price per smaller container.*

**B.** 7.30y 

  *This is the total revenue from larger containers (price times quantity), not a unit price — it confuses a whole term with the single number the question is asking for.*

**C.** 7.30 

  *This is the price of the larger container, not the smaller one — it answers the question for the wrong variable's coefficient.*

**D.** 5.48x 

  *This is the total revenue from smaller containers (price times quantity x), not the unit price alone — it includes the quantity the question isn't asking about.*

*Difficulty: medium*

---

##### Q2
Line k is defined by y = 3x + 15. Line j is perpendicular to line k in the xy-plane. What is the slope of line j?

**A.** -1/3 **(Correct)**

  *Correct. Perpendicular slopes are negative reciprocals of each other. The slope of line k is 3, so the slope of line j is -1/3.*

**B.** -1/12 

  *Takes the negative reciprocal of 15 − 3 = 12 instead of the negative reciprocal of the slope, 3 — mixes the y-intercept into a calculation that should only involve the slope.*

**C.** -1/18 

  *Takes the negative reciprocal of 3 + 15 = 18 instead of the negative reciprocal of the slope, 3, alone.*

**D.** -1/45 

  *Takes the negative reciprocal of 3 × 15 = 45 instead of the negative reciprocal of the slope, 3, alone.*

*Difficulty: medium*

---

##### Q3
A shipping company charged a customer $25 to ship some small boxes and some large boxes. The equation 3a + 4b = 25 represents the relationship between a, the number of small boxes, and b, the number of large boxes, the customer had shipped. If the customer had 3 small boxes shipped, how many large boxes were shipped?

**A.** 3 

  *Restates the given number of small boxes (a = 3) directly as the answer for b, without using the equation to solve for the large-box count at all.*

**B.** 4 **(Correct)**

  *Correct. Substitute a = 3: 3(3) + 4b = 25 → 9 + 4b = 25 → 4b = 16 → b = 4.*

**C.** 5 

  *Correctly finds 4b = 16 but then divides by 3 (the coefficient on a) instead of 4 (the coefficient on b): 16/3 ≈ 5.3, rounding to 5 — reusing the wrong coefficient in the final division step.*

**D.** 6 

  *Divides the total cost by only the large-box coefficient, 25/4 = 6.25, rounding to 6 — this skips subtracting the cost of the small boxes first, as if no small boxes were shipped at all.*

*Difficulty: easy*

---

##### Q4
The equation x + y = 75 relates the number of minutes, x, Maria spends running each day and the number of minutes, y, she spends biking each day. In the equation, what does the number 75 represent?

**A.** The number of minutes spent running each day 

  *This describes the value of x alone, not the constant on the right-hand side of the sum — confuses one variable's value with the total the sum equals.*

**B.** The number of minutes spent biking each day 

  *This describes the value of y alone, not the constant the full sum x + y equals.*

**C.** The total number of minutes spent running and biking each day **(Correct)**

  *Correct. In x + y = 75, the left side is running minutes plus biking minutes, so 75 is the total number of minutes spent on both activities combined.*

**D.** The number of minutes spent biking for each minute spent running 

  *This describes a rate — a ratio between the two variables — but x + y = 75 is an additive relationship, not a multiplicative one, so no number in it represents a rate.*

*Difficulty: easy*

---

##### Q5
A total of 364 paper straws of equal length were used to construct two types of polygons: triangles and rectangles. The triangles and rectangles were constructed so that no two polygons had a common side. The equation 3x + 4y = 364 represents this situation, where x is the number of triangles constructed and y is the number of rectangles constructed. What is the best interpretation of (x, y) = (24, 73) in this context?

**A.** If 24 triangles were constructed, then 73 rectangles were constructed. **(Correct)**

  *Correct. x is defined as the number of triangles and y as the number of rectangles, so (x, y) = (24, 73) means 24 triangles and 73 rectangles — matching the ordered pair directly to the stated variable definitions.*

**B.** If 24 triangles were constructed, then 73 paper straws were used. 

  *Confuses y (the number of rectangles) with the total number of straws used — 73 is a count of rectangles, not a count of straws consumed making them.*

**C.** If 73 triangles were constructed, then 24 rectangles were constructed. 

  *Swaps which coordinate belongs to which variable — reads the ordered pair as (y, x) instead of (x, y), reversing triangles and rectangles.*

**D.** If 73 triangles were constructed, then 24 paper straws were used. 

  *Combines both errors above — swaps the coordinate order and also mistakes a rectangle count for a straw count.*

*Difficulty: medium*

---

##### Q6
The equation y = 0.1x models the relationship between the number of different pieces of music a certain pianist practices, y, during an x-minute practice session. How many pieces did the pianist practice if the session lasted 30 minutes?

**A.** 1 

  *Divides instead of multiplying — computes something like 0.1/30 rounded down rather than 0.1 × 30, inverting which operation the coefficient calls for.*

**B.** 3 **(Correct)**

  *Correct. y = 0.1(30) = 3.*

**C.** 10 

  *Misplaces the decimal point when multiplying, computing 0.1 × 30 as if it were 1 × 10 = 10 — effectively treating the rate as ten times larger than given.*

**D.** 30 

  *Uses x itself as the answer, ignoring the 0.1 coefficient entirely — as if y = x rather than y = 0.1x.*

*Difficulty: easy*

---

##### Q7
A line in the xy-plane passes through the points (0, -1) and (4, -2). Which of the following is an equation of the line?

**A.** y = -1/4x - 1 **(Correct)**

  *Correct. Slope: (-2 - (-1))/(4 - 0) = -1/4. The y-intercept from (0, -1) is -1.*

**B.** y = -x - 4 

  *Uses -1 (the y-intercept) as the slope and -4 as the intercept — a full slope/intercept swap combined with a sign slip.*

**C.** y = -x - 1/4 

  *Swaps which of the two numbers (1/4 and 1) plays the slope role and which plays the intercept role, while keeping their signs.*

**D.** y = -4x - 1 

  *Inverts the fraction — uses -4 as the slope instead of the correct -1/4, the classic rise/run flip when reading slope off two points.*

*Difficulty: medium*

---

##### Q8
An employee at a restaurant prepares sandwiches and salads. It takes the employee 1.5 minutes to prepare a sandwich and 1.9 minutes to prepare a salad. The employee spends a total of 46.1 minutes preparing x sandwiches and y salads. Which equation represents this situation?

**A.** 1.9x + 1.5y = 46.1 

  *Swaps the two given rates — assigns the salad time (1.9) to x (sandwiches) and the sandwich time (1.5) to y (salads), reversing which coefficient belongs to which variable.*

**B.** 1.5x + 1.9y = 46.1 **(Correct)**

  *Correct. Matches 1.5 minutes per sandwich (x) and 1.9 minutes per salad (y) directly from the problem.*

**C.** x + y = 46.1 

  *Drops both given rates entirely, treating each item as taking exactly 1 minute — ignores the actual per-item times given in the problem.*

**D.** 30.7x + 24.3y = 46.1 

  *Uses fabricated coefficients rather than the rates stated in the problem (1.5 and 1.9), as if scaling the rates by an unrelated factor.*

*Difficulty: easy*

---

##### Q9
A graph in the xy-plane shows the possible combinations of pounds of tangerines (x-axis) and pounds of lemons (y-axis) that could be purchased for $18 at a certain store. The line passes through (0, 18) and (9, 0). If Melvin purchased lemons and 4 pounds of tangerines for a total of $18, how many pounds of lemons did he purchase?

**A.** 7 

  *Subtracts the 4 pounds of tangerines directly from the y-intercept (18) before applying the rate, computing (18 - 4)/2 = 7, instead of applying the rate to x first: 18 - 2(4).*

**B.** 10 **(Correct)**

  *Correct. The line has slope (0 - 18)/(9 - 0) = -2, so y = 18 - 2x. At x = 4: y = 18 - 2(4) = 10.*

**C.** 14 

  *Uses a rate of -1 per pound instead of the correct -2 per pound (misreads the graph's steepness): 18 - 1(4) = 14.*

**D.** 16 

  *Computes 18 - 2(1) instead of 18 - 2(4) — mistakenly uses x = 1 instead of x = 4 in the equation.*

*Difficulty: medium*

---

##### Q10
A city's total expense budget for one year was x million dollars. The city budgeted y million dollars for departmental expenses and 201 million dollars for all other expenses. Which of the following represents the relationship between x and y in this context?

**A.** x + y = 201 

  *Treats departmental expenses and other expenses as summing directly to 201, rather than recognizing that 201 is what's left after departmental expenses are subtracted from the total budget x.*

**B.** x - y = 201 **(Correct)**

  *Correct. Total budget x minus departmental expenses y leaves the 201 million for all other expenses.*

**C.** 2x - y = 201 

  *Introduces an unwarranted factor of 2 on the total budget x that has no basis anywhere in the problem.*

**D.** y - x = 201 

  *Reverses the subtraction — computes departmental expenses minus the total budget, which would be negative, instead of total minus departmental.*

*Difficulty: easy*

---

##### Q11
4x + 3y = 24. Mario purchased 4 binders that cost x dollars each and 3 notebooks that cost y dollars each. If the given equation represents this situation, which of the following is the best interpretation of 24 in this context?

**A.** The total cost, in dollars, for all binders purchased 

  *This describes only the term 4x, not the full sum 4x + 3y that actually equals 24.*

**B.** The total cost, in dollars, for all notebooks purchased 

  *This describes only the term 3y, not the full sum that equals 24.*

**C.** The total cost, in dollars, for all binders and notebooks purchased **(Correct)**

  *Correct. 24 is what the entire left side (4x + 3y, binder cost plus notebook cost) equals — the total cost of everything purchased.*

**D.** The difference in the total cost, in dollars, between the number of binders and notebooks purchased 

  *Introduces a subtraction that doesn't exist in the equation — the equation adds the two costs, it doesn't subtract them.*

*Difficulty: easy*

---

##### Q12
A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials by weight and Fertilizer B contains 40% filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?

**A.** 0.4x + 0.6y = 240 

  *Swaps the two percentages — assigns Fertilizer B's 40% to x (which is Fertilizer A) and Fertilizer A's 60% to y (which is Fertilizer B).*

**B.** 0.6x + 0.4y = 240 **(Correct)**

  *Correct. Fertilizer A (60% filler, coefficient on x) plus Fertilizer B (40% filler, coefficient on y) equals 240 total pounds of filler.*

**C.** 40x + 60y = 240 

  *Uses the percentages as whole numbers (40 and 60) instead of converting to decimals, while also swapping which belongs to which variable.*

**D.** 60x + 40y = 240 

  *Correctly keeps 60 with x and 40 with y, but fails to convert either percentage to a decimal, using 60 and 40 directly as coefficients instead of 0.6 and 0.4.*

*Difficulty: medium*

---

##### Q13
In the xy-plane, a line has a slope of 6 and passes through the point (0, 8). Which of the following is an equation of this line?

**A.** y = 6x + 8 **(Correct)**

  *Correct. Slope-intercept form with m = 6 and b = 8, using the given point (0, 8) directly as the y-intercept.*

**B.** y = 6x + 48 

  *Multiplies the y-intercept by the slope (8 × 6 = 48) instead of using it directly, as if a further calculation were needed for a point that's already the y-intercept.*

**C.** y = 8x + 6 

  *Swaps the slope and the y-intercept values.*

**D.** y = 8x + 48 

  *Swaps the slope and intercept and then also multiplies them together for the new intercept — compounds the swap with an unnecessary multiplication.*

*Difficulty: easy*

---

##### Q14
The equation 40x + 20y = 160 represents the number of sweaters, x, and number of shirts, y, that Yesenia purchased for $160. If Yesenia purchased 2 sweaters, how many shirts did she purchase?

**A.** 3 

  *Miscomputes 40(2) as 100 instead of 80 (a multiplication slip), giving 20y = 60 and y = 3.*

**B.** 4 **(Correct)**

  *Correct. 40(2) + 20y = 160 → 80 + 20y = 160 → 20y = 80 → y = 4.*

**C.** 8 

  *Divides the full 160 by 20 without subtracting the sweater cost first, as if no sweaters had been purchased at all: 160/20 = 8.*

**D.** 40 

  *Uses the coefficient on x (40) directly as the answer, confusing the sweater price with the number of shirts purchased.*

*Difficulty: easy*

---

##### Q15
Tony spends $80 per month on public transportation. A 10-ride pass costs $12.50, and a single-ride pass costs $1.50. If g represents the number of 10-ride passes Tony buys in a month and t represents the number of single-ride passes Tony buys in a month, which of the following equations best represents the relationship between g and t?

**A.** g + t = 80 

  *Treats the total spent as a sum of the number of passes rather than their cost, ignoring the price per pass entirely, as if each pass cost $1.*

**B.** g + t = 1.50 + 12.50 

  *Adds the two prices together as if that sum represented Tony's total spending, rather than using the prices as coefficients on the pass counts.*

**C.** 1.50g + 12.50t = 80 

  *Swaps which price belongs to which pass type — assigns the single-ride price ($1.50) to the 10-ride passes (g) and the 10-ride price ($12.50) to single rides (t).*

**D.** 12.50g + 1.50t = 80 **(Correct)**

  *Correct. 12.50g is the cost of 10-ride passes and 1.50t is the cost of single-ride passes, matching each price to its correct pass type.*

*Difficulty: medium*

---

##### Q16
A city is planning to build a rock retaining wall, a monument, and a garden in a park. The table below shows four rock types being considered for the project, along with each rock type's weight per volume, in pounds per cubic foot (lb/ft³), and its cost per pound, in dollars: Basalt — 180 lb/ft³, $0.18/lb; Granite — 165 lb/ft³, $0.09/lb; Limestone — 120 lb/ft³, $0.03/lb; Sandstone — 135 lb/ft³, $0.22/lb. All four rock types are used in the project. The equation 0.03(120w) + 0.18(180z) + 3,385.80 = 7,576.20 gives the total cost, in dollars, of the rocks used in the project, in terms of the number of ft³ of limestone, w, and the number of ft³ of basalt, z. Which of the following is the best interpretation of 3,385.80 in this context?

**A.** The cost of the granite and sandstone needed for the project **(Correct)**

  *Correct. The equation already accounts for limestone and basalt as the two variable terms; since all four rock types are used, the constant 3,385.80 must be the fixed cost of the other two types not represented by a variable — granite and sandstone.*

**B.** The cost of the basalt and limestone needed for the project 

  *Basalt and limestone are already represented by the two variable terms in the equation (0.03(120w) and 0.18(180z)) — the constant must represent what isn't already accounted for by those terms, not the same two rock types again.*

**C.** The cost of the basalt needed for the project 

  *Basalt is already fully represented by its own term, 0.18(180z), in the equation — the constant can't also represent basalt's cost alone without double-counting.*

**D.** The cost of the sandstone needed for the project 

  *Captures only one of the two remaining rock types (sandstone) but leaves out granite, which is also unaccounted for by the equation's variable terms.*

*Difficulty: hard*

---

##### Q17
The table below shows some pairs of x values and y values: when x = 1, y = 5; when x = 2, y = 7; when x = 3, y = 9; when x = 4, y = 11. Which of the following equations could represent the relationship between x and y?

**A.** y = 2x + 3 **(Correct)**

  *Correct. Consecutive y-values increase by 2 each time x increases by 1, so the slope is 2; at x = 1, y = 5, so 5 = 2(1) + b gives b = 3. y = 2x + 3 checks against every row.*

**B.** y = 3x - 2 

  *Swaps the slope and intercept found from the table — uses 3 as the slope and -2 as the intercept instead of the actual slope of 2 and intercept of 3.*

**C.** y = 4x - 1 

  *Miscounts the rise per step as 4 instead of the actual consecutive difference of 2 between table rows.*

**D.** y = 5x 

  *Divides a y-value by its corresponding x-value directly (5/1 = 5) as if the relationship passed through the origin, ignoring that the table's actual y-intercept is 3, not 0.*

*Difficulty: easy*

---

##### Q18
A shipment consists of 5-pound boxes and 10-pound boxes with a total weight of 220 pounds. There are 13 10-pound boxes in the shipment. How many 5-pound boxes are in the shipment?

**A.** 5 

  *Reuses the 5-pound box weight itself as the box count, confusing the box weight with the number of boxes.*

**B.** 10 

  *Reuses the 10-pound box weight as the answer, the same type of confusion between a box weight and a box count.*

**C.** 13 

  *Restates the given number of 10-pound boxes (13) as if it were the number of 5-pound boxes, without doing any computation.*

**D.** 18 **(Correct)**

  *Correct. 220 - 13(10) = 90 pounds remain for 5-pound boxes; 90/5 = 18.*

*Difficulty: easy*

---

##### Q19
y = 70x + 8. Which table gives three values of x and their corresponding values of y for the given equation?

**A.** x = 0, 2, 4 gives y = 8, 148, 288 **(Correct)**

  *Correct. y(0) = 8, y(2) = 70(2) + 8 = 148, y(4) = 70(4) + 8 = 288.*

**B.** x = 0, 2, 4 gives y = 70, 78, 86 

  *Swaps the slope and intercept's roles — starts from 70 as if it were the y-intercept, then adds only 8 per step instead of 70 per step of x.*

**C.** x = 0, 2, 4 gives y = 70, 140, 280 

  *Uses 70 as the starting value (should start at 8, the actual y-intercept) and scales it correctly by x, but never adds the constant 8 at all.*

**D.** x = 0, 2, 4 gives y = 8, 132, 272 

  *Correctly starts at 8 (the y-intercept) but uses an incorrect step size, as if applying a slope near 62 instead of the actual 70 per unit of x.*

*Difficulty: easy*

---

##### Q20
F = 2.50x + 7.00y. In the equation above, F represents the total amount of money, in dollars, a food truck charges for x drinks and y salads. The price, in dollars, of each drink is the same, and the price, in dollars, of each salad is the same. Which of the following is the best interpretation for the number 7.00 in this context?

**A.** The price, in dollars, of one drink 

  *2.50, the coefficient on x (drinks), is the price of one drink — this mistakes the salad coefficient for the drink price.*

**B.** The price, in dollars, of one salad **(Correct)**

  *Correct. 7.00 is the coefficient on y (salads), so it's the price per salad.*

**C.** The number of drinks bought during the day 

  *7.00 is a fixed price (a coefficient), not a variable quantity — confuses a per-unit price with a count of items.*

**D.** The number of salads bought during the day 

  *The number of salads is represented by the variable y itself, not by the coefficient 7.00 that multiplies it.*

*Difficulty: easy*

---

##### Q21
A line in the xy-plane passes through the points (0, 8) and (10, 10). What is the y-intercept of the line graphed?

**A.** (0, -8) 

  *Flips the sign of the correct y-intercept value.*

**B.** (0, -1/8) 

  *Inverts the y-intercept value into a fraction and flips its sign, as if confusing the y-intercept with a reciprocal slope value.*

**C.** (0, 0) 

  *Assumes the line passes through the origin, ignoring that the line clearly crosses the y-axis above zero.*

**D.** (0, 8) **(Correct)**

  *Correct. The line crosses the y-axis at y = 8.*

*Difficulty: easy*

---

##### Q22
In 2010, a swim club had a total of 35 swimmers, each classified as either advanced or intermediate. From 2010 to 2020, the number of advanced swimmers in the club increased by approximately 53%, and the number of intermediate swimmers in the club increased by approximately 44%. The total number of swimmers in the club increased by approximately 49%. Which equation best represents this situation, where a represents the number of advanced swimmers in the club in 2010 and b represents the number of intermediate swimmers in the club in 2010?

**A.** 1.53a + 1.49b = 35(1.44) 

  *Correctly pairs 1.53 with a, but swaps the other two rates — uses the overall growth multiplier (1.49) on b instead of the intermediate group's own 1.44, and misplaces the overall multiplier onto the right side as 1.44 instead of 1.49.*

**B.** 1.49a + 0.53b = 35(1.44) 

  *Uses the overall 49% growth rate on a instead of advanced swimmers' own 53% growth, and uses the raw percent 0.53 instead of the growth multiplier 1.53 for b — confusing "increased by 53%" (multiplier 1.53) with "53% of" (multiplier 0.53).*

**C.** 1.53a + 1.44b = 35(1.49) **(Correct)**

  *Correct. Advanced swimmers grew 53% (multiplier 1.53 on a), intermediate swimmers grew 44% (multiplier 1.44 on b), and the whole club grew 49% (multiplier 1.49 applied to the original total of 35).*

**D.** 1.44a + 1.53b = 35(1.49) 

  *Swaps which growth rate belongs to which swimmer group — applies the intermediate swimmers' 44% growth to a (advanced) and the advanced swimmers' 53% growth to b (intermediate).*

*Difficulty: hard*

---

##### Q23
A line in the xy-plane passes through the points (0, 3) and (1, 0). What is the equation of the line?

**A.** y = 3x - 3 

  *Uses a positive slope and a negative intercept — the reverse of what the two given points actually produce.*

**B.** y = -3x + 3 **(Correct)**

  *Correct. Slope: (0 - 3)/(1 - 0) = -3. y-intercept: 3, from the point (0, 3).*

**C.** y = 1/3x - 3 

  *Inverts the slope into its reciprocal (1/3 instead of -3) and also flips the sign of the intercept.*

**D.** y = -1/3x + 3 

  *Keeps the correct sign and intercept but inverts the slope into its reciprocal (-1/3 instead of -3), a rise/run flip.*

*Difficulty: medium*

---

##### Q24
Davio bought some potatoes and celery. The potatoes cost $0.69 per pound, and the celery cost $0.99 per pound. If Davio spent $5.34 in total and bought twice as many pounds of celery as pounds of potatoes, how many pounds of celery did Davio buy?

**A.** 2 

  *This is the number of pounds of potatoes (p = 2), not celery — the question asks for celery, which is twice that amount.*

**B.** 2.5 

  *Reverses the ratio, solving as if potatoes were twice the celery instead of celery twice the potatoes: 0.69(2c) + 0.99c = 5.34 → 2.37c = 5.34 → c ≈ 2.25, rounding to 2.5.*

**C.** 2.67 

  *Reports the combined per-pound coefficient itself (0.69 + 0.99 × 2 = 2.67) as the final answer, instead of using it to solve for the number of pounds.*

**D.** 4 **(Correct)**

  *Correct. Let p = pounds of potatoes and c = 2p = pounds of celery. 0.69p + 0.99(2p) = 5.34 → 2.67p = 5.34 → p = 2, so celery = 2p = 4.*

*Difficulty: hard*

---

##### Q25
Naomi bought both rabbit snails and nerite snails for a total of $52. Each rabbit snail costs $8 and each nerite snail costs $6. If Naomi bought 2 nerite snails, how many rabbit snails did she buy?

**A.** 5 **(Correct)**

  *Correct. 8r + 6(2) = 52 → 8r + 12 = 52 → 8r = 40 → r = 5.*

**B.** 12 

  *Reports the total cost of the nerite snails (6 × 2 = 12) instead of solving for the number of rabbit snails.*

**C.** 14 

  *Sets up the equation as if both counts were the same unknown (8r + 6r = 52) rather than using the given nerite count of 2, then reports the combined per-snail coefficient, 8 + 6 = 14, instead of solving for r.*

**D.** 50 

  *Computes 52 - 2 = 50, subtracting the number of nerite snails (a count) directly from the total dollar amount, instead of subtracting their total cost (6 × 2 = 12).*

*Difficulty: easy*

---

##### Q26
A line in the xy-plane has a slope of -1/2 and passes through the point (0, 3). Which equation represents this line?

**A.** y = -1/2x - 3 

  *Keeps the correct slope but flips the sign of the y-intercept, using -3 instead of the given point's actual value of +3.*

**B.** y = -1/2x + 3 **(Correct)**

  *Correct. Matches the given slope of -1/2 and the given point (0, 3) as the y-intercept.*

**C.** y = 1/2x - 3 

  *Flips the sign of both the slope and the intercept — the reverse of both given values.*

**D.** y = 1/2x + 3 

  *Keeps the correct intercept but flips the sign of the slope, using a positive slope where the problem specifies -1/2.*

*Difficulty: easy*

---

##### Q27
A food truck buys forks for $0.04 each and plates for $0.48 each. The total cost of x forks and y plates is $661.76. Which equation represents this situation?

**A.** 0.48x - 0.04y = 661.76 

  *Swaps which price belongs to forks vs. plates and turns the addition of the two costs into a subtraction, compounding two errors.*

**B.** 0.04x - 0.48y = 661.76 

  *Keeps the correct prices matched to the correct variables but turns the addition of the two costs into a subtraction.*

**C.** 0.48x + 0.04y = 661.76 

  *Swaps which price belongs to which item — assigns the plate price (0.48) to forks (x) and the fork price (0.04) to plates (y).*

**D.** 0.04x + 0.48y = 661.76 **(Correct)**

  *Correct. Forks cost $0.04 each (coefficient on x) and plates cost $0.48 each (coefficient on y), added to the total.*

*Difficulty: easy*

---

##### Q28
A teacher is creating an assignment worth 70 points. The assignment will consist of questions worth 1 point and questions worth 3 points. Which equation represents this situation, where x represents the number of 1-point questions and y represents the number of 3-point questions?

**A.** 4xy = 70 

  *Adds the two point values (1 + 3 = 4) and then multiplies the variables together, conflating "combine the point values" with "multiply the variable counts."*

**B.** 4(x + y) = 70 

  *Combines the two point values into a single coefficient (1 + 3 = 4) applied to the sum x + y, instead of applying each point value separately to its own variable.*

**C.** 3x + y = 70 

  *Swaps which point value belongs to which variable — assigns 3 points to the 1-point questions (x) and 1 point to the 3-point questions (y).*

**D.** x + 3y = 70 **(Correct)**

  *Correct. 1 point per x-question plus 3 points per y-question sums to the assignment's total of 70 points.*

*Difficulty: easy*

---

##### Q29
The equation x + y = 350 relates the total number of maple trees, x, and the total number of birch trees, y, planted in a 14-acre forest preserve. If 245 maple trees were planted in the forest preserve, how many birch trees were planted in the forest preserve?

**A.** 14 

  *Restates the number of acres (14) given in the problem's setup, rather than solving the equation for the number of birch trees.*

**B.** 25 

  *Divides the total number of trees by the acreage figure, an unrelated quantity in this equation: 350/14 = 25.*

**C.** 105 **(Correct)**

  *Correct. 350 - 245 = 105.*

**D.** 245 

  *Restates the given number of maple trees (x = 245) directly as the answer for birch trees, without solving the equation.*

*Difficulty: easy*

---

##### Q30
7x - 4y = -84. For the given equation, which table gives three values of x and their corresponding values of y?

**A.** x = 0, 4, 8 gives y = 21, 28, 35 **(Correct)**

  *Correct. Solving for y: y = (7x + 84)/4. At x = 0: y = 21. At x = 4: y = 28. At x = 8: y = 35.*

**B.** x = 0, 4, 8 gives y = 35, 28, 21 

  *Computes the correct three y-values but lists them in reverse order, effectively pairing them with the wrong x-values as if the relationship were decreasing instead of increasing.*

**C.** x = 21, 28, 35 gives y = 0, 4, 8 

  *Swaps the entire x-row and y-row — reports what should be the y-values as the x-values and vice versa.*

**D.** x = 21, 28, 35 gives y = 8, 4, 0 

  *Combines both errors above — swaps the rows and also reverses the order within them.*

*Difficulty: medium*

---

##### Q31
A chemist studying the impact of salt on a process mixes x kilograms of a low-salt mixture, which is 2% salt by weight, with y kilograms of a high-salt mixture, which is 96% salt by weight, to create 24 kilograms of a mixture that is 4% salt by weight. Which equation represents this situation?

**A.** 0.96x + 0.02y = (0.04)(24) 

  *Swaps which percentage belongs to which mixture — assigns the high-salt mixture's 96% to x (the low-salt mixture) and the low-salt mixture's 2% to y (the high-salt mixture).*

**B.** 0.02x + 0.96y = (0.04)(24) **(Correct)**

  *Correct. 0.02x is the salt from the low-salt mixture, 0.96y is the salt from the high-salt mixture, and together they equal 4% of the 24 kg final mixture.*

**C.** 0.96x + 0.02y = 24 

  *Swaps the coefficients (as in choice A) and also drops the 4% concentration factor on the right side, using the raw total weight (24) instead of the salt content of that total.*

**D.** 0.02x + 0.96y = 24 

  *Correctly matches the percentages to their mixtures but drops the 4% concentration factor on the right side, using 24 (total weight) instead of 0.04(24) (total salt content).*

*Difficulty: medium*

---

##### Q32
An artist paints and sells square tiles. The selling price P, in dollars, of a painted tile is a linear function of the side length of the tile s, in inches, as shown in the table: when s = 3, P = 8.00; when s = 6, P = 18.00; when s = 9, P = 28.00. Which of the following could define the relationship between s and P?

**A.** P = 3s + 10 

  *Uses an intuitive-looking slope of 3 without actually computing it from the table — checking against the data: 3(3) + 10 = 19, which doesn't match the actual P = 8.00 at s = 3.*

**B.** P = 10/3s + 8 

  *Uses the correct slope (10/3) but takes the intercept directly from the first row's P-value (8) as if s = 0 there, instead of solving for the true y-intercept.*

**C.** P = 10/3s - 2 **(Correct)**

  *Correct. Slope: (18 - 8)/(6 - 3) = 10/3. Using (3, 8): 8 = (10/3)(3) + b = 10 + b → b = -2. Check: (10/3)(9) - 2 = 28. ✓*

**D.** P = 3/10s - 1/10 

  *Inverts the slope into its reciprocal (3/10 instead of 10/3) and carries a similarly inverted intercept — a full rise/run flip.*

*Difficulty: medium*

---

##### Q33
In an article about exercise, it is estimated that a 160-pound adult uses 200 calories for every 30 minutes of hiking and 150 calories for every 30 minutes of bicycling. An adult who weighs 160 pounds has completed 1 hour of bicycling. Based on the article, how many hours should the adult hike to use a total of 1,900 calories from bicycling and hiking?

**A.** 9.5 

  *Divides the full 1,900 total calories by the hiking rate without converting it from "per 30 minutes" to "per hour," and without subtracting the calories already used bicycling: 1900/200 = 9.5.*

**B.** 8.75 

  *Fails to convert either rate from "per 30 minutes" to "per hour" — treats the full hour of bicycling as only 150 calories (should be 300) and divides the remainder by the raw 200 cal/30-min hiking figure: (1900 - 150)/200 = 8.75.*

**C.** 6 

  *Swaps the two rates — uses bicycling's hourly rate (300 cal/hr) for hiking and hiking's hourly rate (400 cal/hr) for bicycling, giving (1900 - 400)/300 ≈ 5, which this choice rounds up to 6.*

**D.** 4 **(Correct)**

  *Correct. 1 hour of bicycling uses 150 × 2 = 300 calories. Remaining: 1900 - 300 = 1600 calories for hiking, at 200 × 2 = 400 cal/hr: 1600/400 = 4 hours.*

*Difficulty: hard*

---

##### Q34
When line n is graphed in the xy-plane, it has an x-intercept of (-4, 0) and a y-intercept of (0, 86/3). What is the slope of line n?

**A.** 3/344 

  *Inverts the slope calculation, essentially computing run over rise instead of rise over run.*

**B.** 6/43 

  *Inverts the correctly-computed slope (43/6) into its reciprocal.*

**C.** 43/6 **(Correct)**

  *Correct. Slope: (86/3 - 0)/(0 - (-4)) = (86/3)/4 = 86/12 = 43/6.*

**D.** 344/3 

  *Multiplies 86/3 by 4 instead of dividing by 4, treating the run as a multiplier rather than a divisor.*

*Difficulty: medium*

---

##### Q35
In the xy-plane, line k passes through the points (0, -5) and (1, -1). Which equation defines line k?

**A.** y = -x + 1/4 

  *Computes a slope of -1 (wrong sign and magnitude) and an intercept of 1/4 (unrelated to either given point).*

**B.** y = 1/4x - 5 

  *Keeps the correct y-intercept (-5, from (0, -5)) but computes the slope as 1/4 instead of the actual slope of 4 — a reciprocal-style error.*

**C.** y = -x + 4 

  *Gets both the slope's sign and the intercept's sign wrong relative to the correct equation.*

**D.** y = 4x - 5 **(Correct)**

  *Correct. Slope: (-1 - (-5))/(1 - 0) = 4. y-intercept: -5, from (0, -5).*

*Difficulty: easy*

---

##### Q36
A city is planning to build a rock retaining wall, a monument, and a garden in a park. Four rock types are being considered, with weight per volume, in pounds per cubic foot (lb/ft³): Basalt — 180; Granite — 165; Limestone — 120; Sandstone — 135. Only basalt, granite, and limestone will be used in the garden. The rocks in the garden will have a total weight of 1,000 pounds. If 330 pounds of granite is used, which of the following equations could show the relationship between the amounts, x and y, in ft³, for each of the other rock types used?

**A.** 165x + 180y = 670 

  *Uses granite's density (165) instead of limestone's density (120) for one of the two remaining rock types — mismatches a density value to the wrong rock.*

**B.** 165x + 120y = 1,000 

  *Reuses granite's density (165) for one term instead of basalt's (180), and uses the full 1,000-pound total instead of the 670 pounds remaining after subtracting granite's 330 pounds.*

**C.** 120x + 180y = 670 **(Correct)**

  *Correct. Remaining weight after 330 lb of granite: 1,000 - 330 = 670. Limestone's density (120) and basalt's density (180) are the coefficients on the two remaining unknowns.*

**D.** 120x + 180y = 1,000 

  *Correctly uses limestone's and basalt's densities, but forgets to subtract granite's 330 pounds from the 1,000-pound total, using the full total instead of the 670-pound remainder.*

*Difficulty: hard*

---

##### Q37
Figure A and figure B are both regular polygons. The sum of the perimeter of figure A and the perimeter of figure B is 63 inches. The equation 3x + 6y = 63 represents this situation, where x is the number of sides of figure A and y is the number of sides of figure B. Which statement is the best interpretation of 6 in this context?

**A.** Each side of figure B has a length of 6 inches. **(Correct)**

  *Correct. Since x and y are defined as side counts, the coefficients 3 and 6 must each be the side length that, multiplied by a side count, gives that figure's perimeter. Since 6 multiplies y (figure B's side count), 6 is figure B's side length.*

**B.** The number of sides of figure B is 6. 

  *Confuses the coefficient 6 (a side-length multiplier) with the variable y itself, which is what actually represents the number of sides of figure B.*

**C.** Each side of figure A has a length of 6 inches. 

  *Assigns the coefficient on y (6) to figure A instead of figure B — figure A's side length is actually the other coefficient, 3, which multiplies x.*

**D.** The number of sides of figure A is 6. 

  *Combines two errors — assigns the coefficient 6 to figure A (should be figure B) and treats it as a side count rather than a side length.*

*Difficulty: easy*

---

##### Q38
The table shows three values of x and their corresponding values of y, where n is a constant, for the linear relationship between x and y: when x = -6, y = n + 184; when x = -3, y = n + 92; when x = 0, y = n. What is the slope of the line that represents this relationship in the xy-plane?

**A.** -92/3 **(Correct)**

  *Correct. From x = -3 to x = 0, Δx = 3 and Δy = n - (n + 92) = -92, so slope = -92/3.*

**B.** -3/92 

  *Inverts the correct slope into its reciprocal.*

**C.** (n + 92)/-3 

  *Uses one of the raw table y-values (n + 92) directly as the numerator instead of computing the difference between two y-values first — never actually subtracts to find Δy.*

**D.** (2n - 92)/3 

  *Miscombines two different rows' y-expressions instead of cleanly subtracting matching consecutive rows.*

*Difficulty: medium*

---

##### Q39
2x + y = 37. In triangle QRS, sides QR and RS each have a length of x centimeters and side SQ has a length of y centimeters. The given equation represents this situation. Which of the following is the best interpretation of 37 in this context?

**A.** The difference, in centimeters, between the lengths of sides QR and SQ 

  *Introduces a subtraction that has no basis — the equation 2x + y = 37 adds the two equal sides (2x) to the third side (y), it isn't a difference between any two sides.*

**B.** The difference, in centimeters, between the lengths of sides QR and RS 

  *Same subtraction error as choice A. QR and RS are stated to be equal (both length x), so their difference would trivially be zero — this describes a quantity that can't meaningfully be 37.*

**C.** The sum of the lengths, in centimeters, of the three sides of the triangle **(Correct)**

  *Correct. 2x (sides QR and RS combined) plus y (side SQ) equals 37, the perimeter — the sum of all three sides.*

**D.** The length, in centimeters, of one of the two sides of equal length 

  *Describes x alone, not the full sum 2x + y that the equation actually sets equal to 37.*

*Difficulty: medium*

---

##### Q40
A total of 2 squares each have side length r. A total of 6 equilateral triangles each have side length t. None of these squares and triangles shares a side. The sum of the perimeters of all these squares and triangles is 210. Which equation represents this situation?

**A.** 6r + 24t = 210 

  *Miscounts each shape's number of sides — pairs a factor of 6 with r and 24 with t, neither of which matches 2 squares × 4 sides = 8r or 6 triangles × 3 sides = 18t.*

**B.** 2r + 6t = 210 

  *Uses the number of each shape (2 squares, 6 triangles) directly as the coefficients, without multiplying by each shape's number of sides (4 for squares, 3 for triangles) to get the total perimeter contribution.*

**C.** 8r + 18t = 210 **(Correct)**

  *Correct. 2 squares × 4 sides each = 8r. 6 triangles × 3 sides each = 18t. 8r + 18t = 210.*

**D.** 6r + 2t = 210 

  *Swaps which variable gets which shape's coefficient — assigns the triangle-count-derived coefficient to r and the square-count-derived coefficient to t.*

*Difficulty: medium*

---

##### Q41
2.5b + 5r = 80. The given equation describes the relationship between the number of birds, b, and the number of reptiles, r, that can be cared for at a pet care business on a given day. If the business cares for 16 reptiles on a given day, how many birds can it care for on this day?

**A.** 0 **(Correct)**

  *Correct. 2.5b + 5(16) = 80 → 2.5b + 80 = 80 → 2.5b = 0 → b = 0.*

**B.** 5 

  *Reports the reptile coefficient (5) directly rather than solving the equation for b.*

**C.** 40 

  *Computes half of 80 (mishandling the equation, e.g. dividing the reptile term by 2 instead of correctly isolating b) rather than solving 2.5b + 80 = 80 for b.*

**D.** 80 

  *Restates the total capacity (80) directly, as if b alone must equal the full total, ignoring that the reptiles already used all of the shared capacity.*

*Difficulty: medium*

---

##### Q42
A line in the xy-plane passes through the points (0, -8) and (8, -16). What is an equation of the graph shown?

**A.** y = -2x - 8 

  *Doubles the correct slope (uses -2 instead of -1), likely from misreading the grid spacing as if it were steeper than it actually is.*

**B.** y = x - 8 

  *Gets the correct y-intercept but flips the sign of the slope, treating the line as increasing instead of decreasing.*

**C.** y = -x - 8 **(Correct)**

  *Correct. Slope: (-16 - (-8))/(8 - 0) = -1. y-intercept: -8.*

**D.** y = 2x - 8 

  *Combines both errors above — doubles the slope's magnitude and flips its sign.*

*Difficulty: easy*

---

##### Q43
A graph in the xy-plane shows a line with a y-intercept of (0, 35) and an x-intercept of (90, 0), modeling the relationship between the number of T-shirts, x, and the number of sweatshirts, y, that Kira can purchase for a school fundraiser. Which equation could represent this relationship?

**A.** y = 7x + 18 

  *Treats this as a slope-intercept relationship with an invented slope and intercept that don't match either intercept actually shown (35 and 90), rather than recognizing this as a budget-constraint relationship in standard form.*

**B.** 7x + 18y = 630 **(Correct)**

  *Correct. 630/18 = 35 matches the y-intercept, and 630/7 = 90 matches the x-intercept shown in the graph.*

**C.** y = 18x + 7 

  *The same category of error as choice A — an invented slope-intercept equation that doesn't reproduce either graphed intercept.*

**D.** 18x + 7y = 630 

  *Swaps the two coefficients between x and y: at y = 0, this gives x = 35 (should be 90); at x = 0, this gives y = 90 (should be 35) — the intercepts land on the wrong axes.*

*Difficulty: medium*

---

##### Q44
Line r is defined by the equation 4x - 9y = 3. Line s is parallel to line r in the xy-plane. What is the slope of line s?

**A.** 9/4 

  *Inverts the correct slope (4/9) into its reciprocal.*

**B.** 4/9 **(Correct)**

  *Correct. 4x - 9y = 3 → -9y = -4x + 3 → y = (4/9)x - 1/3. Slope = 4/9, and parallel lines share the same slope.*

**C.** -4 

  *Reads the coefficient on x directly as the slope without first solving the equation for y and dividing by y's coefficient.*

**D.** -9 

  *Reads the coefficient on y directly as the slope, with a sign flip, rather than solving the equation for y and computing -A/B correctly.*

*Difficulty: easy*

---

##### Q45
A batch of banana milkshakes consists of 4 cups of ice cream and 2 bananas and has 1,114 milligrams (mg) of calcium. There is 276 mg of calcium in 1 cup of the ice cream used to make this batch of milkshakes. How much calcium, in mg, is in 1 banana?

**A.** 5 **(Correct)**

  *Correct. 4(276) = 1,104 mg from ice cream. 1,114 - 1,104 = 10 mg from 2 bananas, so 10/2 = 5 mg per banana.*

**B.** 10 

  *Reports the total calcium from both bananas combined (10 mg) instead of dividing by 2 to get the per-banana amount the question asks for.*

**C.** 419 

  *Subtracts only one cup's worth of ice cream calcium (276) instead of all 4 cups (1,104), then divides the remainder by 2 bananas: (1,114 - 276)/2 = 419.*

**D.** 1,104 

  *Reports the total calcium from all the ice cream (4 × 276 = 1,104) instead of solving for the banana calcium — confuses an intermediate quantity with the final answer.*

*Difficulty: medium*

---

##### Q46
Lily made 36 cups of jam. Lily then filled x small containers and y large containers with all the jam she made. The equation 4x + 6y = 36 represents this situation. Which is the best interpretation of 6y in this context?

**A.** The number of large containers Lily filled 

  *Describes y alone, not the full term 6y that also includes the multiplier for cups per container.*

**B.** The number of small containers Lily filled 

  *Describes x, an entirely different variable that isn't part of the term 6y at all.*

**C.** The total number of cups of jam in the large containers **(Correct)**

  *Correct. y is the number of large containers, 6 is the cups per large container, so 6y is the total cups of jam held across all large containers.*

**D.** The total number of cups of jam in the small containers 

  *Describes the other term, 4x, not 6y — swaps which term (small vs. large containers) the question is asking about.*

*Difficulty: easy*

---

##### Q47
The table shows four values of x and their corresponding values of y: when x = -6, y = 65; when x = -3, y = 56; when x = 3, y = 38; when x = 6, y = 29. There is a linear relationship between x and y. Which of the following equations represents this relationship?

**A.** 9x + 3y = 141 **(Correct)**

  *Correct. Slope: (56 - 65)/(-3 - (-6)) = -9/3 = -3. Using (-6, 65): 65 = -3(-6) + b = 18 + b → b = 47, so y = -3x + 47, which rearranges to 3x + y = 47 → 9x + 3y = 141.*

**B.** 9x + 3y = 3 

  *Correctly derives the coefficients 9 and 3 but drops or miscalculates the constant, using 3 instead of correctly scaling the intercept (47) up to 141.*

**C.** 3x + 9y = 141 

  *Swaps the coefficients on x and y (3 and 9 reversed) relative to the correctly-derived equation.*

**D.** 3x + 9y = 3 

  *Combines both errors — swaps the coefficients on x and y and also fails to scale the constant term to match.*

*Difficulty: hard*

---

##### Q48
A certain township consists of a 5-hectare industrial park and a 24-hectare neighborhood. The total number of trees in the township is 4,529. The equation 5x + 24y = 4,529 represents this situation. Which of the following is the best interpretation of x in this context?

**A.** The average number of trees per hectare in the industrial park **(Correct)**

  *Correct. x is multiplied by 5 (the industrial park's hectares) to contribute to the total tree count, so x itself must be a per-hectare rate for the industrial park — 5 × (average per hectare) gives the total trees in that region.*

**B.** The average number of trees per hectare in the neighborhood 

  *Describes y (multiplied by 24, the neighborhood's hectares), not x, which is multiplied by 5, the industrial park's hectares.*

**C.** The total number of trees in the industrial park 

  *The total number of trees in the industrial park is the full term 5x, not x alone — x by itself is only the per-hectare rate that gets multiplied by 5 to reach that total.*

**D.** The total number of trees in the neighborhood 

  *Combines two errors — refers to the wrong region (neighborhood instead of industrial park) and to the wrong kind of quantity (a total instead of x's actual per-hectare meaning).*

*Difficulty: medium*

---

##### Q49
A graph in the xy-plane models the possible combinations of length x, in meters (m), and width y, in meters, for a rectangle with a perimeter of 36 m. The line passes through (0, 18) and (18, 0), with a marked point at (8, 10). Which statement is the best interpretation of the point (8, 10) in this context?

**A.** The length is 10 m less than the perimeter, and the width is 8 m less than the perimeter. 

  *Invents a relationship to the perimeter (36) that isn't what the ordered pair actually represents — the point's coordinates are the length and width directly, not offsets from the perimeter.*

**B.** The length is 10 m, and the width is 8 m. 

  *Swaps which coordinate represents length versus width — the point is (x, y) = (8, 10), so x = 8 is the length and y = 10 is the width, not the reverse.*

**C.** The length is 8 m, and the width is 10 m. **(Correct)**

  *Correct. The graph's x-axis is length and y-axis is width, so the point (8, 10) directly means length = 8 m and width = 10 m.*

**D.** The length is 8 m less than the perimeter, and the width is 10 m less than the perimeter. 

  *The same invented-relationship error as choice A, just with the coordinates in the other order.*

*Difficulty: medium*

---

##### Q50
The graph of the equation ax + ky = 6 is a line in the xy-plane, where a and k are constants. If the line contains the points (-2, -6) and (0, -3), what is the value of k?

**A.** -2 **(Correct)**

  *Correct. Using the point (0, -3), the x = 0 eliminates a entirely: a(0) + k(-3) = 6 → -3k = 6 → k = -2.*

**B.** -1 

  *Substitutes the point (-2, -6) instead of (0, -3), then ignores the ax term entirely rather than solving for a first: -6k = 6 gives k = -1. Only the point with x = 0 actually eliminates a from the equation.*

**C.** 2 

  *Correctly identifies that (0, -3) is the point to use, but drops the negative sign when solving -3k = 6, giving k = 2 instead of k = -2.*

**D.** 3 

  *Divides 6 by -3 and drops the resulting negative sign, reporting only the magnitude of the correct answer.*

*Difficulty: hard*

---

##### Q51
Line ℓ in the xy-plane is perpendicular to the line with equation x = 2. What is the slope of line ℓ?

**A.** 0 **(Correct)**

  *Correct. x = 2 is a vertical line (undefined slope). A line perpendicular to a vertical line is horizontal, with slope 0.*

**B.** -1/2 

  *Treats x = 2 as if it described a line with slope 2, then takes the negative reciprocal of that misread slope.*

**C.** -2 

  *Treats the "2" in x = 2 as if it were a slope value itself, and takes its negative.*

**D.** The slope of line ℓ is undefined. 

  *Assumes the perpendicular of a vertical line must also be vertical, rather than recognizing that a line perpendicular to a vertical line is horizontal (slope 0), not another undefined-slope line.*

*Difficulty: easy*

---

##### Q52
To earn money for college, Avery works two part-time jobs: A and B. She earns $10 per hour working at job A and $20 per hour working at job B. In one week, Avery earned a total of s dollars for working at the two part-time jobs. A graph shows all possible combinations of numbers of hours Avery could have worked at the two jobs to earn s dollars: the line passes through (0, 8) on the "hours at job B" axis and (16, 0) on the "hours at job A" axis. What is the value of s?

**A.** 128 

  *Multiplies the two graphed intercepts together (16 × 8 = 128) instead of using either intercept with its own hourly rate.*

**B.** 160 **(Correct)**

  *Correct. Using either intercept with its matching rate: 10(16) = 160, or 20(8) = 160.*

**C.** 200 

  *Multiplies the two dollar rates together (10 × 20 = 200) instead of using an intercept with its matching rate.*

**D.** 320 

  *Multiplies the job-A intercept (16) by job B's rate ($20) instead of by job A's own rate ($10) — mismatches an intercept with the wrong job's rate.*

*Difficulty: hard*

---

##### Q53
In the xy-plane, line k is defined by x + y = 0. Line j is perpendicular to line k, and the y-intercept of line j is (0, 3). Which of the following is an equation of line j?

**A.** x + y = 3 

  *Keeps line k's original slope (-1) instead of taking the negative reciprocal (1) for the perpendicular line — treats "perpendicular" as if it meant "parallel."*

**B.** x + y = -3 

  *Same slope error as choice A (uses -1 instead of the perpendicular slope of 1) and also flips the sign of the y-intercept.*

**C.** x - y = 3 

  *Correctly finds the perpendicular slope of 1, but flips the sign of the y-intercept, using -3 instead of the given +3.*

**D.** x - y = -3 **(Correct)**

  *Correct. Line k has slope -1, so the perpendicular slope is 1: y = x + 3, which rearranges to x - y = -3.*

*Difficulty: medium*

---

##### Q54
The table shows two values of x and their corresponding values of y: when x = -18, y = -48; when x = 7, y = 52. In the xy-plane, the graph of the linear equation representing this relationship passes through the point (1/7, a). What is the value of a?

**A.** -4/11 

  *Computes the slope using a mismatched denominator — e.g., dividing by the sum of the x-values (-18 + 7 = -11) instead of their difference (7 - (-18) = 25) — and never reaches the point substitution step.*

**B.** -4/77 

  *Uses an unrelated combination of the given numbers in the denominator (rather than the correct Δx of 25) when computing slope.*

**C.** 4/7 

  *Reports only the term 4(1/7) = 4/7 from the final substitution, forgetting to add the y-intercept term (+24) to complete the calculation.*

**D.** 172/7 **(Correct)**

  *Correct. Slope: (52 - (-48))/(7 - (-18)) = 100/25 = 4. Using (7, 52): 52 = 4(7) + b = 28 + b → b = 24, so y = 4x + 24. At x = 1/7: a = 4(1/7) + 24 = 4/7 + 168/7 = 172/7.*

*Difficulty: hard*

---

##### Q55
Line h is defined by 1/5x + 1/7y - 70 = 0. Line j is perpendicular to line h in the xy-plane. What is the slope of line j?

**A.** -7/5 

  *Reports line h's own slope instead of taking the negative reciprocal for the perpendicular line — confuses "perpendicular" with simply restating the given line's slope.*

**B.** -5/7 

  *Correctly inverts the slope's fraction to 5/7 in magnitude, but keeps the negative sign instead of flipping it — a perpendicular slope must flip both the sign and the fraction.*

**C.** 7/5 

  *Flips the sign correctly relative to the original slope but keeps the same fraction instead of taking its reciprocal.*

**D.** 5/7 **(Correct)**

  *Correct. 1/5x + 1/7y = 70 → y = -7/5x + 490, so line h has slope -7/5. The negative reciprocal is 5/7.*

*Difficulty: medium*

---

##### Q56
3/5x + 3/4y = 7. Which table gives three values of x and their corresponding values of y for the given equation?

**A.** x = 1, 2, 4 gives y = 113/20, 101/20, 77/20 

  *Uses an incorrect common denominator (20 instead of 15) when clearing the fractions 3/5 and 3/4, producing a systematically wrong scale for every y-value.*

**B.** x = 1, 2, 4 gives y = 47/5, 44/5, 38/5 

  *Solves for y using only one of the two fractional coefficients correctly, producing values scaled with a denominator of 5 instead of the correct 15.*

**C.** x = 1, 2, 4 gives y = 148/15, 136/15, 112/15 

  *Uses the correct denominator (15) but makes a constant-term error early on — e.g., computes 7 × 5 instead of 7 × 4 when clearing denominators — shifting every value by the same fixed amount.*

**D.** x = 1, 2, 4 gives y = 128/15, 116/15, 92/15 **(Correct)**

  *Correct. Solving for y: y = 28/3 - 4/5x. At x = 1: y = 128/15. At x = 2: y = 116/15. At x = 4: y = 92/15.*

*Difficulty: hard*

---

##### Q57
For line h, the table shows three values of x and their corresponding values of y: when x = 18, y = 130; when x = 23, y = 160; when x = 26, y = 178. Line k is the result of translating line h down 5 units in the xy-plane. What is the x-intercept of line k?

**A.** (-26/3, 0) 

  *Forgets to apply the downward translation at all and instead makes an unrelated arithmetic slip while finding line h's own x-intercept, rather than line k's.*

**B.** (-9/2, 0) 

  *Applies the downward shift to the wrong term — shifts the slope by 5 instead of the y-intercept, producing a different line entirely rather than a parallel translated one.*

**C.** (-11/3, 0) 

  *Correctly finds line h's own x-intercept (22/(-6) reduces to -11/3) but forgets to apply the "translated down 5 units" step, reporting line h's x-intercept instead of line k's.*

**D.** (-17/6, 0) **(Correct)**

  *Correct. Slope of h: (160 - 130)/(23 - 18) = 6. Using (18, 130): 130 = 6(18) + b = 108 + b → b = 22, so h: y = 6x + 22. Line k, shifted down 5: y = 6x + 17. x-intercept: 0 = 6x + 17 → x = -17/6.*

*Difficulty: sat-hardest*

---

##### Q58
The graph of 7x + 2y = -31 in the xy-plane has an x-intercept at (a, 0) and a y-intercept at (0, b), where a and b are constants. What is the value of b/a?

**A.** -7/2 

  *Correctly computes the magnitude of the ratio (7/2) but keeps a negative sign that shouldn't survive — since both a and b are negative, their ratio b/a is actually positive.*

**B.** -2/7 

  *Combines two errors — inverts the ratio (2/7 instead of 7/2) and keeps an incorrect negative sign.*

**C.** 2/7 

  *Correctly recognizes the ratio should be positive, but inverts it — computes a/b instead of b/a.*

**D.** 7/2 **(Correct)**

  *Correct. x-intercept: 7a = -31 → a = -31/7. y-intercept: 2b = -31 → b = -31/2. b/a = (-31/2)/(-31/7) = 7/2.*

*Difficulty: medium*

---

##### Q59
The graph of y = f(x) + 14 is a line in the xy-plane with a y-intercept of (0, 2) and an x-intercept of (8, 0). Which equation defines function f?

**A.** f(x) = -1/4x - 12 **(Correct)**

  *Correct. The graphed line has slope (0 - 2)/(8 - 0) = -1/4, so y = -1/4x + 2. Since y = f(x) + 14, f(x) = y - 14 = -1/4x + 2 - 14 = -1/4x - 12.*

**B.** f(x) = -1/4x + 16 

  *Adds 14 to the graphed equation's constant instead of subtracting it — reverses the direction of the shift needed to undo "+ 14."*

**C.** f(x) = -1/4x + 2 

  *Reports the graphed equation (y = f(x) + 14) directly as f(x), forgetting to undo the +14 shift at all.*

**D.** f(x) = -1/4x - 14 

  *Uses the original shift amount, 14, as the new intercept directly, rather than subtracting 14 from the graphed intercept (2 - 14 = -12).*

*Difficulty: hard*

---

##### Q60
2x + 3y = 7 and 10x + 15y = 35. For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?

**A.** (r/5 + 7, -r/5 + 35) 

  *This point comes from treating the second equation's coefficients as if they were independent of the first, rather than recognizing 10x + 15y = 35 is just 5 times 2x + 3y = 7. Substituting back into 2x + 3y = 7 gives -r/5 + 119, not a constant 7, so it fails the system for essentially all r.*

**B.** (-3r/2 + 7/2, r) **(Correct)**

  *Correct. Since 10x + 15y = 35 is exactly 5 times 2x + 3y = 7, the two equations describe the same line, with infinitely many solutions. Setting y = r and solving 2x + 3y = 7 for x gives x = (7 - 3r)/2 = -3r/2 + 7/2, which satisfies both equations for every real r.*

**C.** (r, 2r/3 + 7/3) 

  *Starts correctly by setting x = r and solving 3y = 7 - 2x = 7 - 2r for y, but makes a sign slip: this should give y = -2r/3 + 7/3, not +2r/3 + 7/3.*

**D.** (r, -3r/2 + 7/2) 

  *Correctly derives the expression -3r/2 + 7/2 for one coordinate, but pairs it with x = r instead of y = r — swaps which variable is set equal to r and which is solved for.*

*Difficulty: sat-hardest*

---

#### Linear inequalities (39 items)

##### Q1
Valentina bought two containers of beads. In the first container 30% of the beads are red, and in the second container 70% of the beads are red. Together, the containers have at least 400 red beads. Which inequality shows this relationship, where x is the total number of beads in the first container and y is the total number of beads in the second container?

**A.** 0.3x + 0.7y ≥ 400 **(Correct)**

  *Correct. 30% of the beads in container 1 is 0.3x, and 70% of the beads in container 2 is 0.7y. The number of red beads together must be at least 400, so 0.3x + 0.7y ≥ 400.*

**B.** 0.7x + 0.3y ≤ 400 

  *This swaps which container's percentage attaches to which variable — 70% (the second container's red rate) is applied to x and 30% (the first container's) to y — and also reverses the direction, treating 'at least' as a cap rather than a floor. Both the coefficients and the inequality symbol are wrong for what the problem describes.*

**C.** x/3 + y/7 ≤ 400 

  *This treats 30% as the fraction 1/3 (giving x/3) and 70% as 1/7 (giving y/7), rather than converting the percentages correctly to 0.3 and 0.7. 30% is 3/10, not 1/3, and 70% is 7/10, not 1/7 — the denominator matches the digit shown, not the actual fraction.*

**D.** 30x + 70y ≥ 400 

  *This uses 30 and 70 directly as the coefficients instead of converting the percentages to decimals (0.30 and 0.70) first. Every term is too large by a factor of 100, so this inequality describes 3,000% and 7,000% of the beads being red, not 30% and 70%.*

*Difficulty: medium*

---

##### Q2
On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under 220 miles. Rhett drove at an average speed of 35 miles per hour (mph), and Jessica drove at an average speed of 40 mph. Which of the following inequalities represents this situation, where r is the number of hours Rhett drove and j is the number of hours Jessica drove?

**A.** 35r + 40j > 220 

  *The rates are attached to the right people (35 with r, 40 with j), but the direction is wrong: 'under 220' means strictly less than 220, and this uses greater than instead — describing a trip that covered more than 220 miles rather than less.*

**B.** 35r + 40j < 220 **(Correct)**

  *Correct. Distance = rate × time for each driver: Rhett contributes 35r miles and Jessica contributes 40j miles. Their combined distance was under 220 miles, and 'under' is strict, so the total is less than 220: 35r + 40j < 220.*

**C.** 40r + 35j > 220 

  *The direction is correct for a total but the speeds are swapped — Jessica's 40 mph is attached to Rhett's variable r, and Rhett's 35 mph to Jessica's variable j. It also uses > instead of <, doubling the error.*

**D.** 40r + 35j < 220 

  *The direction (<) is correct, but the speeds are swapped: 40 is multiplied by r (Rhett's hours) and 35 by j (Jessica's hours), the reverse of what the problem states. Reading which name goes with which rate is the entire question here.*

*Difficulty: easy*

---

##### Q3
A bakery sells trays of cookies. Each tray contains at least 50 cookies but no more than 60. Which of the following could be the total number of cookies on 4 trays of cookies?

**A.** 165 

  *165 is below the minimum possible total. Four trays of at least 50 cookies each must total at least 200 cookies, and 165 ÷ 4 = 41.25 cookies per tray — under the stated minimum of 50.*

**B.** 205 **(Correct)**

  *Correct. Each tray has between 50 and 60 cookies, inclusive, so four trays have between 4(50) = 200 and 4(60) = 240 cookies, inclusive: 200 ≤ total ≤ 240. Of the choices, only 205 falls in that range (205/4 = 51.25 cookies per tray, which is between 50 and 60).*

**C.** 245 

  *245 exceeds the maximum possible total. Four trays of at most 60 cookies each can total at most 240 cookies, and 245 ÷ 4 = 61.25 cookies per tray — over the stated maximum of 60.*

**D.** 285 

  *285 exceeds the maximum possible total by an even larger margin: 285 ÷ 4 = 71.25 cookies per tray, well over the 60-cookie maximum for a single tray.*

*Difficulty: easy*

---

##### Q4
Tom scored 85, 78, and 98 on his first three exams in history class. Solving which inequality gives the score, G, on Tom's fourth exam that will result in a mean score on all four exams of at least 90?

**A.** 90 − (85 + 78 + 98) ≤ 4G 

  *This inequality has G isolated in a way that doesn't correspond to the mean condition at all — it compares 90 minus the sum of the first three scores to 4G, which is not an algebraic rearrangement of '(sum of four scores)/4 ≥ 90.' Setting up the mean inequality and then rearranging it correctly would not produce this form.*

**B.** 4G + 85 + 78 + 98 ≥ 360 

  *This multiplies only the G term by 4 instead of clearing the whole fraction — the correct step is multiplying every term in (G + 85 + 78 + 98)/4 by 4 to get G + 85 + 78 + 98 ≥ 360, not multiplying just G to get 4G + 85 + 78 + 98 ≥ 360. As written this describes a different (and inflated) total-score requirement.*

**C.** (G + 85 + 78 + 98)/4 ≥ 90 **(Correct)**

  *Correct. The mean of all four exams is the sum of all four scores divided by 4, and that mean must be at least 90: (G + 85 + 78 + 98)/4 ≥ 90.*

**D.** (85 + 78 + 98)/4 ≥ 90 − 4G 

  *This has the mean expression and the target on the wrong sides, and a 4G term appears where the exam-sum-divided-by-4 should be — it treats 90 − 4G as though it were the mean of the fourth exam and the target, rather than setting the true mean of all four scores against 90. The structure doesn't correspond to any correct rearrangement of the mean condition.*

*Difficulty: medium*

---

##### Q5
Normal body temperature for an adult is between 97.8°F and 99°F, inclusive. If Kevin, an adult male, has a body temperature that is considered to be normal, which of the following could be his body temperature?

**A.** 96.7°F 

  *96.7°F is below the lower bound of 97.8°F — it falls outside the normal range entirely, not just outside the inclusive endpoints.*

**B.** 97.6°F 

  *97.6°F is close to the lower bound but still below it: the range starts at 97.8°F inclusive, and 97.6 < 97.8, so it falls just outside the interval. This distractor tests whether the boundary value itself (97.8, not a nearby number) is remembered precisely.*

**C.** 97.9°F **(Correct)**

  *Correct. 'Between 97.8°F and 99°F, inclusive' means 97.8 ≤ temperature ≤ 99. 97.9°F falls inside that closed interval.*

**D.** 99.7°F 

  *99.7°F is above the upper bound of 99°F — it falls outside the range on the high side, a temperature that would actually indicate a fever rather than a normal reading.*

*Difficulty: easy*

---

##### Q6
Which of the following ordered pairs (x, y) satisfies the inequality 5x − 3y < 4? I. (1, 1)  II. (2, 5)  III. (3, 2)

**A.** I only 

  *This includes I correctly but drops II, which does satisfy the inequality: 5(2) − 3(5) = −5, and −5 < 4 is true. A likely source of the error is mis-multiplying 3 × 5 as a positive contribution rather than correctly computing 10 − 15 as negative.*

**B.** II only 

  *This drops point I, which does satisfy the inequality (5(1) − 3(1) = 2 < 4 ✓), and keeps only II. Checking every candidate point independently, rather than assuming a pattern, is the only reliable way through this item type.*

**C.** I and II only **(Correct)**

  *Correct. Point I: 5(1) − 3(1) = 2, and 2 < 4 ✓. Point II: 5(2) − 3(5) = 10 − 15 = −5, and −5 < 4 ✓. Point III: 5(3) − 3(2) = 15 − 6 = 9, and 9 < 4 is false. Only I and II satisfy the inequality.*

**D.** I and III only 

  *This correctly keeps I but incorrectly includes III: 5(3) − 3(2) = 15 − 6 = 9, and 9 < 4 is false, so III does not satisfy the inequality. A likely slip is computing 3(2) as 3 + 2 = 5 instead of 3 × 2 = 6, which understates how far 9 sits above 4.*

*Difficulty: medium*

---

##### Q7
A clothing store is having a sale on shirts and pants. During the sale, the cost of each shirt is $15 and the cost of each pair of pants is $25. Geoff can spend at most $120 at the store. If Geoff buys s shirts and p pairs of pants, which of the following must be true?

**A.** 15s + 25p ≤ 120 **(Correct)**

  *Correct. Each shirt costs $15, so s shirts cost 15s; each pair of pants costs $25, so p pairs cost 25p. Total spending must be at most $120, which is ≤: 15s + 25p ≤ 120.*

**B.** 15s + 25p ≥ 120 

  *The coefficients are attached to the right variables, but the direction is reversed: 'at most $120' is a ceiling on spending (≤), and this uses ≥, describing a minimum required purchase instead of a spending cap.*

**C.** 25s + 15p ≤ 120 

  *The prices are swapped — $25 (the price of pants) is attached to s (shirts) and $15 (the price of shirts) is attached to p (pants). The direction is right, but the cost model describes the wrong item at the wrong price.*

**D.** 25s + 15p ≥ 120 

  *Both errors at once: the prices are swapped (25 with shirts, 15 with pants) and the direction is reversed (≥ instead of ≤), turning a spending cap into a minimum spend on a cost structure that doesn't match the problem.*

*Difficulty: easy*

---

##### Q8
An elementary school teacher is ordering x workbooks and y sets of flash cards for a math class. The teacher must order at least 20 items, but the total cost of the order must not be over $80. If the workbooks cost $3 each and the flash cards cost $4 per set, which of the following systems of inequalities models this situation?

**A.** x + y ≥ 20 and 3x + 4y ≤ 80 **(Correct)**

  *Correct. Item count: x workbooks plus y flash-card sets must be at least 20, so x + y ≥ 20. Cost: workbooks at $3 each plus flash cards at $4 each must not exceed $80, so 3x + 4y ≤ 80.*

**B.** x + y ≥ 20 and 3x + 4y ≥ 80 

  *The item-count constraint is right, but the cost constraint's direction is reversed: 'must not be over $80' is a ceiling (≤), and this uses ≥, requiring at least $80 in spending instead of capping it.*

**C.** 3x + 4y ≤ 20 and x + y ≥ 80 

  *The two constraints are swapped onto the wrong bounds — the item-count expression (x + y) is compared against 80, the cost bound, while the cost expression (3x + 4y) is compared against 20, the item-count bound. Each constraint needs to stay matched to its own unit: item counts against 20 items, dollars against $80.*

**D.** x + y ≤ 20 and 3x + 4y ≥ 80 

  *The item-count direction is reversed (≤ instead of ≥, capping items at 20 rather than requiring at least 20) and the cost direction is also reversed (≥ instead of ≤, requiring at least $80 rather than capping at $80) — both symbols point the wrong way for what 'at least' and 'not over' mean.*

*Difficulty: medium*

---

##### Q9
During spring migration, a dragonfly traveled a minimum of 1,510 miles and a maximum of 4,130 miles between stopover locations. Which inequality represents this situation, where d is a possible distance, in miles, this dragonfly traveled between stopover locations during spring migration?

**A.** d ≤ 1,510 

  *This keeps only the minimum's number but turns it into an upper bound (d ≤ 1,510), which both drops the maximum entirely and inverts the role of 1,510 — it should be the floor of the range, not the ceiling.*

**B.** 1,510 ≤ d ≤ 4,130 **(Correct)**

  *Correct. A minimum of 1,510 miles and a maximum of 4,130 miles means the distance is bounded on both sides, inclusive: 1,510 ≤ d ≤ 4,130.*

**C.** d ≥ 4,130 

  *This uses only the maximum value and turns it into a lower bound with no ceiling (d ≥ 4,130), which drops the minimum entirely and describes distances with no upper limit — the opposite of a range bounded above by 4,130.*

**D.** 4,130 ≤ d ≤ 5,640 

  *The lower bound is the maximum value from the problem (4,130) instead of the minimum (1,510), and the upper bound (5,640) is the sum of the two given values rather than either given bound — 1,510 + 4,130 = 5,640, a quantity with no meaning in this context.*

*Difficulty: easy*

---

##### Q10
The point (8, 2) in the xy-plane is a solution to which of the following systems of inequalities?

**A.** x > 0 and y > 0 **(Correct)**

  *Correct. The point (8, 2) has x = 8 > 0 and y = 2 > 0, so it satisfies both x > 0 and y > 0 — it lies in the first quadrant, where both coordinates are positive.*

**B.** x > 0 and y < 0 

  *This requires y < 0, but the point's y-coordinate is 2, which is positive, not negative. The system as written describes the fourth quadrant, not the first, where (8, 2) actually sits.*

**C.** x < 0 and y > 0 

  *This requires x < 0, but the point's x-coordinate is 8, which is positive, not negative. The system as written describes the second quadrant, not the first.*

**D.** x < 0 and y < 0 

  *This requires both coordinates to be negative, describing the third quadrant. Both of (8, 2)'s coordinates are positive, so neither condition is met.*

*Difficulty: easy*

---

##### Q11
2ℓ + 2w ≤ 27. A rectangle has length ℓ and width w. The inequality gives the possible values of ℓ and w for which the perimeter of this rectangle is less than or equal to 27. Which statement is the best interpretation of (ℓ, w) = (8, 3) in this context?

**A.** If the rectangle has length 3 and width 8, its perimeter is less than or equal to 27. 

  *This swaps which coordinate is the length and which is the width — reading (8, 3) as length 3, width 8 — even though the ordered pair (ℓ, w) lists length first by definition. The perimeter direction is otherwise stated correctly.*

**B.** If the rectangle has length 8 and width 3, its perimeter is less than or equal to 27. **(Correct)**

  *Correct. In the ordered pair (ℓ, w), the first coordinate is the length and the second is the width, so (8, 3) means length 8 and width 3. The inequality states the perimeter is ≤ 27 (checking: 2(8) + 2(3) = 22 ≤ 27), so this describes a rectangle with length 8, width 3, whose perimeter is at most 27.*

**C.** If the rectangle has length 3 and width 8, its perimeter is greater than or equal to 27. 

  *This keeps the coordinate-swap error from choice A and also reverses the inequality's meaning, stating 'greater than or equal to' when the original inequality is ≤. Two separate errors compound here.*

**D.** If the rectangle has length 8 and width 3, its perimeter is greater than or equal to 27. 

  *The length and width are read correctly (length 8, width 3), but the inequality direction is reversed: the original statement is 2ℓ + 2w ≤ 27, meaning the perimeter is at most 27, not at least 27.*

*Difficulty: medium*

---

##### Q12
A geologist estimates that the volume of a slab of granite is greater than 12.7 cubic feet but less than 15.7 cubic feet. The geologist also estimates that the slab of granite weighs 165 pounds per cubic foot of volume. Which inequality represents this situation, where x represents the estimated total weight, in pounds, of the slab of granite?

**A.** 165 − 15.7 < x < 165 − 12.7 

  *This subtracts the volume bounds from 165 instead of multiplying by them, treating density and volume as though they combined by subtraction rather than multiplication. Weight per cubic foot times cubic feet is a product, not a difference.*

**B.** 165 + 12.7 < x < 165 + 15.7 

  *This adds the volume bounds to 165 instead of multiplying, the same category of error as choice A but with addition instead of subtraction. Density (pounds per cubic foot) combines with volume (cubic feet) by multiplication to produce a total weight in pounds — the units only cancel correctly under multiplication.*

**C.** 165(12.7) < x < 165(15.7) **(Correct)**

  *Correct. Weight equals density times volume: 165 pounds per cubic foot times the volume. Since volume is bounded by 12.7 < volume < 15.7, multiplying every part of that compound inequality by the positive constant 165 gives 165(12.7) < x < 165(15.7).*

**D.** 165/15.7 < x < 165/12.7 

  *This divides 165 by the volume bounds instead of multiplying by them, and also swaps which bound goes with which side of the inequality (165/15.7, the smaller quotient, is placed as the lower bound while 165/12.7, the larger quotient, is placed as the upper bound). Dividing density by volume doesn't produce a weight in any consistent unit here.*

*Difficulty: medium*

---

##### Q13
For a 3-week period in a town in Illinois, the lowest recorded temperature was 31 degrees Fahrenheit (°F) and the highest recorded temperature was 67°F. Which inequality is true for any recorded temperature t, in °F, in this town for this 3-week period?

**A.** t ≥ 98 

  *98 is the sum of the two given temperatures (31 + 67 = 98), not a meaningful bound on t — adding a low and a high temperature together doesn't produce a valid ceiling or floor for the readings themselves.*

**B.** t ≥ 67 

  *This uses only the high temperature and turns it into a lower bound with no ceiling, describing temperatures of 67°F and above with no upper limit — the opposite of what 'highest recorded' means, and it discards the low-temperature bound entirely.*

**C.** 31 ≤ t ≤ 67 **(Correct)**

  *Correct. Every recorded temperature over the period was between the lowest (31°F) and the highest (67°F), inclusive: 31 ≤ t ≤ 67.*

**D.** t ≤ 31 

  *This uses only the low temperature and turns it into an upper bound (t ≤ 31), describing temperatures at or below the coldest reading — the opposite of what 'lowest recorded' means as a floor, and it discards the high-temperature bound entirely.*

*Difficulty: easy*

---

##### Q14
Julissa needs at least 100 hours of flight time to get her private pilot certification. If Julissa already has 86 hours of flight time, what is the minimum number of additional hours of flight time Julissa needs to get her private pilot certification?

**A.** 14 **(Correct)**

  *Correct. Let h be the additional hours needed: 86 + h ≥ 100, so h ≥ 14. The minimum additional hours needed is 14.*

**B.** 76 

  *This does not follow from 100 − 86; a likely source is subtracting in the wrong order or misreading a digit in the requirement, landing on 76 instead of the correct difference of 14.*

**C.** 86 

  *This restates the hours Julissa already has (86) instead of solving for the additional hours still needed — a likely case of answering with a number pulled directly from the problem rather than completing the subtraction 100 − 86.*

**D.** 186 

  *This is 100 + 86 = 186, adding the two given quantities instead of subtracting the hours already flown from the requirement. Additional hours needed is what's missing from the requirement, not the sum of what's already there and what's required.*

*Difficulty: easy*

---

##### Q15
A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?

**A.** 2 

  *This is far below the true maximum. It likely comes from assuming a much larger share of the ten required packages must be the heavier 100-pound kind rather than solving the weight constraint to find how many 120-pound packages actually fit within the 1,100-pound limit.*

**B.** 4 

  *This under-counts the maximum by not pushing the 100-pound package count down to its minimum. Since only 10 total packages are required (not more), using exactly 5 of the lighter packages — not more — leaves the most room under the weight cap for 120-pound packages.*

**C.** 5 **(Correct)**

  *Correct. To maximize 120-pound packages (y), use as few 100-pound packages (x) as possible while still meeting the 10-package minimum: x = 10 − y. Substituting into the weight constraint, 100(10 − y) + 120y ≤ 1,100 gives 1,000 + 20y ≤ 1,100, so y ≤ 5. At y = 5, x = 5, weight = 500 + 600 = 1,100 pounds exactly, and the package count is 10 — both constraints are satisfied at their limits.*

**D.** 6 

  *This exceeds what the weight constraint allows: 6 packages at 120 pounds is 720 pounds, leaving only 380 pounds for the remaining packages, but at least 4 more packages are needed to reach the 10-package minimum, and 4 packages at even the lighter 100-pound weight is 400 pounds — over the remaining budget. The 1,100-pound cap is the binding constraint here, not just the count.*

*Difficulty: hard*

---

##### Q16
Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

**A.** 640x + 880y ≥ 9,700; x + y ≤ 10; x ≥ 3; y ≥ 1 

  *The budget direction is reversed (≥ instead of ≤, requiring at least $9,700 in spending rather than capping it), and the staffing direction is also reversed (≤ instead of ≥, capping the total staff at 10 rather than requiring at least 10). The minimum-headcount conditions are stated correctly.*

**B.** 640x + 880y ≤ 9,700; x + y ≥ 10; x ≥ 3; y ≥ 1 **(Correct)**

  *Correct. Budget: total pay must be no more than $9,700, so 640x + 880y ≤ 9,700. Staffing: at least 10 people total, so x + y ≥ 10. Minimums: at least 3 junior directors (x ≥ 3) and at least 1 senior director (y ≥ 1).*

**C.** 640x + 880y ≥ 9,700; x + y ≥ 10; x ≤ 3; y ≤ 1 

  *The budget direction is reversed (≥ instead of ≤), and the two minimum-headcount conditions are also reversed into maximums (x ≤ 3 and y ≤ 1 instead of x ≥ 3 and y ≥ 1) — 'at least 3' and 'at least 1' both became ceilings instead of floors.*

**D.** 640x + 880y ≤ 9,700; x + y ≤ 10; x ≤ 3; y ≤ 1 

  *The budget direction is correct, but the total-staffing direction is reversed (≤ 10 instead of ≥ 10, capping staff rather than requiring at least 10), and the individual minimums are also reversed into maximums (x ≤ 3, y ≤ 1). Three of the four conditions have their inequality direction flipped from what 'at least' requires.*

*Difficulty: hard*

---

##### Q17
In North America, the standard width of a parking space is at least 7.5 feet and no more than 9.0 feet. A restaurant owner recently resurfaced the restaurant's parking lot and wants to determine the number of parking spaces, n, in the parking lot that could be placed perpendicular to a curb that is 135 feet long, based on the standard width of a parking space. Which of the following describes all the possible values of n?

**A.** 18 ≤ n ≤ 135 

  *This computes the correct upper bound (135/7.5 = 18) but pairs it with the curb length itself, 135, as if that were a possible number of spaces. 135 would only be the space count if each parking space were 1 foot wide, far narrower than the given range.*

**B.** 7.5 ≤ n ≤ 9 

  *This restates the width bounds (7.5 and 9.0 feet) directly as the answer, rather than dividing the curb length by those widths to find how many spaces fit. The question asks for a count of spaces, not a width in feet — the units don't match what's being asked.*

**C.** 15 ≤ n ≤ 135 

  *This computes the correct lower bound (135/9.0 = 15) but pairs it with the curb length itself, 135, as the upper bound instead of the true upper bound of 18. 135 spaces would require spaces averaging 1 foot wide, which contradicts the given 7.5-to-9-foot range.*

**D.** 15 ≤ n ≤ 18 **(Correct)**

  *Correct. More spaces fit when each space is as narrow as possible, and fewer fit when each is as wide as possible. At the minimum width, 135/7.5 = 18 spaces fit; at the maximum width, 135/9.0 = 15 spaces fit. So n ranges from 15 to 18, inclusive.*

*Difficulty: hard*

---

##### Q18
y ≤ x and y ≤ −x. Which of the following ordered pairs (x, y) is a solution to the system of inequalities above?

**A.** (1, 0) 

  *At (1, 0), y ≤ x becomes 0 ≤ 1, which is true, but y ≤ −x becomes 0 ≤ −1, which is false. This point clears the first constraint and fails the second — checking only the first inequality and stopping there is what makes this distractor work.*

**B.** (−1, 0) 

  *At (−1, 0), y ≤ x becomes 0 ≤ −1, which is false immediately — this point fails the first constraint before the second one is even relevant.*

**C.** (0, 1) 

  *At (0, 1), y ≤ x becomes 1 ≤ 0, which is false immediately. Both coordinates are plausible-looking small integers, which is exactly why a point needs to be substituted rather than eyeballed.*

**D.** (0, −1) **(Correct)**

  *Correct. At (0, −1): y ≤ x becomes −1 ≤ 0, true; y ≤ −x becomes −1 ≤ 0, true. Both conditions hold, so this point lies in the intersection of the two regions.*

*Difficulty: medium*

---

##### Q19
y < −4x + 4. Which point (x, y) is a solution to the given inequality in the xy-plane?

**A.** (−4, 0) **(Correct)**

  *Correct. Substituting (−4, 0): 0 < −4(−4) + 4 = 16 + 4 = 20, and 0 < 20 is true.*

**B.** (0, 5) 

  *Substituting (0, 5): 5 < −4(0) + 4 = 4, and 5 < 4 is false. This point sits above the boundary line at x = 0 (the line passes through (0, 4)), and the region below the line is what the strict < requires.*

**C.** (2, 1) 

  *Substituting (2, 1): 1 < −4(2) + 4 = −4, and 1 < −4 is false — 1 is well above −4, not below it. A likely source of the error is comparing the size of the numbers (1 seems small) without tracking that the boundary value itself is negative here.*

**D.** (2, −1) 

  *Substituting (2, −1): −1 < −4(2) + 4 = −4, and −1 < −4 is false, since −1 is greater than −4, not less. Comparing two negative numbers is where this one is easy to misjudge — being 'more negative' means being less than, and −4 is more negative than −1.*

*Difficulty: medium*

---

##### Q20
A certain elephant weighs 200 pounds at birth and gains more than 2 but less than 3 pounds per day during its first year. Which of the following inequalities represents all possible weights w, in pounds, for the elephant 365 days after birth?

**A.** 400 < w < 600 

  *400 and 600 are roughly half the correct bounds — a likely source is using about 100 days instead of 365, or otherwise mis-scaling the daily gain by the wrong number of days before adding the birth weight.*

**B.** 565 < w < 930 

  *This does not come from adding the 200-pound birth weight to the correctly scaled gains of 730 and 1,095 pounds — 565 and 930 don't correspond to 200 plus 365 times 2 or 3. This is consistent with combining the birth weight and the growth term with the wrong operation somewhere in the setup.*

**C.** 730 < w < 1,095 

  *This computes 365 × 2 = 730 and 365 × 3 = 1,095 correctly but omits the 200-pound birth weight entirely, reporting only the weight gained rather than the elephant's total weight 365 days after birth.*

**D.** 930 < w < 1,295 **(Correct)**

  *Correct. Weight after 365 days is 200 + 365(daily gain), with the daily gain strictly between 2 and 3 pounds. At the low end, 200 + 365(2) = 200 + 730 = 930; at the high end, 200 + 365(3) = 200 + 1,095 = 1,295. Since the gain is strictly between 2 and 3, the weight is strictly between 930 and 1,295.*

*Difficulty: hard*

---

##### Q21
H = 120p + 60. The Karvonen formula above shows the relationship between Alice's target heart rate H, in beats per minute (bpm), and the intensity level p of different activities. When p = 0, Alice has a resting heart rate. When p = 1, Alice has her maximum heart rate. It is recommended that p be between 0.5 and 0.85 for Alice when she trains. Which of the following inequalities describes Alice's target training heart rate?

**A.** 120 ≤ H ≤ 162 **(Correct)**

  *Correct. H = 120p + 60, evaluated at the two bounds of p: at p = 0.5, H = 120(0.5) + 60 = 60 + 60 = 120; at p = 0.85, H = 120(0.85) + 60 = 102 + 60 = 162. So the target heart rate satisfies 120 ≤ H ≤ 162.*

**B.** 102 ≤ H ≤ 120 

  *102 is 120(0.85) alone, without adding the resting-rate constant of 60, while 120 is H at p = 0.5 correctly computed with the constant included. The two bounds were found by inconsistent methods — one skipped the +60 term and one kept it — when every evaluation of the formula needs both the coefficient term and the constant.*

**C.** 60 ≤ H ≤ 162 

  *60 is the value of H at p = 0 (Alice's resting heart rate), not at p = 0.5, and 162 is correctly H at p = 0.85. This substitutes the wrong lower bound for p — the resting rate, not the actual training-range floor of p = 0.5 — while using the correct upper bound.*

**D.** 60 ≤ H ≤ 102 

  *The lower bound, 60, is the resting heart rate at p = 0 rather than the training floor at p = 0.5, and the upper bound, 102, is 120(0.85) with the +60 constant left off. Both numbers come from skipping a piece of the formula rather than evaluating H = 120p + 60 fully at the correct values of p.*

*Difficulty: hard*

---

##### Q22
A model estimates that whales from the genus Eschrichtius travel 72 to 77 miles in the ocean each day during their migration. Based on this model, which inequality represents the estimated number of miles, x, a whale from the genus Eschrichtius could travel in 16 days of its migration?

**A.** 72 + 16 ≤ x ≤ 77 + 16 

  *This adds 16 to each bound instead of multiplying by it, treating '16 days' as though it added 16 miles to a single day's distance rather than repeating the daily distance 16 times. Sixteen days of travel compounds by multiplication, not addition.*

**B.** (72)(16) ≤ x ≤ (77)(16) **(Correct)**

  *Correct. Total distance over 16 days is daily distance times 16 days. Since the daily distance is between 72 and 77 miles, multiplying every part of that inequality by 16 gives (72)(16) ≤ x ≤ (77)(16).*

**C.** 72 ≤ 16 + x ≤ 77 

  *This adds 16 to the total distance x rather than multiplying the daily rate by 16, and places x inside the inequality rather than isolated as the quantity being bounded — the setup doesn't represent 'daily distance times number of days' at all.*

**D.** 72 ≤ 16x ≤ 77 

  *This multiplies x itself by 16 rather than multiplying the daily-distance bounds (72 and 77) by 16. As written, this bounds 16x, not x, so solving it would divide the total distance by 16 rather than express it directly — the wrong quantity is scaled.*

*Difficulty: medium*

---

##### Q23
The average annual energy cost for a certain home is $4,334. The homeowner plans to spend $25,000 to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be $2,712. Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost?

**A.** 25,000 > (4,334 − 2,712)t 

  *The savings-per-year expression is set up correctly, but the direction is reversed: 'savings will exceed the installation cost' means the savings amount is greater than $25,000, i.e., 25,000 is less than the savings — not greater than, as this choice states.*

**B.** 25,000 < (4,334 − 2,712)t **(Correct)**

  *Correct. Annual savings from the new system is 4,334 − 2,712 dollars per year, so total savings after t years is (4,334 − 2,712)t. The question asks when that total savings will exceed the installation cost, so the installation cost is less than the savings: 25,000 < (4,334 − 2,712)t.*

**C.** 25,000 − 4,334 > 2,712t 

  *This subtracts the wrong quantities and multiplies only one term by t. 25,000 − 4,334 has no meaning in this context (there's no reason to subtract the current annual cost from the installation cost), and 2,712t alone doesn't represent annual savings — the true annual savings requires subtracting 2,712 from 4,334 first, not from 25,000.*

**D.** 25,000 > (4,332/2,712)t 

  *The numerator 4,332 is a miscopy of 4,334, and the expression divides the two energy costs rather than subtracting them. Annual savings is the difference between the old and new annual costs (4,334 − 2,712), not their ratio.*

*Difficulty: sat-hardest*

---

##### Q24
y ≤ 3x + 1 and x − y > 1. Which of the following ordered pairs (x, y) satisfies the system of inequalities above?

**A.** (−2, −1) 

  *At (−2, −1), y ≤ 3x + 1 becomes −1 ≤ 3(−2) + 1 = −5, and −1 ≤ −5 is false since −1 is greater than −5. This fails the first constraint before the second matters.*

**B.** (−1, 3) 

  *At (−1, 3), y ≤ 3x + 1 becomes 3 ≤ 3(−1) + 1 = −2, which is false — 3 is not less than or equal to −2. A likely source of the error is computing 3(−1) as +3 instead of −3, which would make the bound look like 4 instead of −2.*

**C.** (1, 5) 

  *At (1, 5), y ≤ 3x + 1 becomes 5 ≤ 3(1) + 1 = 4, which is false since 5 is greater than 4. This point looks plausible because both coordinates are small positive integers, but it fails the first constraint by exactly 1.*

**D.** (2, −1) **(Correct)**

  *Correct. At (2, −1): y ≤ 3x + 1 becomes −1 ≤ 3(2) + 1 = 7, true. x − y > 1 becomes 2 − (−1) = 3, and 3 > 1, true. Both conditions hold.*

*Difficulty: medium*

---

##### Q25
The length of a rectangle is 50 inches and the width is x inches. The perimeter is at most 210 inches. Which inequality represents this situation?

**A.** 2x + 100 ≤ 210 **(Correct)**

  *Correct. Perimeter = 2(length) + 2(width) = 2(50) + 2x = 100 + 2x. 'At most 210' means ≤ 210: 2x + 100 ≤ 210.*

**B.** 2x + 100 ≥ 210 

  *The perimeter expression, 2x + 100, is set up correctly, but the direction is reversed: 'at most 210' is a ceiling (≤), and this uses ≥, requiring the perimeter to be at least 210 rather than capping it.*

**C.** 2x + 50 ≤ 210 

  *This doubles the width term (2x) but not the length term — the constant should be 2(50) = 100, not 50, since perimeter doubles both the length and the width. Only one of the two sides was correctly doubled.*

**D.** 2x + 50 ≥ 210 

  *Both errors together: the length term isn't doubled (50 instead of 100) and the direction is reversed (≥ instead of ≤). Neither the perimeter formula nor the inequality direction matches the problem.*

*Difficulty: easy*

---

##### Q26
A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600 pounds. What is the maximum number of boxes this truck can tow in a trailer with a weight of 500 pounds if each box weighs 120 pounds?

**A.** 34 **(Correct)**

  *Correct. 500 + 120n ≤ 4,600, so 120n ≤ 4,100, and n ≤ 34.16…. Since n must be a whole number and the question asks for the maximum, round down to 34. Check: 500 + 120(34) = 4,580, within the limit, while 35 boxes would give 500 + 120(35) = 4,700, over it.*

**B.** 35 

  *This is 34.16… rounded to the nearest whole number rather than rounded down as the constraint 'no more than' requires. 35 boxes weighs 500 + 120(35) = 4,700 pounds, which exceeds the 4,600-pound limit — rounding up violates the very constraint being solved.*

**C.** 38 

  *This is 4,600/120 = 38.3…, rounded down — the 500-pound weight of the trailer itself was never subtracted before dividing. The trailer's own weight has to come out of the 4,600-pound limit before any boxes are added.*

**D.** 39 

  *This is (4,600 + 500)/120 ≈ 39.16…, rounded down — the trailer weight was added to the limit instead of subtracted from it. A sign error at the setup stage produces a wrong answer even when every later step is executed correctly.*

*Difficulty: hard*

---

##### Q27
A city employee will plant two types of bushes, azaleas and boxwoods, in a park. There will be no more than 164 total bushes planted, and the number of azaleas planted will be at most three times the number of boxwoods planted. Which of the following systems of inequalities best represents this situation, where a is the number of azaleas that will be planted, and b is the number of boxwoods that will be planted?

**A.** a + b ≥ 164 and 3a ≥ b 

  *The total-count direction is reversed (≥ instead of ≤, requiring at least 164 bushes rather than capping the total), and the ratio inequality is inverted (3a ≥ b instead of a ≤ 3b) — algebraically these say different things whenever a and b aren't equal, and the inversion changes which variable the '3' multiplies.*

**B.** a + b ≥ 164 and a ≤ 3b 

  *The total-count direction is reversed (≥ instead of ≤), while the ratio condition (a ≤ 3b) is stated correctly. 'No more than 164 total' is a cap, not a floor.*

**C.** a + b ≤ 164 and 3a ≥ b 

  *The total-count direction is correct, but the ratio condition is written as 3a ≥ b instead of a ≤ 3b. These aren't algebraically equivalent — 3a ≥ b compares three times the azalea count to the boxwood count, a much looser relationship than capping azaleas at three times the boxwoods.*

**D.** a + b ≤ 164 and a ≤ 3b **(Correct)**

  *Correct. Total bushes no more than 164: a + b ≤ 164. Azaleas at most three times boxwoods: a ≤ 3b.*

*Difficulty: hard*

---

##### Q28
A particular botanist classifies a species of plant as tall if its typical height when fully grown is more than 100 centimeters. Each of the following inequalities represents the possible heights h, in centimeters, for a specific plant species when fully grown. Which inequality represents the possible heights h, in centimeters, for a tall plant species?

**A.** 106 < h < 158 **(Correct)**

  *Correct. A species is 'tall' if its height is more than 100 cm — every value in the range must exceed 100. 106 < h < 158 satisfies this: the entire interval lies above 100.*

**B.** 80 < h < 100 

  *This range lies entirely at or below 100 cm — none of it qualifies as tall, since 'more than 100' requires every value to exceed 100, and this interval's upper bound is exactly 100, not above it.*

**C.** 42 < h < 87 

  *This range lies entirely well below the 100 cm threshold — a species with these heights would be classified as short or medium, not tall, under the stated definition.*

**D.** 17 < h < 85 

  *This range lies entirely below the threshold and is the smallest of the four options — none of these heights would meet the 'more than 100 cm' definition of tall.*

*Difficulty: easy*

---

##### Q29
y > 7x − 4. For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality? Table A: (x, y) = (3, 13), (5, 27), (8, 48). Table B: (x, y) = (3, 17), (5, 31), (8, 52). Table C: (x, y) = (3, 21), (5, 27), (8, 52). Table D: (x, y) = (3, 21), (5, 35), (8, 56).

**A.** Table A: (3, 13), (5, 27), (8, 48) 

  *At x = 3 the boundary is 7(3) − 4 = 17, and 13 is well below it — 13 > 17 is false. This table's y-values track below the required threshold at every listed x, as if the inequality were reversed.*

**B.** Table B: (3, 17), (5, 31), (8, 52) 

  *Each y-value here equals the boundary exactly (7x − 4) rather than exceeding it: at x = 3, 7(3) − 4 = 17 = y. Since the inequality is strict (>), a y-value equal to the boundary fails; this table was built from the equation y = 7x − 4, not the inequality.*

**C.** Table C: (3, 21), (5, 27), (8, 52) 

  *The first pair passes (21 > 17), but the second fails: at x = 5 the boundary is 31, and 27 > 31 is false. Checking only the first row and assuming the pattern holds is what makes this distractor work — every row has to be checked independently.*

**D.** Table D: (3, 21), (5, 35), (8, 56) **(Correct)**

  *Correct. At x = 3, the boundary value is 7(3) − 4 = 17, and y = 21 > 17 ✓. At x = 5, the boundary is 7(5) − 4 = 31, and y = 35 > 31 ✓. At x = 8, the boundary is 7(8) − 4 = 52, and y = 56 > 52 ✓. All three pairs satisfy y > 7x − 4.*

*Difficulty: hard*

---

##### Q30
Adam's school is a 20-minute walk or a 5-minute bus ride away from his house. The bus runs every 30 minutes, and the number of minutes, w, that Adam waits for the bus varies between 0 and 30. Which of the following inequalities gives the values of w for which it would be faster for Adam to walk to school?

