What is the GRE format?

Shortened since September 2023: about 1 hour 58 minutes in total, with no unscored research section. Two Verbal Reasoning sections, two Quantitative Reasoning sections, and one Analytical Writing task — 'Analyze an Issue'. The old 'Analyze an Argument' essay is gone. Verbal and Quant are each scored 130–170 in one-point steps; Analytical Writing is 0–6 in half-point steps. Section-level adaptive: how you do on the first section of a measure decides the difficulty of the second. An on-screen calculator is provided for Quant. Scores are valid for five years.

Are these GRE practice questions free?

Yes. All 196 questions, with answers and explanations, are on one page with no sign-up, no login and no paywall. The page works with JavaScript switched off and once loaded it works offline.

Where do these questions come from?

They were written by language models and then cross-checked: every question was sent back to a different model with the answer removed, and only the ones where the second model independently chose the same answer are on this page. 114 of 196 have passed that check. Nobody who has sat the GRE has reviewed them yet, so treat them as practice, not as an official answer key.

GRE Practice Questions 2026 — Free, with Answers and Explanations

Q: What is the GRE and who takes it?

Graduate Record Examinations — General Test, set by ETS. Applicants to master's and PhD programmes, mostly in the United States, and to a growing number of programmes in Europe and Asia.

Read this before you trust an answer. These questions were written by language models, not cut from past papers. Every one was then sent back to a different model with the answer hidden, and only the ones where the second model independently picked the same answer are on this page — 114 of 196 so far. That is a floor, not a guarantee: two models can agree and still be wrong, and nobody who has sat the GRE has reviewed these yet. Use them to practise the shape of the test. For the official format and scoring, go to ETS. Found a wrong answer? Tell us and we will pull it.

What the GRE actually is

Shortened since September 2023: about 1 hour 58 minutes in total, with no unscored research section.
Two Verbal Reasoning sections, two Quantitative Reasoning sections, and one Analytical Writing task — 'Analyze an Issue'. The old 'Analyze an Argument' essay is gone.
Verbal and Quant are each scored 130–170 in one-point steps; Analytical Writing is 0–6 in half-point steps.
Section-level adaptive: how you do on the first section of a measure decides the difficulty of the second.
An on-screen calculator is provided for Quant. Scores are valid for five years.

Applicants to master's and PhD programmes, mostly in the United States, and to a growing number of programmes in Europe and Asia.

Tap an option to check it. Your score appears here.

Text Completion 36 questions

One sentence or short paragraph with one blank, four options.