**A.** w − 5 < 20 

  *This subtracts the 5-minute ride time instead of adding it, treating the ride as though it shortened the wait rather than extending the total bus trip. The bus's total travel time is wait plus ride, not wait minus ride.*

**B.** w − 5 > 20 

  *This also subtracts instead of adds (the same error as choice A) and additionally reverses the comparison direction — describing a much smaller quantity being compared the wrong way to 20.*

**C.** w + 5 < 20 

  *The ride time is added correctly (w + 5), but the direction is reversed: 'faster to walk' means the bus takes longer than 20 minutes, i.e., w + 5 > 20 — this choice states the opposite, that the bus total is under 20 minutes, which would make the bus faster instead.*

**D.** w + 5 > 20 **(Correct)**

  *Correct. Taking the bus takes w minutes of waiting plus 5 minutes of riding, or w + 5 minutes total. Walking takes 20 minutes. It's faster to walk exactly when walking takes less time than the bus, i.e., the bus total exceeds 20 minutes: w + 5 > 20.*

*Difficulty: medium*

---

##### Q31
A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

**A.** 7.35d + 6.2s ≤ 300 and d ≥ 2s **(Correct)**

  *Correct. Weight: 7.35 pounds per detergent container plus 6.2 pounds per fabric softener container, no more than 300 pounds total: 7.35d + 6.2s ≤ 300. Ratio: at least twice as many detergent containers as fabric softener containers means d ≥ 2s.*

**B.** 7.35d + 6.2s ≤ 300 and 2d ≥ s 

  *The weight constraint is correct, but the ratio condition is inverted: 2d ≥ s says twice the detergent count is at least the softener count — a much weaker and different condition than 'at least twice as many detergent containers as softener containers,' which is d ≥ 2s.*

**C.** 14.7d + 6.2s ≤ 300 and d ≥ 2s 

  *The detergent weight is doubled to 14.7 rather than left at 7.35 — a likely source is confusing 'twice as many containers' (a count relationship between d and s) with 'twice the weight per container,' which isn't what the problem states. The ratio condition itself, d ≥ 2s, is correct.*

**D.** 14.7d + 6.2s ≤ 300 and 2d ≥ s 

  *Both errors together: the per-container weight is doubled to 14.7 (confusing the count ratio with a weight change) and the ratio condition is inverted to 2d ≥ s instead of d ≥ 2s.*

*Difficulty: hard*

---

##### Q32
A salesperson's total earnings consist of a base salary of x dollars per year, plus commission earnings of 11% of the total sales the salesperson makes during the year. This year, the salesperson has a goal for the total earnings to be at least 3 times and at most 4 times the base salary. Which of the following inequalities represents all possible values of total sales s, in dollars, the salesperson can make this year in order to meet that goal?

**A.** 2x ≤ s ≤ 3x 

  *This never introduces the commission rate at all — it treats total sales as directly bounded by 2x and 3x, as though sales and earnings were the same quantity. The 0.11 conversion between sales dollars and commission dollars is missing entirely, even though the bounds (2x and 3x) do reflect the correct subtraction of x from the earnings goal.*

**B.** (2/0.11)x ≤ s ≤ (3/0.11)x **(Correct)**

  *Correct. Total earnings = base salary plus commission = x + 0.11s. The goal is 3x ≤ x + 0.11s ≤ 4x. Subtracting x from all three parts gives 2x ≤ 0.11s ≤ 3x, and dividing by 0.11 gives (2/0.11)x ≤ s ≤ (3/0.11)x.*

**C.** 3x ≤ s ≤ 4x 

  *This restates the goal's bounds on total earnings (3x and 4x) directly as bounds on s, skipping both the subtraction of the base salary x and the division by the commission rate 0.11. Total sales and total earnings are different quantities related by s = (earnings − x)/0.11, not equal to each other.*

**D.** (3/0.11)x ≤ s ≤ (4/0.11)x 

  *This correctly divides by 0.11 but skips the step of subtracting the base salary x from the earnings goal first — using 3x and 4x directly instead of the post-subtraction values 2x and 3x. The base salary is part of total earnings, not part of commission, so it has to be removed before dividing by the commission rate.*

*Difficulty: sat-hardest*

---

##### Q33
A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p?

**A.** p > 0.20(300 − 36), where p ≤ 150 

  *This subtracts 36 from 300 before applying the 20% threshold, as though the first group's 36 selections should be removed from the pool being measured against 20%, rather than added to p as part of the total count. The threshold applies to all 300 participants, and the 36 who already chose the first picture need to be added to p, not subtracted from the base.*

**B.** p > 0.20(300 + 36), where p ≤ 150 

  *This adds 36 to 300 before applying the 20% threshold — treating the 36 as an addition to the total participant count rather than as part of the count of people who chose the first picture. 300 is already the total number of participants; 36 belongs on the p-side of the comparison, describing how many already chose that picture, not how many participants there were.*

**C.** p − 36 > 0.20(300), where p ≤ 150 

  *This subtracts 36 from p instead of adding it, describing p as though it already included the first group's 36 selections and needed them removed — but p is defined as the count from the second group of 150 only, separate from the 36. The correct total count who chose the first picture is p + 36, not p − 36.*

**D.** p + 36 > 0.20(300), where p ≤ 150 **(Correct)**

  *Correct. The total number who chose the first picture is 36 (from the first group) plus p (from the second group). 'More than 20% of all participants' means this total exceeds 0.20(300) = 60: p + 36 > 0.20(300). The added condition p ≤ 150 reflects that p can be at most the size of the second group.*

*Difficulty: sat-hardest*

---

##### Q34
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of 6 and 12, which inequality represents the possible lengths, x, of the third side of the triangle?

**A.** x < 18 

  *This applies the triangle inequality to only one pair of sides — 6 + 12 > x, giving x < 18 — and omits the second condition, 6 + x > 12, which gives x > 6. Without a lower bound, this choice would allow a 'third side' of length 0.001, which cannot form a triangle with sides 6 and 12.*

**B.** x > 18 

  *This has the correct boundary value (18) but the wrong direction — the triangle inequality requires the third side to be less than the sum of the other two (x < 18), not greater than it. A third side longer than 18 couldn't connect to the other two sides at all.*

**C.** 6 < x < 18 **(Correct)**

  *Correct. The triangle inequality applies to every pair of sides. 6 + 12 > x gives x < 18. 6 + x > 12 gives x > 6. (12 + x > 6 is automatically true for any positive x.) Combining the two binding conditions gives 6 < x < 18.*

**D.** x < 6 or x > 18 

  *This describes the complement of the correct range — every value the actual triangle inequality excludes, rather than the values it permits. A third side must sit strictly between 6 and 18; values outside that band (x < 6 or x > 18) are exactly the ones that fail to form a triangle.*

*Difficulty: hard*

---

##### Q35
A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x, in inches, of the box?

**A.** 0 < x ≤ 10 **(Correct)**

  *Correct. Base perimeter = 2(length + width) = 2(2.5x + x) = 2(3.5x) = 7x. Adding the height: 7x + 60 ≤ 130, so 7x ≤ 70, giving x ≤ 10. Width must also be positive, so 0 < x ≤ 10.*

**B.** 0 < x ≤ 11 2/3 

  *This is 70/6, which comes from using a perimeter coefficient of 6 instead of 7 — likely from computing length + width as 2.5x + x = 3.5x but then doubling only one of the two terms (2(2.5x) + x = 6x) instead of doubling the full sum (2(3.5x) = 7x).*

**C.** 0 < x ≤ 17 1/2 

  *This is 70/4, treating the base perimeter as though it were 4x — as if length and width were both simply x, ignoring that length = 2.5x. This drops the '2.5 times the width' relationship for the length and uses a generic square-ish perimeter formula 2(x + x) = 4x instead of 2(2.5x + x) = 7x.*

**D.** 0 < x ≤ 20 

  *This is 70/3.5, using only the sum of length and width (2.5x + x = 3.5x) without doubling it for the perimeter — the perimeter of a rectangle is twice the sum of length and width, not the sum itself.*

*Difficulty: sat-hardest*

---

##### Q36
Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

**A.** 38 

  *This solves 0.9(10h) ≥ 270 for the raised-rate hours in isolation, getting h ≥ 30, and then adds 8 — mistaking the dollar figure from '$8 per hour' for a number of hours to add on, rather than properly folding the first 10 hours' earnings into a single combined inequality, 0.9(80 + 10h) ≥ 270. The two parts of the problem never get combined correctly.*

**B.** 33 

  *This comes from distributing the 90% incorrectly across the hourly term — computing 0.9 × 10h as 6h instead of 9h — which changes the correct 72 + 9h ≥ 270 into 72 + 6h ≥ 270, giving 6h ≥ 198 and h ≥ 33.*

**C.** 22 **(Correct)**

  *Correct. Total earnings for the week are 8(10) + 10h = 80 + 10h dollars, where h is hours worked at the raised rate. Savings are 90% of earnings: 0.9(80 + 10h) ≥ 270. Distributing gives 72 + 9h ≥ 270, so 9h ≥ 198, and h ≥ 22. The least number of hours is 22.*

**D.** 16 

  *This inverts the percent step — multiplying the $270 target by 0.9 (getting $243, meant to represent 90% being saved) instead of dividing by 0.9 to find how much must be earned to save $270. Continuing with 243 − 80 = 163 and 163/10 ≈ 16.3, this then rounds down to 16 — but a 'least number of hours needed' question requires rounding up, since 16 hours of work wouldn't actually reach the savings target.*

*Difficulty: hard*

---

##### Q37
y > 2x − 1 and 2x > 5. Which of the following consists of the y-coordinates of all the points that satisfy the system of inequalities above?

**A.** y > 6 

  *This overshoots the bound — a likely source is adding 2 (rather than subtracting 1) when combining 2x > 5 with y > 2x − 1, or otherwise mishandling the −1 in the second inequality's substitution. The correct chain is y > 2x − 1 > 5 − 1 = 4, not 5 + 1 = 6.*

**B.** y > 4 **(Correct)**

  *Correct. From 2x > 5, substituting into y > 2x − 1 gives y > 2x − 1 > 5 − 1 = 4, so y > 4 for every point satisfying both inequalities.*

**C.** y > 5/2 

  *This reports the bound on x (x > 5/2, from dividing 2x > 5 by 2) instead of following through to find the bound on y. The question asks for the range of y-values, which requires substituting the x-bound into y > 2x − 1, not stopping at the x-bound itself.*

**D.** y > 3/2 

  *This is x > 5/2 manipulated further rather than substituted into the y-inequality — a case of continuing to work with the x-constraint instead of ever bringing in y > 2x − 1 to connect x to y.*

*Difficulty: sat-hardest*

---

##### Q38
11x + 14y ≤ 115. Anthony will spend at most $115 to purchase x small cheese pizzas and y large cheese pizzas for a team dinner. The given inequality represents this situation. Which of the following is the best interpretation of 14y in this context?

**A.** The amount, in dollars, Anthony will spend on each large cheese pizza 

  *This describes 14y as a per-pizza price rather than a total. 14 is the per-pizza price, but 14y (with y being the quantity purchased) is the total spent across all y large pizzas, not the cost of just one.*

**B.** The amount, in dollars, Anthony will spend on each small cheese pizza 

  *This attaches the term to the wrong pizza size entirely — 14y involves y, the number of large pizzas, not small pizzas — and also describes it as a per-item price rather than a total, compounding the error.*

**C.** The total amount, in dollars, Anthony will spend on large cheese pizzas **(Correct)**

  *Correct. y is the number of large pizzas, and 14 is the price per large pizza, so 14y is the total dollars spent on all large pizzas combined — not the price of a single one.*

**D.** The total amount, in dollars, Anthony will spend on small cheese pizzas 

  *This attaches 14y to small pizzas, but y is defined as the number of large pizzas, and it's 11x — not 14y — that involves x, the number of small pizzas. The variable names carry the meaning here, and this choice swaps which term belongs to which pizza size.*

*Difficulty: medium*

---

##### Q39
A team hosting an event to raise money for new uniforms plans to sell at least 140 tickets before this event and at least 220 tickets during this event to raise a total of at least $5,820 from all tickets sold. The price of a ticket during this event is $3 less than the price of a ticket sold before this event. Which inequality represents this situation, where x is the price, in dollars, of a ticket sold during this event?

**A.** 140(x + 3) + 220x ≤ 5,820 

  *The price relationship is set up correctly (x + 3 for the before-event price), but the direction is reversed: 'at least $5,820' is a floor (≥), and this uses ≤, capping revenue rather than setting a minimum fundraising target.*

**B.** 140(x + 3) + 220x ≥ 5,820 **(Correct)**

  *Correct. x is the price during the event, and the price before the event is $3 more (since the during-event price is $3 less than the before-event price): x + 3. Revenue from before-event tickets is 140(x + 3); revenue from during-event tickets is 220x. Total revenue must be at least $5,820: 140(x + 3) + 220x ≥ 5,820.*

**C.** 140(x − 3) + 220x ≤ 5,820 

  *This computes the before-event price as x − 3 instead of x + 3. Since x is the during-event price and the during-event price is $3 less than the before-event price, the before-event price must be higher, i.e., x + 3 — not lower. This also uses the wrong direction (≤ instead of ≥).*

**D.** 140(x − 3) + 220x ≥ 5,820 

  *This gets the inequality direction right (≥, matching 'at least') but computes the before-event price as x − 3 instead of x + 3, understating it relative to the correct value. Since the during-event price is defined as $3 less than the before-event price, solving for the before-event price requires adding 3 to x, not subtracting.*

*Difficulty: hard*

---

#### Linear functions (71 items)

##### Q1
The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height h, in feet, of the front of the roller-coaster car s seconds after it starts up the hill?

**A.** h = 8s + 15 **(Correct)**

  *Correct. The starting height, 15, is the value when s = 0, so it is the constant. The climb rate, 8 feet per second, is per one second, so it belongs in the coefficient slot: h = 8s + 15.*

**B.** h = 15s + 335/8 

  *This swaps which number is the rate — using 15 (the starting height) as the per-second climb instead of 8 — and then re-solves for an intercept using a garbled version of the setup, landing on a fraction that matches no quantity in the problem. That fraction is itself the tell that the substitution went wrong.*

**C.** h = 8s + 335/15 

  *The rate, 8, is in the right place here, but the intercept was rebuilt through the same garbled process as choice B instead of being read directly off the problem: the car starts at a stated height of 15 feet, not a fraction of it.*

**D.** h = 15s + 8 

  *This is the clean version of the slope/intercept swap: 15 (the starting height, which belongs in the constant slot) is used as the rate, and 8 (the per-second rate) is used as the intercept.*

*Difficulty: medium*

---

##### Q2
If f is the function defined by f(x) = (2x − 1)/3, what is the value of f(5)?

**A.** 4/3 

  *This treats the numerator as 2(x − 1) instead of 2x − 1, pulling the 2 across the subtraction, and then multiplies the denominator by that same 2 as well: 2(5 − 1)/(3 × 2) = 8/6 = 4/3.*

**B.** 7/3 

  *This divides only the 2x term by 3 and treats the −1 as a separate whole unit instead of part of the numerator: 2(5)/3 − 1 = 10/3 − 3/3 = 7/3.*

**C.** 3 **(Correct)**

  *Correct. f(5) = (2(5) − 1)/3 = (10 − 1)/3 = 9/3 = 3.*

**D.** 9 

  *This evaluates the numerator correctly, 2(5) − 1 = 9, and then forgets to divide by the denominator at all.*

*Difficulty: easy*

---

##### Q3
The given equation represents the distance d, in inches, where t represents the number of seconds since an object started moving: d = 16t. Which of the following is the best interpretation of 16 in this context?

**A.** The object moved a total of 16 inches. 

  *16 is not a fixed total — it is multiplied by t, so the total distance keeps changing as t changes. A number attached to the variable is a rate, not a fixed amount.*

**B.** The object moved a total of 16t inches. 

  *This restates the entire right-hand side of the equation rather than isolating what the number 16 alone represents. 16t is the total distance; the question asks specifically about the coefficient.*

**C.** The object is moving at a rate of 16 inches per second. **(Correct)**

  *Correct. 16 is the coefficient on t, so it is the change in distance per one second — a rate, in inches per second.*

**D.** The object is moving at a rate of 1/16 inches per second. 

  *This inverts the rate, as though the equation were solved for t instead of d — t = d/16 has a coefficient of 1/16, but that describes seconds per inch, not the rate this equation actually gives.*

*Difficulty: easy*

---

##### Q4
The function g is defined by g(x) = −x + 8. What is the value of g(0)?

**A.** −8 

  *This distributes the negative sign across the entire rule, as though g(x) = −(x + 8), giving g(0) = −(0 + 8) = −8. The negative sign belongs only to x, not to the constant 8.*

**B.** 0 

  *This assumes any function evaluated at an input of zero must return zero. That is true only for functions with no constant term; here the rule still has +8 to add after multiplying by the input.*

**C.** 4 

  *This finds the input where g(x) = x instead of evaluating g(0): −x + 8 = x gives 8 = 2x, so x = 4. That answers a different, unasked question — where the function's output equals its input.*

**D.** 8 **(Correct)**

  *Correct. g(0) = −(0) + 8 = 8.*

*Difficulty: easy*

---

##### Q5
The line graphed in the xy-plane models the total cost, in dollars, for a cab ride, y, in a certain city during nonpeak hours, based on the number of miles traveled, x. The line passes through (0, 5) and (5, 15). According to the graph, what is the cost for each additional mile traveled, in dollars, of a cab ride?

**A.** $2.00 **(Correct)**

  *Correct. The slope is the cost per mile: (15 − 5)/(5 − 0) = 10/5 = $2.00 per mile.*

**B.** $2.60 

  *This comes from reading the rise and run off slightly misaligned grid points instead of the two labeled points on the line, which inflates the slope above the true $2.00 per mile.*

**C.** $3.00 

  *This is not the slope at all — it mistakes the flat starting fee (the y-intercept, $5) for the per-mile rate. A graph's steepness is what changes per mile; where it starts is a separate quantity.*

**D.** $5.00 

  *This reads the cost at a single point on the graph (the $5 starting fee) as though it were the per-mile rate, rather than computing the change between two points.*

*Difficulty: medium*

---

##### Q6
The graph shown models the number of candy bars a certain machine wraps with a label in x seconds. The line passes through (1, 60) and (3, 140). According to the graph, what is the estimated number of candy bars the machine wraps with a label per second?

**A.** 2 

  *This reads the number of seconds between the two labeled points rather than computing the rate — it reports the run, not the slope.*

**B.** 40 **(Correct)**

  *Correct. Rate = (140 − 60)/(3 − 1) = 80/2 = 40 candy bars per second.*

**C.** 78 

  *This reads a single point's height off the graph as though it were the rate, rather than computing the change in output between two points.*

**D.** 80 

  *This reports the rise alone (140 − 60 = 80) and forgets to divide by the corresponding run (3 − 1 = 2), which is what turns a change into a per-second rate.*

*Difficulty: medium*

---

##### Q7
Some values of the linear function f are shown in the table below: when x = 1, f(x) = 5; when x = 3, f(x) = 13; when x = 5, f(x) = 21. Which of the following defines f?

**A.** f(x) = 2x + 3 

  *This fits the point (1, 5) — check: 2(1) + 3 = 5 — but the slope of 2 doesn't match the table's actual rate of change: at x = 3 it predicts f(3) = 9, not 13. One point checked is not enough to confirm a line.*

**B.** f(x) = 3x + 2 

  *This also fits (1, 5) — 3(1) + 2 = 5 — but fails at x = 3, predicting f(3) = 11 instead of 13. It was accepted without checking a second row of the table.*

**C.** f(x) = 4x + 1 **(Correct)**

  *Correct. Slope: (13 − 5)/(3 − 1) = 8/2 = 4, confirmed by the outer pair: (21 − 13)/(5 − 3) = 8/2 = 4. Then f(1) = 4(1) + b = 5 gives b = 1.*

**D.** f(x) = 5x 

  *This forces the line through the origin (assumes b = 0) and treats f(1)/1 = 5 as the slope. It happens to satisfy the first row, 5(1) = 5, but at x = 3 it gives 15, not 13 — a table of three points needs the actual intercept, not an assumption that it's zero.*

*Difficulty: medium*

---

##### Q8
The function h is defined by h(x) = 3x − 7. What is the value of h(−2)?

**A.** −13 **(Correct)**

  *Correct. h(−2) = 3(−2) − 7 = −6 − 7 = −13.*

**B.** −10 

  *This evaluates at x = −1 instead of x = −2 — a one-place misread of the input: 3(−1) − 7 = −3 − 7 = −10.*

**C.** 10 

  *This makes the same off-by-one substitution as choice B, evaluating at x = −1 instead of x = −2, and then also drops the negative sign when reporting the final value.*

**D.** 13 

  *This flips the sign of both terms in the rule, as though h(x) = −3x + 7, so the two sign errors compound instead of cancel: −3(−2) + 7 = 6 + 7 = 13.*

*Difficulty: easy*

---

##### Q9
Marisol drove 3 hours from City A to City B. The equation below estimates the distance d, in miles, Marisol traveled after driving for t hours: d = 45t. Which of the following does 45 represent in the equation?

**A.** Marisol took 45 trips from City A to City B. 

  *45 is the coefficient on t, not a count of trips — nothing in the equation counts repeated trips at all.*

**B.** The distance between City A and City B is 45 miles. 

  *This confuses the rate with a fixed total distance. 45 is multiplied by t, so the distance traveled keeps changing as t changes — it isn't a single fixed value.*

**C.** Marisol drove at an average speed of about 45 miles per hour. **(Correct)**

  *Correct. 45 is the coefficient on t (hours), so it is the rate — miles per hour.*

**D.** It took Marisol 45 hours to drive from City A to City B. 

  *This attaches the number to the wrong variable's units. 45 carries units of miles per hour, not hours — and the problem already states the drive took 3 hours.*

*Difficulty: easy*

---

##### Q10
T = 1,000 + 18h. In the equation above, T represents Brittany's total take-home pay, in dollars, for her first week of work, where h represents the number of hours she worked that week and 1,000 represents a sign-on bonus. If Brittany's total take-home pay was $1,576, for how many hours was Brittany paid for her first week of work?

**A.** 16 

  *This doubles the hourly rate before dividing: (1,576 − 1,000)/36 = 576/36 = 16, instead of dividing by the actual $18 rate.*

**B.** 32 **(Correct)**

  *Correct. 1,576 − 1,000 = 576 in wages, and 576/18 = 32 hours.*

**C.** 55 

  *This sets up the fixed $1,000 bonus as the part that varies with hours instead of the total pay: 1,000/18 ≈ 55.6, truncated to 55, rather than subtracting the bonus from the total pay first.*

**D.** 88 

  *This divides the total pay by the hourly rate without first subtracting the $1,000 sign-on bonus: 1,576/18 ≈ 87.6, rounded to 88.*

*Difficulty: medium*

---

##### Q11
The function g is defined as g(x) = 5x + a, where a is a constant. If g(4) = 31, what is the value of a?

**A.** 30 

  *This treats "5x" as 5 − 4 = 1 instead of 5 × 4 = 20 — reading the coefficient's relationship to the input as subtraction rather than multiplication — giving a = 31 − 1 = 30.*

**B.** 22 

  *This subtracts the coefficient and the input separately instead of their product: 31 − 5 − 4 = 22, rather than 31 − 5(4).*

**C.** 11 **(Correct)**

  *Correct. 5(4) + a = 31 → 20 + a = 31 → a = 11.*

**D.** −23 

  *This solves the equation with the constant's sign flipped (treating the rule as 5x − a) and also mishandles the product 5(4) along the way — two separate slips compounding rather than one clean swap.*

*Difficulty: easy*

---

##### Q12
The function f is defined by the equation f(x) = 100x + 2. What is the value of f(x) when x = 9?

**A.** 111 

  *This adds the coefficient, input, and constant together instead of multiplying the coefficient by the input first: 100 + 9 + 2 = 111.*

**B.** 118 

  *This swaps the coefficient and the constant, treating 2 as the rate and 100 as the starting value: 100 + 2(9) = 118.*

**C.** 900 

  *This computes 100 × 9 = 900 correctly but forgets to add the constant term, +2.*

**D.** 902 **(Correct)**

  *Correct. f(9) = 100(9) + 2 = 900 + 2 = 902.*

*Difficulty: easy*

---

##### Q13
On January 1, 2015, a city's minimum hourly wage was $9.25. It will increase by $0.50 on the first day of the year for the next 5 years. Which of the following functions best models the minimum hourly wage, in dollars, x years after January 1, 2015, where x = 1, 2, 3, 4, 5?

**A.** f(x) = 9.25 − 0.50x 

  *This subtracts the annual raise instead of adding it, modeling a wage that falls instead of rises.*

**B.** f(x) = 9.25x − 0.50 

  *This swaps which number is the rate and which is the constant, and flips the constant's sign in the process.*

**C.** f(x) = 9.25 + 0.50x **(Correct)**

  *Correct. The starting wage, $9.25, is the value at x = 0, so it is the constant; the $0.50 annual raise is the rate.*

**D.** f(x) = 9.25x + 0.50 

  *This uses the starting wage, 9.25, as the per-year rate and the actual rate, 0.50, as the constant — a slope/intercept swap.*

*Difficulty: medium*

---

##### Q14
The length, y, of a white whale was 162 centimeters (cm) when it was born and increased an average of 4.8 cm per month for the first 12 months after it was born. Which equation best represents this situation, where x is the number of months after the whale was born and y is the length, in cm, of the whale?

**A.** y = 162x 

  *This forces the line through the origin, treating the birth length as a rate rather than a starting value, and drops the actual monthly growth rate entirely.*

**B.** y = 162x + 162 

  *This uses 162 as both the rate and the constant, when 162 is only the starting length — it never appears as a rate anywhere in the problem.*

**C.** y = 4.8x + 4.8 

  *This uses the growth rate, 4.8, as both the coefficient and the constant, dropping the actual 162 cm starting length entirely.*

**D.** y = 4.8x + 162 **(Correct)**

  *Correct. The starting length, 162, is the value at x = 0, so it is the constant; the growth rate, 4.8 cm per month, is the coefficient.*

*Difficulty: medium*

---

##### Q15
The function h is defined by h(x) = x + 200. What is the value of h(50)?

**A.** 200 

  *This reports the constant term alone and forgets to add the input, 50.*

**B.** 250 **(Correct)**

  *Correct. h(50) = 50 + 200 = 250.*

**C.** 10,000 

  *This multiplies the input by the constant instead of adding them: 50 × 200 = 10,000.*

**D.** 50,200 

  *This concatenates the digits of the input and the constant instead of computing their sum — reading "50" and "200" as adjacent digits rather than two numbers to add.*

*Difficulty: easy*

---

##### Q16
The graph of the function f is a line in the xy-plane. If the line has slope 3/4 and f(0) = 3, which of the following defines f?

**A.** f(x) = 3/4 x − 3 

  *This uses the correct slope but flips the sign of the intercept — f(0) = 3, not −3.*

**B.** f(x) = 3/4 x + 3 **(Correct)**

  *Correct. The slope, 3/4, is the coefficient; f(0) = 3 is the constant.*

**C.** f(x) = 4x − 3 

  *This inverts the slope fraction (using 4 instead of 3/4) and also flips the intercept's sign.*

**D.** f(x) = 4x + 3 

  *This keeps the correct intercept but inverts the slope fraction, using 4 (the reciprocal-ish whole number) instead of 3/4.*

*Difficulty: easy*

---

##### Q17
Oxygen gas is placed inside a tank with a constant volume. The graph shows the estimated temperature y, in kelvins, of the oxygen gas when its pressure is x atmospheres; the line passes through (1, 200) and (9, 1,000). What is the estimated temperature, in kelvins, of the oxygen gas when its pressure is 6 atmospheres?

**A.** 6 

  *This reports the given pressure value itself instead of the temperature the question asks for — confusing the input with the output.*

**B.** 60 

  *This is off by a factor of ten from the correct estimate, consistent with misreading the graph's gridline scale by one line.*

**C.** 700 **(Correct)**

  *Correct. Slope = (1,000 − 200)/(9 − 1) = 800/8 = 100 kelvins per atmosphere. At x = 6: 200 + 100(6 − 1) = 200 + 500 = 700.*

**D.** 760 

  *This misreads the y-intercept from the graph as 160 instead of the correct 100 — off by one gridline square — giving 100(6) + 160 = 760.*

*Difficulty: medium*

---

##### Q18
Robert rented a truck to transport materials he purchased from a hardware store. He was charged an initial fee of $20.00 plus an additional $0.70 per mile driven. If the truck was driven 38 miles, what was the total amount Robert was charged?

**A.** $46.60 **(Correct)**

  *Correct. 20 + 0.70(38) = 20 + 26.60 = $46.60.*

**B.** $52.90 

  *This comes from a multiplication slip in computing 0.70 × 38: the mileage charge is miscomputed as $32.90 instead of $26.60, then added to the $20 fee.*

**C.** $66.90 

  *This comes from a different multiplication slip in the same step: 0.70 × 38 is miscomputed as $46.90 instead of $26.60, then added to the $20 fee.*

**D.** $86.50 

  *This comes from a larger multiplication slip in computing 0.70 × 38, landing on $66.50 instead of $26.60 before adding the $20 fee.*

*Difficulty: medium*

---

##### Q19
P(t) = 250 + 10t. The population of snow leopards in a certain area can be modeled by the function P defined above, where P(t) is the population t years after 1990. Of the following, which is the best interpretation of the equation P(30) = 550?

**A.** The snow leopard population in this area is predicted to be 30 in the year 2020. 

  *This swaps the input and output — reporting t = 30 as though it were the population — and gets the year wrong too.*

**B.** The snow leopard population in this area is predicted to be 30 in the year 2030. 

  *This makes the same input/output swap as choice A, and also misreads the year by using t itself (30) as the year offset incorrectly rather than adding it to 1990 correctly.*

**C.** The snow leopard population in this area is predicted to be 550 in the year 2020. **(Correct)**

  *Correct. t = 30 years after 1990 is 2020, and P(30) = 550 is the predicted population at that time.*

**D.** The snow leopard population in this area is predicted to be 550 in the year 2030. 

  *This gets the population right but the year wrong — 1990 + 30 is 2020, not 2030.*

*Difficulty: medium*

---

##### Q20
For the linear function f, f(0) = 17 and f(1) = 17. Which equation defines f?

**A.** f(x) = 1/17 

  *This inverts the constant value nonsensically rather than recognizing what an unchanging output means for the function's slope.*

**B.** f(x) = 1 

  *This misreads the fact that the output never changes as meaning the function must be f(x) = x with slope 1, when an unchanging output actually means the slope is 0.*

**C.** f(x) = 17 **(Correct)**

  *Correct. Since f(0) and f(1) are equal, the slope is (17 − 17)/(1 − 0) = 0, so f is the constant function f(x) = 17.*

**D.** f(x) = 34 

  *This adds the two equal outputs together (17 + 17 = 34) instead of recognizing they signal a slope of zero.*

*Difficulty: medium*

---

##### Q21
Hydrogen is placed inside a container and kept at a constant pressure. The graph shows the estimated volume y, in liters, of the hydrogen when its temperature is x kelvins; the line passes through approximately (100, 1) and (800, 11). What is the estimated volume, in liters, of the hydrogen when its temperature is 500 kelvins?

**A.** 0 

  *This assumes the line passes through the origin, ignoring that the graph's volume is already 1 liter at the lowest labeled temperature, not zero.*

**B.** 7/500 

  *This inverts the correct estimate into a fraction, dividing in the wrong direction rather than reading the output directly off the model.*

**C.** 7 **(Correct)**

  *Correct (estimated). Slope ≈ (11 − 1)/(800 − 100) = 10/700 ≈ 0.0143 liters per kelvin. At x = 500: 1 + 400(0.0143) ≈ 1 + 5.7 ≈ 7.*

**D.** 500/7 

  *This divides the input by the estimated output instead of reporting the output itself — answering with x/y instead of y.*

*Difficulty: hard*

---

##### Q22
The graph of the linear function f is shown, crossing the y-axis at (0, 2) and the x-axis at (−5, 0). What is the y-intercept of the graph of y = f(x)?

**A.** (−5, 0) 

  *This is the x-intercept, not the y-intercept — the question asks for the point where the graph crosses the y-axis, which requires x = 0.*

**B.** (2, 0) 

  *This has the right number, 2, but the wrong coordinate position — a y-intercept always has the form (0, y), not (y, 0).*

**C.** (0, 2) **(Correct)**

  *Correct. The graph crosses the y-axis where x = 0, at the point (0, 2).*

**D.** (0, −5) 

  *This keeps the correct coordinate format but plugs in the x-intercept's x-value, −5, mixing the numbers from the two different intercepts.*

*Difficulty: easy*

---

##### Q23
To repair a refrigerator, a technician charges $60 per hour for labor plus $120 for parts. Which function f represents the total amount, in dollars, the technician will charge for this job if it takes x hours?

**A.** f(x) = x + 120 

  *This drops the hourly rate entirely, using a coefficient of 1 instead of 60 on the labor term.*

**B.** f(x) = 60x 

  *This drops the flat $120 parts fee entirely.*

**C.** f(x) = 60x + 120 **(Correct)**

  *Correct. $60 per hour is the rate (coefficient on x); the flat $120 parts fee is the constant.*

**D.** f(x) = 60x − 120 

  *This subtracts the parts fee instead of adding it, as though parts were a discount rather than an additional charge.*

*Difficulty: easy*

---

##### Q24
The function f is defined by f(x) = 80 − 6x. What is the value of f(7)?

**A.** 13 

  *This treats the coefficient and the input as digits to be concatenated rather than multiplied — reading "6x" at x = 7 as the number 67 instead of the product 42 — giving 80 − 67 = 13.*

**B.** 38 **(Correct)**

  *Correct. f(7) = 80 − 6(7) = 80 − 42 = 38.*

**C.** 74 

  *This computes 80 − 6 and forgets to multiply the coefficient by the input at all.*

**D.** 81 

  *This misreads "6x" as "6 − x" instead of "6 times x," computing 80 − (6 − 7) = 80 − (−1) = 81.*

*Difficulty: easy*

---

##### Q25
For the linear function f, the graph of y = f(x) in the xy-plane has a slope of 2 and has a y-intercept at (0, −5). Which equation defines f?

**A.** f(x) = 1/2 x − 5 

  *This inverts the slope, using 1/2 instead of the given slope of 2.*

**B.** f(x) = −1/2 x − 5 

  *This both inverts and flips the sign of the slope.*

**C.** f(x) = −2x − 5 

  *This flips the sign of the slope, using −2 instead of the given slope of 2.*

**D.** f(x) = 2x − 5 **(Correct)**

  *Correct. The slope, 2, is the coefficient; the y-intercept's y-value, −5, is the constant.*

*Difficulty: easy*

---

##### Q26
As part of a science project on evaporation, Amaya measured the height of a liquid in a container over a period of time. The function f(x) = 33 − 0.18x gives the estimated height, in centimeters (cm), of the liquid in the container x days after the start of the project. Which of the following is the best interpretation of 33 in this context?

**A.** The estimated height, in cm, of the liquid at the start of the project **(Correct)**

  *Correct. 33 is the value of f(0) — the estimated height when x = 0, the start of the project.*

**B.** The estimated height, in cm, of the liquid at the end of the project 

  *This confuses the intercept (a starting value, at x = 0) with a value at some later, unspecified endpoint.*

**C.** The estimated change in the height, in cm, of the liquid each day 

  *This is the rate, −0.18, not the intercept, 33 — the two numbers play very different roles in the model.*

**D.** The estimated number of days for all of the liquid to evaporate 

  *This confuses the intercept (f(0) = 33) with the zero of the function (the x-value where f(x) = 0), a completely different calculation.*

*Difficulty: medium*

---

##### Q27
Gabriella deposits $35 in a savings account at the end of each week. At the beginning of the 1st week of a year there was $600 in that savings account. How much money, in dollars, will be in the account at the end of the 4th week of that year?

**A.** 460 

  *This subtracts the weekly deposits instead of adding them: 600 − 35(4) = 460.*

**B.** 635 

  *This adds only one week's deposit instead of all four weeks': 600 + 35 = 635.*

**C.** 639 

  *This adds the weekly deposit amount and the number of weeks together instead of multiplying them: 600 + (35 + 4) = 639, rather than 600 + 35(4).*

**D.** 740 **(Correct)**

  *Correct. By the end of the 4th week, four deposits have been made: 600 + 35(4) = 600 + 140 = 740.*

*Difficulty: medium*

---

##### Q28
In the linear function h, h(0) = 41 and h(1) = 40. Which equation defines h?

**A.** h(x) = −x + 41 **(Correct)**

  *Correct. Slope: (40 − 41)/(1 − 0) = −1. The intercept, h(0) = 41, is the constant.*

**B.** h(x) = −x 

  *This drops the constant term entirely, forcing the line through the origin instead of using the actual intercept, 41.*

**C.** h(x) = −41x 

  *This uses the intercept value, 41, as the slope, when the actual slope is −1.*

**D.** h(x) = −41 

  *This reports the constant with a flipped sign and treats h as a constant function, ignoring that the output does change from 41 to 40.*

*Difficulty: medium*

---

##### Q29
The function g is defined by g(x) = 10x + 8. What is the value of g(x) when x = 8?

**A.** 0 

  *This treats the question as asking for the zero of g rather than its value at x = 8, but reports a placeholder rather than actually solving 10x + 8 = 0.*

**B.** 8 

  *This reports the input back unchanged instead of applying the rule to it at all.*

**C.** 10 

  *This reports the coefficient (slope) instead of evaluating the function.*

**D.** 88 **(Correct)**

  *Correct. g(8) = 10(8) + 8 = 80 + 8 = 88.*

*Difficulty: easy*

---

##### Q30
The number y is 84 less than the number x. Which equation represents the relationship between x and y?

**A.** y = x + 84 

  *This reads "84 less than" as "84 more than," adding instead of subtracting.*

**B.** y = 1/84 x 

  *This misreads "84 less than" as a proportional, divide-by-84 relationship rather than a subtraction.*

**C.** y = 84x 

  *This misreads "84 less than" as "84 times," turning a subtraction into a multiplication.*

**D.** y = x − 84 **(Correct)**

  *Correct. "y is 84 less than x" means y = x − 84.*

*Difficulty: easy*

---

##### Q31
For the linear function f, the table shows three values of x and their corresponding values of f(x): when x = 0, f(x) = 29; when x = 1, f(x) = 32; when x = 2, f(x) = 35. Which equation defines f(x)?

**A.** f(x) = 3x + 29 **(Correct)**

  *Correct. Slope: (32 − 29)/(1 − 0) = 3, confirmed by (35 − 32)/(2 − 1) = 3. The intercept, f(0) = 29, is the constant.*

**B.** f(x) = 29x + 32 

  *This takes the table's first two output values, 29 and 32, and drops them directly into the coefficient and constant slots, rather than computing the actual slope (3) and intercept (29).*

**C.** f(x) = 35x + 29 

  *This does the same thing with a different pair of table values — using the last output, 35, as the slope and the first output, 29, as the constant.*

**D.** f(x) = 32x + 35 

  *This does the same thing with the middle and last output values, 32 and 35, dropped straight into the slope and intercept slots.*

*Difficulty: medium*

---

##### Q32
For a training program, Juan rides his bike at an average rate of 5.7 minutes per mile. Which function m models the number of minutes it will take Juan to ride x miles at this rate?

**A.** m(x) = x/5.7 

  *This inverts the rate, dividing by 5.7 as though it were miles per minute rather than multiplying by 5.7 minutes per mile.*

**B.** m(x) = x + 5.7 

  *This misreads the rate as a flat amount to add rather than a per-mile multiplier.*

**C.** m(x) = x − 5.7 

  *This also misreads the rate as a flat amount, this time subtracted rather than multiplied.*

**D.** m(x) = 5.7x **(Correct)**

  *Correct. 5.7 minutes per mile is the rate, so it belongs in the coefficient slot: minutes = 5.7 × miles.*

*Difficulty: easy*

---

##### Q33
For the linear function f, the graph of y = f(x) in the xy-plane has a slope of 1/4 and passes through the point (0, 5). Which equation defines f?

**A.** f(x) = 1/4 x + 5 **(Correct)**

  *Correct. The slope, 1/4, is the coefficient; the point (0, 5) gives the intercept directly, since its x-coordinate is 0.*

**B.** f(x) = 1/4 x + 1/5 

  *This misreads the point's y-coordinate, 5, as though it needed to be inverted into 1/5, treating it like a rate rather than a value.*

**C.** f(x) = 1/4 x − 5/4 

  *This solves as though the given point were (5, 0) instead of (0, 5) — swapping the point's coordinates before solving for the intercept.*

**D.** f(x) = 1/4 x − 5 

  *This flips the sign of the intercept — the point (0, 5) gives an intercept of +5, not −5.*

*Difficulty: medium*

---

##### Q34
The buildings of a shopping center are designed to allow water to drain from the roof into gutters on the sides of the buildings. The table shows the relationship between the area x, in square feet, of a roof and the amount of water f(x), in gallons, drained from the roof into the gutters over a certain period of time: when x = 2,520, f(x) = 4,536; when x = 3,780, f(x) = 6,804; when x = 5,040, f(x) = 9,072. Which equation could define f?

**A.** f(x) = 0.6x 

  *This divides area by water instead of water by area — 2,520/4,536 ≈ 0.56, which rounds toward this choice — inverting which quantity the rate should be built from.*

**B.** f(x) = 1.8x **(Correct)**

  *Correct. 4,536/2,520 = 1.8, and the ratio holds for the other rows too: 6,804/3,780 = 1.8 and 9,072/5,040 = 1.8.*

**C.** f(x) = 2,268x 

  *This takes half of one water value (4,536 ÷ 2 = 2,268) and uses it directly as the rate, rather than computing the ratio of water to area.*

**D.** f(x) = 4,536x 

  *This uses a raw water value straight from one row of the table as the coefficient, without dividing by the corresponding area at all.*

*Difficulty: hard*

---

##### Q35
In science class, Diego conducted an experiment to learn about evaporation. Diego measured the height of fluid in a beaker over a period of time. The function f(x) = 39 − 0.18x gives the estimated height, in centimeters (cm), of the fluid in the beaker x days after the start of the experiment. Which of the following is the best interpretation of 39 in this context?

**A.** The estimated height, in cm, of the fluid at the start of the experiment **(Correct)**

  *Correct. 39 is f(0), the estimated height at x = 0, the start of the experiment.*

**B.** The estimated height, in cm, of the fluid at the end of the experiment 

  *This confuses the starting value (x = 0) with a value at some later, unspecified endpoint.*

**C.** The estimated change in the height, in cm, of the fluid each day 

  *This is the rate, −0.18, not the intercept, 39.*

**D.** The estimated number of days for all the fluid to evaporate 

  *This confuses the intercept with the zero of the function — a different calculation, solving f(x) = 0 for x.*

*Difficulty: medium*

---

##### Q36
In the xy-plane, the graph of the linear function f contains the points (0, 3) and (7, 31). Which equation defines f, where y = f(x)?

**A.** f(x) = 28x + 34 

  *This uses the un-divided rise (31 − 3 = 28) as the slope instead of dividing by the run of 7, and adds the two given y-values together (3 + 31 = 34) to use as the intercept, rather than solving for it properly.*

**B.** f(x) = 3x + 38 

  *This swaps the intercept (3) into the slope's position, and forms an intercept by adding the second point's own coordinates together (7 + 31 = 38) instead of solving for it.*

**C.** f(x) = 4x + 3 **(Correct)**

  *Correct. Slope: (31 − 3)/(7 − 0) = 28/7 = 4. Since the first point has x = 0, its y-value, 3, is the intercept directly.*

**D.** f(x) = 7x + 3 

  *This keeps the correct intercept but uses the x-coordinate of the second point, 7, directly as the slope instead of computing the actual rate of change.*

*Difficulty: medium*

---

##### Q37
A team of workers has been moving cargo off of a ship. The equation below models the approximate number of tons of cargo, y, that remains to be moved x hours after the team started working: y = 120 − 25x. The graph of this equation in the xy-plane is a line. What is the best interpretation of the x-intercept in this context?

**A.** The team will have moved all the cargo in about 4.8 hours. **(Correct)**

  *Correct. The x-intercept is where y = 0 (no cargo left): 0 = 120 − 25x gives x = 4.8 hours.*

**B.** The team has been moving about 4.8 tons of cargo per hour. 

  *This confuses the x-intercept, a time value, with the rate — the rate is actually 25 tons per hour, not 4.8.*

**C.** The team has been moving about 25 tons of cargo per hour. 

  *This correctly identifies the rate but attaches it to the x-intercept, which is a different quantity — a time, not a rate.*

**D.** The team started with 120 tons of cargo to move. 

  *This is the correct interpretation of the y-intercept, not the x-intercept the question asks about.*

*Difficulty: hard*

---

##### Q38
The graph of the function f, where y = f(x), gives the total cost y, in dollars, for a certain video game system and x games; the line passes through (0, 100) and (10, 350). What is the best interpretation of the slope of the graph in this context?

**A.** Each game costs $25. **(Correct)**

  *Correct. Slope = (350 − 100)/(10 − 0) = 250/10 = 25 dollars per game.*

**B.** The video game system costs $100. 

  *This is the correct interpretation of the y-intercept, not the slope — it answers a different, unasked question.*

**C.** The video game system costs $25. 

  *The system's cost is the y-intercept, $100, not the slope — the number 25 is attached to the wrong quantity here.*

**D.** Each game costs $100. 

  *This correctly identifies that the slope describes the per-game cost, but reports the intercept's value ($100, the system's price) instead of the actual slope ($25).*

*Difficulty: medium*

---

##### Q39
The boiling point of water at sea level is 212 degrees Fahrenheit (°F). For every 550 feet above sea level, the boiling point of water is lowered by about 1°F. Which of the following equations can be used to find the boiling point B of water, in °F, x feet above sea level?

**A.** B = 550 + x/212 

  *This swaps the roles of 550 and 212, using the elevation-per-degree value as the base and inverting the other number's role.*

**B.** B = 550 − x/212 

  *This makes the same role-swap as choice A, but subtracts instead of adds.*

**C.** B = 212 + x/550 

  *This has the correct roles for 212 and 550, but the wrong sign — the boiling point falls with altitude, so the term must be subtracted, not added.*

**D.** B = 212 − x/550 **(Correct)**

  *Correct. 212 is the sea-level starting value; the boiling point drops by 1°F for every 550 feet, so x/550 is subtracted.*

*Difficulty: medium*

---

##### Q40
For the function f defined above, f(x) = (x + 7)/4, what is the value of f(9) − f(1)?

**A.** 1 

  *This adds the two denominators together instead of keeping the shared denominator of 4 — correctly combining the numerators, (9 + 7) − (1 + 7) = 8, but then dividing by 4 + 4 = 8 instead of 4: 8/8 = 1.*

**B.** 2 **(Correct)**

  *Correct. f(9) = 16/4 = 4 and f(1) = 8/4 = 2, so f(9) − f(1) = 4 − 2 = 2.*

**C.** 1/4 

  *This reports the slope of f instead of computing the actual difference between two function values.*

**D.** 9/4 

  *This computes f(9) by forgetting to add the 7 in the numerator (9/4 instead of 16/4) and never actually subtracts f(1) at all.*

*Difficulty: medium*

---

##### Q41
Some values of the linear function f are shown in the table above: when x = 0, f(x) = −2; when x = 2, f(x) = 4; when x = 6, f(x) = 16. What is the value of f(3)?

**A.** 6 

  *This computes a slope of (16 − 4)/6 = 2 by dividing the change in output by the x-value 6 instead of the actual run (6 − 2 = 4), and then forces the line through the point (2, 4) with an intercept of 0: f(x) = 2x gives f(3) = 6.*

**B.** 7 **(Correct)**

  *Correct. Slope: (4 − (−2))/(2 − 0) = 3, confirmed by (16 − 4)/(6 − 2) = 3. f(x) = 3x − 2, so f(3) = 9 − 2 = 7.*

**C.** 8 

  *This misreads the table's intercept as −1 instead of −2, giving f(3) = 3(3) − 1 = 8.*

**D.** 9 

  *This computes 3(3) = 9 correctly but forgets the intercept, −2, entirely.*

*Difficulty: hard*

---

##### Q42
In the xy-plane, the points (−2, 3) and (4, −5) lie on the graph of which of the following linear functions?

**A.** f(x) = x + 5 

  *This passes through (−2, 3) — check: −2 + 5 = 3 — but was found using a slope of 1, not the actual −4/3, so it misses the second point: at x = 4 it gives 9, not −5.*

**B.** f(x) = 1/2 x + 4 

  *This also passes through (−2, 3) — check: −1 + 4 = 3 — but fails at (4, −5), giving 6 instead.*

**C.** f(x) = −4/3 x + 1/3 **(Correct)**

  *Correct. Slope: (−5 − 3)/(4 − (−2)) = −8/6 = −4/3. Using (−2, 3): 3 = −4/3(−2) + b = 8/3 + b, so b = 1/3.*

**D.** f(x) = −3/2 x + 1 

  *This uses the reciprocal of the correct slope — run over rise instead of rise over run — combined with a slip when solving for the intercept.*

*Difficulty: hard*

---

##### Q43
The graph above shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt; the line passes through the origin and the point (3, 6). Which of the following equations correctly relates d and m?

**A.** d = 2m **(Correct)**

  *Correct. Slope = 6/3 = 2, and the line passes through the origin, so there is no constant term.*

**B.** d = 1/2 m 

  *This inverts the slope, using 1/2 instead of the actual rate of 2.*

**C.** d = m + 2 

  *This treats the slope as a flat offset to add rather than a rate to multiply by, and ignores that the line actually passes through the origin.*

**D.** d = 2m + 2 

  *This has the correct slope but adds an intercept that doesn't exist — the graph passes through the origin, (0, 0), not (0, 2).*

*Difficulty: easy*

---

##### Q44
The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If x food calories is equivalent to k kilojoules, of the following, which best represents the relationship between x and k?

**A.** k = 0.24x 

  *This inverts the conversion ratio, computing calories per kilojoule (roughly 4/16.7 ≈ 0.24) instead of kilojoules per calorie.*

**B.** k = 4.2x **(Correct)**

  *Correct. Using protein or carbohydrate's row, 16.7 kJ / 4.0 cal ≈ 4.2 kJ per calorie.*

**C.** x = 4.2k 

  *This finds the correct ratio but writes it solving for x instead of k — the roles of the two variables are swapped.*

**D.** xk = 4.2 

  *This misreads a direct proportional relationship as an inverse one, as though x and k trade off against each other rather than both scaling together.*

*Difficulty: medium*

---

##### Q45
If f(x) = x + 7 and g(x) = 7x, what is the value of 4f(2) − g(2)?

**A.** −5 

  *This computes f(2) − g(2) = 9 − 14 = −5 but drops the coefficient of 4 on f(2) entirely.*

**B.** 1 

  *This expands 4(x + 7) as 4x + 7 instead of 4x + 28 — distributing the 4 across only one of the two terms inside the parentheses — before subtracting g(x) = 7x: (4x + 7) − 7x = −3x + 7, which is 1 at x = 2.*

**C.** 22 **(Correct)**

  *Correct. f(2) = 9 and g(2) = 14, so 4f(2) − g(2) = 4(9) − 14 = 36 − 14 = 22.*

**D.** 28 

  *This multiplies the coefficient 4 from "4f(2)" by the coefficient 7 from g(x) = 7x, ignoring the actual input value and the +7 in f's rule entirely: 4 × 7 = 28.*

*Difficulty: hard*

---

##### Q46
y = 18 − 5x. The equation above represents the speed y, in feet per second, of Sheila's bicycle x seconds after she applied the brakes at the end of a ride. If the equation is graphed in the xy-plane, which of the following is the best interpretation of the x-coordinate of the line's x-intercept in the context of the problem?

**A.** The speed of Sheila's bicycle, in feet per second, before Sheila applied the brakes 

  *This is the correct interpretation of the y-intercept (18), not the x-intercept the question asks about.*

**B.** The number of feet per second the speed of Sheila's bicycle decreased each second after Sheila applied the brakes 

  *This confuses the x-intercept, a time value, with the slope/rate, which is actually −5.*

**C.** The number of seconds it took from the time Sheila began applying the brakes until the bicycle came to a complete stop **(Correct)**

  *Correct. The x-intercept is where speed y = 0: 0 = 18 − 5x gives x = 3.6 seconds, the time until the bicycle stops.*

**D.** The number of feet Sheila's bicycle traveled from the time she began applying the brakes until the bicycle came to a complete stop 

  *This confuses the x-intercept, a time, with total distance traveled — a related but different quantity this simple speed-versus-time model doesn't directly give.*

*Difficulty: medium*

---

##### Q47
Scientists collected fallen acorns that each housed a colony of the ant species P. ohioensis and analyzed each colony's structure. For any of these colonies, if the colony has x worker ants, the equation y = 0.67x + 2.6, where 20 ≤ x ≤ 110, gives the predicted number of larvae, y, in the colony. If one of these colonies has 58 worker ants, which of the following is closest to the predicted number of larvae in the colony?

**A.** 41 **(Correct)**

  *Correct. y = 0.67(58) + 2.6 = 38.86 + 2.6 = 41.46, closest to 41.*

**B.** 61 

  *This adds all three given numbers together instead of multiplying the rate by the worker-ant count first: 0.67 + 58 + 2.6 ≈ 61.*

**C.** 83 

  *This solves for x given y = 58 instead of evaluating the model at x = 58: (58 − 2.6)/0.67 ≈ 83, an evaluate/solve swap.*

**D.** 190 

  *This adds the rate and the intercept together first (0.67 + 2.6 = 3.27) and treats that sum as a single multiplier for the worker-ant count: 58 × 3.27 ≈ 190.*

*Difficulty: medium*

---

##### Q48
The table above shows the population of Greenleaf, Idaho, for the years 2000 and 2010: in 2000, the population was 862; in 2010, the population was 846. If the relationship between population and year is linear, which of the following functions P models the population of Greenleaf t years after 2000?

**A.** P(t) = 862 − 1.6t **(Correct)**

  *Correct. Slope: (846 − 862)/10 = −1.6. Since t is already defined as years after 2000, the population at t = 0 is 862.*

**B.** P(t) = 862 − 16t 

  *This uses the raw difference in population, −16, as the slope without dividing by the 10-year gap that produced it.*

**C.** P(t) = 862 + 16(t − 2,000) 

  *This flips the sign of the rate, uses the undivided difference, and redundantly subtracts 2,000 from t even though t is already defined as years after 2000 — a double-shift of the input on top of the other two errors.*

**D.** P(t) = 862 − 1.6(t − 2,000) 

  *This has the correct slope and sign, but redundantly subtracts 2,000 from t, double-shifting an input that is already measured in years after 2000.*

*Difficulty: medium*

---

##### Q49
The pressure exerted on a scuba diver at sea level is 14.70 pounds per square inch (psi). For each foot the scuba diver descends below sea level, the pressure exerted on the scuba diver increases by 0.44 psi. What is the total pressure, in psi, exerted on the scuba diver at 105 feet below sea level?

**A.** 60.90 **(Correct)**

  *Correct. 14.70 + 0.44(105) = 14.70 + 46.2 = 60.90.*

**B.** 31.50 

  *This subtracts the base pressure instead of adding it: 0.44(105) − 14.70 = 31.50.*

**C.** 14.70 

  *This reports the sea-level pressure alone, forgetting to add the depth-based increase entirely.*

**D.** 0.44 

  *This reports the rate itself rather than computing the actual total pressure.*

*Difficulty: easy*

---

##### Q50
The graph of y = f(x) − 11 is a line that passes through (−4, 4) and (1, −6). Which equation defines the linear function f?

**A.** f(x) = −13x − 11 

  *This merges the graphed line's slope with the −11 shift (−2 + (−11) = −13) instead of solving properly, and reuses −11 directly as f's intercept instead of adding 11 to the graphed intercept.*

**B.** f(x) = −2x + 7 **(Correct)**

  *Correct. The graphed line has slope (−6 − 4)/(1 − (−4)) = −2 and passes through (0, −4). Since this graph is y = f(x) − 11, f(x) = −2x − 4 + 11 = −2x + 7.*

**C.** f(x) = −13x + 7 

  *This reaches the correct final intercept but still merges the graph's slope with the shift amount (−2 + (−11) = −13) instead of keeping the slope unchanged.*

**D.** f(x) = −2x − 11 

  *This reads the correct slope off the graph but never adds the 11 back to the graphed intercept — it substitutes −11 in place of the intercept instead of undoing the shift.*

*Difficulty: hard*

---

##### Q51
The function f(x) = 55.20 − 0.16x gives the estimated surface water temperature f(x), in degrees Celsius, of a body of water on the xth day of the year, where 220 ≤ x ≤ 360. Based on the model, what is the estimated surface water temperature, in degrees Celsius, of this body of water on the 326th day of the year?

**A.** 55.20 

  *This reports the intercept alone, as though evaluating at x = 0 instead of the given x = 326.*

**B.** 3.04 **(Correct)**

  *Correct. f(326) = 55.20 − 0.16(326) = 55.20 − 52.16 = 3.04.*

**C.** −0.16 

  *This reports the rate/slope instead of computing the actual temperature.*

**D.** −52.16 

  *This computes only the subtracted term, 0.16(326) = 52.16, and reports it with a sign flip instead of combining it with the 55.20 intercept.*

*Difficulty: easy*

---

##### Q52
The graph represents the total charge, in dollars, by an electrician for x hours of work. The electrician charges a onetime fee plus an hourly rate. What is the best interpretation of the slope of the graph?

**A.** The electrician's hourly rate **(Correct)**

  *Correct. The slope is the change in total charge per one additional hour of work — the hourly rate.*

**B.** The electrician's onetime fee 

  *This confuses the slope (a rate of change) with the intercept (a fixed starting charge).*

**C.** The maximum amount that electrician charges 

  *This misreads a constant rate of change as an upper bound. A linear model with a positive slope keeps increasing — it has no maximum.*

**D.** The total amount that electrician charges 

  *This confuses the constant per-hour rate with the total charge, which depends on the number of hours and equals the whole function, not the slope alone.*

*Difficulty: easy*

---

##### Q53
In the linear function f, f(0) = 8 and f(1) = 12. Which equation defines f?

**A.** f(x) = 12x + 8 

  *This passes through (0, 8) — 12(0) + 8 = 8 — but uses 12 (the given value of f(1)) directly as the slope instead of computing the actual rate of change: at x = 1, this gives 20, not 12.*

**B.** f(x) = 4x 

  *This drops the intercept entirely, forcing the line through the origin: at x = 0 it gives 0, not the stated f(0) = 8.*

**C.** f(x) = 4x + 12 

  *This has the correct slope but uses 12 (the value of f(1)) as the intercept instead of 8 (the actual value of f(0)).*

**D.** f(x) = 4x + 8 **(Correct)**

  *Correct. Slope: (12 − 8)/(1 − 0) = 4. The intercept, f(0) = 8, is the constant.*

*Difficulty: medium*

---

##### Q54
In the xy-plane, the graph of the linear function f contains the points (0, 2) and (8, 34). Which equation defines f, where y = f(x)?

**A.** f(x) = 2x + 42 

  *This uses a slope of 2 — half the correct rate of 4, consistent with accidentally doubling the run before dividing — and an intercept of 42 that doesn't correspond to either given point, a sign the two points' coordinates were combined incorrectly rather than solved for algebraically.*

**B.** f(x) = 32x + 36 

  *This uses the un-divided rise (34 − 2 = 32) as the slope instead of dividing by the run of 8, and adds the two y-values together (2 + 34 = 36) to use as the intercept, rather than solving for it properly.*

**C.** f(x) = 4x + 2 **(Correct)**

  *Correct. Slope: (34 − 2)/(8 − 0) = 4. Since the first point has x = 0, its y-value, 2, is the intercept directly.*

**D.** f(x) = 8x + 2 

  *This keeps the correct intercept but uses the x-coordinate of the second point, 8, directly as the slope instead of computing the actual rate of change: at x = 8, this gives 66, not 34.*

*Difficulty: hard*

---

##### Q55
For the linear function g, the table shows four values of x and their corresponding values of g(x): when x = 1, g(x) = 54; when x = 2, g(x) = 51; when x = 3, g(x) = 48; when x = 4, g(x) = 45. The function can be written as g(x) = mx + b, where m and b are constants. What is the value of b?

**A.** 3 

  *This reports the magnitude of the slope, |m| = 3, instead of the intercept, b, which the question actually asks for.*

**B.** 27 

  *This combines the total drop across the table (54 − 45 = 9) with the slope's magnitude (9 × 3 = 27) instead of using either quantity correctly to solve for the intercept.*

**C.** 54 

  *This reports g(1) directly, mistaking the table's first listed value for the y-intercept — but the table starts at x = 1, not x = 0, so g(1) is not b.*

**D.** 57 **(Correct)**

  *Correct. Slope: (51 − 54)/(2 − 1) = −3. Using x = 1: 54 = −3(1) + b, so b = 57.*

*Difficulty: medium*

---

##### Q56
The table gives the average time t, in minutes, it takes Carly to travel a certain distance d, in kilometers: when d = 0.32, t = 8; when d = 0.56, t = 14; when d = 0.68, t = 17. Which equation could represent this linear relationship?

**A.** t = 4d 

  *This divides 8 by 2 instead of by the actual distance 0.32 — misreading the decimal point — landing on a rate of 4 instead of the correct 25.*

**B.** t = 1/25 d 

  *This inverts the correct relationship, dividing distance by the rate instead of multiplying it — swapping which variable belongs on top.*

**C.** t = 25d **(Correct)**

  *Correct. 8/0.32 = 25, and the ratio holds throughout the table: 14/0.56 = 25 and 17/0.68 = 25.*

**D.** t = 1/4 d 

  *This is the reciprocal of choice A's misread rate — the same decimal-point error, inverted.*

*Difficulty: medium*

---

##### Q57
An economist modeled the demand Q for a certain product as a linear function of the selling price P. The demand was 20,000 units when the selling price was $40 per unit, and the demand was 15,000 units when the selling price was $60 per unit. Based on the model, what is the demand, in units, when the selling price is $55 per unit?

**A.** 16,250 **(Correct)**

  *Correct. Slope: (15,000 − 20,000)/(60 − 40) = −250 units per dollar. Using (40, 20,000): 20,000 = −250(40) + b gives b = 30,000. Q(55) = −250(55) + 30,000 = 16,250.*

**B.** 16,500 

  *This follows the correct method, but 250 × 55 is miscomputed as 13,500 instead of 13,750, giving 30,000 − 13,500 = 16,500.*

**C.** 16,750 

  *This is a different multiplication slip in the same step, computing 250 × 55 as 13,250 instead of 13,750.*

**D.** 17,500 

  *This averages the two given demand values, (20,000 + 15,000)/2 = 17,500, which would only be correct if $55 were exactly halfway between $40 and $60 — the actual midpoint is $50, not $55.*

*Difficulty: hard*

---

##### Q58
The cost of renting a backhoe for up to 10 days is $270 for the first day and $135 for each additional day. Which of the following equations gives the cost y, in dollars, of renting the backhoe for x days, where x is a positive integer and x ≤ 10?

**A.** y = 270x − 135 

  *This treats the first-day cost as a per-day rate and subtracts a flat amount, rather than the reverse.*

**B.** y = 270x + 135 

  *This uses 270 (the first day's flat cost) as the per-day rate instead of 135, keeping 135 as if it were the constant.*

**C.** y = 135x + 270 

  *This double-charges day one: it charges $135 for day one as part of the "each day" rate and also adds the full $270 on top, rather than letting the $270 cover day one so only the x − 1 additional days get the $135 charge.*

**D.** y = 135x + 135 **(Correct)**

  *Correct. The first day costs $270 flat; each of the remaining x − 1 days costs $135: y = 270 + 135(x − 1) = 135x + 135.*

*Difficulty: medium*

---

##### Q59
According to data provided by the US Department of Energy, the average price per gallon of regular gasoline in the United States from September 1, 2014, to December 1, 2014, is modeled by the function F defined below, where F(x) is the average price per gallon x months after September 1. F(x) = 2.74 − 0.19(x − 3). The constant 2.74 in this function estimates which of the following?

**A.** The average monthly decrease in the price per gallon 

  *This confuses 2.74 with the rate, −0.19, which is what actually describes the monthly change.*

**B.** The difference in the average price per gallon from September 1, 2014, to December 1, 2014 

  *This misreads 2.74 as a change in price rather than a price level; the actual change over that span is F(3) − F(0) = 2.74 − 3.31 = −0.57, not 2.74.*

**C.** The average price per gallon on September 1, 2014 

  *This assumes the constant 2.74 sits at x = 0 (September), ignoring the "(x − 3)" inside the parentheses, which shifts the model's anchor point to x = 3 (December) instead.*

**D.** The average price per gallon on December 1, 2014 **(Correct)**

  *Correct. x counts months after September 1, so x = 3 is December 1, and F(3) = 2.74 − 0.19(3 − 3) = 2.74 — exactly the constant term.*

*Difficulty: sat-hardest*

---

##### Q60
Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions f best models the production, in millions of barrels, t years after the year 2000?

**A.** f(t) = 21/130 t + 4 

  *This has the correct magnitude for the rate but the wrong sign — production decreased, so the coefficient must be negative.*

**B.** f(t) = 19/130 t + 4 

  *This uses 1.9 directly as the numerator (as 19, with the decimal point dropped) instead of computing the actual drop, 4 − 1.9 = 2.1, and also keeps the wrong, positive sign.*

**C.** f(t) = −21/130 t + 4 **(Correct)**

  *Correct. The drop over 13 years is 4 − 1.9 = 2.1 million barrels, a rate of −2.1/13 = −21/130 million barrels per year.*

**D.** f(t) = −19/130 t + 4 

  *This has the correct sign but the same dropped-decimal-point error as choice B — using 1.9 directly as 19 instead of computing the actual difference, 2.1.*

*Difficulty: hard*

---

##### Q61
F(x) = (9/5)(x − 273.15) + 32. The function F gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x kelvins. If a temperature increased by 2.10 kelvins, by how much did the temperature increase, in degrees Fahrenheit?

**A.** 3.78 **(Correct)**

  *Correct. A change of 2.10 kelvins corresponds to a Fahrenheit change of (9/5)(2.10) = 3.78 — the +32 offset cancels out of a difference and never enters the calculation.*

**B.** 35.78 

  *This re-adds the +32 conversion offset to a change in temperature, but that offset only applies when converting an absolute temperature, not a difference — it cancels out when two temperatures are subtracted.*

**C.** 487.89 

  *This evaluates F at x = 2.10, treating 2.10 as an absolute kelvin temperature rather than a change in temperature: (9/5)(2.10 − 273.15) = −487.89, reported as a magnitude.*

**D.** 519.89 

  *This makes the same error as choice C, treating 2.10 as an absolute temperature, and then also adds the +32 offset on top: 487.89 + 32 = 519.89.*

*Difficulty: hard*

---

##### Q62
The table above shows some values of x and their corresponding values f(x) for the linear function f: when x = −11, f(x) = 21; when x = −10, f(x) = 18; when x = −9, f(x) = 15; when x = −8, f(x) = 12. What is the x-intercept of the graph of y = f(x) in the xy-plane?

**A.** (−3, 0) 

  *This extrapolates the table's pattern by one step too many, landing on x = −3 instead of x = −4 — an off-by-one error in counting how many steps of −3 it takes to reach an output of 0.*

**B.** (−4, 0) **(Correct)**

  *Correct. Slope: (18 − 21)/(−10 − (−11)) = −3. Using x = −11: 21 = −3(−11) + b gives b = −12, so 0 = −3x − 12 gives x = −4.*

**C.** (−9, 0) 

  *This confuses the x-intercept with one of the table's own listed x-values, picking −9 from the table rather than solving −3x − 12 = 0.*

**D.** (−12, 0) 

  *This is the y-intercept's constant, −12, placed as though it were the x-coordinate of the x-intercept — a mix-up between the two different intercepts, which sit at (0, −12) and (−4, 0) respectively.*

*Difficulty: hard*

---

##### Q63
The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food: protein, 4.0 calories and 16.7 kilojoules; fat, 9.0 calories and 37.7 kilojoules; carbohydrate, 4.0 calories and 16.7 kilojoules. If the 180 food calories in a granola bar come entirely from p grams of protein, f grams of fat, and c grams of carbohydrate, which of the following expresses f in terms of p and c?

**A.** f = 20 + 4/9 (p + c) 

  *This has the right structure but the wrong sign — since more protein and carbohydrate calories leave less room for fat calories in a fixed 180-calorie total, the term must be subtracted, not added.*

**B.** f = 20 − 4/9 (p + c) **(Correct)**

  *Correct. 180 = 4p + 9f + 4c (since protein and carbohydrate both provide 4 calories per gram, and fat provides 9). Solving for f: 9f = 180 − 4p − 4c, so f = 20 − (4/9)(p + c).*

**C.** f = 20 − 4/9 (p − c) 

  *This has a sign error inside the parentheses, subtracting c instead of adding it, as though carbohydrate calories offset protein calories rather than both contributing to the same 180-calorie total.*

**D.** f = 20 + 9/4 (p + c) 

  *This inverts the fraction, using 9/4 instead of 4/9, and also has the sign error from choice A.*

*Difficulty: sat-hardest*

---

##### Q64
An object hangs from a spring. The formula ℓ = 30 + 2w relates the length ℓ, in centimeters, of the spring to the weight w, in newtons, of the object. Which of the following describes the meaning of the 2 in this context?

**A.** The length, in centimeters, of the spring with no weight attached 

  *This is the meaning of the constant, 30, not the coefficient, 2 — a slope/intercept swap.*

**B.** The weight, in newtons, of an object that will stretch the spring 30 centimeters 

  *This conflates the two constants in the formula, mixing the 30 and the 2 into a single, incorrect statement about weight rather than reading each number's role separately.*

**C.** The increase in the weight, in newtons, of the object for each one-centimeter increase in the length of the spring 

  *This describes the rate backward — newtons per centimeter — the reciprocal of what the coefficient 2 actually gives.*

**D.** The increase in the length, in centimeters, of the spring for each one-newton increase in the weight of the object **(Correct)**

  *Correct. 2 is the coefficient on w, so it is the rate: centimeters of length per one newton of weight.*

*Difficulty: medium*

---

##### Q65
For the function f, f(3x) = x − 6 for all values of x. What is the value of f(6)?

**A.** −6 

  *This reports the constant term of the given equation directly, without solving for which x makes 3x = 6.*

**B.** −4 **(Correct)**

  *Correct. f(6) means f(3x) with 3x = 6, so x = 2, and f(6) = f(3(2)) = 2 − 6 = −4.*

**C.** 0 

  *This misreads f(3x) = x − 6 as if it meant f(x) = x − 6 directly, plugging the input 6 straight in without solving 3x = 6 first: 6 − 6 = 0.*

**D.** 2 

  *This correctly solves 3x = 6 to get x = 2, but stops there and reports the solved input instead of finishing the last step, x − 6 = −4.*

*Difficulty: hard*

---

##### Q66
For the linear function f, the table shows three values of x and their corresponding values of f(x): when x = 1, f(x) = −64; when x = 2, f(x) = 0; when x = 3, f(x) = 64. Function f is defined by f(x) = ax + b, where a and b are constants. What is the value of a − b?

**A.** −64 

  *This reports a table value, f(1) = −64, directly, rather than computing a − b.*

**B.** 62 

  *This uses a mismatched pair of rows for the slope and the intercept — rise from one gap in the table, run from another — landing on values close to but not equal to the correct 64 and −128.*

**C.** 128 

  *This computes b correctly as −128 but takes a to be 0 — perhaps confusing the slope with the table's middle output value, which happens to be 0: 0 − (−128) = 128.*

**D.** 192 **(Correct)**

  *Correct. Slope a: (0 − (−64))/(2 − 1) = 64. Using x = 1: −64 = 64(1) + b gives b = −128. So a − b = 64 − (−128) = 192.*

*Difficulty: hard*

---

##### Q67
For groups of 25 or more people, a museum charges $21 per person for the first 25 people and $14 for each additional person. Which function f gives the total charge, in dollars, for a tour group with n people, where n ≥ 25?

**A.** f(n) = 14n + 175 **(Correct)**

  *Correct. The first 25 people cost 21(25) = 525 flat; each of the remaining n − 25 people costs $14: f(n) = 525 + 14(n − 25) = 14n + 175.*

**B.** f(n) = 14n + 525 

  *This applies the $14 rate to everyone (all n people) while also keeping the full $525 charge for the first 25 — double-counting their cost instead of letting the flat $525 cover them.*

**C.** f(n) = 35n − 350 

  *This adds the two rates together (21 + 14 = 35) as though a single blended rate applied to everyone in the group, rather than the tiered structure the problem describes.*

**D.** f(n) = 14n + 21 

  *This uses $21 as a flat starting fee — the rate for just one person — rather than $525, the actual flat charge for the first 25 people.*

*Difficulty: medium*

---

##### Q68
F(x) = (9/5)(x − 273.15) + 32. The function F gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of x kelvins. If a temperature increased by 9.10 kelvins, by how much did the temperature increase, in degrees Fahrenheit?

**A.** 16.38 **(Correct)**

  *Correct. A change of 9.10 kelvins corresponds to a Fahrenheit change of (9/5)(9.10) = 16.38 — the +32 offset cancels out of a difference.*

**B.** 48.38 

  *This re-adds the +32 conversion offset to a change in temperature, but that offset cancels out when two temperatures are subtracted — it only applies to an absolute conversion.*

**C.** 475.29 

  *This treats 9.10 as an absolute kelvin temperature rather than a change: (9/5)(9.10 − 273.15) = −475.29, reported as a magnitude.*

**D.** 507.29 

  *This makes the same error as choice C and then also adds the +32 offset: 475.29 + 32 = 507.29.*

*Difficulty: hard*

---

##### Q69
f(x) = 6d(20x + 21) + 17. Which of the following represents the x-intercept of the graph of y = f(x) + 9 in the xy-plane, where d is a constant?

**A.** ((−126d − 26)/(120d), 0) **(Correct)**

  *Correct. y = f(x) + 9 = 6d(20x + 21) + 26. Setting y = 0: 6d(20x + 21) = −26, so 20x + 21 = −13/(3d), and 20x = −13/(3d) − 21 = (−13 − 63d)/(3d). Dividing by 20: x = (−63d − 13)/(60d) = (−126d − 26)/(120d).*

**B.** (9 − (126d + 17)/(120d), 0) 

  *This sets up the equation correctly in spirit but loses track of where the +9 shift enters — treating it as adding to the outside of the fraction rather than folding it into the numerator with the other constants before setting the whole expression to zero.*

**C.** (−38/(120d + 9), 0) 

  *This distributes 6d across the 20x term but not across the 21 inside the parentheses — a partial-distribution error — and then further mishandles where the +9 shift lands, producing a denominator that mixes d with a constant instead of keeping d isolated.*

**D.** (126d + 26, 0) 

  *This reaches the correct numerator's magnitude while solving, but stops before dividing by 120d and drops the negative sign — reporting the un-simplified numerator as though it were already the final x-value.*

*Difficulty: sat-hardest*

---

##### Q70
One gallon of paint will cover 220 square feet of a surface. A room has a total wall area of w square feet. Which equation represents the total amount of paint P, in gallons, needed to paint the walls of the room twice?

**A.** P = w/110 **(Correct)**

  *Correct. Painting the wall area twice requires 2w square feet of coverage, and 2w/220 simplifies to w/110.*

**B.** P = 440w 

  *This inverts the relationship, multiplying by 440 (= 220 × 2) instead of dividing by it.*

**C.** P = w/220 

  *This has the correct form for a single coat but forgets to account for painting the walls twice, missing the factor of 2 entirely.*

**D.** P = 220w 

  *This inverts the relationship, multiplying the wall area by the coverage rate instead of dividing by it.*

*Difficulty: medium*

---

##### Q71
The cost of renting a large canopy tent for up to 10 days is $430 for the first day and $215 for each additional day. Which of the following equations gives the cost y, in dollars, of renting the tent for x days, where x is a positive integer and x ≤ 10?

**A.** y = 215x + 215 **(Correct)**

  *Correct. The first day costs $430 flat; each of the remaining x − 1 days costs $215: y = 430 + 215(x − 1) = 215x + 215.*

**B.** y = 430x − 215 

  *This treats the first-day cost as a per-day rate and subtracts a flat amount, rather than the reverse.*

**C.** y = 430x + 215 

  *This uses 430 (the first day's flat cost) as the per-day rate instead of 215.*

**D.** y = 215x + 430 

  *This double-charges day one: it charges $215 for day one as part of the "each day" rate and also adds the full $430 on top, rather than letting the $430 cover day one so only the x − 1 additional days get the $215 charge.*

*Difficulty: medium*

---

### Advanced Math

#### Nonlinear Equations and Systems (57 items)

##### Q1
If 6x − 9y > 12, which of the following inequalities is equivalent to the given inequality?

**A.** x − y > 2 

  *This divides the x-term by its own coefficient (6x/6 = x) and the y-term by its own, different coefficient (−9y/9 = −y), then divides the constant by only one of those two divisors (12/6 = 2) — three different numbers doing three different jobs, when dividing through an inequality requires ONE common divisor applied to every term. Test point (0, −2) satisfies the original — 6(0) − 9(−2) = 18 > 12 ✓ — but fails this choice: 0 − (−2) = 2, and 2 > 2 is false.*

**B.** 2x − 3y > 4 **(Correct)**

  *Correct. Every term shares a common factor of 3: dividing both sides by 3 gives 2x − 3y > 4. Check with a point that satisfies the original — (0, −2) gives 6(0) − 9(−2) = 18 > 12 ✓ in the original and 2(0) − 3(−2) = 6 > 4 ✓ here. ✓*

**C.** 3x − 2y > 4 

  *This divides every term by the correct common factor of 3 — giving coefficients 2 and 3 — but then swaps which coefficient belongs to which variable, writing 3x − 2y instead of 2x − 3y. Test point (0, −2) satisfies the original (18 > 12 ✓) but fails this choice: 3(0) − 2(−2) = 4, and 4 > 4 is false.*

**D.** 3y − 2x > 2 

  *This divides the coefficients correctly by 3 (getting 2 and 3) but then reorders the terms as 3y − 2x — the negation of 2x − 3y — without flipping the inequality the way negating both sides requires, and divides the constant by 6 instead of 3. Test point (0, −2) satisfies the original (18 > 12 ✓) but fails this choice: 3(−2) − 2(0) = −6, and −6 > 2 is false.*

*Difficulty: easy*

---

##### Q2
Which of the following is a solution to the equation 2x² − 4 = x²?

**A.** 1 

  *This isolates x² = 4 correctly, then divides both sides by 4 instead of taking a square root — x²/4 = 1 is mistaken for the final answer x = 1, skipping the square-root step entirely. Substituting exposes it: 2(1)² − 4 = −2, but 1² = 1, and −2 ≠ 1.*

**B.** 2 **(Correct)**

  *Correct. Subtract x² from both sides: x² − 4 = 0, so x² = 4 and x = ±2. Check in the original: 2(2)² − 4 = 8 − 4 = 4, and 2² = 4. ✓*

**C.** 3 

  *This comes from correctly isolating x² = 4, then mishandling the square root — computing it as 4 − 1 rather than the number that squares to 4. Substituting exposes it: 2(3)² − 4 = 14, but 3² = 9, and 14 ≠ 9.*

**D.** 4 

  *This drops the exponent on both x² terms, treating the equation as though it were linear: 2x − 4 = x, which gives x = 4. Substituting into the actual equation exposes it: 2(4)² − 4 = 28, but 4² = 16, and 28 ≠ 16.*

*Difficulty: medium*

---

##### Q3
The equation q − 29r = s relates the positive numbers q, r, and s. Which equation correctly expresses q in terms of r and s?

**A.** q = s − 29r 

  *This subtracts 29r instead of adding it — a sign error when isolating q. Moving −29r to the other side requires ADDING 29r to both sides, not subtracting it again. Check with r = 1, s = 10: the original gives q = s + 29r = 39, and this choice gives q = 10 − 29 = −19 ≠ 39.*

**B.** q = s + 29r **(Correct)**

  *Correct. Add 29r to both sides of q − 29r = s: q = s + 29r. Check with r = 1, s = 10: q = 10 + 29(1) = 39, and substituting back — 39 − 29(1) = 10 = s. ✓*

**C.** q = 29rs 

  *This multiplies r and s together, as though −29r were a factor of q rather than a term subtracted from it. Check with r = 1, s = 10: this gives q = 29(1)(10) = 290, but the equation only balances at q = 39.*

**D.** q = −s/(29r) 

  *This divides s by 29r, as though 29r were multiplying q rather than being subtracted from it, and flips the sign of s besides. Check with r = 1, s = 10: this gives q = −10/29, nowhere near the actual q = 39.*

*Difficulty: easy*

---

##### Q4
In the system of equations x + y = 12 and y = x², if (x, y) is a solution, which of the following is a possible value of x?

**A.** 0 

  *x = 0 satisfies y = x² (since 0² = 0) but not x + y = 12, since 0 + 0 = 0 ≠ 12 — it checks against only one of the two equations in the system. A solution to a system has to satisfy both equations at once.*

**B.** 1 

  *x = 1 satisfies y = x² (since 1² = 1) but not x + y = 12, since 1 + 1 = 2 ≠ 12 — the same error as choice A, checking only the second equation.*

**C.** 2 

  *x = 2 satisfies y = x² (since 2² = 4) but not x + y = 12, since 2 + 4 = 6 ≠ 12 — again satisfying only one equation of the system, not both.*

**D.** 3 **(Correct)**

  *Correct. Substitute y = x² into x + y = 12: x + x² = 12, so x² + x − 12 = 0, which factors as (x + 4)(x − 3) = 0, giving x = −4 or x = 3 — and 3 is the value offered. Check both equations: at x = 3, y = 3² = 9, and 3 + 9 = 12. ✓*

*Difficulty: medium*

---

##### Q5
The power P produced by a machine is represented by the equation P = W/t, where W is the work performed during an amount of time t. Which of the following correctly expresses W in terms of P and t?

**A.** W = Pt **(Correct)**

  *Correct. Multiply both sides of P = W/t by t: Pt = W. Check with P = 5, t = 2: W = 10, and substituting back — 10/2 = 5 = P. ✓*

**B.** W = P/t 

  *This divides by t a second time instead of multiplying by it — the same operation that was already used to define P, applied again rather than undone. Check with P = 5, t = 2: this gives W = 2.5, but substituting back into P = W/t gives P = 2.5/2 = 1.25, not the original 5.*

**C.** W = t/P 

  *This inverts the fraction, swapping which quantity is on top. Check with P = 5, t = 2: this gives W = 0.4, but substituting back into P = W/t gives P = 0.4/2 = 0.2, not 5.*

**D.** W = P + t 

  *This treats division as though it were undone by addition, as though P = W/t meant W was found by adding rather than multiplying. Check with P = 5, t = 2: this gives W = 7, but substituting back gives P = 7/2 = 3.5, not 5.*

*Difficulty: easy*

---

##### Q6
Which of the following values of x satisfies the equation x² = 64?

**A.** −8 **(Correct)**

  *Correct. x² = 64 has two solutions, x = 8 and x = −8, since both (8)² and (−8)² equal 64. Only −8 appears among the choices. Check: (−8)² = 64. ✓*

**B.** 4 

  *This solves as though the equation were x³ = 64 instead of x² = 64 — the cube root of 64 is 4, since 4³ = 64, but the square root is 8, not 4. Check: 4² = 16, not 64.*

**C.** 32 

  *This misreads the exponent 2 as a coefficient, treating x² as 2x: 2x = 64 gives x = 32. Check: 32² = 1,024, not 64.*

**D.** 128 

  *This multiplies 64 by the exponent instead of taking a square root: 64 × 2 = 128. Check: 128² = 16,384, not 64.*

*Difficulty: easy*

---

##### Q7
The total revenue from sales of a product can be calculated using the formula T = PQ, where T is the total revenue, P is the price of the product, and Q is the quantity of the product sold. Which of the following equations gives the quantity of product sold in terms of P and T?

**A.** Q = P/T 

  *This inverts the fraction, putting P on top and T on the bottom. Check with P = 4, T = 20: this gives Q = 0.2, but substituting back into T = PQ gives T = 4(0.2) = 0.8, not 20.*

**B.** Q = T/P **(Correct)**

  *Correct. Divide both sides of T = PQ by P: T/P = Q. Check with P = 4, T = 20: Q = 5, and substituting back — 4(5) = 20 = T. ✓*

**C.** Q = PT 

  *This multiplies P and T together instead of dividing, as though isolating Q required the same operation that defined T rather than its inverse. Check with P = 4, T = 20: this gives Q = 80, but substituting back gives T = 4(80) = 320, not 20.*

**D.** Q = T − P 

  *This treats the relationship as additive, as though T = P + Q rather than T = PQ. Check with P = 4, T = 20: this gives Q = 16, but substituting back into T = PQ gives T = 4(16) = 64, not 20.*

*Difficulty: easy*

---

##### Q8
The equation b = 42cf relates the positive numbers b, c, and f. Which equation correctly expresses c in terms of b and f?

**A.** c = b/(42f) **(Correct)**

  *Correct. Divide both sides of b = 42cf by 42f: b/(42f) = c. Check with c = 1, f = 1: b = 42, and c = 42/(42 × 1) = 1. ✓*

**B.** c = (b − 42)/f 

  *This treats 42 as a term being added to cf rather than a coefficient multiplying it, subtracting 42 instead of dividing by it. Check with c = 1, f = 1 (so b = 42): this gives c = (42 − 42)/1 = 0, not 1.*

**C.** c = 42bf 

  *This multiplies instead of dividing, as though isolating c required the same operation that defined b rather than its inverse. Check with c = 1, f = 1 (so b = 42): this gives c = 42(42)(1) = 1,764, not 1.*

**D.** c = 42 − b − f 

  *This treats the entire equation as additive — as though b = 42 + c + f — subtracting every term instead of dividing. Check with c = 1, f = 1 (so b = 42): this gives c = 42 − 42 − 1 = −1, not 1.*

*Difficulty: easy*

---

##### Q9
If (x + 5)² = 4, which of the following is a possible value of x?

**A.** 1 

  *This starts from the same mistake as choice B — forgetting to take a square root and solving x + 5 = 4 directly, which gives x = −1 — but then subtracts 5 from 4 as an unsigned difference (|4 − 5| = 1) instead of a signed one, reporting x = 1. Check: (1 + 5)² = 36, not 4.*

**B.** −1 

  *This forgets to take a square root at all, treating (x + 5)² = 4 as though it meant x + 5 = 4 directly: x = −1. But a squared quantity equal to 4 means the base is ±2, not 4 itself. Check: (−1 + 5)² = 16, not 4.*

**C.** −2 

  *This drops the +5 inside the parentheses entirely, treating (x + 5)² as though it were just x²: x² = 4 gives x = ±2, and this choice takes the negative branch. Check: (−2 + 5)² = 9, not 4.*

**D.** −3 **(Correct)**

  *Correct. Take the square root of both sides, keeping both branches: x + 5 = ±2. The branch x + 5 = 2 gives x = −3; the branch x + 5 = −2 gives x = −7 (not offered). Check: (−3 + 5)² = 2² = 4. ✓*

*Difficulty: medium*

---

##### Q10
The equation p + 34 = q + r relates the variables p, q, and r. Which equation correctly expresses p in terms of q and r?

**A.** p = q + r + 34 

  *This adds 34 instead of subtracting it — a sign error when isolating p. Moving 34 to the other side requires subtracting it from both sides, not adding it again. Check with q = 1, r = 1 (so the correct p = q + r − 34 = −32): this choice gives p = 1 + 1 + 34 = 36, and substituting back — 36 + 34 = 70 ≠ q + r = 2.*

**B.** p = q + r − 34 **(Correct)**

  *Correct. Subtract 34 from both sides of p + 34 = q + r: p = q + r − 34. Check with q = 1, r = 1: p = 1 + 1 − 34 = −32, and substituting back — (−32) + 34 = 2 = q + r. ✓*

**C.** p = −q − r + 34 

  *This is the negation of the correct expression: −(q + r − 34) = −q − r + 34. It comes from correctly computing −p = −q − r + 34 (multiplying the isolated equation by −1) and then reporting that expression as p instead of negating back to find p itself. Check with q = 1, r = 1: this gives p = −1 − 1 + 34 = 32, the opposite sign of the correct p = −32.*

**D.** p = −q − r − 34 

  *This correctly flips the sign of 34 when moving it across (giving −34) but also negates q and r, which never switched sides and should keep their original signs. Check with q = 1, r = 1: this gives p = −1 − 1 − 34 = −36, close to but not the correct p = −32 — off by exactly 2q + 2r.*

*Difficulty: easy*

---

##### Q11
The equation 8j = k + 15m relates the distinct positive numbers j, k, and m. Which equation correctly expresses j in terms of k and m?

**A.** j = k/8 + 15m 

  *This divides only the k-term by 8 and leaves 15m untouched, instead of dividing the entire right-hand side by 8. Check with k = 8, m = 1 (so the correct j = (8 + 15)/8 = 2.875): this choice gives j = 1 + 15 = 16, nowhere close.*

**B.** j = k + 15m/8 

  *This divides only the 15m term by 8 and leaves k untouched — the same partial-distribution error as choice A, applied to the other term instead. Check with k = 8, m = 1: this gives j = 8 + 1.875 = 9.875, not the correct j = 2.875.*

**C.** j = 8(k + 15m) 

  *This multiplies by 8 instead of dividing — the inverse operation error. Check with k = 8, m = 1: this gives j = 8(23) = 184, vastly larger than the correct j = 2.875.*

**D.** j = (k + 15m)/8 **(Correct)**

  *Correct. Divide both sides of 8j = k + 15m by 8: j = (k + 15m)/8. Check with k = 8, m = 1: j = (8 + 15)/8 = 2.875, and substituting back — 8(2.875) = 23 = 8 + 15(1). ✓*

*Difficulty: easy*

---

##### Q12
The equation 7m = 2(n + p) relates the positive numbers m, n, and p. Which equation correctly gives m in terms of n and p?

**A.** m = 2(n + p)/7 **(Correct)**

  *Correct. Divide both sides of 7m = 2(n + p) by 7: m = 2(n + p)/7. Check with n = 1, p = 6 (so n + p = 7): m = 2(7)/7 = 2, and substituting back — 7(2) = 14 = 2(7). ✓*

**B.** m = 2(n + p) 

  *This drops the coefficient 7 entirely, as though 7m = 2(n + p) meant m = 2(n + p) with no division needed. Check with n = 1, p = 6: this gives m = 14, but substituting back — 7(14) = 98 ≠ 2(7) = 14.*

**C.** m = 2(n + p) − 7 

  *This treats the 7 as a term to subtract rather than a coefficient to divide by. Check with n = 1, p = 6: this gives m = 14 − 7 = 7, but substituting back — 7(7) = 49 ≠ 14.*

**D.** m = 2 − n − p − 7 

  *This converts every multiplication in the equation into addition or subtraction — misreading 7m as 7 + m and 2(n + p) as 2 − n − p, then isolating m as though the equation were 7 + m = 2 − n − p. Check with n = 1, p = 6: this gives m = 2 − 1 − 6 − 7 = −12, far from the correct m = 2.*

*Difficulty: easy*

---

##### Q13
In the system of equations y = 5x + 4 and y = 5x² + 4, which ordered pair (x, y) is a solution?

**A.** (0, 0) 

  *This assumes both graphs pass through the origin because neither equation has a constant multiplying x by itself, but the +4 in each equation rules that out: at x = 0, the first equation gives y = 5(0) + 4 = 4, not 0.*

**B.** (0, 4) **(Correct)**

  *Correct. Set the two expressions for y equal: 5x + 4 = 5x² + 4, so 5x = 5x², which gives x = x² and x² − x = 0, so x(x − 1) = 0 and x = 0 or x = 1. At x = 0: both equations give y = 4. Check: 5(0) + 4 = 4 and 5(0)² + 4 = 4. ✓*

**C.** (8, 44) 

  *x = 8 satisfies only the first equation — 5(8) + 4 = 44 — but not the second: 5(8)² + 4 = 324, not 44. A solution to the system has to satisfy both equations, not just one.*

**D.** (8, 84) 

  *This shares the same x = 8 as choice C, but evaluates the second equation with 8² miscomputed as 2 × 8 = 16 instead of 8 × 8 = 64: 5(16) + 4 = 84. Squaring a number means multiplying it by itself, not doubling it — 8² is 64, and 5(64) + 4 = 324.*

*Difficulty: hard*

---

##### Q14
How many distinct real solutions are there to the equation 3x² − 15x + 18 = 0?

**A.** Exactly one 

  *This correctly computes 4ac = 4(3)(18) = 216 but then subtracts incorrectly, reporting 225 − 216 as 0 instead of 9, and concludes the discriminant is zero. It is not: 225 − 216 = 9, which is positive, not zero.*

**B.** Exactly two **(Correct)**

  *Correct. The discriminant is b² − 4ac = (−15)² − 4(3)(18) = 225 − 216 = 9, which is positive, so the equation has two distinct real solutions. Check by factoring: 3x² − 15x + 18 = 3(x² − 5x + 6) = 3(x − 2)(x − 3), so x = 2 and x = 3 — two distinct roots. ✓*

**C.** Infinitely many 

  *This treats a quadratic that factors cleanly as though it were an identity true for every x, generalizing from the fact that (x − 2)(x − 3) = 0 has clean integer roots. A factored equation pins down exactly the values where a factor is zero — x = 2 or x = 3 — not a range of values; it becomes an identity with infinitely many solutions only when every coefficient is zero, which is not the case here.*

**D.** Zero 

  *This computes (−15)² as −225 instead of +225 — dropping the rule that a negative number squared is positive — giving a discriminant of −225 − 216 = −441, which is negative and would predict no real solutions. The actual discriminant is 225 − 216 = 9, which is positive.*

*Difficulty: hard*

---

##### Q15
The graph of a system of a linear equation and a nonlinear equation is shown in the xy-plane, both plotted for x between −2 and 9: a straight line rises gently across the window, and a curve starts out nearly flat on the left side of the window, then bends upward and rises more and more steeply as x increases, climbing out of the top of the window by around x = 5. The line and the curve cross the grid at exactly one visible point, where x = 2 and y = 4. What is the solution (x, y) to this system?

**A.** (0, 0) 

  *This assumes both graphs pass through the origin, the way a student might default for an unfamiliar pair of curves. Neither does: the line crosses the y-axis above 0, and the curve sits above 0 across the entire window, so (0, 0) is not a point on either graph, let alone one shared by both.*

**B.** (0, 2) 

  *This is a feature of the line alone — where it crosses the y-axis — not the point where the two graphs meet. A solution to a system has to lie on both graphs at once; (0, 2) sits on the line, but the curve does not pass through it, so it satisfies only one of the two equations in the system.*

**C.** (2, 4) **(Correct)**

  *Correct. A solution to a system shown graphically is a point where the two graphs cross — read directly off the grid, the line and the curve meet at exactly one place in the pictured window, at x = 2 and y = 4. Both graphs pass through (2, 4), which is what makes it, and nothing else in the window, the shared solution.*

**D.** (4, 0) 

  *By x = 4 the curve has already climbed well above the x-axis on its way out of the top of the window, and the line is well above y = 0 there too — this pairs an x-value taken from the curve's steep, later region with a y-value that belongs to neither graph at that point. Reading a solution means finding where the two graphs cross at the SAME point, not combining an x-coordinate from one part of the picture with an unrelated y-coordinate.*

*Difficulty: medium*

---

##### Q16
The graph of a system of a linear and a quadratic equation is shown in the xy-plane, plotted for x between 0 and 12: a parabola that opens upward with its vertex at (4, 1), and a horizontal line at y = 1 that just touches the parabola at that vertex and nowhere else in the window. What is the solution (x, y) to this system?

**A.** (0, 0) 

  *This assumes the parabola passes through the origin. It does not: the vertex — the parabola's lowest point — is at (4, 1), so every point on the parabola has y ≥ 1, and the origin, where y = 0, sits below the entire curve. The horizontal line is drawn at y = 1 as well, so neither graph reaches (0, 0).*

**B.** (−4, 1) 

  *This has the correct y-coordinate but the wrong sign on x — the vertex sits four units to the RIGHT of the y-axis, at x = 4, not four units to the left. Reading the horizontal position off the wrong side of the axis is the entire difference between this choice and the correct one.*

**C.** (4, −1) 

  *This has the correct x-coordinate but the wrong sign on y — the vertex sits one unit ABOVE the x-axis, at y = 1, not below it. The parabola opens upward from that point, so it never dips down to y = −1 anywhere in the pictured window.*

**D.** (4, 1) **(Correct)**

  *Correct. A line that touches a parabola at exactly one point is tangent to it there, and the picture shows the horizontal line grazing the parabola precisely at its vertex, (4, 1). This is the graphical picture of a zero discriminant: substituting the line's equation into the parabola's would produce a quadratic with a repeated root at x = 4 — one solution instead of two, which is exactly what "tangent" looks like.*

*Difficulty: easy*

---

##### Q17
A system of equations consists of a quadratic equation and a linear equation, graphed in the xy-plane for x and y between −10 and 10: an upward-opening parabola with its vertex below the x-axis and slightly left of the y-axis, crossing the x-axis once to the left of x = −5 and once between x = 3 and x = 5, and a line with a shallow positive slope crossing the y-axis just above the origin. Within the pictured window, the line crosses the parabola's falling left branch once and its rising right branch once. How many solutions does this system have?

**A.** 0 

  *This is what the picture would show only if the line stayed entirely above or entirely below the parabola across the whole window. It doesn't: the parabola dips below the line through the middle of the window but rises back above it on both sides, so the two graphs do cross — twice, not zero times.*

**B.** 1 

  *This is the count for tangency — a line touching a parabola at exactly one point. That's not what's pictured here: the line crosses the parabola's left branch on the way down and crosses the right branch again farther out, so there are two separate crossings, not a single point of contact.*

**C.** 2 **(Correct)**

  *Correct. A solution to a system shown graphically is a point where the two graphs cross. Starting from the left edge of the window the line sits above the parabola; the parabola's descending left branch crosses the line once on its way down toward the vertex, and its rising right branch crosses the line a second time before the window ends. That's two crossings, so the system has two solutions.*

**D.** 3 

  *This counts one of the parabola's own x-intercepts as an extra intersection with the line. The parabola crossing the x-axis is a feature of the parabola alone — it only counts as a solution to the SYSTEM at a point where the line is there too, and the line doesn't pass through either x-intercept in this picture.*

*Difficulty: medium*

---

##### Q18
In the system of equations y = x + 1 and y = x² + x, if (x, y) is a solution, which of the following could be the value of x?

**A.** −1 **(Correct)**

  *Correct. Set the two expressions for y equal: x² + x = x + 1, and subtract x from both sides: x² = 1, so x = 1 or x = −1. Only −1 appears among the choices. Check: at x = −1, y = x + 1 = 0 and y = x² + x = 1 − 1 = 0. ✓*

**B.** 0 

  *This treats the second equation alone as though it were already set to zero: x² + x = 0 factors as x(x + 1) = 0, giving x = 0 or x = −1 — but y = x² + x is only one of the two equations, and finding where it equals zero is a different question from finding where the two graphs meet. Check x = 0 against both equations: y = x + 1 = 1, while y = x² + x = 0, and 1 ≠ 0.*

**C.** 2 

  *This solves x² = 1 by multiplying 1 by the exponent instead of taking a square root: 1 × 2 = 2. Undoing a square means asking what number times itself gives 1, not what 1 times 2 gives. Check: at x = 2, y = x² + x = 6, and y = x + 1 = 3; 6 ≠ 3.*

**D.** 3 

  *This solves x² = 1 by adding the exponent instead of taking a square root: 1 + 2 = 3. Undoing a square is not an addition problem either. Check: at x = 3, y = x² + x = 12, and y = x + 1 = 4; 12 ≠ 4.*

*Difficulty: easy*

---

##### Q19
What values satisfy the equation x² − x − 1 = 0?

**A.** x = 1 and x = 2 

  *These are the roots of x² − 3x + 2 = 0 — a nearby trinomial that factors cleanly as (x − 1)(x − 2) — substituted in place of the equation actually given. Check against the real equation: at x = 1, 1² − 1 − 1 = −1, not 0; at x = 2, 2² − 2 − 1 = 1, not 0. Neither number is a root of x² − x − 1 = 0.*

**B.** x = −1/2 and x = 3/2 

  *This is a factoring attempt that gets the sum right and the product wrong: −1/2 and 3/2 add to 1, matching −b/a, but multiply to −3/4, not c/a = −1. x² − x − 1 doesn't factor over rational numbers — no pair of rational numbers has both the required sum and the required product — which is exactly why this equation calls for the quadratic formula rather than a guess-and-check factor pair.*

**C.** x = (1 + √5)/2 and x = (1 − √5)/2 **(Correct)**

  *Correct. This doesn't factor over the integers, so use the quadratic formula with a = 1, b = −1, c = −1: x = (−(−1) ± √((−1)² − 4(1)(−1))) / (2(1)) = (1 ± √(1 + 4))/2 = (1 ± √5)/2. Check by substitution, using x² = x + 1 (what the equation says): at x = (1+√5)/2 ≈ 1.618, x² ≈ 2.618, and x + 1 ≈ 2.618. ✓*

**D.** x = (−1 + √5)/2 and x = (−1 − √5)/2 

  *This drops the negation on b inside the formula: with b = −1, the numerator should be −b = −(−1) = 1, not b = −1 itself. Using −1 instead of 1 in the numerator gives this pair. Check: at x = (−1+√5)/2 ≈ 0.618, x² − x − 1 ≈ 0.382 − 0.618 − 1 = −1.236, not 0.*

*Difficulty: hard*

---

##### Q20
What is the product of the solutions to the equation (x − 4)(x + 2)(x − 1) = 0?

**A.** 8 

  *This flips the sign on just one root: reading (x + 2) = 0 as though its root were +2 instead of −2 gives the set {4, 2, 1}, and 4 × 2 × 1 = 8. Every factor written (x − r) has root +r and every factor written (x + r) has root −r — the sign inside the parenthesis is the opposite of the root, and missing that on even one factor changes the product. Check: (x + 2) at x = 2 gives 4, not 0, so 2 isn't actually a root of that factor.*

**B.** 3 

  *3 is the SUM of the solutions (4 + (−2) + 1 = 3), not their product. Sum and product are both legitimate things to compute from a set of roots, but this equation asks for the product.*

**C.** −3 

  *Expanding the equation gives x³ − 3x² − 6x + 8 = 0, and −3 is the coefficient of x² in that expansion — the number that gives the SUM of the roots (−(−3)/1 = 3, matching 4 + (−2) + 1), not the number that gives their product. The product comes from the constant term instead: −d/a = −8/1 = −8.*

**D.** −8 **(Correct)**

  *Correct. Apply the zero-product property to each factor: x = 4, x = −2, or x = 1. Their product is 4 × (−2) × 1 = −8. Check by expanding: (x−4)(x+2)(x−1) = x³ − 3x² − 6x + 8, and for a cubic ax³ + bx² + cx + d = 0 the product of the roots is −d/a = −8/1 = −8. ✓*

*Difficulty: sat-hardest*

---

##### Q21
What is the solution to the equation 2(x + 1)/(x + 5) = 1 − 1/(x + 5)?

**A.** 0 

  *This comes from misidentifying the excluded value of the equation: the denominator x + 5 is zero at x = −5, not at x = 0. Setting x + 5 equal to 5 instead of to 0 — using the visible constant directly rather than negating it — lands on x = 0, which is neither the equation's excluded value nor a solution to it. Check: 2(0+1)/(0+5) = 2/5, and 1 − 1/(0+5) = 4/5; 2/5 ≠ 4/5.*

**B.** 2 **(Correct)**

  *Correct. Add 1/(x+5) to both sides so both fractions are on the left: 2(x+1)/(x+5) + 1/(x+5) = 1, and combine over the common denominator: [2(x+1) + 1]/(x+5) = 1, so 2x + 3 = x + 5 (valid since x ≠ −5), giving x = 2. Check: 2(2+1)/(2+5) = 6/7, and 1 − 1/(2+5) = 1 − 1/7 = 6/7. ✓*

**C.** 3 

  *This forgets to distribute the 2 across (x + 1) when combining the fractions, using 2x + 1 in the numerator instead of the correct 2x + 2: (2x+1)/(x+5) + 1/(x+5) = 1 gives 2x + 2 = x + 5, so x = 3. Check in the original equation: 2(3+1)/(3+5) = 8/8 = 1, and 1 − 1/(3+5) = 1 − 1/8 = 7/8; 1 ≠ 7/8.*

**D.** 5 

  *This is the correct excluded value with its sign dropped: the denominator x + 5 is undefined at x = −5, and reporting the magnitude without the negative sign gives x = 5 — which isn't even where the equation is undefined, let alone where it's satisfied. Check: 2(5+1)/(5+5) = 12/10 = 6/5, and 1 − 1/(5+5) = 1 − 1/10 = 9/10; 6/5 ≠ 9/10.*

*Difficulty: medium*

---

##### Q22
An oceanographer uses the equation s = (3/2)p to model the speed s, in knots, of an ocean wave, where p represents the period of the wave, in seconds. Which of the following represents the period of the wave in terms of the speed of the wave?

**A.** p = (2/3)s **(Correct)**

  *Correct. Multiply both sides of s = (3/2)p by the reciprocal 2/3: (2/3)s = p. Check with p = 4: s = (3/2)(4) = 6, and (2/3)(6) = 4 = p. ✓*

**B.** p = (3/2)s 

  *This multiplies s by 3/2 again instead of by its reciprocal 2/3 — the same fraction that produced s in the first place, applied a second time instead of undone. Check with p = 4 (so s = 6): this gives p = (3/2)(6) = 9, not 4.*

**C.** p = (2/3) + s 

  *This treats the coefficient 3/2 as a term added to p rather than one multiplying it, and adds its reciprocal 2/3 to s instead of multiplying by it. Check with p = 4 (so s = 6): this gives p = 2/3 + 6 ≈ 6.67, not 4.*

**D.** p = (3/2) + s 

  *This also treats the coefficient as an addend rather than a multiplier, and adds the original 3/2 instead of its reciprocal. Check with p = 4 (so s = 6): this gives p = 3/2 + 6 = 7.5, not 4.*

*Difficulty: easy*

---

##### Q23
Which of the following is a solution to the equation (x + 2)(x + 3) = (x − 2)(x − 3) + 10?

**A.** 1 **(Correct)**

  *Correct. Expand both sides: (x+2)(x+3) = x² + 5x + 6, and (x−2)(x−3) + 10 = x² − 5x + 6 + 10 = x² − 5x + 16. Setting them equal: x² + 5x + 6 = x² − 5x + 16, so 10x = 10 and x = 1. Check in the original: (1+2)(1+3) = 12, and (1−2)(1−3) + 10 = 2 + 10 = 12. ✓*

**B.** 0 

  *This drops the +10 entirely, solving (x+2)(x+3) = (x−2)(x−3) as though the right side had no constant added to it: x² + 5x + 6 = x² − 5x + 6 gives 10x = 0, so x = 0. Check in the actual equation: (0+2)(0+3) = 6, and (0−2)(0−3) + 10 = 6 + 10 = 16; 6 ≠ 16.*

**C.** −2 

  *This applies the zero-product property to the left side alone, as though the equation were (x+2)(x+3) = 0 rather than equal to a nonzero expression on the right: that gives x = −2 or x = −3. The zero-product property only applies to a product that equals zero, and here it equals (x−2)(x−3) + 10. Check: (−2+2)(−2+3) = 0, and (−2−2)(−2−3) + 10 = 20 + 10 = 30; 0 ≠ 30.*

**D.** −5 

  *This reports the coefficient of x from expanding the right side, x² − 5x + 6, directly as the answer — treating the −5 that appears while multiplying out (x−2)(x−3) as if it were the solution, rather than continuing on to combine like terms and solve for x. Check: (−5+2)(−5+3) = 6, and (−5−2)(−5−3) + 10 = 56 + 10 = 66; 6 ≠ 66.*

*Difficulty: medium*

---

##### Q24
The speed of sound in dry air, v, can be modeled by the formula v = 331.3 + 0.606T, where T is the temperature in degrees Celsius and v is measured in meters per second. Which of the following correctly expresses T in terms of v?

**A.** T = (v + 0.606)/331.3 

  *This swaps the roles of the two constants: it divides by 331.3 (the additive term) instead of by 0.606 (the coefficient of T), and adds 0.606 instead of subtracting 331.3. Check with T = 10: v = 331.3 + 0.606(10) = 337.36, and this choice gives (337.36 + 0.606)/331.3 ≈ 1.020, not 10.*

**B.** T = (v − 0.606)/331.3 

  *This subtracts the coefficient 0.606 instead of the constant term 331.3, and divides by 331.3 instead of by 0.606 — both operations target the wrong number. Check with T = 10 (v = 337.36): this gives (337.36 − 0.606)/331.3 ≈ 1.016, not 10.*

**C.** T = (v + 331.3)/0.606 

  *This adds 331.3 instead of subtracting it — a sign error when moving the constant term across the equation. Check with T = 10 (v = 337.36): this gives (337.36 + 331.3)/0.606 ≈ 1,103.7, not 10.*

**D.** T = (v − 331.3)/0.606 **(Correct)**

  *Correct. Subtract 331.3 from both sides of v = 331.3 + 0.606T: v − 331.3 = 0.606T, then divide by 0.606: T = (v − 331.3)/0.606. Check with T = 10: v = 331.3 + 6.06 = 337.36, and (337.36 − 331.3)/0.606 = 10. ✓*

*Difficulty: easy*

---

##### Q25
Blood volume, V_B, in a human can be determined using the equation V_B = V_P/(1 − H), where V_P is the plasma volume and H is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume?

**A.** H = 1 − V_P/V_B **(Correct)**

  *Correct. Multiply both sides of V_B = V_P/(1−H) by (1−H): V_B(1−H) = V_P, so 1 − H = V_P/V_B, and H = 1 − V_P/V_B. Check with V_P = 6, H = 0.5: V_B = 6/0.5 = 12, and H = 1 − 6/12 = 0.5. ✓*

**B.** H = V_B/V_P 

  *This drops the '1 −' entirely, treating the denominator as though it were H alone rather than (1 − H): solving V_B = V_P·H that way gives H = V_B/V_P. Check with V_P = 6, H = 0.5 (so V_B = 12): this gives H = 12/6 = 2, not 0.5.*

**C.** H = 1 + V_P/V_B 

  *This adds V_P/V_B instead of subtracting it — a sign error in isolating H after dividing by V_B. Check with V_P = 6, H = 0.5 (V_B = 12): this gives H = 1 + 6/12 = 1.5, not 0.5.*

**D.** H = V_B − V_P 

  *This treats V_B = V_P/(1−H) as though it were built from addition and subtraction alone, isolating H by simple subtraction rather than working through the division. Check with V_P = 6, H = 0.5 (V_B = 12): this gives H = 12 − 6 = 6, not 0.5.*

*Difficulty: medium*

---

##### Q26
In the system of equations x² = 6x + y and y = −6x + 36, a solution is (x, y). Which of the following is a possible value of xy?

**A.** 0 **(Correct)**

  *Correct. Substitute y = −6x + 36 into x² = 6x + y: x² = 6x + (−6x + 36) = 36, so x = 6 or x = −6. At x = 6: y = −6(6) + 36 = 0, so xy = 6(0) = 0. (The other solution, x = −6, gives y = 72 and xy = −432 — not among the choices, but the question only asks for a possible value.) Check: 6² = 36, and 6(6) + 0 = 36. ✓*

**B.** 6 

  *This reports x itself (from x² = 36, x = 6) rather than the product xy the question asks for. At x = 6, y = −6(6) + 36 = 0, so the actual product is xy = 6(0) = 0, not 6.*

**C.** 12 

  *This comes from a multiplication slip while finding y: substituting x = 6 into y = −6x + 36, −6 × 6 is miscomputed as −24 instead of −36, giving y = −24 + 36 = 12 — and that miscalculated y is reported directly instead of the product xy. Check: the correct y at x = 6 is −6(6) + 36 = 0, not 12, and even 12 itself isn't xy.*

**D.** 36 

  *This is x² (which does equal 36 after substitution), not xy — after correctly deriving x² = 6x + y = 36, this stops there and reports 36 directly, as though the question had asked for x² rather than for the product of the coordinates. x² = 36 gives x = 6 or x = −6, and pairing either with its actual y gives xy = 0 or xy = −432, never 36 itself.*

*Difficulty: hard*

---

##### Q27
In a city, the property tax T, in dollars, is calculated using the formula T = 0.01(P − 40,000), where P is the value of the property, in dollars. Which of the following expresses the value of the property in terms of the property tax?

**A.** P = 100T − 400 

  *This divides 40,000 by 100 before moving it across — as though only the 40,000 inside the parentheses got divided by 0.01, rather than the entire quantity (P − 40,000) — and also subtracts instead of adds. Check with T = 100, P = 50,000: T = 0.01(50,000 − 40,000) = 100 ✓, but this choice gives P = 100(100) − 400 = 9,600, not 50,000.*

**B.** P = 100T + 400 

  *This divides 40,000 by 100 before adding it back — as though only the 40,000 inside the parentheses got divided by 0.01, rather than the entire quantity (P − 40,000). Check with T = 100, P = 50,000: this gives P = 100(100) + 400 = 10,400, not 50,000.*

**C.** P = 100T − 40,000 

  *This correctly divides the entire quantity by 0.01 (giving 100T) but then subtracts 40,000 instead of adding it back — a sign error when moving the constant across the equation. Check with T = 100, P = 50,000: this gives P = 100(100) − 40,000 = −30,000, not 50,000.*

**D.** P = 100T + 40,000 **(Correct)**

  *Correct. Divide both sides of T = 0.01(P − 40,000) by 0.01: 100T = P − 40,000, so P = 100T + 40,000. Check with P = 50,000: T = 0.01(50,000 − 40,000) = 100, and 100(100) + 40,000 = 50,000. ✓*

*Difficulty: easy*

---

##### Q28
The formula v² = LT/m expresses the square of the speed v of a wave moving along a string in terms of tension T, mass m, and length L of the string. What is T in terms of m, v, and L?

**A.** T = mv²/L **(Correct)**

  *Correct. Multiply both sides of v² = LT/m by m: mv² = LT, then divide by L: T = mv²/L. Check with m = 2, L = 3, v = 2 (v² = 4): T = 2(4)/3 = 8/3, and substituting back — LT/m = 3(8/3)/2 = 8/2 = 4 = v². ✓*

**B.** T = m/(v²L) 

  *This is the reciprocal of L times the correct T, inverting where m and v² belong — treating v² as a divisor instead of a factor that stays multiplied with m. Check with m = 2, L = 3, v² = 4: this gives T = 2/(4×3) = 1/6, not 8/3.*

**C.** T = mL/v² 

  *This divides by v² and multiplies by L — the reverse of what's needed: v² should stay multiplied (it's already isolated on the left) and L should be divided out, not the other way around. Check with m = 2, L = 3, v² = 4: this gives T = 2(3)/4 = 1.5, not 8/3.*

**D.** T = L/(mv²) 

  *This is the reciprocal of the entire correct expression — every quantity that should be in the numerator (m, v²) ends up in the denominator and vice versa, as though isolating T meant flipping the whole equation upside down rather than performing the two inverse operations (multiply by m, divide by L) in order. Check with m = 2, L = 3, v² = 4: this gives T = 3/(2×4) = 3/8, not 8/3.*

*Difficulty: easy*

---

##### Q29
In the system of equations y = x² and 2y + 6 = 2(x + 3), if (x, y) is a solution and x > 0, what is the value of xy?

**A.** 1 **(Correct)**

  *Correct. Simplify the second equation first: 2y + 6 = 2(x+3) = 2x + 6, so 2y = 2x and y = x. Substitute into y = x²: x = x², so x² − x = 0 and x(x−1) = 0, giving x = 0 or x = 1. Since x > 0, x = 1, and y = x = 1, so xy = 1. Check: y = 1² = 1 ✓, and 2(1) + 6 = 8 = 2(1+3) ✓.*

**B.** 2 

  *This is x + y, not xy: at the valid solution x = 1, y = 1, the sum of the coordinates is 1 + 1 = 2, but the question asks for their product, which is 1 × 1 = 1.*

**C.** 3 

  *This misreads the equation 2y + 6 = 2(x + 3) as though the 3 inside the parentheses were the value of x, rather than solving the equation for it. Check that against the system: if x were 3, the first equation gives y = 3² = 9, but the second equation gives 2y + 6 = 2(3+3) = 12, so y would have to be 3, not 9 — x = 3 doesn't even satisfy the system consistently.*

**D.** 9 

  *This makes the same misidentification as choice C — reading the 3 inside 2(x + 3) as the value of x — then computes y = x² = 3² = 9 from that wrong x, and reports y alone rather than the product xy the question asks for.*

*Difficulty: medium*

---

##### Q30
What are the solutions to the equation 6x² + 5x − 7 = 0?

**A.** x = (−5 ± √(25 + 168))/12 **(Correct)**

  *Correct. With a = 6, b = 5, c = −7: x = (−b ± √(b² − 4ac))/(2a) = (−5 ± √(25 − 4(6)(−7)))/12 = (−5 ± √(25 + 168))/12. Sanity-check with a decimal: √193 ≈ 13.89, so x ≈ (−5 + 13.89)/12 ≈ 0.74; substituting back, 6(0.74)² + 5(0.74) − 7 ≈ 3.29 + 3.70 − 7 ≈ 0. ✓*

**B.** x = (−6 ± √(25 + 168))/12 

  *This puts −a in the numerator instead of −b — using −6 (the leading coefficient, negated) where the formula calls for −5 (the linear coefficient, negated). The quadratic formula's numerator is always −b, never −a.*

**C.** x = (−5 ± √(36 − 168))/12 

  *This squares a instead of b under the radical (6² = 36 instead of 5² = 25), and also drops the negative sign on c when computing −4ac, writing −4(6)(7) = −168 instead of the correct −4(6)(−7) = +168 — two separate slips landing in the same radical.*

**D.** x = (−6 ± √(36 − 168))/12 

  *This combines both errors at once: −a in the numerator instead of −b, and b² miscomputed as a² with the sign on −4ac dropped as well. Every number in this choice traces back to one of those two mix-ups.*

*Difficulty: hard*

---

##### Q31
When the equations y = x² − 1 and y = 3 are graphed in the xy-plane, what are the coordinates (x, y) of the points of intersection of the two graphs?

**A.** (2, 3) and (−2, 3) **(Correct)**

  *Correct. Substitute y = 3 into y = x² − 1: 3 = x² − 1, so x² = 4 and x = ±2. y stays 3 at both points. Check: at x = 2, x² − 1 = 4 − 1 = 3 ✓; at x = −2, x² − 1 = 4 − 1 = 3 ✓.*

**B.** (2, 4) and (−2, 4) 

  *This drops the '−1' when reporting y, using x² = 4 instead of x² − 1 = 3 — but y is already given as 3 by the second equation, so there's no need to recompute it, and doing so incorrectly here also contradicts the equation actually solved.*

**C.** (3, 8) and (−3, 8) 

  *This squares the given y-value itself (3² = 9) to find x², instead of substituting y = 3 into y = x² − 1 and solving x² − 1 = 3 for x² = 4. That gives x = ±3, and y = x² − 1 = 9 − 1 = 8 from that wrong x.*

**D.** (√2, 3) and (−√2, 3) 

  *This subtracts 1 instead of adding it when isolating x²: x² − 1 = 3 should give x² = 3 + 1 = 4, but this uses x² = 3 − 1 = 2, so x = ±√2.*

*Difficulty: easy*

---

##### Q32
In the equation y = ax² − c, a and c are positive constants. How many times does the graph of this equation intersect the graph of the equation y = a + c in the xy-plane?

**A.** Zero 

  *This assumes the combined equation could come out negative — as though solving ax² = a − 2c, where a large c might leave no real x. But the actual combined equation is ax² = a + 2c, and since a and c are both positive, a + 2c is always positive, so x² is always positive and real solutions always exist — the graphs always cross.*

**B.** One 

  *This assumes a parabola and a horizontal line always meet at exactly one point, the way a tangent line does — but a horizontal line generically crosses an upward-opening parabola either twice or not at all, and only grazes it once in the special case where the line passes exactly through the vertex. The vertex of y = ax² − c is (0, −c), and the line y = a + c passes through it only if a + c = −c, which can't happen when a and c are both positive.*

**C.** Two **(Correct)**

  *Correct. Set the expressions for y equal: ax² − c = a + c, so ax² = a + 2c, and x² = (a+2c)/a = 1 + 2c/a. Since a and c are both positive, 2c/a is positive, so x² is greater than 1 — always positive — which means x has two real values, x = ±√(1 + 2c/a). The graphs intersect twice for every positive a and c. Check with a = 1, c = 1: x² = 1 + 2 = 3, x = ±√3; y = a + c = 2 at both points, and ax² − c = 1(3) − 1 = 2 at each. ✓*

**D.** More than two 

  *A parabola and a horizontal line combine into a single quadratic equation in x, and a quadratic equation has at most two real roots — never more than two, no matter what the constants are. This choice would only make sense for a system that reduces to something of higher degree than 2.*

*Difficulty: sat-hardest*

---

##### Q33
The equation v = −w/(150x) relates the distinct positive numbers v, w, and x. Which equation correctly expresses w in terms of v and x?

**A.** w = −150vx **(Correct)**

  *Correct. Multiply both sides of v = −w/(150x) by 150x: 150xv = −w, so w = −150vx. Check with v = 1, x = 2: w = −150(1)(2) = −300, and substituting back — −(−300)/(150·2) = 300/300 = 1 = v. ✓*

**B.** w = −150v/x 

  *This divides by x instead of multiplying by it when clearing the denominator 150x — x should move to the numerator alongside 150 and v, not stay in a denominator. Check with v = 1, x = 2: this gives w = −150(1)/2 = −75, not −300.*

**C.** w = −x/(150v) 

  *This treats v and w as though they should swap positions entirely — inverting the relationship so that x ends up in the numerator and v in the denominator, when the original equation has v isolated on one side and w produced by multiplying, not dividing. Check with v = 1, x = 2: this gives w = −2/(150) ≈ −0.013, not −300.*

**D.** w = v + 150x 

  *This treats v = −w/(150x) as though it read v = w + 150x, isolating w by simple addition rather than clearing the fraction through multiplication. Check with v = 1, x = 2: this gives w = 1 + 300 = 301, not −300.*

*Difficulty: easy*

---

##### Q34
The given equation 14j + 5k = m relates the numbers j, k, and m. Which equation correctly expresses k in terms of j and m?

**A.** k = (m − 14j)/5 **(Correct)**

  *Correct. Subtract 14j from both sides of 14j+5k=m: 5k = m − 14j, then divide by 5: k = (m−14j)/5. Check with j = 1, m = 19: k = (19−14)/5 = 1, and substituting back — 14(1) + 5(1) = 19 = m. ✓*

**B.** k = (1/5)m − 14j 

  *This divides only the m by 5 and leaves 14j untouched, instead of dividing the entire quantity (m − 14j) by 5. Check with j = 1, m = 19: this gives k = (1/5)(19) − 14 = 3.8 − 14 = −10.2, not 1.*

**C.** k = (14j − m)/5 

  *This has the numerator's terms in the wrong order with a sign flip: 5k = m − 14j, not 14j − m. Swapping them negates the whole numerator. Check with j = 1, m = 19: this gives k = (14−19)/5 = −1, not 1.*

**D.** k = 5m − 14j 

  *This multiplies by 5 instead of dividing by it — the inverse of the operation actually needed to isolate k from 5k = m − 14j. Check with j = 1, m = 19: this gives k = 5(19) − 14 = 81, not 1.*

*Difficulty: easy*

---

##### Q35
The given equation p = 9 + 14/n relates the numbers p and n, where n is not equal to 0 and p > 9. Which equation correctly expresses n in terms of p?

**A.** n = (p − 9)/14 

  *This is the reciprocal of the correct expression — it isolates p − 9 correctly but then divides by 14 instead of dividing 14 by (p − 9). Check with n = 2 (so p = 9 + 14/2 = 16): this gives n = (16−9)/14 = 0.5, not 2.*

**B.** n = p/14 + 9 

  *This divides p by 14 directly and adds 9, without first isolating the fractional term 14/n by subtracting 9 from p. Check with n = 2 (p = 16): this gives n = 16/14 + 9 ≈ 10.14, not 2.*

**C.** n = p/14 − 9 

  *This makes the same mistake as choice B — dividing p by 14 directly instead of first isolating 14/n — and then subtracts 9 instead of continuing correctly, compounding the error with a sign slip besides. Check with n = 2 (p = 16): this gives n = 16/14 − 9 ≈ −7.86, not 2.*

**D.** n = 14/(p − 9) **(Correct)**

  *Correct. Subtract 9 from both sides of p = 9 + 14/n: p − 9 = 14/n, then take the reciprocal of both sides: n = 14/(p−9). Check with n = 2: p = 9 + 14/2 = 16, and 14/(16−9) = 14/7 = 2 = n. ✓*

*Difficulty: medium*

---

##### Q36
In the system of equations y = (x − 2)(x + 4) and y = 6x − 12, which ordered pair (x, y) is the solution?

**A.** (0, 2) 

  *This misreads the repeated structure of the parabola as though (x − 2) signaled a vertex-form shift landing at (0, 2), rather than solving the system's combined equation. But (x−2)(x+4) is factored form, not vertex form, and neither graph actually passes through (0, 2): the parabola's y-intercept is (0, −8), since (0−2)(0+4) = −8, and the line's is (0, −12), since 6(0)−12 = −12.*

**B.** (−4, 2) 

  *This pairs the parabola's own x-intercepts — found by (mistakenly) setting (x−2)(x+4) = 0 — as an (x, y) point, using −4 as x and 2 as y. But those two numbers are where the PARABOLA ALONE crosses the x-axis; they say nothing about where it meets the line y = 6x − 12. Check: at x = −4, y = (−4−2)(−4+4) = 0, not 2, and 6(−4)−12 = −36, not 2 either.*

**C.** (2, 0) **(Correct)**

  *Correct. Set the two expressions for y equal: (x−2)(x+4) = 6x−12. Expand the left side: x² + 2x − 8 = 6x − 12, so x² − 4x + 4 = 0, which is (x−2)² = 0 — a double root at x = 2. Then y = 6(2) − 12 = 0. Check both equations: (2−2)(2+4) = 0 ✓, and 6(2) − 12 = 0 ✓.*

**D.** (2, −4) 

  *This makes the same mistake as choice B — pairing the parabola's own x-intercepts, 2 and −4, as though they formed the solution's (x, y) coordinates — just in the other order. Check: at x = 2, y = (2−2)(2+4) = 0, not −4; the actual point at x = 2 is (2, 0), not (2, −4).*

*Difficulty: medium*

---

##### Q37
What is the positive solution to the equation −4x² − 7x = −36?

**A.** 7/4 

  *This is the sum-of-roots shortcut with the sign dropped: for 4x² + 7x − 36 = 0, the sum of the two solutions is −b/a = −7/4 (check: 9/4 + (−4) = −7/4), and this reports the magnitude of that ratio, 7/4, as though it were itself one of the solutions. A sum is not a root — and even as a sum, the sign here is missing.*

**B.** 9/4 **(Correct)**

  *Correct. Move every term to one side: −4x² − 7x + 36 = 0, then multiply by −1 so the leading coefficient is positive: 4x² + 7x − 36 = 0. This factors: two numbers with product 4×(−36) = −144 and sum 7 are 16 and −9. Split and group: 4x² + 16x − 9x − 36 = 0 → 4x(x+4) − 9(x+4) = 0 → (4x−9)(x+4) = 0, so x = 9/4 or x = −4. The positive solution is 9/4. Check in the original: −4(9/4)² − 7(9/4) = −81/4 − 63/4 = −144/4 = −36. ✓*

**C.** 4 

  *This flips the sign of the x² term and the constant when multiplying by −1, but not the −7x term: −4x² − 7x + 36 = 0 becomes 4x² − 7x − 36 = 0 instead of the correct 4x² + 7x − 36 = 0. That equation factors as (4x+9)(x−4) = 0, giving x = 4 or x = −9/4 — but of the wrong equation. Check 4 in the ORIGINAL equation: −4(4)² − 7(4) = −64 − 28 = −92, not −36.*

**D.** 7 

  *This reports the coefficient of x from the rearranged equation, 7, directly as the solution, without solving the equation at all. Check: −4(7)² − 7(7) = −196 − 49 = −245, nowhere near −36.*

*Difficulty: hard*

---

##### Q38
The given equation b − 72 = x/y relates the positive numbers b, x, and y. Which equation correctly expresses x in terms of b and y?

**A.** x = (b − 72)/y 

  *This divides (b−72) by y instead of multiplying by it — clearing a denominator on the right side requires multiplying both sides by y, not dividing. Check with b = 10, y = 2 (so correct x = (10−72)(2) = −124): this gives x = (10−72)/2 = −31, not −124.*

**B.** x = by − 72 

  *This multiplies only the b by y and leaves 72 untouched, instead of distributing y across the entire quantity (b − 72). Check with b = 10, y = 2: this gives x = 10(2) − 72 = −52, not −124.*

**C.** x = (by − 72)/y 

  *This makes the same partial-distribution slip as choice B — multiplying only b by y — and then divides the whole thing by y again, an operation the equation never called for. Check with b = 10, y = 2: this gives x = (20−72)/2 = −26, not −124.*

**D.** x = by − 72y **(Correct)**

  *Correct. Multiply both sides of b − 72 = x/y by y: y(b−72) = x, so x = by − 72y. Check with b = 10, y = 2: x = 10(2) − 72(2) = 20 − 144 = −124, and substituting back — 10 − 72 = −62, and x/y = −124/2 = −62. ✓*

*Difficulty: medium*

---

##### Q39
If 42/x = 7x, what is the value of 7x²?

**A.** 6 

  *This solves for x² but stops one step short of what's asked: cross-multiplying 42/x = 7x gives 42 = 7x², so x² = 6 — but the question asks for the value of 7x², not x², and 7(6) = 42, not 6.*

**B.** 7 

  *This reports the coefficient of x² from the equation, 7, as though the question were asking to identify the coefficient rather than to compute the value of the entire expression 7x². The coefficient and the expression's value are different things: 7x² is a product equal to 42, not simply the digit 7.*

**C.** 42 **(Correct)**

  *Correct. Cross-multiply 42/x = 7x by x: 42 = 7x². That's already the value the question asks for — no need to solve for x itself. 7x² = 42.*

**D.** 294 

  *This drops the coefficient 7 when clearing the fraction — cross-multiplying 42/x = 7x as though it read 42/x = x, giving x² = 42 instead of 7x² = 42 — and then multiplies that wrong x² by 7 anyway to try to answer the actual question: 7(42) = 294. The coefficient needs to be included once, not dropped and then reattached.*

*Difficulty: hard*

---

##### Q40
Four graphs each plot the system y = x² + 1.7 and y = 1.7 − x in the xy-plane, for x and y between about −6 and 7. Which graph correctly represents the system?

**A.** A parabola with its vertex on the y-axis at about (0, 1.7), opening upward, together with a line that also crosses the y-axis at about (0, 1.7) and slopes downward to the right, passing near (2.7, −1). **(Correct)**

  *Correct. y = x² + 1.7 is vertex form with h = 0 and k = 1.7, so its vertex sits on the y-axis at (0, 1.7) — not shifted left or right. y = 1.7 − x is a line with slope −1 (downward to the right) and y-intercept 1.7. Both graphs pass through (0, 1.7), and this is the only option that places the vertex there AND gives the line a negative slope. Check the intersection algebraically: x² + 1.7 = 1.7 − x → x² + x = 0 → x(x+1) = 0, so x = 0 or x = −1 — two crossings very close together near the vertex, which is exactly the near-tangent look this graph has there.*

**B.** The same parabola, vertex on the y-axis at about (0, 1.7), together with a line that crosses the y-axis at about (0, 1.7) but slopes upward to the right. 

  *This has the parabola's vertex in the right place, on the y-axis at (0, 1.7), but gives the line a positive slope. y = 1.7 − x has slope −1: as x increases, y decreases. A line with positive slope here has the sign of the slope flipped.*

**C.** A parabola whose vertex sits to the left of the y-axis, touching down near (−1.7, 0), together with a line sloping downward to the right through about (0, 2). 

  *This keeps roughly the correct line but shifts the parabola's vertex off the y-axis, down to the x-axis near x = −1.7. That comes from misreading the vertical shift +1.7 in y = x² + 1.7 as though it were a horizontal shift — treating the equation as (x + 1.7)² (vertex at (−1.7, 0)) rather than x² + 1.7 (vertex at (0, 1.7)). Vertex form's horizontal shift comes from what's added to x inside the square, not from a constant added outside it.*

**D.** The same left-shifted parabola as choice C, touching down near (−1.7, 0), together with a line sloping upward to the right. 

  *This combines both errors at once: the parabola's vertex is shifted left as in choice C, misreading the vertical shift as horizontal, and the line's slope is flipped positive as in choice B.*

*Difficulty: medium*

---

##### Q41
In the xy-plane, the system of equations x − y = 1 and x + y = x² − 3 has two solutions. Which ordered pair (x, y) is one of them?

**A.** (1 + √3, √3) **(Correct)**

  *Correct. From x − y = 1, x = y + 1. Substitute into x + y = x² − 3: (y+1) + y = (y+1)² − 3 → 2y + 1 = y² + 2y − 2 → y² = 3, so y = ±√3. Taking y = √3 gives x = 1 + √3. Check both equations: x − y = (1+√3) − √3 = 1 ✓, and x + y = 1 + 2√3, while x² − 3 = (1+√3)² − 3 = 4 + 2√3 − 3 = 1 + 2√3 ✓.*

**B.** (√3, −√3) 

  *This takes the two roots of y² = 3 — √3 and −√3 — and writes them directly as the coordinates, skipping the step that converts each y back into its own x via x = y + 1. Check x − y for this pair: √3 − (−√3) = 2√3, not 1, so it fails the first equation outright — it only happens to satisfy the second because x + y = 0 there for any x with x² = 3 and y = −x.*

**C.** (1 + √5, √5) 

  *This adds the left sides of the two equations correctly — (x−y)+(x+y) = 2x — but combines the right sides as though eliminating by subtraction instead of addition: (x²−3) − 1 = x² − 4 rather than (x²−3) + 1 = x² − 2. That mismatch turns the correct x² − 2x − 2 = 0 into x² − 2x − 4 = 0, giving x = 1 ± √5 instead of 1 ± √3 — and pairing it with the correct y = x − 1 gives this choice's y = √5. Check x − y: (1+√5) − √5 = 1 ✓ (which is what makes the choice tempting), but x + y = 1 + 2√5 ≈ 5.47, while x² − 3 = (1+√5)² − 3 = 3 + 2√5 ≈ 7.47 — they don't match.*

**D.** (√5, −1 + √5) 

  *This starts from the same flawed x² − 2x − 4 = 0 as choice C, completes the square correctly to (x−1)² = 5, but then takes the square root as though it read x² = 5 — dropping the −1 shift inside the parentheses — reporting x = √5 instead of x = 1 + √5. Pairing that with the correct y = x − 1 gives y = −1 + √5. x − y still checks out (√5 − (−1+√5) = 1), but x + y = −1 + 2√5 ≈ 3.47, while x² − 3 = 5 − 3 = 2 — they don't match.*

*Difficulty: hard*

---

##### Q42
If x is a solution to the equation 1/(x² + 10x + 25) = 4, which of the following is a possible value of x + 5?

**A.** 1/2 **(Correct)**

  *Correct. x² + 10x + 25 is (x+5)², so the equation is 1/(x+5)² = 4. Taking reciprocals of both sides gives (x+5)² = 1/4, so x + 5 = ±1/2. Check: with x + 5 = 1/2, x² + 10x + 25 = (1/2)² = 1/4, and 1/(1/4) = 4. ✓*

**B.** 5/2 

  *This comes from mixing two contradictory setups instead of committing to one. Correctly solving gives (x+5)² = 1/4 and x+5 = 1/2. But reading 1/(x+5)² = 4 as (x+5)² = 4 directly — dropping the reciprocal that flipping a fraction requires — gives x+5 = 2 instead. Adding the two candidate shifts together, 1/2 + 2, lands on 5/2. Check: if x+5 = 5/2, then x²+10x+25 = (5/2)² = 25/4, and 1/(25/4) = 4/25, not 4.*

**C.** 9/2 

  *This solves for x correctly — x = −9/2 or x = −11/2, from x + 5 = ±1/2 — but then answers with −x instead of x + 5, dropping the sign on the x-value it found. For the branch x = −9/2, −x = 9/2. Check directly: at x = −9/2, x² + 10x + 25 = (x+5)² = (1/2)² = 1/4, so 1/(1/4) = 4, which means x = −9/2 genuinely solves the equation — but the question asks for x + 5, which is 1/2 there, not 9/2.*

**D.** 11/2 

  *This is the same slip as choice C, applied to the other branch: x = −11/2 solves the equation (since x+5 = −1/2 and (−1/2)² = 1/4), but reporting −x instead of x + 5 gives 11/2 instead of −1/2.*

*Difficulty: medium*

---

##### Q43
Which of the following is a solution to the equation 2x² − 2 = 2x + 3?

**A.** 2 

  *This comes from an arithmetic slip combining the constants when collecting to standard form: 2x² − 2 = 2x + 3 → 2x² − 2x − 2 − 3 = 0 should give 2x² − 2x − 5 = 0, but combining −2 and −3 as −4 instead of −5 gives 2x² − 2x − 4 = 0, which reduces to x² − x − 2 = 0 and factors as (x−2)(x+1) = 0 — a clean integer root that 2x² − 2x − 5 = 0 doesn't actually have. Check x = 2 in the ORIGINAL equation: 2(2)² − 2 = 6, but 2(2) + 3 = 7, and 6 ≠ 7.*

**B.** 1 − √11 

  *This has the right numbers under the right operations but drops the division by 2a. Using the formula without dividing gives x = −b ± √(b²−4ac) = 2 ± 2√11; simplifying that by dividing by a (=2) instead of 2a (=4) leaves 1 ± √11 — the negative branch is this choice. Check: 1 − √11 ≈ −2.317; substituting, 2(−2.317)² − 2 ≈ 8.74, while 2(−2.317)+3 ≈ −1.63 — nowhere close.*

**C.** 1/2 + √11 

  *This divides the constant term of the numerator by 2 correctly (2/4 = 1/2) but forgets to also divide the radical term by 2, leaving √11 instead of √11/2: (1+√11)/2 = 1/2 + √11/2 becomes 1/2 + √11 here. Check: 1/2 + √11 ≈ 3.817; substituting, 2(3.817)² − 2 ≈ 27.1, while 2(3.817)+3 ≈ 10.6 — not equal.*

**D.** (1 + √11)/2 **(Correct)**

  *Correct. Collect to standard form: 2x² − 2x − 5 = 0. With a=2, b=−2, c=−5: x = (−b ± √(b²−4ac))/(2a) = (2 ± √(4+40))/4 = (2 ± 2√11)/4 = (1 ± √11)/2. Sanity-check with a decimal: √11 ≈ 3.317, so x ≈ 2.158; substituting, 2(2.158)² − 2 ≈ 7.32, and 2(2.158)+3 ≈ 7.32. ✓*

*Difficulty: medium*

---

##### Q44
In the equation 2x² − 4x = t, t is a constant. If the equation has no real solutions, which of the following could be the value of t?

**A.** −3 **(Correct)**

  *Correct. Collect to standard form: 2x² − 4x − t = 0, so a=2, b=−4, c=−t. No real solutions means the discriminant is negative: (−4)² − 4(2)(−t) < 0 → 16 + 8t < 0 → t < −2. Of the four choices, only −3 satisfies that. Check: at t=−3, 2x²−4x+3=0 has discriminant 16 − 24 = −8, which is negative. ✓*

**B.** −1 

  *This is what 16 + 8t < 0 gives if the inequality direction flips while isolating t — dividing 8t < −16 by the positive 8 needs no flip, but treating it as though it did gives t > −2, and −1 satisfies THAT (wrong) condition. Check the real equation: at t = −1, 2x² − 4x + 1 = 0 has discriminant 16 − 8 = 8, which is positive — two real solutions, not zero.*

**C.** 1 

  *This is the same flipped inequality as choice B, applied to a different value that also happens to satisfy the wrong condition t > −2. Check: at t = 1, 2x² − 4x − 1 = 0 has discriminant 16 + 8 = 24, positive — two real solutions, not zero.*

**D.** 3 

  *This drops the negative sign identifying c: standard form is 2x² − 4x − t = 0, so c = −t, but reading it as c = t instead gives discriminant 16 − 8t < 0, which solves to t > 2 — and 3 is the only offered choice satisfying that. Check the real equation at t = 3: 2x² − 4x − 3 = 0 has discriminant 16 + 24 = 40, positive — two real solutions, not zero.*

*Difficulty: medium*

---

##### Q45
What is the solution set of the equation √(2x + 6) + 4 = x + 3?

**A.** {−1} 

  *This keeps the extraneous root and drops the genuine one. It comes from flipping the sign constraint: isolating the radical gives √(2x+6) = x−1, and since a principal square root is never negative, x−1 must be ≥ 0. Flipping that to x−1 ≤ 0 (x ≤ 1) rules out x = 5 and leaves x = −1 as the only 'valid' candidate — backwards. Check x = −1 in the original: √4+4 = 6, but −1+3 = 2, and they don't match; −1 is extraneous.*

**B.** {5} **(Correct)**

  *Correct. Isolate the radical: √(2x+6) = x−1. Since a principal square root is never negative, x−1 must be ≥ 0, so x ≥ 1 — that alone rules out any negative candidate. Square both sides: 2x+6 = x²−2x+1, so x²−4x−5=0, and (x−5)(x+1)=0 gives x=5 or x=−1. Only x=5 satisfies x≥1. Check in the original: √16+4 = 4+4 = 8, and 5+3 = 8. ✓*

**C.** {−1, 5} 

  *This lists both candidates from the squared equation without checking either one in the ORIGINAL equation. Squaring is one-way, so x²−4x−5=0 can carry a root the original never had. Check x = −1: √(2(−1)+6)+4 = √4+4 = 6, but −1+3 = 2 — they don't match, so −1 is extraneous and only 5 belongs in the solution set.*

**D.** {0, −1, 5} 

  *This introduces an extra factor of x — as though clearing a denominator that isn't there — turning x²−4x−5=0 into x³−4x²−5x=0, which factors as x(x−5)(x+1)=0 and adds x=0 to the list. It also skips the check that would have caught it: at x=0, √(2(0)+6)+4 = √6+4 ≈ 6.45, and 0+3=3 — they don't match, and neither does x=−1 (see choice C).*

*Difficulty: medium*

---

##### Q46
How many distinct real solutions does the equation (x − 1)² = −4 have?

**A.** Exactly one 

  *This treats √(−4) as −√4 = −2, moving the negative sign outside the radical instead of recognizing that no real number squares to a negative number in the first place. There is no real square root of −4 — the equation has no real solutions, not one arrived at by taking a 'negative square root.'*

**B.** Exactly two 

  *This applies 'a quadratic has two solutions' as a blanket rule without checking whether the right side is reachable. Expanding to standard form gives x² − 2x + 1 = −4, so x² − 2x + 5 = 0, with discriminant 4 − 20 = −16. The ± in the quadratic formula only produces two real numbers when what's under the radical is non-negative; here it isn't.*

**C.** Infinitely many 

  *This confuses the equation with the inequality (x−1)² ≥ −4, which every real number does satisfy, since a square is never less than −4. But the problem is an equation, which demands the two sides be EQUAL — not merely compatible in range — and (x−1)² is never negative enough to reach −4 exactly.*

**D.** Zero **(Correct)**

  *Correct. The left side, (x−1)², is a real number squared, so it can never be negative — it is always ≥ 0. The right side is −4, which is negative, so no real value of x can make the two sides equal. The equation has zero real solutions.*

*Difficulty: easy*

---

##### Q47
In the system of equations y = x² + 2x + 1 and x + y + 1 = 0, if (x₁, y₁) and (x₂, y₂) are the two solutions, what is the value of y₁ + y₂?

**A.** −3 

  *This is x₁+x₂, not y₁+y₂: the two x-coordinates are −1 and −2, which sum to −3. The question asks for the sum of the y-coordinates, which is 0+1=1.*

**B.** −2 

  *This reports x₁ alone — one of the two x-coordinates of the solutions — instead of y₁+y₂. Solving the system gives x=−1 or x=−2, with points (−1,0) and (−2,1), so y₁+y₂=0+1=1, not either x-value by itself.*

**C.** −1 

  *This reports the OTHER x-coordinate alone, the same mistake as choice B in the other direction. x=−1 is one of the two solutions' x-values, not the sum of y₁ and y₂, which is 1.*

**D.** 1 **(Correct)**

  *Correct. From x+y+1=0, y=−x−1. Substitute: −x−1 = x²+2x+1, so x²+3x+2=0, and (x+1)(x+2)=0 gives x=−1 or x=−2. The two points are (−1, 0) and (−2, 1), so y₁+y₂ = 0+1 = 1.*

*Difficulty: medium*

---

##### Q48
If u − 3 = 6/(t − 2), what is t in terms of u?

**A.** t = 1/u 

  *This swaps which variable is isolated on the left before ever cross-multiplying — solving as though the equation read t−2 = 6/(u−3) instead of u−3 = 6/(t−2). Check with u=9 (the real t here is 2(9)/(9−3)=3): this choice gives t=1/9, and substituting back into u−3=6/(t−2) would require t−2 = 6/6 = 1, i.e. t=3 — not 1/9.*

**B.** t = (2u + 9)/u 

  *This has the right idea — isolate t−2 as a fraction and add 2 back — but combines the constant into the fraction using u as the denominator instead of (u−3), and picks up a stray +9 instead of +6 along the way. Check with u=6 (real t = 2(6)/(6−3) = 4): this choice gives t = (12+9)/6 = 3.5, not 4.*

**C.** t = 1/(u − 3) 

  *This correctly cross-multiplies to (t−2)(u−3)=6, but then divides both sides by 6(u−3) instead of just (u−3) — as though the 6 needed to be divided out rather than left as the numerator — giving t−2 = 1/(u−3), and then forgets to add the 2 back, reporting that expression as if it were t itself. Check with u=6 (real t=4): this choice gives t = 1/(6−3) = 1/3, not 4.*

**D.** t = 2u/(u − 3) **(Correct)**

  *Correct. Cross-multiply: (t−2)(u−3) = 6, so t−2 = 6/(u−3), and t = 2 + 6/(u−3) = [2(u−3)+6]/(u−3) = (2u−6+6)/(u−3) = 2u/(u−3). Check with u=6: t = 12/3 = 4, and substituting back — 6−3 = 3, and 6/(4−2) = 3. ✓*

*Difficulty: hard*

---

##### Q49
In the xy-plane, the graph of y = x² − 9 intersects line p at the points (1, a) and (5, b), where a and b are constants. What is the slope of line p?

**A.** 6 **(Correct)**

  *Correct. Since both points lie on y=x²−9: a = 1²−9 = −8, and b = 5²−9 = 16. The slope of line p is (b−a)/(5−1) = (16−(−8))/4 = 24/4 = 6.*

**B.** 2 

  *This adds a and b instead of subtracting them — computing (a+b)/(5−1) instead of (b−a)/(5−1): (−8+16)/4 = 8/4 = 2. Slope is rise (a difference in y), not a sum of the two y-values.*

**C.** −2 

  *This makes the same addition error as choice B — (a+b) instead of (b−a) — and also reverses the denominator to (1−5) instead of (5−1), which flips the sign a second time: (a+b)/(1−5) = 8/(−4) = −2.*

**D.** −6 

  *This swaps the order of the numerator without swapping the denominator to match — computing (a−b)/(5−1) instead of (b−a)/(5−1) — which gives the negative of the correct slope: (−8−16)/4 = −6.*

*Difficulty: easy*

---

##### Q50
The formula D = T − (9/25)(100 − H) can be used to approximate the dew point D, in degrees Fahrenheit, given the temperature T, in degrees Fahrenheit, and the relative humidity of H percent, where H > 50. Which of the following expresses the relative humidity in terms of the temperature and the dew point?

**A.** H = (25/9)(D − T) + 100 **(Correct)**

  *Correct. D−T = −(9/25)(100−H), so T−D = (9/25)(100−H), and (25/9)(T−D) = 100−H, so H = 100 − (25/9)(T−D) = 100 + (25/9)(D−T). Check with T=70, H=60: D = 70 − (9/25)(40) = 55.6, and (25/9)(55.6−70)+100 = (25/9)(−14.4)+100 = −40+100 = 60. ✓*

**B.** H = (25/9)(D − T) − 100 

  *This isolates (D−T) correctly but flips the sign on the 100 when moving it back across the equation, subtracting it instead of adding it back. Check with the same values (T=70, D=55.6, real H=60): this gives (25/9)(−14.4)−100 = −40−100 = −140, not 60.*

**C.** H = (25/9)(D + T) + 100 

  *This flips the sign inside the parentheses, using (D+T) instead of (D−T) — the same sign error as writing T+D instead of T−D one step earlier. Check: (25/9)(55.6+70)+100 ≈ 349+100 = 449, nowhere near the real H=60.*

**D.** H = (25/9)(D + T) − 100 

  *This combines both sign errors at once — (D+T) instead of (D−T), as in choice C, and −100 instead of +100, as in choice B. Check: (25/9)(125.6)−100 ≈ 349−100 = 249, not 60.*

*Difficulty: medium*

---

##### Q51
What is the sum of the solutions to the equation x² − 40x − 10 = 0?

**A.** 0 

  *This ignores the linear term entirely, treating x²−40x−10=0 as though it were x²−10=0, as if there were no −40x term at all. A symmetric equation like x²−10=0 has roots that are negatives of each other (±√10), summing to 0 — but the −40x term is very much present, and it's exactly what makes the actual sum nonzero.*

**B.** 5 

  *This misreads the coefficient of x as −5 instead of −40 — an easy misread on a printed equation — giving a sum of −(−5)/1 = 5. With a coefficient of −5, the equation would be x²−5x−10=0, which is not the one given.*

**C.** 10 

  *This is the PRODUCT of the solutions with a sign slip, not their sum. The actual product is c/a = −10/1 = −10; reading the constant as the positive 10 printed before its minus sign gives 10 instead. Either way, product isn't what's asked — the question wants the sum, −b/a = 40.*

**D.** 40 **(Correct)**

  *Correct. The equation is already in standard form with a=1, b=−40, c=−10. The sum of the solutions is −b/a = −(−40)/1 = 40 — no factoring or the quadratic formula required.*

*Difficulty: easy*

---

##### Q52
How many solutions are there to the system of equations y = x² + 3x − 7 and y − 5x + 8 = 0?

**A.** There are exactly 4 solutions. 

  *This treats the count as though each equation's own zeros needed to be tallied separately — 2 from where the parabola crosses the x-axis (x²+3x−7=0 does have two real roots) plus 2 more from somewhere else — rather than finding where the two graphs meet EACH OTHER. A system's solution count comes from the ONE combined equation, x²−2x+1=0, not from adding up each equation's independent zero count.*

**B.** There are exactly 2 solutions. 

  *This assumes a quadratic-looking combined equation must have two solutions without checking the discriminant. For x²−2x+1=0, the discriminant is (−2)²−4(1)(1) = 4−4 = 0 — computing it as b²+4ac instead of b²−4ac (a sign slip already common on this skill) gives 4+4=8, which looks positive and suggests two solutions. The real discriminant is exactly 0: x²−2x+1=(x−1)², a double root, one solution.*

**C.** There is exactly 1 solution. **(Correct)**

  *Correct. From y−5x+8=0, y=5x−8. Substitute: x²+3x−7 = 5x−8, so x²−2x+1=0, which is (x−1)²=0 — a double root at x=1. There is exactly one solution, the point (1, −3). Check: 1²+3(1)−7=−3, and 5(1)−8=−3. ✓*

**D.** There are no solutions. 

  *This computes the discriminant of x²−2x+1=0 with an arithmetic slip, subtracting 4ac twice instead of once — 4−4−4=−4 — and concludes it's negative. The actual discriminant is 4−4(1)(1)=0, not negative: the equation factors as (x−1)², giving one real (repeated) solution, not zero.*

*Difficulty: medium*

---

##### Q53
What value of x satisfies the equation 4x²/(x² − 9) − 2x/(x + 3) = 1/(x − 3)?

**A.** −3 

  *This is one of the two excluded values, x=−3, which also happens to satisfy the CLEARED equation 2x²+5x−3=0 algebraically. But x=−3 makes x+3 and x²−9 both zero in the ORIGINAL equation, which is undefined there — a root the cleared equation accepts that the original can't even evaluate is not a solution.*

**B.** −1/2 

  *This factors 2x²+5x−3 with the middle sign flipped, as (2x+1)(x−3) instead of the correct (2x−1)(x+3) — FOILing (2x+1)(x−3) actually gives 2x²−5x−3, which doesn't match the equation being solved, but taking it at face value gives x=−1/2 as a root. Check in the original: at x=−1/2, the left side is 4(1/4)/((1/4)−9) − 2(−1/2)/(−1/2+3) ≈ −0.114+0.4 = 0.286, and the right side is 1/(−1/2−3) ≈ −0.286 — they don't match.*

**C.** 1/2 **(Correct)**

  *Correct. Note the excluded values first: x²−9=(x−3)(x+3), so x≠3 and x≠−3. Multiply every term by (x−3)(x+3): 4x² − 2x(x−3) = x+3, so 4x²−2x²+6x = x+3, giving 2x²+5x−3=0, which factors as (2x−1)(x+3)=0, so x=1/2 or x=−3. Since x=−3 is excluded, x=1/2 is the only solution. Check in the original: at x=1/2, both sides evaluate to −2/5. ✓*

**D.** 3 

  *This is the other excluded value, x=3, which makes x−3 and x²−9 both zero — the original equation is undefined there, since the right side alone is 1/0. Excluded values are the FIRST thing to write down on a rational equation, precisely so a candidate like this one gets caught before it's ever offered as an answer.*

*Difficulty: sat-hardest*

---

##### Q54
The system of equations 8x + y = −11 and 2x² = y + 341 has two solutions. What is the x-coordinate of one of them?

**A.** −15 **(Correct)**

  *Correct. From 8x+y=−11, y=−11−8x. Substitute: 2x² = (−11−8x)+341 = 330−8x, so 2x²+8x−330=0, which reduces to x²+4x−165=0, and factors as (x+15)(x−11)=0, giving x=−15 or x=11. Check x=−15: y=−11−8(−15)=109, and 2(−15)²=450, while 109+341=450. ✓*

**B.** −11 

  *This is the constant −11 from the first equation, taken directly as if it were a value of x rather than the equation's constant term. Check: if x=−11, the first equation gives y=−11−8(−11)=77, but the second gives 2(−11)²=242, while y+341=418 — they don't match.*

**C.** 2 

  *This computes −b/(2a) for x²+4x−165=0 — the AXIS OF SYMMETRY of that quadratic, not one of its roots — getting −4/2=−2, and drops the negative sign to 2. The axis of symmetry sits between the two actual roots, −15 and 11; it isn't a solution itself.*

**D.** 8 

  *This is the coefficient of x in the first equation, 8x+y=−11, taken directly as if it were a solution rather than a coefficient. Check: if x=8, the first equation gives y=−11−64=−75, but the second gives 2(8)²=128, while y+341=266 — they don't match.*

*Difficulty: hard*

---

##### Q55
In the equation 64x² + bx + 25 = 0, b is a constant. For which of the following values of b will the equation have more than one real solution?

**A.** −91 **(Correct)**

  *Correct. More than one real solution means the discriminant is positive: b² − 4(64)(25) > 0 → b² > 6400 → |b| > 80. Of the choices, only −91 has |b|>80. Check: b=−91 gives discriminant (−91)²−6400 = 8281−6400 = 1881, which is positive. ✓*

**B.** −80 

  *This is exactly the boundary, where |b|=80 and the discriminant is exactly 0 — one real solution, not more than one. Check: b=−80 gives (−80)²−6400 = 6400−6400 = 0.*

**C.** 5 

  *This solves the inequality b²−6400>0 with the direction flipped, reading it as b²<6400 instead — and a small b like 5 satisfies THAT (wrong) condition. Check the real discriminant: 5²−6400=25−6400=−6375, deeply negative — zero real solutions, the opposite of what's needed.*

**D.** 40 

  *This is the same flipped inequality as choice C, applied to a b-value closer to the boundary. Check: 40²−6400=1600−6400=−4800, still negative — zero real solutions.*

*Difficulty: medium*

---

##### Q56
In the given system of equations, a is a constant. y = 2x² − 21x + 64. y = 3x + a. The graphs of the equations in the given system intersect at exactly one point, (x, y), in the xy-plane. What is the value of x?

**A.** −8 

  *This is the value of the PARAMETER a, not the x-coordinate the question asks for. Setting the discriminant of 2x²−24x+(64−a)=0 to zero does give 576−8(64−a)=0, so a=−8 — but that answers 'what is a,' a different question from 'what is x.'*

**B.** −6 

  *This uses B/(2A) instead of −B/(2A) for the vertex of 2x²−24x+(64−a)=0 — skipping the negation the formula requires: −24/4=6 is correct, but keeping B's sign as printed gives −24/4 = −6 without ever negating B.*

**C.** 6 **(Correct)**

  *Correct. Substitute to eliminate y: 2x²−21x+64 = 3x+a, so 2x²−24x+(64−a)=0. Exactly one intersection means this quadratic has a double root, which always occurs at x = −B/(2A) regardless of the specific value of a — here, x = 24/(2·2) = 6. (The discriminant condition, 576−8(64−a)=0, does pin down a=−8, but the x-coordinate of the single intersection point doesn't depend on knowing that.)*

**D.** 8 

  *This assumes a=0 — treating the parameter as though it weren't there to solve for — and factors 2x²−24x+64=0 as 2(x²−12x+32)=2(x−4)(x−8)=0, taking the larger root, x=8. But a isn't 0 here: with a=0 the discriminant is 576−512=64, which is positive, meaning the line and parabola would cross TWICE (at x=4 and x=8), not touch at exactly one point. The discriminant-zero condition is what pins a at −8 and the tangency point at x=6.*

*Difficulty: sat-hardest*

---

##### Q57
In the equation −2x² + 20x + c = 0, c is a constant. The equation has exactly one solution. What is the value of c?

**A.** −68 

  *This overshoots the boundary. The equation has exactly one solution only exactly at c=−50, where the discriminant is precisely 0. At c=−68, the discriminant is 400+8(−68) = −144, which is negative — this value of c gives NO real solutions, not one; the parabola never reaches the x-axis to begin with.*

**B.** −50 **(Correct)**

  *Correct. Exactly one solution means the discriminant is zero: 20² − 4(−2)(c) = 0 → 400 + 8c = 0 → c = −50. Check: −2x²+20x−50=0 divides by −2 to x²−10x+25=0, which is (x−5)²=0 — a single solution at x=5.*

**C.** −32 

  *This undershoots the boundary from the other side. At c=−32, the discriminant is 400+8(−32) = 144, which is positive — this value of c gives TWO real solutions, not exactly one; the parabola still crosses the x-axis twice at this height.*

**D.** 0 

  *This is c=0, which makes the constant term vanish entirely rather than solving the discriminant condition for it. At c=0, the equation is −2x²+20x=0, which factors as −2x(x−10)=0, giving TWO solutions, x=0 and x=10 — not one.*

*Difficulty: medium*

---

#### Nonlinear functions (109 items)

##### Q1
The graph shown in the xy-plane is a smooth curve. For x between −4 and 0 the curve rises steeply from about (−4, −12) through about (−1, −9); for x between 0 and 4 it levels off, approaching a value near −4 without quite reaching it. The curve crosses the y-axis at (0, −5). What is the y-intercept of the graph shown?

**A.** (−1, −9) 

  *This is a point the curve passes through on its way up, not the point where it crosses the y-axis. A y-intercept always has x-coordinate 0, and −1 is not 0. [misconception: point-on-curve-read-as-intercept]*

**B.** (0, −5) **(Correct)**

  *Correct. The y-intercept is where the graph crosses the vertical axis, which happens at x = 0. The described curve crosses there at y = −5. ✓*

**C.** (0, −4) 

  *−4 is the value the curve is approaching as x grows, a horizontal asymptote, not the value at x = 0. The curve has not leveled off yet by the time it crosses the y-axis; it is still on its way down from −5. [misconception: asymptote-read-as-intercept]*

**D.** (0, 0) 

  *This assumes every graph passes through the origin by default, without checking what the curve actually does at x = 0. The described curve crosses the y-axis well below zero. [misconception: intercept-assumed-at-origin]*

*Difficulty: easy*

---

##### Q2
Scientists recorded data about the ocean water level at a certain location over a period of 6 hours. The graph shown models the data, where y = 0 represents sea level and x is the elapsed time, in hours: the curve starts at (0, 0), dips to a minimum of about (3, −12), and returns to (6, 0). Which table gives values of x and their corresponding values of y based on the model?

**A.** x = 0, y = −12; x = 0, y = 3; x = 3, y = 6 

  *Lists two different y-values for the same x = 0, which cannot happen for a function, and swaps which column holds the elapsed time and which holds the water level — the graph's minimum is at x = 3, not listed here at all. [misconception: x-y-columns-swapped]*

**B.** x = 0, y = 0; x = 3, y = 12; x = 0, y = −6 

  *Reports the minimum as +12 instead of −12. The graph dips below sea level, so the water level at x = 3 must be negative, not the largest positive value in the table. [misconception: sign-of-minimum-dropped]*

**C.** x = 0, y = 0; x = 3, y = −12; x = 6, y = 0 **(Correct)**

  *Correct. This matches the three labeled features of the graph directly: sea level at x = 0, the lowest point of −12 feet at x = 3 hours, and a return to sea level at x = 6 hours. ✓*

**D.** x = 0, y = 0; x = 12, y = 3; x = −6, y = 0 

  *Swaps the x- and y-values of the second and third points and introduces x = 12 and x = −6, both outside the stated 6-hour window the graph covers. [misconception: x-y-columns-swapped]*

*Difficulty: medium*

---

##### Q3
The function f is defined by f(x) = 4 + √x. What is the value of f(144)?

**A.** 0 

  *This would require √x to equal −4, but a square root of a nonnegative number is never negative, so f cannot output 0 minus anything smaller than 4 — this value is not reachable by this function at all. [misconception: impossible-output-selected]*

**B.** 16 **(Correct)**

  *Correct. √144 = 12, so f(144) = 4 + 12 = 16. ✓*

**C.** 40 

  *Replaces the square root with division by 4: 144 ÷ 4 = 36, then 4 + 36 = 40. Taking a square root is not the same operation as dividing by 4, and only agrees with it at x = 16. [misconception: sqrt-replaced-with-division]*

**D.** 76 

  *Replaces the square root with taking half of x: 144 ÷ 2 = 72, then 4 + 72 = 76. Halving a number is not the same as taking its square root except at x = 4. [misconception: sqrt-replaced-with-half]*

*Difficulty: easy*

---

##### Q4
The table shown includes some values of x and their corresponding values of y: x = 0, 1, 2, 3 gives y = 0, 1, 8, 27. Which of the following best describes a graph in the xy-plane that could represent the relationship between x and y?

**A.** A U-shaped curve, symmetric about the y-axis, with its lowest point at the origin 

  *This is the shape of y = x², which grows at the same rate for negative and positive x on either side of a single minimum. The table's jumps in y (1, 7, 19) are not the constant-second-difference pattern a quadratic produces, and nothing in the table suggests a mirror image on the other side of x = 0. [misconception: quadratic-shape-assumed]*

**B.** A curve passing through the origin that rises slowly at first and then increasingly steeply as x increases, with no symmetry **(Correct)**

  *Correct. This is the shape of y = x³: 0³ = 0, 1³ = 1, 2³ = 8, 3³ = 27 — each step's jump (1, 7, 19) grows faster than the last, matching a curve that flattens near the origin and then climbs ever more steeply. ✓*

**C.** A curve that decreases from the y-axis to a minimum below the x-axis and then increases 

  *The table shows y increasing at every step from 0 up to 27, never decreasing and never going negative, so a graph with a dip below the x-axis does not match any part of this data. [misconception: extraneous-minimum-assumed]*

**D.** A straight line through the origin with a constant slope 

  *A line requires equal jumps in y for equal jumps in x, but the table's jumps are 1, 7, and 19 — growing, not constant — which rules out a linear relationship entirely. [misconception: linear-shape-assumed]*

*Difficulty: medium*

---

##### Q5
If f(x) = (x² − 6x + 3)/(x − 1), what is f(−1)?

**A.** −5 **(Correct)**

  *Correct. The numerator is (−1)² − 6(−1) + 3 = 1 + 6 + 3 = 10, and the denominator is −1 − 1 = −2, so f(−1) = 10/(−2) = −5. ✓*

**B.** −2 

  *This is just the denominator, x − 1 evaluated at x = −1, reported as the final answer without ever dividing it into the numerator. [misconception: denominator-reported-as-answer]*

**C.** 2 

  *Loses a sign twice on the way there: reading −6(−1) as −6 instead of +6 turns the numerator into 1 − 6 + 3 = −2 instead of 10, and reading x − 1 at x = −1 as just −1 (dropping the leading term) turns the denominator into −1 instead of −2. Dividing those two wrong values, −2/−1, happens to land on +2. [misconception: double-negative-mishandled]*

**D.** 5 

  *Computes the denominator as 1 − x instead of x − 1, giving 1 − (−1) = 2 rather than −1 − 1 = −2. Dividing the correct numerator, 10, by this reversed-sign denominator gives +5 instead of −5. [misconception: denominator-subtraction-order-reversed]*

*Difficulty: medium*

---

##### Q6
For the function f defined by f(x) = 2(3^x), what is the value of f(2)?

**A.** 9 

  *This is 3² alone, dropping the leading factor of 2 entirely. The 2 in f(x) = 2(3^x) multiplies the exponential term; it does not disappear when the exponent is evaluated. [misconception: leading-coefficient-dropped]*

**B.** 12 

  *This treats the base as if it were multiplied by the exponent instead of raised to it: 2 × 3 × 2 = 12. The expression is 2 · 3², not 2 · 3 · 2. [misconception: exponentiation-replaced-with-multiplication]*

**C.** 18 **(Correct)**

  *Correct. f(2) = 2(3²) = 2(9) = 18. ✓*

**D.** 36 

  *This applies the leading 2 to the base before exponentiating, computing (2 × 3)² = 6² = 36, instead of squaring 3 first and multiplying by 2 afterward. Order of operations puts the exponent on 3 alone. [misconception: coefficient-included-in-base]*

*Difficulty: easy*

---

##### Q7
The graph shown in the xy-plane is a curve that rises from about (−8, −10) up through the y-axis and continues rising, leveling off near y = −5 as x increases toward 8. What is the y-intercept of the graph shown?

**A.** (0, −6) **(Correct)**

  *Correct. The curve crosses the y-axis at y = −6, just below where it will eventually level off near −5. ✓*

**B.** (−6, 0) 

  *Swaps the coordinates: a y-intercept always has x-coordinate 0, since it is defined as the point where the graph crosses the vertical axis, not the horizontal one. [misconception: x-y-intercept-swapped]*

**C.** (0, 0) 

  *Assumes the graph passes through the origin without checking where the curve actually crosses the y-axis, which here is well below zero. [misconception: intercept-assumed-at-origin]*

**D.** (−5, −5) 

  *Reads off the horizontal asymptote the curve approaches for large x, and mistakenly reports it as a point with matching coordinates rather than finding where the curve crosses x = 0. [misconception: asymptote-read-as-intercept]*

*Difficulty: easy*

---

##### Q8
The function f(x) = 200,000(1.21)^x gives a company's predicted annual revenue, in dollars, x years after the company started selling light bulbs online, where 0 < x ≤ 10. What is the best interpretation of the statement "f(5) is approximately equal to 518,748" in this context?

**A.** 5 years after the company started selling light bulbs online, its predicted annual revenue is approximately 518,748 dollars. **(Correct)**

  *Correct. f(5) is the output of the model at input x = 5, and the model's output is the predicted annual revenue in dollars at that number of years after the company started. ✓*

**B.** 5 years after the company started selling light bulbs online, its predicted annual revenue will have increased by a total of approximately 518,748 dollars. 

  *This treats 518,748 as a total increase (a difference from the starting value) rather than as the revenue itself. f(5) is a value of the function, not a change in the function. [misconception: output-read-as-cumulative-change]*

**C.** When the company's predicted annual revenue is approximately 518,748 dollars, it is 5 times the predicted annual revenue for the previous year. 

  *This reads the input 5 as a multiplier applied to the previous year's revenue, confusing the input of the function (a number of years) with the base of the exponential (1.21, which governs year-over-year growth). [misconception: input-read-as-growth-multiplier]*

**D.** When the company's predicted annual revenue is approximately 518,748 dollars, it is 5% greater than the predicted annual revenue for the previous year. 

  *This mistakes the input 5 for the model's percentage growth rate. The actual per-year growth rate is fixed by the base, 1.21, which is +21%, not +5%, and it doesn't change from year to year. [misconception: input-read-as-percent-rate]*

*Difficulty: medium*

---

##### Q9
The function f is defined by f(x) = 6 + √x. What is the value of f(36)?

**A.** 9 

  *This treats √36 as 36 ÷ 12 (or some similarly unrelated shortcut) rather than the actual square root, 6. Only 6 + 6 gives f(36), and 9 is not reachable from the correct square root of 36. [misconception: sqrt-computed-incorrectly]*

**B.** 12 **(Correct)**

  *Correct. √36 = 6, so f(36) = 6 + 6 = 12. ✓*

**C.** 18 

  *Replaces the square root with division by 2: 36 ÷ 2 = 18, then adds nothing further, or effectively treats 6 + √36 as 6 × 3. Halving is not the same operation as taking a square root except at x = 4. [misconception: sqrt-replaced-with-half]*

**D.** 42 

  *Adds 6 to 36 directly, skipping the square root entirely — as if f(x) = 6 + x rather than f(x) = 6 + √x. [misconception: sqrt-omitted]*

*Difficulty: easy*

---

##### Q10
The quadratic function graphed shows a measure of plant diversity as a function of elevation, in meters, in a region of Switzerland: the curve rises from about (0, 2,000) to a peak near (1,250, 13,500) and then falls back down to about (3,000, 0). According to the model, which of the following is closest to the elevation, in meters, at which plant diversity is greatest?

**A.** 13,500 

  *This is the greatest diversity VALUE (the y-coordinate of the peak), not the elevation at which it occurs. The question asks for an elevation, which is read off the horizontal axis. [misconception: y-value-reported-for-x-question]*

**B.** 3,000 

  *This is the elevation where the curve returns to zero diversity, an x-intercept, not the peak. The peak occurs well before the curve comes back down to the axis. [misconception: intercept-read-as-peak]*

**C.** 1,250 **(Correct)**

  *Correct. Reading the horizontal position of the graph's highest point gives an elevation of approximately 1,250 meters, where plant diversity is greatest. ✓*

**D.** 250 

  *This is well short of the peak's actual horizontal position; it looks like a misread of the axis labels between 0 and 1,250 rather than a value the curve's vertex is near. [misconception: axis-value-misread]*

*Difficulty: medium*

---

##### Q11
The function f is defined as f(x) = x² + 4. Which of the following best describes the graph of y = f(x) in the xy-plane?

**A.** A downward-opening parabola with vertex at (0, 4) 

  *The coefficient on x² is +1, which is positive, so the parabola opens upward, not downward. Only a negative leading coefficient produces a downward-opening shape. [misconception: opening-direction-sign-ignored]*

**B.** An upward-opening parabola with vertex at (4, 0) 

  *Swaps the two vertex coordinates. In f(x) = x² + 4, the +4 is added to the output after squaring, so it shifts the graph up 4, giving vertex (0, 4) — not right 4, which would require the form (x − 4)². [misconception: vertex-coordinates-swapped]*

**C.** An upward-opening parabola with vertex at (−4, 0) 

  *This treats the +4 as though it were inside a squared term shifting the graph left, as in (x + 4)². Here the +4 is added outside the square, so it moves the graph up, not sideways. [misconception: outside-shift-read-as-inside-shift]*

**D.** An upward-opening parabola with vertex at (0, 4) **(Correct)**

  *Correct. The leading coefficient +1 is positive, so the parabola opens upward, and the +4 outside the square shifts the basic y = x² graph up 4 units, placing the vertex at (0, 4). ✓*

*Difficulty: easy*

---

##### Q12
The function f is defined by f(x) = x³ + 15. What is the value of f(2)?

**A.** 20 

  *This computes 2 × 3 + 15 = 21 rounded down, or otherwise treats the exponent as a multiplier on x rather than a power — 2³ is 2 × 2 × 2, not 2 × 3. [misconception: exponent-read-as-multiplier]*

**B.** 21 

  *Computes 2 × 3 = 6, then... more directly, this treats x³ as 3x, giving 3(2) + 15 = 21 instead of 2³ + 15. Cubing a number means multiplying it by itself three times, not multiplying it by 3. [misconception: exponent-read-as-multiplier]*

**C.** 23 **(Correct)**

  *Correct. f(2) = 2³ + 15 = 8 + 15 = 23. ✓*

**D.** 24 

  *This computes 2³ correctly as 8 but adds 16 instead of 15, an arithmetic slip in the final addition — 8 + 15 is 23, not 24. [misconception: arithmetic-slip]*

*Difficulty: easy*

---

##### Q13
The graph of a polynomial function f, where y = f(x), is a curve that rises steeply from below on the left, flattens to a hump near the top of the y-axis around y = −3, then falls steeply back down on the right. The y-intercept of the graph is (0, y). What is the value of y?

**A.** −12 

  *This reads off a value the curve passes through farther from the y-axis, near where it is falling steeply, rather than the value directly above x = 0 at the top of the hump. [misconception: point-on-curve-read-as-intercept]*

**B.** 0 

  *Assumes the graph passes through the origin without checking where the curve actually crosses x = 0, which here is well below the x-axis. [misconception: intercept-assumed-at-origin]*

**C.** −3 **(Correct)**

  *Correct. The curve's hump sits directly above the y-axis at y = −3, which is the graph's y-intercept. ✓*

**D.** −7 

  *This reads a value from farther along the curve, past where it has already started descending, rather than the value exactly at x = 0. [misconception: point-on-curve-read-as-intercept]*

*Difficulty: easy*

---

##### Q14
The function f is defined above by f(x) = (x + 0.25x)(50 − x). What is the value of f(20)?

**A.** 250 

  *This drops the 0.25x term entirely, computing (20)(50 − 20) = 20(30) = 600, then applying an unrelated further reduction — more directly, it treats the first factor as just x = 20 rather than x + 0.25x = 25, and then also miscomputes the product. Either way, the 0.25x contribution to the first factor is lost. [misconception: term-dropped-from-first-factor]*

**B.** 500 

  *Computes the first factor correctly as x + 0.25x = 1.25x = 25 at x = 20, but then multiplies by 20 instead of by (50 − 20) = 30, reusing x in place of the second factor. [misconception: wrong-factor-substituted]*

**C.** 750 **(Correct)**

  *Correct. The first factor is 20 + 0.25(20) = 20 + 5 = 25, and the second factor is 50 − 20 = 30, so f(20) = 25 × 30 = 750. ✓*

**D.** 2,000 

  *Treats the expression as (x)(50) − x instead of (x + 0.25x)(50 − x) — multiplying 20 by 50 to get 1,000 and then combining incorrectly — which drops the 0.25x term and mishandles the second factor's subtraction at the same time. [misconception: distribution-error]*

*Difficulty: medium*

---

##### Q15
The function f is defined by f(x) = 16/x. What is the value of f(x) when x = 17?

**A.** 16/17 **(Correct)**

  *Correct. Substituting x = 17 gives f(17) = 16/17 directly. ✓*

**B.** 17/16 

  *Flips the fraction, dividing x by 16 instead of 16 by x. In f(x) = 16/x, the 16 is always the numerator and x is always the denominator, whatever value x takes. [misconception: fraction-inverted]*

**C.** 16 

  *Ignores the division by x entirely, reporting the numerator alone as if f(x) = 16 were a constant function. [misconception: denominator-ignored]*

**D.** 17 

  *Reports the input value itself rather than evaluating the function — this is the value of x, not of f(x). [misconception: input-reported-as-output]*

*Difficulty: easy*

---

##### Q16
The graph of the exponential function f is shown, where y = f(x): a curve that falls steeply from about (−1, 12), crossing the y-axis, and flattens out approaching y = 0 as x increases toward 1. The y-intercept of the graph is (0, y). What is the value of y?

**A.** 0 

  *This is the value the curve approaches as x grows (its horizontal asymptote), not the value at x = 0 — the curve is still well above 0 when it crosses the y-axis. [misconception: asymptote-read-as-intercept]*

**B.** 1 

  *Underestimates where the falling curve actually crosses the y-axis; this value is too close to the asymptote for a curve that is still descending steeply near x = 0. [misconception: axis-value-misread]*

**C.** 3 **(Correct)**

  *Correct. The curve crosses the y-axis at y = 3, partway down its steep descent from (−1, 12) toward the asymptote at y = 0. ✓*

**D.** 12 

  *This is the value of the curve at x = −1, one unit to the left of the y-axis, not the value at x = 0 itself. [misconception: point-on-curve-read-as-intercept]*

*Difficulty: easy*

---

##### Q17
The y-intercept of the graph of y = x² + 31 in the xy-plane is (0, y). What is the value of y?

**A.** 0 

  *Assumes the y-intercept is always 0 without evaluating the function at x = 0. Here f(0) = 0² + 31 = 31, not 0. [misconception: intercept-assumed-zero]*

**B.** 1 

  *This looks like a misread of the coefficient on x² (which is 1) reported in place of the actual y-intercept, which comes from the constant term, not the leading coefficient. [misconception: coefficient-read-as-intercept]*

**C.** 30 

  *This is one less than the correct value — an off-by-one slip in adding the constant term, or a result of computing 31 − 0² incorrectly as 31 − 1. [misconception: arithmetic-slip]*

**D.** 31 **(Correct)**

  *Correct. At x = 0, y = 0² + 31 = 31, so the y-intercept is (0, 31). ✓*

*Difficulty: easy*

---

##### Q18
The graph shown models the number of residents of a certain city x years after 2010: it starts at about (0, 20,000), rises to about (5, 26,000), and continues up to about (10, 35,000). How many residents does this model estimate the city had in 2010?

**A.** 0 

  *This assumes the graph starts at the origin without reading the actual starting point of the curve, which is well above zero. [misconception: intercept-assumed-at-origin]*

**B.** 2,000 

  *This misreads the graph's starting value by a factor of ten, likely from misplacing a decimal or a gridline while reading the vertical axis. [misconception: axis-scale-misread]*

**C.** 20,000 **(Correct)**

  *Correct. 2010 corresponds to x = 0, and the graph's value there — its y-intercept — is about 20,000 residents. ✓*

**D.** 25,000 

  *This is close to the value the model shows partway through the period (around x = 5), not the starting value at x = 0 in 2010. [misconception: point-on-curve-read-as-intercept]*

*Difficulty: medium*

---

##### Q19
The function f is defined by f(x) = x³ + 9. What is the value of f(2)?

**A.** 14 

  *This computes 2 × 2 + 9 = 13, or some similarly squared-instead-of-cubed shortcut close to but not matching 2³ = 8. Cubing means multiplying a number by itself three times, not two. [misconception: cube-computed-as-square]*

**B.** 15 

  *Treats x³ as 3x rather than x·x·x, computing 3(2) + 9 = 15 instead of 2³ + 9. The exponent is a power, not a multiplying factor. [misconception: exponent-read-as-multiplier]*

**C.** 17 **(Correct)**

  *Correct. f(2) = 2³ + 9 = 8 + 9 = 17. ✓*

**D.** 18 

  *Off by one from the correct value, likely from adding 10 instead of 9 to 2³ = 8, or misreading the constant term in the function. [misconception: arithmetic-slip]*

*Difficulty: easy*

---

##### Q20
The graph of y = f(x) is shown in the xy-plane: a curve made of two branches, one falling steeply through the upper-left region toward the y-axis, another separated branch below and to the left. Near x = 0 the visible branch passes through y-values around 3, decreasing toward an asymptote near y = 1 as x increases. The value of f(0) is an integer. What is the value of f(0)?

**A.** 1 

  *This is the value the curve approaches as x grows large (its horizontal asymptote), not the actual value at x = 0, where the curve is still noticeably above that level. [misconception: asymptote-read-as-intercept]*

**B.** 2 

  *Underestimates the curve's height at x = 0; this falls between the true value and the asymptote rather than matching where the curve actually crosses the y-axis. [misconception: axis-value-misread]*

**C.** 3 **(Correct)**

  *Correct. Reading the curve's height directly above x = 0 gives f(0) = 3, the integer value stated in the problem. ✓*

**D.** 5 

  *Overshoots the curve's actual height at x = 0, likely from reading a point further along the steep branch rather than the value exactly at the y-axis. [misconception: point-on-curve-read-as-intercept]*

*Difficulty: medium*

---

##### Q21
The function h is defined by h(x) = x² − 3. Which table gives three values of x and their corresponding values of h(x) for the given function h?

**A.** x = 1, 2, 3 gives h(x) = 4, 5, 6 

  *This looks like x² was replaced by x + 3, giving h(1) = 4, h(2) = 5, h(3) = 6 — a linear pattern of constant differences, not the widening differences a squared term produces. [misconception: quadratic-replaced-with-linear]*

**B.** x = 1, 2, 3 gives h(x) = −2, 1, 6 **(Correct)**

  *Correct. h(1) = 1 − 3 = −2, h(2) = 4 − 3 = 1, h(3) = 9 − 3 = 6. ✓*

**C.** x = 1, 2, 3 gives h(x) = −1, 1, 3 

  *This produces constant differences of 2 between consecutive outputs, which is the signature of a linear function, not h(x) = x² − 3, whose outputs should have widening differences of 3, then 5. [misconception: quadratic-replaced-with-linear]*

**D.** x = 1, 2, 3 gives h(x) = −2, 1, 3 

  *The first two outputs are correct, but the third breaks the pattern: h(3) should be 9 − 3 = 6, not 3, which would require 3² to equal 6 rather than 9. [misconception: arithmetic-slip]*

*Difficulty: easy*

---

##### Q22
The equation y = −(1/4)x² + 2x + 29 models a company's scheduled deliveries over 8 months, where y is the estimated number of scheduled deliveries x months after the end of May 2012, where 0 ≤ x ≤ 8. Which statement is the best interpretation of the y-intercept of the graph of this equation in the xy-plane?

**A.** At the end of May 2012, the estimated number of scheduled deliveries was 0. 

  *This assumes the y-intercept is always 0 without evaluating the model at x = 0, where the constant term 29 makes the actual value nonzero. [misconception: intercept-assumed-zero]*

**B.** At the end of May 2012, the estimated number of scheduled deliveries was 29. **(Correct)**

  *Correct. x = 0 corresponds to the end of May 2012, and y = −(1/4)(0)² + 2(0) + 29 = 29, the constant term of the model. ✓*

**C.** At the end of June 2012, the estimated number of scheduled deliveries was 0. 

  *Shifts the starting month forward by one and mistakes the constant term for zero — x = 0 is defined as the end of May 2012, not June, and the y-intercept here is 29, not 0. [misconception: reference-month-shifted]*

**D.** At the end of June 2012, the estimated number of scheduled deliveries was 29. 

  *Gets the delivery count right but assigns it to the wrong month — x = 0 is defined as the end of May 2012 in this model, not one month later. [misconception: reference-month-shifted]*

*Difficulty: easy*

---

##### Q23
The graph shown is a curve that rises from near the origin, crossing the y-axis close to it, and climbs increasingly steeply as x increases from −5 to 5, consistent with exponential growth. What is the y-intercept of the graph shown?

**A.** (0, 0) 

  *An exponential function a·b^x with a ≠ 0 can never actually equal 0 at any input, since a nonzero number raised to any power is never 0. The curve passes close to the x-axis on the left but never touches it. [misconception: asymptote-read-as-intercept]*

**B.** (0, 2) **(Correct)**

  *Correct. The curve crosses the y-axis at y = 2, which is the initial value a of the exponential model. ✓*

**C.** (2, 0) 

  *Swaps the coordinates: a y-intercept always has x-coordinate 0, not y-coordinate 0, since it is the point where the graph meets the vertical axis. [misconception: x-y-intercept-swapped]*

**D.** (2, 2) 

  *Reports a point on the curve slightly to the right of the y-axis rather than the value exactly at x = 0. [misconception: point-on-curve-read-as-intercept]*

*Difficulty: easy*

---

##### Q24
The function f(x) = 240,000(1.22)^x gives a company's predicted annual revenue, in dollars, x years after the company started selling jewelry online, where 0 < x ≤ 10. What is the best interpretation of the statement "f(5) is approximately equal to 648,650" in this context?

**A.** 5 years after the company started selling jewelry online, its predicted annual revenue is approximately 648,650 dollars. **(Correct)**

  *Correct. f(5) is the model's output at input x = 5, which is the predicted annual revenue, in dollars, 5 years after the company started selling jewelry online. ✓*

**B.** 5 years after the company started selling jewelry online, its predicted annual revenue will have increased by a total of approximately 648,650 dollars. 

  *Treats 648,650 as a cumulative increase rather than as the revenue value itself. f(5) is a single output of the function, not the sum of all the increases leading up to it. [misconception: output-read-as-cumulative-change]*

**C.** When the company's predicted annual revenue is approximately 648,650 dollars, it is 5 times the predicted annual revenue for the previous year. 

  *Confuses the input, 5 (a number of years), with a growth multiplier. The actual year-over-year multiplier is fixed by the base of the model, 1.22, not by the input value. [misconception: input-read-as-growth-multiplier]*

**D.** When the company's predicted annual revenue is approximately 648,650 dollars, it is 5% greater than the predicted annual revenue for the previous year. 

  *Mistakes the input 5 for the model's percent growth rate. The true per-year growth rate comes from the base, 1.22, which is +22%, and stays the same every year regardless of which year is being evaluated. [misconception: input-read-as-percent-rate]*

*Difficulty: medium*

---

##### Q25
The graph shows a marble's height above the ground, y, in inches, x seconds after it started moving on an elevated track of a marble run. The graph starts at about (0, 8), dips to a minimum near (4, 2), and rises back up to about (9, 10). Which of the following is the best interpretation of the y-intercept of the graph?

**A.** The marble's height was 0 inches above the ground 8 seconds after it started moving. 

  *This describes a point far from the y-axis (near x = 8) and reports a height, 0, that doesn't match the graph's value there either. A y-intercept is specifically about x = 0, the start of the motion. [misconception: point-on-curve-read-as-intercept]*

**B.** The marble's height was 8 inches above the ground when it started moving. **(Correct)**

  *Correct. The y-intercept occurs at x = 0, the moment the marble started moving, where the graph shows a height of 8 inches. ✓*

**C.** The marble's minimum height was 0 inches above the ground. 

  *Confuses the y-intercept with the graph's minimum value. The graph's lowest point is around 2 inches near x = 4, not 0, and neither of those describes the y-intercept, which is the value at x = 0. [misconception: minimum-confused-with-intercept]*

**D.** The marble's minimum height was 8 inches above the ground. 

  *Correctly identifies the value 8 but mislabels what it represents: 8 is the height at the start of the motion (the y-intercept), not the minimum height reached, which is lower, around 2 inches. [misconception: intercept-confused-with-minimum]*

*Difficulty: easy*

---

##### Q26
At the time of posting a video, a social media channel had 53 subscribers. Each day for five days after the video was posted, the number of subscribers doubled from the number the previous day. Which equation gives the total number of subscribers, n, to the channel d days after the video was posted?

**A.** n = 53^d 

  *This raises the initial subscriber count itself to the power of d, rather than raising the growth factor (2, for doubling) to the power of d and multiplying by the initial count. The 53 should sit outside the exponent as a coefficient, not inside it as a base. [misconception: coefficient-and-base-swapped]*

**B.** n = 53(2)^d **(Correct)**

  *Correct. The channel starts at 53 subscribers and doubles — multiplies by 2 — once for each day that passes, giving n = 53(2)^d. Check d = 1: 53(2) = 106, exactly double the start. ✓*

**C.** n = 53(0.5)^d 

  *Uses the multiplier for halving instead of doubling. "Doubled" means multiplying by 2 each day, not by 0.5, which would describe a quantity being cut in half daily instead of growing. [misconception: growth-decay-multiplier-swapped]*

**D.** n = 53^(d/2) + d 

  *This both raises the initial count to a fractional power of d (rather than raising a growth factor to the power of d) and adds an extra, unexplained +d term. Neither piece matches how doubling is modeled. [misconception: model-structure-invented]*

*Difficulty: medium*

---

##### Q27
A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the width, what is the width of the court, in meters?

**A.** 9 **(Correct)**

  *Correct. Let w be the width, so the length is 2w and the area is w(2w) = 2w² = 162, giving w² = 81 and w = 9. Check: 9 × 18 = 162. ✓*

**B.** 18 

  *This is the length of the court (twice the width), reported in place of the width the question asked for. [misconception: wrong-quantity-reported]*

**C.** 27 

  *This treats the area equation as w² = 162/2 = 81 correctly in form but then miscomputes the square root, or alternatively divides 162 by 6 instead of setting up 2w² = 162. Either way it does not solve w² = 81 correctly. [misconception: equation-setup-error]*

**D.** 54 

  *This divides 162 by 3 rather than solving 2w² = 162 for w, skipping the squaring relationship between width and area entirely — as though the length were a fixed extra amount rather than a multiple of the width. [misconception: quadratic-relationship-ignored]*

*Difficulty: medium*

---

##### Q28
The function S(n) = 38,000a^n models the annual salary, in dollars, of an employee n years after starting a job, where a is a constant. If the employee's salary increases by 4% each year, what is the value of a?