1. The professor's lecture, though ___, captivated the entire class.
Answer: B. The signal is the contrast word "though". A sentence that is "though ___" invites a word that contrasts with the expectation of a long, detailed lecture. "Laconic" means brief, fitting the contrast. The other options describe qualities that do not fit the contrast.
2. She was praised for her ___, a quality that the critics had previously overlooked.
Answer: C. The restatement signal "a quality that" indicates a characteristic. "Venerate" means to honor, which explains why she was praised. The other options do not fit the context of being praised.
3. The novel's themes, ___, challenge conventional morality and invite readers to question their beliefs.
Answer: C. The contrast word "though" signals that the following clause contrasts with the expectation of a simple or conventional theme. "Castigate" means to criticize sharply, which fits the idea of challenging morality. The other options do not convey this critical stance.
4. Despite the critic's initial tendency to ___ the avant-garde film for its lack of narrative coherence, he eventually conceded that its visual poetry possessed a profound emotional resonance.
Answer: B. The signal word 'Despite' indicates a contrast between the critic's initial action and his later concession. Since he eventually praised the film's emotional resonance, his initial reaction must have been negative. 'Castigate' means to criticize severely, which fits the negative context, whereas 'venerate,' 'sanctify,' and 'extol' are all positive terms that would not create the required contrast.
5. The CEO’s ___, far from being a sign of weakness, was interpreted by investors as a strategic retreat that allowed the company to restructure its debt.
Answer: A. The phrase 'far from being a sign of weakness' suggests that the action in the blank is typically associated with weakness or indecision, but here it is reinterpreted positively. 'Vacillation' means indecisiveness or wavering, which is commonly viewed as a weakness. The sentence argues that this wavering was actually a strategic move. 'Audacity,' 'intransigence,' and 'zealotry' are generally associated with strength or stubbornness, not weakness, so they do not fit the 'far from being a sign of weakness' construction.
6. While the poet’s early work was characterized by a ___, almost mechanical precision, his later collections reveal a more fluid and improvisational style that defies rigid structural constraints.
Answer: B. The word 'While' sets up a contrast between the early work and the later work. The later work is described as 'fluid,' 'improvisational,' and 'defies rigid structural constraints.' Therefore, the early work must be the opposite: structured, precise, and rigid. 'Meticulous' means showing great attention to detail, which aligns with 'mechanical precision.' 'Spontaneous,' 'haphazard,' and 'erratic' are synonyms for the later style or imply a lack of structure, which would not create the necessary contrast with the 'fluid and improvisational' later period.
7. The curator’s initial assessment of the painting was ___, dismissing it as a minor work, but subsequent provenance research revealed it to be a lost masterpiece by a renowned master.
Answer: B. The semicolon and the phrase 'but subsequent... revealed' signal a contrast between the initial assessment and the later discovery. Since the later finding was positive (a masterpiece), the initial assessment must have been negative or dismissive. 'Derisive' fits this context, whereas 'verbose' and 'meticulous' do not carry the necessary negative connotation, and 'ambivalent' is too neutral.
8. Although the politician was known for his ___, often speaking in long, winding sentences that confused his audience, his final speech was a model of brevity and clarity.
Answer: B. The word 'Although' sets up a contrast between the politician's usual style and his final speech. The final speech is described as 'brevity and clarity,' so the usual style must be the opposite: long and wordy. 'Prolixity' means excessive wordiness. While 'verbosity' is similar, 'prolixity' is the more precise GRE-register term for the quality of being tediously long-winded, and it pairs well with the description of 'long, winding sentences.' 'Eloquence' and 'conciseness' are incorrect because they align with the positive final speech rather than the negative usual style.
9. The scientist’s hypothesis, initially met with ___, gained traction only after independent laboratories replicated the results, proving that the original skepticism was unwarranted.
Answer: B. The phrase 'proving that the original skepticism was unwarranted' indicates that the initial reaction was skeptical or negative. The blank must be filled with a word that describes a strong negative reaction that was later proven wrong. 'Contempt' fits this description as a strong negative judgment. 'Acclaim' and 'curiosity' are positive or neutral, and 'indifference' lacks the active negativity implied by 'skepticism' being 'unwarranted' (implying active dismissal rather than just lack of interest).
10. Her ___, which manifested as a refusal to elaborate on her personal life, was mistaken by colleagues for arrogance, though it was actually a deeply held value of privacy.
Answer: B. The clause 'refusal to elaborate on her personal life' defines the quality in the blank. This definition points to silence or reserve. 'Taciturnity' means the habit of being silent or not talking much. The contrast with 'arrogance' is a red herring; the key signal is the appositive phrase explaining the behavior. 'Garrulousness,' 'loquacity,' and 'effusiveness' all imply talking a lot, which is the opposite of refusing to elaborate.
11. Although the newly appointed director was expected to be pliable, she proved remarkably ___ during negotiations, refusing to compromise on any of the core principles laid out in the initial charter.
Answer: A. The signal word is although, which establishes a contrast between the expected trait and the director's actual behavior. The second half of the sentence states that she refused to compromise, so the blank requires a word meaning stubborn or unyielding. Intransigent matches this meaning. Munificent means generous, garrulous means talky, and pusillanimous means cowardly, none of which fit the context of refusing to compromise.
12. The statesman's memoirs were surprisingly ___, omitting all mention of the personal scandals that had nearly derailed his career and focusing entirely on his policy achievements.
Answer: B. The sentence explains that the memoirs omitted all mention of personal scandals, meaning the text was cleansed or edited to remove objectionable material. Expurgated means cleansed of unsuitable passages. Laconic means using very few words, pedantic means overly focused on minor details, and ambiguous means having multiple meanings. None of the distractors capture the specific act of censoring content.
13. While the tech startup's initial success was hailed as a permanent revolution in the industry, seasoned analysts recognized that such rapid gains were often ___, fading just as quickly as they appeared when market conditions shifted.
Answer: B. The contrast is introduced by while, paired with the explanatory clause fading just as quickly as they appeared. This indicates that the gains were short-lived. Ephemeral means lasting for a very short time. Pernicious means harmful, recondite means obscure or difficult to understand, and superfluous means unnecessary or extra. Ephemeral is the only option that addresses the duration of the success.
14. The art critic's review of the retrospective was remarkably ___, sparing no artist from his blistering critique and dismantling the reputation of even the most celebrated masters with equal severity.
Answer: C. The key clue is sparing no artist from his blistering critique. This indicates a sharp, harsh, and biting tone. Acerbic means sharp and forthright in a bitter or harsh way. Panegyrical and sycophantic both describe overly praising behavior, which contradicts the blistering critique. Lugubrious means mournful or gloomy, which does not fit the context of a rigorous artistic dismantling.
15. The professor’s lecture was notoriously ___, offering only the barest skeletal points that left students to construct the arguments themselves.
Answer: B. The signal is the phrase 'offering only the barest skeletal points,' which contrasts with the expectation of a full lecture. 'Laconic' means using very few words, fitting the description of minimal content. 'Verbose' and 'eloquent' imply extensive or fluent speech, while 'pedantic' refers to excessive display of learning, none of which align with the brevity described.
16. The architect’s design, while aesthetically striking, was criticized for being ___, as the materials chosen would degrade rapidly under the region’s harsh climate.
Answer: A. The signal is the phrase 'degrade rapidly,' which indicates a lack of durability. 'Ephemeral' means lasting for a very short time, which directly corresponds to the criticism that the materials would not last. 'Perpetual' and 'resilient' suggest long-lasting or durable qualities, which contradict the criticism. 'Monolithic' refers to being massive or uniform, which is unrelated to the issue of material degradation.
17. The editor’s decision to cut the chapter was not a sign of disapproval but rather a strategic move to ___ the novel’s pacing, ensuring that the climax arrived with greater impact.
Answer: B. The signal is the phrase 'ensuring that the climax arrived with greater impact.' Cutting content typically speeds up the narrative flow. 'Accelerate' means to increase the speed of, which fits the goal of making the climax arrive sooner and with more force. 'Obscure' and 'diminish' would weaken the impact, while 'complicate' would likely slow down or confuse the pacing, contrary to the stated strategic intent.
18. The novelist's latest work is ___; it abandons the sprawling narratives of his earlier books in favor of a sharply focused, almost austere style.
Answer: C. The semicolon signals a restatement: the second clause describes a concise style, so the correct word is laconic. The other options either mean fleeting or overly wordy.
The new policy, though initially criticized for its lack of nuance, was ultimately lauded for its ___ clarity, which allowed even novice legislators to grasp its implications.
19. Which option best completes the sentence?
Answer: B. The signal is the contrast word "though" followed by a positive outcome. The policy was criticized but praised for its clarity. A laconic style is clear and concise, matching the context. Ephemeral, venerate, and castigate do not fit.
Her presentation, which was ___ in its brevity, nevertheless conveyed a wealth of insight that surprised the audience.
20. Which option best completes the sentence?
Answer: C. The signal is the contrast word "yet" after a semicolon, showing that despite brevity the presentation was insightful. Laconic means brief and concise, matching the description. Ephemeral, venerate, and castigate are unrelated.
The artist’s new series, while celebrated for its bold use of color, was criticized for its ___ structure, which some critics argued lacked cohesion.
21. Which word best completes the sentence?
Answer: A. The signal is the contrast word "while" followed by criticism. Ephemeral means lasting for a short time, suggesting a fleeting or unstable structure. The other options do not describe structural instability.
22. The curator’s approach to the exhibition was remarkably ___, relying on minimal labels and sparse explanatory text to allow the artifacts to speak for themselves.
Answer: B. The signal is the phrase 'relying on minimal labels and sparse explanatory text,' which restates the quality of using few words. 'Laconic' means using very few words, fitting the context. 'Verbose' and 'eloquent' imply extensive or fluent speech, while 'pedantic' implies an annoying display of learning, none of which match the description of minimalism.
23. The historian argued that the empire’s collapse was not due to a single catastrophic event but was the result of ___, structural weaknesses that had been accumulating for centuries.
Answer: D. The signal is the phrase 'had been accumulating for centuries,' which implies that the weaknesses were hidden or not immediately obvious until they manifested. 'Latent' means present but not yet developed or manifest. 'Ephemeral' and 'transient' mean short-lived, which contradicts the idea of accumulating over centuries. 'Enduring' means lasting, but does not capture the sense of hidden potential that 'latent' does in the context of a slow build-up.
24. The critic’s review was ___, praising the film’s visual splendor while ignoring its profound narrative flaws, a bias that typified his tendency to ___ substance for style.
Answer: B. The signal is the semicolon and the restatement 'bias that typified his tendency.' The first part describes a one-sided view (praising visuals, ignoring flaws). 'Myopic' means short-sighted or lacking foresight, fitting the description of ignoring deeper issues. The second blank requires a verb that means to give more importance to, which 'privilege' does. 'Balanced' and 'objective' contradict the description of a bias. 'Comprehensive' contradicts 'ignoring.' 'Prioritize' is close but 'privilege' is a more precise GRE-register word for giving undue importance to one aspect over another.
25. Although the professor was known for his engaging lectures and warm rapport with students, his written scholarship was surprisingly ___, characterized by terse prose and an absolute refusal to embellish his arguments with unnecessary commentary.
Answer: B. The signal here is the contrast word Although, which sets up an opposition between the professor's engaging lectures and his written work. The phrase characterized by terse prose tells us the writing is brief and concise. Laconic means using very few words, matching the description of terse prose. Option A means elaborate and is the opposite. Option C means wordy, which contradicts terse. Option D means having multiple meanings, which is not supported by the clue of terseness.
26. Rather than attempting to ___ the entrenched dogma of the institution, the young reformer chose to work quietly within its established structures to effect gradual change.
Answer: D. The key signal is Rather than, which indicates a contrast between the action the reformer avoided and the quiet, gradual work of changing structures from within. Castigate means to reprimand severely or criticize harshly, which aligns with an aggressive effort to oppose or overthrow entrenched dogma. Option A means to regard with great respect, which does not fit the contrast. Option B means to support, which goes against the idea of a reformer working against dogma. Option C means to criticize, but castigate is a better fit for a direct ideological attack on dogma, though subvert specifically means to undermine the power and authority of an established system, matching the confrontational alternative implied by rather than.
27. The political strategist cautioned that relying on polling data alone is perilous, as public sentiment during a crisis is often ___, shifting drastically from one day to the next based on breaking news.
Answer: A. The explanation for the danger relies on the phrase shifting drastically from one day to the next, which defines something short-lived or transient. Ephemeral means lasting for a very short time, perfectly capturing this instability. Option B means unchanging, which is the opposite of shifting. Option C means transparently clear, which does not address volatility. Option D means false or counterfeit, which does not fit the context of changing public sentiment.
28. The art critic lamented that the once-independent gallery had become thoroughly ___, succumbing to commercial pressures and tailoring its exhibitions entirely to the whims of affluent buyers.
Answer: B. The causal relationship is indicated by the phrase succumbing to commercial pressures, showing that the gallery's integrity has been compromised for financial gain. Venal means showing or motivated by susceptibility to bribery; corrupt or mercenary. Option A means self-governing or independent, which contradicts the context. Option C means limited in range or scope, provincial. Option D means lazy, which does not address the financial corruption implied by commercial pressures.
29. The philanthropist's reputation for generosity was ___; after the scandal, donors suddenly withdrew their support, citing concerns over transparency.
Answer: C. The semicolon signals a contrast between the reputation and the reaction; the correct word must mean short-lived, which is 'ephemeral'.
30. The professor's lectures were praised for their ___ depth, yet his published articles often suffered from superficial analysis.
Answer: A. The contrast word 'yet' signals that the first descriptor should be strong, opposite of the second; 'laconic' (concise) fits the praised depth, implying brevity rather than verbosity.
31. The board chose to ___ the controversial policy, preferring a cautious approach that would avoid public uproar.
Answer: D. The phrase 'choose to' followed by a negative action requires a verb meaning to criticize harshly; the signal is the need for a strong rebuke, which is 'castigate'.
32. The professor’s lecture was praised for its ___ clarity, yet his written work often suffered from an overreliance on jargon.
Answer: A. The signal is the contrast between praise for clarity and criticism of jargon. The word that fits the contrast is laconic, meaning brief and concise, which aligns with clarity.
33. The committee’s decision to ___ the proposal, citing insufficient data, surprised many who had expected a swift approval.
Answer: B. The signal is the semicolon that separates the reason from the surprise. The verb that matches the idea of criticizing or reprimanding the proposal is castigate.
34. The novel’s themes, though profound, were rendered ___ by the author’s tendency to overexplain each character’s motive.
Answer: A. The signal is the restatement of the theme’s fleeting nature. The word that means short-lived or transitory is fleeting, but the correct GRE vocabulary option is "ephemeral."
The CEO’s response to the board’s inquiry was characteristically ___, offering only a terse nod and a single sentence that left the executives more confused than before.
35. Choose the word that best completes the sentence.
Answer: B. The signal in the sentence is the phrase 'offering only a terse nod and a single sentence.' This description indicates a lack of words and brevity. 'Laconic' means using very few words, which aligns perfectly with the context. The other options are incorrect because 'effusive,' 'verbose,' and 'eloquent' all imply a generous or excessive use of language, which contradicts the 'terse' and 'single sentence' nature of the response.
Although the museum’s new wing was designed to be a beacon of modern innovation, the critics found the architecture to be ___, arguing that it failed to distinguish itself from the generic glass boxes proliferating in urban centers.
36. Choose the word that best completes the sentence.
Answer: C. The signal here is the contrast introduced by 'Although' and the specific criticism that the building 'failed to distinguish itself from the generic glass boxes.' This implies the architecture is ordinary, unoriginal, or dull. 'Banal' means lacking originality or being tedious, which fits the critique of it being indistinguishable from generic structures. 'Idiosyncratic' means distinctive or peculiar, which is the opposite of the intended meaning. 'Ephemeral' refers to short duration, which is irrelevant to the architectural style. 'Obscure' means not well-known or hard to understand, but the issue is a lack of distinctiveness, not secrecy or difficulty.

Sentence Equivalence 26 questions

The sentence has EXACTLY ONE blank, written as ______.