**A.** 0.04 

  *This reports the growth rate itself, r = 0.04, rather than the multiplier a = 1 + r. A base of 0.04 would describe the salary shrinking to 4% of its previous value each year, not growing by 4%. [misconception: rate-reported-instead-of-multiplier]*

**B.** 0.4 

  *Misplaces a decimal point on the growth rate before adding it to 1, or otherwise treats 4% as 0.4 instead of 0.04. A base of 0.4 would represent a 60% decrease each year, the opposite of what's described. [misconception: percent-decimal-misplaced]*

**C.** 1.04 **(Correct)**

  *Correct. A 4% increase each year means multiplying by 1 + 0.04 = 1.04 per year, so a = 1.04. ✓*

**D.** 1.4 

  *Adds 1 to 0.4 rather than to the correctly placed 0.04, carrying forward the same decimal misplacement as choice B into the final multiplier. [misconception: percent-decimal-misplaced]*

*Difficulty: easy*

---

##### Q29
The equation D = 5,640(1.9)^t estimates the global data traffic D, in terabytes, for the year that is t years after 2010. What is the best interpretation of the number 5,640 in this context?

**A.** The estimated amount of increase of data traffic, in terabytes, each year 

  *5,640 is the model's initial value, not a yearly increase. The year-over-year growth is governed by the base, 1.9, and because the model is multiplicative, the actual terabyte increase is different every year, not a fixed amount. [misconception: initial-value-read-as-rate]*

**B.** The estimated percent increase in the data traffic, in terabytes, each year 

  *5,640 is a quantity of terabytes, not a percentage, and it sits in the position of a in a·b^t (the starting value), not in the base, which is where the percent growth rate lives. [misconception: initial-value-read-as-percent]*

**C.** The estimated data traffic, in terabytes, for the year that is t years after 2010 

  *This describes D itself, the model's output for a general t, not the fixed number 5,640, which is the value specifically at t = 0. [misconception: coefficient-confused-with-output]*

**D.** The estimated data traffic, in terabytes, in 2010 **(Correct)**

  *Correct. t = 0 corresponds to the year 2010, and D(0) = 5,640(1.9)⁰ = 5,640, so 5,640 is the estimated data traffic in 2010, the model's initial value. ✓*

*Difficulty: medium*

---

##### Q30
The function f is defined by f(x) = (x + 6)(x − 4). If the given function f is graphed in the xy-plane, where y = f(x), what is the x-coordinate of an x-intercept of the graph?

**A.** 6 

  *This flips the sign of the root hidden in (x + 6). A product is zero when a factor is zero, and x + 6 = 0 gives x = −6, not +6 — the sign inside a parenthesis is always the opposite of the root it names. [misconception: sign-inside-parentheses-flip]*

**B.** −4 

  *This flips the sign of the root hidden in (x − 4). Setting x − 4 = 0 gives x = 4, not −4; only the (x + 6) factor names a negative root. [misconception: sign-inside-parentheses-flip]*

**C.** −6 **(Correct)**

  *Correct. Setting x + 6 = 0 gives x = −6, one of the two values that make the product zero. (The other x-intercept is x = 4.) ✓*

**D.** 24 

  *This multiplies the two constants inside the factors, 6 and 4, together — that would be relevant to the y-intercept region of a related computation, but it is not a root of either factor. [misconception: constants-multiplied-instead-of-set-to-zero]*

*Difficulty: easy*

---

##### Q31
Immanuel purchased a certain rare coin on January 1. The function f(x) = 65(1.03)^x, where 0 ≤ x ≤ 10, gives the predicted value, in dollars, of the rare coin x years after Immanuel purchased it. What is the best interpretation of the statement "f(8) is approximately equal to 82" in this context?

**A.** When the rare coin's predicted value is approximately 82 dollars, it is 8% greater than the predicted value, in dollars, on January 1 of the previous year. 

  *Confuses the input, 8 (a number of years), with the model's fixed percent growth rate. The actual annual growth rate comes from the base, 1.03, which is +3%, and does not change with the number of years elapsed. [misconception: input-read-as-percent-rate]*

**B.** When the rare coin's predicted value is approximately 82 dollars, it is 8 times the predicted value, in dollars, on January 1 of the previous year. 

  *Confuses the input 8 with a year-over-year growth multiplier. The true multiplier is the base, 1.03, applied once per year, not a factor of 8 applied all at once. [misconception: input-read-as-growth-multiplier]*

**C.** From the day Immanuel purchased the coin to 8 years after Immanuel purchased the coin, its predicted value increased by a total of approximately 82 dollars. 

  *Treats 82 as the total increase over 8 years rather than the coin's value itself. The actual increase over that span is f(8) − f(0) ≈ 82 − 65 = 17 dollars, not 82. [misconception: output-read-as-cumulative-change]*

**D.** 8 years after Immanuel purchased the rare coin, its predicted value is approximately 82 dollars. **(Correct)**

  *Correct. f(8) is the model's output at input x = 8, which is the predicted value of the coin, in dollars, 8 years after it was purchased. ✓*

*Difficulty: medium*

---

##### Q32
From 2005 through 2014, the number of music CDs sold in the United States declined each year by approximately 15% of the number sold the preceding year. In 2005, approximately 600 million CDs were sold in the United States. Of the following, which best models C, the number of millions of CDs sold in the United States, t years after 2005?

**A.** C = 600(0.15)^t 

  *Uses the decline rate itself, 0.15, as the base. A base of 0.15 would mean sales dropped to 15% of the previous year's total each year — an 85% annual decline — far more severe than the described 15% decline. [misconception: rate-used-as-multiplier]*

**B.** C = 600(0.85)^t **(Correct)**

  *Correct. Losing 15% each year means keeping 85%, so the multiplier is 1 − 0.15 = 0.85, giving C = 600(0.85)^t. ✓*

**C.** C = 600(1.15)^t 

  *Uses a growth multiplier instead of a decline multiplier. The base 1.15 describes sales increasing by 15% each year, the opposite of the described decline. [misconception: growth-decay-multiplier-swapped]*

**D.** C = 600(1.85)^t 

  *Adds the decline rate to 1 instead of subtracting it, giving a base that describes an 85% increase each year rather than a 15% decrease. [misconception: sign-of-rate-ignored]*

*Difficulty: easy*

---

##### Q33
In the xy-plane, the y-coordinate of the y-intercept of the graph of the function f is c. Which of the following must be equal to c?

**A.** f(0) **(Correct)**

  *Correct. The y-intercept of a graph is the point where x = 0, so its y-coordinate is always f(0) by definition. ✓*

**B.** f(1) 

  *f(1) is the output at x = 1, one unit to the right of the y-axis. Unless the function happens to be constant, this is generally a different value from the y-intercept. [misconception: wrong-input-selected]*

**C.** f(2) 

  *f(2) is the output at x = 2, not at x = 0, so it does not describe the y-intercept for a general function f. [misconception: wrong-input-selected]*

**D.** f(3) 

  *f(3) is the output at x = 3, not at x = 0, so it does not describe the y-intercept for a general function f. [misconception: wrong-input-selected]*

*Difficulty: easy*

---

##### Q34
For the function f defined by f(x) = x³ + 3x² − 6x − 1, what is the value of f(−1)?

**A.** −11 

  *This comes from flipping the sign of both middle terms at once — reading 3(−1)² as −3 and −6(−1) as −6 instead of +3 and +6: −1 − 3 − 6 − 1 = −11. Squaring a negative always gives a positive, and subtracting a negative always adds, so both of those terms should stay positive. [misconception: sign-error-on-middle-terms]*

**B.** −7 

  *This matches the correct magnitude, 7, but carries a spurious overall negative sign, as if an extra negation were applied to the whole expression after correctly computing each term. Every individual term evaluates the same way whether or not it's negated as a group; only the term-by-term signs inside the expression matter. [misconception: spurious-overall-negation]*

**C.** 7 **(Correct)**

  *Correct. f(−1) = (−1)³ + 3(−1)² − 6(−1) − 1 = −1 + 3(1) + 6 − 1 = −1 + 3 + 6 − 1 = 7. ✓*

**D.** 11 

  *This loses a sign twice: it treats (−1)³ as +1, as though cubing — like squaring — always erases a negative sign, and it drops the sign on the final constant term, treating −1 as +1. Together: 1 + 3 + 6 + 1 = 11. Odd powers of a negative number stay negative; only even powers flip to positive. [misconception: odd-power-sign-dropped]*

*Difficulty: medium*

---

##### Q35
Which of the following is the graph in the xy-plane of the equation y = 4(2^x)? Description of the four candidate graphs: (A) a curve falling steeply from the upper left, crossing near y = 100 at x = −3 and dropping toward an asymptote at y = 0 as x increases; (B) a curve falling more gradually from the left, leveling near y = 25 for large x rather than approaching 0; (C) a curve rising from near 0 on the left, crossing the y-axis around y = 4, and climbing steeply to about 100 by x = 4; (D) a curve rising from near 0 on the left, crossing the y-axis around y = 4, and climbing even more steeply, exceeding 100 well before x = 4.

**A.** The falling curve described in (A), approaching y = 0 as x increases 

  *y = 4(2^x) has base 2 > 1, which means the outputs grow as x increases, not shrink. A falling curve describes decay, which would need a base between 0 and 1, such as 4(0.5^x). [misconception: growth-decay-direction-reversed]*

**B.** The falling curve described in (B), leveling at a positive value instead of approaching 0 

  *This has the wrong direction (falling instead of rising) and also gives the function a nonzero horizontal asymptote, which would require an added constant such as 4(0.5^x) + 25 — the given equation has no such added term and its asymptote is y = 0. [misconception: growth-decay-direction-reversed]*

**C.** The rising curve described in (C), crossing the y-axis at 4 and reaching about 100 by x = 4 **(Correct)**

  *Correct. y = 4(2^x) has initial value 4 (at x = 0) and grows since the base 2 exceeds 1; by x = 4, y = 4(2⁴) = 4(16) = 64, and continuing to climb reaches the 100 range shortly after — matching a curve through (0, 4) that reaches about 100 near x = 4 to 5. ✓*

**D.** The rising curve described in (D), exceeding 100 well before x = 4 

  *This grows too fast for base 2. Reaching 100 well before x = 4 would require a larger base — for instance 4(3^x) reaches 4(3³) = 108 already by x = 3 — steeper growth than 4(2^x) actually produces. [misconception: base-overstated]*

*Difficulty: medium*

---

##### Q36
An object's kinetic energy, in joules, is equal to the product of one-half the object's mass, in kilograms, and the square of the object's speed, in meters per second. What is the speed, in meters per second, of an object with a mass of 4 kilograms and kinetic energy of 18 joules?

**A.** 3 **(Correct)**

  *Correct. Kinetic energy = (1/2)(mass)(speed)², so 18 = (1/2)(4)(v²) = 2v², giving v² = 9 and v = 3 (speed is nonnegative). ✓*

**B.** 6 

  *This solves 18 = 2v as though the model were linear in speed rather than quadratic — dropping the square on the speed term entirely, which is the whole point of a kinetic-energy relationship. [misconception: square-on-variable-dropped]*

**C.** 9 

  *This reports v² = 9 itself as the final answer without taking the square root to find v. The question asks for the speed, which is v, not v². [misconception: square-root-step-skipped]*

**D.** 36 

  *This computes 18 × 2 = 36 (undoing the one-half by multiplying, correctly) but then never divides by the mass or takes a square root — treating 36 as speed itself when it is actually mass × speed², an intermediate quantity that still needs two more steps. [misconception: solve-terminated-early]*

*Difficulty: medium*

---

##### Q37
The height, in feet, of an object x seconds after it is thrown straight up in the air can be modeled by the function h(x) = −16x² + 20x + 5. Based on the model, which of the following statements best interprets the equation h(1.4) = 1.64?

**A.** The height of the object 1.4 seconds after being thrown straight up in the air is 1.64 feet. **(Correct)**

  *Correct. h(1.4) = 1.64 means that when the input (time) is 1.4 seconds, the output (height) is 1.64 feet — the input is time and the output is height, in that order. ✓*

**B.** The height of the object 1.64 seconds after being thrown straight up in the air is 1.4 feet. 

  *Swaps which number is the input and which is the output. In h(1.4) = 1.64, the 1.4 goes into the function (it's the time), and 1.64 comes out (it's the resulting height) — not the reverse. [misconception: input-output-swapped]*

**C.** The height of the object 1.64 seconds after being thrown straight up in the air is approximately 1.4 times as great as its initial height. 

  *Reinvents the relationship as a ratio to the initial height rather than reading the equation as a straightforward input/output pair. Neither number in h(1.4) = 1.64 is being compared to h(0) here. [misconception: output-read-as-ratio]*

**D.** The speed of the object 1.4 seconds after being thrown straight up in the air is approximately 1.64 feet per second. 

  *h models height, not speed — the units given for h(x) are feet, and 1.64 is a height in feet, not a rate in feet per second. This model contains no information about the object's speed at any moment. [misconception: output-quantity-misidentified]*

*Difficulty: medium*

---

##### Q38
An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the greatest airflow. The engineer discovered that the function f(θ) = −0.28(θ − 27)² + 880 models the airflow f(θ), in cubic feet per minute, as a function of the angle of the fan, θ, in degrees. According to the model, what angle, in degrees, gives the greatest airflow?

**A.** −0.28 

  *This is the leading coefficient of the vertex form, which controls how sharply the parabola opens, not the angle at which the maximum occurs. The angle is read from inside the squared term. [misconception: leading-coefficient-read-as-vertex]*

**B.** 0.28 

  *This drops the sign on the leading coefficient and reports it in place of the vertex's location — but the leading coefficient, with either sign, is never the input value that produces the extreme output. [misconception: leading-coefficient-read-as-vertex]*

**C.** 27 **(Correct)**

  *Correct. In vertex form a(θ − h)² + k, the extreme value occurs at θ = h. Here (θ − 27)² means h = 27, and since a = −0.28 is negative, this is a maximum. ✓*

**D.** 880 

  *880 is the greatest airflow VALUE (the k in vertex form), not the angle at which it occurs. The question asks for an angle, which is the θ-value, not the maximum output itself. [misconception: y-value-reported-for-x-question]*

*Difficulty: medium*

---

##### Q39
Sara opened a savings account at a bank. The table shows the exponential relationship between the time t, in years, since Sara opened the account and the total amount d, in dollars, in the account: at t = 0, d = 670.00; at t = 1, d = 674.02; at t = 2, d = 678.06. If Sara made no additional deposits or withdrawals, which of the following equations best represents the relationship between t and d?

**A.** d = 0.006(1 + 670)^t 

  *Swaps which number is the starting amount and which is the growth rate. The starting balance, 670, belongs outside as the coefficient, and the small rate, 0.006, belongs inside the base as 1 + r — this equation has them reversed. [misconception: coefficient-and-rate-swapped]*

**B.** d = 670(1 + 0.006)^t **(Correct)**

  *Correct. The starting balance is 670, and the growth rate can be found from consecutive terms: 674.02/670 ≈ 1.006, so the account grows by a factor of 1.006 per year, giving d = 670(1.006)^t. Check t = 1: 670(1.006) = 674.02 ✓.*

**C.** d = 0.006(670t) 

  *This builds a linear model (a constant amount added, scaled by t) rather than an exponential one, despite the problem explicitly stating the relationship is exponential. A linear model would produce a constant dollar increase each year, but the actual increases (4.02, then 4.04) are growing, not constant. [misconception: exponential-model-replaced-with-linear]*

**D.** d = 670(0.006 + t) 

  *This also builds a linear-type model, adding t to a small constant and scaling by 670, rather than raising a growth multiplier to the power of t. It does not reflect the compounding, multiplicative pattern in the table. [misconception: exponential-model-replaced-with-linear]*

*Difficulty: medium*

---

##### Q40
A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2% less than the number of students enrolled the year before. Which of the following functions models the relationship between the number of students enrolled, f(x), and the number of years after 2015, x?

**A.** f(x) = 0.02(3,000)^x 

  *Uses the decline rate itself, 0.02, as the coefficient, and raises the starting enrollment to a power of x, which is backwards — the starting enrollment belongs outside the exponent as the coefficient, and the multiplier belongs inside as the base. [misconception: coefficient-and-base-swapped]*

**B.** f(x) = 0.98(3,000)^x 

  *Correctly finds the multiplier, 0.98, but puts it in the coefficient position and raises 3,000 to a power of x, again swapping which number is the fixed starting amount and which is the repeated multiplier. [misconception: coefficient-and-base-swapped]*

**C.** f(x) = 3,000(0.02)^x 

  *Uses the decline rate itself, 0.02, as the base instead of the multiplier 1 − 0.02 = 0.98. A base of 0.02 describes enrollment dropping to 2% of the previous year's total each year — a 98% annual decline — far more severe than described. [misconception: rate-used-as-multiplier]*

**D.** f(x) = 3,000(0.98)^x **(Correct)**

  *Correct. A 2% decrease each year means multiplying by 1 − 0.02 = 0.98 per year, applied to the starting enrollment of 3,000. ✓*

*Difficulty: easy*

---

##### Q41
A rubber ball bounces upward one-half the height that it falls each time it hits the ground. If the ball was originally dropped from a distance of 20.0 feet above the ground, what was its maximum height above the ground, in feet, between the third and fourth time it hit the ground?

**A.** 1.25 

  *This is the bounce height between the fourth and fifth hits (20 halved four times: 10, 5, 2.5, 1.25), one bounce too far past the interval the question asks about. [misconception: off-by-one-bounce]*

**B.** 5 

  *This is the bounce height between the second and third hits (20 halved twice: 10, then 5), one bounce short of the interval the question asks about. [misconception: off-by-one-bounce]*

**C.** 2.5 **(Correct)**

  *Correct. Each bounce is half the previous drop: after the 1st hit it rises to 10, after the 2nd hit to 5, and after the 3rd hit to 2.5 — that rise of 2.5 feet is the maximum height reached between the 3rd and 4th hits. ✓*

**D.** 10 

  *This is the bounce height between the first and second hits (half of the original 20-foot drop), two bounces short of the interval the question asks about. [misconception: off-by-one-bounce]*

*Difficulty: hard*

---

##### Q42
The function f is defined by f(x) = x² − 18x − 360. If the given function f is graphed in the xy-plane, where y = f(x), what is an x-intercept of the graph?

**A.** (−12, 0) **(Correct)**

  *Correct. Factoring gives f(x) = (x − 30)(x + 12), so the zeros are x = 30 and x = −12; (−12, 0) is one of the two x-intercepts. ✓*

**B.** (−30, 0) 

  *This flips the sign of the root hidden in (x − 30). Setting x − 30 = 0 gives x = 30, not −30 — the sign inside a factor's parenthesis is always the opposite of the root it names. [misconception: sign-inside-parentheses-flip]*

**C.** (−360, 0) 

  *This reports the constant term of the standard-form expression as though it were a root. The constant term, −360, is f(0), the y-intercept's value — not an x-intercept at all. [misconception: constant-read-as-root]*

**D.** (12, 0) 

  *This flips the sign of the root hidden in (x + 12). Setting x + 12 = 0 gives x = −12, not +12. [misconception: sign-inside-parentheses-flip]*

*Difficulty: medium*

---

##### Q43
According to Moore's law, the number of transistors included on microprocessors doubles every 2 years. In 1985, a microprocessor was introduced that had 275,000 transistors. Based on this information, in which of the following years does Moore's law estimate the number of transistors to reach 1.1 million?

**A.** 1987 

  *This assumes only one doubling has occurred, but one doubling from 275,000 gives 550,000 transistors — only half of 1.1 million. A second doubling is still needed. [misconception: insufficient-doublings-counted]*

**B.** 1989 **(Correct)**

  *Correct. 1.1 million ÷ 275,000 = 4 = 2², so two doublings are needed, and each doubling takes 2 years: 2 × 2 = 4 years after 1985 is 1989. Check: 275,000 → 550,000 (1987) → 1,100,000 (1989). ✓*

**C.** 1991 

  *This assumes three doublings are needed (275,000 doubled three times reaches 2.2 million, double the target), one doubling too many for reaching exactly 1.1 million. [misconception: excess-doublings-counted]*

**D.** 1994 

  *This overshoots by assuming the doubling period is longer than 2 years, or by counting extra doubling cycles beyond the two actually needed to reach 1.1 million. [misconception: excess-doublings-counted]*

*Difficulty: medium*

---

##### Q44
The function h(t) = −16t² + 110t + 72 models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?

**A.** The initial height, in feet, of the object **(Correct)**

  *Correct. h(0) = −16(0)² + 110(0) + 72 = 72, so 72 is the object's height at t = 0, the moment it was launched — its initial height. ✓*

**B.** The maximum height, in feet, of the object 

  *72 is the height at t = 0, not the peak of the parabola. Because the coefficient on t² is negative, the object rises above 72 before eventually returning to the ground, so the maximum height is a larger number reached later, at the vertex. [misconception: initial-value-read-as-maximum]*

**C.** The initial speed, in feet per second, of the object 

  *This confuses the constant term with the coefficient of t. The 72 is added without being multiplied by t, so it carries no per-second units — it's a height, not a speed. The initial speed is governed by the coefficient 110. [misconception: constant-term-confused-with-rate]*

**D.** The maximum speed, in feet per second, of the object 

  *72 is a fixed height value in the model, not a speed at all, and this model does not directly give speeds — h(t) outputs a height in feet, not a rate in feet per second. [misconception: output-quantity-misidentified]*

*Difficulty: medium*

---

##### Q45
The function N(d) = 115(0.90)^d can be used to model the number of species of brachiopods at various ocean depths d, where d is in hundreds of meters. Which of the following does the model predict?

**A.** For every increase in depth by 1 meter, the number of brachiopod species decreases by 115. 

  *115 is the model's initial value (the number of species at d = 0), not a fixed amount lost per meter. The model is multiplicative, not additive, so the loss per unit depth is never a constant number of species. [misconception: initial-value-read-as-additive-rate]*

**B.** For every increase in depth by 1 meter, the number of brachiopod species decreases by 10%. 

  *This reads the base correctly as a 10% decrease per step, but misreads the step size — d is measured in hundreds of meters, so each unit increase in d is 100 meters, not 1. [misconception: period-of-input-misread]*

**C.** For every increase in depth by 100 meters, the number of brachiopod species decreases by 115. 

  *Correctly identifies that one unit of d is 100 meters, but then treats 115 (the initial value) as a fixed per-step loss rather than reading the base 0.90 as the actual per-step multiplier — the multiplier means the loss shrinks each step, never a constant 115. [misconception: initial-value-read-as-additive-rate]*

**D.** For every increase in depth by 100 meters, the number of brachiopod species decreases by 10%. **(Correct)**

  *Correct. Since d is in hundreds of meters, one unit of d is 100 meters, and the base 0.90 = 1 − 0.10 means the species count is multiplied by 0.90 — a 10% decrease — for each such 100-meter increase. ✓*

*Difficulty: medium*

---

##### Q46
The area A, in square centimeters, of a rectangular painting can be represented by the expression w(w + 29), where w is the width, in centimeters, of the painting. Which expression represents the length, in centimeters, of the painting?

**A.** w 

  *This is the width itself, not the length — the width is the factor that's repeated in front, while the length is the other factor. [misconception: width-reported-as-length]*

**B.** 29 

  *29 is only part of the length expression, the constant added to the width. The full length also includes the width itself: length = w + 29, not 29 alone. [misconception: partial-expression-reported]*

**C.** (w + 29) **(Correct)**

  *Correct. Area = width × length, and here area is written as w(w + 29), so the width is w and the length is the other factor, (w + 29). ✓*

**D.** w(w + 29) 

  *This is the full area expression, not the length alone — it still includes the width factor multiplied in. [misconception: area-reported-as-length]*

*Difficulty: easy*

---

##### Q47
The table above gives the values of the function f for some values of x: f(0) = 5, f(1) = 5/2, f(2) = 5/4, f(3) = 5/8. Which of the following equations could define f?

**A.** f(x) = 5(2^(x+1)) 

  *This grows rather than shrinks — every output would be larger than the last, but the table shows f halving at each step, not doubling. [misconception: growth-decay-direction-reversed]*

**B.** f(x) = 5(2^x) 

  *Also grows instead of shrinking: f(1) would be 5(2) = 10, but the table shows f(1) = 5/2, a decrease, not an increase. [misconception: growth-decay-direction-reversed]*

**C.** f(x) = 5(2^(−(x+1))) 

  *This shrinks in the right direction but is shifted by one step: f(0) would be 5(2^(−1)) = 5/2, not 5, since the extra +1 inside the exponent applies an extra halving too early. [misconception: exponent-shift-error]*

**D.** f(x) = 5(2^(−x)) **(Correct)**

  *Correct. f(0) = 5(2⁰) = 5, f(1) = 5(2⁻¹) = 5/2, f(2) = 5(2⁻²) = 5/4, f(3) = 5(2⁻³) = 5/8 — each step halves the previous output, matching the table exactly. ✓*

*Difficulty: medium*

---

##### Q48
The function f is defined by f(x) = (x + 4)(x − 1)(2x − 3). Which of the following is NOT an x-intercept of the graph of the function in the xy-plane?

**A.** (−4, 0) 

  *This IS an x-intercept: setting x + 4 = 0 gives x = −4, one of the function's actual zeros. [misconception: actual-root-marked-as-non-root]*

**B.** (−2/3, 0) **(Correct)**

  *Correct — this is NOT an x-intercept. None of the three factors equals zero at x = −2/3: x + 4 = 10/3, x − 1 = −5/3, and 2x − 3 = −13/3, none of them zero. ✓*

**C.** (1, 0) 

  *This IS an x-intercept: setting x − 1 = 0 gives x = 1, one of the function's actual zeros. [misconception: actual-root-marked-as-non-root]*

**D.** (3/2, 0) 

  *This IS an x-intercept: setting 2x − 3 = 0 gives x = 3/2, one of the function's actual zeros. [misconception: actual-root-marked-as-non-root]*

*Difficulty: medium*

---

##### Q49
There were no jackrabbits in Australia before 1788, when 24 jackrabbits were introduced. By 1920 the population of jackrabbits had reached 10 billion. If the population had grown exponentially, this would correspond to a 16.2% increase, on average, in the population each year. Which of the following functions best models the population p(t) of jackrabbits t years after 1788?

**A.** p(t) = 1.162(24)^t 

  *Swaps which number is the starting population and which is the growth multiplier. The starting count, 24, belongs outside as the coefficient, and the multiplier, 1.162, belongs inside as the base — this has them reversed. [misconception: coefficient-and-base-swapped]*

**B.** p(t) = 24(2)^(1.162t) 

  *Inserts an extra factor of 2 into the exponent's base that has no basis in the problem — a 16.2% annual increase is captured entirely by using 1.162 as the base itself, with no separate doubling built in. [misconception: model-structure-invented]*

**C.** p(t) = 24(1.162)^t **(Correct)**

  *Correct. A 16.2% annual increase means multiplying by 1 + 0.162 = 1.162 each year, applied to the starting population of 24. ✓*

**D.** p(t) = (24 · 1.162)^t 

  *Multiplies the starting population and the growth multiplier together before raising the whole product to the power of t, which raises the starting population itself by a power of t — that's not how a·b^t is structured, and it grows vastly faster than the actual population. [misconception: model-structure-invented]*

*Difficulty: easy*

---

##### Q50
A sample of a certain isotope takes 29 years to decay to half its original mass. The function s(t) = 184(0.5)^(t/29) gives the approximate mass of this isotope, in grams, that remains t years after a 184-gram sample starts to decay. Which statement is the best interpretation of s(87) = 23 in this context?

**A.** Approximately 23 grams of the sample remains 87 years after the sample starts to decay. **(Correct)**

  *Correct. s(87) = 23 means that when the input (elapsed time) is 87 years, the output (remaining mass) is 23 grams. Check: 87/29 = 3 half-lives, and 184 → 92 → 46 → 23. ✓*

**B.** The mass of the sample has decreased by approximately 23 grams 87 years after the sample starts to decay. 

  *23 is the mass remaining, not the amount lost. The actual decrease from the original 184 grams is 184 − 23 = 161 grams, a very different number from 23. [misconception: remaining-quantity-read-as-change]*

**C.** The mass of the sample has decreased by approximately 87 grams 23 years after the sample starts to decay. 

  *Swaps which number is the input (time) and which is the output (mass), and additionally misreads the output as a decrease rather than a remaining amount. [misconception: input-output-swapped]*

**D.** Approximately 87 grams of the sample remains 23 years after the sample starts to decay. 

  *Swaps which number is the input and which is the output: 87 is the elapsed time that goes into the function, and 23 is the resulting mass that comes out, not the reverse. [misconception: input-output-swapped]*

*Difficulty: medium*

---

##### Q51
The product of two positive integers is 546. If the first integer is 11 greater than twice the second integer, what is the smaller of the two integers?

**A.** 7 

  *This does not satisfy the given product: if the second integer were 7, the first would be 2(7) + 11 = 25, and 7 × 25 = 175, not 546. [misconception: solution-not-checked]*

**B.** 14 **(Correct)**

  *Correct. Let the second integer be x, so the first is 2x + 11; then x(2x + 11) = 546 gives 2x² + 11x − 546 = 0, which factors (or solves via the quadratic formula) to x = 14 (discarding the negative root). Then the first integer is 2(14) + 11 = 39, and 14 × 39 = 546 ✓, so the smaller integer is 14.*

**C.** 39 

  *This is the LARGER of the two integers (2(14) + 11 = 39), reported in place of the smaller one the question asked for. [misconception: wrong-quantity-reported]*

**D.** 78 

  *This does not satisfy the given relationship between the two integers or their product; it appears to come from an arithmetic slip (such as doubling 39) rather than solving the quadratic that the problem sets up. [misconception: solution-not-checked]*

*Difficulty: hard*

---

##### Q52
The equation E(t) = 5(1.8)^t gives the estimated number of employees at a restaurant, where t is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?

**A.** The estimated number of employees when the restaurant opened **(Correct)**

  *Correct. E(0) = 5(1.8)⁰ = 5, so 5 is the estimated employee count at t = 0, when the restaurant opened. ✓*

**B.** The increase in the estimated number of employees each year 

  *5 is the model's starting value, not a fixed yearly increase. Because the model is multiplicative, the actual increase in employees is different (and growing) every year, never a constant amount. [misconception: initial-value-read-as-additive-rate]*

**C.** The number of years the restaurant has been open 

  *5 is a fixed constant in the equation, not the variable t, which is what represents the number of years elapsed. The number of years is an input to the function, not a value baked into it. [misconception: coefficient-confused-with-variable]*

**D.** The percent increase in the estimated number of employees each year 

  *5 sits in the coefficient position (the starting value), not in the base, which is where the percent growth rate lives. The actual percent increase per year comes from the base, 1.8, which is +80%. [misconception: initial-value-read-as-percent]*

*Difficulty: easy*

---

##### Q53
The function g is defined by g(x) = x² + 55. What is the minimum value of the given function?

**A.** 0 

  *This is the minimum value of x² alone, ignoring the +55 shift added to the function. The minimum of g is the minimum of x² plus 55, not 0. [misconception: constant-shift-ignored]*

**B.** 55 **(Correct)**

  *Correct. x² is never negative and reaches its own minimum of 0 at x = 0, so g(x) = x² + 55 reaches its minimum, 55, at x = 0. ✓*

**C.** 110 

  *This doubles the constant term, perhaps from adding 55 twice or confusing this with a different computation — the minimum only requires adding 55 once to the minimum of x², which is 0. [misconception: arithmetic-slip]*

**D.** 3,025 

  *This is 55², the square of the constant rather than the constant itself added to the minimum of x². Squaring 55 has no role in finding the minimum of x² + 55. [misconception: constant-squared-instead-of-added]*

*Difficulty: easy*

---

##### Q54
The function g is defined by g(x) = 11(1/12)^x. If the given function g is graphed in the xy-plane, where y = g(x), what is the y-intercept of the graph?

**A.** (0, 11) **(Correct)**

  *Correct. At x = 0, g(0) = 11(1/12)⁰ = 11(1) = 11, so the y-intercept is (0, 11). ✓*

**B.** (0, 132) 

  *This computes 11 × 12 = 132 instead of 11 × (1/12)⁰ = 11 × 1. Any nonzero base raised to the power 0 equals 1, regardless of what that base is — it does not get multiplied through as though the exponent were 1. [misconception: zero-exponent-rule-misapplied]*

**C.** (0, 1) 

  *This reports (1/12)⁰ = 1 alone, dropping the leading coefficient of 11 that multiplies it. The full y-intercept requires 11 × 1, not 1 by itself. [misconception: leading-coefficient-dropped]*

**D.** (0, 12) 

  *This reports the denominator of the base, 12, in place of the actual y-intercept — the base 1/12 does not appear directly in the output at x = 0; only the coefficient 11 does, since anything to the 0 power is 1. [misconception: base-denominator-reported]*

*Difficulty: easy*

---

##### Q55
A rectangle has a length of x units and a width of (x − 15) units. If the rectangle has an area of 76 square units, what is the value of x?

**A.** 4 

  *This does not satisfy the area equation: if x = 4, the width would be 4 − 15 = −11, a negative length, which isn't valid for a rectangle, and 4(−11) = −44 ≠ 76. [misconception: extraneous-or-invalid-root-selected]*

**B.** 19 **(Correct)**

  *Correct. Area = x(x − 15) = 76 gives x² − 15x − 76 = 0, which factors as (x − 19)(x + 4) = 0, so x = 19 or x = −4; only x = 19 gives a valid positive width (19 − 15 = 4), and 19 × 4 = 76 ✓.*

**C.** 23 

  *This does not satisfy the area equation: if x = 23, the width would be 23 − 15 = 8, and 23 × 8 = 184, not 76. [misconception: solution-not-checked]*

**D.** 76 

  *This treats the area itself as though it were the value of x, skipping the entire quadratic set-up and solve. [misconception: area-value-reported-as-x]*

*Difficulty: medium*

---

##### Q56
An object is kicked from a platform. The equation h = −4.9t² + 7t + 9 represents this situation, where h is the height of the object above the ground, in meters, t seconds after it is kicked. Which number represents the height, in meters, from which the object was kicked?

**A.** 0 

  *This assumes the object starts at ground level, but the equation's constant term is nonzero, meaning the object was kicked from a platform above the ground, not from height 0. [misconception: intercept-assumed-zero]*

**B.** 4.9 

  *This is the coefficient on t², which controls how gravity curves the path, not the starting height. The starting height comes from evaluating h at t = 0. [misconception: wrong-coefficient-selected]*

**C.** 7 

  *This is the coefficient on t, related to the object's initial upward speed, not its starting height. At t = 0, this term contributes 7(0) = 0 to the height. [misconception: wrong-coefficient-selected]*

**D.** 9 **(Correct)**

  *Correct. At t = 0, h = −4.9(0)² + 7(0) + 9 = 9, so the object was kicked from a height of 9 meters. ✓*

*Difficulty: easy*

---

##### Q57
A graph in the xy-plane shows a curve that oscillates near the x-axis for negative x, rises to a local maximum of about 20 near x = 2, then falls steeply to about −100 by x = 5, and rises again for x beyond 6; it appears to touch the x-axis without crossing near x = −5, and to cross the x-axis near x = 0 and near x = 4, with the far ends of the graph both trending downward. Which of the following could be the equation of the graph shown in the xy-plane?

**A.** y = −(1/10)x(x − 4)(x + 5) 

  *Every factor here has an odd exponent (1), so the graph would cross the x-axis at all three zeros, x = 0, 4, and −5, with no touch-and-turn anywhere — but the description shows the curve merely touching the axis near x = −5, not crossing it. [misconception: multiplicity-ignored]*

**B.** y = −(1/10)x(x − 4)(x + 5)² **(Correct)**

  *Correct. The squared factor (x + 5)² gives an even multiplicity at x = −5, so the graph touches but does not cross there, while the single factors x and (x − 4) give crossings at x = 0 and x = 4. The degree is 1 + 1 + 2 = 4 (even) with a negative leading coefficient, sending both ends downward, matching the description. ✓*

**C.** y = −(1/10)x(x − 5)(x + 4) 

  *This places the zeros at x = 0, 5, and −4 instead of the described 0, 4, and −5, and again gives every factor odd multiplicity, so the graph would cross at every zero instead of touching at one of them. [misconception: root-locations-misassigned]*

**D.** y = −(1/10)x(x − 5)²(x + 4) 

  *This puts the squared (touching) factor at x = 5 instead of x = −5, and shifts the other zero to −4 instead of 4 — the multiplicity structure is right in form, but attached to the wrong roots for the graph described. [misconception: root-locations-misassigned]*

*Difficulty: hard*

---

##### Q58
The function p is defined by p(n) = 7n³. What is the value of n when p(n) is equal to 56?

**A.** 2 **(Correct)**

  *Correct. 7n³ = 56 gives n³ = 8, so n = 2, since 2³ = 8. Check: 7(2³) = 7(8) = 56 ✓.*

**B.** 8/3 

  *This divides 56 by 7 correctly to get 8, but then divides by 3 instead of taking a cube root — treating the exponent 3 as a divisor rather than a power to undo with a root. [misconception: cube-root-replaced-with-division]*

**C.** 7 

  *This reports the coefficient of the function, 7, rather than solving for n. The coefficient is a fixed multiplier in the equation, not the unknown being solved for. [misconception: coefficient-reported-instead-of-variable]*

**D.** 8 

  *This solves 7n³ = 56 correctly down to n³ = 8, but stops there and reports n³ instead of taking the cube root to find n itself. [misconception: cube-root-step-skipped]*

*Difficulty: medium*

---

##### Q59
The function f is defined by f(x) = 270(0.1)^x. What is the value of f(0)?

**A.** 0 

  *This assumes any base raised to the power 0 equals 0, but any nonzero base raised to the power 0 equals 1, not 0 — the exponent 0 means "no multiplications applied," leaving the coefficient untouched. [misconception: zero-exponent-rule-misapplied]*

**B.** 1 

  *This correctly evaluates (0.1)⁰ = 1 but then drops the leading coefficient of 270 that multiplies it, reporting the exponential factor alone instead of 270 times that factor. [misconception: leading-coefficient-dropped]*

**C.** 27 

  *This computes 270 × 0.1¹ = 27 instead of 270 × 0.1⁰ = 270 × 1, effectively treating the exponent as 1 rather than 0. [misconception: exponent-value-misapplied]*

**D.** 270 **(Correct)**

  *Correct. Any nonzero base raised to the power 0 equals 1, so f(0) = 270(0.1)⁰ = 270(1) = 270. ✓*

*Difficulty: easy*

---

##### Q60
The area of a triangle is 270 square centimeters. The length of the base of the triangle is 12 centimeters greater than the height of the triangle. What is the height, in centimeters, of the triangle?

**A.** 15 

  *This does not satisfy the area equation: if the height were 15, the base would be 27, and (1/2)(27)(15) = 202.5, not 270. [misconception: solution-not-checked]*

**B.** 18 **(Correct)**

  *Correct. Let h be the height, so the base is h + 12, and (1/2)(h)(h + 12) = 270 gives h² + 12h − 540 = 0, which factors as (h − 18)(h + 30) = 0, so h = 18 (discarding the negative root). Check: (1/2)(18)(30) = 270 ✓.*

**C.** 30 

  *This is the BASE of the triangle (18 + 12 = 30), reported in place of the height the question asked for. [misconception: wrong-quantity-reported]*

**D.** 36 

  *This does not satisfy the area equation: if the height were 36, the base would be 48, and (1/2)(48)(36) = 864, far more than 270. [misconception: solution-not-checked]*

*Difficulty: medium*

---

##### Q61
On April 1, there were 233 views of an advertisement posted on a website. Every 2 days after April 1, the number of views of the advertisement had increased by 70% of the number of views 2 days earlier. The function f gives the predicted number of views x days after April 1. Which equation defines f?

**A.** f(x) = 233(0.70)^(x/2) 

  *Uses the growth rate itself, 0.70, as the base rather than the multiplier 1 + 0.70 = 1.70. A base of 0.70 describes the views shrinking to 70% of their previous value every 2 days, the opposite of the described increase. [misconception: growth-decay-multiplier-swapped]*

**B.** f(x) = 233(0.70)^(2x) 

  *Combines two errors: it uses the decay-direction multiplier 0.70 instead of 1.70, and it also inverts the period conversion, multiplying by 2 instead of dividing by 2 to count how many 2-day periods have passed. [misconception: growth-decay-multiplier-swapped]*

**C.** f(x) = 233(1.70)^(x/2) **(Correct)**

  *Correct. A 70% increase every 2 days means multiplying by 1.70 once per 2-day period, and x days is x/2 such periods, giving f(x) = 233(1.70)^(x/2). Check x = 2: 233(1.70)¹ = 396.1, a 70% increase over 233. ✓*

**D.** f(x) = 233(1.70)^(2x) 

  *Uses the correct growth multiplier but inverts the period conversion, multiplying x by 2 instead of dividing by 2 — this applies the 70% increase far too often, as though it happened twice per day rather than once every 2 days. [misconception: inverted-period-conversion]*

*Difficulty: hard*

---

##### Q62
For the given function f, defined by f(x) = x⁵ + 9x + 17, the graph of y = f(x) in the xy-plane passes through the point (0, b), where b is a constant. What is the value of b?

**A.** 0 

  *Assumes the graph passes through the origin without evaluating f at x = 0, where the constant term makes the actual value nonzero. [misconception: intercept-assumed-zero]*

**B.** 9 

  *This reports the coefficient of the linear term, 9, rather than evaluating the whole function at x = 0. At x = 0 the terms x⁵ and 9x both vanish, leaving only the constant term. [misconception: wrong-coefficient-selected]*

**C.** 5 

  *This reports the degree of the leading term (the exponent 5) rather than the function's value at x = 0. [misconception: exponent-read-as-value]*

**D.** 17 **(Correct)**

  *Correct. At x = 0, f(0) = 0⁵ + 9(0) + 17 = 17, so b = 17. ✓*

*Difficulty: easy*

---

##### Q63
An entomologist recommended a program to reduce a certain invasive beetle population in an area. The function f(x) = 4,000(0.75)^x estimates this beetle species' population x years after 2012, where x ≤ 7. Which of the following is the best interpretation of 4,000 in this context?

**A.** The estimated initial beetle population for this species and area in 2012 **(Correct)**

  *Correct. f(0) = 4,000(0.75)⁰ = 4,000, so 4,000 is the model's value at x = 0, the estimated beetle population in 2012, before any decline. ✓*

**B.** The estimated beetle population for this species and area 7 years after 2012 

  *This describes f(7), the population at the far end of the stated domain, not 4,000, which is the population at x = 0. Since the population is decaying, f(7) is a much smaller number than 4,000. [misconception: initial-value-confused-with-endpoint]*

**C.** The estimated percent decrease in the beetle population for this species and area each year 

  *4,000 sits in the coefficient position (the starting population), not in the base, which is where the percent decay rate lives. The actual percent decrease per year comes from the base, 0.75, which is −25%. [misconception: initial-value-read-as-percent]*

**D.** The estimated percent decrease in the beetle population for this species and area every 7 years 

  *This also mistakes the coefficient for a percentage, and additionally invents a 7-year period that doesn't appear anywhere in the model — the base 0.75 applies once per single year, not once every 7 years. [misconception: initial-value-read-as-percent]*

*Difficulty: medium*

---

##### Q64
The quadratic function h is defined by h(x) = 2(x − 4)² − 32. In the xy-plane, the graph of y = h(x) intersects the x-axis at the points (0, 0) and (t, 0), where t is a constant. What is the value of t?

**A.** 1 

  *This does not satisfy h(x) = 0: h(1) = 2(1 − 4)² − 32 = 2(9) − 32 = −14, not 0, so (1, 0) is not on the graph. [misconception: solution-not-checked]*

**B.** 2 

  *This does not satisfy h(x) = 0: h(2) = 2(2 − 4)² − 32 = 2(4) − 32 = −24, not 0, so (2, 0) is not on the graph. [misconception: solution-not-checked]*

**C.** 4 

  *4 is the x-coordinate of the vertex, not a root — h(4) = 2(0)² − 32 = −32, the parabola's minimum, well below the x-axis, not on it. [misconception: vertex-read-as-root]*

**D.** 8 **(Correct)**

  *Correct. Setting h(x) = 0 gives 2(x − 4)² = 32, so (x − 4)² = 16, giving x − 4 = ±4, so x = 8 or x = 0. Since (0, 0) is already given, the other intercept is t = 8. ✓*

*Difficulty: medium*

---

##### Q65
The function f(x) = 9,000(0.66)^x models the number of advertisements a company sent to its clients each year, where x represents the number of years since 1997, and 0 ≤ x ≤ 5. If y = f(x) is graphed in the xy-plane, which of the following is the best interpretation of the y-intercept of the graph in this context?

**A.** The minimum estimated number of advertisements the company sent to its clients during the 5 years was 1,708. 

  *Confuses the y-intercept (the value at x = 0) with the minimum over the domain. Because the base 0.66 is less than 1, the function is decreasing, so its minimum on 0 ≤ x ≤ 5 occurs at x = 5, not at x = 0 where the y-intercept lives. [misconception: minimum-confused-with-intercept]*

**B.** The minimum estimated number of advertisements the company sent to its clients during the 5 years was 9,000. 

  *Gets the value right but mislabels what it represents: 9,000 is f(0), the largest value on this decreasing function's domain, not its minimum, which occurs at the other end, x = 5. [misconception: maximum-confused-with-minimum]*

**C.** The estimated number of advertisements the company sent to its clients in 1997 was 1,708. 

  *Correctly identifies 1997 as x = 0, but reports the wrong value there — f(0) = 9,000(0.66)⁰ = 9,000, not 1,708, which is closer to a value later in the domain. [misconception: wrong-value-at-correct-input]*

**D.** The estimated number of advertisements the company sent to its clients in 1997 was 9,000. **(Correct)**

  *Correct. x = 0 corresponds to 1997, and f(0) = 9,000(0.66)⁰ = 9,000(1) = 9,000, the model's y-intercept. ✓*

*Difficulty: medium*

---

##### Q66
Function f is defined by f(x) = −a^x + b, where a and b are constants. In the xy-plane, the graph of y = f(x) − 12 has a y-intercept at (0, −75/7). The product of a and b is 320/7. What is the value of a?

**A.** 4 

  *This does not satisfy the product condition together with the y-intercept equation: with a = 4, solving f(0) − 12 = −75/7 for b gives b = 16/7, and 4(16/7) = 64/7, not 320/7. [misconception: system-not-checked]*

**B.** 8 

  *This does not satisfy both conditions simultaneously: with a = 8, b would need to be 16/7 (from the y-intercept equation alone, independent of a), giving a product of 8(16/7) = 128/7, not 320/7. [misconception: system-not-checked]*

**C.** 10 

  *This does not satisfy the product condition: with a = 10 and b = 16/7 fixed by the y-intercept equation, the product is 10(16/7) = 160/7, not 320/7. [misconception: system-not-checked]*

**D.** 20 **(Correct)**

  *Correct. At x = 0, f(0) − 12 = (−a⁰ + b) − 12 = −1 + b − 12 = b − 13, and this equals −75/7, so b = 13 − 75/7 = (91 − 75)/7 = 16/7. The product ab = 320/7 then gives a(16/7) = 320/7, so a = 320/16 = 20. Check: −1 + 16/7 − 12 = −13 + 16/7 = (−91 + 16)/7 = −75/7 ✓.*

*Difficulty: hard*

---

##### Q67
A machine launches a softball from ground level. The softball reaches a maximum height of 51.84 meters above the ground at 1.8 seconds and hits the ground at 3.6 seconds. Which equation represents the height above ground h, in meters, of the softball t seconds after it is launched?

**A.** h = −t² + 3.6 

  *This has no leading coefficient matching the physical scale of the motion and puts the landing time, 3.6, in the constant position — but the constant term of a launched-from-ground-level model should be 0 (the height at t = 0), and 3.6 is a time, not a height. [misconception: given-values-in-wrong-positions]*

**B.** h = −t² + 51.84 

  *Places the maximum height as though it occurred at t = 0, ignoring that the peak actually happens at t = 1.8 seconds — this form has its vertex at t = 0, ruled out by the problem's own timing. [misconception: vertex-time-ignored]*

**C.** h = −16(t + 51.84)² − 3.6 

  *Puts the maximum height value, 51.84, inside the squared term (where the vertex's time-coordinate belongs) and gives the whole expression a negative constant shift, which would make every height negative — the vertex form has the roles of h and t's vertex coordinates reversed. [misconception: vertex-coordinates-swapped]*

**D.** h = −16(t − 1.8)² + 51.84 **(Correct)**

  *Correct. Vertex form places the peak — height 51.84 at time 1.8 seconds — directly: h = −16(t − 1.8)² + 51.84. Check at t = 0 (launch, ground level): −16(1.8)² + 51.84 = −16(3.24) + 51.84 = −51.84 + 51.84 = 0 ✓, and at t = 3.6 (landing): −16(1.8)² + 51.84 = 0 ✓ by the same symmetric distance from the vertex.*

*Difficulty: medium*

---

##### Q68
The function f is defined by f(x) = a^x + b, where a and b are constants. In the xy-plane, the graph of y = f(x) has an x-intercept at (2, 0) and a y-intercept at (0, −323). What is the value of b?

**A.** −324 **(Correct)**

  *Correct. The y-intercept gives f(0) = a⁰ + b = 1 + b = −323, so b = −323 − 1 = −324. ✓*

**B.** −323 

  *This reports the y-intercept's output value, −323, directly as b, skipping the step of subtracting the a⁰ = 1 term that's added on top of b in the model. [misconception: constant-term-isolation-skipped]*

**C.** 323 

  *This drops the negative sign from the given y-intercept value before solving, treating f(0) as +323 instead of −323, which reverses the sign of the final answer for b as well. [misconception: sign-of-given-value-dropped]*

**D.** 2 

  *This reports the x-coordinate of the x-intercept, which is not needed to find b from the y-intercept alone — b comes entirely from the equation f(0) = 1 + b = −323. [misconception: wrong-given-value-used]*

*Difficulty: medium*

---

##### Q69
The revenue f(x), in dollars, that a company receives from sales of a product is given by the function f(x) = −500x² + 25,000x, where x is the unit price, in dollars, of the product. The graph of y = f(x) in the xy-plane intersects the x-axis at 0 and a. What does a represent?

**A.** The revenue, in dollars, when the unit price of the product is $0 

  *This describes the OTHER x-intercept, x = 0, not a. At x = 0, revenue is f(0) = 0, which is a given intercept already, not the unknown one the question asks about. [misconception: wrong-intercept-described]*

**B.** The unit price, in dollars, of the product that will result in maximum revenue 

  *The price giving maximum revenue is the x-coordinate of the vertex, the midpoint of the two zeros (0 and a), not a zero itself. At an x-intercept the revenue is $0, which is the opposite of maximum. [misconception: vertex-confused-with-root]*

**C.** The unit price, in dollars, of the product that will result in a revenue of $0 **(Correct)**

  *Correct. Factoring gives f(x) = −500x(x − 50), so the zeros are x = 0 and x = 50; a = 50 is the OTHER price (besides $0 itself) at which revenue is $0 — for instance, a price so high that nothing sells. ✓*

**D.** The maximum revenue, in dollars, that the company can make 

  *This describes the y-coordinate of the vertex (an output, in dollars of revenue), not a, which is an x-intercept — a price, in dollars, where revenue is exactly $0, the opposite of a maximum revenue. [misconception: vertex-y-value-confused-with-root]*

*Difficulty: medium*

---

##### Q70
A culture of bacteria is growing at an exponential rate, as shown in the table: on Day 1 there are 2.5×10⁵ bacteria per milliliter, on Day 2 there are 5.0×10⁵, and on Day 3 there are 1.0×10⁶. At this rate, on which day would the number of bacteria per milliliter reach 5.12×10⁸?

**A.** Day 5 

  *This assumes only 4 doublings past Day 1 are needed, but 4 doublings from 2.5×10⁵ only reaches 4.0×10⁶ — far short of the 5.12×10⁸ target, which needs many more doublings. [misconception: insufficient-doublings-counted]*

**B.** Day 9 

  *This undercounts the doublings needed: 5.12×10⁸ ÷ 2.5×10⁵ = 2,048 = 2¹¹, so 11 doublings past Day 1 are required, landing on Day 12, not Day 9. [misconception: insufficient-doublings-counted]*

**C.** Day 11 

  *This is off by one day: 5.12×10⁸ ÷ 2.5×10⁵ = 2,048 = 2¹¹, so 11 doublings are needed starting from Day 1, which lands on Day 1 + 11 = Day 12, not Day 11. [misconception: off-by-one-period]*

**D.** Day 12 **(Correct)**

  *Correct. The population doubles daily starting from 2.5×10⁵ on Day 1. Since 5.12×10⁸ ÷ 2.5×10⁵ = 2,048 = 2¹¹, 11 doublings are needed, reaching Day 1 + 11 = Day 12. ✓*

*Difficulty: medium*

---

##### Q71
The function f is defined by f(x) = (x − 14)(x + 19). For what value of x does f(x) reach its minimum?

**A.** −266 

  *This is the product of the two roots' constants, 14 × (−19) = −266, which relates to the y-intercept of the expanded form, not the x-coordinate of the vertex. [misconception: constants-multiplied-instead-of-averaged]*

**B.** −19 

  *This is one of the two roots (from x + 19 = 0), not the vertex — the vertex sits at the midpoint of the two roots, not on either one. [misconception: root-read-as-vertex]*

**C.** −33/2 

  *This averages the two constants as printed, (14 + (−19))/2 = −5/2... more precisely this value comes from an arithmetic slip while combining the roots incorrectly; regardless, it does not equal the correct midpoint of the actual roots 14 and −19. [misconception: roots-averaged-incorrectly]*

**D.** −5/2 **(Correct)**

  *Correct. The zeros of f are x = 14 and x = −19 (from x − 14 = 0 and x + 19 = 0), and the vertex sits at their midpoint: (14 + (−19))/2 = −5/2. ✓*

*Difficulty: easy*

---

##### Q72
The population P of a certain city y years after the last census is modeled by the equation P = P₀(1 + r)^y, where r is a constant and P₀ is the population when y = 0. If during this time the population of the city decreases by a fixed percent each year, which of the following must be true?

**A.** r < −1 

  *If r were less than −1, the base 1 + r would be negative, which would make the population alternate between positive and negative values as y increases — not a sensible model of a shrinking population. [misconception: base-sign-not-considered]*

**B.** −1 < r < 0 **(Correct)**

  *Correct. A fixed-percent decrease each year means the multiplier 1 + r is between 0 and 1 (population shrinks but stays positive), which requires r itself to be between −1 and 0. ✓*

**C.** 0 < r < 1 

  *This range makes the base 1 + r greater than 1, which describes population GROWTH each year, not the decrease described in the problem. [misconception: growth-decay-direction-reversed]*

**D.** r > 1 

  *This makes the base 1 + r greater than 2, describing extremely rapid growth (more than doubling every year), the opposite of the described decrease. [misconception: growth-decay-direction-reversed]*

*Difficulty: easy*

---

##### Q73
The table above gives selected values of a polynomial function p: p(−2) = 5, p(−1) = 0, p(0) = −3, p(1) = −1, p(2) = 0. Based on the values in the table, which of the following must be a factor of p?

**A.** (x − 3) 

  *This would require p(3) = 0, but the table gives no value at x = 3 at all, and nothing in the given data supports 3 being a root. [misconception: unsupported-root-claimed]*

**B.** (x + 3) 

  *This would require p(−3) = 0, but the table gives no value at x = −3, and nothing in the given data supports −3 being a root. [misconception: unsupported-root-claimed]*

**C.** (x − 1)(x + 2) 

  *This would require p(1) = 0 and p(−2) = 0, but the table shows p(1) = −1 (not 0) and p(−2) = 5 (not 0) — neither x = 1 nor x = −2 is an actual root. [misconception: non-zero-values-treated-as-roots]*

**D.** (x + 1)(x − 2) **(Correct)**

  *Correct. The table shows p(−1) = 0 and p(2) = 0, so both x = −1 and x = 2 are roots of p, meaning (x + 1) and (x − 2) must both be factors. ✓*

*Difficulty: medium*

---

##### Q74
The function f is defined by f(x) = (x + 3)(x + 1). The graph of f in the xy-plane is a parabola. Which of the following intervals contains the x-coordinate of the vertex of the graph of f?

**A.** −4 < x < −3 

  *This interval lies entirely to the left of both roots of f (−3 and −1); the vertex of a parabola always sits between its two real roots, never outside them. [misconception: vertex-placed-outside-roots]*

**B.** −3 < x < 1 **(Correct)**

  *Correct. The roots of f are x = −3 and x = −1, so the vertex sits at their midpoint, x = (−3 + (−1))/2 = −2, and −2 falls within the interval −3 < x < 1. ✓*

**C.** 1 < x < 3 

  *This interval is well to the right of both roots of f (−3 and −1); the vertex sits between the roots, at x = −2, not off to the positive side. [misconception: vertex-placed-outside-roots]*

**D.** 3 < x < 4 

  *This interval is far from both roots of f (−3 and −1) and from their midpoint, −2, which is where the vertex actually sits. [misconception: vertex-placed-outside-roots]*

*Difficulty: medium*

---

##### Q75
A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?

**A.** 8 

  *This is the WIDTH of the garden, not the length — solving w(w + 5) = 104 gives w = 8, and the question asks for the length, which is 5 feet more than that. [misconception: wrong-quantity-reported]*

**B.** 13 **(Correct)**

  *Correct. Let w be the width, so the length is w + 5, and w(w + 5) = 104 gives w² + 5w − 104 = 0, which factors as (w − 8)(w + 13) = 0, so w = 8 (discarding the negative root). The length is then 8 + 5 = 13. Check: 8 × 13 = 104 ✓.*

**C.** 20 

  *This does not satisfy the area equation: if the width were 20 − 5 = 15, the area would be 15 × 20 = 300, not 104. [misconception: solution-not-checked]*

**D.** 104 

  *This treats the area itself as though it were the length, skipping the entire quadratic set-up needed to separate length from width. [misconception: area-value-reported-as-length]*

*Difficulty: medium*

---

##### Q76
For the function f, f(0) = 86, and for each increase in x by 1, the value of f(x) decreases by 80%. What is the value of f(2)?

**A.** 17.2 

  *This computes 86 × 0.2 = 17.2, applying the 20%-remaining multiplier only once instead of twice — one decrease step, when the question asks about two steps, from x = 0 to x = 2. [misconception: insufficient-steps-applied]*

**B.** 3.44 **(Correct)**

  *Correct. Decreasing by 80% each step means keeping 20%, so the multiplier is 0.2 per step. Applying it twice: f(2) = 86(0.2)² = 86(0.04) = 3.44. ✓*

**C.** 68.8 

  *This subtracts 20% of 86 (17.2) from 86 once, treating the decrease as additive (subtracting a fixed amount) rather than multiplicative (retaining a fixed percentage), and only applies one step besides. [misconception: linear-reasoning-on-multiplicative-model]*

**D.** 34.4 

  *This computes 86 × 0.4 = 34.4, as if the retained fraction after two 80% decreases were 40% rather than the correctly compounded 0.2² = 4%. Two successive 80% losses compound multiplicatively, they don't just double the single-step retained fraction. [misconception: compounding-not-applied]*

*Difficulty: medium*

---

##### Q77
The equation M = 1,800(1.02)^t models the number of members, M, of a gym t years after the gym opens. Of the following, which equation models the number of members of the gym q quarter years after the gym opens?

**A.** M = 1,800(1.02)^(q/4) **(Correct)**

  *Correct. There are 4 quarters in a year, so t years equals 4t quarter years, meaning q quarter years is t = q/4 years. Substituting gives M = 1,800(1.02)^(q/4). ✓*

**B.** M = 1,800(1.02)^(4q) 

  *Inverts the period conversion, multiplying q by 4 instead of dividing by 4. Since a quarter is a shorter span than a year, q quarter years corresponds to a SMALLER number of years, t = q/4, not a larger one. [misconception: inverted-period-conversion]*

**C.** M = 1,800(1.005)^(4q) 

  *Attempts to convert the annual rate to a quarterly rate but does it backwards on both the base and the exponent: dividing 1.02 by roughly 4 to get 1.005 while also multiplying (rather than dividing) the exponent by 4 double-applies the period conversion in the same direction twice. [misconception: period-conversion-applied-twice]*

**D.** M = 1,800(1.082)^q 

  *This treats 1.082 as though it were the quarterly growth multiplier, but 1.02^(1/4) ≈ 1.005 is the actual quarterly multiplier — 1.082 is roughly 1.02⁴, the multiplier for FOUR years compressed into one quarter, backwards from what's needed. [misconception: period-conversion-inverted-in-base]*

*Difficulty: medium*

---

##### Q78
The functions f and g are defined by the given equations, where x ≥ 0: I. f(x) = 33(0.4)^(x+3); II. g(x) = 33(0.16)(0.4)^(x−2). Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where x ≥ 0?

**A.** I only 

  *Since 0 < 0.4 < 1, f is decreasing on x ≥ 0, so its maximum is f(0) = 33(0.4)³ = 33(0.064) = 2.112. But the form 33(0.4)^(x+3) shows 33 as its coefficient, not 2.112 — the true maximum is hidden inside the shifted exponent, not displayed as a visible constant. [misconception: shifted-exponent-coefficient-mistaken-for-max]*

**B.** II only **(Correct)**

  *Correct. Since 0.16 = 0.4², the form 33(0.16)(0.4)^(x−2) is algebraically 33(0.4)²(0.4)^(x−2) = 33(0.4)^x — so g(0) = 33, and this maximum, 33, is literally one of the multiplied constants written in the given form. In f, no such simplification occurs: 33(0.4)^(x+3) = 33(0.4)³(0.4)^x = 2.112(0.4)^x, and 2.112 is nowhere written directly. ✓*

**C.** I and II 

  *This is true for II (33 does equal g's maximum, and is directly displayed), but not for I — f's true maximum, 2.112, requires computing 33(0.4)³ and is not equal to any single constant appearing in the written form 33(0.4)^(x+3). [misconception: shifted-exponent-coefficient-mistaken-for-max]*

**D.** Neither I nor II 

  *This misses that II does display its maximum directly: 0.16 happens to equal 0.4², which makes 33(0.16)(0.4)^(x−2) algebraically identical to 33(0.4)^x, so the visible constant 33 is exactly g(0), the true maximum on x ≥ 0. [misconception: hidden-simplification-missed]*

*Difficulty: sat-hardest*

---

##### Q79
The surface area of a cube is 6(a/4)², where a is a positive constant. Which of the following gives the perimeter of one face of the cube?

**A.** a/4 

  *This is the side length of the cube (matching the surface-area formula 6s² with s = a/4), not the perimeter of a face, which requires multiplying the side length by 4. [misconception: side-length-reported-as-perimeter]*

**B.** a **(Correct)**

  *Correct. Surface area 6s² matches the given 6(a/4)² with side length s = a/4, and the perimeter of one square face is 4s = 4(a/4) = a. ✓*

**C.** 4a 

  *This multiplies the side length formula's DENOMINATOR incorrectly, treating a itself (rather than a/4) as the side length before multiplying by 4 — but the side length is a/4, not a, so 4(a/4) = a, not 4a. [misconception: side-length-misidentified]*

**D.** 6a 

  *This carries the "6" from the surface-area formula (which counts the 6 faces of the cube) into the perimeter calculation, where it has no role — the perimeter of a single face only involves that face's 4 sides. [misconception: surface-area-coefficient-carried-over]*

*Difficulty: easy*

---

##### Q80
The function h is defined by h(x) = a^x + b, where a and b are positive constants. The graph of y = h(x) in the xy-plane passes through the points (0, 10) and (−2, 325/36). What is the value of ab?

**A.** 1/4 

  *This does not satisfy both given points: solving from (0, 10) gives b = 9, and 325/36 − 9 = 1/36 should equal a⁻², so a² = 36 and a = 6, giving ab = 54, not 1/4. [misconception: system-not-solved-fully]*

**B.** 1/2 

  *This also does not satisfy both given points — following the correct method (b = 9, then a = 6 from the second point) gives ab = 54, not 1/2. [misconception: system-not-solved-fully]*

**C.** 54 **(Correct)**

  *Correct. From (0, 10): a⁰ + b = 1 + b = 10, so b = 9. From (−2, 325/36): a⁻² + 9 = 325/36, so a⁻² = 325/36 − 324/36 = 1/36, giving a² = 36 and a = 6 (positive constant). So ab = 6(9) = 54. ✓*

**D.** 60 

  *This is close to the correct value but comes from a small arithmetic slip somewhere in isolating a² = 36 or in the final multiplication — the correctly solved constants are a = 6 and b = 9, whose product is 54, not 60. [misconception: arithmetic-slip]*

*Difficulty: hard*

---

##### Q81
The table shows three values of x and their corresponding values of y, where y = f(x) + 4 and f is a quadratic function: x = 21, y = −8; x = 23, y = 8; x = 25, y = −8. What is the y-coordinate of the y-intercept of the graph of y = f(x) in the xy-plane?

**A.** −8 

  *This reports one of the given table values directly, at x = 21 or x = 25, rather than solving for f's actual value at x = 0, which is far outside the table and requires reconstructing the full quadratic first. [misconception: table-value-reported-without-solving]*

**B.** 8 

  *This reports the peak value of the SHIFTED function f(x) + 4 at x = 23, not the y-intercept of f itself at x = 0, which requires undoing the +4 shift and extrapolating the parabola all the way back to x = 0. [misconception: shifted-peak-reported-instead-of-intercept]*

**C.** 4 

  *This reports the size of the vertical shift between f and f(x) + 4, not an actual output value of either function at any specific input. [misconception: shift-amount-reported-as-output]*

**D.** −2,112 **(Correct)**

  *Correct. The table is symmetric about x = 23 with a peak value of 8 there, so g(x) = f(x) + 4 has vertex (23, 8): g(x) = a(x − 23)² + 8. Using x = 21 (2 away from the vertex): a(4) + 8 = −8, so a = −4. Then f(x) = −4(x − 23)² + 4, and f(0) = −4(529) + 4 = −2,116 + 4 = −2,112. ✓*

*Difficulty: hard*

---

##### Q82
A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object is launched off an elevated surface. The model indicates the object has an initial height of 10 feet above the ground and reaches its maximum height of 1,034 feet above the ground 8 seconds after being launched. Based on the model, what is the height, in feet, of the object above the ground 10 seconds after being launched?

**A.** 234 

  *This undershoots the correct value; it looks like it comes from using an incorrect leading coefficient in the vertex form, such as one derived from a mismatched pair of the given values. [misconception: leading-coefficient-miscalculated]*

**B.** 778 

  *This does not match the vertex-form model built from the given initial height and maximum: with h(t) = a(t − 8)² + 1,034 and h(0) = 10, solving gives a = −16, and h(10) = −16(4) + 1,034 = 970, not 778. [misconception: vertex-form-not-set-up-correctly]*

**C.** 970 **(Correct)**

  *Correct. Using vertex form h(t) = a(t − 8)² + 1,034 with the initial condition h(0) = 10: a(64) + 1,034 = 10, so a = −16. Then h(10) = −16(10 − 8)² + 1,034 = −16(4) + 1,034 = −64 + 1,034 = 970. ✓*

**D.** 1,014 

  *This is very close to the maximum, 1,034, suggesting the object's descent from its peak was underestimated — at t = 10, two seconds have passed since the peak, and the drop −16(2)² = −64 feet from 1,034 should be reflected fully. [misconception: descent-underestimated]*

*Difficulty: hard*

---

##### Q83
The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function defined in terms of t, where t is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when t = 0, then what is the total distance traveled, in meters, by the object after 30.0 seconds?

**A.** 300 

  *This assumes distance grows linearly with time (tripling the 10-second value of 50 to get the 30-second value), but the problem states distance is modeled quadratically, and the given data (50 at t = 10, 200 at t = 20 — quadrupling, not doubling) confirms the growth is not linear. [misconception: quadratic-model-treated-as-linear]*

**B.** 350 

  *This does not fit the quadratic model d(t) = 0.5t² determined by the given points: d(30) = 0.5(900) = 450, not 350. [misconception: model-not-solved-fully]*

**C.** 400 

  *This scales the 20-second value (200) by a factor of 2, treating the relationship as if doubling time from 20 to 30 doubled distance again — but 30 is only 1.5 times 20, and a quadratic model scales by the SQUARE of the time ratio, 1.5² = 2.25, not 2. [misconception: quadratic-scaling-miscalculated]*

**D.** 450 **(Correct)**

  *Correct. With d(0) = 0, a quadratic model is d(t) = at² + bt (no constant term). From d(10) = 50: 100a + 10b = 50. From d(20) = 200: 400a + 20b = 200. Solving these two equations gives a = 0.5, b = 0, so d(t) = 0.5t². Check: d(20) = 0.5(400) = 200 ✓. Then d(30) = 0.5(900) = 450. ✓*

*Difficulty: hard*

---

##### Q84
The function h is defined by h(x) = x³ + ax² + bx + c, where a, b, and c are integer constants. If the zeros of the function are −5, 6, and 7, what is the value of c?

**A.** −210 

  *This drops the sign, treating c as the direct product of the roots without the alternating sign that comes from expanding (x − r₁)(x − r₂)(x − r₃) for a cubic with leading coefficient 1 — the constant term is −(r₁ · r₂ · r₃), not r₁ · r₂ · r₃ directly. [misconception: sign-of-constant-term-dropped]*

**B.** 8 

  *This is the sum of the three zeros, −5 + 6 + 7 = 8, which relates to the coefficient a (as −a equals the sum of the roots), not to c, which comes from their product. [misconception: sum-of-roots-reported-instead-of-product]*

**C.** 42 

  *This is the product of just two of the three zeros (6 × 7 = 42), leaving out the third root, −5, entirely from the computation of c. [misconception: root-omitted-from-product]*

**D.** 210 **(Correct)**

  *Correct. With zeros −5, 6, and 7, h(x) = (x + 5)(x − 6)(x − 7). The constant term is h(0) = (5)(−6)(−7) = 5(42) = 210. Expanding confirms it: (x + 5)(x − 6)(x − 7) = x³ − 8x² − 23x + 210, so c = 210. ✓*

*Difficulty: hard*

---

##### Q85
Kao measured the temperature of a cup of hot chocolate placed in a room with a constant temperature of 70 degrees Fahrenheit (°F). The temperature of the hot chocolate was 185°F at 6:00 p.m. when it started cooling. The temperature of the hot chocolate was 156°F at 6:05 p.m. and 135°F at 6:10 p.m. The hot chocolate's temperature continued to decrease. Of the following functions, which best models the temperature T(m), in degrees Fahrenheit, of Kao's hot chocolate m minutes after it started cooling?

**A.** T(m) = 185(1.25)^m 

  *This models temperature GROWING without bound, but the hot chocolate is cooling — its temperature is decreasing toward the room's 70°F, not increasing indefinitely from 185°F. The base should be less than 1, not 1.25. [misconception: growth-decay-direction-reversed]*

**B.** T(m) = 185(0.85)^m 

  *This decays, but toward 0 rather than toward the room's temperature of 70°F, and it doesn't match the data: T(5) = 185(0.85)⁵ ≈ 82°F, far below the actual 156°F recorded 5 minutes in. A cooling object's temperature approaches the room's temperature, not zero. [misconception: asymptote-omitted]*

**C.** T(m) = (185 − 70)(0.75)^(m/5) 

  *This correctly finds the difference above room temperature (115°F) and a plausible 5-minute decay factor, but never adds back the 70°F room temperature the difference is measured against — without it, the model predicts the hot chocolate cools all the way to 0°F instead of leveling off at 70°F. [misconception: asymptote-omitted]*

**D.** T(m) = 70 + 115(0.75)^(m/5) **(Correct)**

  *Correct. The temperature approaches the room's 70°F as m grows, so 70 is the horizontal asymptote added back on top of a decaying difference. That difference starts at 185 − 70 = 115°F and shrinks by a consistent factor every 5 minutes: check m = 5, 70 + 115(0.75) = 70 + 86.25 = 156.25 ≈ 156°F ✓; and m = 10, 70 + 115(0.5625) = 70 + 64.7 ≈ 135°F ✓.*

*Difficulty: sat-hardest*

---

##### Q86
The population of a town is currently 50,000, and the population is estimated to increase each year by 3% from the previous year. Which of the following equations can be used to estimate the number of years, t, it will take for the population of the town to reach 60,000?

**A.** 50,000 = 60,000(0.03)^t 

  *This puts the target population, 60,000, in the coefficient position and the starting population's roles are reversed — the equation should start from the CURRENT population, 50,000, and grow toward the target, 60,000, not the other way around, and 0.03 alone (not 1.03) is the wrong multiplier for growth besides. [misconception: coefficient-and-target-swapped]*

**B.** 50,000 = 60,000(3)^t 

  *This also swaps which population is the starting coefficient, and additionally uses a base of 3, which would describe the population tripling every year — far more extreme than the described 3% growth. [misconception: coefficient-and-target-swapped]*

**C.** 60,000 = 50,000(0.03)^t 

  *Uses the growth rate itself, 0.03, as the base rather than the multiplier 1 + 0.03 = 1.03. A base of 0.03 would mean the population shrinks to 3% of its previous size every year, not grows by 3%. [misconception: rate-used-as-multiplier]*

**D.** 60,000 = 50,000(1.03)^t **(Correct)**

  *Correct. Starting from the current population of 50,000, growing by 3% each year means multiplying by 1.03 per year, and t is the number of years until the population reaches the target, 60,000. ✓*

*Difficulty: easy*

---

##### Q87
The quadratic function h(x) = −16x² + 100x + 10 models the height above the ground h, in feet, of a projectile x seconds after it had been launched vertically. If y = h(x) is graphed in the xy-plane, which of the following represents the real-life meaning of the positive x-intercept of the graph?

**A.** The initial height of the projectile 

  *The initial height is h(0), the y-intercept (10 feet), not an x-intercept. An x-intercept is a value of x where the height is 0, not a value of h itself. [misconception: x-intercept-confused-with-y-intercept]*

**B.** The maximum height of the projectile 

  *The maximum height is the y-coordinate of the vertex, an output value of the function, not an x-intercept, which by definition is a point where the output (height) equals 0 — the opposite of a maximum. [misconception: vertex-confused-with-root]*

**C.** The time at which the projectile reaches its maximum height 

  *This describes the x-coordinate of the vertex, not an x-intercept. The vertex's x-coordinate is where height is greatest; an x-intercept is where height is exactly 0 — two different points on the graph. [misconception: vertex-confused-with-root]*

**D.** The time at which the projectile hits the ground **(Correct)**

  *Correct. An x-intercept is where h(x) = 0, meaning the projectile's height above the ground is zero — that is, the moment it lands. The positive x-intercept is the physically meaningful one, since negative time doesn't apply here. ✓*

*Difficulty: medium*

---

##### Q88
For the exponential function f, the table above shows several values of x and their corresponding values of f(x), where a is a constant greater than 1: f(1) = a, f(2) = a⁵, f(3) = a⁹. If k is a constant and f(k) = a²⁹, what is the value of k?

**A.** 8 **(Correct)**

  *Correct. The exponent on a increases by 4 for every increase of 1 in x: from x = 1 to x = 2 it goes 1 → 5 (+4), and from x = 2 to x = 3 it goes 5 → 9 (+4), so f(x) = a^(4x−3). Setting 4k − 3 = 29 gives 4k = 32, so k = 8. Check: f(8) = a^(4·8−3) = a²⁹ ✓.*

**B.** 6 

  *This solves 4x = 29 directly, as though the exponent pattern were simply 4x rather than 4x − 3. Checking the pattern against the table (f(1) = a, not a⁴) shows the exponent needs a −3 correction that this value skips. [misconception: exponent-pattern-offset-ignored]*

**C.** 7 

  *This is close to the correct value but comes from a small slip in solving 4k − 3 = 29, such as computing 4k = 28 instead of 32. [misconception: arithmetic-slip]*

**D.** 29 

  *This reports the target exponent itself, 29, as though it were the input k, rather than solving the equation 4k − 3 = 29 for k. [misconception: exponent-value-reported-as-input]*

*Difficulty: hard*

---

##### Q89
What is the minimum value of the function f defined by f(x) = (x − 2)² − 4?

**A.** −4 **(Correct)**

  *Correct. Since (x − 2)² is never negative, it contributes nothing at x = 2 and something positive everywhere else, so the minimum value of f is −4, reached at x = 2. ✓*

**B.** −2 

  *This reports the x-coordinate of the vertex, 2, with a sign flip, rather than the minimum VALUE of the function, which is the k in vertex form, −4. [misconception: vertex-coordinates-confused]*

**C.** 2 

  *This is where the minimum occurs (the x-coordinate of the vertex), not what the minimum value actually is — the question asks for the minimum output, not the input that produces it. [misconception: answered-wrong-coordinate]*

**D.** 4 

  *This drops the negative sign on the constant term outside the square, treating f(x) = (x − 2)² − 4 as though it ended in +4 rather than −4. [misconception: sign-of-constant-dropped]*

*Difficulty: easy*

---

##### Q90
Let the function p be defined as p(x) = [(x − c)² + 160] / (2c), where c is a constant. If p(c) = 10, what is the value of p(12)?

**A.** 10.00 

  *This assumes p(12) equals p(c) without checking whether 12 = c, or otherwise treats the function as constant. Since p is not a constant function, its value generally changes as the input changes. [misconception: function-assumed-constant]*

**B.** 10.25 

  *This is close to the correct value but comes from a small slip while evaluating (12 − 8)² or dividing by 2c — the correctly solved c = 8 gives p(12) = [16 + 160]/16 = 11, not 10.25. [misconception: arithmetic-slip]*

**C.** 10.75 

  *This also falls short of the correctly computed value; with c = 8 correctly found from p(c) = 10, p(12) evaluates to exactly 11, not a value this close to but below it. [misconception: arithmetic-slip]*

**D.** 11.00 **(Correct)**

  *Correct. First find c from p(c) = 10: p(c) = [(c − c)² + 160]/(2c) = 160/(2c) = 10, so 2c = 16 and c = 8. Then p(12) = [(12 − 8)² + 160]/(2·8) = [16 + 160]/16 = 176/16 = 11. ✓*

*Difficulty: hard*

---

##### Q91
The graph of the equation y = 576^(2x+2) in the xy-plane has a y-intercept of (r, s). Which of the following equivalent equations displays the value of s as a constant, a coefficient, or the base?

**A.** y = 331,776^(x+1) **(Correct)**

  *Correct. Since 576^(2x+2) = 576^(2(x+1)) = (576²)^(x+1) = 331,776^(x+1), and s = 576² = 331,776 (the value at x = 0, since r = 0), the value s is displayed directly as the base of this equivalent form. ✓*

**B.** y = 24^(4x+4) 

  *Since 576 = 24², this rewrites the base correctly (576^(2x+2) = 24^(4x+4)), but neither 24 nor any exponent in this form equals s = 331,776 directly — the true y-intercept value is not displayed as a visible constant here. [misconception: equivalent-form-without-target-value]*

**C.** y = (1/24)(13,824)(576)^(2x) 

  *This rewrites the coefficient and exponent in a way that does correctly reconstruct the same function, but the individual visible constants, 1/24 and 13,824, are not themselves equal to s = 331,776, so the y-intercept isn't displayed directly by any single token here. [misconception: equivalent-form-without-target-value]*

**D.** y = (1/576)576^(2x+3) 

  *This is an equivalent form of the same function, but the visible coefficient, 1/576, is not equal to s = 331,776 — the y-intercept value here is buried inside the exponential term rather than displayed as an explicit constant. [misconception: equivalent-form-without-target-value]*

*Difficulty: sat-hardest*

---

##### Q92
The functions f and g are defined by the given equations: f(x) = 3 + |−2x − x²| and g(w) = |−w/(w−1)| − w + 5. If f(−4) = c, where c is a constant, what is the value of g(c)?

**A.** −4.9 **(Correct)**

  *Correct. f(−4) = 3 + |−2(−4) − (−4)²| = 3 + |8 − 16| = 3 + |−8| = 3 + 8 = 11, so c = 11. Then g(11) = |−11/(11−1)| − 11 + 5 = |−11/10| − 6 = 1.1 − 6 = −4.9. ✓*

**B.** 6.0 

  *This drops the absolute value bars in g, treating |−11/10| as though it could be −1.1, then combines incorrectly with the remaining terms — but an absolute value is always nonnegative, so |−11/10| = 1.1, not −1.1. [misconception: absolute-value-sign-dropped]*

**C.** 11.0 

  *This reports c itself, f(−4) = 11, rather than continuing on to evaluate g(c) = g(11), which the question actually asks for. [misconception: intermediate-value-reported-as-final]*

**D.** 16.1 

  *This appears to add rather than subtract w in g's expression, computing |−11/10| + 11 + 5 = 17.1 or a similarly mis-signed combination, instead of subtracting w and adding 5 as g's definition requires. [misconception: sign-in-formula-mishandled]*

*Difficulty: sat-hardest*

---

##### Q93
The function p(t) = 90,000(1.06)^t models the population of Lowell t years after a census. Which of the following functions best models the population of Lowell m months after the census?

**A.** r(m) = (90,000/12)(1.06)^m 

  *This divides the starting population by 12 instead of converting the TIME unit — the coefficient 90,000 is the population at the census and should stay whole; it's the exponent that needs to be rewritten in months, not the initial population that needs to be split up. [misconception: wrong-quantity-divided-by-period]*

**B.** r(m) = 90,000(1.06/12)^m 

  *This divides the growth multiplier itself by 12 rather than taking its 12th root — dividing 1.06 by 12 makes the base far too small (less than 1, implying rapid monthly decline), which is not how converting an annual multiplier to a monthly one works. [misconception: base-divided-instead-of-rooted]*

**C.** r(m) = 90,000(1.06/12)^(m/12) 

  *This both mishandles the base (dividing rather than taking a 12th root) and mishandles the exponent conversion in the wrong direction — m months is m/12 years, so the EXPONENT should be m/12 with the ORIGINAL base 1.06, not a divided base with an extra division on top. [misconception: base-and-exponent-both-mishandled]*

**D.** r(m) = 90,000(1.06)^(m/12) **(Correct)**

  *Correct. Since m months equals m/12 years, substituting t = m/12 into the original model gives r(m) = 90,000(1.06)^(m/12), keeping the same annual base but converting the time unit inside the exponent. ✓*

*Difficulty: medium*

---

##### Q94
A model estimates that at the end of each year from 2015 to 2020, the number of squirrels in a population was 150% more than the number of squirrels in the population at the end of the previous year. The model estimates that at the end of 2016, there were 180 squirrels in the population. Which of the following equations represents this model, where n is the estimated number of squirrels in the population t years after the end of 2015 and t ≤ 5?

**A.** n = 72(1.5)^t 

  *This uses 1.5 as the growth multiplier, but "150% more" means the population increases by an additional 150% of itself each year, which is a multiplier of 1 + 1.5 = 2.5, not 1.5 (which would describe only a 50% increase). [misconception: percent-increase-misread-as-multiplier]*

**B.** n = 72(2.5)^t **(Correct)**

  *Correct. "150% more" each year means multiplying by 1 + 1.50 = 2.5. Since t = 0 is the end of 2015 and t = 1 (the end of 2016) gives 180 squirrels: n(0) × 2.5 = 180, so n(0) = 72. Check: 72(2.5)¹ = 180 ✓.*

**C.** n = 180(1.5)^t 

  *This uses the wrong multiplier (1.5 instead of 2.5) and also places the count at t = 1 (180, the end of 2016) as though it were the starting count at t = 0 (the end of 2015), when the two are different years. [misconception: wrong-starting-point-used]*

**D.** n = 180(2.5)^t 

  *This uses the correct multiplier but places the end-of-2016 count, 180, at t = 0 (the end of 2015) instead of at t = 1 where it actually belongs — that shifts the whole model one year early. [misconception: wrong-starting-point-used]*

*Difficulty: medium*

---

##### Q95
The function f is defined by f(x) = 4x² − 50x + 126. For what value of x does f(x) reach its minimum?

**A.** 6.25 **(Correct)**

  *Correct. The minimum of a parabola occurs at x = −b/(2a) = −(−50)/(2·4) = 50/8 = 6.25. ✓*

**B.** 12.5 

  *This divides 50 by 4 only, forgetting to also double the leading coefficient in the denominator: −b/(2a) requires 2 × 4 = 8 in the denominator, not just 4. [misconception: denominator-not-doubled]*

**C.** 3.125 

  *This divides 50 by 16 instead of by 8, doubling the denominator one time too many — the formula −b/(2a) needs the denominator 2a = 8, not 4a = 16. [misconception: denominator-doubled-twice]*

**D.** 25 

  *This divides 50 by 2 but forgets to also account for the leading coefficient 4 in the denominator at all — the full formula is −b/(2a) = −(−50)/8, not −(−50)/2. [misconception: leading-coefficient-omitted]*

*Difficulty: easy*

---

##### Q96
When the quadratic function f is graphed in the xy-plane, where y = f(x), its vertex is (−3, 6). One of the x-intercepts of this graph is (−17/4, 0). What is the other x-intercept of the graph?

**A.** (−29/4, 0) 

  *This reflects the given intercept the wrong distance from the vertex — adding the full distance between −3 and −17/4 to −17/4 again instead of reflecting it across x = −3, which overshoots. [misconception: reflection-distance-doubled-incorrectly]*

**B.** (−7/4, 0) **(Correct)**

  *Correct. The vertex's x-coordinate, −3, is the midpoint of the two x-intercepts. The distance from −3 to −17/4 is |−3 − (−17/4)| = |5/4| = 5/4, so the other intercept is 5/4 on the other side: −3 + 5/4 = −7/4. ✓*

**C.** (5/4, 0) 

  *This computes a plausible-looking distance but reflects it from the wrong reference point, or drops a sign somewhere in the process, landing on the positive side of the axis rather than −7/4. [misconception: reflection-reference-point-wrong]*

**D.** (17/4, 0) 

  *This simply flips the sign of the given intercept, treating the vertex as though it were at x = 0 (so that x-intercepts would be mirror images across the y-axis) rather than at its actual location, x = −3. [misconception: vertex-location-ignored]*

*Difficulty: medium*

---

##### Q97
For the function f, for each increase in the value of x by c, where c is a positive constant, the value of f(x) increases by a factor of 27. Which of the following equivalent forms of the function f displays 1/c as a coefficient of x? (A) f(x) = 48(3)^((1/2)x); (B) f(x) = 48(3³)^((1/6)x); (C) f(x) = 48(9)^((1/4)x); (D) f(x) = 48(27^((1/3)x))^(1/2).

**A.** f(x) = 48(3)^((1/2)x) 

  *All four forms are algebraically equal to 48(3^(x/2)) — check: (3³)^(x/6) = 3^(3x/6) = 3^(x/2); (9)^(x/4) = (3²)^(x/4) = 3^(x/2); (27^(x/3))^(1/2) = 27^(x/6) = (3³)^(x/6) = 3^(x/2). Since increasing x by 1 multiplies f by 3^(1/2), increasing x by c multiplies f by (3^(1/2))^c = 27 = 3³ gives c/2 = 3, so c = 6 and 1/c = 1/6. This form's exponent coefficient is 1/2, not 1/6. [misconception: wrong-exponent-coefficient-identified]*

**B.** f(x) = 48(3³)^((1/6)x) **(Correct)**

  *Correct. Since c = 6 (as derived above, from (3^(1/2))^c = 3³ = 27 giving c = 6), 1/c = 1/6, and this form's exponent literally shows (1/6)x as its coefficient of x — no further simplification needed to see it. ✓*

**C.** f(x) = 48(9)^((1/4)x) 

  *This form's exponent coefficient is 1/4, not 1/c = 1/6. All four choices are equivalent to the same function, but only the one written with base 3³ and exponent (1/6)x displays 1/6 directly as the coefficient of x. [misconception: wrong-exponent-coefficient-identified]*

**D.** f(x) = 48(27^((1/3)x))^(1/2) 

  *The coefficient of x inside the inner exponent here is 1/3, not 1/6 — the 1/6 only appears after multiplying the inner 1/3 by the outer 1/2, a simplification this form doesn't display directly as written. [misconception: wrong-exponent-coefficient-identified]*

*Difficulty: sat-hardest*

---

##### Q98
The function f(x) = (1/9)(x − 7)² + 3 gives a metal ball's height above the ground, f(x), in inches, x seconds after it started moving on a track, where 0 ≤ x ≤ 10. Which of the following is the best interpretation of the vertex of the graph of y = f(x) in the xy-plane?

**A.** The metal ball's minimum height was 3 inches above the ground. **(Correct)**

  *Correct. In vertex form a(x − h)² + k with a = 1/9 > 0, the parabola opens upward, so k = 3 is the minimum VALUE of the function — the ball's lowest height, 3 inches. ✓*

**B.** The metal ball's minimum height was 7 inches above the ground. 

  *This reports h = 7, the x-coordinate of the vertex (a TIME, in seconds), as though it were the minimum height (an output, in inches). The minimum height is k = 3, not h = 7. [misconception: vertex-coordinates-swapped]*

**C.** The metal ball's height was 3 inches above the ground when it started moving. 

  *This correctly identifies 3 as a height but misplaces WHEN it occurs — the vertex is at x = 7, not x = 0, so 3 inches is the ball's height 7 seconds in, not its starting height at x = 0. [misconception: vertex-time-confused-with-start]*

**D.** The metal ball's height was 7 inches above the ground when it started moving. 

  *This swaps both which number is a time versus a height AND when the described event occurs — h = 7 is a time (seconds), not a height, and it doesn't describe x = 0, the actual start of the motion. [misconception: vertex-coordinates-swapped]*

*Difficulty: easy*

---

##### Q99
In the given quadratic function f(x) = ax² + 4x + c, a and c are constants. The graph of y = f(x) in the xy-plane is a parabola that opens upward and has a vertex at the point (h, k), where h and k are constants. If k < 0 and f(−9) = f(3), which of the following must be true? I. c < 0; II. a ≥ 1.

**A.** I only 

  *Statement I doesn't have to be true: since f(−9) = f(3), the axis of symmetry is at x = (−9+3)/2 = −3, giving a = 2/3 (from −b/(2a) = −3 with b = 4). Then k = f(−3) = c − 6, and k < 0 only forces c < 6, not c < 0 — c could be 0, or even a small positive number, and k would still be negative. [misconception: insufficient-inequality-overstated]*

**B.** II only 

  *Statement II doesn't have to be true: since f(−9) = f(3), the axis of symmetry is x = (−9+3)/2 = −3, and −4/(2a) = −3 gives a = 4/6 = 2/3, which is less than 1, not greater than or equal to 1. [misconception: vertex-symmetry-not-used]*

**C.** I and II 

  *Neither statement is forced to be true. The symmetry condition f(−9) = f(3) pins down a = 2/3 exactly (ruling out II, since 2/3 < 1), and k < 0 only bounds c from above (c < 6), never forcing it below 0 (ruling out I). [misconception: vertex-symmetry-not-used]*

**D.** Neither I nor II **(Correct)**

  *Correct. Since f(−9) = f(3), the axis of symmetry is x = (−9+3)/2 = −3 = h, and −b/(2a) = −4/(2a) = −3 gives a = 2/3, so a ≥ 1 is false (rules out II). Also k = f(−3) = (2/3)(9) − 12 + c = c − 6, and k < 0 only requires c < 6 — c could be 0 or positive, so c < 0 is not forced (rules out I). ✓*

*Difficulty: sat-hardest*

---

##### Q100
The function f gives the value, in dollars, of a certain piece of equipment after x months of use: f(x) = 5,470(0.64)^(x/12). If the value of the equipment decreases each year by p% of its value the preceding year, what is the value of p?

**A.** 4 

  *This reads 0.64 as though it needed to be divided by 12 to give an annual rate, but the exponent x/12 already converts months to years, so 0.64 IS the annual (per 12-month) multiplier directly — no further division is needed. [misconception: period-already-converted-divided-again]*

**B.** 5 

  *This is a plausible-looking but unsupported value; it does not come from 1 − 0.64 = 0.36 (a 36% decrease) or from any correct manipulation of the given exponent and base. [misconception: unsupported-value-selected]*

**C.** 36 **(Correct)**

  *Correct. Since the exponent is x/12, one full year (x = 12) makes the exponent equal 1, so the value is multiplied by 0.64 exactly once per year. Retaining 64% of value means losing 1 − 0.64 = 0.36, or 36%, each year. ✓*

**D.** 64 

  *This reports the RETAINED percentage (64%) rather than the percentage LOST, which is what the question asks for. Retaining 64% of value means the value decreased by 100% − 64% = 36%, not 64%. [misconception: retained-percent-reported-instead-of-lost]*

*Difficulty: medium*

---

##### Q101
The functions g and h are defined by the given equations, where x ≥ 0: I. g(x) = 18(1.16)(1.4)^(x+2); II. h(x) = 18(1.4)^(x+4). Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where x ≥ 0?

**A.** I only 

  *Since 1.4 > 1, g is increasing on x ≥ 0, so its minimum is g(0) = 18(1.16)(1.4)² = 18(1.16)(1.96) ≈ 40.92 — but no visible constant in the written form 18(1.16)(1.4)^(x+2) equals this, since 1.16 is not a power of 1.4 the way it would need to be to simplify away. [misconception: unrelated-coefficient-mistaken-for-min]*

**B.** II only 

  *Since 1.4 > 1, h is increasing on x ≥ 0, so its minimum is h(0) = 18(1.4)⁴ ≈ 69.1 — but the visible coefficient in 18(1.4)^(x+4) is 18, which requires evaluating (1.4)⁴ to reach the true minimum; it isn't displayed directly. [misconception: unsimplified-coefficient-mistaken-for-min]*

**C.** I and II 

  *Neither form actually displays its minimum as a bare visible constant. For I, 1.16 is not a power of 1.4, so no simplification collapses the shift into the coefficient; for II, the coefficient 18 alone is not equal to h(0), which requires multiplying by (1.4)⁴ first. [misconception: unsimplified-coefficient-mistaken-for-min]*

**D.** Neither I nor II **(Correct)**

  *Correct. Unlike a case where the extra multiplier is a clean power of the base (which would let the shifted exponent collapse into a visible coefficient), 1.16 is not a power of 1.4, so g's minimum cannot be read off as a written constant. And h's coefficient, 18, is simply not equal to its actual minimum, 18(1.4)⁴ ≈ 69.1, without further computation. ✓*

*Difficulty: hard*

---

##### Q102
The area of a triangle is equal to x² square centimeters. The length of the base of the triangle is 2x + 22 centimeters, and the height of the triangle is x − 10 centimeters. What is the value of x?

**A.** 11 

  *This does not satisfy the area equation: (1/2)(2(11)+22)(11−10) = (1/2)(44)(1) = 22, but x² = 121 when x = 11 — the two sides don't match. [misconception: solution-not-checked]*

**B.** 55 

  *This is roughly half the correct value, suggesting the factor of 1/2 in the triangle-area formula was applied an extra, unneeded time somewhere in isolating x. [misconception: extra-half-factor-applied]*

**C.** 110 **(Correct)**

  *Correct. Area = (1/2)(base)(height) = (1/2)(2x + 22)(x − 10) = x². Expanding: (x + 11)(x − 10) = x², so x² − 10x + 11x − 110 = x², which simplifies to x − 110 = 0, giving x = 110. ✓*

**D.** 220 

  *This doubles the correct value, likely from forgetting to divide by 2 for the triangle-area formula at some point, or from an error while expanding (x + 11)(x − 10). [misconception: half-factor-omitted]*

*Difficulty: medium*

---

##### Q103
Function f is a quadratic function where f(−20) = 0 and f(−4) = 0. The graph of y = f(x) in the xy-plane has a vertex at (r, −64). What is the value of r?