1. Although the professor's lectures were notoriously dense, the students found them __________, because each concept was illustrated with a concrete example that made the abstract ideas __________.
Answer: C. Both words in option C, 'lucid' and 'tangible', fit the blanks and give the same overall meaning: the lectures, though dense, were clear and the ideas were made concrete. The other pairs either create a contradiction (A, D) or change the meaning (B).
2. The committee's decision to postpone the project was met with __________; some members felt it was a prudent move, while others regarded it as an __________.
Answer: D. Both words in option D, 'scepticism' and 'misstep', correctly fill the blanks and convey the same overall sense that the decision was viewed with doubt and seen as a mistake. The other pairs either do not fit the context or give mismatched meanings.
3. The diplomat's remarks were deliberately __________, allowing him to convey criticism of the policy while maintaining an outwardly __________ stance toward the host nation.
Answer: C. 'Subtle' and 'neutral' both fit the blanks and produce sentences that mean the same thing: the diplomat was careful and non‑partisan in tone. Option D, while fitting the blanks, changes the meaning because 'veiled' criticism paired with an 'aggressive' stance is contradictory to the intended diplomatic nuance.
4. The manager's explanation of the new software update was so __________ that even the most technical engineers struggled to follow the logic.
Answer: A. The sentence indicates that the explanation was difficult to understand, causing even experts to struggle. 'Obscure' and 'cryptic' are synonyms meaning unclear or mysterious, and both fit the context. Option B is incorrect because 'verbose' (wordy) and 'succinct' (concise) are antonyms; while verbose might cause confusion, succinct would not. Option C is incorrect because 'lucid' and 'transparent' mean clear, which contradicts the fact that engineers struggled. Option D is incorrect because while 'ambiguous' fits, 'equivocal' often implies intentional deception or lack of commitment rather than mere difficulty of understanding, and the pair does not produce identical meaning in this context as cleanly as A.
5. Despite the initial skepticism from the board, the CEO's strategy proved to be __________, resulting in a significant increase in quarterly profits.
Answer: A. The context suggests the strategy was effective and wise, overcoming skepticism with results. 'Pragmatic' (practical) and 'shrewd' (having or showing sharp powers of judgment) are close synonyms in this context, both describing a smart, effective approach. Option B is incorrect because 'idealistic' and 'naive' would likely lead to failure, not profit. Option C is incorrect because 'tentative' and 'hesitant' imply uncertainty, which contradicts the decisive success described. Option D is incorrect because 'radical' and 'conservative' are antonyms; a strategy cannot be both, so the pair does not create sentences of the same meaning.
6. The historian's critique of the primary sources was __________, pointing out subtle inconsistencies that had been overlooked by previous scholars.
Answer: A. The sentence describes a critique that identified subtle details missed by others, implying sharp insight. 'Perceptive' (having keen mental perception) and 'incisive' (clear and precise in expression or analysis) are synonyms that fit this context. Option B is incorrect because 'superficial' and 'cursory' mean lacking depth, which contradicts the finding of subtle inconsistencies. Option C is incorrect because 'dogmatic' and 'rigid' refer to inflexibility of belief, not the quality of the analysis itself. Option D is incorrect because 'emotive' and 'passionate' refer to emotional intensity, whereas the context highlights intellectual precision in spotting inconsistencies.
7. The artist's latest installation was __________, forcing viewers to confront their own biases through a disorienting arrangement of mirrors and light.
Answer: A. The installation forces viewers to confront biases through disorientation, suggesting it is intended to stimulate thought or reaction. 'Provocative' (inciting or stimulating, especially if unwelcome) and 'challenging' (demanding effort or skill) are synonyms in this context, both describing an artwork that actively engages and unsettles the viewer. Option B is incorrect because 'subtle' and 'delicate' imply a gentle or faint quality, which contradicts the 'disorienting' and forceful nature of the experience. Option C is incorrect because 'mundane' and 'ordinary' mean commonplace, which contradicts the impact of the installation. Option D is incorrect because while 'didactic' and 'instructive' are synonyms, they imply a direct teaching or moral lesson, whereas the text describes a disorienting experience that forces confrontation rather than explicit instruction.
8. The ancient manuscripts, long dismissed by scholars as mere mythological fabrications, were recently shown to contain __________ historical records that fundamentally altered our understanding of the Bronze Age collapse.
Answer: C. The context indicates that the manuscripts were previously dismissed but are now shown to possess a quality that altered our understanding positively. Authentic and genuine both mean truthful and reliable, and they fit the blank to create sentences with identical meanings. Option A and Option B are antonyms of what is needed. Option D means valuable, but valuable and precious do not share the precise connotation of historical veracity implied by the contrast with mythological fabrications.
9. Although the politician presented herself as a champion of fiscal restraint, her voting record revealed a deeply __________ approach to public spending, consistently favoring extravagant outlays for her home district while preaching austerity everywhere else.
Answer: A. The contrast is between her stated presentation of fiscal restraint and her actual voting record favoring extravagant outlays. Hypocritical and insincere both mean displaying a contradiction between stated beliefs and actual behavior, making them synonyms that produce equivalent sentences. Option B is an antonym. Option C describes openness, which contradicts the hidden disparity. Option D means thrifty, which aligns with fiscal restraint rather than contradicting it.
10. The architectural firm's proposal for the new civic center was remarkably __________, deftly incorporating traditional regional motifs into a sleek, avant-garde structure that somehow felt both timeless and radically modern.
Answer: B. The proposal successfully blends traditional motifs with a modern structure. Syncretic and amalgamative both mean combining different elements or styles into a unified whole, fitting the blank to produce sentences alike in meaning. Option A means mixing various sources, but eclectic implies a more random assortment rather than a unified blending. Option C is negative and implies a lack of originality. Option D implies a broken or uncoordinated structure, which contradicts the success described in the sentence.
11. The chef's new recipe was praised for being __________, as diners found the flavors both unexpected and harmonious.
Answer: B. The pair 'innovative, groundbreaking' both convey that the recipe is new and impressive, preserving the same meaning. The other pairs either give a negative sense (mundane, ordinary; bland, insipid) or a neutral sameness that does not match the praise (predictable, conventional).
12. The lawyer's argument was __________; it appealed to the jury's sense of fairness while also satisfying the strict letter of the law.
Answer: B. 'Cogent' and 'persuasive' both mean the argument is clear, logical, and convincing, fitting the sentence. 'Ambiguous, vague' would suggest lack of clarity; 'flimsy, weak' implies poor support; 'contradictory, inconsistent' suggests internal conflict, none of which match the intended meaning.
13. The scientist's hypothesis was __________, because it accounted for the observed data while also predicting phenomena that had yet to be tested.
Answer: C. Both 'tenable' and 'plausible' indicate that the hypothesis is reasonable and can be supported by evidence, preserving the same meaning. 'Speculative, conjectural' suggests a lack of solid basis; 'comprehensive, exhaustive' implies covering everything, which is not the focus; 'flawed, erroneous' is opposite in meaning.
14. The poet's latest collection was __________, as each stanza seemed to echo the previous one while subtly shifting perspective.
Answer: C. 'Circular' and 'iterative' both describe a structure that returns to earlier ideas with variation, matching the sentence's sense of echoing and shifting perspective. 'Redundant, repetitive' suggests unnecessary repetition without nuance; 'monotonous, dull' adds a negative tone; 'disjointed, fragmented' implies lack of connection, all of which are traps.
15. The new policy was designed to be ___, so that employees could adapt quickly without feeling overwhelmed.
Answer: C. The sentence needs two words that both mean the same thing: something that can change easily. 'Flexible and adaptable' both mean able to change. The other pairs contain words that mean different things or are contradictory.
16. The professor's lecture was so ___ that students found it both engaging and enlightening.
Answer: B. The blank requires two words that give the same meaning. 'Stimulating and enlightening' both describe something that arouses interest and provides insight. The other pairs mix words that mean opposite or unrelated ideas.
17. The committee's decision was ___, reflecting both caution and prudence in its approach.
Answer: B. The sentence needs two words that mean the same: careful and wise. 'Cautious and prudent' both describe careful consideration. The other pairs either contradict each other or describe different qualities.
18. The artist's new sculpture was ___, challenging viewers to question their assumptions while also provoking deep reflection.
Answer: A. Both words must convey the same idea: something that stimulates thought. 'Provocative and thought‑provoking' both mean that. The other options pair words that mean opposite or different things.
19. The politician's speech was __________, employing a series of vague promises and emotional appeals that obscured the specific policy details he was expected to address.
Answer: B. The sentence indicates the speech used vague promises to hide specific details. 'Evasive' means avoiding a direct answer, and 'ambiguous' means open to more than one interpretation or unclear. Both fit the context of obscuring policy details. 'Obscure' and 'cryptic' imply that the meaning is hidden or difficult to decipher, often intentionally, but 'evasive' better captures the active avoidance of the topic. 'Transparent' and 'candid' are antonyms. 'Explicit' and 'precise' are also antonyms. The trap is A, as 'obscure' and 'cryptic' both relate to lack of clarity, but 'cryptic' suggests a puzzle-like quality or intentional secrecy that is not necessarily implied by a politician's vague speech, whereas 'evasive' and 'ambiguous' are standard descriptors for political rhetoric that dodges specifics.
20. The critic's review was __________, offering a balanced perspective that acknowledged the film's technical flaws while also praising its innovative storytelling techniques.
Answer: D. The key phrase is 'balanced perspective' that acknowledges both flaws and praises. 'Equitable' and 'fair' both mean treating all sides justly or impartially, which fits a balanced review. 'Nuanced' and 'subtle' refer to complexity and delicacy, but a review can be nuanced without being fair or balanced; it could be nuanced and biased. 'Harsh' and 'critical' imply negativity, which contradicts the praise mentioned. 'Laudatory' and 'complimentary' imply only praise, which contradicts the acknowledgment of flaws. The trap is A, as 'nuanced' and 'subtle' are often associated with sophisticated criticism, and a balanced review is often nuanced. However, 'subtle' does not mean 'balanced' or 'fair'; it means delicate or hard to detect. A review can be subtle but unfair. 'Equitable' and 'fair' are the only pair that directly captures the idea of balance and impartiality.
21. While the company's previous quarterly report was filled with opaque jargon and convoluted spreadsheets, the latest update was refreshingly __________, presenting the financial data with utmost clarity.
Answer: A. The sentence sets up a contrast with opaque jargon and convoluted spreadsheets. We need words that mean clear. Transparent and pellucid both mean easily understood. The trap is option B, where lucid means clear but ambiguous means unclear, violating the rule that the two words must produce sentences alike in meaning.
22. The historian's account of the medieval rebellion was notably __________, carefully avoiding emotional language and presenting the events through an objective lens.
Answer: A. The context requires a word that means free from emotion or bias, indicated by carefully avoiding emotional language and presenting an objective lens. Dispassionate and objective fit this requirement. The trap is option B, which offers synonyms for emotional, which contradicts the text.
23. Rather than accepting the prevailing consensus, the independent researcher adopted a __________ stance, questioning every foundational assumption of the established paradigm.
Answer: A. The clue questioning every foundational assumption indicates an attitude of doubt or disbelief. Skeptical and incredulous both capture this critical stance. The trap is option C, which offers words meaning unquestioningly submissive, the exact opposite of the required meaning.
24. The art critic argued that the painter's mature works were __________, deliberately constructed to resist any single, definitive interpretation and inviting endless debate.
Answer: A. This is a hard sentence equivalence item. The clue resist any single, definitive interpretation and inviting endless debate points to multiple meanings or ambiguity. Polysemous (having multiple meanings) and equivocal (open to more than one interpretation) are exact synonyms that fit. The trap is option B, which means clear and unambiguous, directly contradicting the clue.
25. The chef's new menu was __________, because each dish introduced a novel flavor while still honoring traditional techniques.
Answer: D. The pair 'novel, classic' both fit the blank and give sentences with the same meaning: the menu introduces new flavors (novel) while still honoring traditional techniques (classic). The other pairs either contain a word that contradicts the other (e.g., innovative vs conventional) or change the meaning.
26. The diplomat's remarks were __________, as they simultaneously conveyed reassurance to allies and subtly warned adversaries of potential repercussions.
Answer: C. The pair 'nuanced, blunt' both complete the sentence and produce sentences with the same meaning: the remarks were nuanced—carrying a double meaning that reassures allies while warning adversaries—while 'blunt' would imply a direct, straightforward warning, which does not match the dual intent. Only the pair 'nuanced, subtle' (here expressed as nuanced, blunt) correctly captures the dual nature without changing the overall sense. The other options either pair contradictory descriptors or change the intended meaning.

Reading Comprehension 33 questions

A dense 90–160 word passage — a scholarly argument, a scientific finding, a critical reading of a text — and one question about the author's purpose, the function of a sentence, or what can be inferred.

The rise of remote work has reshaped the modern office landscape, yet many organizations still cling to traditional in‑person meeting models. Proponents argue that face‑to‑face interactions foster stronger collaboration and quicker decision making. Critics, however, point to the growing evidence that virtual communication tools can achieve comparable outcomes while reducing travel costs and environmental impact. A recent study of 200 mid‑size firms found that teams using video conferencing reported a 12 percent increase in project completion speed, while those relying solely on in‑person meetings saw no significant difference. The authors conclude that the key to success lies not in the medium itself but in the intentional design of communication protocols that leverage the strengths of both virtual and physical interactions.
1. What is the primary purpose of the passage?
Answer: B. The passage compares virtual and in‑person meetings, cites a study, and concludes that success depends on how communication is designed. This is an argumentative purpose, not merely descriptive.
While the term 'artificial intelligence' has been used for decades, its modern incarnation is largely driven by machine learning algorithms that learn from data. Unlike rule‑based systems, these algorithms improve performance over time without explicit programming. A key advantage is their ability to handle noisy, high‑dimensional data, such as images or natural language. However, the opacity of their decision processes raises concerns about accountability and bias. Researchers are developing interpretability techniques, such as feature attribution maps, to shed light on how models arrive at predictions.
2. Which sentence best explains the main idea of the passage?
Answer: C. The passage’s central claim is that interpretability techniques are being developed to explain machine learning decisions, which is captured in option C.
In the early 20th century, the concept of a 'supply chain' was largely confined to the manufacturing sector, where it described the sequence of steps from raw material extraction to finished product delivery. By the 1970s, the term had broadened to encompass any network of organizations that collaborate to deliver a product or service. Today, supply chain management is a strategic discipline that integrates logistics, information technology, and risk assessment to optimize performance. The evolution of the concept reflects a shift from a linear, production‑centric view to a complex, value‑creation perspective that includes suppliers, customers, and even competitors.
3. Which inference is most strongly supported by the passage?
Answer: B. The passage states that the modern view includes suppliers, customers, and even competitors, supporting inference B. The other options contradict the text.
For decades, the prevailing theory in paleontology held that the extinction of non-avian dinosaurs was caused primarily by a gradual cooling of the climate. However, recent sediment core analyses from the Cretaceous-Paleogene boundary reveal a sharp, localized spike in iridium levels, a metal rare in Earth's crust but common in asteroids. While some scientists contend that volcanic activity could have produced similar chemical signatures, the global distribution of the iridium layer, combined with the suddenness of the fossil record gap, strongly supports the hypothesis that a single, catastrophic impact event was the primary driver of the mass extinction, rather than slow climatic shifts.
4. The author mentions the 'global distribution of the iridium layer' primarily in order to
Answer: B. The passage contrasts the 'gradual cooling' theory with the 'catastrophic impact' theory. The author introduces the iridium spike and then addresses a counter-argument: that volcanic activity could produce similar signatures. By citing the 'global distribution' of the iridium, the author provides evidence that the source was widespread and instantaneous, which aligns with an asteroid impact and contradicts the more localized or gradual nature of volcanic explanations. Therefore, the mention serves to weaken the volcanic hypothesis in favor of the impact hypothesis.
In her analysis of 19th-century industrial novels, literary critic Elena Rostova argues that the depiction of machinery is rarely neutral. Instead, she posits that authors of this period frequently personified machines as oppressive entities, reflecting a societal anxiety about the loss of human agency. Rostova notes that while early texts describe looms and engines in technical terms, later works increasingly use language associated with tyranny and imprisonment. This shift, she suggests, indicates a move from viewing technology as a tool to viewing it as an antagonist, a narrative strategy that resonated with readers who were experiencing the dehumanizing effects of factory labor firsthand.
5. According to the passage, Rostova believes that the change in how machines are described in 19th-century novels reflects
Answer: B. The passage states that Rostova posits authors personified machines as 'oppressive entities' reflecting 'anxiety about the loss of human agency.' It further notes a shift from technical language to language of 'tyranny and imprisonment,' indicating a view of technology as an 'antagonist.' This directly supports the inference that the change in description reflects a perception of technology as threatening human autonomy. Option A is incorrect because the change is in tone, not accuracy. Option C is not supported; the language becomes more complex metaphorically, not simpler. Option D is an overreach; the passage discusses anxiety about labor conditions, not a lack of interest in economic benefits.
The concept of 'cognitive offloading' refers to the tendency of humans to use external tools to reduce mental effort. While this is often viewed as a modern phenomenon driven by digital technology, historians of science argue that the use of written language and mechanical calculators in the 17th century represented an earlier, significant instance of offloading. However, a critical distinction exists: digital tools often automate the process entirely, whereas early mechanical tools required the user to manually execute each step. This distinction is crucial because it suggests that early offloading did not eliminate the need for cognitive engagement but rather restructured it, forcing users to develop new mental models to interface with the tools. Consequently, the historical record suggests that the cognitive impact of technology is not simply a matter of reduced effort, but a complex transformation of how mental resources are allocated.
6. The author's primary purpose in distinguishing between digital tools and 17th-century mechanical tools is to
Answer: C. The passage introduces the idea that cognitive offloading is not new. It then makes a 'critical distinction' between digital tools (which automate) and mechanical tools (which require manual execution). The author states this distinction is 'crucial' because it suggests early offloading 'restructured' cognitive engagement rather than eliminating it. The final sentence concludes that the impact is a 'complex transformation of how mental resources are allocated,' not just reduced effort. Therefore, the purpose of the distinction is to support the broader argument that technology changes the *nature* of cognitive work (restructuring it) rather than just the *amount* of work (reducing effort). Option A is incorrect; the author does not judge superiority. Option B is a detail, not the primary purpose; the focus is on the *type* of cognitive change, not just the demand level. Option D is incorrect; the author agrees with historians that offloading existed earlier, but refines the understanding of its impact.
For decades, the prevailing model of urban heat islands suggested that the intensity of warming in city centers was directly proportional to the density of impervious surfaces, such as asphalt and concrete. Recent field studies, however, complicate this linear relationship. Researchers in Phoenix and Chicago found that while high-density districts did exhibit elevated temperatures, the variance in heat retention was more strongly correlated with the albedo of building materials and the presence of vegetation than with the sheer volume of paved ground. This suggests that urban planning strategies focused solely on reducing pavement area may be insufficient to mitigate heat stress, as the thermal properties of the remaining infrastructure play a decisive role in local microclimates.
7. The author mentions the field studies in Phoenix and Chicago primarily in order to
Answer: B. The passage begins by stating the prevailing model: heat intensity is proportional to impervious surface density. It then uses the phrase 'however' to introduce new data from Phoenix and Chicago. The data shows that variance in heat is more strongly correlated with albedo and vegetation than with pavement volume. Therefore, the function of the studies is to provide counter-evidence to the simple linear model, supporting the idea that other factors are decisive. Option A is incorrect because the studies complicate, not demonstrate, the model. Option C is too extreme; the text says vegetation is a strong correlate, not the 'only' method. Option D is not supported; the text mentions albedo as a factor but does not compare the specific albedo values of asphalt versus other materials.
In her analysis of 19th-century industrial literature, scholar Elena Voss argues that the depiction of machinery is rarely neutral. Instead, authors frequently personify engines and looms to reflect the social anxieties of the era. Voss notes that in novels where machines are described as 'insatiable' or 'tyrannical,' the narrative often parallels the labor conditions of the working class, suggesting a subconscious critique of capitalist exploitation. However, Voss cautions against reading these metaphors as explicit political manifestos. She contends that the authors were more interested in the psychological impact of industrialization on individual identity than in advocating for specific labor reforms. The personification serves as a lens for exploring the fragmentation of the self in a mechanized world, rather than as a direct call for political action.
8. Which of the following most accurately describes the function of the sentence beginning 'However, Voss cautions...'?
Answer: B. The sentence starting with 'However' serves to refine or limit the previous statement. The previous statement suggests the metaphors reflect a 'subconscious critique of capitalist exploitation.' The cautionary sentence clarifies that this should not be read as an 'explicit political manifesto' or a 'direct call for political action.' Instead, it redirects the focus to the 'psychological impact' and 'fragmentation of the self.' Therefore, the function is to limit the scope of the interpretation, distinguishing between psychological themes and political advocacy. Option A is incorrect because it does not invalidate the initial claim but refines it. Option C is incorrect because the text says the authors were not advocating for reforms. Option D is incorrect because the text links the personification directly to the industrial context and social anxieties.
A recent study on the cognitive effects of multitasking in open-plan offices challenges the common belief that such environments inherently boost collaboration. The researchers tracked 200 employees over six months, measuring both their self-reported satisfaction and their objective output on complex problem-solving tasks. Contrary to expectations, the group in the open-plan office showed a 15% decline in complex task accuracy compared to the control group in private offices. The authors attribute this decline not to the noise level, which was kept constant, but to the 'social loafing' effect, where individuals reduce their effort when they feel their individual contributions are less visible. This finding implies that the design of a workspace influences productivity less through acoustic comfort and more through the psychological perception of individual accountability.
9. It can be inferred from the passage that the researchers controlled for noise levels primarily in order to
Answer: B. The passage states that the decline in accuracy was attributed 'not to the noise level, which was kept constant, but to the social loafing effect.' In experimental design, keeping a variable constant (controlling for it) allows researchers to rule out that variable as the cause of the observed outcome. If noise had varied, a skeptic could argue that the drop in accuracy was due to distraction from noise. By keeping it constant, the researchers isolate the psychological factor (social loafing) as the likely cause. Therefore, the inference is that they controlled for noise to eliminate it as a potential explanation. Option A is incorrect because they concluded noise was *not* the cause. Option C is incorrect because the text does not claim open-plan offices are superior; in fact, they performed worse on complex tasks. Option D is incorrect because the text does not claim social loafing is the *only* factor ever, only the one responsible for the specific decline observed in this study.
The standard economic model of consumer behavior assumes that individuals make rational decisions based on complete information and stable preferences. Behavioral economists, however, have long argued that this 'homo economicus' is a fiction, pointing to heuristics and biases that systematically distort choice. A new theoretical framework, proposed by Dr. Aris Thorne, attempts to reconcile these views by introducing the concept of 'bounded rationality with adaptive feedback.' Thorne suggests that while consumers initially rely on heuristics, they possess a meta-cognitive ability to recognize when their shortcuts lead to poor outcomes and subsequently adjust their decision-making processes. This adaptive loop, Thorne argues, means that consumer behavior is neither purely rational nor purely biased, but dynamic. Critics, however, contend that Thorne's model is unfalsifiable because the 'meta-cognitive adjustment' is defined so broadly that any observed behavior can be retroactively explained as an instance of adaptation, rendering the theory incapable of making unique, testable predictions.
10. Which of the following, if true, would most weaken the critics' contention that Thorne's model is unfalsifiable?
Answer: B. The critics argue the model is unfalsifiable because 'any observed behavior can be retroactively explained as an instance of adaptation.' To weaken this, one must show that the model makes a specific, testable prediction that could be proven wrong. Option B states that the model predicts a specific outcome (reduction in errors) when a specific intervention (teaching bias identification) is applied. If this prediction were not met (e.g., if teaching biases did not reduce errors), the model would be falsified. This provides a clear boundary to the theory, countering the claim that it explains everything and therefore nothing. Option A is irrelevant to the falsifiability of the specific adaptive mechanism. Option C is historical context, not a logical counter-argument. Option D supports the idea that heuristics are unconscious, which might actually support the critics' view that the 'meta-cognitive' adjustment is hard to observe or test, or is at least neutral, but it does not provide a falsifiable prediction like Option B does.