**A.** −12 **(Correct)**

  *Correct. The vertex's x-coordinate is the midpoint of the two zeros: (−20 + (−4))/2 = −24/2 = −12. ✓*

**B.** −16 

  *This averages the two zeros incorrectly, perhaps by adding their absolute values and dividing by a mismatched count, rather than computing (−20 + (−4))/2. [misconception: roots-averaged-incorrectly]*

**C.** −24 

  *This is the SUM of the two zeros, −20 + (−4) = −24, reported without the final division by 2 needed to find their midpoint. [misconception: division-by-two-omitted]*

**D.** −64 

  *This reports the vertex's y-coordinate (the given minimum value) in place of its x-coordinate, which is what r actually represents. [misconception: vertex-coordinates-swapped]*

*Difficulty: easy*

---

##### Q104
The graph of y = f(x) is shown, where f(x) = ab^x + c, and a, b, and c are constants: the curve falls from about (−10, −6), passing through the visible window entirely below the x-axis, and approaches a horizontal asymptote near y = −9 as x increases, never rising back up to the axis. For how many values of x does f(x) = 0?

**A.** Three 

  *An exponential function ab^x + c has at most one horizontal asymptote and is strictly increasing or strictly decreasing everywhere — its graph can cross any horizontal line, including the x-axis, at most once, never three times. [misconception: exponential-treated-as-polynomial]*

**B.** Two 

  *A strictly monotonic curve (always increasing or always decreasing, as every exponential function is) can cross a horizontal line like the x-axis at most once, not twice. [misconception: exponential-treated-as-polynomial]*

**C.** One 

  *This would be true if the curve actually crossed the x-axis somewhere, but the entire visible graph stays below the axis, approaching its asymptote near y = −9 without ever climbing back up to y = 0. [misconception: asymptote-mistaken-for-crossing]*

**D.** Zero **(Correct)**

  *Correct. The graph never reaches y = 0: it stays below the x-axis throughout, approaching a horizontal asymptote near y = −9 as x increases, so f(x) = 0 has no solution among the values shown. ✓*

*Difficulty: medium*

---

##### Q105
The function f is defined by f(t) = 55t − 2t². The function g is defined by g(t) = f(t) + 3. Which expression represents the maximum value of g(t)?

**A.** 3 + (55/4)² 

  *This is missing a factor of 2 on the squared term. The maximum of f(t) = 55t − 2t² is 55²/8, which equals 2(55/4)², not (55/4)² alone — the leading coefficient 2 doesn't disappear when computing the vertex's height. [misconception: leading-coefficient-factor-dropped]*

**B.** 3 + 2(55/4)² **(Correct)**

  *Correct. f's maximum occurs at t = −b/(2a) = −55/(2·(−2)) = 55/4, and f(55/4) = 55(55/4) − 2(55/4)² = 2(55/4)²·... more directly, f's maximum value works out to 2(55/4)², so g's maximum is that plus the +3 shift: 3 + 2(55/4)². ✓*

**C.** 3 − 2(55/4)² 

  *This treats f's maximum as a negative quantity, but f(t) = 55t − 2t² opens downward (negative leading coefficient) and reaches a maximum of 2(55/4)², a positive number — not its negative. [misconception: sign-of-vertex-value-flipped]*

**D.** 3 − (55/4)² 

  *This combines two errors: it drops the leading coefficient 2 from the vertex-value formula, and it also flips the sign of the resulting quantity, both of which move the expression away from f's actual maximum, 2(55/4)². [misconception: leading-coefficient-dropped-and-sign-flipped]*

*Difficulty: hard*

---

##### Q106
The function f gives the product of a number, x, and a number that is 91 more than x. Which equation defines f?

**A.** f(x) = x² + x + 91 

  *This adds x and 91 as separate terms rather than forming the product x(x + 91) first — the phrase "product of x and (x + 91)" calls for multiplication, not addition of x and 91 onto x². [misconception: product-replaced-with-sum]*

**B.** f(x) = x² + 91 

  *This drops the middle term that comes from correctly distributing x(x + 91) = x² + 91x, keeping only the x² and the constant while losing the 91x term entirely. [misconception: distribution-term-dropped]*

**C.** f(x) = x² + 91x **(Correct)**

  *Correct. "A number that is 91 more than x" is x + 91, and the product of x and that number is x(x + 91) = x² + 91x. ✓*

**D.** f(x) = x² + 91x + 91 

  *This correctly distributes x(x + 91) = x² + 91x but then adds an extra, unjustified +91 with no basis in the problem — there is no additional constant term in "the product of x and a number that is 91 more than x." [misconception: extraneous-constant-added]*

*Difficulty: easy*

---

##### Q107
A park ranger hung squirrel houses each in the shape of a right rectangular prism for fox squirrels. Each house has a height of 11 inches. The length of each house's base is x inches, which is 1 inch more than the width of the house's base. Which function V gives the volume of each house, in cubic inches, in terms of the length of the house's base?

**A.** V(x) = 11x(x − 1) **(Correct)**

  *Correct. Volume = length × width × height. The length is x, and since the length is 1 inch more than the width, the width is x − 1. So V(x) = (x)(x − 1)(11) = 11x(x − 1). ✓*

**B.** V(x) = 11x(x + 1) 

  *This flips the relationship between length and width: since the LENGTH (x) is 1 inch MORE than the width, the width must be x − 1, not x + 1 — writing x + 1 would make the width larger than the length, contradicting the given relationship. [misconception: width-relationship-sign-flipped]*

**C.** V(x) = x(x + 11)(x − 1) 

  *This treats the fixed height, 11, as though it depended on x by writing it as x + 11, but the height is a constant 11 inches, not a variable expression — only the base dimensions (length and width) are given in terms of x. [misconception: constant-treated-as-variable]*

**D.** V(x) = x(x + 11)(x + 1) 

  *This makes the same error as choice C in treating the constant height as x + 11, and additionally flips the width relationship to x + 1 instead of x − 1, compounding two separate mistakes. [misconception: constant-treated-as-variable]*

*Difficulty: medium*

---

##### Q108
An auditorium has seats for 1,800 people. Tickets to attend a show at the auditorium currently cost $4.00. For each $1.00 increase to the ticket price, 100 fewer tickets will be sold. This situation can be modeled by the equation y = −100x² + 1,400x + 7,200, where x represents the increase in ticket price, in dollars, and y represents the revenue, in dollars, from ticket sales. If this equation is graphed in the xy-plane, at what value of x is the maximum of the graph?

**A.** 4 

  *This reports the CURRENT ticket price, $4.00, given in the setup of the problem, rather than solving the vertex formula −b/(2a) using the coefficients of the actual revenue equation. [misconception: given-context-value-reported-instead-of-solving]*

**B.** 7 **(Correct)**

  *Correct. The maximum occurs at x = −b/(2a) = −1,400/(2·(−100)) = −1,400/(−200) = 7. ✓*

**C.** 14 

  *This divides 1,400 by 100 only, forgetting to also double the leading coefficient in the vertex formula's denominator: −b/(2a) needs 2 × 100 = 200 in the denominator, not just 100. [misconception: denominator-not-doubled]*

**D.** 18 

  *This does not come from the vertex formula applied to this equation's coefficients; it does not satisfy −b/(2a) = −1,400/(−200) = 7, and appears to be an unrelated value from elsewhere in the problem's setup. [misconception: unrelated-value-selected]*

*Difficulty: medium*

---

##### Q109
The function g is defined by g(x) = |x|/a − 14, where a < 0. What is the product of g(15a) and g(7a)?

**A.** 609 **(Correct)**

  *Correct. Since a < 0, |15a| = −15a and |7a| = −7a. So g(15a) = |15a|/a − 14 = (−15a)/a − 14 = −15 − 14 = −29, and g(7a) = (−7a)/a − 14 = −7 − 14 = −21. The product is (−29)(−21) = 609. ✓*

**B.** −609 

  *This drops a sign somewhere in the final multiplication — both g(15a) and g(7a) work out to negative numbers, and the product of two negative numbers is always positive, not negative. [misconception: sign-of-product-dropped]*

**C.** 441 

  *This computes (−21)(−21) = 441, using g(7a) = −21 for both factors and dropping g(15a) = −29 entirely, effectively squaring the wrong value instead of finding the actual product of the two different outputs. [misconception: wrong-value-repeated]*

**D.** 225 

  *This treats |a| as though a were positive, computing |15a|/a as +15 instead of −15 (since a < 0, |15a|/a is actually −15, not +15) — mishandling the absolute value's sign given the constraint a < 0 changes both factors and their product. [misconception: absolute-value-sign-mishandled]*

*Difficulty: sat-hardest*

---

### Problem-Solving & Data Analysis

#### Evaluating Statistical Claims (11 items)

##### Q1
> The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park.

Which of the following is true about the city council's survey?

**A.** It shows that the majority of city residents are in favor of the dog park. 

  *The sample was drawn only from residents who already own dogs — a group with an obvious built-in interest in a dog park — so it cannot speak for city residents as a whole. Treating the dog owners' 500-person result as if it described every city resident ignores that the sampling frame (dog owners) does not match the population the council actually wanted to know about (all city residents).*

**B.** The survey sample should have included more residents who are dog owners. 

  *Adding more dog owners to a sample that is already restricted to dog owners does not fix the mismatch between the sample and the target population — it makes the sample even more concentrated in the group least representative of city residents generally, since dog owners are the population most predisposed to favor a dog park.*

**C.** The survey sample should have consisted entirely of residents who do not own dogs. 

  *Restricting the sample to only non-dog-owners would trade one unrepresentative frame for another equally unrepresentative one, systematically excluding the very residents most invested in the question. A sample biased in the opposite direction is not a fix — it is a different bias.*

**D.** The survey sample is biased because it is not representative of all city residents. **(Correct)**

  *Correct. The council wanted to know the opinions of all city residents, but the survey drew its sample only from residents who own dogs — a subgroup very likely to favor a dog park more than the city as a whole. Because the sampling frame (dog owners) is narrower than, and systematically different from, the target population (all city residents), the result is biased and cannot be treated as representative of city residents in general.*

*Difficulty: easy*

---

##### Q2
> A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie.

Which of the following inferences can appropriately be drawn from this survey result?

**A.** At least 95% of people who go see movies will dislike this movie. 

  *This swaps the frame the sample was actually drawn from (people who liked the book) for an entirely different and much broader group — everyone who goes to see movies. Moviegoers in general were never part of the sampling frame; only people who already indicated they liked the book had any chance of being selected.*

**B.** At least 95% of people who read books will dislike this movie. 

  *"People who read books" is a far larger group than the sampling frame actually used. The 200 respondents were selected specifically from people who liked THIS particular book, not from readers in general, so the result cannot be extended to everyone who reads books.*

**C.** Most people who dislike this book will like this movie. 

  *The sample was drawn from people who LIKE the book, and nothing was measured about people who dislike the book — the study is silent on that group entirely. This choice also flips the result itself, turning a 95% dislike finding into a claim about liking the movie.*

**D.** Most people who like this book will dislike this movie. **(Correct)**

  *Correct. The sampling frame was people who indicated they liked the book, so the result generalizes to that group and no further. The hedge "most" correctly reflects a strong majority (95%) without overclaiming an exact figure, and the sentence names the right population in the right direction: it is about people who like the book, and it is about disliking the movie, matching exactly what was measured.*

*Difficulty: medium*

---

##### Q3
> Residents of a town were surveyed to determine whether they are satisfied with the concession stand at the local park. A random sample of 200 residents was selected. All 200 responded, and 87% said they are satisfied.

Based on this information, which of the following statements must be true?

I. Of all the town residents, 87% would say they are satisfied with the concession stand at the local park.
II. If another random sample of 200 residents were surveyed, 87% would say they are satisfied.

**A.** Neither **(Correct)**

  *Correct. Statement I treats the sample statistic (87%, computed from these 200 residents) as if it were the exact population parameter — but a different random sample of 200 residents would very likely produce a percentage close to but not identical to 87%, so the true town-wide figure is only estimated, not proven, by this one sample. Statement II makes the same error from the other direction, assuming a second random sample must reproduce the identical 87% rather than a similar but generally different value; random samples vary from each other by chance (sampling variability), so neither statement is guaranteed.*

**B.** I only 

  *This accepts Statement I, treating the sample's 87% as an exact, guaranteed value for the entire town. A sample statistic is an estimate of the population parameter, not the parameter itself — a different sample of the same size would likely land near 87% but not exactly on it, so nothing about this one sample makes the town-wide figure exactly 87%.*

**C.** II only 

  *This accepts Statement II, assuming that any random sample of 200 residents must reproduce this exact 87% figure. Random sampling is a chance process, so repeating it produces results that cluster around the true population value without landing on the same number every time — assuming otherwise ignores sampling variability entirely.*

**D.** I and II 

  *This accepts both statements, compounding the statistic-versus-parameter confusion in Statement I with the zero-variability assumption in Statement II. Neither a single sample's result nor a repeat of that sample is guaranteed to hit exactly 87% — a sample estimates a population value and varies from one draw to the next by chance, and this choice denies both facts at once.*

*Difficulty: hard*

---

##### Q4
> A survey was conducted using a sample of history professors selected at random from the California State Universities. The professors surveyed were asked to name the publishers of their current texts.

What is the largest population to which the results of the survey can be generalized?

**A.** All professors in the United States 

  *This drops both restrictions the sampling frame actually had: the sample was history professors only, and it was drawn only from the California State University system. Professors of other subjects, and professors at universities outside that system, had no chance of being selected, so neither restriction can be dropped.*

**B.** All history professors in the United States 

  *This correctly keeps the subject restriction (history) but drops the institutional restriction — the sample was drawn only from history professors at the California State Universities, so history professors at any other university in the country had zero chance of being selected and cannot be included in the generalization.*

**C.** All history professors at all California State Universities **(Correct)**

  *Correct. The sampling frame was history professors selected at random specifically from the California State University system, so the largest group the result can be generalized to is history professors at all California State Universities — no broader (professors elsewhere had no chance of selection) and no narrower than that full frame (random selection licenses generalizing to the entire list it was drawn from).*

**D.** All professors at all California State Universities 

  *This correctly keeps the institutional restriction (California State Universities) but drops the subject restriction — only history professors were sampled and asked about publishers of their current texts, so professors in other departments, who were never part of the sampling frame, cannot be included.*

*Difficulty: medium*

---

##### Q5
> A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, "Are you satisfied with the quality of air in the city?" Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city.

Based on the results of the survey, which of the following statements must be true?

1. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.
2. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.
3. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.

**A.** None **(Correct)**

  *Correct. Statement 1 treats the sample statistic (78%, from these 1,000 adults) as an exact population parameter, when it is only an estimate — a different random sample from the same city would likely land near but not exactly on 78%. Statement 2 makes the same error, assuming a second random sample must reproduce the identical figure rather than a similar one, ignoring sampling variability. Statement 3 is the most serious error of the three: it extends the result to adults in an entirely different city, a population that had no chance whatsoever of appearing in this sample, since the frame was adults in this specific large city.*

**B.** II only 

  *This accepts that a second random sample from the same city must produce the identical 78%, which ignores that random sampling is a chance process — repeated samples cluster around the true value without landing on the exact same number each time.*

**C.** I and II only 

  *This accepts both that the sample statistic exactly equals the city's true parameter (Statement 1) and that a repeat sample must reproduce it exactly (Statement 2) — two versions of the same underlying mistake, treating a single chance-based estimate as if it were a fixed, exactly reproducible fact.*

**D.** I and III only 

  *In addition to the statistic-versus-parameter error in Statement 1, this accepts Statement 3, which applies the result to a completely different city — a population with zero probability of selection in this survey, since the sample was drawn exclusively from adults in the original large city. Nothing about air-quality satisfaction in one city licenses any conclusion about a different one.*

*Difficulty: sat-hardest*

---

##### Q6
> A sample of 40 fourth-grade students was selected at random from a certain school. The 40 students completed a survey about the morning announcements, and 32 thought the announcements were helpful.

Which of the following is the largest population to which the results of the survey can be applied?

**A.** The 40 students who were surveyed 

  *This refuses to extend the result past the exact 40 students surveyed, even though those 40 were selected at random from all fourth-graders at the school — random selection licenses generalizing to the full group it was drawn from, and stopping at the sample itself gives away a conclusion the design has already earned.*

**B.** All fourth-grade students at the school **(Correct)**

  *Correct. The 40 students were selected at random from the fourth-grade students at this school, so that full group — all fourth-graders at the school — is the sampling frame, and it is the largest population the result can be applied to.*

**C.** All students at the school 

  *This drops the grade-level restriction built into the sampling frame — only fourth-graders were sampled, so students in other grades at the school had no chance of being selected and cannot be included in the generalization.*

**D.** All fourth-grade students in the county in which the school is located 

  *This expands past the school entirely, to fourth-graders anywhere in the county. The random selection was made only from fourth-graders at this one school; fourth-graders at other schools in the county had zero chance of being part of the sample.*

*Difficulty: easy*

---

##### Q7
> A trivia tournament organizer wanted to study the relationship between the number of points a team scores in a trivia round and the number of hours that a team practices each week. For the study, the organizer selected 55 teams at random from all trivia teams in a certain tournament. The table below displays the information for the 40 teams in the sample that practiced for at least 3 hours per week: of the teams that practiced 3 to 5 hours per week, 6 scored 6 to 13 points and 4 scored 14 or more points, for a subtotal of 10 teams; of the teams that practiced more than 5 hours per week, 4 scored 6 to 13 points and 26 scored 14 or more points, for a subtotal of 30 teams; combining both practice groups, 10 teams scored 6 to 13 points and 30 teams scored 14 or more points, for a combined total of 40 teams.

Which of the following is the largest population to which the results of the study can be generalized?

**A.** All trivia teams in the tournament that scored 14 or more points in the round 

  *Scoring 14 or more points is an outcome recorded within the table, not a criterion used to select teams into the study. Generalizing to "teams that scored 14 or more" confuses a result of the study with the population the sample was actually drawn from.*

**B.** The 55 trivia teams in the sample 

  *This stops at the sample itself, but the 55 teams were selected AT RANDOM from all trivia teams in the tournament — that random draw is exactly what licenses generalizing beyond the 55 to the full list they were drawn from, so refusing to extend past the sample gives away a conclusion the design already earned.*

**C.** The 40 trivia teams in the sample that practiced for at least 3 hours per week 

  *The 40 teams shown in the table are a subgroup of the 55 randomly selected teams, filtered down to those that happened to practice at least 3 hours per week for display purposes — that filter was not how the original sample was drawn. The random selection that determines the generalizable frame was made from all trivia teams in the tournament, not from teams meeting a practice-hours threshold.*

**D.** All trivia teams in the tournament **(Correct)**

  *Correct. The organizer selected 55 teams at random from all trivia teams in the tournament — that random draw is what sets the frame, and it was made from the full tournament, not from any practice-hours subgroup. The table's restriction to the 40 teams that practiced at least 3 hours per week describes how the data happens to be displayed, not a change to the population the original random sample was drawn from, so the result generalizes to all trivia teams in the tournament.*

*Difficulty: sat-hardest*

---

##### Q8
> A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students' accuracy in adding fractions. For the study, the psychologist chose a random sample of 35 students from all of the students at one of the middle schools in a large city. The psychologist found that students who played the game showed significant improvement in accuracy when adding fractions.

What is the largest group to which the results of the study can be generalized?

**A.** The 35 students in the sample 

  *This refuses to extend past the exact 35 students sampled, but they were selected at random from the full student body of the school — random selection licenses generalizing to that entire frame, so stopping at the sample alone gives away a conclusion the design already earned.*

**B.** All students at the school **(Correct)**

  *Correct. The 35 students were selected at random from all of the students at this one middle school — not restricted to any grade or subgroup within it — so that full student body is the sampling frame, and it is the largest group the result generalizes to.*

**C.** All middle school students in the city 

  *This expands past the one school the sample was actually drawn from to every middle school in the city. Students at other middle schools had no chance of being selected — only students at this one particular school were in the sampling frame.*

**D.** All students in the city 

  *This is the most extreme overreach available, combining the error of extending beyond this one school with a further expansion past middle-school age entirely. Neither other schools nor other grade levels had any chance of appearing in a sample drawn only from students at this one middle school.*

*Difficulty: medium*

---

##### Q9
> Near the end of a US cable news show, the host invited viewers to respond to a poll on the show's website that asked, "Do you support the new federal policy discussed during the show?" At the end of the show, the host reported that 28% responded "Yes," and 70% responded "No."

Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?

**A.** The percentages do not add up to 100%, so any possible conclusions from the poll are invalid. 

  *This misdiagnoses the flaw as arithmetic. Percentages not summing to 100 (28% + 70% = 98%, with the remainder likely undecided or not selecting either option) has nothing to do with why the poll fails to represent the country — a survey's categories can fail to sum to 100 for an ordinary reason like an unselected option, without that being the source of any sampling bias.*

**B.** Those who responded to the poll were not a random sample of the population of the United States. **(Correct)**

  *Correct. The respondents were self-selected viewers of one show who chose, on their own initiative, to visit a website and answer — nothing about that process gives Americans in general an equal or even any chance of participating. Voluntary response defines the sample by willingness to react to this specific show's framing of the policy, which is unrelated to being a random cross-section of the country, so the result reflects this self-selected group and not the population of the United States.*

**C.** There were not 50% "Yes" responses and 50% "No" responses. 

  *This assumes a legitimate poll must produce an even 50/50 split, which is not true of any real survey — a lopsided result is not itself evidence that the design is flawed. The actual problem is who was able to respond, not what fraction landed on each side.*

**D.** The show did not allow viewers enough time to respond to the poll. 

  *Nothing in the description says viewers lacked time to respond, so this invents a detail the passage never provides. Even if response time were limited, that would be a minor secondary issue compared to the fundamental problem that respondents opted themselves into the poll rather than being randomly selected from the population.*

*Difficulty: easy*

---

##### Q10
> To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4.

Which of the following statements must be true?

**A.** The mean number of children per household in the community is 2.4. 

  *This treats the sample statistic (2.4, computed from these 20 families) as if it were the exact community-wide parameter. Even setting aside the sampling method, a sample mean is an estimate of the population mean, not a guaranteed exact value for it.*

**B.** A determination about the mean number of children per household in the community should not be made because the sample size is too small. 

  *This misdiagnoses the flaw as one of size rather than selection. Twenty families is not inherently too small a sample for some purposes — the real defect is where and how the families were found (all at a playground at one time), not how many of them were surveyed.*

**C.** The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community. **(Correct)**

  *Correct. Surveying families at a playground selects specifically for households that have children present at a playground — a location and moment that systematically excludes households with no children, households with only older children unlikely to be at a playground, and households whose children simply weren't there that day. This makes the sampling method flawed in a way that is likely to bias the estimate of children per household, regardless of how many families were surveyed.*

**D.** The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community. 

  *This is the opposite of the correct diagnosis. Sampling at a playground is close to a textbook example of a systematically biased location for a question about children per household, since it structurally overrepresents households with young children present and underrepresents or excludes households without them.*

*Difficulty: medium*

---

##### Q11
> For a baobab tree habitat in South Africa, a scientist randomly selected 50 baobab trees that were 17 years old and randomly assigned them to two groups. Each group was subjected to a different watering pattern for 2 consecutive years to observe whether the watering pattern affects the trees' growth rate.

Based on the design of the study, what is the largest group to which the results can be applied?

**A.** All the 50 baobab trees that were selected in this habitat 

  *This refuses to extend past the exact 50 trees selected, but they were chosen at random from all 17-year-old baobab trees in this habitat — random selection licenses generalizing to that entire frame, so stopping at the sample alone gives away a conclusion the design already earned.*

**B.** All the baobab trees that were 19 years old in this habitat 

  *This shifts the age forward, apparently reasoning from the fact that 2 years passed during the study. But the sampling frame is defined by the trees' age AT SELECTION — 17 years old — not their age once the study ended; no tree that was 19 years old when the study began had any chance of being selected.*

**C.** All the baobab trees that were 17 years old in South Africa 

  *This correctly keeps the age restriction but drops the habitat restriction — the random selection was made only from trees within this one specific habitat, so 17-year-old baobab trees in other habitats across South Africa had no chance of being selected.*

**D.** All the baobab trees that were 17 years old in this habitat **(Correct)**

  *Correct. The scientist randomly selected the 50 trees specifically from 17-year-old baobab trees within this one habitat, so that full group — all 17-year-old baobab trees in this habitat — is the sampling frame, and it is the largest population the results generalize to. (Random assignment to the two watering groups additionally licenses a causal conclusion about watering pattern and growth rate, but the question asks only about the population the result covers, which is governed by the random selection, not the random assignment.)*

*Difficulty: hard*

---

#### Inference from Sample Statistics and Margin of Error (16 items)

##### Q1
A city has 50 city council members. A reporter polled a random sample of 20 city council members and found that 6 of those polled supported a specific bill. Based on the sample, which of the following is the best estimate of the number of city council members in the city who support the bill?

**A.** 6 

  *This reports the raw count from the sample — 6 people out of the 20 polled — without scaling it up to the full 50-member council at all. The sample is fewer than half the council; the count observed in it is not the count expected across the whole group.*

**B.** 9 

  *This applies the sample's rate (6/20 = 30%) only to the 30 council members who were NOT polled — 30% × 30 = 9 — and then reports that alone, leaving out the 6 supporters the poll already found. The estimate needs to account for the whole council, sampled and unsampled together.*

**C.** 15 **(Correct)**

  *Correct. The sample rate is 6/20 = 0.30, or 30%. Applying that rate to the full council: 0.30 × 50 = 15.*

**D.** 30 

  *30 is 50 − 20, the number of council members who were NOT part of the sample — a number that falls out of the setup but answers a different question (how many were left unpolled) rather than how many are estimated to support the bill.*

*Difficulty: easy*

---

##### Q2
A random sample of 50 people from a town with a population of 14,878 were asked to name their favorite flavor of ice cream. If 7 people in the sample named chocolate as their favorite ice-cream flavor, about how many people in the town would be expected to name chocolate?

**A.** 350 

  *This is 7 × 50 — the number of respondents multiplied by the sample size itself, rather than by the town's population. The sample size belongs in the denominator of the rate (7/50), not as a multiplier on the count.*

**B.** 2,100 **(Correct)**

  *Correct. The sample rate is 7/50 = 0.14. Applying it to the town: 0.14 × 14,878 ≈ 2,083, which rounds to about 2,100 — the closest answer choice.*

**C.** 7,500 

  *This treats 7 out of 50 as roughly a fifty-fifty split rather than computing 7/50 = 0.14 directly, then applies that rough half to the population: 0.5 × 14,878 ≈ 7,439, rounding to about 7,500 — more than three times the actual rate.*

**D.** 10,500 

  *This comes from simplifying 7/50 by shrinking only the denominator (dividing 50 by 5 to get 10) while leaving the numerator at 7, producing 7/10 = 70% instead of 7/50 = 14%. Applying 70% to the population: 0.70 × 14,878 ≈ 10,415, rounding to about 10,500.*

*Difficulty: easy*

---

##### Q3
A certain forest is 253 acres. To estimate the number of trees in the forest, a ranger randomly selects 5 different 1-acre parcels in the forest and determines the number of trees in each parcel. The numbers of trees in the sample acres are 51, 59, 45, 52, and 73. Based on the mean of the sample, which of the following ranges contains the best estimate for the number of trees in the entire forest?

**A.** 11,000 to 12,000 

  *This uses only the smallest sampled parcel (45 trees) instead of the mean of all five: 45 × 253 = 11,385, which falls in this range. A single low parcel is not the average, and discarding the other four measurements throws away exactly the information a mean is built to combine.*

**B.** 12,500 to 13,500 

  *This drops the highest sampled value (73) as if it were unreliable, then averages the remaining four: (51 + 59 + 45 + 52)/4 = 51.75, and 51.75 × 253 ≈ 13,093, which falls in this range. Nothing in the problem licenses discarding a data point — it is a legitimate parcel count, and removing it silently shifts the estimate down.*

**C.** 13,500 to 14,500 **(Correct)**

  *Correct. The sample mean is (51 + 59 + 45 + 52 + 73)/5 = 280/5 = 56 trees per acre. Scaling to the full forest: 56 × 253 = 14,168, which falls in this range.*

**D.** 18,000 to 19,000 

  *This is the mirror of choice A: it uses only the largest sampled parcel (73 trees) instead of the mean of all five: 73 × 253 = 18,469, which falls in this range. One extreme parcel has replaced the average of all five, in the opposite direction from choice A.*

*Difficulty: medium*

---

##### Q4
At a large high school, 300 students were selected at random and were asked in a survey about a menu change in the school cafeteria. All 300 students completed the survey. It was estimated that 38% of the students were in support of a menu change, with a margin of error of 5.5%. Which of the following is the best interpretation of the survey results?

**A.** The percent of the students at the school who support a menu change is 38%. 

  *38% is the sample's estimate, known exactly; the school-wide percent is unknown, which is exactly why a margin of error was reported alongside it. Stating the estimate as a flat fact discards the interval entirely.*

**B.** The percent of the students at the school who support a menu change is greater than 38%. 

  *A margin of error builds a two-sided band centered on the estimate, not a claim that the true value lies above it. Nothing in the data supports a one-directional inequality like this one.*

**C.** Plausible values of the percent of the students at the school who support a menu change are between 32.5% and 43.5%. **(Correct)**

  *Correct. Build the interval: 38 − 5.5 = 32.5 and 38 + 5.5 = 43.5. The quantity is the school-wide percent in support, and the verb is the hedged "plausible values," not a certainty claim.*

**D.** Plausible values of the number of the students at the school who support a menu change are between 295 and 305. 

  *295 to 305 is a range built around the sample SIZE of 300, not around the survey's finding. All 300 selected students completed the survey, so that count is already known exactly and needs no margin of error — the actual open question is what PERCENT of them support the change, which choice C answers.*

*Difficulty: medium*

---

##### Q5
In a study, the data from a random sample of a population had a mean of 37, with an associated margin of error of 3. Which of the following is the most appropriate conclusion that can be made about the population mean?

**A.** It is less than 37. 

  *This applies the margin in only one direction, as if it were a ceiling rather than a two-sided band. A margin of error builds a plausible range on BOTH sides of the estimate — 34 to 40 — not a claim that the true mean sits below the estimate.*

**B.** It is greater than 37. 

  *The mirror of choice A: this applies the margin only upward, as if it were a floor. The plausible range extends both below and above the estimate, and nothing in the data favors one direction over the other.*

**C.** It is between 34 and 40. **(Correct)**

  *Correct. Build the interval: 37 − 3 = 34 and 37 + 3 = 40.*

**D.** It is less than 34 or greater than 40. 

  *This is the complement of the correct interval — it claims the population mean lies OUTSIDE the plausible range, inverting which region the margin of error identifies as likely.*

*Difficulty: easy*

---

##### Q6
A company designs and makes handbags. To estimate the mean weight of the handbags made by the company on a particular day, a sample of the handbags made by the company on that day was selected at random. Based on the sample, it is estimated that the mean weight of all handbags made by the company on that day is 27.8 ounces (oz), with an associated margin of error of 0.02 oz. Based on this estimate and associated margin of error, which of the following is the most plausible conclusion?

**A.** The mean weight of all handbags made by the company on that day is between 27.78 oz and 27.82 oz. **(Correct)**

  *Correct. Build the interval: 27.8 − 0.02 = 27.78 and 27.8 + 0.02 = 27.82. The population is that day's full run, the parameter is a mean weight, and the interval is stated as plausible for that mean.*

**B.** The actual weights of all handbags made by the company on that day are between 27.78 oz and 27.82 oz. 

  *This reads a range built for a MEAN as if it bounded every individual handbag. Individual handbag weights vary more than the estimate of their average does — a single bag could easily weigh 27.5 oz or 28.1 oz even though the mean is tightly bracketed.*

**C.** The actual weights of all handbags from the sample are between 27.78 oz and 27.82 oz. 

  *The sampled handbags were already weighed individually; their weights are known exactly and need no plausible range at all. The interval exists to reach the UNSAMPLED handbags from that day's run, not to redescribe the ones already measured.*

**D.** The mean weight of all handbags made by the company on that day is 27.8 oz. 

  *27.8 oz is the sample's mean, known exactly; the population's true mean is unknown, which is exactly why a margin of error was reported alongside it. Asserting the estimate as fact discards the interval.*

*Difficulty: medium*

---

##### Q7
A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds. Which of the following conclusions is best supported by the sample data?

**A.** The majority of all fish in the pond weigh less than 2 pounds. 

  *The sample was 150 largemouth bass specifically, not a sample of the pond's fish across every species. Extending a bass-only statistic to "all fish" reaches a population — every species in the pond — that this sample never represented.*

**B.** The average weight of all fish in the pond is approximately 2 pounds. 

  *The reported statistic is a PROPORTION — 30% of bass weighed more than 2 pounds — not a mean weight; no average was estimated at all. This choice invents a quantity nobody measured, on top of extending it to the wrong population.*

**C.** Approximately 30% of all fish in the pond weigh more than 2 pounds. 

  *The number is right and the population is not: this extends a statistic about largemouth bass specifically to "all fish" in the pond, which includes every other species that was never sampled. Carrying the exact right number is what makes this the most tempting wrong choice.*

**D.** Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds. **(Correct)**

  *Correct. The sample was drawn at random from the pond's largemouth bass, so the 30% figure generalizes to that population — and no further.*

*Difficulty: medium*

---

##### Q8
A park ranger asked a random sample of visitors how far they hiked during their visit. Based on the responses, the estimated mean was found to be 4.5 miles, with an associated margin of error of 0.5 miles. Which of the following is the best conclusion from these data?

**A.** It is likely that all visitors hiked between 4 and 5 miles. 

  *This reads an interval built for the MEAN hike distance as a bound on every individual visitor's hike. Individual hikes vary far more than an estimate of their average does; a visitor could easily have hiked 1 mile or 9 miles.*

**B.** It is likely that most visitors hiked exactly 4.5 miles. 

  *4.5 miles is the sample MEAN, an average — it does not mean most individuals hiked that exact distance. The same average of 4.5 could come from hikes of 2 miles and 7 miles without a single visitor hiking anywhere near 4.5.*

**C.** It is not possible that any visitor hiked less than 3 miles. 

  *This treats the margin of error as an absolute bound — which it isn't even for the mean (about one interval in twenty built this way misses), let alone for individuals, whose hikes can and do fall well outside the interval for the average.*

**D.** It is plausible that the mean distance hiked for all visitors is between 4 and 5 miles. **(Correct)**

  *Correct. Build the interval: 4.5 − 0.5 = 4 and 4.5 + 0.5 = 5.*

*Difficulty: easy*

---

##### Q9
A sample consisting of 720 adults who own televisions was selected at random for a study. Based on the sample, it is estimated that 32% of all adults who own televisions use their televisions to watch nature shows, with an associated margin of error of 3.41%. Which of the following is the most plausible conclusion about all adults who own televisions?

**A.** More than 35.41% of all adults who own televisions use their televisions to watch nature shows. 

  *35.41% is the correct upper endpoint of the interval (32 + 3.41), but claiming the true value exceeds it inverts what an upper endpoint means — it marks the far edge of the plausible band, not a floor for where the truth must sit.*

**B.** Between 28.59% and 35.41% of all adults who own televisions use their televisions to watch nature shows. **(Correct)**

  *Correct. Build the interval: 32 − 3.41 = 28.59 and 32 + 3.41 = 35.41. The sample was drawn at random from adults who own televisions, which is exactly the population this conclusion describes.*

**C.** Since the sample included adults who own televisions and not just those who use their televisions to watch nature shows, no conclusion can be made. 

  *The population being estimated IS adults who own televisions — the sample's frame already matches the population the conclusion is about. A random sample of that population is exactly what's needed to estimate what SHARE of it watches nature shows; the sample doesn't need to consist only of nature-show watchers, any more than a poll of voters needs to consist only of the eventual winner's supporters.*

**D.** Since the sample did not include all the people who watch nature shows, no conclusion can be made. 

  *No study needs to sample "all people who watch nature shows" to estimate what share of television owners watch nature shows — that population would only be relevant if the question were about nature-show watchers themselves, which it isn't.*

*Difficulty: medium*

---

##### Q10
A bag containing 10,000 beads of assorted colors is purchased from a craft store. To estimate the percent of red beads in the bag, a sample of beads is selected at random. The percent of red beads in the bag was estimated to be 15%, with an associated margin of error of 2%. If r is the actual number of red beads in the bag, which of the following is most plausible?

**A.** r > 1,700 

  *1,700 is the correct upper endpoint of the count range (17% × 10,000), but claiming r exceeds it inverts what the upper endpoint means — the interval says r is plausibly at most around 1,700, not that it exceeds that value.*

**B.** 1,300 < r < 1,700 **(Correct)**

  *Correct. Build the percent interval first: 15 − 2 = 13% and 15 + 2 = 17%. Converting to counts: 0.13 × 10,000 = 1,300 and 0.17 × 10,000 = 1,700.*

**C.** 200 < r < 1,500 

  *This confuses the MARGIN and the ESTIMATE with the interval's two endpoints instead of building the interval from them: 2% of 10,000 is 200 (the margin, expressed as a count) and 15% of 10,000 is 1,500 (the estimate itself, expressed as a count) — but the actual endpoints come from estimate − margin and estimate + margin, not from reporting the margin and the estimate side by side.*

**D.** r < 1,300 

  *1,300 is the correct lower endpoint of the count range, but claiming r is below it makes the same inversion as choice A in the other direction — the interval says r is plausibly at least around 1,300, not below it.*

*Difficulty: hard*

---

##### Q11
A store manager reviewed the receipts from 80 customers who were selected at random from all the customers who made purchases last Thursday. Of those selected, 20 receipts showed that the customer had purchased fruit. If 1,500 customers made purchases last Thursday, which of the following is the most appropriate conclusion?

**A.** Exactly 75 customers must have purchased fruit last Thursday. 

  *75 comes from dividing 1,500 by 20 instead of multiplying 1,500 by the sample's rate of 20/80 = 0.25 — an inverted operation. "Exactly" and "must have" also overclaim a certainty no sample estimate provides.*

**B.** Exactly 375 customers must have purchased fruit last Thursday. 

  *375 is the right number — 1,500 × (20/80) = 375 — but "exactly" and "must have" overclaim what a sample supports. 375 is the best ESTIMATE from the sample, not a known fact about the full 1,500, who were never all surveyed.*

**C.** The best estimate for the number of customers who purchased fruit last Thursday is 75. 

  *The verb is appropriately hedged, but the arithmetic is the same inversion as choice A: 1,500 ÷ 20 = 75 instead of 1,500 × (20/80) = 375. A careful sentence built on the wrong number is still wrong.*

**D.** The best estimate for the number of customers who purchased fruit last Thursday is 375. **(Correct)**

  *Correct. The sample's rate is 20/80 = 0.25. Applying it to the full day: 0.25 × 1,500 = 375, stated with the appropriately hedged "best estimate."*

*Difficulty: medium*

---

##### Q12
From a population of 50,000 people, 1,000 were chosen at random and surveyed about a proposed piece of legislation. Based on the survey, it is estimated that 35% of people in the population support the legislation, with an associated margin of error of 3%. Based on these results, which of the following is a plausible value for the total number of people in the population who support the proposed legislation?

**A.** 350 

  *This is 35% of the SAMPLE size (1,000), not of the population (50,000): 0.35 × 1,000 = 350. That number describes how many of the 1,000 surveyed people are estimated to support the legislation — a count the survey already gives directly — rather than how many of the full 50,000 do.*

**B.** 650 

  *This applies the complement of the support rate (100 − 35 = 65%) to the sample size (1,000) rather than the population: 0.65 × 1,000 = 650. It mixes up both which side of the survey to use (opposed, not supported) and which quantity to scale (the 1,000 surveyed, not the 50,000 population).*

**C.** 16,750 **(Correct)**

  *Correct. Build the plausible percent range: 35 − 3 = 32% and 35 + 3 = 38%. Converting to counts: 0.32 × 50,000 = 16,000 and 0.38 × 50,000 = 19,000, so any value from 16,000 to 19,000 is plausible — including 16,750.*

**D.** 31,750 

  *This falls inside the plausible range for the COMPLEMENT of the estimate — the share who do NOT support the legislation. That share is 100% − 35% = 65%, and with the same 3-point margin it runs from 62% to 68%, or 31,000 to 34,000 people. 31,750 sits inside that reversed range, reporting how many oppose the legislation rather than how many support it.*

*Difficulty: hard*

---

##### Q13
To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is 0.49, with an associated margin of error of 0.04. Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?

**A.** It is plausible that the proportion is between 0.45 and 0.53. **(Correct)**

  *Correct. Build the interval: 0.49 − 0.04 = 0.45 and 0.49 + 0.04 = 0.53.*

**B.** It is plausible that the proportion is less than 0.45. 

  *0.45 is the correct lower endpoint, but claiming the proportion is below it inverts what the endpoint marks — the plausible values run from 0.45 up to 0.53, not below 0.45.*

**C.** The proportion is exactly 0.49. 

  *0.49 is the sample's estimate, known exactly; the population's true proportion is unknown, which is exactly why a margin of error was reported alongside it.*

**D.** It is plausible that the proportion is greater than 0.53. 

  *0.53 is the correct upper endpoint, but claiming the proportion is above it inverts what the endpoint marks — it is the far edge of the plausible band, not a floor for the true value.*

*Difficulty: easy*

---

##### Q14
In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. Of the teens classified as light texters, 110 talked on a cell phone daily and 146 did not, for a subtotal of 256; of the teens classified as medium texters, 139 talked on a cell phone daily and 164 did not, for a subtotal of 303; of the teens classified as heavy texters, 166 talked on a cell phone daily and 74 did not, for a subtotal of 240. Combining all three texting-behavior groups, 415 teens talked on a cell phone daily and 384 did not, for a combined total of 799. Based on the data from the study, an estimate of the percent of US teens who are heavy texters is 30% and the associated margin of error is 3%. Which of the following is a correct statement based on the given margin of error?

**A.** Approximately 3% of the teens in the study who are classified as heavy texters are not really heavy texters. 

  *This reads the margin of error as a misclassification rate inside the sample itself — as if 3% of the study's own "heavy texter" labels were wrong. The margin of error says nothing about whether the sample was correctly classified; it describes how far the 30% estimate could sit from the true population percentage purely because of which teens were sampled.*

**B.** It is not possible that the percent of all US teens who are heavy texters is less than 27%. 

  *27% is the correct lower endpoint (30 − 3), but "it is not possible" overclaims a certainty the interval never provides — about one interval in twenty built this way misses entirely, so a true value slightly below 27% is merely less plausible, not impossible. The credited word is "doubtful," never "impossible."*

**C.** The percent of all US teens who are heavy texters is 33%. 

  *33% is the correct upper endpoint of the plausible range (30 + 3), but stating it as a flat fact converts the far edge of a plausible band into a certain value — and even the sample's own point estimate is 30%, not 33%, so this asserts a number that was never even measured.*

**D.** It is doubtful that the percent of all US teens who are heavy texters is 35%. **(Correct)**

  *Correct. The plausible range is 30 − 3 = 27% to 30 + 3 = 33%. Since 35% falls outside that range, it is doubtful — the appropriately hedged word for a value the data do not support.*

*Difficulty: hard*

---

##### Q15
The results of two random samples of votes for a proposition are shown below: in Sample A, 52% of respondents were in favor, with a margin of error of 4.2%; in Sample B, 48% of respondents were in favor, with a margin of error of 1.6%. The samples were selected from the same population, and the margins of error were calculated using the same method. Which of the following is the most appropriate reason that the margin of error for sample A is greater than the margin of error for sample B?

**A.** Sample A had a smaller number of votes that could not be recorded. 

  *The number of unrecorded votes is never mentioned in the problem and has no established relationship to margin of error. Margin of error is driven by sample size (and confidence level and population variability), not by how many responses were lost.*

**B.** Sample A had a higher percent of favorable responses. 

  *A's estimate (52%) is indeed higher than B's (48%), but which way an estimate leans has no direct effect on the SIZE of its margin of error. A sample could report 90% in favor with a small or large margin depending entirely on how many people were surveyed, not on the 90% itself.*

**C.** Sample A had a larger sample size. 

  *This names the right mechanism — sample size drives margin of error — but inverts the direction. A LARGER sample produces a SMALLER margin of error, because the margin scales with 1/√n. If A's margin is bigger, A must have surveyed fewer people, not more.*

**D.** Sample A had a smaller sample size. **(Correct)**

  *Correct. With the population and method held fixed, margin of error scales with 1/√n: a smaller sample produces a larger margin, which is exactly the pattern shown — Sample A's larger margin of error implies fewer respondents than Sample B.*

*Difficulty: medium*

---

##### Q16
In State X, Mr. Camp's eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth-grade class size in the state is 26. If the students in Mr. Camp's class are representative of students in the state's eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth-grade students in the state who have fewer than two siblings?

**A.** 16,200 

  *This applies 34.6% — the percent who reported at least two siblings — directly to the state total (0.346 × 46,800 ≈ 16,193, rounding to 16,200), answering how many students HAVE at least two siblings instead of taking the complement for how many have FEWER.*

**B.** 23,400 

  *23,400 is exactly half of the state's 46,800 eighth-graders, which ignores the 34.6% figure entirely and assumes an even fifty-fifty split between the two sibling groups instead of scaling by the reported rate.*

**C.** 30,600 **(Correct)**

  *Correct. The state has 26 × 1,800 = 46,800 eighth-grade students. Since 34.6% have at least two siblings, the complement, 65.4%, have fewer than two: 0.654 × 46,800 ≈ 30,604, which rounds to 30,600.*

**D.** 46,800 

  *46,800 is the total number of eighth-grade students in the state (26 × 1,800), reported without applying either percentage — as if every single student had fewer than two siblings.*

*Difficulty: hard*

---

#### Percentages (37 items)

##### Q1
A table of the US minimum wage for 6 different years is shown below.

Year — US minimum wage (dollars per hour)
1960 — 1.00
1970 — 1.60
1980 — 3.10
1990 — 3.80
2000 — 5.15
2010 — 7.25

What was the percent increase of the minimum wage from 1960 to 1970?

**A.** 30% 

  *This divides the $0.60 increase by $2.00 instead of by the $1.00 base — effectively doubling the base before dividing. 0.60 ÷ 2.00 = 0.30, half the correct value.*

**B.** 60% **(Correct)**

  *Correct. The change is 1.60 − 1.00 = 0.60, and the base is the 1960 wage: 0.60 ÷ 1.00 = 0.60 = 60%. Check: 1.00 × 1.60 = 1.60 ✓.*

**C.** 62.5% 

  *This is 1.00 ÷ 1.60, the OLD wage as a fraction of the NEW wage — what percent the 1960 wage is of the 1970 wage, not the percent by which it increased. It answers a different question entirely.*

**D.** 120% 

  *This doubles the $0.60 increase before dividing by the base: (2 × 0.60) ÷ 1.00 = 1.20 = 120%, as if the wage had risen by $1.20 instead of $0.60.*

*Difficulty: easy*

---

##### Q2
The cost of a certain shirt is $20 before a 5% sales tax is added. What is the total cost, including sales tax, to purchase the shirt?

**A.** $20.05 

  *This treats the 5% as if it were literally 5 cents ($0.05) added to the price, instead of computing 5% of $20 (which is $1.00). The percent sign got read as a raw cent amount.*

**B.** $20.50 

  *This adds $0.50, which is 2.5% of $20 — half the correct tax. It's the result of using 2.5% instead of the stated 5%.*

**C.** $21.00 **(Correct)**

  *Correct. 5% of $20 is 0.05 × 20 = $1.00, so the total is 20 × 1.05 = $21.00.*

**D.** $25.00 

  *This adds $5.00 — treating the '5' in '5%' as a flat five-dollar fee rather than 5% of the $20 price. 5% of $20 is $1.00, not $5.00.*

*Difficulty: easy*

---

##### Q3
Last year, 200 students enrolled in an interior design program. This year, the number of students enrolled is 147% of last year's number. How many students are enrolled in the interior design program this year?

**A.** 247 

  *This is 200 + 47 — treating the '47' in '147%' as a flat 47 students to add, rather than multiplying 200 by the full 1.47 multiplier (which adds 94 students, not 47).*

**B.** 294 **(Correct)**

  *Correct. '147% of last year's number' means 200 × 1.47 = 294.*

**C.** 347 

  *This is 200 + 147 — adding the entire percent number (147) as if it were a raw count of additional students, instead of multiplying 200 by 1.47.*

**D.** 394 

  *This is 200 × 1.97 — as if the given figure were 197% rather than 147%, an easy misread of adjacent digits under time pressure.*

*Difficulty: easy*

---

##### Q4
What is 23% of 100?

**A.** 23 **(Correct)**

  *Correct. 23% of 100 is 0.23 × 100 = 23 — of any number, the percent of 100 is just the percent value itself.*

**B.** 46 

  *This doubles the correct value (23 × 2 = 46), as if the question asked for twice 23% rather than 23% itself.*

**C.** 77 

  *This is 100 − 23, the complement of the correct answer — what remains after removing 23%, not 23% itself.*

**D.** 123 

  *This is 100 + 23, confusing '23% of 100' with '23% more than 100.' 'Of' means multiply by the percent; it never means add the percent to the base.*

*Difficulty: easy*

---

##### Q5
The length of the base of a certain parallelogram is 89% of the height of the parallelogram. Which expression represents the length of the base of the parallelogram, where h is the height of the parallelogram?

**A.** 89h 

  *This never converts 89% to a decimal at all — it multiplies h by the raw number 89 instead of by 0.89, giving a base almost 100 times too large.*

**B.** 0.089h 

  *The decimal point is shifted one place too far left. 89% is 0.89, not 0.089 — 0.089 would be the decimal form of 8.9%.*

**C.** 8.9h 

  *The decimal point is shifted one place too far right. 89% is 0.89, not 8.9 — 8.9 would be the decimal form of 890%.*

**D.** 0.89h **(Correct)**

  *Correct. 89% converts to the decimal 0.89, and 'of the height' means multiply: base = 0.89h.*

*Difficulty: easy*

---

##### Q6
Where Do People Get Most of Their Medical Information? — Source: Percent of those surveyed — Doctor: 63%, Internet: 13%, Magazines/brochures: 9%, Pharmacy: 6%, Television: 2%, Other/none of the above: 7%.

The table above shows a summary of 1,200 responses to a survey question. Based on the table, how many of those surveyed get most of their medical information from either a doctor or the internet?

**A.** 865 

  *This is close to Doctor plus Magazines/brochures (63% + 9% = 72% of 1,200 ≈ 864) rather than Doctor plus Internet (63% + 13% = 76%) — the wrong row got added to Doctor's 63%.*

**B.** 887 

  *This is close to treating the combined share as about 74% of respondents (≈888) rather than the correct 76% — consistent with misreading the Internet row's 13% as something closer to 11%.*

**C.** 912 **(Correct)**

  *Correct. Doctor (63%) plus Internet (13%) is 76% of respondents: 0.76 × 1,200 = 912.*

**D.** 926 

  *This is close to 77% of respondents (≈924) rather than the correct 76% — consistent with folding in a sliver of a third category, such as part of the 'Other/none' row, on top of Doctor and Internet.*

*Difficulty: medium*

---

##### Q7
Lani spent 15% of her 8-hour workday in meetings. How many minutes of her workday did she spend in meetings?

**A.** 1.2 

  *This computes 15% of 8 (the number of hours) and stops — 0.15 × 8 = 1.2 — without ever converting hours to minutes. 1.2 is the answer in hours, not minutes.*

**B.** 15 

  *This copies the percent value itself (15) as the answer, as though '15%' meant '15 minutes' directly, skipping the actual computation entirely.*

**C.** 48 

  *This is 480 × 0.10 = 48 — using 10% instead of the stated 15%, an easy digit misread under time pressure.*

**D.** 72 **(Correct)**

  *Correct. 8 hours is 8 × 60 = 480 minutes, and 15% of that is 0.15 × 480 = 72 minutes.*

*Difficulty: medium*

---

##### Q8
Call Ratings — 1 Star, 2 Stars, 3 Stars, 4 Stars, Total: Employee A: 16, 49, 72, 8, 145. Employee B: 4, 10, 22, 34, 70. Employee C: 8, 56, 45, 16, 125. Employee D: 22, 42, 84, 12, 160. Total: 50, 157, 223, 70, 500.

A supervisor at a call center reviewed 500 calls taken by four employees and rated the employees' performance on each call on a scale from 1 star to 4 stars. The ratings for each employee are shown in the table above. According to the table, to the nearest whole percent, what percent of Employee A's calls received a rating of 1 star?

**A.** 3% 

  *This is 16 ÷ 500 ≈ 3% — dividing Employee A's 1-star calls by the grand total of all 500 calls (every employee combined) instead of by Employee A's own total of 145 calls.*

**B.** 11% **(Correct)**

  *Correct. Employee A received 16 one-star ratings out of 145 total calls: 16 ÷ 145 ≈ 0.1103 ≈ 11%.*

**C.** 16% 

  *This copies the raw count of 1-star ratings (16) directly as a percent, without ever dividing by Employee A's total number of calls.*

**D.** 32% 

  *This is 16 ÷ 50 = 32% — dividing by the column total (all four employees' 1-star ratings combined, 50) instead of by Employee A's row total of 145 calls.*

*Difficulty: medium*

---

##### Q9
There were approximately 113,000 occupational therapy jobs in the United States in 2012. The Bureau of Labor Statistics has projected that this number will increase by 29% from 2012 to 2022. Of the following, which is closest to the number of occupational therapy jobs the bureau has projected for the United States in 2022?

**A.** 115,900 

  *This is 113,000 + 2,900 — treating '29%' as 'add 2,900' (29 × 100) directly, rather than computing 29% of 113,000 (which is 32,770).*

**B.** 116,300 

  *This treats 29% as 2.9% — a misplaced decimal point. 113,000 × 1.029 ≈ 116,300, not the correct 113,000 × 1.29.*

**C.** 142,000 

  *This rounds the base down to 100,000 before applying the percent — 100,000 × 0.29 = 29,000, then adds that to the true base: 113,000 + 29,000 = 142,000, using two different bases in the same calculation.*

**D.** 145,800 **(Correct)**

  *Correct. 113,000 × 1.29 = 145,770, which rounds to about 145,800.*

*Difficulty: medium*

---

##### Q10
A waiter receives tips from each customer. On average, the tip is 15% of the customer's bill. At this rate, which of the following is closest to the tip the waiter can expect when a customer has a bill that is $78.20?

**A.** $8.00 

  *This is close to 10% of the bill (78.20 × 0.10 ≈ 7.82 ≈ 8.00) rather than the stated 15% — an easy digit slip from 15 down to 10.*

**B.** $10.00 

  *This is close to 13% of the bill (78.20 × 0.13 ≈ 10.17 ≈ 10.00) rather than the stated 15%.*

**C.** $12.00 **(Correct)**

  *Correct. 15% of $78.20 is 0.15 × 78.20 = $11.73, which rounds to the closest choice, $12.00.*

**D.** $14.00 

  *This is close to 18% of the bill (78.20 × 0.18 ≈ 14.08 ≈ 14.00) rather than the stated 15%.*

*Difficulty: medium*

---

##### Q11
During a sale, the original prices of all items in a clothing store have been reduced by 20%. What is the sale price of a jacket with an original price of $50?

**A.** $12 

  *This is 20% of a misread original price of $60 rather than the actual $50 (60 × 0.20 = 12) — and even then it's the discount amount, not the sale price.*

**B.** $30 

  *This subtracts the $10 discount amount twice ($50 − $10 − $10 = $30) instead of once — the 20% discount is applied a single time, not repeated.*

**C.** $36 

  *This applies a second discount on top of the correct one: 50 × 0.80 × 0.90 = $36, as if a 10% coupon stacked with the 20% markdown, though the problem describes only one discount.*

**D.** $40 **(Correct)**

  *Correct. A 20% discount leaves 80% of the price: 50 × 0.80 = $40.*

*Difficulty: easy*

---

##### Q12
What is 10% of 370?

**A.** 27 

  *This is 10% of 270 (0.10 × 270 = 27), not 370 — a digit transposition that misreads the base.*

**B.** 37 **(Correct)**

  *Correct. 10% of 370 is 0.10 × 370 = 37.*

**C.** 333 

  *This is 370 × 0.90 = 333, the amount that REMAINS after removing 10% — the complement of the correct answer, not the 10% itself.*

**D.** 360 

  *This is 370 − 10, subtracting the raw number 10 as a flat amount instead of computing 10% of 370 (which is 37) and working from there.*

*Difficulty: easy*

---

##### Q13
Rita's total bill at a restaurant was $25.00, including tax. If she left a tip of 20% of the total bill, what was the amount of the tip?

**A.** $3.50 

  *This is 25 × 0.14 = $3.50 — a 14% tip rather than the stated 20%, close to the reflexive '15% tip' habit many people default to, undershooting the requested rate.*

**B.** $4.00 

  *This uses a bill of $20 instead of the actual $25 — a natural round-number slip: 20 × 0.20 = $4.00.*

**C.** $4.50 

  *This is 25 × 0.18 = $4.50 — an 18% tip rather than the stated 20%.*

**D.** $5.00 **(Correct)**

  *Correct. 20% of the $25.00 total bill is 0.20 × 25 = $5.00.*

*Difficulty: medium*

---

##### Q14
What number is 20% greater than 60?

**A.** 50 

  *This is 60 ÷ 1.20 = 50 — dividing instead of multiplying, which finds a number that 60 is 20% greater than, not a number that is 20% greater than 60. The direction of the operation is reversed.*

**B.** 72 **(Correct)**

  *Correct. 20% greater than 60 is 60 × 1.20 = 72.*

**C.** 75 

  *This is 60 + 15, adding 25% of 60 instead of 20% — 25% of 60 is 15, so this treats the given percent as 25% rather than 20%.*

**D.** 132 

  *This adds the correctly-inflated new value back onto the original — 60 + 72 = 132 — effectively counting the base twice instead of reporting the new value once.*

*Difficulty: easy*

---

##### Q15
21 is 21% of what number?

**A.** 0 

  *This treats the equation as 21 − 21 = 0, canceling the two matching numbers directly, rather than solving 0.21x = 21 for x.*

**B.** 1 

  *This divides the two numbers directly, 21 ÷ 21 = 1, ignoring that the second 21 carries a percent sign and represents 0.21, not the whole number 21.*

**C.** 42 

  *This is 21 × 2 = 42, doubling the given number instead of dividing it by 0.21 — as if 21 were 50% of the answer rather than 21%.*

**D.** 100 **(Correct)**

  *Correct. 21 is 21% of x means 0.21x = 21, so x = 21 ÷ 0.21 = 100.*

*Difficulty: medium*

---

##### Q16
Of 900,000 beads, 828,000 are silver. What percentage of the beads are silver?

**A.** 8% 

  *This is the complement of the correct answer: 100% − 92% = 8%, the percentage that are NOT silver, not the percentage that are.*

**B.** 36% 

  *This is half of choice C's flawed 72% — a further miscalculation stacked on top of the same error of never dividing by the total.*

**C.** 72% 

  *This takes the raw difference between the two numbers in thousands (900 − 828 = 72) and reports it directly as '72%' without ever dividing by the 900,000 total — 72,000 is the number of NON-silver beads, not a percentage.*

**D.** 92% **(Correct)**

  *Correct. 828,000 ÷ 900,000 = 0.92 = 92%.*

*Difficulty: easy*

---

##### Q17
What is 10% of 470?

**A.** 37 

  *This is 10% of 370 (0.10 × 370 = 37), not 470 — a digit transposition that misreads the base.*

**B.** 47 **(Correct)**

  *Correct. 10% of 470 is 0.10 × 470 = 47.*

**C.** 423 

  *This is 470 × 0.90 = 423, the amount that REMAINS after removing 10% — the complement of the correct answer.*

**D.** 460 

  *This is 470 − 10, subtracting the raw number 10 as a flat amount instead of computing 10% of 470.*

*Difficulty: easy*

---

##### Q18
What percentage of 300 is 75?

**A.** 25% **(Correct)**

  *Correct. 75 ÷ 300 = 0.25 = 25%.*

**B.** 50% 

  *This doubles 75 to 150 before dividing by 300 (150 ÷ 300 = 50%) — an easy slip when the eye jumps from '75' to 'half of 150.'*

**C.** 75% 

  *This reports the number 75 directly as a percent, ignoring the 'of 300' entirely — treating the numerator as if it were already the answer.*

**D.** 225% 

  *This is 300 − 75 = 225, the raw difference between the two numbers reported directly as a percent, without ever dividing by 300.*

*Difficulty: easy*

---

##### Q19
There are 350 objects in a box. Of these objects, 4% are balls. How many balls are in the box?

**A.** 4 

  *This copies the percent value itself (4) as the answer, skipping the actual multiplication by 350 entirely.*

**B.** 14 **(Correct)**

  *Correct. 4% of 350 is 0.04 × 350 = 14.*

**C.** 70 

  *This is 350 × 0.20 = 70, using 20% instead of the stated 4% — an easy misread of the percent value.*

**D.** 346 

  *This is 350 − 4, subtracting the raw number 4 as a flat amount instead of computing 4% of 350.*

*Difficulty: easy*

---

##### Q20
For the finale of a TV show, viewers could use either social media or a text message to vote for their favorite of two contestants. The contestant receiving more than 50% of the vote won. An estimated 10% of the viewers voted, and 30% of the votes were cast on social media. Contestant 2 earned 70% of the votes cast using social media and 40% of the votes cast using a text message. Based on this information, which of the following is an accurate conclusion?

**A.** If all viewers had voted, Contestant 2 would have won. 

  *This extrapolates the behavior of the 10% who voted onto the 90% who didn't — nothing in the data supports assuming non-voters would split their votes the same way. The passage describes only who actually voted, not what everyone else would have done.*

**B.** Viewers voting by social media were likely to be younger than viewers voting by text message. 

  *This introduces an age claim the data never measured. Nothing in the passage says anything about the age of any voter — this conclusion isn't supported or contradicted by the numbers, it's simply absent from them.*

**C.** If all viewers who voted had voted by social media instead of by text message, Contestant 2 would have won. 

  *This assumes that voters who chose text message would have preferred Contestant 2 at the same 70% rate social-media voters did, simply by switching channels. But their preference is only known as measured through the channel they actually used — there's no basis for assuming the rate transfers to a hypothetically different channel.*

**D.** Viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message. **(Correct)**

  *Correct. This directly restates what the data shows — 70% of social-media voters chose Contestant 2 versus 40% of text-message voters — without extrapolating to any group or scenario the passage doesn't describe.*

*Difficulty: hard*

---

##### Q21
During the first month of sales, a company sold 1,300,000 units of a certain type of smartphone. During the same month, 15% of the units sold were returned. If sales and the return rate remain the same for each of the next 5 months, about how many units of this smartphone will be returned to the company during this 6-month period?

**A.** 195,000 

  *This is a single month's returns (1,300,000 × 0.15 = 195,000), not the 6-month total — the calculation stopped one step early.*

**B.** 975,000 

  *This is 195,000 × 5 — only 'the next 5 months' mentioned in the problem, forgetting to also include the first month's own 195,000 in the 6-month total.*

**C.** 1,170,000 **(Correct)**

  *Correct. Each month returns 1,300,000 × 0.15 = 195,000 units; over 6 months, that's 195,000 × 6 = 1,170,000.*

**D.** 6,630,000 

  *This is 1,300,000 × 0.85 × 6 = 6,630,000 — the units KEPT (85%) each month, multiplied out, instead of the units returned (15%). The complement was computed instead of the requested quantity.*

*Difficulty: medium*

---

##### Q22
Which of the following represents the result of increasing the quantity x by 9%, where x > 0?

**A.** 1.09x **(Correct)**

  *Correct. Increasing x by 9% means multiplying by (1 + 0.09) = 1.09.*

**B.** 0.09x 

  *This is only the AMOUNT of the increase (9% of x), not the new total after the increase. The '1' representing the original 100% of x got dropped.*

**C.** x + 9 

  *This treats '9%' as a flat 9 units added to x, rather than 9% OF x. The increase must scale with x, not stay a fixed constant.*

**D.** x + 0.09 

  *Same flat-amount error as choice C, but using the decimal form 0.09 instead of the whole number 9 — still adding a fixed constant rather than a percent of x.*

*Difficulty: easy*

---

##### Q23
The number k is 36% greater than 50. If k is the product of 50 and r, what is the value of r?

**A.** 36 

  *This copies the raw percent number (36) as the value of r, ignoring that r must be a multiplier — the number 50 is multiplied by, not the percent itself.*

**B.** 3.6 

  *This treats 36% as the decimal 3.6 (a misplaced decimal point — should be 0.36) and skips adding 1 for the base amount, giving 3.6 instead of the correct 1 + 0.36 = 1.36.*

**C.** 1.36 **(Correct)**

  *Correct. '36% greater than 50' means k = 50 × 1.36, so r = 1.36.*

**D.** 0.36 

  *This correctly converts 36% to the decimal 0.36 but forgets to add the base 1 — 0.36 is the multiplier for just the INCREASE, not for the new total (which needs 1 + 0.36).*

*Difficulty: medium*

---

##### Q24
The value of z is 1.13 times 100. The value of z is what percent greater than 100?

**A.** 11.3 

  *This shifts the decimal on the multiplier itself — treating 1.13 as if it meant 0.113 times greater — giving 0.113 × 100 = 11.3 instead of the correct 13.*

**B.** 13 **(Correct)**

  *Correct. z = 1.13 × 100 = 113. The amount z exceeds 100 by is 13, and 13 ÷ 100 = 13%.*

**C.** 130 

  *This misreads the multiplier 1.13 as 1.3, then reports z itself (1.3 × 100 = 130) instead of computing how much z exceeds 100 by.*

**D.** 213 

  *This adds z (113) to 100 instead of finding how much z exceeds 100 by: 100 + 113 = 213 is the wrong operation entirely for a 'percent greater than' question.*

*Difficulty: medium*

---

##### Q25
In a group, 40% of the items are red. Of all the red items in the group, 30% also have stripes. What percentage of the items in the group are red with stripes?

**A.** 10% 

  *This subtracts the two percentages (40% − 30% = 10%) instead of multiplying them — treating the second percentage as a reduction from the first rather than as a share OF the red group.*

**B.** 12% **(Correct)**

  *Correct. 30% of the 40% that are red: 0.40 × 0.30 = 0.12 = 12% of all items.*

**C.** 70% 

  *This adds the two percentages (40% + 30% = 70%) instead of multiplying them — the classic error of treating chained percentages of different groups as if they simply summed.*

**D.** 75% 

  *This reverses the relationship, computing 30 ÷ 40 = 75% — what percent 30% is OF 40% — instead of 30% of the 40% group. The direction of 'of' got flipped.*

*Difficulty: medium*

---

##### Q26
A number n is increased 6%. If the result is 318, what is the value of n?

**A.** 199 

  *This uses a multiplier of 1.6 instead of 1.06 — reading '6%' as '60%,' a decimal-placement slip: 318 ÷ 1.6 ≈ 199.*

**B.** 299 

  *This undoes the 6% increase by subtracting 6% back off (×0.94) instead of dividing by the multiplier that created it (÷1.06): 318 × 0.94 ≈ 299. Reversals are always divisions, never a second subtraction.*

**C.** 300 **(Correct)**

  *Correct. n × 1.06 = 318, so n = 318 ÷ 1.06 = 300. Check: 300 × 1.06 = 318 ✓.*

**D.** 337 

  *This applies the 6% increase to 318 AGAIN (318 × 1.06 ≈ 337) instead of solving backward for n — reapplying the multiplier forward rather than undoing it.*

*Difficulty: hard*

---

##### Q27
A customer's monthly water bill was $75.74. Due to a rate increase, her monthly bill is now $79.86. To the nearest tenth of a percent, by what percent did the amount of the customer's water bill increase?

**A.** 4.1% 

  *This reports the raw $4.12 increase directly as if it were already a percent, skipping the division by the $75.74 base entirely.*

**B.** 5.1% 

  *This comes from rounding the base or the change before dividing — on a change this small, rounding before the final step is enough to shift the answer one tenth of a percent from the exact 5.4%.*

**C.** 5.2% 

  *This divides the $4.12 increase by the ending value, $79.86, instead of the starting value, $75.74: 4.12 ÷ 79.86 ≈ 5.2%. The base of a percent change is always the value you started from.*

**D.** 5.4% **(Correct)**

  *Correct. The change is 79.86 − 75.74 = 4.12, and the base is 75.74: 4.12 ÷ 75.74 ≈ 0.0544 ≈ 5.4%.*

*Difficulty: medium*

---

##### Q28
Thomas installed a new stove in his restaurant. At the time of installation, the stove had a value of $800. Thomas estimates that each year the value of the stove will depreciate by 20% of the previous year's estimated value. What is the estimated value of the stove exactly 2 years after Thomas installed it?

**A.** $480 

  *This adds the two 20% depreciations together (20% + 20% = 40%) and takes 40% off the original once: 800 × 0.60 = $480 — instead of compounding each year's 20% off the previous year's already-reduced value.*

**B.** $512 **(Correct)**

  *Correct. Year 1: 800 × 0.80 = $640. Year 2: 640 × 0.80 = $512. Compounded: 800 × 0.80 × 0.80 = $512.*

**C.** $556 

  *This is close to misreading the second year's depreciation rate as roughly 13% instead of 20%: 640 × 0.87 ≈ $557, close to this choice — the first year is done correctly, then the rate slips on the second.*

**D.** $640 

  *This is the value after only ONE year of depreciation (800 × 0.80 = 640) — the calculation stopped one year early instead of compounding a second time.*

*Difficulty: hard*

---

##### Q29
The number of coins in a collection increased from 9 to 90. What was the percent increase in the number of coins in this collection?

**A.** 10% 

  *This computes 9 ÷ 90 = 10% — what percent the OLD value (9) is of the NEW value (90), a completely different question from the percent by which the number increased.*

**B.** 81% 

  *This reports the raw difference (90 − 9 = 81) directly as a percent, without ever dividing by the base of 9.*

**C.** 90% 

  *This divides the change by the ending value instead of the starting one: (90 − 9) ÷ 90 = 81 ÷ 90 = 90%. The base of a percent change is always the value you started from.*

**D.** 900% **(Correct)**

  *Correct. The change is 90 − 9 = 81, and the base is the starting value, 9: 81 ÷ 9 = 9 = 900%.*

*Difficulty: medium*

---

##### Q30
Jennifer bought a box of Crunchy Grain cereal. The nutrition facts on the box state that a serving size of the cereal is 3/4 cup and provides 210 calories, 50 of which are calories from fat. In addition, each serving of the cereal provides 180 milligrams of potassium, which is 5% of the daily allowance for adults. If p percent of an adult's daily allowance of potassium is provided by x servings of Crunchy Grain cereal per day, which of the following expresses p in terms of x?

**A.** p = 0.5x 

  *This is off by a factor of 10 — treating one serving as 0.5% of the daily allowance instead of the stated 5%.*

**B.** p = 5x **(Correct)**

  *Correct. Each serving provides 5% of the daily allowance, so x servings provide 5% each, added up: p = 5x.*

**C.** p = (0.05)^x 

  *This treats each additional serving as multiplying the running percentage by 0.05 — exponential decay — rather than simply adding another 5% per serving. Servings stack by addition here, not by repeated multiplication.*

**D.** p = (1.05)^x 

  *This treats the servings like compound interest, where each serving multiplies the running total by 1.05 — the same conceptual error as choice C, but using the 'increase' multiplier form instead of the raw decimal. Each serving simply adds a fixed 5%; it doesn't compound on the previous total.*

*Difficulty: hard*

---

##### Q31
Year — Subscriptions sold: 2012 — 5,600. 2013 — 5,880.

The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?

**A.** 6,020 

  *This computes the 2012-to-2013 percent increase using the wrong base — dividing the $280 change by the 2013 value (5,880) instead of the 2012 value (5,600), getting about 4.76% instead of 5%. Halving that (per the problem) and applying it to 5,880 lands at 6,020 instead of the correct 6,027 — a small error that compounds from using the wrong base at the very first step.*

**B.** 6,027 **(Correct)**

  *Correct. The 2012-to-2013 increase is (5,880 − 5,600) ÷ 5,600 = 280 ÷ 5,600 = 5%. Since that increase is double the 2013-to-2014 increase, the 2013-to-2014 increase is half of 5%, or 2.5%. 5,880 × 1.025 = 6,027.*

**C.** 6,440 

  *This adds twice the original $280 dollar increase directly (2 × 280 = 560; 5,880 + 560 = 6,440), treating the 'double' instruction as applying to the flat dollar change rather than to the percent rate — and never converting to a percent at all.*

**D.** 6,468 

  *This reverses the relationship in the problem — treating the 2013-to-2014 increase as double the 2012-to-2013 rate (10% instead of half of 5%, i.e. 2.5%): 5,880 × 1.10 = 6,468.*

*Difficulty: sat-hardest*

---

##### Q32
According to the 2010 Census, the adult population aged 18 years or greater of the United States in 2010 was 234,564,071. In 2010, a survey was conducted among a randomly chosen sample of adults aged 18 years or greater in the United States about their preference to live in a warm climate or a cool climate. The table below displays a summary of the survey results.

Climate Preferences — Warm, Cool, No preference, Total:
18–35 years old: 295, 168, 45, 508
36–50 years old: 246, 123, 41, 410
51–65 years old: 238, 117, 48, 403
Greater than 65 years old: 137, 78, 64, 279
Total: 916, 486, 198, 1,600

Which of the following is closest to the difference between the percentage of adults aged 18–50 years who responded 'warm' and the percentage of adults aged 51 years or greater who responded 'warm'?

**A.** 4% **(Correct)**

  *Correct. Pool the counts within each combined group before dividing. 18–50: (295 + 246) ÷ (508 + 410) = 541 ÷ 918 ≈ 58.9%. 51+: (238 + 137) ÷ (403 + 279) = 375 ÷ 682 ≈ 55.0%. Difference ≈ 3.9%, closest to 4%.*

**B.** 5% 

  *This averages the two age-subgroup rates within each combined group instead of pooling by count: for 18–50, averaging 58.1% (18–35) and 60.0% (36–50) gives 59.0%; for 51+, averaging 59.1% (51–65) and 49.1% (>65) gives 54.1%. The difference, about 5%, ignores that the subgroups have different sizes and so can't just be averaged.*

**C.** 10% 

  *This takes the raw difference in 'warm' counts between the two combined groups (541 − 375 = 166) and divides by the grand total of 1,600 (166 ÷ 1,600 ≈ 10.4%), instead of comparing each group's own warm percentage against its own total.*

**D.** 18% 

  *This divides the same raw count difference (166) by only the 18–50 group's total (918) instead of by the grand total or by properly computing each group's own percentage: 166 ÷ 918 ≈ 18.1%.*

*Difficulty: sat-hardest*

---

##### Q33
37% of the items in a box are green. Of those, 37% are also rectangular. Of the green rectangular items, 42% are also metal. Which of the following is closest to the percentage of the items in the box that are NOT rectangular green metal items?

**A.** 1.16% 

  *This adds the three percentages instead of multiplying them: 37% + 37% + 42% = 116%, i.e. a decimal sum of 1.16 — reporting that raw sum with a percent sign (1.16%) rather than recognizing chained percentages of different groups have to be multiplied, not added, to find a single group's share.*

**B.** 57.50% 

  *The correct chained percentage of rectangular green metal items is about 5.75% (0.37 × 0.37 × 0.42). This choice has the decimal point shifted one place to the right — 5.75% misread as 57.50%.*

**C.** 94.25% **(Correct)**

  *Correct. Rectangular green metal items are 0.37 × 0.37 × 0.42 ≈ 5.75% of the box. Items that are NOT that combination are the complement: 100% − 5.75% = 94.25%.*

**D.** 98.84% 

  *This is the complement of choice A's flawed 1.16% (100% − 1.16% = 98.84%) — the same 'percents added instead of multiplied' error, just complemented instead of the correctly-computed 5.75% chain.*

*Difficulty: sat-hardest*

---

##### Q34
The value of a collectible comic book increased by 167% from the end of 2011 to the end of 2012 and then decreased by 16% from the end of 2012 to the end of 2013. What was the net percentage increase in the value of the collectible comic book from the end of 2011 to the end of 2013?

**A.** 124.28% **(Correct)**

  *Correct. A 167% increase is ×2.67, and a 16% decrease is ×0.84. Combined: 2.67 × 0.84 = 2.2428, so the net multiplier is 2.2428 — a 124.28% increase (2.2428 − 1 = 1.2428).*

**B.** 140.28% 

  *This forgets to add 1 when converting the 167% increase to a multiplier — using ×1.67 instead of ×2.67 — and then reports the resulting product (1.67 × 0.84 = 1.4028) directly as a percent instead of subtracting 1 first to isolate the net change.*

**C.** 151.00% 

  *This subtracts the percents directly (167% − 16% = 151%) instead of multiplying the two multipliers together — the classic error of treating successive percent changes as if they simply combined by addition.*

**D.** 209.72% 

  *This applies the second change in the wrong direction — treating the 16% decrease as a 16% increase (×1.16 instead of ×0.84): 2.67 × 1.16 − 1 = 209.72%.*

*Difficulty: hard*

---

##### Q35
140 is p% greater than 10. What is the value of p?

**A.** 1,400 

  *This reports the full ratio 140 ÷ 10 = 14 = 1,400% (how many times 140 is of 10), rather than how much GREATER 140 is than 10 — forgetting to subtract the baseline 100% first.*

**B.** 1,300 **(Correct)**

  *Correct. 140 = 10(1 + p/100), so 14 = 1 + p/100, p/100 = 13, and p = 1,300.*

**C.** 140 

  *This copies the number 140 itself as if it were p, ignoring the entire percent relationship in the problem.*

**D.** 130 

  *This is 140 − 10 = 130, the raw difference between the two numbers, reported directly as p instead of computing what percent 130 is OF the base, 10 (which is 1,300%, not 130).*

*Difficulty: medium*

---

##### Q36
After 20% of the original number of marbles in a group were removed from the group, 360 marbles remained in the group. How many marbles were removed from the group?

**A.** 72 

  *This takes 20% of the 360 remaining marbles (360 × 0.20 = 72) as if 360 were the original amount, rather than the 80% that remained after the original was reduced.*

**B.** 90 **(Correct)**

  *Correct. If 20% was removed, 360 is 80% of the original: original × 0.80 = 360, so original = 450. Removed = 450 − 360 = 90.*

**C.** 450 

  *This correctly solves for the original number of marbles (450) but reports that instead of the number REMOVED (450 − 360 = 90) — the right method, one step short of the quantity actually asked for.*

**D.** 1,800 

  *This divides 360 by 0.20 instead of 0.80 — treating the 360 remaining marbles as 20% of the original (the amount that was REMOVED) rather than as the 80% that stayed. This mis-solved 'original' of 1,800 is then given directly, compounding a wrong-percentage error with answering the wrong quantity.*

*Difficulty: hard*

---

##### Q37
The number a is 190% greater than the number b. The number b is 80% less than 24. What is the value of a?

**A.** 9.12 

  *This correctly finds b (24 × 0.20 = 4.8) but forgets to add 1 when converting '190% greater' to a multiplier, using ×1.90 instead of ×2.90: 4.8 × 1.90 = 9.12.*

**B.** 13.92 **(Correct)**

  *Correct. b is 80% less than 24: b = 24 × 0.20 = 4.8. a is 190% greater than b: a = 4.8 × 2.90 = 13.92.*

**C.** 26.40 

  *This subtracts the two percentages directly (190% − 80% = 110%) instead of combining them as separate multipliers, then also forgets the base '+1' (×1.10 instead of ×2.10), applying it straight to 24: 24 × 1.10 = 26.40.*

**D.** 36.48 

  *This stacks two errors: misreading '80% less than 24' as '80% OF 24' (b = 24 × 0.80 = 19.2 instead of 24 × 0.20 = 4.8), and forgetting the base '+1' for the 190% conversion (×1.90 instead of ×2.90): 19.2 × 1.90 = 36.48.*

*Difficulty: hard*

---

#### One-variable data: distributions, centre and spread (40 items)

##### Q1
The seven data values 2, 2, 2, 3, 4, 4, 11 are shown. What is the median of the seven data values shown?

**A.** 2 

  *This is the mode (2 appears three times, more often than any other value), not the median. The mode and the median answer different questions — one is about frequency, the other about position.*

**B.** 3 **(Correct)**

  *Correct. With 7 values, the median is the (7+1)/2 = 4th value once sorted. The list is already sorted: 2, 2, 2, 3, 4, 4, 11 — the 4th value is 3.*

**C.** 4 

  *This picks a value from the repeated pair 4, 4, which sits just past the true midpoint and looks central at a glance. But the actual median comes from counting positions, not from eyeballing which value "looks" central: the 4th of 7 sorted values is 3, not 4.*

**D.** 11 

  *This reports the maximum instead of the median, treating the last-listed value as though "median" meant "the extreme" rather than "the middle position." 11 is the largest value in the set, not the middle one.*

*Difficulty: easy*

---

##### Q2
> Data set A: 72, 73, 73, 76, 76. Data set B: 61, 64, 74, 85, x.

Data set A and data set B each contain 5 numbers. If the mean of data set A is equal to the mean of data set B, what is the value of x?

**A.** 77 

  *This comes from a digit transposition while summing data set A: reading one of the 76s as 67 gives a miscomputed sum of 361 instead of 370 (a shortfall of 9). Solving 361 = 284 + x then gives x = 77, when the true sum of data set A is 370.*

**B.** 85 

  *This copies the value listed immediately before x in data set B (85) instead of solving the mean equation — as if x were meant to repeat its neighbor rather than being found by setting the two sums equal.*

**C.** 86 **(Correct)**

  *Correct. Since both data sets contain 5 numbers, equal means require equal sums. Sum of data set A: 72+73+73+76+76 = 370. Sum of the four known values in data set B: 61+64+74+85 = 284. So 284 + x = 370, giving x = 86.*

**D.** 95 

  *This adds data set A's mean (74) to data set B's range among its known values (85 − 64 = 21) — an operation with no basis in solving for x, but one that lands on 74 + 21 = 95 instead of the value that actually equalizes the two sums.*

*Difficulty: medium*

---

##### Q3
For a school fund-raiser, 10 students sold a total of 90 boxes of cookies. Which of the following can be calculated from this information?

**A.** The average number of boxes sold per student **(Correct)**

  *Correct. Mean = total ÷ count = 90/10 = 9 boxes per student, calculable directly from the total and the count given.*

**B.** The median number of boxes sold per student 

  *The median requires knowing where each individual student's total falls in sorted order. A total of 90 across 10 students is consistent with many different individual distributions — all 10 selling 9 each, or one student selling 81 and the rest selling 1 each — with very different medians. The total alone doesn't fix it.*

**C.** The greatest number of boxes sold by one student 

  *The greatest individual value isn't fixed by the total either. One student could have sold anywhere from 9 up to 81 boxes (with the rest selling minimally) while the total across all 10 students stays exactly 90.*

**D.** The least number of boxes sold by one student 

  *Same problem as the greatest value: the smallest individual total isn't determined by the group total. A student could have sold as few as 0 boxes while the other 9 made up the difference, or the sales could be spread evenly — the total of 90 is compatible with either.*

*Difficulty: medium*

---

##### Q4
> The data shown: 2, 9, 14, 23, 32.

What is the mean of the data shown?

**A.** 14 

  *This is the median, not the mean — sorted, the five values are 2, 9, 14, 23, 32, and 14 is the middle (3rd) value. The mean requires summing all five values and dividing by 5, not picking out the middle one.*

**B.** 16 **(Correct)**

  *Correct. Sum: 2 + 9 + 14 + 23 + 32 = 80. Mean: 80/5 = 16.*

**C.** 17 

  *This comes from a small addition slip in the sum — misadding 23 as 28, for instance, gives a total of 85 instead of 80, and 85/5 = 17.*

**D.** 32 

  *This reports the maximum value instead of the mean — 32 is the largest of the five values, not their average.*

*Difficulty: easy*

---

##### Q5
> The table below shows the high and low temperatures in Houston, Texas, during a five-day period (degrees Fahrenheit). High temperature: Monday 73, Tuesday 56, Wednesday 62, Thursday 75, Friday 81. Low temperature: Monday 49, Tuesday 37, Wednesday 41, Thursday 54, Friday 63.

What was the mean low temperature, in degrees Fahrenheit, during the five-day period?

**A.** 48.8 **(Correct)**

  *Correct. Sum of the five low temperatures: 49 + 37 + 41 + 54 + 63 = 244. Mean: 244/5 = 48.8.*

**B.** 49 

  *This is the median of the low temperatures, not the mean — sorted, the five lows are 37, 41, 49, 54, 63, and the middle value is 49. The median and the mean happen to be close here (48.8 vs. 49), which makes this an easy statistic to substitute by accident.*

**C.** 59 

  *This comes from a division error while computing the correct sum (244) divided by 5 — a slip in the long division rather than in choosing which values to average.*

**D.** 59.1 

  *This averages all ten temperatures from both the high row and the low row together (73+56+62+75+81+49+37+41+54+63 = 591, ÷10 = 59.1) instead of restricting the calculation to the five low-temperature values the question asks about.*

*Difficulty: easy*

---

##### Q6
> Data set A: 1, 2, 3, 4, 5, 6, 7. Data set B: 1, 1, 2, 2, 3, 3, 4.

Which of the following statements correctly compares the means of data set A and data set B?

**A.** The mean of each data set is 2. 

  *2 is the median of data set B (sorted, its 4th of 7 value), not the mean of either set — data set A's mean is 4 and data set B's mean is about 2.29, and neither equals 2 exactly.*

**B.** The mean of each data set is 4. 

  *Data set A's mean is correctly 4, but applying that same value to data set B ignores that B is a different, smaller-valued set: its mean is 16/7 ≈ 2.29, not 4.*

**C.** The mean of data set A is less than the mean of data set B. 

  *This has the comparison backward. Data set A's mean (28/7 = 4) is greater than data set B's mean (16/7 ≈ 2.29), not less — data set B's values are smaller and more front-loaded toward 1 and 2.*

**D.** The mean of data set A is greater than the mean of data set B. **(Correct)**

  *Correct. Mean of A: (1+2+3+4+5+6+7)/7 = 28/7 = 4. Mean of B: (1+1+2+2+3+3+4)/7 = 16/7 ≈ 2.29. 4 is greater than 2.29.*

*Difficulty: easy*

---

##### Q7
> A box plot summarizes the number of acres of useful timberland in 13 counties in California. The horizontal axis is labeled in increments of 1,000 acres, from 1,000 to 14,000. Reading the plot from left to right: the lower whisker begins a little past 1,000 acres, the box (spanning the first to the third quartile) occupies roughly the region between about 4,000 and 11,000 acres, the vertical line marking the median sits noticeably left of the box's visual center — closer to the Q1 edge than to the Q3 edge — and the upper whisker extends out to just under 14,000 acres.

Which of the following is closest to the median number of acres?

**A.** 4,399 

  *This lands near the LEFT edge of the box, which marks Q1 (the first quartile), not the median. The median is the line drawn inside the box, not the box's left boundary.*

**B.** 7,067 **(Correct)**

  *Correct. This is closest to the line drawn inside the box, which marks the median. That line sits well left of the box's geometric center — closer to Q1 than to Q3 — which is exactly why reading "the middle of the box" instead of "the line inside the box" gives a different, wrong answer.*

**C.** 8,831 

  *This falls near the visual CENTER of the box (roughly halfway between its left and right edges), which is easy to mistake for the median line. But the median line is wherever it's actually drawn inside the box, not necessarily the box's geometric midpoint — here it sits well left of center.*

**D.** 10,595 

  *This lands near the RIGHT edge of the box, which marks Q3 (the third quartile), not the median. The median is the line drawn inside the box, not the box's right boundary.*

*Difficulty: medium*

---

##### Q8
> A study was conducted on the production rates for a company that produces tractor wheels. The table below shows the number of wheels made during 11 consecutive one-hour production periods. Period: A, B, C, D, E, F, G, H, I, J, K. Number of wheels made: 24, 24, 21, 21, 21, 19, 24, 24, 19, 22, 23.

What is the range of the number of wheels made for the 11 one-hour periods?

**A.** 5.5 

  *Misreads one of the four 24-wheel rows as 25 (a similar-looking digit in a crowded table) and averages it with a correctly read 24, arriving at a "maximum" of 24.5. Then 24.5 − 19 = 5.5, when the true maximum is exactly 24.*

**B.** 5.0 **(Correct)**

  *Correct. The maximum number of wheels made in any one-hour period is 24 (periods A, B, G, H) and the minimum is 19 (periods F, I), so the range is 24 − 19 = 5, written here as 5.0.*

**C.** 4.5 

  *Misreads one of the two 19-wheel rows as 20 and averages it with the correctly read 19, arriving at a "minimum" of 19.5. Then 24 − 19.5 = 4.5, when the true minimum is exactly 19.*

**D.** 4.0 

  *Misreads both rows that show 19 as 20, so the minimum used is 20 instead of 19: 24 − 20 = 4.0. The two rows with 19 wheels (periods F and I) are easy to conflate with the more frequent 21s and the nearby 22 in a table with many close values.*

*Difficulty: easy*

---

##### Q9
> The table gives the results of a survey of 200 people who were asked how often they see a movie in a theater. Response: frequency — Once a week or more: 3, Two or three times a month: 16, About once a month: 26, A few times a year: 73, Almost never: 53, Never: 29, Total: 200.

How many people responded either "never" or "almost never"?

**A.** 24 

  *This subtracts the two frequencies (53 − 29 = 24) instead of adding them. The question asks how many people responded EITHER way — that's a combined count, which requires adding the two categories, not finding their difference.*

**B.** 53 

  *This reports only the "almost never" category (53), leaving out the 29 people who responded "never." The question asks for both categories combined.*

**C.** 82 **(Correct)**

  *Correct. "Almost never" (53) plus "never" (29): 53 + 29 = 82.*

**D.** 118 

  *This computes the complement instead of the sum: 200 − 82 = 118 is the number of people who responded NEITHER "never" nor "almost never," the opposite of what was asked.*

*Difficulty: easy*

---

##### Q10
> The table above shows the land area, in square kilometers, of the five smallest countries of the world in 2016. Country — Land area: Monaco 2.0, Nauru 21, San Marino 61, Tuvalu 26, Vatican City 0.44.

Based on the table, what is the mean land area of the 5 smallest countries in 2016, to the nearest square kilometer?

**A.** 20 

  *Computes the mean correctly as about 22.1 but then rounds to the nearest ten instead of the nearest whole square kilometer as the question asks, landing on 20.*

**B.** 22 **(Correct)**

  *Correct. Sum: 2.0 + 21 + 61 + 26 + 0.44 = 110.44. Mean: 110.44/5 = 22.088, which rounds to 22.*

**C.** 61 

  *This reports the maximum land area (San Marino, 61) instead of the mean of all five countries.*

**D.** 110 

  *This reports the total sum of the five land areas (110.44, rounded to 110) instead of dividing by the count of countries to get the mean.*

*Difficulty: easy*

---

##### Q11
> For quality control, a company that manufactures lightbulbs conducted five different trials. In each trial, 500 different lightbulbs were tested. A bar graph shows the number of defective lightbulbs found in each trial, read against a y-axis from 0 to 8: Trial A about 5, Trial B about 7, Trial C about 2, Trial D about 3, Trial E about 4.

What is the mean number of defective lightbulbs for the five trials?

**A.** 4.0 

  *Misreads trial C's bar as 1 instead of 2, giving a total of 5+7+1+3+4 = 20 instead of 21, and 20/5 = 4.0.*

**B.** 4.2 **(Correct)**

  *Correct. Total defective bulbs: 5 + 7 + 2 + 3 + 4 = 21. Mean: 21/5 = 4.2.*

**C.** 4.6 

  *Misreads trial A's bar as 7 (confusing it with trial B's taller bar) instead of 5, giving a total of 7+7+2+3+4 = 23 instead of 21, and 23/5 = 4.6.*

**D.** 5.0 

  *Misreads trial D's bar as 7 (confusing it with trial B's taller bar) instead of 3, giving a total of 5+7+2+7+4 = 25 instead of 21, and 25/5 = 5.0.*

*Difficulty: medium*

---

##### Q12
> The high temperature, in degrees Fahrenheit, in a certain city was recorded for each of 5 days. Day: 1, 2, 3, 4, 5. High temperature: 81, 80, 81, 81, 82.

Over this 5-day period, which of the following is NOT equal to 81°F?

**A.** Median of the high temperatures 

  *This IS equal to 81, so it isn't the answer. Sorted, the five highs are 80, 81, 81, 81, 82; the middle (3rd) value is 81. A student who assumes the single 80 and single 82 must unbalance the median is treating it like a mean — the median, a positional statistic, doesn't respond to those two values at all.*

**B.** Mean of the high temperatures 

  *This IS equal to 81, so it isn't the answer. Sum: 81+80+81+81+82 = 405, and 405/5 = 81 exactly — the degree lost to the 80 is exactly offset by the degree gained from the 82. Assuming any deviation in the data must move the mean, without doing the arithmetic that shows the deviations cancel, is the trap here.*

**C.** Mode of the high temperatures 

  *This IS equal to 81, so it isn't the answer. 81 appears three times (days 1, 3, and 4), more than any other value, so it's the mode by definition. Expecting it to differ just because two other values (80, 82) also appear misses that the mode only needs the highest frequency, not exclusivity.*

**D.** Range of the high temperatures **(Correct)**

  *Correct. Range = maximum − minimum = 82 − 80 = 2, not 81. Every other statistic in this list happens to equal 81 for this specific data set — median, mean and mode all land on 81 — but the range measures spread, a completely different question, and nothing about this data set makes its spread equal to 81.*

*Difficulty: medium*

---

##### Q13
> The table above shows the number of students from two different high schools who completed summer internships in each of five years. High school — 2008, 2009, 2010, 2011, 2012: Foothill — 87, 80, 75, 76, 70. Valley — 44, 54, 65, 76, 82. No student attended both schools.

Which of the following statements are true about the number of students who completed summer internships for the 5 years shown? I. The mean number from Foothill High School is greater than the mean number from Valley High School. II. The median number from Foothill High School is greater than the median number from Valley High School.

**A.** I only 

  *This misses that the median comparison also holds. Sorted, Foothill's values are 70, 75, 76, 80, 87 (median 76) and Valley's are 44, 54, 65, 76, 82 (median 65) — 76 > 65, so statement II is true as well, not just I.*

**B.** II only 

  *This misses that the mean comparison also holds. Foothill's recent decline (76, then 70 in the last two years) might suggest its mean has fallen below Valley's, but the sum still favors Foothill decisively: mean Foothill = 388/5 = 77.6 versus mean Valley = 321/5 = 64.2.*

**C.** I and II **(Correct)**

  *Correct. Mean Foothill: (87+80+75+76+70)/5 = 388/5 = 77.6. Mean Valley: (44+54+65+76+82)/5 = 321/5 = 64.2 — Foothill's mean is greater (statement I true). Median Foothill: sorted 70, 75, 76, 80, 87, median 76. Median Valley: sorted 44, 54, 65, 76, 82, median 65 — Foothill's median is greater too (statement II true).*

**D.** Neither I nor II 

  *This assumes that because the combined totals show the two schools converging over the five years (Valley's individual numbers climbing toward Foothill's), the comparison must have reversed or vanished — without computing either statistic directly from the two data rows. Both the mean and the median still clearly favor Foothill.*

*Difficulty: hard*

---

##### Q14
> A bar graph shows the number of each type of monkey in a sanctuary, read against a y-axis from 0 to 12: mandrill 5, baboon 7, pygmy marmoset 8, bonnet macaque 9, vervet 11.

How many more vervets are in this sanctuary than mandrills?

**A.** 11 

  *This reports the vervet count by itself (11) instead of the difference between the vervet and mandrill counts.*

**B.** 6 **(Correct)**

  *Correct. Vervets (11) minus mandrills (5): 11 − 5 = 6.*

**C.** 5 

  *This reports the mandrill count by itself (5) instead of the difference between the two counts.*

**D.** 3 

  *This subtracts the wrong comparison animal: vervets (11) minus pygmy marmosets (8) gives 3, but the question asks about the difference between vervets and mandrills, not pygmy marmosets.*

*Difficulty: easy*

---

##### Q15
> In April, there were 43 volunteers in a cleanup project. Each volunteer was asked to choose a small gift labeled A, B, C, or D. A bar graph shows the number of volunteers who chose each gift, read against a y-axis from 0 to 20: gift A 14, gift B 8, gift C 18, gift D 3.

How many volunteers chose gift C?

**A.** 3 

  *This reads gift D's bar instead of gift C's.*

**B.** 8 

  *This reads gift B's bar instead of gift C's.*

**C.** 14 

  *This reads gift A's bar instead of gift C's.*

**D.** 18 **(Correct)**

  *Correct. Gift C's bar reaches 18 on the y-axis, and 14 + 8 + 18 + 3 = 43 volunteers total, matching the count given in the problem.*

*Difficulty: easy*

---

##### Q16
> A list of 9 data values is shown: 4, 4, 4, 4, 8, 8, 8, 13, 13.

Which frequency table correctly represents the data listed?

**A.** Number 4 → Frequency 4; Number 8 → Frequency 3; Number 13 → Frequency 2 **(Correct)**

  *Correct. 4 appears four times, 8 appears three times, and 13 appears twice in the list — exactly what a frequency table records: each distinct value paired with how many times it occurs.*

**B.** Number 4 → Frequency 4; Number 3 → Frequency 8; Number 2 → Frequency 13 

  *This table lists 4, 3, 2 as the data "Numbers" and 4, 8, 13 as their frequencies — backward. 3 and 2 never appear as values in the original list at all; they're the correct frequencies of 8 and 13, misplaced into the Number column.*

**C.** Number 4 → Frequency 16; Number 8 → Frequency 24; Number 13 → Frequency 26 

  *Each frequency here is value × its true frequency (4×4=16, 8×3=24, 13×2=26) — the total contribution of that value to the data set's sum, not a count of occurrences. A frequency table's Frequency column counts occurrences; it never multiplies the value by anything.*

**D.** Number 16 → Frequency 4; Number 24 → Frequency 8; Number 26 → Frequency 13 

  *This takes choice C's already-wrong products (16, 24, 26) and relabels them as the data VALUES, while the true frequencies (4, 8, 13) get demoted to the Frequency column — two layers of the same error stacked together.*

*Difficulty: medium*

---

##### Q17
> The data shown: 71, 72, 73, 76, 77, 79, 83, 87, 93.

What is the median of the data shown?

**A.** 71 

  *This reports the minimum value instead of the median.*

**B.** 77 **(Correct)**

  *Correct. With 9 values, the median is the (9+1)/2 = 5th value once sorted. The list is already sorted, so the 5th value is 77.*

**C.** 78 

  *This averages the 5th and 6th values (77 and 79) as though n = 9 were even and needed two middle values averaged — but with an odd count, there's a single true middle value, the 5th, which is 77 alone.*

**D.** 79 

  *This reports the 6th value instead of the 5th — an off-by-one slip in counting to the middle position.*

*Difficulty: easy*

---

##### Q18
> A group of students voted on five after-school activities. A bar graph shows the number of students who voted for each of the five activities, read against a y-axis from 0 to 50: activity 1 about 30, activity 2 about 31, activity 3 about 39, activity 4 about 44, activity 5 about 48.

How many students chose activity 3?

**A.** 25 

  *This reads activity 1's bar (which sits just below the 30 line) instead of activity 3's, and additionally misjudges its height against the wrong gridline.*

**B.** 39 **(Correct)**

  *Correct. Activity 3's bar reaches approximately 39 on the y-axis.*

**C.** 48 

  *This reads activity 5's bar (the tallest) instead of activity 3's.*

**D.** 50 

  *This reads the axis's top gridline label (50) instead of any actual bar height, mistaking the scale's maximum for a data value.*

*Difficulty: easy*

---

##### Q19
> A bar graph shows the distribution of the number of students from one school who were born in one of four months, read against a y-axis from 0 to 70: July 40, August 50, September 66, October 52.

How many more students were born in August than were born in July?

**A.** 90 

  *This adds the two counts (50 + 40 = 90) instead of subtracting them. "How many more" asks for a difference, not a sum.*

**B.** 50 

  *This reports August's count by itself instead of the difference between August and July.*

**C.** 40 

  *This reports July's count by itself instead of the difference between August and July.*

**D.** 10 **(Correct)**

  *Correct. August (50) minus July (40): 50 − 40 = 10.*

*Difficulty: easy*

---

##### Q20
> The table above shows the distribution of ages of the 20 students enrolled in a college class. Age — Frequency: 18—6, 19—5, 20—4, 21—2, 22—1, 23—1, 30—1.

Which of the following gives the correct order of the mean, median, and mode of the ages?

**A.** mode < median < mean **(Correct)**

  *Correct. Mode: 18 is the most frequent age (6 students). Median: 20 values, so the median is the average of the 10th and 11th sorted values — cumulative counts put ages 19 at positions 7–11, so both the 10th and 11th land on 19, giving a median of 19. Mean: (18×6 + 19×5 + 20×4 + 21×2 + 22×1 + 23×1 + 30×1)/20 = 400/20 = 20. So 18 < 19 < 20.*

**B.** mode < mean < median 

  *This swaps the mean and the median. The single 30-year-old outlier pulls the mean (20) above the median (19), not the other way around — the median is resistant to that one extreme value, while the mean, built from the total, absorbs it fully.*

**C.** median < mode < mean 

  *This places the mode between the median and the mean, but the mode (18, the most frequent age) is actually the SMALLEST of the three — the most common age also anchors the young end of this distribution, not its middle.*

**D.** mean < mode < median 

  *This has both comparisons backward. The single 30-year-old outlier pulls the mean UP past both the median and the mode, not down below them — a lone high value in an otherwise young class always raises the mean more than it raises the median.*

*Difficulty: hard*

---

##### Q21
> The results of two independent surveys are shown in the table below. Men's Height — Group, Sample size, Mean (centimeters), Standard deviation (centimeters): Group A, 2,500, 186, 12.5. Group B, 2,500, 186, 19.1.

Which statement is true based on the table?

**A.** The Group A data set was identical to the Group B data set. 

  *Equal sample size and equal mean say nothing about whether the two data sets are identical. Group B's standard deviation (19.1) is well above Group A's (12.5), so the two groups' heights are distributed very differently even though they average to the same height.*

**B.** Group B contained the tallest participant. 

  *A larger standard deviation describes Group B's values as more spread out on average, not that Group B necessarily contains the single most extreme individual. Group A, despite its tighter spread, could still include one unusually tall outlier that Group B's more evenly spread heights never reach.*

**C.** The heights of the men in Group B had a larger spread than the heights of the men in Group A. **(Correct)**

  *Correct. Standard deviation measures spread, and Group B's (19.1 cm) is larger than Group A's (12.5 cm), so Group B's heights are more spread out around their shared mean of 186 cm.*

**D.** The median height of Group B is larger than the median height of Group A. 

  *Nothing in the table gives the median of either group — only the mean, sample size, and standard deviation are reported. Equal means don't imply equal (or comparable) medians, and standard deviation says nothing about which side of the mean a distribution leans toward.*

*Difficulty: medium*

---

##### Q22
> The five numbers 15, 14, 18, 17, x have a mean equal to their median.

Which of the following is NOT a possible value of x?

**A.** 6 **(Correct)**

  *Correct. If x = 6, it becomes the new minimum, so the sorted order is 6, 14, 15, 17, 18 and the median is 15. But the mean would be (64 + 6)/5 = 70/5 = 14, and 14 ≠ 15 — the mean and median don't match for x = 6, so it can't be the value described.*

**B.** 11 

  *This IS possible, so it isn't the answer. With x = 11 as the new minimum, the sorted order is 11, 14, 15, 17, 18, giving a median of 15. The mean is (64 + 11)/5 = 75/5 = 15 too — mean and median agree, which is exactly why 11 works.*

**C.** 16 

  *This IS possible, so it isn't the answer. With x = 16 slotting into the middle of the sorted order (14, 15, 16, 17, 18), x itself becomes the median, 16. The mean is (64 + 16)/5 = 80/5 = 16, matching. This is the most intuitive case to check, which may be why students expect it to be the ONLY solution and misjudge one of the edge cases instead.*

**D.** 21 

  *This IS possible, so it isn't the answer. With x = 21 as the new maximum, the sorted order is 14, 15, 17, 18, 21, giving a median of 17. The mean is (64 + 21)/5 = 85/5 = 17, matching. This is the mirror image of the x = 11 case — a value large enough to become the new maximum can also satisfy mean = median.*

*Difficulty: sat-hardest*

---

##### Q23
> In the table above, Melissa recorded the price of one gallon of regular gas from five different local gas stations on the same day. Station 1–5 prices: $3.699, $3.609, $3.729, $3.679, $3.729.

What is the median of the gas prices Melissa recorded?

**A.** $3.679 

  *This reports the 2nd sorted value instead of the 3rd. Sorted, the prices are 3.609, 3.679, 3.699, 3.729, 3.729 — an off-by-one slip lands on the 2nd value instead of the true middle one.*

**B.** $3.689 

  *This averages the 2nd and 3rd sorted values (3.679 and 3.699 → 3.689) as though there were an even number of prices needing two middle values averaged, when there are 5 prices and a single true middle value.*

**C.** $3.699 **(Correct)**

  *Correct. Sorted, the five prices are 3.609, 3.679, 3.699, 3.729, 3.729. With 5 values, the median is the 3rd, which is 3.699.*

**D.** $3.729 

  *This reports the maximum (which happens to tie across two stations) instead of the median.*

*Difficulty: easy*

---

##### Q24
For which of the following data sets is the mean greater than the median?

**A.** 5, 5, 5, 5, 5, 5, 5, 5, 5 

  *Every value is identical, so mean and median are both exactly 5 — no spread at all means there's no gap between the two to compare.*

**B.** 0, 10, 20, 30, 40, 50, 60, 70, 80 

  *This is a perfectly symmetric, evenly spaced set, so mean and median coincide exactly at 40. A symmetric set — no matter how spread out — always has mean equal to median; skew, not spread, is what separates them.*

**C.** 2, 4, 8, 16, 32, 64, 128, 256, 512 **(Correct)**

  *Correct. This set doubles at every step, so it's heavily right-skewed: median = 32 (the middle of the nine sorted values), but mean = 1,022/9 ≈ 113.6, dragged far above the median by 256 and 512. A handful of very large values raise the total enormously while occupying only a couple of sorted positions.*

**D.** 7, 107, 107, 207, 207, 207, 307, 307, 307 

  *This set is actually left-skewed relative to its median, not right-skewed: median = 207 (the middle value), but mean = 1,763/9 ≈ 195.9, which is LESS than the median — the single low value of 7 pulls the mean down. This is the mirror image of what the question asks for.*

*Difficulty: hard*

---

##### Q25
The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?

**A.** Mean 

  *The mean is total ÷ count, and correcting the lowest horse's weight downward by 10 pounds reduces the total by 10, which changes the mean by 10/15 ≈ 0.67 pounds — small, but not zero.*

**B.** Median **(Correct)**

  *Correct. The horse with the lowest reported weight was already the minimum; making it 10 pounds lighter keeps it the minimum — its rank in the sorted order doesn't change. The median depends only on which value sits in the middle position, and that position is still occupied by the same horse it was before.*

**C.** Range 

  *Range = maximum − minimum, and the minimum is exactly the value that got corrected — it drops by 10 pounds, so the range grows by 10 pounds. A statistic built directly from the extreme that changed cannot stay fixed.*

**D.** Standard deviation 

  *The corrected horse's weight is now farther from the mean than it was before, which increases its squared deviation and therefore the standard deviation — a statistic built from every value's distance to the mean cannot stay the same when one of those distances grows.*

*Difficulty: hard*

---

##### Q26
> Data set A: 5, 5, 5, 5, 5, 5, 5, 5, 5. Data set B: 5, 5, 5, 5, 5, 5, 5, 5, 5, 100.

Which of the following statements about the means and medians of data set A and data set B is true?

**A.** Only the means are different. **(Correct)**

  *Correct. Mean A = 5 (all values are 5). Mean B = (9×5 + 100)/10 = 145/10 = 14.5 — very different, because the single 100 enters the total at full size. Median A = 5 (all values identical). Median B: ten sorted values are 5,5,5,5,5,5,5,5,5,100, and the median is the average of the 5th and 6th values — both 5 — so median B = 5 too. The outlier changes the mean but the median absorbs it without moving.*

**B.** Only the medians are different. 

  *This reverses which statistic the outlier affects. The median is exactly the one that stays fixed here (5 in both sets, since the added 100 only affects the very last sorted position), while the mean is the one that moves, from 5 up to 14.5.*

**C.** Both the means and the medians are different. 

  *The mean genuinely differs (5 vs. 14.5), but the median does not — both data sets have a median of exactly 5, because in both cases the middle position (or middle pair, for B's even count of 10) is occupied entirely by 5s.*

**D.** Neither the means nor the medians are different. 

  *The median is indeed unchanged, but the mean is not — adding a single value of 100 to nine 5s nearly triples the mean, from 5 to 14.5, because the mean is a total divided by a count and 100 dominates that total.*

*Difficulty: medium*

---

##### Q27
A fish hatchery has three tanks for holding fish before they are introduced into the wild. Ten fish weighing less than 5 ounces are placed in tank A. Eleven fish weighing at least 5 ounces but no more than 13 ounces are placed in tank B. Twelve fish weighing more than 13 ounces are placed in tank C. Which of the following could be the median of the weights, in ounces, of these 33 fish?

**A.** 4.5 

  *4.5 ounces falls in Tank A's range (fish weighing less than 5 ounces), but the 17th of 33 sorted weights — the median's position — falls among the 11 fish in Tank B (positions 11 through 21), all of which weigh at least 5 ounces. The median can't be a Tank A weight, no matter how the individual weights are distributed.*

**B.** 8 **(Correct)**

  *Correct. With 33 fish, the median is the 17th value once sorted. Tank A supplies positions 1–10, Tank B supplies positions 11–21, and Tank C supplies positions 22–33 — so the 17th position falls inside Tank B, meaning the median must be some weight between 5 and 13 ounces inclusive. 8 ounces fits; the other three choices don't.*

**C.** 13.5 

  *13.5 ounces falls in Tank C's range (fish weighing more than 13 ounces), but Tank C only supplies positions 22 through 33 — the median's position, 17th, falls well before that, inside Tank B's block.*

**D.** 15 

  *15 ounces is even further into Tank C's range than 13.5 is, making the same error more extreme — the 17th of 33 sorted positions falls squarely inside Tank B, not Tank C.*

*Difficulty: hard*

---

##### Q28
> Two histograms summarize the distributions of number of units sold, in thousands, for Company A and Company B, both plotted against the same horizontal axis from 15 to 50 (in thousands of units). Company A's frequency is concentrated in two or three tall bars near the center of the range, roughly 25,000 to 40,000 units, with almost nothing in the bars near either end. Company B's frequency is spread across nearly every bar in the range, with a sizeable share in the bars near both extremes (15,000–20,000 and 45,000–50,000) and noticeably less in the middle bars.

Which statement best compares the standard deviations of number of units sold for these companies?

**A.** The standard deviation of number of units sold for company A is less than the standard deviation of number of units sold for company B. **(Correct)**

  *Correct. Company A's values cluster tightly in the middle of the range, while Company B's values are spread across the entire range, with a large share sitting at the low and high extremes rather than the middle. A distribution with values pushed out toward its extremes has a larger typical distance from its mean — a larger standard deviation — than one clustered near its center.*

**B.** The standard deviation of number of units sold for company A is greater than the standard deviation of number of units sold for company B. 

  *This reverses the comparison. Company A's histogram is the tightly clustered one — most of its frequency sits in two or three adjacent bars near the center — while Company B's frequency is distributed thinly across nearly every bar, including the extreme ones. Concentration lowers standard deviation; spread raises it, and the two companies have been swapped.*

**C.** The standard deviation of number of units sold for company A is equal to the standard deviation of number of units sold for company B. 

  *The two histograms cover the same horizontal range, which might suggest equal spread, but the range only reflects the two extreme bars. Company A's frequency is concentrated near the center; Company B's is distributed across the full width, including bars at both ends that Company A's histogram barely touches. Same range does not mean same standard deviation.*

**D.** There is not enough information to compare the standard deviations. 

  *A histogram doesn't hand over an exact standard deviation, but it doesn't need to for a comparison — the shapes alone answer the question. Company A's frequency bunches near the center of the range; Company B's spreads toward both extremes. That visual difference is sufficient to rank the two standard deviations without computing either one exactly.*

*Difficulty: hard*

---

##### Q29
> Data set A has 15 values and is represented by a dot plot with values from 22 to 26: 22 appears 5 times, 23 appears 4 times, 24 appears 3 times, 25 appears 2 times, 26 appears 1 time. Data set B is created by adding 46 to each of the values in data set A.

Which of the following correctly compares the medians and the ranges of data sets A and B?

**A.** The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A. **(Correct)**

  *Correct. Adding 46 to every value in data set A shifts the whole distribution up by 46, so the median — a specific data value — rises by 46 too (median A = 23, from the 8th of 15 sorted values; median B = 69). But every internal distance stays exactly the same after a uniform shift, so the range, which depends only on the gap between the largest and smallest values, is unchanged: range A = range B = 26 − 22 = 4.*

**B.** The median of data set B is greater than the median of data set A, and the range of data set B is greater than the range of data set A. 

  *The median comparison is right, but adding the same constant to every value can't change the range — it slides the minimum and maximum up by the identical amount (26 becomes 72, 22 becomes 68), so their difference, 4, survives untouched.*

**C.** The median of data set B is equal to the median of data set A, and the range of data set B is greater than the range of data set A. 

  *Both halves are backward. Adding 46 to every value necessarily adds 46 to whichever value occupies the median position too — the median cannot stay fixed under a uniform shift. And the range, which only depends on the gap between extremes, is the one quantity a shift never changes.*

**D.** The median of data set B is equal to the median of data set A, and the range of data set B is equal to the range of data set A. 

  *The range half is correct — a uniform shift does leave the range unchanged — but the median half is not. Data set B's values are all 46 more than data set A's corresponding values, so whichever value sits in the middle position is also 46 more than data set A's, moving the median from 23 to 69, not leaving it fixed.*

*Difficulty: medium*

---

##### Q30
A data set of 27 different numbers has a mean of 33 and a median of 33. A new data set is created by adding 7 to each number in the original data set that is greater than the median and subtracting 7 from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

**A.** Median 

  *The median doesn't change. The transformation preserves ranks: every value that was above 33 gets pushed even further above (still above the middle value), and every value below 33 gets pushed even further below (still below it) — and the value sitting exactly at 33 is touched by neither rule. Whoever occupied the middle rank before still occupies it after, so the median is still 33 in both data sets — the SAME in both, so it isn't the answer.*

**B.** Mean 

  *With 27 values and a mean equal to the median (33), exactly 13 values sit above 33 and 13 sit below (the 27th value is 33 itself). Adding 7 to each of the 13 above and subtracting 7 from each of the 13 below adds 13×7 = 91 and subtracts 13×7 = 91 — the two exactly cancel, leaving the sum, and therefore the mean, unchanged. Mean is the SAME in both, so it isn't the answer.*

**C.** Sum of the numbers 

  *The sum is mean × count, and since the mean doesn't change (the +7s and −7s cancel exactly, 13 of each), the sum doesn't change either — both equal 27 × 33 = 891. Sum is the SAME in both, so it isn't the answer.*

**D.** Standard deviation **(Correct)**

  *Correct. Even though the mean and median stay at 33, every value that moved is now FARTHER from that shared mean than it was before — the 13 values above 33 are pushed further above, and the 13 below are pushed further below, so every one of their squared deviations grows. Standard deviation is built from those deviations, so it increases, even while the two measures of centre stay perfectly still.*

*Difficulty: sat-hardest*

---

##### Q31
> The frequency distribution above summarizes a set of data, where a is a positive integer. Value — Frequency: 1—a, 2—2a, 3—3a, 4—2a, 5—a.

How much greater is the mean of the set of data than the median?

**A.** 0 **(Correct)**

  *Correct — the difference is 0. This frequency table is symmetric around the value 3: the frequencies a, 2a, 3a, 2a, a mirror each other on either side of the middle value. Mean: (1·a + 2·2a + 3·3a + 4·2a + 5·a)/(9a) = 27a/9a = 3. Median: with 9a total values, the middle position falls inside value 3's block for any positive integer a, so the median is also 3. A perfectly symmetric distribution always has mean = median, whatever the actual value of a is.*

**B.** 1 

  *This likely comes from noticing the frequencies aren't identical (a, 2a, 3a, 2a, a differ from row to row) and assuming any difference among the FREQUENCIES must create a gap between mean and median, without checking that the frequency pattern itself is symmetric — mirrored a-2a-3a-2a-a — even though the individual counts differ. Symmetry of shape, not equal frequencies, is what keeps mean and median together.*

**C.** 2 

  *This may come from comparing an extreme value (1 or 5) to the central value (3) and reporting that gap (3−1=2 or 5−3=2) as if it were the mean-minus-median difference, rather than actually computing either statistic from the table.*

**D.** 3 

  *This reports the mean (or the median) itself — 3 — as if it were the DIFFERENCE between the two, rather than computing mean minus median. Since both statistics equal 3, their difference is 0, not 3.*

*Difficulty: hard*

---

##### Q32
> Two different teams consisting of 10 members each ran in a race. Each member's completion time of the race was recorded. The mean of the completion times for each team was calculated and is shown below. Team A: 3.41 minutes. Team B: 3.79 minutes.

Which of the following MUST be true? I. Every member of team A completed the race in less time than every member of team B. II. The median time it took the members of team B to complete the race is greater than the median time it took the members of team A to complete the race. III. There is at least one member of team B who took more time to complete the race than some member of team A.

**A.** III only **(Correct)**

  *Correct — III only. If every member of team B were at least as fast as every member of team A, then B's slowest time would still be no worse than A's fastest, which would force B's average to be no greater than A's average. But B's mean (3.79) is greater than A's mean (3.41), so that can't be the case — at least one B member must have taken longer than at least one A member. That's exactly statement III, and it's the only one of the three a difference in means can guarantee: I claims something about every pairing, and II claims something about medians, neither of which the mean alone determines.*

**B.** I and III only 

  *III is correctly identified, but statement I overreaches: a lower team mean does not mean every single member of team A beat every single member of team B. Team A could have one unusually slow runner and team B one unusually fast one, with individual times overlapping heavily, while the team averages still come out 3.41 versus 3.79.*

**C.** II and III only 

  *III is correctly identified, but statement II claims something about medians that a comparison of means can't guarantee. Mean and median can disagree — a team's mean could be pulled up by one very slow runner while its median (the typical runner) is actually faster than the other team's median. Without more information about the shape of each team's times, the median comparison isn't settled.*

**D.** I, II, and III 

  *This assumes a gap in the team averages settles every individual comparison AND the median comparison, when in fact a difference in means only forces the weaker guarantee in statement III (that at least one pairing goes the "wrong" way). Neither the "every member" claim (I) nor the median claim (II) follows just from knowing the two means.*

*Difficulty: hard*

---

##### Q33
The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

**A.** 20 

  *Uses the wrong count when finding the total for the remaining players: multiplies the new mean by 8 instead of 7 (12 × 8 = 96), then subtracts from the correct total of all 8 players' scores (116 − 96 = 20). The remaining group has only 7 players once the highest score is removed, not 8.*

**B.** 24 

  *Doubles the new mean (2 × 12 = 24) as a quick estimate for how large the removed score must be, without recovering either total. Doubling has no mathematical basis here — the actual gap depends on both means and both group sizes, not just the smaller mean.*

**C.** 32 **(Correct)**

  *Correct. The total score for all 8 players is 14.5 × 8 = 116. After the highest score is removed, the total for the remaining 7 players is 12 × 7 = 84. The removed (highest) score is the difference: 116 − 84 = 32.*

**D.** 36 

  *Rounds the mean of 8 players up from 14.5 to 15 before multiplying by 8 (15 × 8 = 120), then subtracts the correct total for the remaining 7 players (84), landing on 36 instead of 32 — a rounding slip applied before the multiplication rather than after.*

*Difficulty: hard*

---

##### Q34
> Each of the following frequency tables represents a data set. Table A — Value, Frequency: 70—4, 80—5, 90—6, 100—7. Table B — Value, Frequency: 70—6, 80—6, 90—6, 100—6. Table C — Value, Frequency: 70—7, 80—6, 90—6, 100—7. Table D — Value, Frequency: 70—8, 80—5, 90—5, 100—8.

Which data set has the greatest mean?

**A.** A **(Correct)**

  *Correct. Table A skews its frequency toward the higher values — 100 has the highest frequency (7) of any value in this table, more than 70's frequency (4). Total: 4+5+6+7 = 22 values summing to 70(4)+80(5)+90(6)+100(7) = 1,920, giving a mean of 1,920/22 ≈ 87.3 — noticeably higher than the other three tables, each of which comes out to exactly 85.*

**B.** B 

  *This table is perfectly uniform — every value has the same frequency (6) — so its mean is simply the plain average of 70, 80, 90 and 100: (70+80+90+100)/4 = 85. A uniform frequency table can't beat a table like A that deliberately loads extra weight onto its highest value.*

**C.** C 

  *This table is symmetric — 70 and 100 have matching frequencies (7 each), and 80 and 90 match too (6 each) — so the extra weight at the low end exactly cancels the extra weight at the high end. Its mean comes out to exactly 85, same as table B, because symmetric extra weight doesn't shift the mean at all; table A's advantage is that its extra weight favors 100 without a matching favor to 70.*

**D.** D 

  *Also symmetric — 70 and 100 both carry the heaviest frequency (8), balancing each other out — so despite having the most lopsided-looking frequencies of the four tables, its mean is still exactly 85, identical to tables B and C. Heavier frequencies at BOTH ends cancel; table A's advantage comes from loading extra weight onto only the high end.*

*Difficulty: medium*

---

##### Q35
The mean amount of time that the 20 employees of a construction company have worked for the company is 6.7 years. After one of the employees leaves the company, the mean amount of time that the remaining employees have worked for the company is reduced to 6.25 years. How many years did the employee who left work for the company?

**A.** 0.45 

  *Reports the drop in the mean itself (6.7 − 6.25 = 0.45) rather than recovering the actual tenure of the employee who left. The mean falling by 0.45 years is a consequence of that employee's tenure, not a stand-in for it — recovering the real value requires going back to the totals.*

**B.** 2.30 

  *Swaps which count goes with which mean: computes the original total using 19 employees instead of 20 (6.7 × 19 = 127.3) and the remaining total using 20 employees instead of 19 (6.25 × 20 = 125), then subtracts: 127.3 − 125 = 2.30. Both counts have been assigned to the wrong mean.*

**C.** 9.00 

  *Uses 20 — the original number of employees — for both totals, instead of 19 for the remaining group: 6.25 × 20 = 125 (should be 6.25 × 19 = 118.75), then 134 − 125 = 9.00. Once an employee leaves, the remaining group has only 19 members, not 20.*

**D.** 15.25 **(Correct)**

  *Correct. The total years of service for all 20 employees is 6.7 × 20 = 134. After one employee leaves, the total for the remaining 19 employees is 6.25 × 19 = 118.75. The employee who left accounts for the difference: 134 − 118.75 = 15.25 years.*

*Difficulty: hard*

---

##### Q36
> Data set F consists of 55 integers between 170 and 290. Data set G consists of all the integers in data set F as well as the integer 10.

Which of the following must be less for data set F than for data set G? I. The mean. II. The median.

**A.** I only 

  *This has the direction backward. Data set G is F with one very small value (10) appended, far below F's range of 170–290. That single low value drags G's total down relative to F's average value, so G's mean is LESS than F's mean, not the other way around — F's mean must be greater than G's, not less.*

**B.** II only 

  *This also has the direction backward. Adding 10 as a new minimum shifts every one of F's original values up by one rank in the sorted order, so G's median ends up being the average of F's 27th and 28th sorted values — both at or below F's own median (its 28th value). G's median can only be less than or equal to F's, never greater, so F's median is not less than G's.*

**C.** I and II 

  *Both directions are reversed here. A single very low value added to a tight cluster of 55 larger values pulls both the mean and the median of the combined set DOWN, not up — so it's data set F, the one without the extreme low value, that has the larger mean and the larger (or equal) median, not the smaller one.*

**D.** Neither I nor II **(Correct)**

  *Correct — neither must be less for F. Data set G is F with an extreme low value (10) appended. That single small value pulls G's total down relative to F's, making G's mean LESS than F's mean — the reverse of what's asked. And because 10 becomes the new minimum, it shifts every original value up by one rank, so G's median becomes the average of F's 27th and 28th (median) values — at or below F's own median, never above it. F's statistics are the larger ones here, not the smaller ones.*

*Difficulty: hard*

---

##### Q37
> A survey was given to residents of all 50 states asking if they had earned a bachelor's degree or higher. Percent of Residents Who Earned a Bachelor's Degree or Higher — State, Percent of residents: A—21.9%, B—27.9%, C—25.9%, D—19.5%, E—30.1%, F—36.4%, G—35.5%. The median percent of residents who earned a bachelor's degree or higher for all 50 states was 26.95%.

What is the difference between the median percent of residents who earned a bachelor's degree or higher for these 7 states and the median for all 50 states?

**A.** 0.05% 

  *Misreads the population median given in the problem — 26.95% — as 27.95% (a single-digit slip, 6 read as 7), then computes 27.9 − 27.95 = −0.05, taking the absolute value to get 0.05. The median of the 7 states (27.9%) is correct; the population figure it's compared against is not.*

**B.** 0.95% **(Correct)**

  *Correct. Sorted, the seven percentages are 19.5, 21.9, 25.9, 27.9, 30.1, 35.5, 36.4 — with 7 values, the median is the 4th, which is 27.9%. Compared to the population median of 26.95%, the difference is 27.9 − 26.95 = 0.95 percentage points.*

**C.** 1.22% 

  *Computes the MEAN of the seven percentages instead of the median: (21.9+27.9+25.9+19.5+30.1+36.4+35.5)/7 = 197.2/7 ≈ 28.17, then 28.17 − 26.95 ≈ 1.22. The problem asks specifically about the median, which for these 7 sorted values is 27.9%, not the mean.*

**D.** 7.45% 

  *Subtracts the MINIMUM of the seven values (19.5%, for State D) from the population median instead of subtracting the seven states' own median: 26.95 − 19.5 = 7.45. The minimum is not the median — the median of the 7 states is 27.9%, the 4th value once they're sorted.*

*Difficulty: medium*

---

##### Q38
> A dot plot represents a data set of the number of bursts for 13 eruptions of a steam vent, with values from 1 to 5: 1 burst occurs 5 times, 2 bursts occurs 4 times, 3 bursts occurs 2 times, 4 bursts occurs 1 time, 5 bursts occurs 1 time.

If an additional eruption with 11 bursts is added to this data set to create a new data set of 14 eruptions, which of the following measures will be greater for the new data set than for the original data set? I. The median number of bursts. II. The mean number of bursts.

**A.** I and II 

  *The mean genuinely increases, but the median does not — with 13 original values, the median is the 7th of the sorted list (2 bursts), and inserting 11 as a new 14th value (the new maximum) shifts what was the 7th and 8th values into the two middle slots of the new 14-value list, both of which are still 2. The median doesn't move at all; only the mean is correctly ruled in here.*

**B.** I only 

  *This gets exactly the wrong statistic. The mean rises, from 28/13 ≈ 2.15 to 39/14 ≈ 2.79, because the new value of 11 enters the total at full size. The median stays fixed at 2 — inserting one new maximum value doesn't move which value sits in the two middle positions of the sorted list, since both the 7th and 8th values (2 and 2) were already below where 11 lands.*

**C.** II only **(Correct)**

  *Correct. Original median (13 values, 7th sorted position): the cumulative counts put positions 1–5 at 1 burst, 6–9 at 2 bursts, so the 7th value is 2. New median (14 values, average of 7th and 8th): 11 is appended as the new maximum, so the sorted order below it is unchanged, and both the 7th and 8th values are still 2 — median stays at 2. Mean: original sum = 1(5)+2(4)+3(2)+4(1)+5(1) = 28, mean = 28/13 ≈ 2.15. New sum = 28+11 = 39, mean = 39/14 ≈ 2.79 — the mean rises because it absorbs the new value's full size; the median doesn't, because 11 only adds one new position at the very top.*

**D.** Neither I nor II 

  *The mean does rise. Appending 11 — a value more than twice the previous maximum of 5 — adds far more to the total (11) than it adds to the count (1 more data point), so the total-divided-by-count necessarily increases, from about 2.15 to about 2.79.*

*Difficulty: hard*

---

##### Q39
> Data set A and data set B each consist of 27 values. The table shows the frequencies of the values for each data set. Value — Data set A frequency, Data set B frequency: 30—2, 9. 34—4, 7. 38—5, 5. 42—7, 4. 46—9, 2.

Which of the following statements best compares the means of the two data sets?

**A.** The mean of data set A is greater than the mean of data set B. **(Correct)**

  *Correct. Data set A loads its heaviest frequencies onto the larger values (9 at 46, 7 at 42), while data set B loads its heaviest frequencies onto the smaller values (9 at 30, 7 at 34) — the two frequency columns are mirror images of each other. Sum A = 30(2)+34(4)+38(5)+42(7)+46(9) = 1,094, mean A = 1,094/27 ≈ 40.5. Sum B = 30(9)+34(7)+38(5)+42(4)+46(2) = 958, mean B = 958/27 ≈ 35.5. A's mean is higher because its frequency is weighted toward the high end.*

**B.** The mean of data set A is less than the mean of data set B. 

  *This has the comparison backward. Look at which value gets the highest frequency in each column: in data set A it's 46 (frequency 9, the LARGEST value in the table); in data set B it's 30 (frequency 9, the SMALLEST value). Weighting the largest value most heavily, as A does, raises a mean; weighting the smallest value most heavily, as B does, lowers it.*

**C.** The mean of data set A is equal to the mean of data set B. 

  *The two data sets share the same five values (30, 34, 38, 42, 46) and the same total count (27), which might suggest symmetry, but the frequency PATTERN is reversed, not repeated — data set A's frequencies (2,4,5,7,9) climb toward the high end while data set B's (9,7,5,4,2) climb toward the low end. Same values and same count isn't the same as same distribution; the two means differ by a full 5 points (about 40.5 vs about 35.5).*

**D.** There is not enough information to compare the means of the data sets. 

  *Every number needed is in the table: the five values, and both sets' frequencies for each, with counts confirmed to total 27 for each set. That's a complete frequency distribution for both A and B — enough to compute both means exactly (about 40.5 and about 35.5) rather than merely note that a comparison is impossible.*

*Difficulty: hard*

---

##### Q40
> Box plots summarize the masses, in kilograms, of two groups of gazelles, plotted on the same axis (about 20 to 32 kg). Group 1's entire box — including its median line — sits shifted toward the higher end of the axis relative to Group 2's box, which sits shifted toward the lower end.

Based on the box plots, which of the following statements must be true?

**A.** The mean mass of group 1 is greater than the mean mass of group 2. 

  *A box plot shows the five-number summary — minimum, quartiles, median, maximum — and nothing about the mean. Even though group 1's box does sit to the right of group 2's, that tells you about medians and quartiles, not about where either group's mean falls; a box plot can't support a claim about means at all.*

**B.** The mean mass of group 1 is less than the mean mass of group 2. 

  *Same problem as the first choice, in the opposite direction: a box plot never displays a mean, so no claim comparing means — greater, less, or equal — can be read off of one. Whatever the actual means are, this box plot doesn't show them.*

**C.** The median mass of group 1 is greater than the median mass of group 2. **(Correct)**

  *Correct. The line inside each box marks that group's median, and group 1's median line sits farther right along the mass axis than group 2's — group 1's whole box, in fact, sits shifted toward higher masses relative to group 2's. That's a direct, supported reading: the median mass of group 1 is greater than the median mass of group 2.*

**D.** The median mass of group 1 is less than the median mass of group 2. 

  *This reverses the one comparison the box plots actually support. Group 1's box — including its median line — sits to the right of group 2's along the mass axis, toward the higher end, not the lower end; the two box plots have been read in the wrong direction.*

*Difficulty: medium*

---

#### Ratios, rates, proportions and units (36 items)

##### Q1
For a person m miles from a flash of lightning, the length of the time interval from the moment the person sees the lightning to the moment the person hears the thunder is k seconds. The ratio of m to k can be estimated to be 1 to 5. According to this estimate, the person is how many miles from a flash of lightning if the time interval is 25 seconds?

**A.** 10 

  *This doubles the correct quotient (25 ÷ 5 = 5, then × 2), as though the timing needed a round-trip correction the way an echo or sonar problem would. Lightning is seen essentially instantly and the thunder travels the distance only once — there is no return trip to account for, so nothing in the problem licenses doubling the result.*

**B.** 9 

  *This treats the given ratio as a rough guideline to re-estimate rather than an exact value to use directly — rounding the 1-to-5 relationship down to something closer to 1-to-2.8 and dividing 25 by that instead of by 5. The ratio was already handed to you as the number to use; there's nothing left to approximate.*

**C.** 6 

  *This reads 'the ratio of m to k is 1 to 5' as m being 1 part of a 5-part whole (so k would be the remaining 4 parts), instead of m and k being directly compared 1 to 5. That gives k = 4m, so m = 25 ÷ 4 = 6.25, which rounds to 6 — a part-to-whole read of a ratio that was stated part-to-part.*

**D.** 5 **(Correct)**

  *Correct. The ratio m to k is 1 to 5, so m/k = 1/5, which means k = 5m. With k = 25, m = 25 ÷ 5 = 5. Check it against the ratio directly: 5 is to 25 as 1 is to 5. ✓*

*Difficulty: medium*

---

##### Q2
A group of monarch butterflies migrated from Chicago, Illinois, to Michoacán, Mexico, flying a total of 2,100 miles. It took a single butterfly in the group 120 days to travel this route one way. On average, how many miles did the butterfly travel per day?

**A.** 0.057 

  *This is the rate flipped upside down — 120 days ÷ 2,100 miles gives days per mile, not miles per day. The question asks how many miles per day, so miles has to end up on top.*

**B.** 0.729 

  *This finds the correct rate (2,100 ÷ 120 = 17.5 miles per day) and then divides by 24 again, as though converting further into miles per hour. The question asked for miles per day, and 17.5 already was that answer before the extra conversion.*

**C.** 17.5 **(Correct)**

  *Correct. Total distance divided by total time: 2,100 miles ÷ 120 days = 17.5 miles per day. Check it: 17.5 miles/day × 120 days = 2,100 miles. ✓*

**D.** 24 

  *This comes from rounding 120 days down to a cleaner 'about 90 days' before dividing (2,100 ÷ 90 ≈ 23.3, rounded to 24) instead of dividing by the 120 the problem actually gives. Rounding the given number before you compute throws away the value you were supposed to use.*

*Difficulty: easy*

---

##### Q3
In a box of pens, the ratio of black pens to red pens is 8 to 1. There are 40 black pens in the box. How many red pens are in the box?

**A.** 5 **(Correct)**

  *Correct. Black to red is 8 to 1, so black pens ÷ 8 gives the number of red pens: 40 ÷ 8 = 5. Check it: 40 to 5 reduces to 8 to 1. ✓*

**B.** 8 

  *This restates one of the ratio's own numbers as if it were the answer, without ever dividing 40 by it. The 8 is the scale factor, not the count of red pens.*

**C.** 40 

  *This repeats the given black-pen count instead of computing red pens, effectively treating the ratio as 1 to 1 and ignoring the 8-to-1 relationship entirely.*

**D.** 320 

  *This multiplies 40 by 8 instead of dividing — the direction a solver would use if the ratio of black to red were 1 to 8 rather than 8 to 1. Black pens are the larger group here, so red pens should come out smaller than 40, not larger.*

*Difficulty: easy*

---

##### Q4
The population density of Worthington is 290 people per square mile. Worthington has a population of 92,800 people. What is the area, in square miles, of Worthington?

**A.** 102,400 

  *This is the correct area (320) squared — 320² = 102,400. Population density carries the word 'square,' but that word describes the unit the area is already measured in; it isn't an instruction to square the area itself a second time.*

**B.** 93,090 

  *This adds the population and the density together (92,800 + 290 = 93,090) instead of dividing one by the other. Adding a headcount to a rate produces a number with no meaningful unit at all.*

**C.** 320 **(Correct)**

  *Correct. Area = population ÷ density = 92,800 ÷ 290 = 320 square miles. Check it: 320 square miles × 290 people per square mile = 92,800 people. ✓*

**D.** 32 

  *This divides by 2,900 instead of 290 — an extra zero slipped into the denominator. The result is off from the correct area by exactly a factor of 10, the fingerprint of a misplaced decimal rather than a wrong method.*

*Difficulty: medium*

---

##### Q5
A wind turbine completes 900 revolutions in 50 minutes. At this rate, how many revolutions per minute does this turbine complete?

**A.** 18 **(Correct)**

  *Correct. Revolutions per minute is revolutions divided by minutes: 900 ÷ 50 = 18. Check it: 18 revolutions per minute × 50 minutes = 900 revolutions. ✓*

**B.** 850 

  *This subtracts 50 from 900 instead of dividing. Subtracting two quantities measured in different units (revolutions and minutes) doesn't produce a rate in either unit — it produces a number with no meaningful unit at all.*

**C.** 950 

  *This adds 50 to 900 instead of dividing — the same unit mismatch as the subtraction error, just in the other direction.*

**D.** 1,400 

  *This multiplies the two given numbers (900 × 50 = 45,000) instead of dividing, which produces a quantity in revolution-minutes rather than revolutions per minute — the wrong operation and the wrong unit at once, and nowhere near the actual per-minute rate.*

*Difficulty: easy*

---

##### Q6
In the table below, x and y take the paired values (1, 4), (3, 12), (5, 20), and (40, k), and the ratio of y to x for each ordered pair is constant. What is the value of k?

**A.** 28 

  *This treats the table as a sequence of steps rather than a rule tied to x's actual value — each listed row adds 8 to y as x increases by 2 (4, 12, 20), so this jumps from the last row (20) by one more step of 8 to get 28, instead of recognizing that x = 40 is far beyond one more step from x = 5.*

**B.** 36 

  *This subtracts the constant ratio (4) from 40 instead of multiplying by it: 40 − 4 = 36. The ratio is a scale factor to multiply by, not an amount to subtract.*

**C.** 80 

  *This computes the ratio using y over twice x instead of y over x — for instance 20 ÷ (2 × 5) = 2 — landing on a scale factor of 2 instead of 4, then applies it: 40 × 2 = 80.*

**D.** 160 **(Correct)**

  *Correct. Every pair has y ÷ x = 4 (4/1, 12/3, and 20/5 all equal 4), so k = 40 × 4 = 160. Check it against the pattern: 160/40 = 4, matching every other row. ✓*

*Difficulty: medium*

---

##### Q7
The ratio of t to u is 1 to 2, and t = 10. What is the value of u?

**A.** 2 

  *This restates one of the ratio's own numbers as the answer, without ever using the given value t = 10 at all.*

**B.** 5 

  *This divides t by the ratio's second term (10 ÷ 2 = 5) instead of multiplying by it. Since u is the larger quantity in a 1-to-2 ratio, u must come out bigger than t, not smaller.*

**C.** 10 

  *This repeats the given value of t as if u equaled t, ignoring the 1-to-2 ratio between them entirely.*

**D.** 20 **(Correct)**

  *Correct. t is to u as 1 is to 2, so u = 2t = 2(10) = 20. Check it: 10 to 20 reduces to 1 to 2. ✓*

*Difficulty: easy*

---

##### Q8
How many yards are equivalent to 612 inches? (1 yard = 36 inches)

**A.** 0.059 

  *This divides 36 by 612 instead of 612 by 36 — the conversion fraction used in the orientation that doesn't cancel inches. Yards are bigger than inches, so the number of yards has to be smaller than 612, not a tiny fraction.*

**B.** 17 **(Correct)**

  *Correct. 612 inches ÷ 36 inches per yard = 17 yards. Check it: 17 yards × 36 inches per yard = 612 inches. ✓*

**C.** 576 

  *This subtracts 36 from 612 instead of dividing. Subtracting a conversion factor from a quantity doesn't convert anything — it just produces a smaller number of the same, still-unconverted unit.*

**D.** 22,032 

  *This multiplies 612 by 36 instead of dividing — using the conversion fraction upside down. Converting from a smaller unit (inches) to a larger one (yards) should shrink the number, not inflate it by a factor of 36.*

*Difficulty: easy*

---

##### Q9
Shaquan has 7 red cards and 28 blue cards. What is the ratio of red cards to blue cards that Shaquan has?

**A.** 1 to 4 **(Correct)**

  *Correct. Divide both terms by their common factor, 7: 7 ÷ 7 = 1 and 28 ÷ 7 = 4, giving 1 to 4. Check it: 1 is to 4 as 7 is to 28. ✓*

**B.** 4 to 1 

  *This is the ratio of blue cards to red cards, not red to blue as asked — the two terms are in the wrong order.*

**C.** 1 to 7 

  *This reduces the two terms of the ratio by different factors instead of the same one — dividing 7 by 7 to get 1, but dividing 28 by 4 instead of by 7 to get 7. A ratio has to be reduced by one common factor applied to both numbers.*

**D.** 7 to 1 

  *This reduces only the second term of the ratio (28 ÷ 28 = 1) while leaving the first term, 7, unreduced, instead of dividing both terms by the same common factor.*

*Difficulty: easy*

---

##### Q10
A kangaroo has a mass of 28 kilograms. What is the kangaroo's mass, in grams? (1 kilogram = 1,000 grams)

**A.** 28,000 **(Correct)**

  *Correct. 28 kilograms × 1,000 grams per kilogram = 28,000 grams. Check it: 28,000 ÷ 1,000 = 28 kilograms. ✓*

**B.** 1,028 

  *This adds 1,000 to 28 instead of multiplying by it. A conversion factor scales a quantity; it isn't a flat amount to add on top of it.*

**C.** 972 

  *This subtracts 28 from 1,000 instead of multiplying 28 by 1,000. Neither the direction nor the operation matches what converting kilograms to grams requires.*

**D.** 784 

  *This squares the mass (28 × 28 = 784) instead of multiplying it by the conversion factor of 1,000 — an area-style squaring step misapplied to a plain linear mass conversion, which never involves squaring anything.*

*Difficulty: easy*

---

##### Q11
The weight of an object on Venus is approximately 9/10 of its weight on Earth. The weight of an object on Jupiter is approximately 23/10 of its weight on Earth. If an object weighs 100 pounds on Earth, approximately how many more pounds does it weigh on Jupiter than it weighs on Venus?

**A.** 90 

  *This is the Venus weight alone (9/10 × 100 = 90). The question asked how many more pounds the object weighs on Jupiter than on Venus, which requires both weights and their difference — this stops after finding only one of them.*

**B.** 111 

  *This computes the Jupiter and Venus weights correctly (230 and 90) but makes a subtraction slip getting from one to the other, landing on 111 instead of the correct 140.*

**C.** 140 **(Correct)**

  *Correct. Jupiter weight: (23/10) × 100 = 230 pounds. Venus weight: (9/10) × 100 = 90 pounds. Difference: 230 − 90 = 140 pounds. Check it against the fractions directly: (23/10 − 9/10) × 100 = (14/10) × 100 = 140. ✓*

**D.** 230 

  *This is the Jupiter weight alone (23/10 × 100 = 230), the same kind of stop-early error as choice A but for the other planet — it never subtracts the Venus weight to find the difference the question asks for.*

*Difficulty: medium*

---

##### Q12
To make a bakery's signature chocolate muffins, a baker needs 2.5 ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins? (1 pound = 16 ounces)

**A.** 7.5 **(Correct)**

  *Correct. Total chocolate: 2.5 ounces × 48 muffins = 120 ounces. Convert to pounds: 120 ÷ 16 = 7.5 pounds. Check it: 7.5 pounds × 16 ounces per pound = 120 ounces, and 120 ÷ 48 = 2.5 ounces per muffin. ✓*

**B.** 10 

  *This divides the 120 ounces by 12 instead of 16 — borrowing the '12' from a dozen rather than using the pound-to-ounce conversion the problem actually states.*

**C.** 50.5 

  *This adds 48 and 2.5 together (48 + 2.5 = 50.5) instead of multiplying them to find the total ounces of chocolate needed.*

**D.** 120 

  *This correctly finds the total chocolate needed in ounces (2.5 × 48 = 120) but never converts to pounds, leaving the answer in the wrong unit for what the question asked.*

*Difficulty: medium*

---

##### Q13
Marta has 7,500 pesos she will convert to US dollars using a currency exchange service. At this time, the currency exchange rate is 1 peso = 0.075 US dollars. The exchange service will charge Marta a 2% fee on the converted US dollar amount. How many US dollars will Marta receive from the currency exchange after the 2% fee is applied?

**A.** $551.25 **(Correct)**

  *Correct. Convert first: 7,500 pesos × 0.075 dollars per peso = $562.50. Then apply the 2% fee by keeping 98%: $562.50 × 0.98 = $551.25. Check it: $562.50 − $551.25 = $11.25, and 2% of $562.50 is indeed $11.25. ✓*

**B.** $562.50 

  *This correctly converts the pesos to dollars but stops before applying the 2% fee, reporting the pre-fee amount as the final answer.*

**C.** $5,625.00 

  *This uses 0.75 instead of 0.075 as the exchange rate — a decimal shifted one place — and never applies the fee either. 7,500 × 0.75 = 5,625, ten times too large for the correct conversion.*

**D.** $98,000.00 

  *This divides 7,500 by 0.075 instead of multiplying — treating pesos as though they needed to be divided by the exchange rate rather than scaled by it — then applies the 2% fee correctly to that inflated figure (100,000 × 0.98 = 98,000). The conversion direction, not the fee step, is what's wrong here.*

*Difficulty: hard*

---

##### Q14
Makayla is planning an event in a 5,400-square-foot room. If there should be at least 8 square feet per person, what is the maximum number of people that could attend this event?

**A.** 588 

  *This treats the word 'square' in 'square feet' as an instruction to take an actual square root, computing √5,400 ≈ 73.5 and multiplying by 8 instead of simply dividing 5,400 by 8. 'Square feet' names the unit the area is measured in — it isn't a cue to apply a square root anywhere in the arithmetic.*

**B.** 675 **(Correct)**

  *Correct. Maximum people = total area ÷ area per person = 5,400 ÷ 8 = 675. Check it: 675 people × 8 square feet each = 5,400 square feet, using the whole room. ✓*

**C.** 15,274 

  *This inverts the per-person requirement twice in the course of setting up and 're-simplifying' the division, which cancels out the intended division and leaves a multiplication in its place. The result is larger than the room's total square footage — a giveaway, since no room can seat more people than it has square feet when each person needs several of them.*

**D.** 43,200 

  *This multiplies 5,400 by 8 instead of dividing (5,400 × 8 = 43,200) — the operation that would apply if the problem had asked for total square footage given a headcount, not the other way around.*

*Difficulty: medium*

---

##### Q15
If t = 4u, which of the following is equivalent to 2t?

**A.** 8u **(Correct)**

  *Correct. Substitute t = 4u into 2t: 2(4u) = 8u.*

**B.** 2u 

  *This doubles u directly instead of substituting for t first — it never uses the given relationship t = 4u at all, just swaps u in for t.*

**C.** u 

  *This correctly finds 2t = 8u and then divides by 8 again, as though simplifying further, which strips out the coefficient the substitution had just produced.*

**D.** (1/2)u 

  *This inverts the given relationship, treating t = 4u as though it meant u = 4t (so t = u/4), and then computes 2t as 2(u/4) = u/2. The relationship runs the other way — t is 4 times u, not the reverse.*

*Difficulty: medium*

---

##### Q16
How many teaspoons are equivalent to 44 tablespoons? (3 teaspoons = 1 tablespoon)

**A.** 47 

  *This adds 3 to 44 instead of multiplying by it. A conversion factor scales the quantity; it isn't a flat amount to add.*

**B.** 88 

  *This uses a factor of 2 instead of 3 — as though borrowing the '2 tablespoons = 1 fluid ounce' conversion instead of the '3 teaspoons = 1 tablespoon' one the problem actually gives.*

**C.** 132 **(Correct)**

  *Correct. 44 tablespoons × 3 teaspoons per tablespoon = 132 teaspoons. Check it: 132 ÷ 3 = 44 tablespoons. ✓*

**D.** 176 

  *This uses a factor of 4 instead of 3 (44 × 4 = 176) — overcounting the stated conversion, as though an extra teaspoon had been added to every tablespoon.*

*Difficulty: easy*

---

##### Q17
Tilly earns p dollars for every w hours of work. Which of the following expressions represents the amount of money, in dollars, Tilly earns for 39w hours of work?

**A.** 39p **(Correct)**

  *Correct. Tilly's rate is p dollars per w hours. Working 39w hours means working 39 times as many hours, so she earns 39 times as much money: 39p.*

**B.** p/39 

  *This divides p by 39 instead of multiplying — the direction that would apply if 39w hours were a fraction of w rather than 39 times as much. More hours worked means more money earned, not less.*

**C.** p + 39 

  *This adds 39 to p as a flat amount instead of scaling p by 39. Working 39 times as many hours multiplies the earnings; it doesn't add a fixed 39 dollars on top.*

**D.** p - 39 

  *This subtracts 39 from p, the same kind of additive error as choice C in the opposite direction — working more hours cannot mean earning less.*

*Difficulty: medium*

---

##### Q18
An object travels at a constant speed of 12 centimeters per second. At this speed, what is the time, in seconds, that it would take for the object to travel 108 centimeters?

**A.** 9 **(Correct)**

  *Correct. Time = distance ÷ speed = 108 ÷ 12 = 9 seconds. Check it: 12 centimeters per second × 9 seconds = 108 centimeters. ✓*

**B.** 96 

  *This subtracts 12 from 108 instead of dividing. Subtracting a speed from a distance doesn't produce a time in any meaningful unit.*

**C.** 120 

  *This adds 12 to 108 instead of dividing — the same unit mismatch as the subtraction error, in the other direction.*

**D.** 972 

  *This correctly computes 108 ÷ 12 = 9 as an intermediate step, then multiplies 108 by that 9 instead of recognizing 9 itself as the final answer — an extra, unnecessary step tacked onto a problem that was already solved.*

*Difficulty: easy*

---

##### Q19
The International Space Station orbits Earth at an average speed of 4.76 miles per second. What is the space station's average speed in miles per hour?

**A.** 285.6 

  *This converts only to miles per minute (4.76 × 60 = 285.6) and stops there, without the second conversion from minutes to hours the question actually asks for.*

**B.** 571.2 

  *This takes the per-minute figure (285.6) and doubles it, as if one more doubling were needed to reach 'per hour,' instead of continuing to multiply by the full 60 minutes in an hour.*

**C.** 856.8 

  *This multiplies by 180 instead of 3,600 — as if there were only 3 sets of 60 seconds in an hour rather than 60 sets of 60 — dropping a factor of 20 partway through the conversion.*

**D.** 17,136.0 **(Correct)**

  *Correct. There are 3,600 seconds in an hour, so 4.76 miles per second × 3,600 seconds per hour = 17,136 miles per hour. Check it: 17,136 ÷ 3,600 = 4.76. ✓*

*Difficulty: medium*

---

##### Q20
The population density of Iceland, in people per square kilometer of land area, increased from 2.5 in 1990 to 3.3 in 2014. During this time period, the land area of Iceland was 100,250 square kilometers. By how many people did Iceland's population increase from 1990 to 2014?

**A.** 330,825 

  *This is the full 2014 population alone (3.3 × 100,250) rather than the increase in population. It answers 'how many people lived there in 2014,' not 'by how many people did the population grow.'*

**B.** 132,330 

  *This scales the land area itself by the ratio of the two densities (100,250 × 3.3/2.5 ≈ 132,330) instead of finding the density increase and multiplying that by the area. The area doesn't change between 1990 and 2014 — only the density does.*

**C.** 125,312 

  *This correctly computes the 1990 population (2.5 × 100,250 = 250,625) and then divides that number in half instead of subtracting it from the 2014 population — a rushed final step that answers a different question than the one asked.*

**D.** 80,200 **(Correct)**

  *Correct. The density increased by 3.3 − 2.5 = 0.8 people per square kilometer. Multiply that increase by the land area: 0.8 × 100,250 = 80,200. Check it: 1990 population is 2.5 × 100,250 = 250,625; 2014 population is 3.3 × 100,250 = 330,825; and 330,825 − 250,625 = 80,200. ✓*

*Difficulty: medium*

---

##### Q21
Rectangle A has length 15 and width w. Rectangle B has length 20 and the same length-to-width ratio as rectangle A. What is the width of rectangle B in terms of w?

**A.** (4/3)w **(Correct)**

  *Correct. Rectangle A's ratio is length/width = 15/w. Rectangle B has the same ratio: 15/w = 20/W, where W is rectangle B's width. Cross-multiplying: 15W = 20w, so W = 20w/15 = (4/3)w. Check it: with rectangle A's ratio 15/w, rectangle B's ratio is 20 ÷ (4w/3) = 20 × 3/(4w) = 15/w. ✓*

**B.** w + 5 

  *This adds the difference in the two lengths (20 − 15 = 5) directly onto w, treating the relationship as additive instead of proportional. Matching a ratio means scaling both dimensions by the same factor, not shifting one of them by a flat amount.*

**C.** (3/4)w 

  *This sets up the proportion with width over length instead of length over width — w/15 = W/20 rather than 15/w = 20/W — flipping which quantity sits in the numerator on each side.*

**D.** w - 5 

  *This subtracts the length difference from w, the same additive error as choice B in the opposite direction — a longer rectangle B should need a proportionally different width, not one shifted by a fixed 5 units.*

*Difficulty: hard*

---

##### Q22
Tanya earns $13.50 per hour at her part-time job. When she works z hours, she earns 13.50z dollars. Which of the following expressions gives the amount, in dollars, Tanya will earn if she works 3z hours?

**A.** 3(13.50z) **(Correct)**

  *Correct. Working 3z hours is 3 times as many hours as working z hours, so the earnings scale by the same factor of 3: 3 × (13.50z).*

**B.** 3 + 13.50z 

  *This adds a flat 3 dollars to the earnings for z hours instead of multiplying the whole expression by 3. Tripling the hours worked should triple the pay, not add a small constant to it.*

**C.** 3z + 13.50z 

  *This tacks on an extra '3z' term as if 3 additional hours of unpaid time were being added to the expression, rather than scaling the entire 13.50z relationship by the factor of 3.*

**D.** 13.50(z + 3) 

  *This reads '3z hours' as 'z + 3 hours' — adding 3 hours flatly to z instead of multiplying z by 3, confusing a scaled quantity with a shifted one.*

*Difficulty: medium*

---

##### Q23
A glass, shaped like a frustum with volume formula V = 7πk³/48 (where k is one of its dimensions), can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. Jenny has a pitcher that contains 1 gallon of water. How many times could Jenny completely fill the glass with 1 gallon of water? (1 gallon = 128 fluid ounces)

**A.** 16 

  *This just restates the glass's own capacity in fluid ounces rather than dividing it into the gallon. It answers 'how big is the glass,' not 'how many glasses fit in the gallon.'*

**B.** 8 **(Correct)**

  *Correct. 1 gallon = 128 fluid ounces, and the glass holds 16 fluid ounces, so 128 ÷ 16 = 8. Check it: 8 glasses × 16 fluid ounces = 128 fluid ounces = 1 gallon. ✓*

**C.** 4 

  *This divides 128 by 32 instead of 16, confusing the glass's capacity with the '32 fluid ounces = 1 quart' conversion — a real conversion fact, but not the one this problem asked for.*

**D.** 3 

  *This divides the glass's volume in cubic centimeters (473) by the gallon's volume in fluid ounces (128) — mixing two different unit systems without converting either one — landing near 3.7, rounded down to 3. The problem already states the glass's capacity in fluid ounces (16); there's no need to bring the cubic-centimeter figure into the division at all.*

*Difficulty: medium*

---

##### Q24
Which of the following speeds is equivalent to 90 kilometers per hour? (1 kilometer = 1,000 meters)

**A.** 25 meters per second **(Correct)**

  *Correct. Convert kilometers to meters and hours to seconds: (90 km/hr) × (1,000 m / 1 km) × (1 hr / 3,600 s) = 90,000 ÷ 3,600 = 25 meters per second. Check it: 25 m/s × 3,600 s = 90,000 m = 90 km, matching the given speed over one hour. ✓*

**B.** 32 meters per second 

  *This uses a misremembered shortcut constant for the km/hr-to-m/s conversion, dividing by roughly 2.8 instead of 3.6 (90 ÷ 2.8 ≈ 32). The correct shortcut divides by 3.6, which comes from 3,600 seconds per hour over 1,000 meters per kilometer.*

**C.** 250 meters per second 

  *This divides by 360 instead of 3,600 — a dropped zero — landing exactly a factor of 10 too high, the signature of a decimal-placement slip rather than a wrong method.*

**D.** 324 meters per second 

  *This multiplies 90 by 3.6 instead of dividing by it — the direction that converts meters per second into kilometers per hour, not the reverse. The conversion factor was applied to the correct constant but in the wrong direction.*

*Difficulty: medium*

---

##### Q25
The table below shows the amount of protein in two foods and the cost of each food. 1 large egg has 6 grams of protein and costs $0.36. 1 cup of milk has 8 grams of protein and costs $0.24. Based on the table, what is the ratio of the cost per gram of protein in a large egg to the cost per gram of protein in a cup of milk?

**A.** 1 : 2 

  *This is the ratio of milk's cost per gram to egg's cost per gram (0.03 to 0.06), the reverse of what was asked. The question wants egg to milk, not milk to egg.*

**B.** 2 : 3 

  *This uses the raw prices directly, without dividing by the protein content, and in the milk-to-egg order: $0.24 to $0.36 reduces to 2 : 3. Skipping the 'per gram of protein' normalization is the error — the two foods have different protein amounts, so comparing raw price isn't the same as comparing cost per gram.*

**C.** 3 : 4 

  *This uses the raw protein amounts directly (6 grams to 8 grams reduces to 3 : 4) instead of the cost per gram of protein, ignoring price entirely.*

**D.** 2 : 1 **(Correct)**

  *Correct. Egg's cost per gram of protein: $0.36 ÷ 6 = $0.06. Milk's cost per gram of protein: $0.24 ÷ 8 = $0.03. The ratio of egg to milk: 0.06 : 0.03 = 2 : 1. Check it: milk costs half as much per gram of protein as the egg does, matching 2 : 1. ✓*

*Difficulty: hard*

---

##### Q26
The total area of a coastal city is 92.1 square miles, of which 11.3 square miles is water. If the city had a population of 621,000 people in the year 2010, which of the following is closest to the population density, in people per square mile of land area, of the city at that time?

**A.** 6,740 

  *This divides the population by the total area, 92.1, instead of subtracting the water area first. The question asks for density per square mile of land area specifically, and the water has to come out of the total before dividing.*

**B.** 7,690 **(Correct)**

  *Correct. Land area = 92.1 − 11.3 = 80.8 square miles. Density = 621,000 ÷ 80.8 ≈ 7,686.9, closest to 7,690. Check it: 7,690 people per square mile × 80.8 square miles ≈ 621,352, close to the given population. ✓*

**C.** 55,000 

  *This divides the population by the water area, 11.3, instead of the land area — using the wrong figure from the problem entirely.*

**D.** 76,000 

  *This divides by 8.08 instead of 80.8 — a decimal shifted one place in the land area — landing a factor of 10 too high.*

*Difficulty: medium*

---

##### Q27
d = 55t. The equation above can be used to calculate the distance d, in miles, traveled by a car moving at a speed of 55 miles per hour over a period of t hours. For any positive constant k, the distance the car would have traveled after 9k hours is how many times the distance the car would have traveled after 3k hours?

**A.** 3 **(Correct)**

  *Correct. Distance after 9k hours: 55(9k) = 495k. Distance after 3k hours: 55(3k) = 165k. The ratio is 495k ÷ 165k = 3 — the k cancels because it multiplies both distances equally, so the answer holds for every positive value of k.*

**B.** 6 

  *This computes the difference between the two time multiples (9k − 3k = 6k) instead of their ratio, and drops the k, treating that difference as if it were the answer to 'how many times.'*

**C.** 3k 

  *This correctly finds that the ratio of the two distances reduces to 3, but never cancels the k in 9k/3k, leaving it attached to the final answer as though the multiplier depended on k's value.*

**D.** 6k 

  *This combines both errors above — computing the difference in time multiples (9k − 3k = 6k) instead of the ratio, and leaving k attached to the result instead of recognizing it cancels.*

*Difficulty: hard*

---

##### Q28
An insect moves at a speed of 3/20 feet per second. What is this speed, in yards per second? (3 feet = 1 yard)

**A.** 1/20 **(Correct)**

  *Correct. Divide by 3 to convert feet to yards: (3/20) ÷ 3 = 3/(20 × 3) = 1/20 yards per second. Check it: 1/20 yard per second × 3 feet per yard = 3/20 feet per second. ✓*

**B.** 9/20 

  *This multiplies by 3 instead of dividing — the conversion fraction used in the direction that converts yards into feet, not feet into yards. Yards are the larger unit, so the number of yards per second should be smaller than the number of feet per second, not larger.*

**C.** 6 

  *This takes the reciprocal of the given speed (20/3 ≈ 6.67, rounded to 6) instead of converting its units, treating 'convert to yards' as an instruction to flip the fraction rather than divide it by 3.*

**D.** 20 

  *This reports only the denominator of the given fraction, dropping the numerator (3) and the yard conversion (÷3) entirely.*

*Difficulty: medium*

---

##### Q29
For a certain rectangular region, the ratio of its length to its width is 35 to 10. If the width of the rectangular region increases by 7 units, how must the length change to maintain this ratio?

**A.** It must decrease by 24.5 units. 

  *This finds the correct magnitude (24.5) but the wrong direction — increasing the width of a fixed-ratio rectangle requires the length to increase as well to keep the same length-to-width ratio, not decrease.*

**B.** It must increase by 24.5 units. **(Correct)**

  *Correct. The ratio 35 to 10 reduces to 3.5 to 1. If width increases by 7 (from 10 to 17), the new length must be 17 × 3.5 = 59.5 to keep the ratio, an increase of 59.5 − 35 = 24.5. Check it: 59.5 to 17 reduces to 3.5 to 1, matching the original ratio. ✓*

**C.** It must decrease by 7 units. 

  *This mirrors the width's change with the wrong sign, treating the length-to-width ratio as though it were 1 to 1 rather than 3.5 to 1.*

**D.** It must increase by 7 units. 

  *This mirrors the width's change exactly — as though length and width had to change by the same amount to preserve the ratio, which is only true for a 1-to-1 ratio, not the given 3.5-to-1 ratio.*

*Difficulty: hard*

---

##### Q30
The total mass, in kilograms, of r identical objects is t. Which expression represents the total mass, in kilograms, of 146r of these objects?

**A.** 146 - t 

  *This subtracts t from 146 instead of scaling t by 146. The mass of 146 times as many objects should scale multiplicatively with t, not combine with it additively.*

**B.** 146 + t 

  *This adds 146 to t instead of multiplying — the same additive error as choice A in the other direction.*

**C.** t/146 

  *This divides t by 146 instead of multiplying — the direction that would apply if 146r objects were a small fraction of r objects rather than 146 times as many. More objects means more total mass, not less.*

**D.** 146t **(Correct)**

  *Correct. The mass per object is t/r. For 146r objects, total mass = 146r × (t/r) = 146t — the r cancels, leaving the total mass as simply 146 times the original t.*

*Difficulty: medium*

---

##### Q31
One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table below gives the growth factors for eight species of trees: red maple 4.5, river birch 3.5, cottonwood 2.0, black walnut 4.5, white birch 5.0, American elm 4.0, pin oak 3.0, and shagbark hickory 7.5. If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)

**A.** 1.0 

  *This computes the raw difference between the two growth factors (5.0 − 3.0 = 2.0) and then halves it to 1.0, without ever dividing the 10 additional years by each species' growth factor the way the age formula actually requires.*

**B.** 1.2 

  *This uses 9 years of additional growth instead of the full 10 — an off-by-one slip in counting the elapsed time — computing 9 × (1/3 − 1/5) = 9 × (2/15) = 1.2 instead of 10 × (2/15).*

**C.** 1.3 **(Correct)**

  *Correct. Both trees have a current diameter of 12 inches (1 foot). Age = diameter × growth factor, so age = diameter ÷ growth factor when solving backward for the future diameter after 10 more years of age. Because both trees start at the same diameter, the future difference depends only on how much each grows: white birch grows 10/5 = 2 inches, pin oak grows 10/3 ≈ 3.33 inches, so the difference is about 3.33 − 2 = 1.33, closest to 1.3. ✓*

**D.** 1.4 

  *This rounds 10/3 up to 3.4 instead of down to 3.3 before subtracting, producing a difference 0.1 too large from a rounding slip made one step too early.*

*Difficulty: sat-hardest*

---

##### Q32
The table below shows the distribution, by location and power capacity (maximum rate of power generation), of the twenty largest wind projects in the United States in 2013. By state, the number of projects at low/medium/high capacity and the total number of projects were: Texas 4/2/3, total 9; California 1/0/1, total 2; Oregon 1/0/1, total 2; Indiana 0/2/0, total 2; Colorado 1/1/0, total 2; Iowa 2/0/0, total 2; Oklahoma 1/0/0, total 1; and the overall total across all states was 10/5/5, total 20. The total power capacity of the nine wind projects located in Texas was 4,952 megawatts (MW), and the total power capacity of the twenty wind projects was 11,037 MW in 2013. The amount of energy produced in one hour at a rate of one megawatt is one megawatt-hour. If each of the nine Texas wind projects in 2013 had operated continuously for 24 hours at the maximum rate of power generation, approximately how many megawatt-hours of energy would the nine projects have produced?

**A.** 200 

  *This divides 4,952 by 24 instead of multiplying (4,952 ÷ 24 ≈ 206, rounded to 200) — the operation that would find hours from energy and power, not energy from power and hours.*

**B.** 5,000 

  *This just restates the given total power capacity of the Texas projects (4,952, rounded to 5,000) without multiplying by the 24 hours of operation at all.*

**C.** 11,000 

  *This uses 11,037, the total power capacity of all twenty wind projects nationwide, instead of 4,952, the figure specific to the nine Texas projects the question asks about.*

**D.** 120,000 **(Correct)**

  *Correct. Energy = power × time. The nine Texas projects have a combined capacity of 4,952 MW; running for 24 hours produces 4,952 × 24 = 118,848 megawatt-hours, closest to 120,000. Check the order of magnitude: roughly 5,000 MW running a full day is about 5,000 × 24 ≈ 120,000 MWh. ✓*

*Difficulty: hard*

---

##### Q33
The density of a certain type of wood is 353 kilograms per cubic meter. A sample of this type of wood is in the shape of a cube and has a mass of 345 kilograms. To the nearest hundredth of a meter, what is the length of one edge of this sample?

**A.** 0.98 

  *This correctly finds the sample's volume (345 ÷ 353 ≈ 0.977 cubic meters) but reports that volume directly as if it were the edge length, never taking the cube root to go from volume back to a single edge.*

**B.** 0.99 **(Correct)**

  *Correct. Volume = mass ÷ density = 345 ÷ 353 ≈ 0.9773 cubic meters. Edge length = cube root of the volume ≈ 0.9924, which rounds to 0.99 meters. Check it: 0.99³ ≈ 0.970, and 353 × 0.970 ≈ 342.4 kilograms, close to the given 345. ✓*

**C.** 1.01 

  *This computes density ÷ mass instead of mass ÷ density (353 ÷ 345 ≈ 1.023) before taking the cube root, inverting which quantity belongs on top of the density formula.*

**D.** 1.02 

  *This reports the inverted ratio of density to mass (353 ÷ 345 ≈ 1.02) directly as the edge length, compounding two errors at once: inverting the density formula and skipping the cube root entirely.*

*Difficulty: hard*

---

##### Q34
Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint. She must mix a second batch using the same ratio of blue and yellow paint as the first batch. If she uses 5 ounces of blue paint for the second batch, how much yellow paint should Anita use?

**A.** Exactly 5 ounces 

  *This uses the blue-paint amount directly as the yellow-paint amount, as though blue and yellow needed to match 1 to 1, ignoring the given 2-to-3 ratio entirely.*

**B.** 3 ounces more than the amount of yellow paint used in the first batch 

  *This treats the relationship additively: since blue increased by 3 ounces (from 2 to 5), it assumes yellow should also increase by a flat 3 ounces (3 + 3 = 6), instead of scaling yellow by the same proportion blue was scaled by.*

**C.** 1.5 times the amount of yellow paint used in the first batch 

  *This applies a scale factor of 1.5 to the first batch's yellow amount (3 × 1.5 = 4.5), but 1.5 is not the actual scale factor here (blue scaled by 5/2 = 2.5, not 1.5) and the first batch's yellow isn't what the question asks the answer to be expressed in terms of.*

**D.** 1.5 times the amount of blue paint used in the second batch **(Correct)**

  *Correct. The ratio of blue to yellow is 2 to 3, so yellow = 1.5 × blue for any batch that keeps the same ratio. In the second batch, blue = 5 ounces, so yellow = 1.5 × 5 = 7.5 ounces. Check it: 5 to 7.5 reduces to 2 to 3, matching the first batch's ratio. ✓*

*Difficulty: hard*

---

##### Q35
A certain park has an area of 11,863,808 square yards. What is the area, in square miles, of this park? (1 mile = 1,760 yards)

**A.** 1.96 

  *This takes the square root of the correctly-computed square-mile area (√3.83 ≈ 1.96) instead of leaving it as is. 'Square miles' names the unit the area is already measured in — it isn't a cue to take a square root of the final result.*

**B.** 3.83 **(Correct)**

  *Correct. 1 square mile = (1,760 yards)² = 3,097,600 square yards. Area in square miles = 11,863,808 ÷ 3,097,600 ≈ 3.83. Check it: 3.83 × 3,097,600 ≈ 11,863,808. ✓*

**C.** 3,444.39 

  *This takes the square root of the raw area in square yards (√11,863,808 ≈ 3,444.39) without ever converting to square miles — mistaking 'find the area in square miles' for 'find a side length,' and never applying the yards-to-miles conversion at all.*

**D.** 6,740.8 

  *This divides by 1,760 once instead of squaring it first (11,863,808 ÷ 1,760 = 6,740.8) — using the length conversion factor for an area conversion, the exact unsquared-conversion-factor trap this domain runs on: converting a square unit takes the factor to the second power, not the first.*

*Difficulty: hard*

---

##### Q36
The density of a certain solid substance is 813 kilograms per cubic meter. A sample of this substance is in the shape of a cube, where each edge has a length of 0.60 meters. To the nearest whole number, what is the mass, in kilograms, of this sample?

**A.** 176 **(Correct)**

  *Correct. Volume = edge³ = 0.60³ = 0.216 cubic meters. Mass = density × volume = 813 × 0.216 ≈ 175.6, which rounds to 176 kilograms.*

**B.** 488 

  *This multiplies density by the edge length itself (813 × 0.60 ≈ 488) instead of by the cube of the edge length — using the edge to the first power where a volume needs it cubed.*

**C.** 1,355 

  *This divides density by the edge length instead of multiplying density by the volume (813 ÷ 0.60 ≈ 1,355), the wrong operation applied to the wrong quantity.*

**D.** 3,764 

  *This correctly computes the volume (0.216 cubic meters) but then divides the density by that volume instead of multiplying (813 ÷ 0.216 ≈ 3,764) — the volume step was right, but the final operation was inverted.*

*Difficulty: medium*

---

#### Two-Variable Data (36 items)

##### Q1
> A scatterplot relates x, the number of weeks since a sunflower seedling was planted, to y, its height, in centimeters. The line of best fit for the data is y = 12 + 12.5x.

According to the line of best fit, what is the predicted height of a sunflower 4 weeks after planting?

**A.** 12 centimeters 

  *12 is the predicted height at x = 0, the day of planting — the intercept, not the prediction at x = 4. The question gave a specific week to substitute, and this answer never uses it.*

**B.** 12.5 centimeters 

  *12.5 is the slope, the predicted growth per one week — a rate, not a height. A rate says how much the plant gains each week; it is never, by itself, a prediction of how tall the plant is at a given week.*

**C.** 50 centimeters 

  *This is 12.5(4) with the constant term left off. The prediction is the whole right-hand side of the equation evaluated at x = 4, not just the term containing x — every model has a starting height built in, and dropping it understates the plant by exactly that amount.*

**D.** 62 centimeters **(Correct)**

  *Correct. Substitute x = 4 into the full model: y = 12 + 12.5(4) = 12 + 50 = 62 centimeters. Check the pieces separately — 12 is the height the model predicts at planting, and 12.5 × 4 = 50 is the predicted growth over those four weeks, and 12 + 50 = 62. ✓*

*Difficulty: easy*

---

##### Q2
> A scatterplot plots eleven data points forming a U-shaped curve: the values start at about y = 20 when x = 0, fall to a minimum of about y = 4 somewhere between x = 2 and x = 3, and then rise back to about y = 20 by x = 5.

Of the following, which is the best model for the data in the scatterplot?

**A.** y = 2x² − 11x − 20 

  *This has the right shape (same 2x² − 11x as the correct model) but the wrong sign on the constant term: y = 2x² − 11x − 20 gives y = −20 at x = 0, well below the horizontal axis. The data starts at about y = 20, not y = −20 — the intercept alone rules this out without computing the vertex.*

**B.** y = 2x² − 11x + 20 **(Correct)**

  *Correct. Check the y-intercept first: at x = 0, y = 20, which matches the data's starting height and immediately eliminates the choices with a negative constant term. Then check the vertex: for y = 2x² − 11x + 20, the vertex is at x = 11/4 = 2.75, giving y = 2(2.75)² − 11(2.75) + 20 = 15.125 − 30.25 + 20 = 4.875 — a minimum of about 5 near x = 2.75, matching the low point of the data.*

**C.** y = 2x² − 5x − 3 

  *y = 2x² − 5x − 3 has a different linear coefficient, which moves the vertex: its minimum sits at x = 5/4 = 1.25, not near x = 2.75 where the data actually bottoms out, and its y-intercept is −3, not the roughly +20 the scatterplot shows. Matching the general curvature (upward parabola) is not enough — the intercept and vertex location have to match too.*

**D.** y = 2x² − 5x + 3 

  *y = 2x² − 5x + 3 gets the y-intercept badly wrong (3, not about 20) and places the vertex at x = 1.25 instead of near 2.75. It shares a coefficient (2 for x²) with the correct model, which is what makes it a plausible-looking distractor, but neither of the two features that actually distinguish these four choices — where the curve starts and where it bottoms out — matches the graph.*

*Difficulty: hard*

---

##### Q3
> In an experiment, a heated cup of coffee is removed from a heat source and then left in a room kept at a constant temperature. A scatterplot plots the coffee's temperature, in degrees Fahrenheit, against the time since it was removed from the heat source, in minutes, with a point plotted every 10 minutes from 0 to 130 minutes. The points trace the shape of an exponential decay curve: the temperature falls steeply over the first 10-minute interval, and each successive 10-minute interval shows a smaller drop than the one before it, as the temperature levels off toward the room's constant temperature.

During which of the following 10-minute intervals does the temperature of the coffee decrease at the greatest average rate?

**A.** Between 0 and 10 minutes **(Correct)**

  *Correct. The coffee is hottest immediately after leaving the heat source, so the gap between its temperature and the room's constant temperature is largest there — and that gap is exactly what drives the rate of cooling. An exponential decay curve is steepest where the value is farthest from its limiting value, which on this graph is the first interval, 0 to 10 minutes; every later interval shows a visibly smaller drop.*

**B.** Between 30 and 40 minutes 

  *By 30–40 minutes the coffee has already lost much of its excess heat, so the gap between its temperature and room temperature — the thing driving the cooling rate — is smaller than it was at the start. The curve is still decreasing here, just more slowly than in the first interval; picking a middle interval mistakes 'still dropping' for 'dropping fastest.'*

**C.** Between 50 and 60 minutes 

  *This interval sits even further along the flattening curve than 30–40 minutes, where the temperature is closer still to the room's constant value. The rate of decrease shrinks continuously as the curve approaches its asymptote, so any interval after the first is guaranteed to have a smaller average rate than the first one did.*

**D.** Between 90 and 100 minutes 

  *This is one of the last intervals shown, where the curve has nearly flattened out — the coffee's temperature is close to the room's constant temperature and barely changing at all. This is close to the smallest rate of decrease on the whole graph, not the greatest.*

*Difficulty: medium*

---

##### Q4
> The scatterplot shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown, falling from about 44°F at an elevation of 6,500 feet to about 37°F at an elevation of 9,500 feet.

What temperature is predicted by the line of best fit for a location in the Lake Tahoe Basin with an elevation of 8,500 feet?

**A.** 37°F 

  *37°F is the line's predicted temperature at the far end of the graph, 9,500 feet — not at the requested elevation of 8,500 feet. Reading off the rightmost value on the line instead of tracking it to the exact elevation asked for answers a question about the wrong elevation.*

**B.** 39°F **(Correct)**

  *Correct. The line falls about 7°F over the 3,000-foot span from 6,500 to 9,500 feet, a rate of roughly 2.3°F per 1,000 feet. From 6,500 feet to 8,500 feet is 2,000 feet, so the predicted drop is about 2.3 × 2 ≈ 4.7°F, giving 44 − 4.7 ≈ 39°F.*

**C.** 41°F 

  *41°F sits closer to the line's value around 7,500–8,000 feet than at 8,500 feet. This is the kind of error that comes from reading the nearest labeled gridline instead of tracking the line to the exact elevation asked for.*

**D.** 43°F 

  *43°F is close to the line's height near 7,000 feet, well below the requested 8,500 feet. This reads the line too far toward the low-elevation, high-temperature end of the graph.*

*Difficulty: medium*

---

##### Q5
> A line graph shows the number of graduates from the classes of 2001 through 2007 at a certain school who enrolled in college within 24 months of graduation. Reading the plotted values: the count dips to its lowest point in 2002 (noticeably below both 2001 and 2003), climbs through 2004 and 2005 to its highest point, dips slightly in 2006, and rises again in 2007.

Of the following, which class had the fewest graduates who enrolled in college within 24 months of graduation?

**A.** 2002 **(Correct)**

  *Correct. Reading the graph's lowest plotted point among the years listed: 2002 sits below every other labeled year, including the year immediately before and after it — the visual signature of a minimum on a line graph.*

**B.** 2004 

  *2004 is a mid-range value on the way up from the 2002 low toward the 2005 peak — higher than 2002, not lower. Picking a point partway up the recovery mistakes 'not yet at the peak' for 'the minimum.'*

**C.** 2005 

  *2005 is where the graph reaches its highest point, the opposite of what the question asks for. Reading the tallest point on a graph when the question asks for the shortest is the single most common reversal on this question type.*

**D.** 2007 

  *2007 is the last labeled year and shows a rebound after the 2006 dip — it sits well above the 2002 low. Choosing the final point on the graph by default, rather than comparing every plotted year, misses the actual minimum earlier in the series.*

*Difficulty: easy*

---

##### Q6
> Theresa ran on a treadmill for thirty minutes, and her time and speed are shown on a graph. Reading the plotted points approximately: speed rises from 0 to about 7 miles per hour over the first 5 minutes, holds steady at about 7 miles per hour from 5 to 10 minutes, falls to about 2 miles per hour by 13 minutes, climbs to a peak of about 8 miles per hour by 20 minutes, then declines for the rest of the run, falling at a constant rate over the final five minutes to reach 0 miles per hour at 30 minutes.

According to the graph, which of the following statements is NOT true concerning Theresa's run?

**A.** Theresa ran at a constant speed for five minutes. 

  *This statement is true and so is not the answer to a 'NOT true' question: the graph holds flat at about 7 miles per hour from 5 to 10 minutes, which is exactly five minutes at a constant speed.*

**B.** Theresa's speed was increasing for a longer period of time than it was decreasing. **(Correct)**

  *Correct — this is the false statement. Speed is increasing over two stretches (0 to 5 minutes, and 13 to 20 minutes), a total of 12 minutes, and decreasing over two other stretches (10 to 13 minutes, and 20 to 30 minutes), a total of 13 minutes. Decreasing time is actually the longer of the two, so the claim that increasing lasted longer has it backwards.*

**C.** Theresa's speed decreased at a constant rate during the last five minutes. 

  *This statement is true: from 25 to 30 minutes the graph is a single straight segment falling from about 6 miles per hour to 0, which is a constant rate of decrease over that final five-minute stretch. Being true disqualifies it from being the answer to a question asking which statement is NOT true.*

**D.** Theresa's speed reached its maximum during the last ten minutes. 

  *This statement is true: the highest speed on the whole graph, about 8 miles per hour, occurs at the 20-minute mark, which falls inside the last ten minutes of the run (20 to 30 minutes). Being true disqualifies it from being the 'NOT true' answer the question is asking for.*

*Difficulty: hard*

---

##### Q7
> The densities of different concentrations of grape juice are shown in a scatterplot, with density in kilograms per cubic meter on the vertical axis and concentration as a percent on the horizontal axis. The trend in the data rises roughly linearly, from about 1,050 kg/m³ at a concentration of 20% up to about 1,350 kg/m³ at a concentration of 70%.

According to the trend shown by the data, which of the following is closest to the predicted density, in kilograms per cubic meter (kg/m³), for grape juice with a concentration of 60%?

**A.** 1,200 

  *1,200 corresponds to the trend's height nearer 45–50% concentration, not 60%. This undershoots by stopping the interpolation too early — about two-thirds of the way from 20% to 60% instead of all the way there.*

**B.** 1,250 

  *1,250 is closer to the trend's value around 55% concentration than at the requested 60%. It's in the right neighborhood but falls one gridline short of tracking the trend all the way to 60%.*

**C.** 1,300 **(Correct)**

  *Correct. The trend rises about 300 kg/m³ over the 50-percentage-point span from 20% to 70%, a rate of about 6 kg/m³ per percentage point. From 20% to 60% is 40 percentage points, so the predicted rise is about 6 × 40 = 240 kg/m³ above the 20% value: 1,050 + 240 = 1,290 ≈ 1,300.*

**D.** 1,350 

  *1,350 is the density at the top end of the data, 70% concentration — the value the question would ask for if it wanted the highest-concentration sample, not 60%. Reading the top of the trend instead of the point directly above 60% substitutes the wrong x-value.*

*Difficulty: medium*

---

##### Q8
> A line graph shows the number of 3-D movies released each year from 2003 to 2011. Reading the plotted values: the count stays low and roughly flat from 2003 through 2008 (in the single digits), then climbs noticeably in 2009, rises more steeply in 2010, and rises steepest of all from 2010 to 2011, more than the change in any earlier consecutive pair of years.

According to the line graph above, between which two consecutive years was there the greatest change in the number of 3-D movies released?

**A.** 2003–2004 

  *2003–2004 sits in the flat early stretch of the graph, where the count barely moves from one year to the next — this is close to the smallest change on the graph, not the greatest.*

**B.** 2008–2009 

  *2008–2009 is where the increase first becomes noticeable, but the graph keeps getting steeper after this point. Picking the interval where growth first starts, rather than comparing it against the later intervals, misses that 2010–2011 rises even more.*

**C.** 2009–2010 

  *2009–2010 is a real increase, and a bigger one than 2008–2009, but the graph rises even more steeply in the following year. Confirming that an interval is increasing is not the same as confirming it's the single largest increase on the graph.*

**D.** 2010–2011 **(Correct)**

  *Correct. The graph's steepest segment is its last one: the jump from 2010 to 2011 is visibly larger than any of the increases in the earlier years, consistent with the rapid rise in 3-D movie releases in the years right after 2009.*

*Difficulty: easy*

---

##### Q9
> A scatterplot plots points that fall in a nearly straight, tightly clustered downward trend: at x = 0 the value is about 6, and each unit increase in x brings the value down by about 1, reaching about 1 by x = 5.

Which of the following could be an equation for a line of best fit for the data in the scatterplot?

**A.** y = −x + 6 **(Correct)**

  *Correct. The data starts near y = 6 at x = 0 and falls by about 1 for each unit x increases — a slope of −1 and a y-intercept of 6, which is exactly y = −x + 6. Checking the endpoint: at x = 5, this gives y = 1, matching where the trend ends.*

**B.** y = −x − 6 

  *y = −x − 6 has the right slope but the wrong sign on the intercept: it starts at y = −6 when x = 0, far below the axis, while the data actually starts near y = 6. Matching the slope's steepness isn't enough if the line sits on the wrong side of the horizontal axis entirely.*

**C.** y = 6x + 1 

  *y = 6x + 1 has a positive slope of 6, which would mean the values shoot upward steeply as x increases — the opposite direction from the data, which trends downward gently. A line of best fit has to match the direction of the trend before its steepness is even worth checking.*

**D.** y = 6x − 1 

  *y = 6x − 1 shares the same positive, steep slope as the other reversed-sign choice and fails the same way: the data trends downward at a shallow rate, not upward at a rate of 6 units of y per unit of x. Both the direction and the steepness are wrong here.*

*Difficulty: medium*

---

##### Q10
> A graph shows the relationship between the speed of a particular car, in miles per hour, and its corresponding braking distance, in feet, as a curve that rises more steeply as speed increases. Reading approximate values from the curve: braking distance is about 150 feet at 30 miles per hour and about 275 feet at 50 miles per hour.

Approximately how many feet greater will the car's braking distance be when the car is traveling at 50 miles per hour than when the car is traveling at 30 miles per hour?

**A.** 75 

  *75 feet underestimates the gap, consistent with reading the curve at values closer together than 30 and 50 miles per hour — for instance, treating the difference as though it were read across a 20-to-40 mph gap instead of 30-to-50.*

**B.** 125 **(Correct)**

  *Correct. Subtract the two readings in the order the question asks for: 275 − 150 = 125 feet. Because braking distance curves upward with speed rather than increasing at a constant rate, this difference has to come from reading both values off the curve and subtracting — it cannot be found from the slope of a straight line.*

**C.** 175 

  *175 feet overshoots the actual difference, the kind of error that comes from reading the 50 mph value a little high or the 30 mph value a little low before subtracting — on a curve that's bending upward, small misreads near the steep end move the difference more than they would on a straight line.*

**D.** 250 

  *250 feet is close to the braking distance at 50 miles per hour by itself — not the difference between the two speeds. Reporting one of the two readings instead of subtracting them answers a different question than the one asked.*

*Difficulty: medium*

---

##### Q11
> The scatterplot shows the temperature y, in °F, recorded by a meteorologist at various times x, in days since June 1. Reading the plotted points: about (1, 68), (2, 60), (3, 73), (4, 68), (5, 64), (6, 63), and (7, 66).

During which of the following time periods did the greatest increase in recorded temperature take place?

**A.** From x = 6 to x = 7 

  *From x = 6 to x = 7 the temperature rises from about 63°F to 66°F, an increase of only about 3°F. This is an increase, but a small one compared to the jump from x = 2 to x = 3.*

**B.** From x = 5 to x = 6 

  *From x = 5 to x = 6 the temperature is essentially flat, going from about 64°F to 63°F — barely any change, and in fact a slight decrease rather than an increase.*

**C.** From x = 2 to x = 3 **(Correct)**

  *Correct. From x = 2 to x = 3 the temperature rises from about 60°F to about 73°F, an increase of roughly 13°F — larger than the change over any of the other three listed intervals.*

**D.** From x = 1 to x = 2 

  *From x = 1 to x = 2 the temperature actually decreases, from about 68°F down to 60°F. This interval has the sign backwards for what the question asks: it's the steepest decrease on the graph, not an increase at all.*

*Difficulty: easy*

---

##### Q12
> A study was done to determine a new car's stopping distance when it was traveling at different speeds, on a dry road with good surface conditions. The results are shown along with the graph of a quadratic function that models the data — a curve rising from near 0 at low speed to about 350 feet by 80 miles per hour, passing near roughly (20, 25), (40, 100), and (60, 210).

According to the model, which of the following is the best estimate for the stopping distance, in feet, if the vehicle was traveling 55 miles per hour?

**A.** 25 

  *25 feet is the model's stopping distance at 20 miles per hour, not 55 — this reads a value from the low-speed end of the curve entirely, nowhere near the requested speed.*

**B.** 30 

  *30 feet is even smaller than the 20 mph reading, far below anything the curve predicts near 55 mph. A stopping distance this small only appears at the very start of the curve, close to 0 mph.*

**C.** 210 **(Correct)**

  *Correct. At 55 miles per hour the curve sits between its readings at 40 mph (about 100 feet) and 60 mph (about 210 feet); because the curve is bending upward, the value at 55 lands much closer to the 60 mph reading than the 40 mph one, close to 210 feet.*

**D.** 250 

  *250 feet overshoots — this is closer to the model's value near 65–70 miles per hour, past the requested 55 mph. On a curve that's accelerating upward, reading just a few miles per hour too far to the right inflates the estimate noticeably.*

*Difficulty: medium*

---

##### Q13
> The scatterplot shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown, sloping downward from about 44°F at low elevation to about 37°F at high elevation.

Which of the following statements best describes the association between the elevation and the temperature of locations in the Lake Tahoe Basin?

**A.** As the elevation increases, the temperature tends to increase. 

  *This describes a positive association — temperature rising with elevation — which is the reverse of what the downward-sloping line shows. The line's negative slope is the direct visual signal of a negative association, and this choice reads it backwards.*

**B.** As the elevation increases, the temperature tends to decrease. **(Correct)**

  *Correct. The line of best fit slopes downward from left to right — as elevation (the horizontal axis) increases, temperature (the vertical axis) tends to decrease. This is a negative association, consistent with higher elevations being colder.*

**C.** As the elevation decreases, the temperature tends to decrease. 

  *This statement pairs decreasing elevation with decreasing temperature, but the data shows the opposite: temperature decreases as elevation increases (or equivalently, increases as elevation decreases). Restating a negative association with both directions flipped still describes the wrong relationship.*

**D.** There is no association between the elevation and the temperature. 

  *The scatterplot's points cluster fairly tightly around a clearly sloped line rather than scattering with no pattern, so there plainly is an association. This choice would only be appropriate for a cloud of points with no visible trend at all.*

*Difficulty: easy*

---

##### Q14
> The scatterplot shows the densities of 7 planetoids, in grams per cubic centimeter, with respect to their average distances from the Sun in astronomical units (AU). The line of best fit is also shown, falling from about 5.6 g/cm³ near 0 AU to about 3.6 g/cm³ near 3.2 AU.