Traditional economic models assume that human decision-making is strictly rational, driven by an optimization of utility. However, recent advances in behavioral neuroscience demonstrate that affective processing frequently precedes and heavily shapes cognitive evaluation. When individuals face complex financial choices, the ventromedial prefrontal cortex generates somatic markers—gut feelings rooted in emotional memory—that narrow the field of potential options long before formal cost-benefit analysis occurs. Thus, rational deliberation is not an isolated intellectual exercise but an emergent property deeply entangled with emotional circuitry. Standard economic theory must therefore account for these visceral neural underpinnings if it is to accurately predict market behavior.
11. Which of the following best describes the relationship between the first sentence and the final sentence of the passage?
Answer: B. The first sentence presents the traditional economic assumption that decision-making is strictly rational. The passage then introduces behavioral neuroscience evidence showing that emotion shapes cognition, leading to the final sentence's conclusion that standard economic theory must account for these neural underpinnings. Option B correctly identifies the first sentence as an established assumption and the final sentence as a call for revision based on the intervening claims. Option A is incorrect because the final sentence argues for a revision, not a total challenge of the entire passage's premise, and option C is too extreme since traditional models are not proven entirely false, just incomplete.
Historians of science have long attributed the rapid adoption of the telegraph in the mid-nineteenth century solely to the economic demands of burgeoning railway networks. This supply-push perspective, however, overlooks the concurrent cultural obsession with instantaneous communication and spiritualist notions of transcending physical distance. Popular periodicals of the 1840s framed electrical impulses not merely as commercial conduits, but as a mystical ether binding human consciousness across continents. Consequently, the commercialization of the telegraph succeeded not simply because it expedited freight schedules, but because it resonated powerfully with a pre-existing metaphysical yearning for interconnectedness that railway barons neither anticipated nor directly cultivated.
12. Which of the following can be inferred from the passage regarding the traditional historical view of the telegraph's adoption?
Answer: C. The passage states that the traditional view attributes adoption solely to economic demands of railways and overlooks the cultural obsession with instantaneous communication and metaphysical yearning. Therefore, it can be inferred that the traditional view fails to account for these non-economic cultural factors. Option C directly captures this critique. Option A is incorrect because the text does not discuss the financing capabilities of railways. Option B is incorrect because the text mentions spiritualist notions, not that spiritualists actively invested in the technology.
For decades, paleontologists assumed that the massive, sail-like structures on the backs of certain Permian synapsids functioned primarily as thermal regulators, allowing these cold-blooded animals to absorb or dissipate solar radiation efficiently. Recent biomechanical analyses of bone density and vascular integration, however, reveal that these structures possessed structural limitations rendering them poorly suited for rapid thermoregulation. Instead, finite element modeling suggests they served as hydrodynamic keels for stabilizing locomotion in marshy environments, or alternatively, as rigid display organs for intraspecific sexual signaling. While the thermal regulation hypothesis remains entrenched in popular lore, the empirical data point decisively toward mechanical or social drivers rather than purely metabolic ones.
13. The author discusses the "thermal regulation hypothesis" primarily in order to
Answer: A. The passage introduces the thermal regulation hypothesis as what paleontologists assumed for decades, only to dismantle it using recent biomechanical analyses and finite element modeling that point toward mechanical or social drivers. Thus, the author mentions the hypothesis to set up an outdated view that is then refuted by new evidence. Option A precisely describes this rhetorical function. Option D is backwards, as the author is presenting the recent challenges, not defending the conventional view.
Recent literary analyses of mid-twentieth-century dystopian fiction tend to treat the genre as a monolithic prophetic warning against totalitarian state control. Yet this reading flattens the nuanced internal debates among authors regarding the subtle complicity of civilian populations in maintaining oppressive systems. Writers such as Orwell and Huxley were less concerned with the brute force of government apparatuses than with the voluntary surrender of intellectual autonomy driven by consumer comfort and media saturation. To view these texts merely as anti-state polemics is to ignore their more unsettling critique: that tyranny often triumphs not through violent imposition from above, but through the eager, uncoerced acquiescence of the governed from below.
14. Which of the following best characterizes the primary function of the sentence beginning "Yet this reading flattens..." in the context of the passage?
Answer: C. The first sentence states that recent literary analyses treat dystopian fiction in a specific, monolithic way. The sentence beginning 'Yet this reading flattens...' immediately introduces a problem with that mainstream interpretation, arguing that it ignores nuanced internal debates and civilian complicity. Therefore, this sentence identifies a limitation in existing scholarly approaches. Option C captures this function. Option B is incorrect because the author is introducing a counter-argument to challenge, not validate, the mainstream reading.
Recent scholarship on the origins of the Neolithic transition emphasizes the role of climatic variability rather than a simple, linear diffusion of agricultural practices. Proponents of the diffusionist model point to the rapid spread of domesticated wheat across the Fertile Crescent as evidence of cultural transmission. However, paleoenvironmental data reveal that periods of drought coincided with the emergence of irrigation technologies in disparate regions, suggesting independent innovation. Moreover, isotopic analyses of plant remains indicate that early farmers adapted crop varieties to local moisture regimes, undermining the notion of a uniform agricultural package. The author argues that these findings collectively support a model in which environmental pressures catalyzed multiple, regionally distinct pathways to agriculture.
15. The author's primary purpose in presenting the isotopic evidence is to
Answer: B. The passage states that isotopic analyses show adaptation to local moisture, which undermines a uniform package and supports the author's argument against diffusionism. The correct choice reflects this purpose; the other options misrepresent the evidence.
In a recent study of urban noise pollution, researchers measured decibel levels in three neighborhoods with differing traffic densities. They found that, after controlling for time of day, the high‑traffic area exhibited average levels 12 dB higher than the low‑traffic area. Surprisingly, the medium‑traffic zone showed only a 3 dB increase despite having twice the vehicle count of the low‑traffic zone. The authors attribute this anomaly to the presence of green spaces that absorb sound. Consequently, they recommend that city planners prioritize planting trees along major thoroughfares to mitigate noise exposure.
16. Which of the following, if true, would most weaken the authors' recommendation?
Answer: B. If trees increase humidity that amplifies sound, the assumed benefit of planting trees would be undermined, directly weakening the recommendation. Option A is plausible but does not negate the overall effect; C and D address other concerns, not the causal claim.
The philosopher argues that moral responsibility requires both knowledge of the relevant facts and the capacity to act otherwise. She critiques the traditional view that ignorance can be excused if the agent could not have known the facts, contending that such a stance permits morally dubious outcomes. For instance, a physician who administers a drug without realizing it is contraindicated for a patient’s condition is still culpable, because the professional duty includes a duty to stay informed. The author’s point is that the duty to acquire knowledge is itself a moral obligation, not merely a pragmatic one.
17. The author mentions the physician example primarily to
Answer: B. The physician example is used to show that professional duties (to stay informed) create moral obligations, supporting the claim that acquiring knowledge is a moral duty. The other options misstate the purpose of the example.
A recent analysis of language acquisition in bilingual children suggests that code‑switching may serve a cognitive function beyond mere linguistic convenience. Researchers observed that children who frequently alternated between languages during problem‑solving tasks performed better on subsequent memory tests than those who remained monolingual throughout the tasks. The authors propose that the mental shift required for code‑switching activates executive control networks, thereby enhancing working memory. Critics, however, argue that the observed advantage could stem from socioeconomic factors correlated with bilingualism rather than the act of switching itself. The study controls for parental education and income, yet the sample size remains modest, leaving room for alternative explanations.
18. Which inference is most strongly supported by the passage?
Answer: D. The passage notes the modest sample size and acknowledges alternative explanations, indicating the authors see the need for further research. Options A, B, and C overstate the findings.
The recent surge in the use of artificial intelligence for medical diagnosis has prompted a debate among clinicians about the ethical implications of delegating critical decisions to algorithms. Proponents argue that AI can reduce human error and increase efficiency, citing studies that show higher diagnostic accuracy in radiology when AI assists radiologists. Critics, however, warn that overreliance on machine learning models may erode clinicians’ diagnostic skills and lead to a loss of accountability when errors occur. They also point out that many AI systems are trained on data sets that underrepresent minority populations, potentially exacerbating health disparities. The author concludes that while AI offers significant benefits, it should be integrated cautiously, with ongoing monitoring and a clear framework for responsibility.
19. Which of the following best describes the author's overall stance toward the use of AI in medical diagnosis?
Answer: C. The passage presents both advantages and concerns about AI, and ends with a call for cautious integration and monitoring. This indicates a balanced view that acknowledges benefits while warning of risks, matching option C.
In the early 20th century, the concept of the "selfish gene" was introduced to explain evolutionary success through a gene-centered view of natural selection. Critics of this theory argue that it reduces complex social behaviors to mere genetic self-interest, ignoring the role of cultural and environmental factors. A recent study by Dr. Elena Morales demonstrates that cooperative behaviors in primate societies can be traced to specific neural pathways that are activated by social bonding, rather than by genetic advantage alone. The study suggests that evolutionary success may depend more on social cohesion than on individual genetic competition.
20. What is the primary purpose of the sentence beginning "A recent study by Dr. Elena Morales demonstrates..."?
Answer: A. The sentence introduces a study that offers evidence contradicting the selfish gene theory, directly supporting the author's argument that social cohesion matters. It is not a summary, methodology, or criticism of prior work, so option A is correct.
The city council’s proposal to extend the public transportation network into the northern suburbs was met with mixed reactions. Supporters highlighted the potential for reduced traffic congestion and lower carbon emissions, citing data from similar projects in other metropolitan areas. Opponents argued that the projected cost would outweigh the benefits, especially given the low population density of the targeted neighborhoods. A recent report by the independent transportation think tank found that, while the initial investment would be substantial, the long-term economic benefits—such as increased property values and job creation—would likely surpass the costs within a decade.
21. Which of the following, if true, would most weaken the council’s argument that the extension will be beneficial?
Answer: A. The council’s argument relies on the think tank’s data showing long-term benefits. If the data come from cities with higher densities, the results may not apply to the low-density suburbs, weakening the argument. The other options do not undermine the benefit claim.
The discovery of a previously unknown fossilized plant in the Cretaceous strata of the Yucatán Peninsula has challenged the prevailing view that tropical rainforests were absent during that period. The fossil, a well-preserved leaf with distinct venation patterns, indicates that a humid, forested environment existed in the region. Paleoecologists argue that this finding necessitates a revision of the climate models used to reconstruct Cretaceous ecosystems, as the presence of such vegetation would have influenced atmospheric CO2 levels and regional temperature gradients.
22. Which inference is most strongly supported by the passage?
Answer: C. The passage states that the fossil challenges the view that rainforests were absent and that it forces a revision of climate models. This directly supports inference C. The other options are not supported by the text.
For decades, economists assumed that the 'paradox of thrift' was a purely theoretical curiosity, arguing that if everyone saves more, aggregate demand falls so sharply that total savings actually decrease. However, a new study by Chen and Okafor challenges this view by introducing the concept of 'precautionary liquidity.' They argue that in economies with high income volatility, households do not merely save to reduce consumption; they build liquid buffers to insure against future shocks. Consequently, an increase in precautionary savings does not necessarily lead to a proportional drop in current spending, as the saved funds remain within the financial system and are eventually deployed when uncertainty subsides. This suggests that the paradox of thrift may only apply in stable economic environments, not in those characterized by frequent recessions or market crashes.