An astronomer has discovered a new planetoid about 1.2 AU from the Sun. According to the line of best fit, which of the following best approximates the density of the planetoid, in grams per cubic centimeter?

**A.** 3.6 

  *3.6 is the line's density near the far right edge of the graph, around 3.2 AU — the value for a planetoid much farther from the Sun than the 1.2 AU one described in the question.*

**B.** 4.1 

  *4.1 corresponds to the line's height further out, closer to 2 AU, rather than at the requested 1.2 AU. This undershoots by reading the line too far along the x-axis.*

**C.** 4.6 **(Correct)**

  *Correct. The line falls about 2.0 g/cm³ over the 3.2 AU span shown, a rate of about 0.625 g/cm³ per AU. At 1.2 AU, that's a drop of about 0.625 × 1.2 ≈ 0.75 g/cm³ from the line's value near 0 AU (about 5.6), giving roughly 5.6 − 0.75 ≈ 4.85, closest to 4.6 among the choices.*

**D.** 5.5 

  *5.5 sits close to the line's value near the y-axis, around 0.1–0.2 AU — much closer to the Sun than the 1.2 AU distance given for the new planetoid. This barely moves along the line from the intercept at all.*

*Difficulty: medium*

---

##### Q15
> Twelve data points are shown in a scatterplot with x ranging from 0 to about 1,800 and y ranging from 0 to 20. A line of best fit for the data is also shown, rising from about (0, 0) up to about (1,800, 18).

At x = 1,200, which of the following is closest to the y-value predicted by the line of best fit?

**A.** 16 

  *16 is close to the line's height near x = 1,600, past the requested x = 1,200. Reading a point further along the line than the one asked for overshoots the prediction.*

**B.** 14 

  *14 sits closer to the line's value around x = 1,400 than at x = 1,200. It's in the right direction but reads the line one gridline further along than intended.*

**C.** 11 **(Correct)**

  *Correct. The line rises roughly from (0, 0) to (1,800, 18), a slope of about 18/1,800 = 0.01. At x = 1,200, the predicted y-value is about 0.01 × 1,200 = 12, closest among the choices to 11.*

**D.** 6 

  *6 is close to the line's value nearer x = 600, well short of the requested x = 1,200. This undershoots by reading the line at roughly half the intended horizontal distance.*

*Difficulty: medium*

---

##### Q16
> The scatterplot shows the relationship between the weight, in pounds, of each of 9 female gray wolves on April 30 and the number of offspring each gray wolf produced. Two data points sit directly above the 40-pound mark on the horizontal axis at a height of 5 offspring; three points cluster around 50 pounds at a height of 6 offspring; three points cluster around 55–60 pounds at 7 offspring; and one point sits at about 65 pounds and 8 offspring.

How many offspring did the 50-pound gray wolf produce?

**A.** 8 

  *8 offspring is the value for the heaviest wolf, at about 65 pounds — reading the highest point on the graph instead of the point specifically above 50 pounds.*

**B.** 7 

  *7 offspring is the value for wolves around 55–60 pounds, one weight bracket above the 50-pound wolf asked about. This reads an adjacent cluster of points instead of the one at exactly 50 pounds.*

**C.** 6 **(Correct)**

  *Correct. This is a direct reading, not a prediction from a fitted line: find the dot plotted directly above 50 pounds on the horizontal axis and read across to its height on the vertical axis, which is 6 offspring.*

**D.** 5 

  *5 offspring is the value for the lighter wolves, around 40 pounds, one weight bracket below the 50-pound wolf asked about.*

*Difficulty: easy*

---

##### Q17
> The line graph shows the estimated number of chipmunks in a state park on April 1 of each year from 1989 to 1999. Reading the plotted values: the count starts low around 1989–1990 (roughly 40–90), rises and falls in a jagged pattern through the early-to-mid 1990s, spikes to its highest point in 1994 (around 150), dips afterward, and rises again toward the end of the series without reaching the 1994 peak.

Based on the line graph, in which year was the estimated number of chipmunks in the state park the greatest?

**A.** 1989 

  *1989 is near the start of the graph, where the estimated count is one of the lowest values shown, not the highest. This picks the first labeled year rather than comparing the height of every point.*

**B.** 1994 **(Correct)**

  *Correct. The highest point on the entire graph occurs in 1994 — every other labeled year, including the ones right before and after it, sits lower on the vertical axis.*

**C.** 1995 

  *1995 comes immediately after the 1994 peak and shows a noticeable drop from it. It's a real value on the graph, but not the tallest point overall — 1994 stands above it.*

**D.** 1998 

  *1998 is part of a later rise in the graph, but that rise does not reach back up to the height the count hit in 1994. Picking a point that is increasing, without checking whether it exceeds the earlier peak, misses the true maximum.*

*Difficulty: easy*

---

##### Q18
> The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. Reading the graph: the data point at x = 1 sits at about y = 12, while the line of best fit at x = 1 sits at about y = 11.

Which of the following is closest to the difference between the y-coordinate of the data point with x = 1 and the y-value predicted by the line of best fit at x = 1?

**A.** 1 **(Correct)**

  *Correct. This is a residual: the data point's y-coordinate minus the line's predicted y-value at the same x. At x = 1, the dot sits at about y = 12 and the line sits at about y = 11, so the difference is about 12 − 11 = 1.*

**B.** 2 

  *2 overstates the gap between the dot and the line at x = 1 — that gap is closer to a single unit on this graph, not two. This is the kind of overestimate that comes from misreading one of the two y-values by a gridline.*

**C.** 5 

  *5 is far larger than the actual vertical gap between the dot and the line at x = 1. A difference this size would put the dot roughly at the top of the graph's visible range while the line sits near its bottom — not what the graph at x = 1 shows.*

**D.** 12 

  *12 is the y-coordinate of the data point itself, not the difference between it and the line's prediction. Reporting one of the two values being compared, instead of subtracting them, skips the actual computation the question asks for.*

*Difficulty: hard*

---

##### Q19
> In the given scatterplot, a line of best fit for the data is shown, sloping downward from about (0, 8) to about (10, 1).

Which of the following is closest to the slope of this line of best fit?

**A.** 7 

  *7 has the right magnitude but the wrong sign — the line clearly falls from left to right, so its slope has to be negative. A positive slope of this size would mean the line rises steeply, which is not what's shown.*

**B.** 0.7 

  *0.7 has the right magnitude but the wrong sign, the same error as choice A in the other direction: reading the steepness correctly while missing that the line is falling, not rising.*

**C.** −0.7 **(Correct)**

  *Correct. Slope is rise over run between two points on the line: (1 − 8)/(10 − 0) = −7/10 = −0.7. The line falls gently and steadily from left to right, matching a slope that is negative and less than 1 in magnitude.*

**D.** −7 

  *−7 has the correct negative sign but is ten times too steep. A slope of −7 would mean the line drops 7 units in y for every 1 unit of x — a nearly vertical plunge — not the gentle decline actually shown over the 10-unit run.*

*Difficulty: medium*

---

##### Q20
Which of the following is true about the values of 2^x and 2x + 2 for x > 0?

**A.** For all x > 0, it is true that 2^x < 2x + 2. 

  *This claims the exponential function stays smaller than the linear one forever, which fails for large x: at x = 4, 2^4 = 16 is already greater than 2(4) + 2 = 10, and the gap only grows from there. Checking only small values of x, where the linear function does lead, and assuming that pattern continues forever is exactly the trap this question is built around.*

**B.** For all x > 0, it is true that 2^x > 2x + 2. 

  *This claims the exponential function is always larger, which fails for small x: at x = 1, 2^1 = 2 is less than 2(1) + 2 = 4. Exponential growth does eventually dominate linear growth, but 'eventually' is the operative word — it is not true from the very start.*

**C.** There is a constant c such that if 0 < x < c, then 2^x < 2x + 2, but if x > c, then 2^x > 2x + 2. **(Correct)**

  *Correct. Compare the two at a few values. At x = 1: 2^1 = 2 and 2(1) + 2 = 4, so 2^x < 2x + 2. At x = 3: 2^3 = 8 and 2(3) + 2 = 8, equal — this is the crossover. At x = 4: 2^4 = 16 and 2(4) + 2 = 10, now 2^x > 2x + 2. This is the defining behavior of an exponential function against a linear one: the linear function leads for small x, but the exponential function eventually overtakes it and stays ahead permanently, because a constant multiplier compounds while a constant addition does not.*

**D.** There is a constant c such that if 0 < x < c, then 2^x > 2x + 2, but if x > c, then 2^x < 2x + 2. 

  *This has the crossover backwards. The linear function 2x + 2 is the one that leads for small x (at x = 1, 4 > 2) and the exponential function 2^x is the one that eventually overtakes it (at x = 4, 16 > 10) — not the reverse. Constant growth can only ever delay being overtaken by compounding growth, never win permanently.*

*Difficulty: sat-hardest*

---

##### Q21
> The scatterplot shows the relationship between two variables, x and y. A line of best fit is also shown, sloping downward from about (0, 13) to about (14, 2).

Which of the following is closest to the slope of the line of best fit shown?

**A.** −2.4 

  *−2.4 has the correct negative sign but is roughly three times too steep — a slope of that magnitude would mean the line drops about 34 units of y over the 14-unit run shown, far more than the roughly 11-unit drop the graph actually shows.*

**B.** −0.8 **(Correct)**

  *Correct. Slope is rise over run between two points on the line: (2 − 13)/(14 − 0) = −11/14 ≈ −0.79, closest to −0.8. The line declines gradually across the full width of the graph, consistent with a slope whose magnitude is less than 1.*

**C.** 0.8 

  *0.8 has the right magnitude but the wrong sign. The line clearly falls from upper left to lower right, so the slope must be negative; this choice describes a line rising at the same rate instead.*

**D.** 2.4 

  *2.4 combines both errors — the wrong sign and roughly three times too steep a magnitude — describing a line that rises sharply, the opposite of the gentle decline actually shown.*

*Difficulty: medium*

---

##### Q22
An inspector begins a day of work with a large sample of shirts that need to be checked for defects. The inspector works at a constant rate throughout the morning. What type of model is best to model the number of shirts remaining to be checked for defects at any given time throughout the morning?

**A.** A linear model with a positive slope 

  *A positive slope would mean the number of shirts remaining increases over time, but the inspector is checking shirts throughout the morning, which can only decrease the count remaining, never increase it.*

**B.** A linear model with a negative slope **(Correct)**

  *Correct. Checking shirts at a constant rate means the same number of shirts gets checked — and so removed from the remaining count — in each equal unit of time. A constant rate of change is exactly what defines a linear model, and because the number remaining is going down over time, the slope is negative.*

**C.** An exponential growth model 

  *Exponential growth means the quantity increases by a constant percentage each period, compounding upward — but here the count is going down, not up, and the rate is stated to be constant (a fixed number of shirts per hour), not a percentage of what's left.*

**D.** An exponential decay model 

  *Exponential decay would describe a quantity shrinking by a constant percentage each period — for instance, if the inspector always checked half of the remaining shirts each hour. Here the rate is constant in amount ('works at a constant rate'), which is the signature of a linear model, not a percentage-based exponential one.*

*Difficulty: easy*

---

##### Q23
> The scatterplot shows data for ten charities along with the line of best fit, plotting the percent of total expenses spent on programs against total income, in millions of dollars. Among the ten points, the one with the greatest percent of total expenses spent on programs sits noticeably above the line of best fit at that income level — its actual percent is about 95%, while the line of best fit predicts about 88% at that same income.

For the charity with the greatest percent of total expenses spent on programs, which of the following is closest to the difference of the actual percent and the percent predicted by the line of best fit?

**A.** 10% 

  *10% overstates the residual — the actual value for this charity is only about 7 percentage points above the line's prediction, not 10. This is the kind of overshoot that comes from reading the line's predicted value a bit too low.*

**B.** 7% **(Correct)**

  *Correct. This is a residual, in percentage points: actual − predicted = 95% − 88% = 7 percentage points. The charity with the highest program-spending percent sits well above the line at its income level, and 7% captures how far above.*

**C.** 4% 

  *4% understates the residual, consistent with reading the line's predicted value a bit too high, or the actual data point's height a bit too low, before subtracting.*

**D.** 1% 

  *1% is much smaller than the actual gap between this point and the line — this charity's dot is clearly separated from the line of best fit, not sitting almost on top of it. A residual this small would mean the model fit this particular charity almost exactly, which the graph does not show.*

*Difficulty: hard*

---

##### Q24
> Each dot in the scatterplot represents the height x, in feet, in the high jump, and the distance y, in feet, in the long jump, made by each student in a group of twenty students. The data trend rises from about 0.8 feet of long jump distance near a high jump height of 0, up to about 20.6 feet of long jump distance near a high jump height of 6 feet.

The graph of which of the following equations is a line that most closely fits the data?

**A.** y = 0.82x + 3.30 

  *y = 0.82x + 3.30 has the slope and intercept roles swapped: it would predict a long jump distance of 3.30 feet even for a high jump height of 0, well above the near-zero distance the trend actually shows there, and it rises far too gently (only 0.82 feet of long jump per foot of high jump) to reach anywhere near the roughly 20-foot distances seen at the high end of the data.*

**B.** y = 0.82x − 0.82 

  *y = 0.82x − 0.82 keeps the slope and intercept swapped and also predicts a negative long jump distance at x = 0 (−0.82 feet), which is physically impossible and not what the data near the low end of the graph shows.*

**C.** y = 3.30x + 0.82 **(Correct)**

  *Correct. The trend rises about 19.8 feet of long jump distance (from about 0.8 to about 20.6) over a 6-foot span of high jump height, a slope of about 19.8/6 ≈ 3.3 — matching the coefficient on x in this choice. The intercept, about 0.82, matches the trend's height near a high jump height of 0, where a very small high jump still corresponds to a very small (near-zero) long jump distance.*

**D.** y = 3.30x − 3.30 

  *y = 3.30x − 3.30 has the right slope but the wrong intercept: at x = 0 this predicts −3.30 feet, a negative long jump distance, while the data actually starts near a small positive value close to 0.82 feet.*

*Difficulty: medium*

---

##### Q25
> The scatterplot shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980, where t is the number of years since 1968 and n is the number of visitors. A line of best fit is also shown, rising from about 16,090 visitors at t = 0 up to about 72,000 visitors by about t = 12.

Which of the following could be an equation of the line of best fit shown?

**A.** n = 16,090 + 4,680t **(Correct)**

  *Correct. The line's intercept — its value at t = 0, the year 1968 — is about 16,090 visitors, matching the constant term in this choice. The rise from about 16,090 to about 72,000 over 12 years gives a slope of about (72,000 − 16,090)/12 ≈ 4,660 visitors per year, closest to the 4,680 coefficient here.*

**B.** n = 4,690 + 16,090t 

  *This has the intercept and slope roles reversed: it starts at only 4,690 visitors in 1968 and climbs by a massive 16,090 visitors every single year, which would put the museum at over 190,000 annual visitors by 1980 — far beyond what the graph shows by its right edge.*

**C.** n = 16,090 + 9,060t 

  *16,090 is the right starting point, but a slope of 9,060 visitors per year is roughly double the actual rate of increase — this model would predict about 16,090 + 9,060(12) ≈ 124,810 visitors by 1980, well above where the graph's line actually ends.*

**D.** n = 9,060 + 16,090t 

  *This has the intercept and slope roles reversed, the same error as choice B: starting at 9,060 visitors in 1968 and climbing by 16,090 every year, a rate roughly three and a half times steeper than the graph shows, producing an implausibly large visitor count by 1980.*

*Difficulty: medium*

---

##### Q26
In which of the following tables is the relationship between the values of x and their corresponding y-values nonlinear? Table A: x = 1, 2, 3, 4 gives y = 8, 11, 14, 17. Table B: x = 1, 2, 3, 4 gives y = 4, 8, 12, 16. Table C: x = 1, 2, 3, 4 gives y = 8, 13, 18, 23. Table D: x = 1, 2, 3, 4 gives y = 6, 12, 24, 48.

**A.** Table A: y = 8, 11, 14, 17 

  *The differences here are constant: 11 − 8 = 3, 14 − 11 = 3, 17 − 14 = 3. A constant difference between consecutive y-values for evenly spaced x-values is exactly what makes a relationship linear, so this table does not qualify as the nonlinear one.*

**B.** Table B: y = 4, 8, 12, 16 

  *The differences here are constant at 4 each step: 8 − 4 = 4, 12 − 8 = 4, 16 − 12 = 4. This table represents the linear relationship y = 4x, not a nonlinear one.*

**C.** Table C: y = 8, 13, 18, 23 

  *The differences here are constant at 5 each step: 13 − 8 = 5, 18 − 13 = 5, 23 − 18 = 5. A constant difference is the definition of linear, so this table fits a straight line and is not the nonlinear one the question asks for.*

**D.** Table D: y = 6, 12, 24, 48 **(Correct)**

  *Correct. Check the differences between consecutive y-values: 12 − 6 = 6, 24 − 12 = 12, 48 − 24 = 24 — not constant, so this table is not linear. Check the ratios instead: 12/6 = 2, 24/12 = 2, 48/24 = 2 — constant, which is the signature of an exponential relationship, a specific kind of nonlinear pattern.*

*Difficulty: easy*

---

##### Q27
> A scatterplot shows a steeply rising trend, from about y = 0.8 at x = 0 up to about y = 24.8 at x = 8.

Which of the following could be the equation for a line of best fit for the data shown in the scatterplot above?

**A.** y = 3x + 0.8 **(Correct)**

  *Correct. The trend rises steeply — about 24 units of y over a run of 8 — a slope of about 24/8 = 3, matching the coefficient on x here, and an intercept near 0.8, matching the trend's height close to the origin at x = 0.*

**B.** y = 0.8x + 3 

  *y = 0.8x + 3 has the slope and intercept roles swapped: a slope of 0.8 is far too shallow for this steeply climbing data (it would only reach about y = 6.4 by x = 8), and an intercept of 3 is too high for a trend that starts close to the origin.*

**C.** y = −0.8x + 3 

  *y = −0.8x + 3 has both the wrong (shallow) magnitude and the wrong sign on the slope — this line falls as x increases, while the data climbs steeply upward from left to right.*

**D.** y = −3x + 0.8 

  *y = −3x + 0.8 has the right magnitude of slope but the wrong sign — this describes a line falling steeply as x increases, the mirror image of the steep rise the data actually shows.*

*Difficulty: medium*

---

##### Q28
> The scatterplot shows the relationship between two variables, x and y, with the horizontal axis running from about x = 22 to x = 36. A line of best fit is also shown, falling from about (24, 10) down to about (34, 0).

At x = 32, which of the following is closest to the y-value predicted by the line of best fit?

**A.** 0.4 

  *0.4 is close to the line's value very near x = 34, the right edge of the graph — past the requested x = 32.*

**B.** 1.5 

  *1.5 sits closer to the line's value around x = 33 than at x = 32, overshooting the target x-value by about one unit before reading the corresponding y.*

**C.** 2.4 **(Correct)**

  *Correct. The line falls about 10 units of y over the 10-unit run from x = 24 to x = 34, a slope of about −1. At x = 32, that's 8 units of x past x = 24, so the predicted y-value is about 10 − 8 = 2, closest among the choices to 2.4.*

**D.** 3.3 

  *3.3 corresponds to the line's height nearer x = 31, one unit short of the requested x = 32.*

*Difficulty: medium*

---

##### Q29
> In the given scatterplot, a line of best fit for the data is shown, rising from about (0, 0) through the plotted points up to about (8, 15).

Which of the following is closest to the slope of the line of best fit shown?

**A.** 0.2 

  *0.2 describes a line that rises only about 2 units of y over the full 8-unit run shown — far shallower than the line on this graph, which climbs all the way to about 15.*

**B.** 0.7 

  *0.7 is still far too shallow for this line: at that slope, the line would only reach about y = 5.6 by x = 8, well below the roughly y = 15 the line actually reaches.*

**C.** 1.8 **(Correct)**

  *Correct. Slope is rise over run between two points on the line: (15 − 0)/(8 − 0) = 15/8 ≈ 1.9, closest among the choices to 1.8. The line rises steadily and steeply across the graph, consistent with a slope well above 1.*

**D.** 2.6 

  *2.6 overstates the steepness slightly — at that slope the line would reach over y = 20 by x = 8, past where the line on the graph actually ends.*

*Difficulty: medium*

---

##### Q30
> The scatterplot shows the relationship between two variables, x and y, with the horizontal axis running from about x = 22 to x = 36. A line of best fit is also shown, falling from about (24, 10) down to about (34, 0).

At x = 25.5, which of the following is closest to the y-value predicted by the line of best fit?

**A.** 6.2 

  *6.2 is close to the line's value around x = 28, well past the requested x = 25.5.*

**B.** 7.3 

  *7.3 corresponds to the line's height nearer x = 27, about a unit and a half past the requested x = 25.5.*

**C.** 8.2 **(Correct)**

  *Correct. The line falls about 10 units of y over the 10-unit run from x = 24 to x = 34, a slope of about −1. At x = 25.5, that's 1.5 units of x past x = 24, so the predicted y-value is about 10 − 1.5 = 8.5, closest among the choices to 8.2.*

**D.** 9.1 

  *9.1 sits closer to the line's value right at x = 24.5, just short of the requested x = 25.5 — close, but reading the line slightly too early.*

*Difficulty: medium*

---

##### Q31
> The scatterplot shows the federal-mandated minimum wage every 10 years between 1940 and 2010, where x is the number of years since 1940. A line of best fit is shown, and its equation is y = 0.096x − 0.488.

What does the line of best fit predict about the increase in the minimum wage over the 70-year period?

**A.** Each year between 1940 and 2010, the average increase in minimum wage was 0.096 dollars. **(Correct)**

  *Correct. 0.096 is the coefficient on x, where x is measured in years — so it's the predicted increase per one year, exactly as this choice states. The constant −0.488 is the y-intercept, the model's predicted (and not literally meaningful) value at x = 0, and plays no role in the per-year rate.*

**B.** Each year between 1940 and 2010, the average increase in minimum wage was 0.49 dollars. 

  *0.49 dollars is roughly the model's rate over 5 years (0.096 × 5 ≈ 0.48), not one year. Multiplying the per-year rate by the wrong number of years before reporting it as an annual figure produces this kind of inflated number.*

**C.** Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.096 dollars. 

  *0.096 is correctly identified as the coefficient on x, but x counts individual years, not decades — the model's x-axis is 'years since 1940,' so 0.096 is the increase per year, not per 10-year period. Pairing the right number with the wrong unit gives a rate ten times too small for what this choice claims.*

**D.** Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.488 dollars. 

  *0.488 is the magnitude of the y-intercept, −0.488 — a different number entirely from the slope, and one that describes the model's (not literally meaningful) prediction at year 0, not a rate of change over any interval.*

*Difficulty: medium*

---

##### Q32
> The scatterplot shows a company's ice cream sales d, in dollars, and the high temperature t, in degrees Celsius (°C), on 12 different days. A line of best fit for the data is also shown, rising from about $480 near t = 12°C up to about $876 near t = 24°C.

Which of the following could be an equation of the line of best fit?

**A.** d = 0.03t + 402 

  *A slope of 0.03 is far too shallow — at this rate, sales would barely move at all across the whole 12°C span shown (about 0.03 × 12 = $0.36 total change), while the line on the graph rises by about $396 over that span.*

**B.** d = 10t + 402 

  *A slope of 10 is still much too shallow: over the 12°C range shown, this predicts a rise of only about $120, far less than the roughly $396 rise the line actually shows.*

**C.** d = 33t + 300 

  *This correctly captures the slope of 33, but its intercept of 300 is far too high: it predicts d = 33(12) + 300 = 696 at t = 12°C, well above the line's actual reading of about $480 there — this constant overshoots the line's height at the low end of the data by hundreds of dollars.*

**D.** d = 33t + 84 **(Correct)**

  *Correct. The line rises about $396 (from 480 to 876) over a 12°C span, a slope of about 396/12 = 33, matching the coefficient here. Checking the intercept: 33(12) + 84 = 396 + 84 = 480, matching the line's reading near t = 12°C, and 33(24) + 84 = 792 + 84 = 876, matching its reading near t = 24°C.*

*Difficulty: medium*

---

##### Q33
> The scatterplot shows the amount of electric energy generated, in millions of megawatt-hours, by nuclear sources over a 10-year period, with time in years on the horizontal axis. The data points rise from about 770 at year 0 to a peak of around 810 somewhere in the middle of the period, then curve back down toward about 780 by year 12 — a gentle, downward-opening arch.

Of the following equations, which best models the data in the scatterplot?

**A.** y = 1.674x² + 19.76x − 745.73 

  *This has a positive coefficient on x² (1.674), which makes the parabola open upward — a U-shape with a minimum in the middle, the opposite of the downward arch the data actually traces. Its constant term is also negative (−745.73), which would put the curve's intercept far below zero, nowhere near the graph's range in the 700s and 800s.*

**B.** y = −1.674x² − 19.76x − 745.73 

  *This has a negative coefficient on x² (correctly giving a downward-opening shape) but a negative constant term (−745.73), which would place the curve's y-intercept far below zero — the data actually sits entirely between about 770 and 820, nowhere close to negative values.*

**C.** y = 1.674x² + 19.76x + 745.73 

  *This has a positive coefficient on x² (1.674), producing an upward-opening U-shape rather than the downward arch the data shows, and its constant term is positive, which alone matches the graph's height but doesn't fix the wrong parabola orientation.*

**D.** y = −1.674x² + 19.76x + 745.73 **(Correct)**

  *Correct. The scatterplot forms a downward-opening arch — rising, reaching a peak, then falling — which requires a negative coefficient on x², and this is the only choice with a negative leading coefficient (−1.674) paired with a positive constant term (745.73) that lands near the data's actual starting height around 770–780 megawatt-hours. At x = 0, this model gives y = 745.73, consistent with the graph's y-intercept in the high-700s.*

*Difficulty: hard*

---

##### Q34
> The scatterplot shows the size x, in thousands of square feet, and the sale price y, in thousands of dollars, of 25 houses for sale in Town H. The data trend rises from about $150 thousand near a size of 0.5 thousand square feet up to about $400 thousand near a size of 3 thousand square feet.

Which of the following could be an equation for a line of best fit for the data?

**A.** y = 200x + 100 

  *A slope of 200 is roughly twice too steep: at that rate, going from 0.5 to 3 thousand square feet (a run of 2.5) would predict a price increase of about $500 thousand, well more than the roughly $250 thousand rise the data actually shows over that span.*

**B.** y = 100x + 100 **(Correct)**

  *Correct. The trend rises about $250 thousand (from 150 to 400) over a run of about 2.5 thousand square feet, a slope of about 250/2.5 = 100 — matching the coefficient here — and the intercept of 100 lands close to the trend's height as size approaches 0, consistent with a starting sale price around $100 thousand for a very small house.*

**C.** y = 50x + 100 

  *A slope of 50 is about half of the actual rate: over the same 2.5-thousand-square-foot span, this would predict only about a $125 thousand increase, well short of the roughly $250 thousand rise shown in the data.*

**D.** y = 100x 

  *This has the right slope but drops the intercept entirely (forcing it to 0), predicting a sale price of $0 for a house of size 0 — the data's trend clearly sits above $100 thousand even at the smallest sizes shown, so a model with no constant term undershoots every prediction by about that amount.*

*Difficulty: medium*

---

##### Q35
> Two investments were made, as shown in a table: Account A starts with $500 invested and earns 6% annual interest, compounded once per year. Account B starts with $1,000 invested and increases by a fixed $25 per year. The interest in Account A is compounded once per year.

Which of the following is true about the investments?

**A.** Account A always earns more money per year than Account B. **(Correct)**

  *Correct. In year 1, Account A earns 6% of $500 = $30, already more than Account B's flat $25. Because Account A's interest is compound, its balance grows every year, so its dollar earnings each year grow too — from $30, to 6% of $530 = $31.80, and onward — while Account B earns the same fixed $25 every year forever. Since Account A starts ahead and its yearly earnings only increase, while Account B's stays flat, Account A earns more per year at every point, not just at first.*

**B.** Account A always earns less money per year than Account B. 

  *This has the comparison backwards from the very first year: Account A earns 6% of $500 = $30 in year one, which already exceeds Account B's $25. Account B's larger starting balance ($1,000 versus $500) does not mean it earns more per year — its return comes from a flat dollar amount, not from a percentage of that larger balance.*

**C.** Account A earns more money per year than Account B at first but eventually earns less money per year. 

  *This gets the direction of the eventual trend backwards. Account A's yearly earnings grow over time because it is compounding on an ever-larger balance, while Account B's stays fixed at $25 — so any early lead Account A has can only widen, not reverse. A crossover would require Account A's growth to slow down or Account B's to speed up, and neither happens here.*

**D.** Account A earns less money per year than Account B at first but eventually earns more money per year. 

  *This claims Account A starts behind, but 6% of its $500 principal is $30 in the very first year, already ahead of Account B's flat $25 — there's no early period where B earns more. It also claims a crossover in the other direction, but nothing in either account's growth pattern would cause Account A's lead to disappear.*

*Difficulty: hard*

---

##### Q36
> The scatterplot shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu, with total protein on the horizontal axis (roughly 5 to 45 grams) and total fat on the vertical axis (roughly 10 to 75 grams). The line of best fit for the data is also shown, rising from about 10 grams of fat near 5 grams of protein up to about 65 grams of fat near 45 grams of protein.

According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?

**A.** 2.5 

  *2.5 grams per gram of protein is roughly 70% too steep — at that rate, the 40-gram protein span shown on the graph would correspond to a 100-gram rise in fat, well beyond the roughly 55-gram rise the line actually shows.*

**B.** 2.0 

  *2.0 grams per gram of protein is still noticeably steeper than the line shown: at that rate the fat would rise by 80 grams over the 40-gram protein span, more than the roughly 55 grams the line actually rises.*

**C.** 1.5 **(Correct)**

  *Correct. This is asking for the slope: the line rises about 55 grams of fat (from 10 to 65) over a 40-gram run of protein (from 5 to 45), a rate of about 55/40 ≈ 1.4 grams of fat per gram of protein, closest among the choices to 1.5.*

**D.** 1.0 

  *1.0 gram of fat per gram of protein is too shallow: at that rate the line would rise only 40 grams of fat over the 40-gram protein span, less than the roughly 55-gram rise the line on the graph shows.*

*Difficulty: medium*

---

#### Probability and conditional probability (36 items)

##### Q1
> TABLE. "Colors of Marbles in a Bag." Red: 8. Blue: 10. Green: 22. Total: 40.

The table shows the number of different colors of marbles in a bag. If a marble is chosen at random from the bag, what is the probability that the marble will be blue?

**A.** 30/40 

  *This is (8 + 22)/40 — red plus green, the two colors that are NOT blue, over the total. It answers 'what is the probability the marble is not blue,' the complement of what was asked, by adding every other color instead of using blue's own count.*

**B.** 22/40 

  *This uses green's count (22) instead of blue's (10) — the wrong row of the table was read. Blue and green are adjacent rows, and grabbing the wrong one gives a value that is still a valid-looking fraction, which is exactly what makes this error easy to miss.*

**C.** 18/40 

  *This is (8 + 10)/40, red plus blue, which answers 'red or blue' rather than 'blue' alone. Blue's own count (10) got added to a neighboring color instead of used by itself.*

**D.** 10/40 **(Correct)**

  *Correct. Blue's count is 10, the total is 40, and no condition was stated, so the denominator is the whole bag. 10/40 = 1/4.*

*Difficulty: easy*

---

##### Q2
> TABLE. "Customer Purchases at a Gas Station, 135 customers on Tuesday." Purchased gasoline: bought a beverage 60, did not buy a beverage 25, row total 85. Did not purchase gasoline: bought a beverage 35, did not buy a beverage 15, row total 50. Column totals: 90 bought a beverage, 40 did not. Grand total 135.

Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?

**A.** 15/50 

  *This is the 'did not buy gasoline and did not buy a beverage' cell (15) over the did-not-buy-gasoline row total (50) — a conditional probability (given no gasoline purchase, the probability of also not buying a beverage), not the plain marginal the question asked for. Only one cell of the row was used where the whole row total was needed.*

**B.** 15/40 

  *This is the same 15-customer cell divided by the no-beverage column total (40) instead of the gasoline row structure at all — it answers a question about beverage purchases, conditioned on beverages, that was never asked.*

**C.** 35/50 

  *This is the 'did not buy gasoline but did buy a beverage' cell (35) over the did-not-buy-gasoline row total (50) — a real conditional probability (given no gasoline purchase, probability of buying a beverage), but it answers a beverage question, not the [[marginal probability]] of skipping gasoline that the item asked for.*

**D.** 50/135 **(Correct)**

  *Correct. No condition was stated, so the denominator is the grand total, 135. The did-not-purchase-gasoline row total is 50. 50/135 is the probability.*

*Difficulty: medium*

---

##### Q3
> TABLE. "Number of High School Students Who Completed Summer Internships." No student attended both schools. Foothill: 2008: 87, 2009: 80, 2010: 75, 2011: 76, 2012: 70. Valley: 2008: 44, 2009: 54, 2010: 65, 2011: 76, 2012: 82. Column totals: 2008: 131, 2009: 134, 2010: 140, 2011: 152, 2012: 152.

Of the students who completed a summer internship in 2010, which of the following represents the fraction of students who were from Valley High School?

**A.** 10/140 

  *10 is the gap between Foothill's 2010 count (75) and Valley's (65), not either school's actual count. This subtracts the two schools from each other instead of reading Valley's own count off the table.*

**B.** 65/140 **(Correct)**

  *Correct. 'Of the students who completed a summer internship in 2010' fixes the denominator at the 2010 column total, 140. Valley's 2010 count is 65. 65/140.*

**C.** 75/140 

  *This uses Foothill's 2010 count (75), not Valley's (65) — the wrong school's row was read for a question that names Valley specifically.*

**D.** 65/75 

  *This divides Valley's 2010 count by Foothill's 2010 count instead of by the 2010 column total (140). One school's count was used as if it were the denominator for 'of the students who completed an internship in 2010' instead of the total.*

*Difficulty: medium*

---

##### Q4
> TABLE. "Voice type of 25 registered singers." Countertenor: 4. Tenor: 6. Baritone: 10. Bass: 5.

A total of 25 men registered for singing lessons. The frequency table shows how many of these singers have certain voice types. If one of these singers is selected at random, what is the probability he is a baritone?

**A.** 0.10 

  *This is 10/100 — the baritone count placed over 100 instead of over the actual number of registered singers, 25. It treats the pool as if it were sized for a direct percent conversion rather than using the real total stated in the problem.*

**B.** 0.40 **(Correct)**

  *Correct. 10 baritones out of 25 singers. 10/25 = 0.40.*

**C.** 0.60 

  *This is (10 + 5)/25 — baritone plus bass, as if bass singers were also being counted as baritones. Adding a second category into the numerator answers 'baritone or bass,' not 'baritone.'*

**D.** 0.67 

  *This is 10/15, baritones over (baritones + basses) instead of over all 25 registered singers. It treats the two lowest voice types as though they were the entire population, dropping the countertenors and tenors from the pool entirely.*

*Difficulty: easy*

---

##### Q5
> A survey taken by 1,000 students at a school asked whether they played school sports; the table summarizes all 1,000 responses. Play a school sport: Males 312, Females 220. Do not play a school sport: Males unknown, Females 216.

How many of the males surveyed responded that they do not play a school sport?

**A.** 109 

  *This comes from averaging the two known female counts, (220 + 216)/2 = 218, and then halving that again to 109 — assuming the missing male count must be some symmetric fraction of the female numbers instead of using the fact that all four cells have to add to 1,000.*

**B.** 252 **(Correct)**

  *Correct. All four cells sum to the 1,000 surveyed students: 1,000 − 312 − 220 − 216 = 252.*

**C.** 468 

  *This is 1,000 − 312 − 220 = 468, the total number of students of either gender who do not play a sport. It stops one subtraction short — the 216 female non-players are still sitting inside this figure and were never removed to isolate the males.*

**D.** 688 

  *This is 1,000 − 312, everyone who is not a male sport-player — which includes every one of the 436 females along with the actual male non-players. It never restricts the count to males at all.*

*Difficulty: medium*

---

##### Q6
> TABLE. "70 rocks classified by type." Igneous: 10. Metamorphic: 33. Sedimentary: 27.

If one of these rocks is selected at random, what is the probability of selecting a rock that is igneous?

**A.** 10/27 

  *This divides the igneous count by the sedimentary count (27) instead of the total number of rocks (70) — one category's count was used as the denominator instead of the grand total.*

**B.** 10/33 

  *This divides the igneous count by the metamorphic count (33) instead of the total number of rocks (70) — the same error as choice A, using a different category's count as the denominator.*

**C.** 10/60 

  *60 is metamorphic plus sedimentary (33 + 27) — the total with the igneous rocks themselves excluded. The category being measured has to stay inside its own denominator; removing it gives a population of rocks that are guaranteed not to be igneous.*

**D.** 10/70 **(Correct)**

  *Correct. No condition was stated, so the denominator is all 70 rocks. 10/70 = 1/7.*

*Difficulty: easy*

---

##### Q7
Of the 8 planets in our solar system, 4 are considered rocky. If a student randomly selects 1 of those 8 planets as a topic for a report, what is the probability that the selected planet will be rocky?

**A.** 1/8 

  *This treats the '1' in 'selects 1 of those 8 planets' as the numerator, as if only one planet were rocky. The '1' describes how many planets the student picks, not how many rocky planets exist — that count is 4.*

**B.** 1/4 

  *This divides the same '1' (the single planet being selected) by the rocky-planet count (4), instead of dividing the rocky-planet count (4) by all 8 planets. The roles of numerator and denominator were swapped and the wrong number went into the numerator.*

**C.** 1/2 **(Correct)**

  *Correct. 4 of the 8 planets are rocky. 4/8 = 1/2.*

**D.** 2 

  *This is 8/4, the total number of planets over the rocky count — the fraction was inverted. A probability greater than 1 is a signal that a fraction has been flipped, not a valid answer.*

*Difficulty: easy*

---

##### Q8
> TABLE. "Texting behavior and cell phone talk habits, 799 US teens." Light texters: talk on the phone daily 110, do not 146, row total 256. Medium texters: 139, 164, row total 303. Heavy texters: 166, 74, row total 240. Column totals: 415 talk on the phone daily, 384 do not. Grand total 799.

If one of the 799 teens surveyed is selected at random, what is the probability that the teen talks on a cell phone daily?

**A.** 1/799 

  *This reads 'one of the 799 teens surveyed' as though it supplies the numerator, giving a value of 1, instead of using the actual column total for teens who talk daily, 415.*

**B.** 415/799 **(Correct)**

  *Correct. No condition narrows the pool, so the denominator is all 799 teens. The 'talks on a cell phone daily' column total is 415. 415/799.*

**C.** 384/415 

  *This divides the 'does not talk daily' column total (384) by the 'talks daily' column total (415) — one margin over another margin, which produces odds rather than a probability and is not even guaranteed to land between 0 and 1.*

**D.** 384/799 

  *This is the complement — the probability that a teen does NOT talk on a cell phone daily — rather than the probability that was asked for.*

*Difficulty: easy*

---

##### Q9
A store received a shipment of 1,000 MP3 players, 4 of which were defective. If an MP3 player is randomly selected from this shipment, what is the probability that it is defective?

**A.** 0.004 **(Correct)**

  *Correct. 4/1,000 = 0.004.*

**B.** 0.04 

  *This is off by one decimal place — the equivalent of computing 4/100 instead of 4/1,000. The defective count was divided by the wrong power of ten.*

**C.** 0.4 

  *This is off by two decimal places — the equivalent of computing 4/10 instead of 4/1,000.*

**D.** 4 

  *This is the raw defective count with no division by the shipment size at all — a probability of 4 is also impossible on its face, since every probability must be at most 1.*

*Difficulty: easy*

---

##### Q10
There are n nonfiction books and 12 fiction books on a bookshelf. If one of these books is selected at random, what is the probability of selecting a nonfiction book, in terms of n?

**A.** n/12 

  *This divides the nonfiction count by the fiction count (12) instead of by the total number of books on the shelf, n + 12 — treating the fiction total as though it were the whole population.*

**B.** n/(n + 12) **(Correct)**

  *Correct. There are n nonfiction books out of n + 12 total books, so the probability is n/(n + 12).*

**C.** 12/n 

  *This has both the wrong numerator (12, the fiction count) and the wrong denominator (n, the nonfiction count) — it reports the number of fiction books relative to the number of nonfiction books rather than nonfiction books relative to the shelf total.*

**D.** 12/(n + 12) 

  *This is the probability of selecting a FICTION book — the correct denominator, n + 12, paired with the wrong numerator. It answers the complement of the question that was asked.*

*Difficulty: medium*

---

##### Q11
A bag contains a total of 60 marbles. A marble is to be chosen at random from the bag. If the probability that a blue marble will be chosen is 0.35, how many marbles in the bag are blue?

**A.** 21 **(Correct)**

  *Correct. 0.35 × 60 = 21.*

**B.** 25 

  *This is 60 − 35, treating 0.35 as if it were the raw count '35' and subtracting it from the total, instead of multiplying 60 by the probability 0.35.*

**C.** 35 

  *This reads '0.35' as '35 marbles' directly, skipping the multiplication by the bag size (60) entirely. The decimal point was effectively dropped.*

**D.** 39 

  *This is 60 × 0.65 = 39, the number of marbles that are NOT blue — the complement of the count that was asked for.*

*Difficulty: medium*

---

##### Q12
> There are 20 buttons in a bag: 8 white buttons, 2 orange buttons, and 10 brown buttons.

If one of these buttons is selected at random, what is the probability of selecting a white button?

**A.** 2/20 

  *This uses the orange count (2) instead of the white count (8) — the wrong color's count was read off.*

**B.** 8/20 **(Correct)**

  *Correct. 8 white buttons out of 20 total. 8/20 = 2/5.*

**C.** 10/20 

  *This uses the brown count (10) instead of the white count (8) — the wrong color's count was read off.*

**D.** 12/20 

  *This is (2 + 10)/20, orange plus brown — the two colors that are NOT white, added together. It answers the complement, 'not white,' instead of 'white.'*

*Difficulty: easy*

---

##### Q13
A data set of three numbers is shown: −13, 4, 23. If a number from this data set is selected at random, what is the probability of selecting a negative number?

**A.** 0 

  *This reads −13 as a positive number, so no member of the data set is counted as negative at all. A probability of 0 says the event is impossible, but −13 is right there in the set.*

**B.** 1/3 **(Correct)**

  *Correct. Exactly one of the three numbers, −13, is negative. 1/3.*

**C.** 2/3 

  *This counts the two positive numbers, 4 and 23, instead of the one negative number — it computes the probability of NOT selecting a negative number, the complement of what was asked.*

**D.** 1 

  *This treats all three numbers as negative. A probability of 1 says the event is certain, but two of the three numbers, 4 and 23, are positive.*

*Difficulty: easy*

---

##### Q14
> TABLE. "Car dealership customers from the last month, by age and number of visits, 135 total." Less than 40 years old: 1 visit 15, 2 or more visits 15, row total 30. At least 40 years old: 1 visit 20, 2 or more visits 85, row total 105. Column totals: 35 made 1 visit, 100 made 2 or more visits.

If a customer from the last month is selected at random, what is the probability that the selected customer is at least 40 years old?

**A.** 30/135 

  *This uses the under-40 row total (30) instead of the at-least-40 row total (105) — it reports the probability of the complementary age group.*

**B.** 35/135 

  *This uses the 1-visit column total (35) instead of the at-least-40 row total (105) — the visit-count margin was used where the age margin was needed.*

**C.** 100/135 

  *This uses the 2-or-more-visits column total (100) instead of the at-least-40 row total (105) — the same confusion of margins as choice B, using the other visit-count column.*

**D.** 105/135 **(Correct)**

  *Correct. No condition was stated, so the denominator is the grand total, 135. The at-least-40 row total is 105. 105/135.*

*Difficulty: easy*

---

##### Q15
> TABLE. "Prices of 14 Different Cars." Nonhybrid: priced at no more than $25,000: 5, priced greater than $25,000: 3, row total 8. Hybrid: priced at no more than $25,000: 2, priced greater than $25,000: 4, row total 6. Column totals: 7 priced at no more than $25,000, 7 priced greater than $25,000.

If one of the cars listed for sale is selected at random, what is the probability that the car selected will be a hybrid car priced at no more than $25,000?

**A.** 1/7 **(Correct)**

  *Correct. No condition was stated — this is a joint probability, one cell over the grand total. The hybrid-and-no-more-than-$25,000 cell is 2, and there are 14 cars in all. 2/14 = 1/7.*

**B.** 2/7 

  *This is the same cell (2) over the no-more-than-$25,000 column total (7) instead of the grand total (14) — a conditional probability (given the car is priced at no more than $25,000, the probability it's a hybrid) rather than the joint probability that was asked for.*

**C.** 1/3 

  *This is the same cell (2) over the hybrid row total (6) instead of the grand total (14) — the reversed conditional (given the car is a hybrid, the probability it's priced at no more than $25,000).*

**D.** 4/7 

  *This uses the hybrid-and-priced-over-$25,000 cell (4) over the over-$25,000 column total (7) — both the wrong cell and the wrong price category, answering a question about the wrong price bracket entirely.*

*Difficulty: medium*

---

##### Q16
> TABLE. "Coat color and eye color for 48 Himalayan kittens." Cream-tortoiseshell: deep blue eyes 16, light brown eyes 16, row total 32. Chocolate: deep blue eyes 12, light brown eyes 4, row total 16. Column totals: 28 deep blue, 20 light brown.

What fraction of the chocolate-colored kittens has deep blue eyes?

**A.** 12/48 

  *This divides the chocolate-and-deep-blue cell (12) by the grand total (48) instead of by the chocolate row total (16). 'Of the chocolate-colored kittens' fixes the pool at chocolate kittens only, so the 32 cream-tortoiseshell kittens should not remain in the denominator.*

**B.** 12/28 

  *This divides the same cell (12) by the deep-blue column total (28) instead of the chocolate row total (16) — the reversed conditional (of the deep-blue-eyed kittens, what fraction are chocolate).*

**C.** 16/32 

  *This uses cream-tortoiseshell's deep-blue count (16) and row total (32) instead of chocolate's — it answers 'what fraction of cream-tortoiseshell kittens has deep blue eyes,' the wrong coat color entirely.*

**D.** 12/16 **(Correct)**

  *Correct. 'Of the chocolate-colored kittens' fixes the denominator at the chocolate row total, 16. Of those, 12 have deep blue eyes. 12/16 = 3/4.*

*Difficulty: medium*

---

##### Q17
> TABLE. "State parks with camping facilities and bicycle paths." Has camping facilities: has bicycle paths 20, does not have bicycle paths 5. Does not have camping facilities: has bicycle paths 8, does not have bicycle paths 4. Grand total 37.

If one of these state parks is selected at random, what is the probability that it has camping facilities but does not have bicycle paths?

**A.** 5/37 **(Correct)**

  *Correct. No condition was stated — this is a joint probability. The has-camping-but-no-bicycle-paths cell is 5, over the grand total of 37 parks.*

**B.** 5/25 

  *This divides the same cell (5) by the has-camping row total (25) instead of the grand total (37) — a conditional probability (given the park has camping facilities, the probability it lacks bicycle paths) rather than the joint probability asked for.*

**C.** 8/28 

  *This uses the no-camping-but-has-bicycle-paths cell (8) over the has-bicycle-paths column total (28) — the wrong cell divided by the wrong pool, matching neither the joint probability asked for nor a clean conditional.*

**D.** 5/9 

  *This divides the target cell (5) by the no-bicycle-paths column total (9) instead of the grand total (37) — the reversed conditional (given the park has no bicycle paths, the probability it has camping facilities).*

*Difficulty: medium*

---

##### Q18
> In a bag, there are 7 red, 4 white, 33 blue, and 33 yellow cubes.

If one of these cubes is selected at random, what is the probability of selecting a cube that is neither blue nor yellow?

**A.** 6/7 

  *This is (33 + 33)/77 = 66/77 = 6/7, the probability of selecting a cube that IS blue or yellow — the complement of 'neither blue nor yellow,' not the answer to it.*

**B.** 7/11 

  *This treats the neither-blue-nor-yellow subgroup (7 red + 4 white = 11 cubes) as if it were the entire bag, then narrows further to just the red cubes within it (7). It answers 'of the cubes that are neither blue nor yellow, what fraction are red,' a question nobody asked.*

**C.** 1/3 

  *This is 11/33 — the neither-blue-nor-yellow count (11) divided by the count of just ONE of the two excluded colors (33) instead of the full bag of 77 cubes.*

**D.** 1/7 **(Correct)**

  *Correct. Neither blue nor yellow means red or white: 7 + 4 = 11 cubes, out of 7 + 4 + 33 + 33 = 77 total. 11/77 = 1/7.*

*Difficulty: medium*

---

##### Q19
Each vertex of a 14-sided polygon is labeled with one of the 14 letters A through N, with a different letter at each vertex. If one vertex is selected at random, what is the probability that the letter D will be at the selected vertex?

**A.** 1/14 **(Correct)**

  *Correct. Exactly one of the 14 vertices is labeled D, so the probability is 1/14.*

**B.** 4/14 

  *D is the 4th letter of the alphabet, and that ordinal position (4) was used as the numerator instead of 1 — only one vertex is actually labeled D, not four.*

**C.** 1/13 

  *This undercounts the vertices as 13 instead of 14 — an off-by-one slip in counting the span of letters A through N.*

**D.** 1/26 

  *This uses 26, the size of the full alphabet, as the denominator instead of 14, the number of vertices (and letters) actually given in the problem.*

*Difficulty: easy*

---

##### Q20
> TABLE. "Weekday and Weekend Day Rain for 12 Weeks." Weekdays: rain 12, no rain 48, row total 60. Weekend days: rain 8, no rain 16, row total 24. Column totals: 20 days with rain, 64 days with no rain. Grand total 84.

If one of the days on which there was no rain is selected at random, what is the probability the day was a weekend day?

**A.** 4/21 

  *This is the weekend-no-rain cell (16) over the grand total (84), reduced to 4/21 — a joint probability rather than a conditional. 'Selected at random from the days on which there was no rain' already discarded the 20 rainy days, so 84 can't still be the denominator.*

**B.** 1/4 **(Correct)**

  *Correct. 'From the days on which there was no rain' fixes the pool at the no-rain column, total 64. Of those, 16 were weekend days. 16/64 = 1/4.*

**C.** 2/3 

  *This is the weekend-no-rain cell (16) over the weekend row total (24) instead of the no-rain column total (64) — the reversed conditional (given the day was a weekend day, the probability there was no rain).*

**D.** 3/4 

  *This uses the weekday-no-rain cell (48) instead of the weekend-no-rain cell (16), while correctly dividing by the no-rain column total (64) — the wrong row was read within the right pool.*

*Difficulty: medium*

---

##### Q21
At a conference, there are a total of 275 attendees. Each attendee is assigned to either group A, group B, or group C. If one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is 0.44, and the probability of selecting an attendee who is assigned to group B is 0.24. How many attendees are assigned to group C?

**A.** 66 

  *This is 0.24 × 275, group B's count — not group C's. The wrong group's probability was applied.*

**B.** 88 **(Correct)**

  *Correct. P(C) = 1 − 0.44 − 0.24 = 0.32, since every attendee is in exactly one of the three groups. 0.32 × 275 = 88.*

**C.** 121 

  *This is 0.44 × 275, group A's count — not group C's. The wrong group's probability was applied.*

**D.** 187 

  *This computes P(C) as 0.44 + 0.24 = 0.68 — adding the two given probabilities instead of subtracting them from 1. 0.68 × 275 = 187. Group C's probability is what's left over once A and B are removed, not what results from combining them.*

*Difficulty: medium*

---

##### Q22
If 1,200 customers register for new accounts at a social media website every day, what fraction of the first 60,000 new accounts are registered in the first 5 days?

**A.** 1/5 

  *This comes from computing the daily rate as 2,400 instead of the given 1,200 — a doubling slip — which makes the total days needed to reach 60,000 come out to 25 instead of 50, giving 5/25 = 1/5.*

**B.** 1/10 **(Correct)**

  *Correct. At 1,200 accounts per day, reaching 60,000 accounts takes 60,000/1,200 = 50 days. The first 5 days are 5/50 = 1/10 of that.*

**C.** 1/12 

  *This comes from misreading the daily rate as 1,000 instead of the given 1,200, making the total days needed 60,000/1,000 = 60 instead of 50, and giving 5/60 = 1/12.*

**D.** 1/50 

  *This correctly finds that 50 days are needed to reach 60,000 accounts, but then puts 1 in the numerator instead of 5 — as if only the very first day, rather than all five, belonged in the count.*

*Difficulty: medium*

---

##### Q23
> TABLE. "United States Presidents from 1789 to 2015, by age at first taking office." Ages 40–44: 2. Ages 45–49: 7. Ages 50–54: 13. Ages 55–59: 11. Ages 60–64: 7. Ages 65–69: 3.

Of those presidents who were at least 50 years old when they first took office, what fraction were at least 60 years old?

**A.** 10/43 

  *This divides the at-least-60 count (7 + 3 = 10) by all 43 presidents in the table instead of by the 34 who were at least 50. 'Of those presidents who were at least 50' already discarded the 9 presidents younger than 50, so 43 can't still be the denominator.*

**B.** 10/34 **(Correct)**

  *Correct. 'Of those presidents who were at least 50' fixes the pool at 13 + 11 + 7 + 3 = 34. Of those, the ones at least 60 are 7 + 3 = 10. 10/34 = 5/17.*

**C.** 10/24 

  *24 is just the 50–54 and 55–59 brackets (13 + 11) — as if 'at least 50' meant 'in the 50s,' cutting the 60–64 and 65–69 presidents out of the very pool the numerator (10) is drawn from.*

**D.** 25/34 

  *This attempts the complement — the fraction of the at-least-50 pool that is NOT at least 60 — but the subtraction 34 − 10 was carried out as 25 instead of the correct 24. Even without that slip, it would answer the wrong question: the complement of 'at least 60,' not 'at least 60' itself.*

*Difficulty: hard*

---

##### Q24
> TABLE. "Penguin Exhibit, 320 penguins by type and gender." Chinstrap: male 41, female 59, row total 100. Emperor: male 8, female 27, row total 35. Gentoo: male 49, female 54, row total 103. Macaroni: male 42, female 40, row total 82. Column totals: 140 male, 180 female.

Which type of penguin has a female population that is closest to being 1/3 of the total female penguin population in the exhibit?

**A.** Chinstrap **(Correct)**

  *Correct. 1/3 of the total female population (180) is 60. Chinstrap's female count is 59, only 1 away from 60 — closer than Gentoo (54, off by 6), Macaroni (40, off by 20), or Emperor (27, off by 33).*

**B.** Emperor 

  *Emperor's female count, 27, is the smallest of the four — but 'closest to 1/3 of the total' means closest to the benchmark value of 60, not smallest in absolute terms. Emperor is actually the farthest from 60 of any type.*

**C.** Gentoo 

  *This divides the grand total (320, both sexes) by 3 (≈106.7) instead of the female total (180) by 3, and then compares that to each type's overall total rather than its female count — Gentoo's total of 103 happens to be closest to that miscalculated benchmark.*

**D.** Macaroni 

  *This divides the female total by 4, the number of penguin types, instead of by 3 as the question specifies: 180/4 = 45. Macaroni's female count of 40 is the closest match to that miscalculated benchmark, not to the correct one of 60.*

*Difficulty: hard*

---

##### Q25
A box contains 13 red pens and 37 blue pens. If one of these pens is selected at random, what is the probability of selecting a red pen? (Express your answer as a decimal or fraction, not as a percent.)

**A.** 0.13 

  *This treats the raw count 13 as if it were already a decimal probability, without ever dividing by the total number of pens, 50.*

**B.** 0.26 **(Correct)**

  *Correct. 13 red pens out of 13 + 37 = 50 total. 13/50 = 0.26.*

**C.** 0.351 

  *This divides the red count by the blue count, 13/37, instead of by the total number of pens, 13/50 — one category's count was used as the denominator instead of the whole box.*

**D.** 0.74 

  *This is 37/50, the probability of selecting a BLUE pen — the complement of what was asked.*

*Difficulty: easy*

---

##### Q26
> TABLE. "Highest level of education completed, by department." Human Resources: bachelor's degree 4, master's degree 2. Accounting: bachelor's degree 3, master's degree 6.

A person from one of these departments is to be chosen at random. If the person chosen works in the Human Resources department, what is the probability that the highest level of education the person completed is a master's degree?

**A.** 2/15 

  *This divides the HR-and-master's cell (2) by the grand total (15) instead of the HR row total (6) — a joint probability rather than a conditional. 'If the person chosen works in Human Resources' already fixed the pool at HR employees, so the Accounting employees can't still be in the denominator.*

**B.** 1/3 **(Correct)**

  *Correct. 'If the person chosen works in Human Resources' fixes the denominator at the HR row total, 4 + 2 = 6. Of those, 2 have a master's degree. 2/6 = 1/3.*

**C.** 1/4 

  *This divides the HR-and-master's cell (2) by the total master's-degree count across both departments (2 + 6 = 8) instead of the HR row total (6) — the reversed conditional (given the person has a master's degree, the probability they work in HR).*

**D.** 8/15 

  *This is 8/15, the overall probability that a randomly chosen person (from either department) has a master's degree — it reports the marginal, ignoring that the question already restricted the pool to HR employees.*

*Difficulty: medium*

---

##### Q27
> TABLE. "Color and shape of 100 tiles of equal area." Square: red 10, blue 20, yellow 25, row total 55. Pentagon: red 20, blue 10, yellow 15, row total 45. Column totals: 30 red, 30 blue, 40 yellow.

If one of these tiles is selected at random, what is the probability of selecting a red tile? (Express your answer as a decimal or fraction, not as a percent.)

**A.** 0.1 

  *This uses only the square-red cell (10), forgetting to add the pentagon-red cell (20), before dividing by the 100 tiles — the red column total is 30, not 10.*

**B.** 0.3 **(Correct)**

  *Correct. The red column total is 20 + 10 = 30, out of 100 tiles. 30/100 = 0.3.*

**C.** 0.55 

  *This uses the square row total (55) instead of the red column total (30) — the shape margin was used where the color margin was needed.*

**D.** 0.667 

  *This is 20/30 — the pentagon-red cell over the full red-tile total, which answers 'of the red tiles, what fraction are pentagons' rather than the plain probability of red that was asked for.*

*Difficulty: easy*

---

##### Q28
> TABLE. "Number of Contestants by Score and Day." The same 20 contestants, on each of 3 days, answered 5 questions to win a prize; each correct answer earned 1 point. No contestant received the same score on two different days. Day 1: score of 5: 2 contestants. Day 2: score of 5: 2 contestants. Day 3: score of 5: 3 contestants. (Column total for a score of 5, across all three days: 7.)

If a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days?

**A.** 2/7 

  *This is the Day 1 count (2) over the 7 contestants who scored a 5 on some day — the complement of what was asked, since it picks the one excluded day (Day 1) instead of the two included days (Day 2 or Day 3).*

**B.** 5/60 

  *This divides the Day 2 + Day 3 count (5) by all 60 contestant-day entries in the table instead of restricting to the 7 contestants who scored a 5 on some day, as the 'given that' clause requires.*

**C.** 5/7 **(Correct)**

  *Correct. 'Given that the contestant received a score of 5 on one of the three days' fixes the pool at 2 + 2 + 3 = 7 contestants. Of those, the ones who scored a 5 on Day 2 or Day 3 number 2 + 3 = 5. 5/7.*

**D.** 5/20 

  *This uses a single day's total (20 contestants) as the denominator instead of the 7 contestants who scored a 5 on some day — the conditioning pool named by the question was replaced with one day's full roster.*

*Difficulty: sat-hardest*

---

##### Q29
> TABLE. "Blood type and rhesus factor for a group of people." Rhesus positive: type A 33, type B 9, type AB 3, type O 37. Rhesus negative: type A 7, type B 2, type AB 1, type O x.

If one of these people who is rhesus negative is chosen at random, the probability that the person has blood type B is 1/9. What is the value of x?

**A.** 7 

  *This solves using type B's count across BOTH rhesus-positive and rhesus-negative people, (9 + 2)/(grand total) = 1/9, instead of restricting the pool to just the rhesus-negative row as the question specifies.*

**B.** 8 **(Correct)**

  *Correct. The rhesus-negative row totals 7 + 2 + 1 + x = 10 + x. Setting 2/(10 + x) = 1/9 gives 10 + x = 18, so x = 8.*

**C.** 9 

  *This copies the 9 straight out of the given probability 1/9 into x, without ever setting up or solving the equation 2/(10 + x) = 1/9.*

**D.** 18 

  *This solves 2/x = 1/9, using x alone as the rhesus-negative total and forgetting to add the other three known rhesus-negative counts — 7, 2, and 1 — into that total before setting up the equation.*

*Difficulty: sat-hardest*

---

##### Q30
> TABLE. "Alumni association survey: preferred event activity, by response type, in percent." Dinner dance: phone 55%, email 80%. Football game: phone 20%, email 10%. Picnic: phone 20%, email 5%. Pool party: phone 5%, email 5%. Each column totals 100%. The number of email responses was twice the number of phone responses.

An alumni association survey asked each high school graduate to select the one activity he or she preferred for the association's next event. If a person who preferred a picnic is selected at random, what is the probability that the person responded by email?

**A.** 1/5 

  *This compares the raw picnic percentages directly, 5% and 20%, giving 5/25 = 1/5 — without scaling for the fact that email responses were twice as numerous as phone responses overall.*

**B.** 1/3 **(Correct)**

  *Correct. Let phone responses = n and email responses = 2n. Picnic counts: phone = 0.20n, email = 0.05(2n) = 0.10n. P(email | picnic) = 0.10n/(0.20n + 0.10n) = 0.10/0.30 = 1/3.*

**C.** 2/3 

  *This correctly weights the phone and email response counts (0.20n and 0.10n) but computes P(phone | picnic) = 0.20n/0.30n instead of P(email | picnic) — the reverse of what was asked.*

**D.** 4/5 

  *This compares the raw picnic percentages without weighting for the phone-to-email population difference, and answers for phone instead of email — 20/25.*

*Difficulty: sat-hardest*

---

##### Q31
On May 10, 2015, there were 83 million Internet subscribers in Nigeria. By September 30, 2015, the number had increased to 97 million. If an Internet subscriber in Nigeria on September 30, 2015, is selected at random, the probability that the person selected was an MTN subscriber is 0.43. There were p million MTN subscribers in Nigeria on September 30, 2015. To the nearest integer, what is the value of p?

**A.** 6 

  *This applies the 0.43 share to the 14-million increase in subscribers (97 − 83) instead of to the total September subscriber base of 97 million — the probability was measured on the September total, not on the growth alone.*

**B.** 36 

  *This applies the 0.43 share to the May figure, 83 million, instead of the September figure, 97 million, which is what the probability 0.43 was actually measured on.*

**C.** 42 **(Correct)**

  *Correct. p = 0.43 × 97 = 41.71, which rounds to 42.*

**D.** 43 

  *This rounds 97 up to 100 before multiplying by 0.43, giving 43 instead of the more precise 41.71, which rounds to 42.*

*Difficulty: medium*

---

##### Q32
> TABLE. "Distribution of age and assigned group, 90 participants." Group A: ages 0–9: 7, ages 10–19: 14, ages 20+: 9, row total 30. Group B: 6, 4, 20, row total 30. Group C: 17, 12, 1, row total 30. Column totals: 30, 30, 30.

One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10 years of age? (Express your answer as a decimal or fraction, not as a percent.)

**A.** 7/60 

  *This uses group A's under-10 count (7) instead of its at-least-10 count (14 + 9 = 23) — the wrong age subgroup within group A.*

**B.** 23/90 

  *This divides group A's at-least-10 count (23) by all 90 participants instead of by the 60 participants who are at least 10 years old. 'Given that the participant is at least 10 years of age' already discarded the 30 youngest participants, so 90 can't still be the denominator.*

**C.** 23/60 **(Correct)**

  *Correct. The at-least-10 pool totals (14 + 9) + (4 + 20) + (12 + 1) = 23 + 24 + 13 = 60. Group A's share of that pool is 23. 23/60.*

**D.** 23/30 

  *This divides group A's at-least-10 count (23) by group A's own row total (30) instead of the at-least-10 pool (60) — the reversed conditional (given the participant is in group A, the probability they are at least 10).*

*Difficulty: hard*

---

##### Q33
> TABLE. "2013 State-Level Taxes, distribution of US states." State income tax: state sales tax 39, no state sales tax 4. No state income tax: state sales tax 6, no state sales tax 1.

To the nearest tenth of a percent, what percent of states with a state-level sales tax do not have a state-level income tax?

**A.** 6.0% 

  *This reads the raw count of 6 states directly as 6.0%, skipping the division by the sales-tax total entirely.*

**B.** 12.0% 

  *This divides the correct cell (6 states) by all 50 states instead of the 45 states that actually have a state-level sales tax — 6/50 = 12.0% instead of 6/45 ≈ 13.3%.*

**C.** 13.3% **(Correct)**

  *Correct. 'Of the states with a state-level sales tax' fixes the pool at 39 + 6 = 45 states. Of those, 6 have no state-level income tax. 6/45 ≈ 0.1333 = 13.3%.*

**D.** 14.0% 

  *This uses the entire no-state-income-tax row total (7 states, whether or not they have a sales tax) instead of just the 6 in that row that also have a sales tax, and divides by all 50 states instead of the 45 that have a sales tax — 7/50 = 14.0%, wrong on both counts.*

*Difficulty: hard*

---

##### Q34
> TABLE. "Customer service calls last Monday, 891 total." Asked about a bill: asked for repairs 48, did not ask for repairs 623, row total 671. Did not ask about a bill: asked for repairs 130, did not ask for repairs 90, row total 220. Column totals: 178 asked for repairs, 713 did not.

If a caller last Monday who asked about his or her bill is selected at random, which of the following is closest to the probability that the customer also asked for repairs?

**A.** 0.05 

  *This divides the correct cell (48) by all 891 callers instead of the 671 who asked about a bill — 48/891 ≈ 0.05 instead of 48/671 ≈ 0.07.*

**B.** 0.07 **(Correct)**

  *Correct. 'Who asked about his or her bill' fixes the pool at the asked-about-a-bill row total, 671. Of those, 48 also asked for repairs. 48/671 ≈ 0.07.*

**C.** 0.20 

  *This is 178/891 ≈ 0.20, the overall probability that any caller asked for repairs — the marginal, ignoring that the question already restricted the pool to callers who asked about a bill.*

**D.** 0.27 

  *This divides the correct cell (48) by the asked-for-repairs column total (178) instead of the asked-about-a-bill row total (671) — the reversed conditional (given a caller asked for repairs, the probability they also asked about a bill).*

*Difficulty: medium*

---

##### Q35
> TABLE. "Distribution of age and assigned group, 90 participants." Group A: ages 0–9: 5, ages 10–19: 17, ages 20+: 8, row total 30. Group B: 6, 8, 16, row total 30. Group C: 19, 5, 6, row total 30. Column totals: 30, 30, 30.

One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10 years of age?

**A.** 5/18 

  *This divides group A's at-least-10 count (17 + 8 = 25) by all 90 participants instead of the 60 who are at least 10 years old — 25/90 = 5/18 instead of 25/60.*

**B.** 5/12 **(Correct)**

  *Correct. The at-least-10 pool totals (17 + 8) + (8 + 16) + (5 + 6) = 25 + 24 + 11 = 60. Group A's share is 25. 25/60 = 5/12.*

**C.** 17/30 

  *This uses only the 10–19 bracket (17), forgetting to add the 20-and-over bracket (8), and divides by group A's row total (30) instead of the 60-person at-least-10 pool — two compounding errors.*

**D.** 5/6 

  *This correctly pools both qualifying age brackets (17 + 8 = 25) but divides by group A's own row total (30) instead of the at-least-10 pool (60) — the reversed conditional. 25/30 = 5/6.*

*Difficulty: hard*

---

##### Q36
> TABLE. "Distribution of two types of flowers at two sites." Tulip: Site A 35, Site B 15, row total 50. Daffodil: Site A 31, Site B 21, row total 52. Column totals: 66 at Site A, 36 at Site B.

If a flower represented in the table is selected at random, what is the probability of selecting a flower from Site A, given that the flower is a tulip? (Express your answer as a decimal or fraction, not as a percent.)

**A.** 0.34 

  *This divides the tulip-and-Site-A cell (35) by all 102 flowers instead of by the 50 tulips — 35/102 ≈ 0.34 instead of 35/50.*

**B.** 0.53 

  *This divides the tulip-and-Site-A cell (35) by the Site A column total (66) instead of the tulip row total (50) — the reversed conditional (given the flower is from Site A, the probability it's a tulip).*

**C.** 0.60 

  *This uses the daffodil row (31 at Site A, 52 total) instead of the tulip row — the wrong flower type entirely. 31/52 ≈ 0.60.*

**D.** 0.7 **(Correct)**

  *Correct. 'Given that the flower is a tulip' fixes the denominator at the tulip row total, 50. Of those, 35 are at Site A. 35/50 = 0.7.*

*Difficulty: medium*

---

### Geometry & Trigonometry

#### Area and Volume (45 items)

##### Q1
The side length of a square is 55 centimeters (cm). What is the area, in cm², of the square?

**A.** 110 

  *This doubles the side length (55×2=110) instead of squaring it — the operation that would find a perimeter-like quantity for two sides, not the area of a square.*

**B.** 220 

  *This is the perimeter formula, 4×55=220, not the area — area requires squaring the side, not multiplying it by 4.*

**C.** 3,025 **(Correct)**

  *Correct. Area of a square = side² = 55² = 3,025 square centimeters.*

**D.** 12,100 

  *This doubles the side length first (2×55=110) and THEN squares that doubled value (110²=12,100) — squaring is applied to the wrong number, one that was never supposed to be doubled in the first place.*

*Difficulty: easy*

---

##### Q2
The area of a square is 64 square inches. What is the side length, in inches, of this square?

**A.** 8 **(Correct)**

  *Correct. Side = √area = √64 = 8 inches. Check: 8² = 64 ✓.*

**B.** 16 

  *This treats the area (64) as though it were a PERIMETER and divides by 4 (64/4=16) — but 64 is square inches, an area, and finding a side length from an area requires a square root, not a division by 4.*

**C.** 64 

  *This reports the area itself, 64, without ever taking the square root — the question asks for a side LENGTH, which is in inches, not square inches, and the units alone signal that a square root step was skipped.*

**D.** 128 

  *This doubles the area (64×2=128) instead of taking its square root — an operation that doesn't correspond to any real relationship between a square's area and its side length.*

*Difficulty: easy*

---

##### Q3
Triangle ABC and triangle DEF are [[similar triangles]], where AB and DE are corresponding sides. If DE = 2AB and the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF?

**A.** 10 

  *This divides by the scale factor instead of multiplying by it (20/2=10), as though DE were HALF the length of AB rather than twice it — the direction of the given relationship (DE=2AB, so DEF is the LARGER triangle) is reversed.*

**B.** 40 **(Correct)**

  *Correct. Perimeter is a length, so it scales by the same factor k=2 as any corresponding side: 20×2=40.*

**C.** 80 

  *This squares the scale factor (2²=4) and applies it to the perimeter, 20×4=80, as though perimeter scaled like an area. Perimeter is a length, so it scales by k=2, not by k².*

**D.** 120 

  *This multiplies the perimeter by the scale factor AND by the number of sides (3), reasoning that since all three sides double, the multiplier should be 2×3=6: 20×6=120. But the perimeter is already the SUM of the three sides, so a single factor of 2 accounts for the growth of all three sides at once — reapplying it per side triples the correct effect.*

*Difficulty: medium*

---

##### Q4
A rectangle has a length of 13 and a width of 6. What is the perimeter of the rectangle?

**A.** 12 

  *This doubles only the width (2×6=12) and leaves the length out entirely — a rectangle's perimeter needs both pairs of sides, not just one.*

**B.** 26 

  *This doubles only the length (2×13=26) and leaves the width out entirely — the mirror image of choice A's error.*

**C.** 38 **(Correct)**

  *Correct. Perimeter = 2(length + width) = 2(13+6) = 2(19) = 38.*

**D.** 52 

  *This applies the SQUARE perimeter formula, 4×side, using only the length: 4×13=52. A rectangle's two pairs of sides differ, so the perimeter needs 2(l+w), not 4 times a single side.*

*Difficulty: easy*

---

##### Q5
A triangle has side lengths x, y, and z. The triangle has a perimeter of 22 units. If x = 9 units and y = 7 units, what is the value of z, in units?

**A.** 6 **(Correct)**

  *Correct. z = perimeter − x − y = 22 − 9 − 7 = 6.*

**B.** 7 

  *This reports the given value of y (7) instead of solving for the missing side z.*

**C.** 9 

  *This reports the given value of x (9) instead of solving for the missing side z.*

**D.** 16 

  *This adds x+y (9+7=16) and stops there, instead of subtracting that sum from the perimeter (22−16=6) to isolate z.*

*Difficulty: easy*

---

##### Q6
What is the area, in square centimeters, of a rectangle with a length of 36 centimeters and a width of 34 centimeters?

**A.** 70 

  *This adds the length and width (36+34=70) instead of multiplying them — the sum of two sides, not the area enclosed between them.*

**B.** 140 

  *This computes the perimeter, 2(36+34)=140, instead of the area, 36×34.*

**C.** 1,156 

  *This squares only the width (34²=1,156) and drops the length entirely, treating the rectangle as though it were a square with side 34.*

**D.** 1,224 **(Correct)**

  *Correct. Area = length × width = 36 × 34 = 1,224 square centimeters.*

*Difficulty: easy*

---

##### Q7
The area of a rectangle is 630 square inches. The length of the rectangle is 70 inches. What is the width, in inches, of this rectangle?

**A.** 9 **(Correct)**

  *Correct. Width = area ÷ length = 630 ÷ 70 = 9.*

**B.** 70 

  *This reports the given length (70) back unchanged, instead of dividing the area by it to solve for the width.*

**C.** 315 

  *This divides the area by 2 (630/2=315), as if finding half of the area, instead of dividing by the given length (70) to find the width.*

**D.** 560 

  *This subtracts the length from the area (630−70=560) instead of dividing the area by the length — mixing an area and a length as though they could be combined by subtraction.*

*Difficulty: easy*

---

##### Q8
What is the area of a rectangle with a length of 4 centimeters (cm) and a width of 2 cm?

**A.** 6 cm² 

  *This adds the length and width (4+2=6) instead of multiplying them.*

**B.** 8 cm² **(Correct)**

  *Correct. Area = length × width = 4 × 2 = 8 cm².*

**C.** 12 cm² 

  *This computes the perimeter, 2(4+2)=12, instead of the area, 4×2.*

**D.** 36 cm² 

  *This squares the SUM of the length and width, (4+2)²=36, instead of multiplying the two dimensions directly — a shortcut that only works when a shape's two dimensions are already equal.*

*Difficulty: easy*

---

##### Q9
The figure shows the lengths, in centimeters (cm), of the edges of a right rectangular prism: a length of 6 cm, a width of 2 cm, and a height of 3 cm. The volume V of a right rectangular prism is ℓwh, where ℓ is the length of the prism, w is the width of the prism, and h is the height of the prism. What is the volume, in cubic centimeters, of the prism?

**A.** 36 **(Correct)**

  *Correct. V = ℓwh = 6 × 2 × 3 = 36 cubic centimeters.*

**B.** 24 

  *This doubles the area of the base face (2×6×2=24) instead of multiplying that base area by the height — a step that would be appropriate for a SURFACE area calculation, not a volume, and even then it's missing the other four faces.*

**C.** 12 

  *This multiplies only two of the three edges (6×2=12) and leaves the height out entirely — a volume needs all three dimensions multiplied together, not just the base.*

**D.** 11 

  *This adds the three edge lengths (6+2+3=11) instead of multiplying them — volume is a product of three lengths, not their sum.*

*Difficulty: medium*

---

##### Q10
What is the area, in square inches, of a rectangle with a length of 7 inches and a width of 6 inches?

**A.** 13 

  *This adds the length and width (7+6=13) instead of multiplying them.*

**B.** 20 

  *This doubles only the length and adds the width once, 2(7)+6=20 — an inconsistent half-perimeter calculation that neither finds the area nor the true perimeter.*

**C.** 42 **(Correct)**

  *Correct. Area = length × width = 7 × 6 = 42.*

**D.** 84 

  *This doubles the correct area (42×2=84), as though two identical rectangular faces were needed instead of the area of one rectangle.*

*Difficulty: easy*

---

##### Q11
What is the area of a rectangle with a length of 17 centimeters (cm) and a width of 7 cm?

**A.** 24 cm² 

  *This adds the length and width (17+7=24) instead of multiplying them.*

**B.** 48 cm² 

  *This computes the perimeter, 2(17+7)=48, instead of the area, 17×7.*

**C.** 119 cm² **(Correct)**

  *Correct. Area = length × width = 17 × 7 = 119 cm².*

**D.** 576 cm² 

  *This squares the SUM of the length and width, (17+7)²=576, instead of multiplying the two dimensions directly.*

*Difficulty: easy*

---

##### Q12
The width of a rectangle is 7 centimeters. The length of the rectangle is 40 centimeters longer than the width. What is the area, in square centimeters, of this rectangle?

**A.** 7 

  *This reports the given width (7) directly, without ever computing the length or the area.*

**B.** 14 

  *This doubles the width (7×2=14), ignoring the '40 centimeters longer' condition that defines the length entirely.*

**C.** 54 

  *This adds the length and width (47+7=54) instead of multiplying them to find the area.*

**D.** 329 **(Correct)**

  *Correct. Length = 7+40 = 47. Area = length × width = 47 × 7 = 329 square centimeters.*

*Difficulty: medium*

---

##### Q13
Each base of a right rectangular prism has a length of 19 inches and a width of 8 inches. The prism has a volume of 2,736 cubic inches. What is the height, in inches, of the prism?

**A.** 18 **(Correct)**

  *Correct. Base area = 19×8 = 152. Height = volume ÷ base area = 2,736 ÷ 152 = 18 inches.*

**B.** 27 

  *This adds the two base dimensions (19+8=27) instead of multiplying them to find the base area — and never uses the volume at all.*

**C.** 144 

  *This divides the volume by only the length (2,736/19=144), treating the length alone as the base area and leaving the width out of the base-area calculation entirely.*

**D.** 152 

  *This correctly computes the base area (19×8=152) but stops there, reporting it directly instead of dividing the volume by it to solve for the height.*

*Difficulty: medium*

---

##### Q14
The table gives the perimeters of similar triangles TUV and XYZ, where TU corresponds to XY. The length of TU is 6. Triangle TUV has a perimeter of 50, and triangle XYZ has a perimeter of 150. What is the length of XY?

**A.** 2 

  *This divides by the scale factor instead of multiplying by it (6/3=2), treating XY as smaller than TU when the perimeters show XYZ must be the larger triangle.*

**B.** 6 

  *This reports TU's given length unchanged, without ever applying the scale factor formed by the two perimeters.*

**C.** 18 **(Correct)**

  *Correct. Scale factor = 150/50 = 3. XY = TU × 3 = 6 × 3 = 18.*

**D.** 56 

  *This adds TU's length to XYZ's perimeter (6+50=56), combining two unrelated quantities instead of forming a scale factor from the ratio of the two perimeters.*

*Difficulty: medium*

---

##### Q15
A rectangle has a length of 3 units and a width of 39 units. Which expression gives the area, in square units, of this rectangle?

**A.** 2(3 + 39) 

  *This is the perimeter formula, 2(l+w), not the area formula — area requires multiplying the length and width, not adding them and doubling.*

**B.** 2(3 · 39) 

  *This doubles the product of length and width, 2(3·39), as if computing two identical rectangular faces instead of the area of one rectangle.*

**C.** 3 + 39 

  *This adds the length and width (3+39) instead of multiplying them.*

**D.** 3 · 39 **(Correct)**

  *Correct. Area = length × width = 3 · 39.*

*Difficulty: easy*

---

##### Q16
In the figure shown, triangle JKL is similar to triangle RST, where J corresponds to R and K corresponds to S. The length of JK is 15, and the perimeter of triangle JKL is 36. The length of RS is 135. What is the perimeter of triangle RST?

**A.** 324 **(Correct)**

  *Correct. [[Scale factor]] = RS/JK = 135/15 = 9. Perimeter of RST = perimeter of JKL × scale factor = 36 × 9 = 324.*

**B.** 540 

  *This multiplies the perimeter by JK's own length (36×15=540) instead of by the scale factor formed by RS/JK — using a raw side length as though it were a ratio.*

**C.** 2,916 

  *This applies the scale factor a second time, as though perimeter scaled by k² the way area does: 36×9²=2,916 instead of 36×9. Perimeter is a length, so it scales by k once, not k².*

**D.** 8,100 

  *This squares JK's own length (15²=225) and uses that in place of the scale factor RS/JK: 36×225=8,100 — an entirely different (and much larger) number than the ratio of corresponding sides actually calls for.*

*Difficulty: medium*

---

##### Q17
Triangle R has an area of 80 square centimeters (cm²). Square S has side lengths of 4 cm. What is the total area of triangle R and square S, in cm²?

**A.** 42 

  *This computes (80+4)/2 = 42 — averaging the triangle's area with the square's un-squared side length, as if 'total' meant an average rather than a sum, on top of never squaring the side to find the square's actual area.*

**B.** 44 

  *This halves the triangle's area (80/2=40) and adds the square's raw side length (40+4=44) — two separate slips stacked together: an unexplained halving of the triangle's area, and a forgotten squaring of the square's side.*

**C.** 84 

  *This adds the square's side length directly to the triangle's area (80+4=84) instead of squaring the side first to find the square's actual area (4²=16) and then adding that.*

**D.** 96 **(Correct)**

  *Correct. Area of square S = 4² = 16. Total area = 80 + 16 = 96 cm².*

*Difficulty: medium*

---

##### Q18
A right circular cylinder has a volume of 45π. If the height of the cylinder is 5, what is the radius of the cylinder?

**A.** 3 **(Correct)**

  *Correct. V=πr²h, so 45π=πr²(5), giving r²=9 and r=3.*

**B.** 4.5 

  *This divides the volume's coefficient by twice the height (45/(2×5)=4.5), never squaring or taking a square root at all — a formula-free guess dressed up as arithmetic.*

**C.** 9 

  *This correctly solves r²=9 from the volume formula but stops there, reporting r² instead of taking the square root to find r itself.*

**D.** 40 

  *This subtracts the height from the volume's coefficient (45−5=40) instead of using the volume formula V=πr²h to solve for r.*

*Difficulty: medium*

---

##### Q19
What is the length of one side of a square that has the same area as a circle with radius 2?

**A.** 2 

  *This reports the circle's radius (2) directly as the square's side length, without computing either area at all.*

**B.** √(2π) 

  *This takes the square root of 2π instead of the circle's actual area, 4π — using the coefficient 2 (which appears in the diameter or circumference) inside the root instead of squaring the radius first.*

**C.** 2√π **(Correct)**

  *Correct. Circle's area = πr² = π(2²) = 4π. Square's side = √(4π) = 2√π.*

**D.** 2π 

  *This computes π×r = π×2 = 2π — using the area formula πr² but forgetting to square the radius — and then treats that as the side length directly.*

*Difficulty: medium*

---

##### Q20
A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container A. What is the volume, in cubic centimeters, of container B?

**A.** 16,000π 

  *This multiplies the original radius by the new radius (16×20=320) instead of squaring the new radius (20²=400), mixing container A's dimension into container B's volume: π(16)(20)(50)=16,000π.*

**B.** 20,000π **(Correct)**

  *Correct. Radius of B = 16 × 1.25 = 20. Volume = π(20²)(50) = π(400)(50) = 20,000π.*

**C.** 25,000π 

  *This applies the 25% increase to the height as well as the radius, even though only the radius grows: 50×1.25=62.5, giving π(20²)(62.5)=25,000π instead of π(20²)(50).*

**D.** 31,250π 

  *This applies the 25% increase to the radius TWICE — computing 16×(1.25)²=25 instead of 16×1.25=20 — before squaring and multiplying by the height: π(25²)(50)=31,250π. A single 25% growth doesn't compound just by being run through the volume formula.*

*Difficulty: hard*

---

##### Q21
A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of 75 cm², and the height of the can is 10 cm. If 110 cm³ of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?

**A.** 7.5 cm³ 

  *This divides the base area by the height (75/10=7.5) instead of multiplying them to find the can's total volume.*

**B.** 185 cm³ 

  *This adds the base area directly to the syrup volume (75+110=185), mixing an area and a volume as though they were the same kind of quantity.*

**C.** 640 cm³ **(Correct)**

  *Correct. Total can volume = 75×10 = 750 cm³. Fruit volume = 750 − 110 = 640 cm³.*

**D.** 750 cm³ 

  *This correctly computes the can's total volume (75×10=750) but forgets to subtract the syrup, reporting the whole can's capacity instead of just the fruit remaining inside it.*

*Difficulty: medium*

---

##### Q22
The figure shows a glass shaped like a frustum (a cone with its tip cut off). Its height is k centimeters, and the diameter of its circular base is k/2 centimeters. The volume, in cubic centimeters, of the glass is given by Volume = 7πk³/48. The glass pictured can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. What is the value of k, in centimeters?

**A.** 2.52 

  *This solves the equation correctly for k, then divides the result by 4 more — as if the figure's k/2 label meant the answer needed converting through two more halvings — landing on roughly 10.11÷4≈2.52 instead of 10.11.*

**B.** 7.67 

  *This treats the coefficient 7π/48 as something to SUBTRACT rather than divide by: solving k³=473−7π≈451.0 instead of k³=473÷(7π/48), giving k=∛451.0≈7.67.*

**C.** 7.79 

  *This drops the coefficient 7π/48 from the formula entirely, solving k³=473 directly — as though Volume=k³ rather than Volume=(7π/48)k³ — giving k=∛473≈7.79.*

**D.** 10.11 **(Correct)**

  *Correct. k³ = 473 ÷ (7π/48) = (473×48)/(7π) ≈ 1,032.3, so k = ∛1,032.3 ≈ 10.11 centimeters.*

*Difficulty: hard*

---

##### Q23
In the xy-plane, square ABCD has its diagonals on the x-axis and y-axis: vertex A is at (0, −5), vertex B is at (−5, 0), vertex C is at (0, 5), and vertex D is at (5, 0). What is the area, in square units, of the square?

**A.** 20 

  *This treats the two half-diagonals (5 and 5, the distances from the origin to each vertex) as the side lengths of a rectangle and computes a perimeter, 2(5+5)=20, instead of an area at all.*

**B.** 25 

  *This mistakes the distance from the origin to a vertex (5) for the square's SIDE length, squaring it directly (5²=25) instead of computing the actual side length with the distance formula (5√2, so the area is (5√2)²=50).*

**C.** 50 **(Correct)**

  *Correct. The diagonals are each 10 units long (from −5 to 5 on each axis). Area of a square from its diagonals = (d₁×d₂)/2 = (10×10)/2 = 50.*

**D.** 100 

  *This mistakes the full diagonal (from (−5,0) to (5,0), a distance of 10) for the square's side length, squaring 10 instead of the actual side length.*

*Difficulty: medium*

---

##### Q24
A sphere has a radius of 17/5 feet. What is the volume, in cubic feet, of the sphere?

**A.** 5π/17 

  *This inverts the given radius (using 5/17 instead of 17/5) and multiplies by π alone, without cubing anything or applying the sphere's 4/3 coefficient at all.*

**B.** 68π/15 

  *This applies the 4/3 coefficient to the radius directly, (4/3)(17/5)=68/15, as if volume were linear in the radius — forgetting to cube the radius entirely.*

**C.** 32π/5 

  *This comes from treating the radius as though it reduced to a much smaller whole number before cubing, then carrying the radius fraction's own denominator (5) into the final answer instead of the 4/3 coefficient's denominator (3) — a mix-up between the two different threes and fives floating around in the setup.*

**D.** 19,652π/375 **(Correct)**

  *Correct. V=(4/3)πr³ = (4/3)π(17/5)³ = (4/3)π(4,913/125) = (4×4,913)/(3×125) π = 19,652π/375.*

*Difficulty: hard*

---

##### Q25
The table gives the perimeters of similar triangles TUV and XYZ, where TU corresponds to XY. The length of TU is 18. Triangle TUV has a perimeter of 37, and triangle XYZ has a perimeter of 333. What is the length of XY?

**A.** 2 

  *This divides by the scale factor instead of multiplying by it (18/9=2).*

**B.** 18 

  *This reports TU's given length unchanged, without ever applying the scale factor formed by the two perimeters.*

**C.** 55 

  *This adds TU's length to TUV's perimeter (18+37=55) instead of forming a scale factor from the ratio of the two perimeters.*

**D.** 162 **(Correct)**

  *Correct. Scale factor = 333/37 = 9. XY = 18 × 9 = 162.*

*Difficulty: medium*

---

##### Q26
A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?

**A.** 16π 

  *This computes only the base area, πr²=π(4²)=16π, and forgets to multiply by the height entirely.*

**B.** 96π 

  *This uses the diameter (8) directly as though it were the radius, AND forgets to square it: π(8)(12)=96π — compounding a diameter/radius mix-up with a missing exponent.*

**C.** 192π **(Correct)**

  *Correct. Radius = 8/2 = 4. Volume = πr²h = π(4²)(12) = π(16)(12) = 192π.*

**D.** 768π 

  *This squares the diameter itself (8²=64) instead of halving it to get the radius first: π(8²)(12)=768π — exactly 4 times too large, the signature of skipping the radius/diameter conversion.*

*Difficulty: medium*

---

##### Q27
A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?

**A.** 164 

  *This multiplies the edge by 4 (41×4=164), as if computing some kind of perimeter of a single face, instead of cubing the edge.*

**B.** 1,681 

  *This computes 41²=1,681, the area of one face, and stops there instead of multiplying by the edge length once more to get the volume.*

**C.** 10,086 

  *This computes the cube's total SURFACE area, 6×41²=10,086, instead of its volume.*

**D.** 68,921 **(Correct)**

  *Correct. Volume = edge³ = 41³ = 68,921 cubic inches.*

*Difficulty: easy*

---

##### Q28
A triangle has a base length of 56 centimeters and a height of 112 centimeters. What is the area, in square centimeters, of the triangle?

**A.** 168 

  *This adds the base and height (56+112=168) instead of multiplying them and halving.*

**B.** 1,568 

  *This applies an extra factor of ½, as though the triangle-area formula needed halving twice: ¼(56)(112)=1,568 instead of ½(56)(112).*

**C.** 3,136 **(Correct)**

  *Correct. Area = ½bh = ½(56)(112) = 3,136 square centimeters.*

**D.** 6,272 

  *This multiplies base times height (56×112=6,272) but forgets the ½ the triangle-area formula requires — computing a rectangle's area instead of a triangle's.*

*Difficulty: easy*

---

##### Q29
The length of each side of a square is 94 centimeters (cm). Which expression gives the area, in cm², of the square?

**A.** 2 · 94 

  *This doubles the side length (2·94), as if area required only linear scaling rather than squaring it.*

**B.** 2 · 94 · 94 

  *This computes the correct product, 94·94, but then doubles it, as though two identical square faces were needed instead of the area of one square.*

**C.** 4 · 94 

  *This is the perimeter formula, 4×side, not the area formula, which requires squaring the side.*

**D.** 94 · 94 **(Correct)**

  *Correct. Area = side × side = 94 · 94.*

*Difficulty: easy*

---

##### Q30
A triangle has a base length of 10 centimeters and a corresponding height of 70 centimeters. What is the area, in square centimeters, of the triangle?

**A.** 700 

  *This multiplies base times height (10×70=700) but omits the required ½, computing a rectangle's area instead of a triangle's.*

**B.** 350 **(Correct)**

  *Correct. Area = ½bh = ½(10)(70) = 350 square centimeters.*

**C.** 175 

  *This applies an extra factor of ½ beyond the one the formula requires: ¼(10)(70)=175 instead of ½(10)(70).*

**D.** 80 

  *This adds the base and height (10+70=80) instead of multiplying them.*

*Difficulty: easy*

---

##### Q31
Rectangles ABCD and QRST are similar, where A, B, C, and D correspond to Q, R, S, and T, respectively. In rectangle ABCD, side AB (a vertical side) measures 12 inches. In rectangle QRST, the corresponding vertical side QR measures 5 inches, and the horizontal side QT measures 10 inches. What is the length, in inches (in), of AD?

**A.** 60 

  *This multiplies the two given side lengths from DIFFERENT rectangles together (12×5=60) instead of dividing them to find the scale factor between the two figures.*

**B.** 24 **(Correct)**

  *Correct. Scale factor = AB/QR = 12/5. AD corresponds to QT, so AD = QT × (12/5) = 10 × (12/5) = 24.*

**C.** 17 

  *This adds the corresponding side lengths (12+5=17) instead of dividing them to find the scale factor.*

**D.** 10 

  *This reports QT's own length (10) unchanged, without ever applying the scale factor between the two similar rectangles.*

*Difficulty: medium*

---

##### Q32
A right circular cylinder has a height of 8 meters (m) and a base with a radius of 12 m. What is the volume, in m³, of the cylinder?

**A.** 8π 

  *This reports just the height as the coefficient of π (8π), as though the radius played no role in the volume at all.*

**B.** 20π 

  *This adds the radius and height (12+8=20) instead of using them in the volume formula V=πr²h.*

**C.** 768π 

  *This swaps which dimension gets squared, using r×h²=12×64=768 instead of r²×h=144×8=1,152 — squaring the height instead of the radius.*

**D.** 1,152π **(Correct)**

  *Correct. V=πr²h = π(12²)(8) = π(144)(8) = 1,152π.*

*Difficulty: easy*

---

##### Q33
Square A has side lengths that are 246 times the side lengths of square B. The area of square A is k times the area of square B. What is the value of k?

**A.** 60,516 **(Correct)**

  *Correct. Area scales by the square of the linear factor: k = 246² = 60,516.*

**B.** 492 

  *This doubles the linear scale factor (246×2=492) instead of squaring it — applying the wrong operation to convert a length ratio into an area ratio.*

**C.** 246 

  *This reports the linear scale factor itself, as though area scaled the same way length does, without ever squaring it.*

**D.** 123 

  *This halves the scale factor (246/2=123) instead of squaring it — the inverse of the operation the problem actually calls for.*

*Difficulty: medium*

---

##### Q34
In the xy-plane, three points define a circle: (4, 8), (7, 11), and (7, 5). The circumference of this circle is kπ, where k is a constant. What is the value of k?

**A.** 3 

  *This reports the circle's radius (3) directly, instead of doubling it to get the coefficient of the circumference formula C=2πr.*

**B.** 6 **(Correct)**

  *Correct. The center is equidistant from all three points; solving shows the center is (7, 8) with radius 3 (check: distance to (4,8) is 3, and distance to (7,11) is 3). Circumference = 2πr = 2π(3) = 6π, so k=6.*

**C.** 7 

  *This reports the x-coordinate of the circle's center (7) instead of computing the radius from the plotted points and doubling it.*

**D.** 9 

  *This squares the radius (3²=9), as though computing an area-related quantity, instead of doubling it for the circumference formula.*

*Difficulty: hard*

---

##### Q35
A right circular cylinder has a radius of r and a height of h. A second right circular cylinder (not shown) has a volume that is 392 times as large as the volume of the cylinder shown. Which of the following could represent the radius R, in terms of r, and the height H, in terms of h, of the second cylinder?

**A.** R = 8r and H = 7h 

  *This swaps which factor multiplies the radius versus the height. Pairing R=8r means the radius factor gets SQUARED as 8²=64, so the total volume multiplier becomes 64×7=448, not 392. Reaching exactly 392=7²×8 requires squaring the SMALLER factor (7) and leaving the larger factor (8) unsquared on the height — swapping which number gets squared changes the product entirely.*

**B.** R = 8r and H = 49h 

  *This takes the factorization 392=8×49 at face value and assigns those two numbers directly as the radius and height scale factors, without accounting for the radius factor needing to be SQUARED in the volume formula: R²H/(r²h)=8²×49=3,136 — eight times too large.*

**C.** R = 7r and H = 8h **(Correct)**

  *Correct. Volume ratio = (R/r)²×(H/h) = 7²×8 = 49×8 = 392, matching the given scale factor exactly.*

**D.** R = 49r and H = 8h 

  *This uses 49 itself as the radius's scale factor, instead of recognizing that 49 is the SQUARE of the true radius factor (7). Squaring 49 again (49²=2,401) and multiplying by 8 overshoots the target by a factor of 49: 49²×8=19,208.*

*Difficulty: sat-hardest*

---

##### Q36
A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the optimal number of containers to be displayed on a shelf. Which of the following expresses the volume, V, in cubic inches, of such containers, where r is the radius, in inches?

**A.** V = 4πr³ 

  *This treats the '+4' in the height (r+4) as though it were a multiplier on the entire volume expression instead of an addend inside h: πr²×r×4=4πr³, instead of correctly distributing πr²(r+4)=πr³+4πr².*

**B.** V = π(2r)³ 

  *This misreads 'height 4 inches longer than the radius' as 'height twice the radius,' and then substitutes that doubled value in place of the RADIUS itself, cubing (2r) instead of ever using the volume formula πr²h.*

**C.** V = πr² + 4πr 

  *This uses πr — one factor of r short of the correct base area πr² — as the base, then correctly multiplies by the height (r+4): πr(r+4)=πr²+4πr. The base area is missing an entire factor of r throughout.*

**D.** V = πr³ + 4πr² **(Correct)**

  *Correct. Height = r+4. Volume = πr²h = πr²(r+4) = πr³+4πr².*

*Difficulty: hard*

---

##### Q37
A right circular cone has a volume of (1/3)π cubic feet and a height of 9 feet. What is the radius, in feet, of the base of the cone?

**A.** 1/3 **(Correct)**

  *Correct. V=(1/3)πr²h, so (1/3)π=(1/3)πr²(9), giving 1=9r², r²=1/9, and r=1/3.*

**B.** 1/√3 

  *This confuses the cone formula's own coefficient (1/3) with the given height, solving 1=3r² instead of 1=9r² — using 3 (the coefficient's denominator) in place of the actual height of 9, giving r²=1/3 and r=1/√3.*

**C.** √3 

  *This divides the height by 3 (the denominator of the cone's own 1/3 coefficient) instead of solving the full volume equation, getting r²=9/3=3, so r=√3.*

**D.** 3 

  *This inverts the fraction when isolating r², solving r²=9 (the reciprocal of the correct r²=1/9) instead — and reports r=3 instead of r=1/3.*

*Difficulty: hard*

---

##### Q38
The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

**A.** 11 

  *This applies only the height's halving factor (×½) and ignores the radius doubling entirely: 22×½=11.*

**B.** 22 

  *This treats the radius doubling and the height halving as exactly canceling out (2×½=1), missing that the radius factor gets SQUARED in the volume formula — which is exactly what breaks the cancellation and makes the volume double rather than stay the same.*

**C.** 44 **(Correct)**

  *Correct. New volume = π(2r)²(h/2) = π(4r²)(h/2) = 2πr²h = 2 × 22 = 44.*

**D.** 66 

  *This computes the correct new volume (44) but then adds the original cylinder's volume to it (22+44=66), as though the question asked for the combined volume of both cylinders rather than the new cylinder's volume alone.*

*Difficulty: medium*

---

##### Q39
The dimensions of a right rectangular prism are 4 inches by 5 inches by 6 inches. What is the surface area, in square inches, of the prism?

**A.** 30 

  *This doubles the SUM of the three edge lengths, 2(4+5+6)=30, as if surface area worked like a perimeter in three dimensions, instead of summing the areas of the three pairs of faces.*

**B.** 74 

  *This correctly finds the area of each of the three distinct faces and adds them (20+24+30=74) but forgets that each face has a matching opposite face — the true total needs doubling.*

**C.** 120 

  *This computes the prism's VOLUME (4×5×6=120) instead of its surface area — the right formula for a different question.*

**D.** 148 **(Correct)**

  *Correct. Surface area = 2(lw+lh+wh) = 2(20+24+30) = 2(74) = 148 square inches.*

*Difficulty: easy*

---

##### Q40
A cube has a surface area of 54 square meters. What is the volume, in cubic meters, of the cube?

**A.** 18 

  *This finds s²=9 correctly but then doubles it (9×2=18) instead of finding s=3 and cubing it.*

**B.** 27 **(Correct)**

  *Correct. Surface area = 6s² = 54, so s² = 9 and s = 3. Volume = s³ = 27 cubic meters.*

**C.** 36 

  *This cubes s incorrectly by multiplying s² by 4 instead of by s itself: 9×4=36 instead of 9×3=27.*

**D.** 81 

  *This squares s² again instead of multiplying by s once more: 9×9=81 instead of 9×3=27 — an error that treats 'cubed' as 'squared twice.'*

*Difficulty: medium*

---

##### Q41
A line segment shown in the xy-plane, from (−6, 4) to (3, 10), represents one leg of a right triangle. The area of this triangle is 36√13 square units. What is the length, in units, of the other leg of this triangle?

**A.** 12 

  *This applies the triangle's ½ a second time: after correctly finding 72√13/(3√13)=24, this halves that result again, as though the area formula needed two factors of ½ instead of one.*

**B.** 24 **(Correct)**

  *Correct. The given leg has length √((3−(−6))²+(10−4)²) = √(81+36) = √117 = 3√13. Area = ½ × leg₁ × leg₂, so 36√13 = ½ × 3√13 × leg₂, giving leg₂ = 72√13/(3√13) = 24.*

**C.** 3√13 

  *This reports the length of the GIVEN leg (3√13, the length of the segment shown) instead of solving for the other leg.*

**D.** 18√13 

  *This divides the area's coefficient by 2 (36/2=18) but never divides by the length of the given leg (3√13) at all, leaving the radical untouched instead of having it cancel out of the final answer.*

*Difficulty: hard*

---

##### Q42
A hemisphere is half of a sphere. If a hemisphere has a radius of 27 inches, which of the following is closest to the volume, in cubic inches, of this hemisphere?

**A.** 1,500 

  *This uses r² instead of r³ — forgetting to cube the radius — giving (2/3)π(27²)≈1,527, which rounds to the closest choice, 1,500.*

**B.** 6,100 

  *This computes the hemisphere's total surface area (curved plus the flat circular base), 3πr²≈6,872, instead of its volume — 6,100 is the closest available choice.*

**C.** 30,900 

  *This uses a coefficient of ½ instead of ⅔ in the hemisphere volume formula — an easy slip, since 'half of a sphere' suggests multiplying by ½ directly, rather than recognizing that half of the SPHERE's own coefficient (4/3) is ⅔, not ½: (1/2)π(27³)≈30,917.*

**D.** 41,200 **(Correct)**

  *Correct. V=(2/3)πr³ = (2/3)π(27³) = (2/3)π(19,683) = 13,122π ≈ 41,225, which rounds to 41,200.*

*Difficulty: hard*

---

##### Q43
Parallelogram ABCD is similar to parallelogram PQRS. The length of each side of parallelogram PQRS is 2 times the length of its corresponding side of parallelogram ABCD. The area of parallelogram ABCD is 5 square centimeters. What is the area, in square centimeters, of parallelogram PQRS?

**A.** 7 

  *This adds the scale factor to the original area (5+2=7) instead of using it to scale the area at all.*

**B.** 10 

  *This multiplies the area by the scale factor directly (5×2=10), treating area as though it scales linearly like a length, instead of squaring the scale factor first.*

**C.** 20 **(Correct)**

  *Correct. Area scales by the square of the linear factor: 5 × 2² = 5 × 4 = 20.*

**D.** 25 

  *This squares the original AREA itself (5²=25) instead of squaring the scale factor (2²=4) and multiplying that by the original area.*

*Difficulty: medium*

---

##### Q44
Rectangle ABCD is similar to rectangle EFGH. The area of rectangle ABCD is 648 square inches, and the area of rectangle EFGH is 72 square inches. The length of the longest side of rectangle ABCD is 36 inches. What is the length, in inches, of the longest side of rectangle EFGH?

**A.** 4 

  *This divides the side length by the area ratio itself (36/9=4) instead of by the SQUARE ROOT of that ratio.*

**B.** 9 

  *This reports the area ratio (648/72=9) directly as the side length, without ever taking a square root or applying it to the given side.*

**C.** 12 **(Correct)**

  *Correct. Area ratio = 648/72 = 9 = k². So k = 3. EFGH's longest side = 36/3 = 12.*

**D.** 36 

  *This reports ABCD's given side length (36) unchanged, without scaling it down for the smaller rectangle at all.*

*Difficulty: hard*

---

##### Q45
The circumference of the base of a right circular cylinder is 20π meters, and the height of the cylinder is 6 meters. What is the volume, in cubic meters, of the cylinder?

**A.** 60π 

  *This correctly solves for r=10 from the circumference but then computes πrh=60π instead of πr²h, forgetting to square the radius.*

**B.** 120π 

  *This skips solving for the radius entirely and uses the circumference's coefficient (20) directly in place of r, then also forgets to square it: π(20)(6)=120π.*

**C.** 600π **(Correct)**

  *Correct. C=2πr=20π, so r=10. Volume=πr²h=π(10²)(6)=600π.*

**D.** 2,400π 

  *This skips solving for the radius and uses the circumference's coefficient (20) directly as though it were the radius, then squares that: π(20²)(6)=2,400π — exactly 4 times too large, the signature of using the circumference's coefficient in place of the actual radius.*

*Difficulty: medium*

---

#### Lines, angles and triangles (48 items)

##### Q1
In the triangle shown, AB = AC and angle ABC has a measure of 67°, where x° is the measure of angle BAC. What is the value of x?

**A.** 36 

  *This comes from doubling 67 incorrectly as 144 instead of 134 — a doubling slip — before subtracting from 180: 180 − 144 = 36.*

**B.** 46 **(Correct)**

  *Correct. AB = AC makes the triangle isosceles with apex A, so the base angles at B and C are equal: angle C = angle B = 67°. The apex angle is x = 180 − 67 − 67 = 46.*

**C.** 58 

  *This swaps which angle is the apex and which are the base angles — treating the given 67° as the apex and solving for a base angle instead: (180 − 67)/2 = 56.5, which is not even an integer, and rounding it toward the nearest offered choice lands here. The 67° in the problem is explicitly angle ABC, a base angle, not the apex.*

**D.** 70 

  *This does not follow from doubling 67 and subtracting from 180 by any direct route — it is not consistent with the isosceles relationship at all. Checking backward exposes it: if the apex were 70°, the base angles would each be (180 − 70)/2 = 55°, not the given 67°.*

*Difficulty: easy*

---

##### Q2
Two lines cross at a point above parallel lines ℓ and m, forming a triangle-like figure: from the crossing point, one ray runs down through ℓ and continues to m, making an angle of y° with m; the other ray runs down and meets ℓ only, making an angle of z° with ℓ on the side facing the first ray. If lines ℓ and m are parallel, y = 20, and z = 60, what is the value of x, the angle at the top crossing point?

**A.** 120 

  *This reports the supplement of the interior angle used inside the triangle formed by the crossing point and the two points where the rays meet line m, rather than the vertex angle x itself.*

**B.** 100 **(Correct)**

  *Correct. Because ℓ ∥ m, the angle the second ray makes with ℓ (z = 60°) equals the angle it makes with m by corresponding angles. That makes the larger triangle — formed by the top crossing point and the two points on m — have angles x (at the top), y = 20° (at one base point), and 60° (at the other base point, transferred from z). Since the triangle's angles sum to 180: x = 180 − 20 − 60 = 100.*

**C.** 90 

  *This treats the two rays as perpendicular by default, ignoring the actual y and z values entirely.*

**D.** 80 

  *This adds y and z directly (20 + 60 = 80) instead of first transferring z across the parallel lines via corresponding angles, then using the triangle's angle sum. It skips the parallel-line step entirely.*

*Difficulty: hard*

---

##### Q3
In triangle XYZ, the measure of angle X is 24° and the measure of angle Y is 98°. What is the measure of angle Z?

**A.** 58° **(Correct)**

  *Correct. A triangle's angles sum to 180°, so angle Z = 180 − 24 − 98 = 58.*

**B.** 74° 

  *This computes the DIFFERENCE between the two given angles (98 − 24 = 74) instead of subtracting their sum from 180. The third angle of a triangle is never found by differencing the other two.*

**C.** 122° 

  *This is 24 + 98 — the sum of the two given angles, reported directly without the final step of subtracting from 180. It is the amount left over after Z is removed, not Z itself.*

**D.** 212° 

  *This adds an assumed right angle to the two given angles (24 + 98 + 90 = 212), as if the triangle also contained a 90° angle. Nothing states this triangle is right, and no triangle can have three angles summing to more than 180° in the first place.*

*Difficulty: medium*

---

##### Q4
Line t crosses parallel lines m and n. At the crossing with m, the angle between t and m (on the lower-left side) measures 134°. At the crossing with n, the corresponding angle (same relative position) measures w°. Line m is parallel to line n. What is the value of w?

**A.** 13 

  *This reads only the first two digits of the given 134°, dropping the trailing digit, and reports a garbled version of the given number rather than solving for w.*

**B.** 34 

  *This reads only the last two digits of the given 134°, dropping the leading digit, and again reports a garbled version of the given number instead of the answer.*

**C.** 66 

  *The correct same-side (co-interior) supplement of 134° is 180 − 134 = 46°, not the relationship being used here in the first place — corresponding angles across parallel lines are EQUAL, not supplementary. 66 does not match either the correct answer or a clean supplement calculation, and most likely comes from a further arithmetic slip on top of using the wrong relationship.*

**D.** 134 **(Correct)**

  *Correct. w and the given 134° angle sit in the same relative position at each of the two crossings (both on the lower-left, between line t and the parallel line). Since m ∥ n, corresponding angles are equal: w = 134.*

*Difficulty: easy*

---

##### Q5
At a certain time and day, the Washington Monument in Washington, DC, casts a shadow that is 300 feet long. At the same time, a nearby cherry tree casts a shadow that is 16 feet long. Given that the Washington Monument is approximately 555 feet tall, which of the following is closest to the height, in feet, of the cherry tree?

**A.** 10 

  *This inverts the proportion (using shadow-to-height instead of height-to-shadow) and computes roughly 300 × 16/555 ≈ 8.6, rounding to the nearest offered choice.*

**B.** 20 

  *This computes the shadow ratio 300/16 ≈ 18.75 and mistakes THIS ratio itself for the tree's height, rounding it to the nearest choice — without ever bringing the monument's actual height of 555 ft into a proportion.*

**C.** 30 **(Correct)**

  *Correct. Two objects casting shadows at the same moment have the same height-to-shadow ratio: tree height/16 = 555/300, so tree height = 555 × 16/300 = 29.6, which rounds to 30.*

**D.** 35 

  *This divides the monument's height directly by the tree's shadow length (555/16 ≈ 34.7, rounding to 35), skipping the monument's own shadow length (300) entirely — an incomplete proportion.*

*Difficulty: medium*

---

##### Q6
In the figure, segment AD intersects segment BE at point C. In triangle ABC, angle A measures 20° and angle B is x°. In triangle CDE, angle E measures 40° and angle D is y°. Angle ACB and angle DCE are vertical angles. If x = 100, what is the value of y?

**A.** 100 

  *This reports x directly, as though angle D in the second triangle were automatically equal to angle B in the first — but vertical angles make only angle ACB equal to angle DCE, not every angle across the two triangles equal to each other.*

**B.** 90 

  *This mistakes the vertical-angle relationship for a halving relationship — taking half of x (100/2 = 50) as angle DCE instead of the value actually forced by triangle ABC's angle sum (180 − 20 − 100 = 60), then continuing: 180 − 50 − 40 = 90.*

**C.** 80 **(Correct)**

  *Correct. In triangle ABC, angle ACB = 180 − 20 − 100 = 60°. Since AD and BE cross at C, angle DCE is vertical to angle ACB, so angle DCE = 60° too. In triangle CDE, angle E = 40°, so y = 180 − 60 − 40 = 80.*

**D.** 60 

  *This correctly finds angle ACB = angle DCE = 60° (via triangle ABC's angle sum and the vertical-angle transfer) but stops there, reporting that intermediate value instead of continuing into triangle CDE to find y.*

*Difficulty: sat-hardest*

---

##### Q7
In the triangle shown, two sides meeting at the top vertex are extended upward past that vertex, crossing to form an X. The angle x° is marked at the left of this X (between the upward extension of the right side and the original left side). At the base, the two base angles of the original triangle measure 70° and 50°. What is the value of x?

**A.** 110 

  *This computes the supplement of only ONE base angle (180 − 70 = 110), ignoring the other base angle. By the exterior angle theorem, x should use BOTH remote interior angles, not just one.*

**B.** 120 **(Correct)**

  *Correct. x is the exterior angle formed by extending the two sides past the top vertex, and the exterior angle theorem says an exterior angle equals the sum of the two remote interior angles: x = 70 + 50 = 120.*

**C.** 130 

  *This computes the supplement of only the OTHER base angle (180 − 50 = 130), again using just one remote angle instead of both.*

**D.** 140 

  *This adds one base angle to itself instead of adding both distinct base angles (70 + 70 = 140), rather than 70 + 50.*

*Difficulty: hard*

---

##### Q8
In the right triangle shown, one angle measures 13°, the right angle is at the vertex between the two legs, and a° is the third angle. What is the value of a?

**A.** 13 

  *This reports the given 13° angle back, rather than solving for the different, unknown third angle.*

**B.** 77 **(Correct)**

  *Correct. A triangle's angles sum to 180°: 90 + 13 + a = 180, so a = 77.*

**C.** 90 

  *This reports the given right angle itself instead of solving for the third, unknown angle.*

**D.** 103 

  *This adds the two given angles (90 + 13 = 103) instead of subtracting their sum from 180 — treating the triangle's angle sum rule backwards.*

*Difficulty: easy*

---

##### Q9
In triangle ABC, the measure of angle B is 52° and the measure of angle C is 17°. What is the measure of angle A?

**A.** 21° 

  *This assumes the triangle also contains a right angle (a common unwarranted default) and subtracts an extra 90° from the correctly-found 111°: 111 − 90 = 21.*

**B.** 35° 

  *This computes the DIFFERENCE between the two given angles (52 − 17 = 35) instead of using the triangle's angle sum. The third angle is never found by subtracting one given angle from another.*

**C.** 69° 

  *This is 52 + 17, the sum of the two given angles, reported directly instead of subtracting that sum from 180 for the final answer.*

**D.** 111° **(Correct)**

  *Correct. A triangle's angles sum to 180°: angle A = 180 − 52 − 17 = 111.*

*Difficulty: medium*

---

##### Q10
Line j is parallel to line k, and a transversal crosses both. At the crossing with j, the angle between the transversal and j (on one side) measures 133°, and x° is the adjacent angle on the other side of the transversal at that same crossing. What is the value of x?

**A.** 133 

  *This treats x as equal to the given 133° angle, as if they were vertical angles — but x and 133° sit on either side of the transversal at the SAME crossing, sharing a ray along line j, which makes them a linear pair (supplementary), not vertical angles.*

**B.** 67 

  *This takes half of 133° (≈66.5, rounding to 67), as if x split the 133° angle evenly — but x is the SEPARATE angle on the other side of the transversal, not a bisected portion of the given angle.*

**C.** 90 

  *This assumes the transversal is perpendicular to line j regardless of the given 133°, ignoring the actual value entirely.*

**D.** 47 **(Correct)**

  *Correct. x and the 133° angle are adjacent along line j on either side of the transversal, forming a linear pair that sums to 180°: x = 180 − 133 = 47.*

*Difficulty: easy*

---

##### Q11
Line t is parallel to line m... (correction: line m is parallel to line n). Transversal t crosses both. At the crossing with m, the angle between t and m (lower-left side) measures 170°. At the crossing with n, the corresponding angle (same relative position) measures w°. What is the value of w?

**A.** 17 

  *This reads only part of the given 170°, dropping the trailing zero, and reports a garbled version of the given number rather than solving for w.*

**B.** 30 

  *This misreads the given 170° as 150° (an easy digit slip) and then applies the co-interior supplementary relationship to that misread value: 180 − 150 = 30 — the wrong relationship (equal corresponding angles are needed here, not supplementary ones) compounded with a misread number.*

**C.** 70 

  *This applies the co-interior (same-side interior) supplementary relationship instead of the corresponding-angle relationship that actually applies here, and further miscalculates the supplement of 170° (which is 10°, not 70°) along the way.*

**D.** 170 **(Correct)**

  *Correct. w and the given 170° sit in the same relative position at each of the two crossings. Since m ∥ n, corresponding angles are equal: w = 170.*

*Difficulty: hard*

---

##### Q12
Triangle ABC is [[dilation|dilated]] by a scale factor of 3 to obtain triangle XYZ, where A corresponds to X, B to Y, and C to Z. Angle A measures 60°, and side AC (labeled d) has length 16. What is the measure, in degrees, of angle X?

**A.** 20 

  *This divides the angle by the scale factor (60/3 = 20), mistakenly treating angles as if they scale under dilation the way lengths do. Dilation changes side lengths by the scale factor but leaves every angle measure unchanged.*

**B.** 57 

  *This subtracts the scale factor from the angle (60 − 3 = 57), another way of letting the irrelevant scale factor and the side length d = 16 contaminate an angle calculation that never needed them.*

**C.** 60 **(Correct)**

  *Correct. [[Dilation]] preserves every angle measure exactly, regardless of the scale factor or any side length. Angle X corresponds to angle A, so angle X = 60°. The scale factor (3) and d = 16 are not needed for this question.*

**D.** 63 

  *This adds the scale factor to the angle (60 + 3 = 63), again letting an irrelevant number bleed into the angle answer instead of recognizing that dilation leaves angle measures untouched.*

*Difficulty: medium*

---

##### Q13
Line ℓ intersects parallel lines j and k. At the crossing with j, w° is the angle between ℓ and j on one side, and x° is the vertically opposite angle at that same crossing. At the crossing with k, the angle between ℓ and k in the position corresponding to w° measures 40°; y° is the angle vertically opposite that 40° angle, and z° is the angle supplementary to the 40° angle along line k. Which additional piece of information is sufficient to prove that lines j and k are parallel?

**A.** w = 40 **(Correct)**

  *Correct. w and the 40° angle sit in corresponding positions at their respective crossings. If w = 40, the two lines create equal [[corresponding angles]] with transversal ℓ, which by the converse of the corresponding angles postulate proves j ∥ k.*

**B.** x = 140 

  *x is vertically opposite w at the SAME crossing, so x is always equal to w regardless of whether j and k are parallel — this is a fact about a single crossing, not a comparison between the two lines. Stating x = 140 really just says w = 140, which does not match the 40° needed for the corresponding-angle proof, and gives no valid path to concluding the lines are parallel.*

**C.** y = 40 

  *y is vertically opposite the given 40° angle at the SAME crossing (with k), so y = 40 is true automatically no matter how j and k are related to each other. It adds no new information that could establish parallelism.*

**D.** z = 140 

  *z is supplementary to the given 40° angle at the SAME crossing (a linear pair along k), so z = 140 is true automatically regardless of j and k's relationship. Like y = 40, it adds no new information about how the two lines compare.*

*Difficulty: sat-hardest*

---

##### Q14
In the figure, segments AF, BE, and CD are parallel. Points B and E lie on segment AC and segment FD, respectively. If AB = 9, BC = 18.5, and FE = 8.5, what is the length of ED, to the nearest tenth?

**A.** 16.8 

  *This is close to correct but comes from a denominator slip: computing FE × BC and then dividing by a misread value near 9.36 instead of 9, e.g. 8.5 × 18.5 ≈ 157.25, divided by ≈9.36 ≈ 16.8, instead of the correct divisor of 9.*

**B.** 17.5 **(Correct)**

  *Correct. Three parallel segments cut by two transversals (AC and FD) divide those transversals proportionally: AB/BC = FE/ED. So ED = FE × BC/AB = 8.5 × 18.5/9 ≈ 17.47, which rounds to 17.5.*

**C.** 18.4 

  *This misreads BC (18.5) as 19.5 — an easy adjacent-digit slip — and otherwise applies the correct proportion: 8.5 × 19.5/9 ≈ 18.42, rounding to 18.4.*

**D.** 19.6 

  *This swaps AB and FE in the proportion, setting it up as FE/BC = AB/ED instead of AB/BC = FE/ED. That gives ED = AB × BC/FE = 9 × 18.5/8.5 ≈ 19.59, rounding to 19.6 — the two 'known' sides traded places.*

*Difficulty: sat-hardest*

---

##### Q15
Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10 feet tall and has a shadow that is 5 feet long. At the same time, the shadow of the other tree is 2 feet long. How tall, in feet, is the other tree?

**A.** 3 

  *This computes 10 − 5 − 2 = 3, treating the relationship as a chain of subtractions instead of a proportion between height and shadow.*

**B.** 4 **(Correct)**

  *Correct. Both trees cast shadows under the same sun angle, so height/shadow is constant: 10/5 = 2, and the second tree's height is 2 × 2 = 4 ft.*

**C.** 8 

  *This computes 10 − 2 = 8, subtracting the second tree's shadow directly from the first tree's height instead of setting up the height-to-shadow proportion.*

**D.** 27 

  *This answer is directionally impossible: a shorter shadow (2 ft, versus the first tree's 5 ft) under the same sun angle must mean a shorter object, not one taller than the reference tree itself (10 ft). It most likely comes from combining the given numbers additively rather than setting up a proportion at all.*

*Difficulty: easy*

---

##### Q16
Right triangles ABC and DEF are shown, each with a right angle marked (at C and at F respectively). Angle A measures 32° and angle D measures 58°. Which of the following is equal to the ratio BC/AB?

**A.** DE/DF 

  *This is the reciprocal of the correct ratio, with numerator and denominator swapped.*

**B.** DF/DE **(Correct)**

  *Correct. Triangle ABC has angles 32° (A), 90° (C), 58° (B); triangle DEF has angles 58° (D), 90° (F), 32° (E). Matching equal angles gives the correspondence A↔E, B↔D, C↔F. Side BC is opposite A, corresponding to the side opposite E, which is DF; side AB is the hypotenuse (opposite the right angle C), corresponding to the hypotenuse DE. So BC/AB = DF/DE.*

**C.** DF/EF 

  *This uses EF — the leg opposite the 58° angle at D — as the denominator instead of the hypotenuse DE, which is what corresponds to AB (the hypotenuse of triangle ABC).*

**D.** EF/DE 

  *This swaps which leg is used in the numerator — EF (opposite the 58° angle D) instead of DF (opposite the 32° angle E, which is what actually corresponds to BC).*

*Difficulty: hard*

---

##### Q17
Lines r and s are parallel and are intersected by lines m and n. If y < 65, which of the following must be true, where x and y are positioned so that x and y are supplementary due to the parallel lines?

**A.** x < 115 

  *This keeps the same inequality direction as y < 65 without accounting for the flip that happens when you subtract from a fixed total: since x = 180 − y, a SMALLER y produces a LARGER x, not a smaller one.*

**B.** x > 115 **(Correct)**

  *Correct. Because the lines are parallel, x and y are supplementary: x + y = 180, so x = 180 − y. Since y < 65, subtracting a smaller y from 180 gives a larger x: x > 180 − 65 = 115.*

**C.** x + y < 180 

  *This mistakes the guaranteed EQUALITY x + y = 180 (which holds exactly, because the lines are parallel) for a strict inequality. x + y is never less than 180 here — it is always exactly 180.*

**D.** x + y > 180 

  *Same error as x + y < 180, in the other direction — both mistake the guaranteed equality x + y = 180 (from the parallel lines) for a strict inequality that it never actually is.*

*Difficulty: hard*

---

##### Q18
Triangle ABC is similar to triangle XYZ, such that A, B, and C correspond to X, Y, and Z respectively. The length of each side of triangle XYZ is 2 times the length of its corresponding side in triangle ABC. The measure of side AB is 16. What is the measure of side XY?

**A.** 14 

  *This subtracts the scale factor from AB instead of multiplying by it: 16 − 2 = 14.*

**B.** 16 

  *This reports AB unchanged, as if the two triangles were congruent rather than merely similar with a scale factor of 2.*

**C.** 18 

  *This adds the scale factor to AB instead of multiplying by it: 16 + 2 = 18.*

**D.** 32 **(Correct)**

  *Correct. Every side of XYZ is 2 times the corresponding side of ABC, so XY = 2 × AB = 2 × 16 = 32.*

*Difficulty: easy*

---

##### Q19
In triangle JKL, the measures of angle K and angle L are each 48°. What is the measure of angle J, in degrees?

**A.** 42 

  *This halves the correct answer (84/2 = 42), as if angle J related to the other angles by a halving rule rather than by the triangle's angle sum.*

**B.** 48 

  *This reports one of the given base angles back, assuming the triangle is equilateral (all three angles equal) rather than simply isosceles with two equal 48° angles and a possibly-different third angle.*

**C.** 84 **(Correct)**

  *Correct. A triangle's angles sum to 180°: angle J = 180 − 48 − 48 = 84.*

**D.** 132 

  *This subtracts only ONE of the two given 48° angles from 180 (180 − 48 = 132), forgetting that BOTH angle K and angle L must be removed from the total to isolate angle J.*

*Difficulty: easy*

---

##### Q20
In the given triangle, a = 45, where the triangle has angles 31°, 2b°, and a° at its three vertices. What is the value of b?

**A.** 52 **(Correct)**

  *Correct. A triangle's angles sum to 180°: 31 + 2b + 45 = 180, so 2b = 104, giving b = 52.*

**B.** 59 

  *This correctly finds 2b = 104 (from 180 − 31 − 45) but then subtracts a (45) instead of dividing by 2: 104 − 45 = 59.*

**C.** 76 

  *This adds the two given angles directly (31 + 45 = 76) instead of first finding the expression 2b via the triangle's angle sum and then solving for b.*

**D.** 104 

  *This correctly finds 2b = 180 − 31 − 45 = 104 but reports 2b itself instead of dividing by 2 to get b.*

*Difficulty: medium*

---

##### Q21
In the figure, three lines intersect at point P, forming a straight line through P with three angles x°, y°, and z° between it and the two other lines, where x and z are adjacent to the straight portion and y is the angle at the bottom between the two crossing lines. If x = 65 and y = 75, what is the value of z?

**A.** 140 

  *This reports the supplement of the correct answer (180 − 40 = 140) — treating z's vertical or adjacent angle above the line as z itself instead of the angle below it.*

**B.** 80 

  *This doubles the correct value (2 × 40 = 80), as if z appeared twice around point P.*

**C.** 40 **(Correct)**

  *Correct. Angles x, y, and z together make up a straight angle along the top line: x + y + z = 180, so z = 180 − 65 − 75 = 40.*

**D.** 20 

  *This halves the correctly-found 40° (40/2 = 20), as if z needed to be split evenly with an adjacent angle that doesn't actually need splitting.*

*Difficulty: medium*

---

##### Q22
In the figure, lines ℓ and k are parallel, and a is the measure of an angle formed with a transversal that is co-interior (same-side interior) with a given 64° angle. What is the value of a?

**A.** 26 

  *This treats a and 64° as complementary (90 − 64 = 26) rather than co-interior and supplementary. Complementary pairs only arise when a right angle is actually part of the figure.*

**B.** 64 

  *This treats a and the given 64° angle as equal (as corresponding or alternate angles would be) rather than supplementary, which is the relationship that actually holds for co-interior angles.*

**C.** 116 **(Correct)**

  *Correct. a and the given 64° angle are co-interior (same-side interior) angles across the parallel lines, which are supplementary: a = 180 − 64 = 116.*

**D.** 154 

  *This adds 64° to 90° instead of subtracting it from 180° — treating the relationship as if the transversal met the parallel lines at a right angle: 90 + 64 = 154.*

*Difficulty: easy*

---

##### Q23
Triangle ABC and triangle DEF are shown. The relationship between the side lengths of the two triangles is such that AB/DE = BC/EF = AC/DF = 3. If the measure of angle BAC is 20°, what is the measure, in degrees, of angle EDF?

**A.** 60 

  *This multiplies the angle by the given side-ratio (3), treating angle measure as though it scales the way side lengths do: 20 × 3 = 60. [[similar triangles|Similar triangles]] have identical angle measures regardless of their size ratio.*

**B.** 20 **(Correct)**

  *Correct. Since the correspondence is A↔D, B↔E, C↔F (matching how the side ratios are written), angle BAC corresponds to angle EDF. Similar triangles have equal corresponding angles no matter the side-length ratio, so angle EDF = 20°.*

**C.** 17 

  *Subtracts the scale factor from the angle: 20 − 3 = 17.*

**D.** 23 

  *Adds the scale factor to the angle: 20 + 3 = 23.*

*Difficulty: easy*

---

##### Q24
In the figure, segments AE and BD are parallel, with B on segment AC and D on segment CE. If angle BDC measures 58° and angle ACE measures 62°, what is the measure of angle CAE?

**A.** 58° 

  *This reports the given angle BDC directly instead of using it inside triangle BCD to find angle CBD, then transferring that value to angle CAE via corresponding angles.*

**B.** 60° **(Correct)**

  *Correct. BD ∥ AE makes angle CBD (at B, in triangle BCD) correspond to angle CAE (at A, in triangle ACE), since C is the shared vertex and BD ∥ AE means triangle CBD ~ triangle CAE. In triangle BCD, angle BCD = angle ACE = 62° (same angle, since B is on CA and D is on CE), and angle BDC = 58°, so angle CBD = 180 − 62 − 58 = 60°. By the similarity, angle CAE = angle CBD = 60°.*

**C.** 62° 

  *This reports the given angle ACE directly instead of continuing through triangle BCD to find angle CBD and transferring it.*

**D.** 120° 

  *This reports the supplement of the correct answer, confusing the corresponding-angle relationship (equal, since BD ∥ AE) with a co-interior relationship (supplementary).*

*Difficulty: hard*

---

##### Q25
Triangles ABC and DEF are congruent, where A corresponds to D, and B and E are right angles. The measure of angle A is 69°. What is the measure, in degrees, of angle F?

**A.** 111 

  *This forgets that angle E = 90° is also part of triangle DEF's angle sum, computing only 180 − 69 = 111 instead of 180 − 69 − 90.*

**B.** 90 

  *This reports the given right angle (E's measure) instead of solving for the different, unknown angle F.*

**C.** 69 

  *This reports angle A (= angle D, by congruence) directly instead of solving for angle F.*

**D.** 21 **(Correct)**

  *Correct. Angle D = angle A = 69° (corresponding angles under the congruence), and angle E = 90°. In triangle DEF: angle F = 180 − 69 − 90 = 21.*

*Difficulty: medium*

---

##### Q26
In triangle PQR, side QR is extended to point S. The measure of angle PQR is 132°, and the measure of angle PRS is 163°. What is the measure of angle QPR?

**A.** 48° 

  *This computes the supplement of angle PQR (180 − 132 = 48) instead of using the exterior angle theorem, which relates angle PRS to BOTH remote interior angles at once.*

**B.** 31° **(Correct)**

  *Correct. Since QR is extended to S, angle PRS is the exterior angle of triangle PQR at vertex R, equal to the sum of the two remote interior angles: angle PRS = angle PQR + angle QPR. So 163 = 132 + angle QPR, giving angle QPR = 31.*

**C.** 24° 

  *This takes half of the already-incorrect supplement from choice A (48/2 = 24), compounding an unnecessary halving on top of using the wrong relationship in the first place.*

**D.** 17° 

  *This computes the supplement of angle PRS (180 − 163 = 17) instead of correctly subtracting angle PQR from angle PRS via the exterior angle theorem.*

*Difficulty: hard*

---

##### Q27
In triangle DEF, the measure of angle D is 47° and the measure of angle E is 97°. In triangle RST, the measure of angle R is 47° and the measure of angle S is 97°. Which of the following additional pieces of information is needed to determine whether triangle DEF is similar to triangle RST?

**A.** The measure of angle F 

  *Angle F is already determined by the two given angles (180 − 47 − 97 = 36°), so stating it explicitly adds no new information — it doesn't help decide anything not already forced by the given angles D and E.*

**B.** The measure of angle T 

  *Angle T is already determined (180 − 47 − 97 = 36°) by angles R and S, so knowing it explicitly is redundant with what's already given.*

**C.** The measures of angle F and angle T 

  *Both angles are already forced by the given information (each triangle's third angle is determined once two angles are known), so asking for both is doubly redundant.*

**D.** No additional information is needed. **(Correct)**

  *Correct. Two pairs of angles are already equal: angle D = angle R = 47° and angle E = angle S = 97°. By AA similarity, two triangles with two pairs of equal angles are automatically similar — the third angle is not independent information, since it is forced by the other two. No further data is needed.*

*Difficulty: hard*

---

##### Q28
In the figure, triangle CAE is similar to triangle CBD, with B on segment CA and D on segment CE. The measure of angle CBD is 57°, and AE = 26(BD). What is the measure of angle CAE?

**A.** (26 · 57)° 

  *This multiplies the angle by the given side-ratio (26) instead of recognizing that similar triangles have identical angle measures regardless of their size ratio.*

**B.** (26 + 57)° 

  *This adds the scale factor to the angle instead of leaving the angle unchanged.*

**C.** 57° **(Correct)**

  *Correct. Angle CAE corresponds to angle CBD under the similarity (matching how the triangles are named: C↔C, A↔B, E↔D). Similar triangles have equal corresponding angles regardless of the side-length ratio (26), so angle CAE = angle CBD = 57°.*

**D.** 26° 

  *This reports the scale factor (26) itself as if it were the angle measure, ignoring the actual given angle of 57° entirely.*

*Difficulty: medium*

---

##### Q29
In triangle ABC, the measure of angle A is 50°. If triangle ABC is isosceles, which of the following is NOT a possible measure of angle B?

**A.** 50° 

  *This IS possible: if angle B equals angle A (both 50°), the triangle is isosceles with A and B as the equal pair, leaving angle C = 180 − 50 − 50 = 80°. A student who only checks the 'B equals the third angle' pairing (missing the 'B equals A' case) might wrongly rule this out.*

**B.** 65° 

  *This IS possible: if angle B equals angle C (with A = 50° the unique angle), then B = (180 − 50)/2 = 65°. This is the pairing most people check first, which is exactly why the other two valid values (50° and 80°) are easy to miss.*

**C.** 80° 

  *This IS possible: if angle C equals angle A (both 50°), then B = 180 − 50 − 50 = 80°, with B as the unique apex angle. This pairing is easy to overlook if 'isosceles' is only checked one way.*

**D.** 100° **(Correct)**

  *Correct. There are exactly three ways to make triangle ABC isosceles with angle A = 50°: B = A gives B = 50°; B = C gives B = 65°; A = C gives B = 80°. None of the three produces B = 100°, so it is the one value angle B cannot take.*

*Difficulty: hard*

---

##### Q30
In the given figure, segment AC extends to point D. If the measure of angle BAC is equal to the measure of angle BCA, and angle BCD (the exterior angle formed at C) measures 110°, what is the value of x, the measure of angle ABC?

**A.** 110 

  *This reports the given exterior angle BCD directly instead of solving for the interior angle x at B.*

**B.** 70 

  *This correctly finds angle BCA = 180 − 110 = 70° (and, since angle BAC = angle BCA, that angle too) but reports one of these base angles instead of continuing to find x, the apex angle at B.*

**C.** 55 

  *This mistakenly treats the exterior angle as splitting evenly between the two remote interior angles (110/2 = 55) rather than first finding angle BCA = 180 − 110 = 70 and using the fact that angle BAC equals it.*

**D.** 40 **(Correct)**

  *Correct. Angle BCD is exterior to the triangle at C, so angle BCA = 180 − 110 = 70°. Since angle BAC = angle BCA = 70°, the triangle's angle sum gives x = 180 − 70 − 70 = 40.*

*Difficulty: hard*

---

##### Q31
In the figure, lines j and k cross at a point that also lies on line m, with a right angle marked where a separate vertical line ℓ crosses m to its right; ℓ continues down to cross line n as well, where it meets a continuation of line k, forming angle b°. On either side of the j-k crossing point on m, two equal angles a° are marked. Below, on line n, an angle of 130° is marked where line j crosses n. Lines m and n are parallel. What is the value of b?

**A.** 40 **(Correct)**

  *Correct. Since j is a transversal crossing parallel lines m and n, the angle a (on line m, same side as the 130° angle on n) is co-interior with 130°, so a = 180 − 130 = 50°. In the right triangle formed by m, the vertical line ℓ, and k (right angle where ℓ meets m), the angle at the top vertex equals a = 50° (the two a angles are equal by the figure), so b = 180 − 90 − 50 = 40.*

**B.** 50 

  *This reports a itself (the intermediate angle found from the co-interior relationship with 130°) instead of continuing into the right triangle to solve for b.*

**C.** 65 

  *This halves the given 130° (130/2 = 65) instead of correctly using the co-interior supplementary relationship (180 − 130 = 50) to find a first.*

**D.** 80 

  *This forgets that the triangle formed by m, ℓ, and k has a right angle at the vertex on m (since ℓ ⊥ m), and instead treats it as isosceles with two 50° angles: 180 − 2(50) = 80.*

*Difficulty: sat-hardest*

---

##### Q32
In the figure, points D, E, and A lie on a line, with C above segment DA, B above and to the right of C, and segment DB drawn so that C lies on it (D, C, B collinear); segment BE is also drawn, crossing CA at C. AC = CD. The measure of angle EBC is 45°, and the measure of angle ACD is 104°. What is the value of x, the measure of angle BEA?

**A.** 38 

  *This correctly finds the base angle of isosceles triangle ACD (angle CDA = angle CAD = (180 − 104)/2 = 38°) but reports that intermediate angle instead of continuing through the rest of the figure to x.*

**B.** 45 

  *This reports the given angle EBC directly instead of working it through triangle BDE and the final supplementary step.*

**C.** 97 

  *This correctly finds angle BED (the angle of triangle BDE at E, on the D-side of line DA) as 180 − 38 − 45 = 97°, but reports this angle instead of its supplement x = angle BEA, which is the angle on the OTHER side of E along the straight line DA.*

**D.** 83 **(Correct)**

  *Correct. Since AC = CD, triangle ACD is isosceles with apex angle 104° at C, giving base angles (180 − 104)/2 = 38° each — so angle CDA = 38°, which is also angle BDE (since C lies on DB). In triangle BDE, angle BDE = 38° and angle DBE = angle EBC = 45° (since C lies on DB, ray BC = ray BD), so angle BED = 180 − 38 − 45 = 97°. Since D, E, A are collinear, x = angle BEA = 180 − 97 = 83.*

*Difficulty: sat-hardest*

---

##### Q33
Three lines, r, s, and t, intersect pairwise to form a small triangle. At the top vertex, line s continues straight past the crossing, and the angle between this continuation and the side going to the right vertex — the exterior angle of the triangle at the top — measures 106°. At the right vertex, the interior angle of the triangle measures 23°. At the bottom-left vertex, x° is the angle on the outside of the triangle (between the extension of one side past that vertex and the other side). What is the value of x?

**A.** 51 

  *This treats 106°, 23°, and x° as the three INTERIOR angles of a single triangle summing to 180° (180 − 106 − 23 = 51), missing that 106° is actually the triangle's EXTERIOR angle at that vertex, not an interior angle alongside x° and 23°.*

**B.** 83 

  *This is the triangle's actual interior angle at the bottom-left vertex, correctly found via the exterior angle theorem (106 = interior + 23, so interior = 83) — but x° is the angle on the OTHER side of that vertex, supplementary to this interior angle, not the interior angle itself: x = 180 − 83 = 97.*

**C.** 129 

  *This adds the exterior angle to the interior angle it should be split from (106 + 23 = 129), reversing the exterior angle theorem's subtraction instead of using it correctly.*

**D.** 97 **(Correct)**

  *Correct. By the exterior angle theorem, the 106° exterior angle at the top vertex equals the sum of the two remote interior angles: 106 = (interior angle at the bottom-left vertex) + 23, so that interior angle is 83°. x° is the angle on the other side of that vertex, supplementary to the 83° interior angle along the straight line there: x = 180 − 83 = 97.*

*Difficulty: sat-hardest*

---

##### Q34
In the figure, quadrilateral MNQR has diagonals MQ and NR intersecting at point P, with NP = QP and MP = PR. The angle at P between PQ and PR measures 60°, and the angle at Q between QN and QR (angle NQR... more precisely, the angle of the figure at Q, adjacent to the diagonal) measures 70°. What is the measure, in degrees, of angle QMR?

**A.** 120 

  *This reports an intermediate apex angle (angle MPR, found along the way) instead of continuing to the base angle that answers the question.*

**B.** 50 

  *This reports an intermediate angle from an earlier step in the two-triangle chain instead of the final target angle.*

**C.** 60 

  *This reports the given 60° angle at P directly, as if angle QMR were simply equal to it, without doing the isosceles-triangle work that actually connects them.*

**D.** 30 **(Correct)**

  *Correct. Working through triangle QPR (angle Q = 70°, angle P = 60°, so angle R = 50°), then using vertical and supplementary angle relationships around point P to find angle MPR = 120°, and finally applying MP = PR (isosceles, apex angle 120°) gives the base angles (180 − 120)/2 = 30° each. Since ray MQ = ray MP, angle QMR = angle PMR = 30.*

*Difficulty: sat-hardest*

---

##### Q35
In the figure, N is the apex of a triangle with M and P at its base, and Q is the foot of the altitude from N to MP, with a right angle marked at Q. Side MN = 3 and side NP = 4. What is the length of NQ?

**A.** 2.2 

  *This is lower than the correct altitude and doesn't match any of the standard sub-results (MQ = 1.8, QP = 3.2, altitude = 2.4). It most likely comes from a computational slip while applying the altitude formula 3 × 4/5, such as dividing by a mis-copied denominator near 5.5 instead of 5.*

**B.** 2.3 

  *Close to the correct 2.4 but slightly under — consistent with a slightly misread side length feeding into the same formula, e.g. using 3.9 instead of 4 for NP: 3 × 3.9/5 ≈ 2.34, rounding to 2.3.*

**C.** 2.4 **(Correct)**

  *Correct. Since MN = 3 and NP = 4 form a 3-4-5 right triangle with the right angle at N, the hypotenuse MP = 5. The altitude from the right angle to the hypotenuse equals the product of the legs divided by the hypotenuse: NQ = (3 × 4)/5 = 2.4.*

**D.** 2.5 

  *This is half the hypotenuse (5/2 = 2.5), confusing the altitude to the hypotenuse with the MEDIAN to the hypotenuse — a different segment that, in a right triangle, really is exactly half the hypotenuse. The altitude is shorter than the median except at the special case where the two legs are equal.*

*Difficulty: hard*

---

##### Q36
In the figure, triangle SRU has a cevian from R to point T on side SU, and RT = TU. The angle at S between SR and SU measures 31°, and the angle RTU (at T, between TR and TU) measures 114°. What is the value of x, the angle at R between RS and RU?

**A.** 72 

  *This does not follow from a single clean step in the chain; checking it against the given 31° and 114° shows it is inconsistent with the angle relationships the figure forces, most likely from a compounding slip across the multi-step chase.*

**B.** 66 

  *This computes the supplement of the apex angle (180 − 114 = 66) but stops there, reporting the full remaining amount instead of splitting it in half for the SINGLE base angle: the two base angles of isosceles triangle RTU are equal and together make up 66°, so each one alone is 33°, not 66°.*

**C.** 64 **(Correct)**

  *Correct. Since RT = TU, triangle RTU is isosceles with apex angle 114° at T, giving base angles of (180 − 114)/2 = 33° each — so angle TRU = 33°. Angle x is the full angle SRU at vertex R, which splits into angle SRT and angle TRU. Tracing through the two triangles that share the crossing of cevians SV and RT (where V is where segment SR's companion cevian meets the base), angle SRT works out to 31°, matching angle S — so x = angle SRT + angle TRU = 31 + 33 = 64.*

**D.** 58 

  *This is close to half the apex angle (114/2 = 57) rather than working through the correct two-step chain (supplement, then halve, then add angle S) — a sign of skipping the halving-of-the-supplement step and estimating instead.*

*Difficulty: sat-hardest*

---

##### Q37
In right triangle ABC, angle C is a right angle, and D is the foot of the altitude from B to AC, with AD = 5 and DC = 7. If the area of triangle ABC is at least 48 but no more than 60, and y (= BC) is an integer, what is one possible value of x, the length of the altitude from D to AB?

**A.** 10/3 **(Correct)**

  *Correct. Area = (1/2)(AC)(BC) = (1/2)(12)(y) = 6y, so 48 ≤ 6y ≤ 60 gives 8 ≤ y ≤ 10, and y must be an integer, so y ∈ {8, 9, 10}. By similar triangles (the small triangle at A is similar to the whole triangle, with AD = 5 corresponding to AC = 12), x/y = 5/12. For y = 8: x = 5(8)/12 = 40/12 = 10/3.*

**B.** 4 

  *This would require y = 12(4)/5 = 9.6, which is not an integer — y must be a whole number for this to be valid.*

**C.** 3 

  *This would require y = 12(3)/5 = 7.2, which is not an integer, and also gives an area of only 6(7.2) = 43.2 — below the required minimum of 48.*

**D.** 9/2 

  *This would require y = 12(4.5)/5 = 10.8 — not an integer, and the resulting area (6 × 10.8 = 64.8) exceeds the maximum of 60.*

*Difficulty: sat-hardest*

---

##### Q38
In triangle RST, angle T is a right angle, point L lies on RS, point K lies on ST, and LK is parallel to RT. If the length of RT is 72 units, the length of LK is 24 units, and the area of triangle RST is 792 square units, what is the length of KT, in units?

**A.** 22 

  *This correctly finds ST = 792 × 2/72 = 22 from the area formula but stops there, reporting the whole leg ST instead of continuing to find KT.*

**B.** 22/3 

  *This correctly finds the scale ratio 24/72 = 1/3 and computes SK = ST/3 = 22/3, but reports SK (the segment near S) instead of KT (the segment near T, which is ST − SK).*

**C.** 44/3 **(Correct)**

  *Correct. Area = (1/2)(RT)(ST) = 792, so ST = 792 × 2/72 = 22. Since LK ∥ RT, triangle SLK ~ triangle SRT with ratio LK/RT = 24/72 = 1/3, so SK = ST/3 = 22/3. Then KT = ST − SK = 22 − 22/3 = 66/3 − 22/3 = 44/3.*

**D.** 8 

  *This divides LK (24) by 3 directly (24/3 = 8) instead of applying the 1/3 ratio to ST to find SK first — treating LK itself as the quantity to scale down rather than using the ratio on the correct side.*

*Difficulty: sat-hardest*

---

##### Q39
In the figure, parallel lines q and t are intersected by lines r and s, which cross each other at a point above q, forming angle a° there. Line s continues down through q (crossing at angle b° on one side) and then through t; line r continues down through q and then through t, where two equal angles, each w°, are marked on either side of a bisecting mark at that crossing. If a = 43 and b = 122, what is the value of w?

**A.** 58 

  *This reports an early intermediate value in the angle chase (the interior angle at the q-crossing on the b° side, 180 − 122 = 58) instead of continuing through the full chain to w.*

**B.** 79 

  *This correctly finds the corresponding angle where line r crosses t (79°, via the triangle formed above q: 180 − 43 − 58 = 79, then transferred by corresponding angles since q ∥ t) but reports this value directly instead of recognizing that w is HALF of the adjacent 101° angle, not the corresponding angle itself.*

**C.** 101 

  *This correctly finds the full angle adjacent to the 79° corresponding angle (180 − 79 = 101) but forgets that the figure splits this 101° angle into the two equal w angles, so each w is half of it, not the whole 101°.*

**D.** 50.5 **(Correct)**

  *Correct. In the triangle formed above q (apex angle a = 43°), the angle on the b-side is 180 − 122 = 58° (interior), so the third angle of that small triangle is 180 − 43 − 58 = 79°. By corresponding angles (q ∥ t), line r makes this same 79° angle where it crosses t. The two marked w angles together make up the angle adjacent to that 79° angle, namely 180 − 79 = 101°, and since the two w's are equal, each is 101/2 = 50.5°.*

*Difficulty: sat-hardest*

---

##### Q40
In the figure, BD = 6 and AD = 8, with D the foot of the altitude from B to AC (right angle at D), and angle ABC a right angle. What is the length of DC?

**A.** 3 

  *This uses BD/2 = 3 directly, confusing the altitude relationship with simple halving.*

**B.** 6 

  *This reports BD itself, assuming DC = BD without justification — an assumed symmetry that isn't actually given.*

**C.** 8 

  *This reports AD directly instead of solving for the different segment DC.*

**D.** 4.5 **(Correct)**

  *Correct. Since angle ABC = 90° and BD is the altitude to the hypotenuse AC, the geometric mean relationship applies: BD² = AD × DC. So 36 = 8 × DC, giving DC = 4.5.*

*Difficulty: hard*

---

##### Q41
In the figure, WZ and XY intersect at point Q, with angle W (at vertex W, between WX and WZ) equal to angle Y (at vertex Y, between YX and YZ), both equal to a°. YQ = 63, WQ = 70, WX = 60, and XQ = 120. What is the length of YZ?

**A.** 35 

  *This uses XQ (120) instead of YQ (63) as the corresponding segment: WX × WQ/XQ = 60 × 70/120 = 35, mismatching which given segment pairs with which.*

**B.** 200/3 

  *This sets up the ratio backwards — WQ/YQ inverted to YQ/WQ — giving YZ = WX × WQ/YQ = 60 × 70/63 = 200/3 ≈ 66.7.*

**C.** 60 

  *This assumes the two triangles are congruent (not just similar) and reports YZ = WX directly.*

**D.** 54 **(Correct)**

  *Correct. Angle W = angle Y (given), and angle WQX = angle ZQY (vertical angles, since W, Q, Z are collinear and X, Q, Y are collinear). By AA, triangle WQX ~ triangle YQZ (W↔Y, Q↔Q, X↔Z). So WQ/YQ = WX/YZ: 70/63 = 60/YZ, giving YZ = 60 × 63/70 = 54.*

*Difficulty: hard*

---

##### Q42
In the figure, RT = TU. The measure of angle VST is 29°, and the measure of angle RVS is 41°, where V lies on segment UR, T lies on segment US, and S, R are the outer vertices of triangle URS. What is the value of x, the angle RTU?

**A.** 139 

  *This correctly finds angle SVU = 180 − 41 = 139° (the supplement of the given angle RVS) but stops there instead of continuing through triangle SVU to find angle U, and then the isosceles triangle RTU.*

**B.** 24 

  *This doubles the base angle of the small isosceles triangle (2 × 12 = 24) instead of using it correctly in the apex-angle formula (180 − 2 × 12).*

**C.** 12 

  *This correctly finds the base angle of the small isosceles triangle (angle TRU = angle U = 12°) but reports this base angle instead of the apex angle x that was actually asked for.*

**D.** 156 **(Correct)**

  *Correct. In triangle SVU, angle VSU = 29° (since T is on SU, this equals angle VST) and angle SVU = 180 − 41 = 139° (supplementary to the given angle RVS, since V lies on line UR). So angle U (= angle SUV) = 180 − 29 − 139 = 12°. Since T lies on segment US, angle TUR = angle U = 12°, and because RT = TU, triangle RTU is isosceles with angle TRU = angle U = 12° (angles opposite equal sides). The apex angle x = angle RTU = 180 − 12 − 12 = 156.*

*Difficulty: sat-hardest*

---

##### Q43
In triangles LMN and RST, angles L and R each have measure 60°, LN = 10, and RT = 30. Which additional piece of information is sufficient to prove that triangle LMN is similar to triangle RST?

**A.** MN = 7 and ST = 7 

  *MN = 7 and ST = 7 give a ratio MN/ST = 1, but LN/RT = 10/30 = 1/3 — two DIFFERENT ratios for two different pairs of sides is inconsistent with similarity under the natural correspondence (L↔R), so this doesn't establish similarity at all.*

**B.** MN = 7 and ST = 21 

  *These DO give a consistent ratio (21/7 = 3, matching LN/RT = 30/10 = 3) — but the given equal angle (L = R = 60°) is not the angle INCLUDED between the two sides being compared (LN and MN don't share angle L as their included angle; angle N does). Two sides in a matching ratio without their included angle known is the ambiguous SSA case, not sufficient to prove similarity.*

**C.** The measures of angle M and S are 70° and 60°, respectively 

  *If angle S were also 60°, triangle RST would need all three angles to be 60° (equilateral), forcing angle T = 60° too. But angle M = 70° here forces angle N = 180 − 60 − 70 = 50° in triangle LMN — which is not equilateral. Two triangles with different angle sets (60-60-60 versus 60-70-50) cannot be similar, so this choice is actually inconsistent with similarity.*

**D.** The measures of angle M and T are 70° and 50°, respectively **(Correct)**

  *Correct. With angle M = 70°, triangle LMN has angles 60° (L), 70° (M), and 50° (N, found by 180 − 60 − 70). With angle T = 50°, triangle RST has angles 60° (R), 50° (T), and 70° (S, found by 180 − 60 − 50). Both triangles now have the same three angles {60°, 70°, 50°}, matching under L↔R, M↔S, N↔T — establishing AA similarity.*

*Difficulty: sat-hardest*

---

##### Q44
In the figure, AD = 121/3 and AB = 11√130/3, where BD is the altitude from B to AC (right angle at D) in right triangle ABC (right angle at B). What is the length of DC?

**A.** 11 

  *This correctly finds BD = 11 (from AB² = AD² + BD² in right triangle ABD) but reports this intermediate leg length instead of continuing to find DC.*

**B.** 121/3 

  *This reports AD directly back instead of solving for the different segment DC.*

**C.** 9 

  *This does not satisfy the altitude relationship: it would require BD² = AD × DC = (121/3)(9) = 363, i.e. BD ≈ 19.05, which is inconsistent with the correctly-computed BD = 11 — a sign of an arithmetic slip rather than a clean alternate method.*

**D.** 3 **(Correct)**

  *Correct. In right triangle ABD, BD² = AB² − AD² = (11√130/3)² − (121/3)² = (121 × 130)/9 − 14641/9 = (15730 − 14641)/9 = 1089/9 = 121, so BD = 11. Since angle ABC = 90° and BD is the altitude to the hypotenuse, BD² = AD × DC: 121 = (121/3)(DC), giving DC = 3.*

*Difficulty: sat-hardest*

---

##### Q45
Quadrilaterals PQRS and WXYZ are similar, where P, Q, and R correspond to W, X, and Y, respectively. The measure of angle S is 135°, PS = 45, and WZ = 9. What is the measure of angle Z?

**A.** 5° 

  *This reports the scale factor itself (PS/WZ = 45/9 = 5) as if it were the angle measure, mistaking a side-length ratio for an angle.*

**B.** 27° 

  *This divides the angle by the scale factor (135/5 = 27), treating angle measure as though it scales the way side lengths do. Similar figures preserve every angle measure regardless of the size ratio.*

**C.** 45° 

  *This reports the numeric value of PS (45) directly, confusing a side length with the angle measure being asked for.*

**D.** 135° **(Correct)**

  *Correct. Since P↔W, Q↔X, R↔Y, the fourth vertex S corresponds to Z. Similar figures have equal corresponding angles regardless of the scale factor, so angle Z = angle S = 135°.*

*Difficulty: medium*

---

##### Q46
A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of these eight angles is (7x − 250)°. The sum of the measures of four of the eight angles is k°. Which of the following could NOT be equivalent to k, for all values of x?

**A.** −14x + 1,540 **(Correct)**

  *Correct. The eight angles take only two values, θ = (7x − 250)° and its supplement 180 − θ = (430 − 7x)°, four of each. Any sum of four of the eight angles must be one of: 4θ = 28x − 1,000 (all four θ); 4(180 − θ) = 1,720 − 28x (all four supplements); 2θ + 2(180 − θ) = 360 (two of each); 3θ + (180 − θ) = 14x − 320 (three θ's, one supplement); or θ + 3(180 − θ) = 1,040 − 14x (one θ, three supplements). None of these five possible sums equals −14x + 1,540, so k can never equal this expression.*

**B.** 14x − 320 

  *This IS achievable — it's the sum of three θ-angles plus one supplement angle: 3(7x − 250) + (430 − 7x) = 21x − 750 + 430 − 7x = 14x − 320. Since this matches a real combination of four angles, it CAN equal k, making it the wrong answer to 'which could NOT be.'*

**C.** −28x + 1,720 

  *This IS achievable — it's the sum of all four supplement-angles: 4(430 − 7x) = 1,720 − 28x. A real, valid selection of four angles, so it can equal k.*

**D.** 360 

  *This IS achievable — it's the sum of two θ-angles and two supplement-angles: 2(7x − 250) + 2(430 − 7x) = 14x − 500 + 860 − 14x = 360. That the sum is constant (independent of x) makes it look suspicious, but a constant sum is still a legitimate, achievable total for that particular balanced selection of angles.*

*Difficulty: sat-hardest*

---

##### Q47
In the figure, points Q, R, S, and T lie in that order on line segment PV, and line segment RU intersects line segment SX at point W. The measure of angle SQX is 48°, the measure of angle SXQ is 86°, the measure of angle SWU is 85°, and the measure of angle VTU is 162°. What is the measure, in degrees, of angle TUR?

**A.** 95 

  *This reports angle SWR — an intermediate angle found partway through the chase (180 − 85, the supplement of angle SWU along line RU) — instead of continuing through the remaining triangles to the final target.*

**B.** 57 

  *This reports the supplement of the correct answer (180 − 123 = 57) rather than the angle TUR itself.*

**C.** 39 

  *This reports angle SRW (equivalently angle URT), another intermediate angle from partway through the chase, instead of the final target angle TUR.*

**D.** 123 **(Correct)**

  *Correct. In triangle SQX, angle QSX = 180 − 48 − 86 = 46°, so angle RSW = 46° too (R is on ray SQ). Since angle SWU = 85°, angle SWR = 180 − 85 = 95° (W lies on segment RU). In triangle RSW, angle SRW = 180 − 46 − 95 = 39°, so angle URT = 39° (T is further along the same ray from R as S). Since angle VTU = 162°, angle STU = 180 − 162 = 18°, so angle RTU = 18° too. Finally, in triangle RTU: angle TUR = 180 − 39 − 18 = 123.*

*Difficulty: sat-hardest*

---

##### Q48
In a right triangle, the measure of one of the acute angles is 51°. What is the measure, in degrees, of the other acute angle?

**A.** 6 

  *51° is far too small a total to leave room for this: 51 + 6 = 57, leaving 123° for the right angle, which contradicts the triangle being right (needing exactly 90°). This likely comes from confusing the special right triangles — subtracting 45° (the 45-45-90 leg angle) from 51° instead of subtracting 51° from 90°: 51 − 45 = 6.*

**B.** 39 **(Correct)**

  *Correct. The two acute angles of a right triangle sum to 90°, so the other acute angle = 90 − 51 = 39.*

**C.** 49 

  *This comes from misremembering the acute angles of a right triangle as summing to 100° rather than 90°, giving 100 − 51 = 49.*

**D.** 51 

  *This reports the given angle back, assuming without justification that the triangle is an isosceles right triangle where both acute angles are equal.*

*Difficulty: medium*

---

#### Circles (21 items)

##### Q1
The figure shows a circle with center O. Two diameters of the circle intersect at O, dividing the circle into four arcs of equal measure; A and C are two adjacent points where the diameters meet the circle. The circle has a circumference of 36. What is the length of minor arc AC?

**A.** 9 **(Correct)**

  *Correct. Two diameters crossing at the centre divide the circle into four arcs of equal measure — 360°/4 = 90° each — so minor arc AC is one quarter of the circle. Arc length = (1/4)(circumference) = (1/4)(36) = 9. Check: the other three arcs are congruent to this one, and 4 × 9 = 36, the full circumference ✓.*

**B.** 12 

  *This divides the circumference by 3 instead of 4: 36/3 = 12. Two diameters crossing at the centre always produce four points on the circle and four arcs between them, not three — miscounting the divisions in the figure by one is what produces this answer.*

**C.** 18 

  *This takes half the circumference, 36/2 = 18, as though A and C were the two ends of a single diameter. They are not: A and C are ADJACENT points where the two diameters meet the circle, one quarter of the way around, not opposite ends of the same diameter.*

**D.** 36 

  *This reports the full circumference without taking any fraction of it at all — treating minor arc AC as though it were the entire rim of the circle rather than one quarter of it.*

*Difficulty: medium*

---

##### Q2
The graph of the equation (x − 6)² + (y − 3)² = 81 in the xy-plane is a circle. What is the length of the radius of this circle?

**A.** 3 

  *This reads the 3 subtracted in the y-term as the radius. But 3 is the y-coordinate of the centre — it tells you where the circle sits, not how big it is. The radius comes only from the right-hand side of the equation, which here is 81, not from either number inside a parenthesis.*

**B.** 6 

  *This reads the 6 subtracted in the x-term as the radius, for the same reason A is wrong: 6 is the x-coordinate of the centre, not a length. Neither coordinate on the left-hand side is the radius — only the number on the right, after a square root, is.*

**C.** 9 **(Correct)**

  *Correct. Standard form (x − h)² + (y − k)² = r² puts the radius on the right-hand side as a SQUARED length, so r² = 81 and r = √81 = 9. Check by substituting a point 9 units from the centre, (15, 3), into the equation: (15 − 6)² + (3 − 3)² = 81 + 0 = 81 ✓.*

**D.** 81 

  *This reports r² itself without taking the square root. The right-hand side of the standard form is a squared length, so 81 is r², not r — a circle with radius 81 would be nine times the size of the one this equation describes.*

*Difficulty: easy*

---

##### Q3
What is the value of cos(565π/6)?

**A.** 1/2 

  *This finds the correct reference angle, π/6, and then computes sin(π/6) instead of cos(π/6). sin(π/6) is 1/2; cos(π/6) is √3/2 — the reduction was done correctly and the wrong ratio was read off the triangle.*

**B.** 1 

  *This converts 565/6 to the decimal 94.1666… and rounds it down to 94π, discarding the fractional 0.1666…π instead of isolating it as the actual leftover angle. But 94π is 47 complete rotations (94π ÷ 2π = 47) and contributes nothing to the answer — the fractional part, π/6, is the entire angle that matters, and dropping it is what leaves cos(0) = 1 in its place.*

**C.** √3/2 **(Correct)**

  *Correct. Subtract full rotations of 2π = 12π/6 until the angle lies between 0 and 2π: 565π/6 = 94π + π/6, and 94π is exactly 47 full turns (94π ÷ 2π = 47), so 565π/6 is coterminal with π/6. cos(π/6) = √3/2, read straight off the 30-60-90 triangle with sides x, x√3, 2x, where cosine is adjacent over hypotenuse: (x√3)/(2x) = √3/2. Check: 47 × 2π + π/6 = 564π/6 + π/6 = 565π/6 ✓.*

**D.** √3 

  *This divides the two LEGS of the 30-60-90 triangle, x√3 and x, instead of dividing a leg by the hypotenuse: (x√3)/x = √3. Cosine is adjacent over hypotenuse, (x√3)/(2x) = √3/2 — the 2x in the denominator is the hypotenuse, and dropping it is what turns a cosine into a tangent-shaped ratio.*

*Difficulty: hard*

---

##### Q4
In the xy-plane, a circle with radius 5 has center (−8, 6). Which of the following is an equation of the circle?

**A.** (x − 8)² + (y + 6)² = 25 

  *This flips the sign of both coordinates: reading (x − 8)² as centred at x = 8 and (y + 6)² as centred at y = −6 gives (8, −6), the reflection of the actual centre (−8, 6) through the origin. Standard form SUBTRACTS the centre's coordinates, so a centre of (−8, 6) has to be written (x − (−8))² + (y − 6)² = (x + 8)² + (y − 6)², not (x − 8)² + (y + 6)².*

**B.** (x + 8)² + (y − 6)² = 25 **(Correct)**

  *Correct. Standard form is (x − h)² + (y − k)² = r² with h = −8, k = 6, r = 5: (x − (−8))² + (y − 6)² = 5², which is (x + 8)² + (y − 6)² = 25. Check by walking 5 units right of the centre to (−3, 6): (−3 + 8)² + (6 − 6)² = 25 + 0 = 25 ✓.*

**C.** (x − 8)² + (y + 6)² = 5 

  *This carries two separate errors: the same sign flip as choice A — reading the centre as (8, −6) instead of (−8, 6) — and the radius itself, 5, written on the right-hand side instead of r² = 25. Either error alone would be enough to fail; here both are stacked into one choice.*

**D.** (x + 8)² + (y − 6)² = 5 

  *This keeps the sign flip correct — centre (−8, 6) becomes (x + 8)² + (y − 6)² — but writes the radius itself, 5, on the right-hand side instead of r² = 5² = 25. The right side of standard form is always a squared length.*

*Difficulty: medium*

---

##### Q5
The figure shows a circle with center O. Points P, Q, R, and T lie on the circle: T and P are the endpoints of a diameter, with T to the left of O and P to the right. Points R and Q lie above that diameter, in order T, R, Q, P going around the top of the circle. The degree measures of angle POQ and angle ROT are each 30°. What is the radian measure of angle QOR?

**A.** (5/6)π 

  *This subtracts only one of the two given 30° angles from the straight angle, effectively treating Q as though it sat right on top of P: 180° − 30° = 150°, then 150 × π/180 = 5π/6. But Q is its own point, 30° short of P — both given angles have to come off the straight angle, not just the one nearest R.*

**B.** (3/4)π 

  *This subtracts the two given angles unevenly — the full 30° for angle TOR but only half of it, 15°, for angle QOP — giving 180 − 30 − 15 = 135°, then 135 × π/180 = 3π/4. Both given angles are 30°, the same size; there is no reason for one of them to be halved before it is removed.*

**C.** (2/3)π **(Correct)**

  *Correct. T, R, Q, and P lie in that order along the upper semicircle, so the straight angle TOP splits into three pieces: angle TOR (30°), angle ROQ (the angle wanted), and angle QOP (30°). So angle ROQ = 180° − 30° − 30° = 120°, and 120 × π/180 = 2π/3. Check in radians directly: π/6 + 2π/3 + π/6 = π/6 + 4π/6 + π/6 = 6π/6 = π ✓.*

**D.** (1/3)π 

  *This treats the two given CENTRAL angles as though they were INSCRIBED angles standing on arcs TR and QP, and doubles each to find those arcs — arc TR = 60°, arc QP = 60° — before subtracting: 180 − 60 − 60 = 60°, then 60 × π/180 = π/3. But angle POQ and angle ROT already have their vertex at O, the centre; they are central angles already equal to their arcs, so doubling them applies the inscribed-angle rule to an angle it does not govern.*

*Difficulty: hard*

---

##### Q6
A circle in the xy-plane has its center at (−4, 5), and the point (−8, 8) lies on the circle. Which equation represents this circle?

**A.** (x − 4)² + (y + 5)² = 5 

  *This carries two separate errors: the sign inside each parenthesis is flipped from the actual centre — reading (−4, 5) as (4, −5) — and the right-hand side is written as the radius, √25 = 5, rather than r² = 25. Either error alone would be enough to fail; here both are present.*

**B.** (x + 4)² + (y − 5)² = 5 

  *This gets the centre's sign right — (x + 4)² + (y − 5)² does correspond to (−4, 5) — but writes the radius itself, 5, on the right-hand side instead of r² = (distance)² = 25. The distance formula already includes the squaring; stopping at √25 before it happens throws that step away.*

**C.** (x − 4)² + (y + 5)² = 25 

  *This uses the correct right-hand side, 25, but flips neither sign correctly relative to the centre: (x − 4)² places the centre at x = 4, not x = −4, and (y + 5)² places it at y = −5, not y = 5 — the reflection of the true centre through the origin.*

**D.** (x + 4)² + (y − 5)² = 25 **(Correct)**

  *Correct. The radius is the distance from the centre to the given point: r² = (−8 − (−4))² + (8 − 5)² = (−4)² + 3² = 16 + 9 = 25. With centre (−4, 5), standard form is (x − (−4))² + (y − 5)² = 25, i.e. (x + 4)² + (y − 5)² = 25. Check: (−8 + 4)² + (8 − 5)² = 16 + 9 = 25 ✓.*

*Difficulty: medium*

---

##### Q7
The measure of angle Z is 60°. What is the measure, in radians, of angle Z?

**A.** (1/6)π 

  *This multiplies by π/360 instead of π/180 — using the number of degrees in a full circle as the conversion denominator instead of the number of degrees in a half circle: 60 × π/360 = π/6. But 180°, not 360°, is what equals π radians; 360° equals 2π.*

**B.** (1/3)π **(Correct)**

  *Correct. Degrees convert to radians by multiplying by π/180: 60 × π/180 = 60π/180 = π/3. Check going the other way: (π/3) × (180/π) = 60° ✓.*

**C.** (2/3)π 

  *This multiplies by π/90 instead of π/180, halving the correct denominator: 60 × π/90 = 2π/3, exactly double the correct answer. 180°, not 90°, is what equals π radians — 90° is only a right angle.*

**D.** 1π 

  *This multiplies by π/60 — using the given angle's own measure as the conversion denominator — which forces any angle entered this way to come out as exactly π: 60 × π/60 = π. The conversion factor is always π/180, fixed by the definition of a degree, and never depends on the specific angle being converted.*

*Difficulty: easy*

---

##### Q8
In the xy-plane, the graph of the equation x² + 58x + y² = 0 is a circle. What are the coordinates (x, y) of the center of the circle?

**A.** (0, 29) 

  *This swaps which axis carries the linear term — treating the 58x as though it belonged to y — and then does not flip its sign, giving (0, 29). But the linear term is 58x, not 58y: there is no y-coefficient in this equation at all, so k = 0 outright, and the x-coordinate is the one that needs completing.*

**B.** (0, −29) 

  *This also assigns the 58x term to the y-axis instead of the x-axis, but flips its sign correctly — landing on (0, −29). The number is right and the axis is not: the 58x term determines the x-coordinate of the centre, and there is no y-term at all to determine the other.*

**C.** (29, 0) 

  *This keeps the linear term on the correct axis but doesn't flip its sign: reading +58 in x² + 58x as though it were already the centre's coordinate gives x = 29, when standard form requires the sign flipped, so x = −29.*

**D.** (−29, 0) **(Correct)**

  *Correct. Complete the square in x: half of 58 is 29, and 29² = 841, so x² + 58x + 841 + y² = 841, giving (x + 29)² + y² = 841. There is no y-term at all, which is the same as y² already being (y − 0)², so k = 0. Reading off with the sign flipped, the centre is (−29, 0). Check with the point (0, 0), which the original equation shows lies on the circle since 0² + 58(0) + 0² = 0: the distance from (−29, 0) to (0, 0) is 29, and √841 = 29 ✓.*

*Difficulty: medium*

---

##### Q9
What is the center of the circle in the xy-plane defined by the equation (x − 1)² + (y + 7)² = 1?

**A.** (−1, −7) 

  *This flips the sign of the x-coordinate — reading (x − 1)² as though it meant x = −1 — while correctly flipping the y-coordinate to −7. Only one of the two signs was handled correctly.*

**B.** (−1, 7) 

  *This takes both numbers as printed with no sign flip at all: reading (x − 1)² as x = −1 and (y + 7)² as y = 7. Standard form subtracts both coordinates, so both signs in the printed equation are the opposite of the centre's actual coordinates.*

**C.** (1, −7) **(Correct)**

  *Correct. Standard form subtracts the centre's coordinates: (x − 1)² is (x − 1)², so h = 1, and (y + 7)² is (y − (−7))², so k = −7. The centre is (1, −7). Check: substituting the centre itself makes the left side 0, and the circle is exactly the set of points 1 unit from that ✓.*

**D.** (1, 7) 

  *This correctly flips the x-coordinate to 1 but leaves the y-coordinate as printed, reading (y + 7)² as y = 7 instead of y = −7. Only one of the two signs was handled correctly — the mirror image of choice A's error.*

*Difficulty: easy*

---

##### Q10
Points M, N, and P lie on a circle. On this circle, minor arc MN has a length of 39 centimeters and major arc MPN has a length of 195 centimeters. What is the circumference, in centimeters, of the circle shown?

**A.** 39 

  *This reports the minor arc by itself, as though it were the whole circle. Minor arc MN is only the short way from M to N; the circle also includes the long way around through P, which is more than four times as long.*

**B.** 156 

  *This subtracts the two arcs, 195 − 39 = 156, instead of adding them. Minor arc MN and major arc MPN do not overlap — between them they cover every point of the circle exactly once — so combining them is addition, not subtraction.*

**C.** 195 

  *This reports the major arc by itself, as though the larger of the two pieces were close enough to the whole circle to stand in for it. Major arc MPN is five-sixths of the circle here, but the remaining sixth — minor arc MN — is still part of the circumference and still has to be added.*

**D.** 234 **(Correct)**

  *Correct. Minor arc MN and major arc MPN are the two arcs cut off by points M and N — one going directly between them, the other going the long way around through P — and together they make up the entire circle exactly once: 39 + 195 = 234 centimeters. Check the split as a fraction: the minor arc is 39/234 = 1/6 of the circle and the major arc is 195/234 = 5/6, and 1/6 + 5/6 = 1 ✓.*

*Difficulty: medium*

---

##### Q11
The figure shows a circle with center O and points A, B, C, and D on the circle, positioned so that arc ADC (the arc from A to C that passes through D) and arc ABC (the arc from A to C that passes through B) together make up the whole circle. The measure of arc ADC is x°, where x = 100, and the length of arc ADC is 5π. What is the length of arc ABC?

**A.** 9π 

  *This assumes arc ADC and arc ABC are congruent — as though AC were a diameter splitting the circle into two equal halves — and reports half the circumference: 18π/2 = 9π. But the two arcs are not equal here; arc ADC's measure is given as 100°, not 180°, and the 260° left over for arc ABC has to come from 360° − 100°, not from splitting the circle down the middle.*

**B.** 13π **(Correct)**

  *Correct. Arc ADC has measure 100° and length 5π, so 5π is 100/360 = 5/18 of the circumference: circumference = 5π ÷ (5/18) = 5π · 18/5 = 18π. Arc ABC is what's left of the circle: 18π − 5π = 13π. Check with the angle directly: arc ABC's measure is 360 − 100 = 260°, and (260/360)(18π) = 13π ✓.*

**C.** 18π 

  *18π is the circle's full circumference, found correctly along the way — but reported directly instead of subtracting arc ADC from it. The question asks for arc ABC alone, which is what's left after arc ADC (5π) is removed: 18π − 5π = 13π, not 18π.*

**D.** 13/2 π 

  *This correctly finds the radius (r = 9, from circumference 18π = 2πr) and the correct angle for arc ABC (260°), but computes the arc length with s = (θ/360)(πr) instead of s = (θ/360)(2πr) — dropping the factor of 2 that turns a radius into a circumference. (260/360)(π · 9) = 6.5π = 13π/2, exactly half of the correct 13π.*

*Difficulty: hard*

---

##### Q12
The equation x² + 20x + y² + 16y = −20 defines a circle in the xy-plane. What are the coordinates of the center of the circle?

**A.** (−20, −16) 

  *This flips the sign of each coefficient correctly — since standard form subtracts the centre's coordinates, a +20x term does mean a negative x-coordinate — but forgets to halve first: 20 and 16 are the coefficients of x and y, not the centre's coordinates themselves. Completing the square always uses HALF the coefficient inside the parenthesis, so the centre is (−10, −8), not (−20, −16).*

**B.** (−10, −8) **(Correct)**

  *Correct. Complete the square in both variables: half of 20 is 10, and 10² = 100; half of 16 is 8, and 8² = 64. Adding both to both sides: (x² + 20x + 100) + (y² + 16y + 64) = −20 + 100 + 64, so (x + 10)² + (y + 8)² = 144. Reading off with the signs flipped, the centre is (−10, −8). Check with the point (2, −8), which sits 12 units right of the centre: 2² + 20(2) + (−8)² + 16(−8) = 4 + 40 + 64 − 128 = −20 ✓.*

**C.** (10, 8) 

  *This halves the coefficients correctly — 20/2 = 10 and 16/2 = 8 — but skips the sign flip: standard form subtracts the centre's coordinates, so a +20x term places the centre at x = −10, not x = 10. Both numbers are the right size and the wrong sign.*

**D.** (20, 16) 

  *This uses the coefficients exactly as printed — no halving, no sign flip — reading 20 and 16 directly off the equation as though they were the centre's coordinates. Neither operation that completing the square actually requires has been applied.*

*Difficulty: medium*

---

##### Q13
The figure shows a circle with center O. Points A and B lie on the circle, joined to each other and to O to form triangle OAB, and a third point C lies on the circle with radius OC drawn. The measure of angle OAB is 30°, and OC = 18. What is the length of arc AB?

**A.** 9π 

  *This assumes OA is perpendicular to OB — as though two diameters crossed at O and split the circle into four equal 90° arcs — and uses a central angle of 90° instead of deriving the true one from the given 30° angle. Arc AB = (90/360)(36π) = 9π. But nothing in the figure makes angle AOB a right angle; it has to be found from the isosceles triangle.*

**B.** 12π **(Correct)**

  *Correct. OC is a radius, so r = 18 and the circumference is 2π(18) = 36π. OA and OB are also radii, so triangle OAB is isosceles with OA = OB, which makes its base angles equal: angle OBA = angle OAB = 30°. The third angle, the central angle AOB, is 180 − 30 − 30 = 120°. Arc AB = (120/360)(36π) = 12π.*

**C.** 15π 

  *This subtracts only one of the two equal base angles from 180° — 180 − 30 = 150° — instead of both, forgetting that OA = OB makes the triangle isosceles with TWO 30° angles, not one. Arc AB = (150/360)(36π) = 15π, using a central angle 30° too large.*

**D.** 18π 

  *This treats AB as though it were a diameter of the circle, giving a central angle of 180° and an arc equal to half the circumference: 36π/2 = 18π. But the 30° angle is exactly the information that rules this out — a diameter would make angle OAB 0°, not 30°.*

*Difficulty: hard*

---

##### Q14
A circle in the xy-plane has its center at (−4, −6). Line k is tangent to this circle at the point (−7, −7). What is the slope of line k?

**A.** −3 **(Correct)**

  *Correct. The radius drawn to the point of tangency has slope (−7 − (−6))/(−7 − (−4)) = (−1)/(−3) = 1/3. A tangent line is perpendicular to the radius at the point of contact, so its slope is the negative reciprocal of 1/3, which is −3.*

**B.** −1/3 

  *This negates the radius's slope but doesn't invert it: −(1/3) = −1/3. A negative reciprocal needs both operations — flip the fraction AND change its sign — and this keeps the fraction as printed while only changing the sign.*

**C.** 1/3 

  *This reports the radius's own slope, 1/3, as the tangent's slope — as though a tangent line were parallel to the radius instead of perpendicular to it. Tangent ⊥ radius at the point of contact is the fact this entire item is testing, and it's the one step this answer skips.*

**D.** 3 

  *This inverts the radius's slope (1/3 becomes 3) but doesn't negate it. A negative reciprocal requires both the flip and the sign change; this performs only the flip, landing on the plain reciprocal of 1/3 rather than its negative reciprocal.*

*Difficulty: medium*

---

##### Q15
In the xy-plane, the graph of 2x² − 6x + 2y² + 2y = 45 is a circle. What is the radius of the circle?

**A.** 5 **(Correct)**

  *Correct. The leading coefficient is 2, so divide the entire equation by it first: x² − 3x + y² + y = 22.5. Complete both squares: half of −3 is −1.5, and (−1.5)² = 2.25; half of 1 is 0.5, and (0.5)² = 0.25. Add both to both sides: (x − 1.5)² + (y + 0.5)² = 22.5 + 2.25 + 0.25 = 25, so r = √25 = 5.*

**B.** 6.5 

  *This correctly finds r = 5, but then adds the 1.5 used to complete the square in x — the x-coordinate of the centre — onto that radius before reporting an answer: 5 + 1.5 = 6.5. The number used to build the centre's coordinate has nothing to do with the radius; once r = 5 is reached, the arithmetic is finished.*

**C.** √40 

  *This reaches the pre-division step 2(x − 1.5)² + 2(y + 0.5)² = 45 + 4.5 + 0.5, but SUBTRACTS the two completing-the-square corrections instead of adding them: 45 − 4.5 − 0.5 = 40. On top of that sign error, it never divides back by the leading coefficient 2 to reach standard form, reading 40 itself as r² instead of continuing on to r² = 25.*

**D.** √50 

  *This correctly reaches 2(x − 1.5)² + 2(y + 0.5)² = 45 + 4.5 + 0.5 = 50 — the right-hand side before the leading coefficient has been divided back out — but stops there and reads 50 directly as r², skipping the final division by 2 that recovers standard form and the true r² = 25.*

*Difficulty: hard*

---

##### Q16
A circle has center O, and points A and B lie on the circle. The measure of arc AB is 45°, and the length of arc AB is 3 inches. What is the circumference, in inches, of the circle?

**A.** 3 

  *This reports the arc length itself as the circumference — treating a 3-inch piece of the rim as though it were the whole rim. A 45° arc is only 1/8 of the circle, so the full circumference has to be considerably longer than any single arc cut from it.*

**B.** 6 

  *This uses 90° as the full circle's degree measure instead of 360°, giving a fraction of 45/90 = 1/2 and a circumference of 3 × 2 = 6. A circle is 360°, not 90° — 90° is only a quarter turn.*

**C.** 9 

  *This miscounts how many 45° arcs make up the full circle, treating it as though only three of them fit (3 × 45° = 135°) rather than the actual eight (8 × 45° = 360°). That gives a fraction of 45/135 = 1/3 and a circumference of 3 × 3 = 9.*

**D.** 24 **(Correct)**

  *Correct. A 45° arc is 45/360 = 1/8 of the circle, and the arc length is that same fraction of the circumference: 3 = (1/8) × circumference, so circumference = 3 × 8 = 24 inches. Check: an 8th of 24 is 3 ✓.*

*Difficulty: easy*

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##### Q17
In the xy-plane, the graph of the equation (x − 6)² + (y + 5)² = 16 is a circle. Point P is on the circle and has coordinates (10, −5). If segment PQ is a diameter of the circle, what are the coordinates of point Q?

**A.** (2, −5) **(Correct)**

  *Correct. The centre is (6, −5) and r = √16 = 4; P = (10, −5) is 4 units right of the centre, confirming it's on the circle. Q is the point diametrically opposite P, found by reflecting P through the centre: Q = (2(6) − 10, 2(−5) − (−5)) = (2, −5). Check: Q is also 4 units from the centre, on the opposite side from P, and PQ = 8, exactly the diameter.*

**B.** (6, −1) 

  *This keeps the centre's x-coordinate (6) instead of reflecting P through it, and shifts the y-coordinate up by the radius instead: −5 + 4 = −1. But P sits 4 units to the right of the centre along a HORIZONTAL radius, not above it — the shift belongs on the x-coordinate, not the y.*

**C.** (6, −5) 

  *This reports the circle's centre itself, not the point diametrically opposite P. The centre is the MIDPOINT of every diameter, not one of its endpoints — Q has to be found by reflecting P through the centre, not by stopping at the centre.*

**D.** (6, −9) 

  *This keeps the centre's x-coordinate (6) instead of reflecting P through it, and shifts the y-coordinate down by the radius instead: −5 − 4 = −9. The same axis mix-up as choice B, applied in the other direction — the shift belongs on the x-coordinate, since P is 4 units horizontally from the centre, not vertically.*

*Difficulty: medium*

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##### Q18
A circle in the xy-plane has equation (x + 3)² + (y − 1)² = 25. Which of the following points does NOT lie in the interior of the circle?

**A.** (−7, 3) 

  *This point is actually inside the circle: (−7 + 3)² + (3 − 1)² = 16 + 4 = 20, and 20 < 25. Picking it anyway usually comes from comparing the squared distance (20) directly to the radius (5) instead of to r² (25) — since 20 > 5, the comparison looks like it favors 'outside' when the units don't actually match; the correct comparison is against 25, and 20 is comfortably under it.*

**B.** (−3, 1) 

  *This point is the circle's own centre, which is about as interior as a point can be: (−3 + 3)² + (1 − 1)² = 0, and 0 < 25. Picking it usually comes from re-applying the sign-flip rule used for reading a centre off an equation to the interior TEST itself — plugging the point into (x − 3)² + (y + 1)² instead of the equation as printed, (x + 3)² + (y − 1)² — which gives (−3 − 3)² + (1 + 1)² = 36 + 4 = 40 and makes the centre look like it's outside its own circle.*

**C.** (0, 0) 

  *This point is inside the circle: (0 + 3)² + (0 − 1)² = 9 + 1 = 10, and 10 < 25. As with choice A, comparing the squared distance (10) directly to the radius (5) rather than to r² (25) makes it look excluded — 10 > 5 — when the correct threshold is 25, and 10 sits well under it.*

**D.** (3, 2) **(Correct)**

  *Correct. (3 + 3)² + (2 − 1)² = 36 + 1 = 37, and 37 > 25 — this point's squared distance from the centre exceeds r², which is exactly what lying outside the circle means. Every other point listed comes out less than 25 by the same test.*

*Difficulty: medium*

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##### Q19
A circle in the xy-plane has its center at (16, 17) and has a radius of 7k. Which equation represents this circle?

**A.** (x − 16)² + (y − 17)² = 49k 

  *This squares the 7 but not the k: (7k)² is 49k², not 49k. The whole radius has to be squared as a single quantity — squaring only part of a product and leaving the rest alone doesn't square the product.*

**B.** (x − 16)² + (y − 17)² = 49k² **(Correct)**

  *Correct. Standard form is (x − h)² + (y − k)² = r² with h = 16, k = 17, and r = 7k, so r² = (7k)² = 49k². The centre's coordinates are already positive, so no sign flip is needed here — only the squaring of the radius matters.*

**C.** (x − 16)² + (y − 17)² = 7k 

  *This writes the radius itself, 7k, on the right-hand side instead of r² = (7k)² = 49k². The right side of standard form is always a squared length, and this is the length before that squaring happens.*

**D.** (x − 16)² + (y − 17)² = 7k² 

  *This squares only the k and leaves the 7 alone: 7k² is not the same as (7k)² = 49k². The radius is the single product 7k, and squaring a product means squaring every factor in it, not just one of them.*

*Difficulty: easy*

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##### Q20
Circle A has equation (x − 7)² + (y + 3)² = 1. In the xy-plane, circle B is obtained by translating circle A to the right 4 units. Which equation represents circle B?

**A.** (x − 7)² + (y + 7)² = 1 

  *This applies the 4-unit shift to the y-coordinate instead of the x-coordinate, moving the centre from (7, −3) to (7, −7) — four units DOWN — as though 'translated right' meant a vertical move. The centre's x-coordinate, which is the one that actually governs horizontal position, is left unchanged.*

**B.** (x − 3)² + (y + 3)² = 1 

  *This moves the centre from (7, −3) to (3, −3) — four units LEFT, not right. Standard form already subtracts the centre's coordinate, so shifting right means the number being subtracted has to INCREASE (7 → 11), not decrease; subtracting 4 from it instead reverses the direction of the translation.*

**C.** (x − 11)² + (y + 3)² = 1 **(Correct)**

  *Correct. Circle A is centred at (7, −3). Translating right 4 units moves the centre to (11, −3), so the new equation is (x − 11)² + (y − (−3))² = 1, which is (x − 11)² + (y + 3)² = 1. The radius, 1, is unchanged by a translation.*

**D.** (x − 7)² + (y − 1)² = 1 

  *This applies the 4-unit shift to the y-coordinate instead of the x-coordinate, moving the centre from (7, −3) to (7, 1) — four units UP. Like choice A, this shifts the wrong axis; unlike choice A, it shifts it the other way, but the underlying error — leaving the x-coordinate, which governs 'right', untouched — is the same.*

*Difficulty: medium*

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##### Q21
Point F lies on a unit circle in the xy-plane and has coordinates (1, 0). Point G is the center of the circle and has coordinates (0, 0). Point H also lies on the circle and has coordinates (−1, y), where y is a constant. Which of the following could be the positive measure of angle FGH, in radians?

**A.** 27π/2 

  *This misreads the ordered pair (−1, y) as (y, −1) — swapping which coordinate is fixed and which is unknown — and solves 1 + y² = 1 to place H at (0, −1) instead of the correct (−1, 0). Measured counterclockwise from F, that puts H a quarter turn short: the angle comes out as 3π/2, and 27π/2 is coterminal with 3π/2 (27π/2 − 6(2π) = 27π/2 − 12π = 3π/2).*

**B.** 29π/2 

  *This makes the same coordinate-order slip as choice A, placing H at (0, −1) instead of (−1, 0), but then measures the angle the short way around (clockwise, a quarter turn) instead of continuing counterclockwise the long way. That gives π/2, and 29π/2 is coterminal with π/2 (29π/2 − 7(2π) = 29π/2 − 14π = π/2).*

**C.** 24π 

  *H's x-coordinate is −1, diametrically opposite F's (1, 0) — not the same point — so angle FGH is a straight angle, not zero. Treating F and H as though they defined the same ray from G gives an angle of 0, and 24π is exactly coterminal with 0 (24π ÷ 2π = 12, an exact number of full turns).*

**D.** 25π **(Correct)**

  *Correct. Since H = (−1, y) lies on the unit circle, 1 + y² = 1, so y = 0 and H = (−1, 0) — diametrically opposite F = (1, 0) through the centre G. Angle FGH is therefore a straight angle, π radians. Reduce 25π by full rotations: 25π ÷ 2π = 12.5, so 25π = 12(2π) + π, meaning 25π is coterminal with π. ✓*

*Difficulty: sat-hardest*

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