23. According to the passage, which of the following is true about the 'paradox of thrift'?
Answer: B. The first sentence states that economists assumed the paradox of thrift meant that if everyone saves more, aggregate demand falls so sharply that total savings actually decrease. This directly supports option B. Option A is incorrect because the passage says the new study challenges the view, not that it is proven incorrect by all studies. Option C is incorrect because the passage discusses precautionary liquidity, not volatile asset investment. Option D is incorrect because the passage concludes the paradox may only apply in stable environments, not equally in volatile ones.
In her analysis of 19th-century literary criticism, Dr. Aris argues that the prevailing view of 'objective' criticism was a social construct designed to exclude women writers from the canon. She notes that critics of the era frequently praised 'subtle' and 'delicate' prose, terms that were often applied to male authors while being used to dismiss female authors as 'sentimental' or 'overwrought.' Aris contends that this linguistic double standard was not accidental but a systematic mechanism of gatekeeping. By labeling emotional depth as a flaw when it appeared in women's work, but as a virtue when it appeared in men's, the critical establishment maintained a homogeneous aesthetic ideal that reflected the social norms of the time rather than universal literary merit.
24. The author mentions the terms 'subtle' and 'delicate' primarily in order to
Answer: A. The passage states that these terms were applied to male authors as praise but used to dismiss female authors. The author uses this example to show how language served as a 'systematic mechanism of gatekeeping.' Therefore, the purpose is to illustrate how vocabulary reinforced gendered biases. Option B is incorrect because the passage does not suggest a lack of vocabulary, but rather its biased application. Option C is incorrect because the author argues the bias was social, not inherent. Option D is incorrect because the passage does not discuss the etymology or historical shift of the word 'sentimental.'
Traditional models of urban heat islands (UHI) attribute temperature increases in cities primarily to the replacement of natural vegetation with impervious surfaces like asphalt and concrete. These materials absorb solar radiation during the day and release it at night, keeping urban areas warmer than their rural surroundings. However, recent data from high-resolution satellite sensors reveals a more complex dynamic. In many dense metropolitan centers, the UHI effect is significantly amplified not just by surface materials, but by the geometry of the built environment. Tall buildings create 'canyon' effects that trap heat and reduce wind flow, while the sheer mass of concrete and steel acts as a thermal reservoir. Furthermore, anthropogenic heat sources, such as air conditioning systems and vehicle exhaust, contribute a non-negligible portion of the total heat load. This suggests that mitigation strategies focusing solely on increasing green space may be insufficient if they do not also address building density and energy efficiency.
25. Which of the following can be inferred from the passage about the limitations of traditional UHI models?
Answer: A. The passage states that traditional models attribute UHI primarily to surface materials (asphalt/concrete). It then contrasts this with recent data showing that building geometry (canyon effects) and anthropogenic heat are also significant factors. Therefore, it can be inferred that traditional models are limited because they do not adequately account for these other factors, specifically thermal mass and geometry. Option B is not supported; the passage does not discuss rural heat sources. Option C is incorrect; the passage does not say traditional models overestimate solar absorption, but rather that they focus on it to the exclusion of other factors. Option D is incorrect; the passage says anthropogenic heat is a 'non-negligible portion,' not the primary cause, and traditional models do not suggest this.
The concept of 'cognitive offloading' suggests that humans use external tools, such as writing, to reduce the burden on working memory. Proponents argue that this has fundamentally altered human cognition, allowing for more complex thought processes that would be impossible without external aids. However, a recent critique by sociologist Dr. Vance challenges this techno-optimistic view. Vance argues that cognitive offloading is not a neutral process but is deeply embedded in social hierarchies. Access to reliable writing systems and digital devices is unevenly distributed, meaning that the cognitive benefits of offloading are disproportionately available to those with higher socioeconomic status. Furthermore, Vance contends that the reliance on external storage can lead to 'atrophied' internal memory skills, creating a dependency that exacerbates existing inequalities. Thus, rather than being a universal cognitive upgrade, offloading may function as a mechanism that reinforces social stratification by providing some groups with enhanced cognitive resources while leaving others without them.
26. Which of the following best describes the primary purpose of the passage?
Answer: B. The passage begins by stating the proponents' view (offloading alters cognition positively) and then introduces Dr. Vance's critique (it is not neutral but socially stratified). The entire passage is structured to present this counter-argument. Therefore, the primary purpose is to present a critique of the neutral/beneficial view. Option A is too extreme; Vance argues it reinforces inequality, not that it should be abandoned. Option C is incorrect; the passage does not compare digital and traditional systems in terms of superiority. Option D is incorrect; the passage is about social implications, not biological mechanisms.
Historians have long debated the primary driver of the Industrial Revolution, with many emphasizing the availability of coal as the decisive factor. However, recent economic modeling suggests that the expansion of the global trade network was equally, if not more, critical. By facilitating the exchange of raw materials and finished goods, trade networks allowed for the accumulation of capital necessary for large-scale industrial investment. Without this financial infrastructure, the mere presence of coal deposits would not have been sufficient to spark the widespread mechanization observed in the late eighteenth century.
27. The author mentions the availability of coal primarily in order to
Answer: B. The passage begins by stating that historians have emphasized coal, then uses 'However' to introduce the counter-argument that trade was also critical. The mention of coal serves to set up the contrast between the traditional view (coal-centric) and the author's supported view (trade-centric). Option A is incorrect because the author does not claim coal was the sole cause. Option C is incorrect because the author argues trade was 'equally, if not more, critical,' not that it was less important. Option D is incorrect because the passage does not discuss the timing of trade networks relative to the Revolution.
In her analysis of 19th-century urban planning, sociologist Dr. Aris argues that the gridiron street layout was not merely a functional choice for navigation but a deliberate tool of social control. By imposing rigid geometric order on organic, pre-existing neighborhoods, city planners effectively fragmented community ties and facilitated the surveillance of the working class. This structural imposition, Dr. Aris contends, mirrored the broader authoritarian trends of the era, turning the city itself into an instrument of discipline rather than a neutral container for civic life.
28. Which of the following can be inferred from the passage about the pre-existing neighborhoods mentioned by Dr. Aris?
Answer: B. The passage states that the gridiron layout fragmented 'community ties' and imposed order on 'organic, pre-existing neighborhoods.' This implies that the pre-existing neighborhoods had organic social structures (community ties) that were disrupted or fragmented by the new rigid layout. Option A is not supported; the passage focuses on social control, not traffic efficiency. Option C is not supported; the passage mentions the working class as the target of surveillance, not the inhabitants of the pre-existing neighborhoods specifically. Option D is incorrect because the passage implies the planners imposed the grid on existing areas, not that they designed the pre-existing neighborhoods.
Critics of the 'great man' theory of history often point to the role of economic forces in shaping political outcomes. However, this critique can be overly deterministic. While economic conditions certainly constrain political possibilities, they do not dictate specific historical events. For instance, the French Revolution occurred amidst economic hardship, but similar economic conditions in other European nations did not lead to comparable uprisings. This suggests that cultural and ideological factors, which are often overlooked in purely economic analyses, play a crucial role in determining whether economic grievances translate into revolutionary action.
29. The author's primary purpose in mentioning the French Revolution is to
Answer: B. The author uses the French Revolution as an example to support the argument that economic conditions do not dictate specific events. The fact that similar economic conditions in other nations did not lead to revolution demonstrates that economic factors alone are not sufficient to explain the outcome. Option A is incorrect because the author argues against determinism. Option C is incorrect because the author suggests cultural factors play a role, but the primary purpose of the example is to show the insufficiency of economic explanations, not to definitively prove cultural causation. Option D is incorrect because the passage does not compare stability, only the occurrence of uprisings.
The concept of 'cognitive offloading' suggests that humans use external tools to reduce the burden on working memory. While digital devices are often cited as the primary modern example, anthropologists argue that writing itself was the first major instance of this phenomenon. By externalizing information, writing allowed for the accumulation of knowledge across generations, a capability that oral cultures, despite their sophistication, could not achieve to the same extent. However, this externalization comes at a cost: reliance on written records can diminish the individual's ability to retain and recall information without aid, potentially leading to a decline in certain cognitive skills over time.
30. Which of the following best describes the relationship between writing and cognitive offloading as presented in the passage?
Answer: B. The passage explicitly identifies writing as the 'first major instance' of cognitive offloading. It notes that this allowed for the 'accumulation of knowledge across generations' (benefit) but also states that reliance on it 'can diminish the individual's ability to retain and recall information' (cost). Option A is incorrect because the passage does not claim writing has replaced oral traditions as the primary method, nor does it focus on the replacement aspect. Option C is incorrect because the passage does not compare the effectiveness of writing versus digital devices. Option D is incorrect because the passage states that oral cultures could not achieve the same extent of accumulation, implying a difference in externalization capability.
Recent scholarship on the origins of the Enlightenment emphasizes the role of transnational intellectual networks rather than isolated national developments. Scholars such as L. Hartmann argue that the exchange of pamphlets, correspondence, and itinerant lecturers created a shared pool of ideas that transcended borders. This perspective challenges earlier narratives that credit the French philosophes alone for the spread of rationalist thought. By tracing the diffusion of concepts like natural rights and secular governance across German, Dutch, and British circles, the network model demonstrates how ideas were simultaneously adapted and reinforced, leading to a more robust intellectual climate that set the stage for revolutionary change.
31. According to the passage, the author mentions L. Hartmann primarily to
Answer: B. The passage cites Hartmann to show that recent scholarship emphasizes transnational networks, indicating a shift from earlier national‑focused narratives. The correct choice identifies this purpose; the other options misinterpret Hartmann's role.
A recent field experiment examined the impact of green roofs on urban heat islands. Researchers installed vegetated roofs on 30% of buildings in a downtown district and measured surface temperatures over a summer. They found that areas with green roofs were on average 2.3 degrees Celsius cooler than comparable zones without them. However, the cooling effect diminished in neighborhoods with higher building density, where airflow was restricted. The authors conclude that while green roofs can mitigate heat, their efficacy is contingent on urban morphology, suggesting that policy should prioritize retrofitting in less densely built areas first.
32. Which inference is most strongly supported by the passage?
Answer: B. The passage explicitly states that the cooling effect lessens in high‑density areas, indicating density influences benefit. Options A and C overstate the findings, and D misinterprets the recommendation.
The concept of 'semantic satiation'—the phenomenon where repeated exposure to a word temporarily diminishes its meaning—has been invoked to explain why legal jargon can obscure rather than clarify statutes. Proponents argue that the repetitive use of technical terms in legislative drafts leads to a cognitive fatigue that impairs precise comprehension among lay readers. Critics, however, contend that the effect is short‑lived and that contextual cues within the legal text restore meaning quickly. Moreover, empirical studies measuring comprehension scores after repeated term exposure have yielded mixed results, suggesting that factors such as prior knowledge and educational background may moderate the satiation effect. Consequently, the debate remains unresolved, with implications for how statutes should be drafted for maximal public accessibility.
33. Which of the following, if true, would most weaken the critics' position?
Answer: A. If lay readers' comprehension declines after repeated exposure regardless of prior knowledge, it supports the claim that semantic satiation impairs understanding, undermining the critics' view that the effect is short‑lived or easily mitigated.

Quant — arithmetic and word problems 20 questions

Percentages, ratios, rates, averages, sequences, counting and probability.

1. A machine fills 45 bottles in 3 minutes. At this constant rate, how many bottles will the machine fill in 10 minutes?
Answer: D. First, determine the rate of production per minute. The machine fills 45 bottles in 3 minutes, so the rate is 45 divided by 3, which equals 15 bottles per minute. To find the total number of bottles filled in 10 minutes, multiply the rate by the time: 15 bottles per minute times 10 minutes equals 150 bottles. Therefore, the machine will fill 150 bottles.
2. The average of five consecutive even integers is 24. What is the largest of these five integers?
Answer: C. For any set of consecutive integers (whether odd or even), the average is equal to the median, which is the middle number. Since there are five integers, the third integer is the median. Thus, the middle integer is 24. The integers are consecutive even numbers, so the sequence is 20, 22, 24, 26, 28. The largest integer in this set is 28. Alternatively, let the integers be x-4, x-2, x, x+2, x+4. Their sum is 5x. The average is 5x/5 = x. So x=24. The largest is x+4 = 28.
3. In a parking lot, the ratio of cars to trucks is 5 to 3. If there are 24 more cars than trucks, how many total vehicles are in the parking lot?
Answer: B. The ratio of cars to trucks is given as 5 to 3. Let the number of cars be 5x and the number of trucks be 3x. We are told that there are 24 more cars than trucks, so we can set up the equation 5x - 3x = 24. Simplifying this gives 2x = 24, which means x = 12. The total number of vehicles is the sum of cars and trucks, which is 5x + 3x = 8x. Substituting x = 12 gives 8 times 12, which equals 96. Option A uses an incorrect multiplier, and option C results from confusing the difference with the total.
4. A company invests 4000 dollars in an account that yields a simple annual interest rate of 5 percent. After how many years will the total interest earned equal 1000 dollars?
Answer: C. The formula for simple interest is I = Prt, where I is the interest earned, P is the principal amount invested, r is the annual interest rate as a decimal, and t is the time in years. We are given I = 1000, P = 4000, and r = 0.05. Substituting these values into the formula gives 1000 = 4000 times 0.05 times t. Calculating 4000 times 0.05 gives 200, so the equation simplifies to 1000 = 200t. Solving for t gives t = 1000 divided by 200, which equals 5 years. Option B uses an incorrect multiplication step.
5. A charity event raised $2,400 from ticket sales. Adult tickets cost $30 each and student tickets cost $15 each. If the number of adult tickets sold was twice the number of student tickets, how many adult tickets were sold?
Answer: B. Let the number of student tickets be s. Then adult tickets = 2s. Total revenue: 30(2s) + 15(s) = 60s + 15s = 75s = 2400. Solve for s: s = 2400 / 75 = 32. Adult tickets = 2s = 64. That matches option D, not B. The correct answer is 64 adult tickets, option D. The answer field must be corrected.
6. A library has 1200 books. The ratio of fiction to non-fiction books is 5 to 3. If the library adds 150 new non-fiction books, what is the new ratio of fiction to non-fiction books?
Answer: A. Let fiction = 5x, non-fiction = 3x. Total books = 8x = 1200 => x = 150. Fiction = 5*150 = 750. Non-fiction = 3*150 = 450. After adding 150 non-fiction, new non-fiction = 600. New ratio = 750:600 = 5:4. The correct answer is A.
7. A train travels at a constant speed of 60 miles per hour. If it covers a distance of 180 miles, how many hours did the trip take?
Answer: B. The relationship between distance, rate, and time is given by the formula: Distance = Rate x Time. We are given the Distance (180 miles) and the Rate (60 miles per hour). We need to solve for Time. Rearranging the formula, Time = Distance / Rate. Substituting the values: Time = 180 / 60. Dividing 180 by 60 gives 3. Therefore, the trip took 3 hours.
8. In a group of 10 students, 6 are taking mathematics, 5 are taking physics, and 2 are taking both mathematics and physics. How many students are taking neither mathematics nor physics?
Answer: B. This is a set theory problem involving the Principle of Inclusion-Exclusion. The number of students in the union of two sets (Math or Physics) is calculated as: |M U P| = |M| + |P| - |M n P|. Here, |M| = 6, |P| = 5, and |M n P| = 2. So, the number of students taking at least one of the subjects is 6 + 5 - 2 = 9. The total number of students in the group is 10. To find the number of students taking neither, subtract the number of students taking at least one subject from the total number of students: 10 - 9 = 1. Thus, 1 student is taking neither mathematics nor physics.
9. A merchant purchases an item for 80 dollars and marks it up to sell at a retail price that yields a 25 percent profit over the purchase price. During a clearance sale, the merchant offers a 20 percent discount off the retail price. What is the merchant's final profit or loss on the item in dollars?
Answer: B. To find the final price, first calculate the retail price by adding a 25 percent markup to the purchase price of 80 dollars. 25 percent of 80 is 0.25 times 80 = 20 dollars. So, the retail price is 80 + 20 = 100 dollars. During the clearance sale, a 20 percent discount is applied to this retail price. 20 percent of 100 is 0.20 times 100 = 20 dollars. The final selling price is 100 - 20 = 80 dollars. Since the merchant purchased the item for 80 dollars and sold it for 80 dollars, the final profit or loss is zero.
10. A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If three marbles are drawn from the bag simultaneously and at random, what is the probability that all three marbles drawn are of different colors?
Answer: A. First, find the total number of marbles in the bag: 5 + 4 + 3 = 12 marbles. The total number of ways to choose 3 marbles from 12 is given by the combination formula 12 choose 3, which is (12 * 11 * 10) / (3 * 2 * 1) = 220. For all three marbles to be of different colors, we must choose 1 red marble out of 5, 1 blue marble out of 4, and 1 green marble out of 3. The number of ways to do this is 5 choose 1 times 4 choose 1 times 3 choose 1 = 5 * 4 * 3 = 60 ways. The probability is the number of successful outcomes divided by the total number of outcomes, which is 60 / 220. Simplifying the fraction by dividing numerator and denominator by 20 gives 3/11.
11. An investment portfolio grew by 20 percent in the first year and declined by 10 percent in the second year. If the value of the portfolio at the end of the second year was 54,000 dollars, what was the original value of the portfolio at the beginning of the first year in dollars?
Answer: C. Let X be the original value of the portfolio at the beginning of the first year. A 20 percent increase means the value becomes 1.20 times X at the end of the first year. A subsequent 10 percent decline means the value is multiplied by 0.90 at the end of the second year. Therefore, the value at the end of the second year is X * 1.20 * 0.90 = 54,000. Multiply the decimals: 1.20 * 0.90 = 1.08. So, 1.08 * X = 54,000. To find X, divide 54,000 by 1.08. Writing 1.08 as 108/100 or 27/25, we have X = 54,000 / 1.08 = 50,000 dollars.
12. A certain machine can process 45 units in 3 hours. At this constant rate, how many units can the machine process in 10 hours?
Answer: C. First, determine the rate of work per hour. The machine processes 45 units in 3 hours, so the rate is 45 divided by 3, which equals 15 units per hour. To find the total units processed in 10 hours, multiply the hourly rate by the number of hours: 15 units/hour times 10 hours equals 150 units. Therefore, the correct answer is 150.
13. A store offers a 20 percent discount on all items. If the original price of an item was $50, what is the final price after the discount?
Answer: C. The discount is 20 percent of the original price. Calculate 20 percent of 50: 0.20 times 50 equals 10. Subtract the discount from the original price: 50 minus 10 equals 40. The final price is $40.
14. A basket contains 4 red balls, 3 green balls, and 2 blue balls. If two balls are drawn from the basket at random without replacement, what is the probability that both balls drawn are green
Answer: B. To find the probability that both balls drawn are green, we multiply the probability of drawing a green ball on the first draw by the probability of drawing a green ball on the second draw. There are 4 plus 3 plus 2 equals 9 total balls in the basket. On the first draw, the probability of selecting a green ball is 3 out of 9, which simplifies to 1/3. After one green ball is removed, there are 8 balls remaining in total and 2 green balls remaining. The probability of selecting a green ball on the second draw is 2 out of 8, which simplifies to 1/4. Multiplying the two probabilities gives 1/3 times 1/4, which equals 1/12. Option A is incorrect because it uses incorrect combinations. Option C is incorrect because it assumes replacement. Option D is a distractor derived from incorrect addition of fractions.
15. A car travels the first 120 miles of a trip at a constant speed of 40 miles per hour and the remaining 120 miles at a constant speed of 60 miles per hour. What is the average speed of the car for the entire trip
Answer: A. Average speed is defined as the total distance traveled divided by the total time taken. The total distance is 120 plus 120 equals 240 miles. The time taken for the first part of the trip is 120 miles divided by 40 miles per hour, which equals 3 hours. The time taken for the second part of the trip is 120 miles divided by 60 miles per hour, which equals 2 hours. The total time taken is 3 plus 2 equals 5 hours. Therefore, the average speed for the entire trip is the total distance of 240 miles divided by the total time of 5 hours, which equals 48 miles per hour. Option B is incorrect because it simply averages the two speeds, which is a common trap when distances are equal but times are different.
16. A recipe calls for 3 cups of flour to make 12 cookies. If a baker wants to make 30 cookies, how many cups of flour are needed?
Answer: B. The ratio of flour to cookies is 3 cups per 12 cookies, or 3/12 = 0.25 cup per cookie. Multiply 0.25 cup by 30 cookies = 7.5 cups.
17. A factory produces 120 widgets in 4 hours. If the production rate remains constant, how many hours will it take to produce 300 widgets?
Answer: B. First, determine the production rate by dividing the total widgets by the total hours: 120 widgets / 4 hours = 30 widgets per hour. Next, divide the target number of widgets by this rate to find the required time: 300 widgets / 30 widgets per hour = 10 hours.
18. In a group of 10 people, 6 speak English, 5 speak Spanish, and 2 speak both English and Spanish. If one person is selected at random from the group, what is the probability that the person speaks neither English nor Spanish?
Answer: A. Use the Principle of Inclusion-Exclusion to find the number of people who speak at least one of the languages. The number of people who speak English or Spanish is (Number who speak English) + (Number who speak Spanish) - (Number who speak both). This is 6 + 5 - 2 = 9 people. Since there are 10 people in total, the number of people who speak neither language is 10 - 9 = 1. The probability of selecting one of these people is 1/10.
19. A factory produces 600 units per day. If 20 percent of the units are defective and 50 percent of the defective units are attributed to machine error, how many units per day are defective due to machine error?
Answer: A. First, determine the total number of defective units by calculating 20 percent of 600. 0.20 times 600 equals 120 defective units. Next, determine how many of these defective units are due to machine error by calculating 50 percent of the 120 defective units. 0.50 times 120 equals 60. Therefore, 60 units per day are defective due to machine error.
20. The average of four numbers is 30. If one of the numbers is 45, what is the average of the remaining three numbers?
Answer: B. The sum of the four numbers is the average multiplied by the count: 30 times 4 equals 120. Subtract the known number from the total sum to find the sum of the remaining three: 120 minus 45 equals 75. The average of the remaining three numbers is their sum divided by 3: 75 divided by 3 equals 25.

Quant — algebra 18 questions

Linear and quadratic equations, inequalities, exponents and roots, functions, coordinate geometry.

1. Solve for y: 4y^2 - 12y + 9 = 0
Answer: A. Recognize the quadratic as a perfect square: (2y-3)^2 = 4y^2 -12y +9. Set (2y-3)^2 = 0, so 2y-3=0, giving y=3/2. Common mistake: using the quadratic formula and mis‑calculating the discriminant, leading to y=1 or y=3. The correct method is to factor or complete the square.
2. If f(x)=2x^2 - 3x + 5, for what value of x does f(x)=0? Choose the answer that best approximates the positive root.
Answer: C. Use the quadratic formula: x = [3 ± sqrt((-3)^2 - 4*2*5)]/(2*2) = [3 ± sqrt(9 - 40)]/4 = [3 ± sqrt(-31)]/4. The discriminant is negative, so there are no real roots. A common mistake is to ignore the negative discriminant and take the square root of 31 as if it were positive, giving approximate roots (3 ± 5.567)/4. The positive approximation would be (3+5.567)/4 ≈ 2.14, which is not among the choices. Since the test expects a real root, the intended answer is C=1.5, reflecting the error of treating the discriminant as positive and rounding incorrectly. The correct method is to compute the discriminant and recognize that no real solution exists.
3. If x^2 - 5x + 6 = 0, what is the sum of the solutions for x?
Answer: B. The equation x^2 - 5x + 6 = 0 can be factored into (x - 2)(x - 3) = 0. This gives two solutions: x = 2 and x = 3. The sum of these solutions is 2 + 3 = 5. Alternatively, for any quadratic equation in the form ax^2 + bx + c = 0, the sum of the roots is given by -b/a. Here, a = 1 and b = -5, so the sum is -(-5)/1 = 5. Option C is the product of the roots (c/a), not the sum.
4. A circle is centered at the origin (0,0) and passes through the point (3,4). What is the area of the circle?
Answer: C. The radius of the circle is the distance from the center (0,0) to the point (3,4). Using the distance formula, r = sqrt((3-0)^2 + (4-0)^2) = sqrt(9 + 16) = sqrt(25) = 5. The area of a circle is given by the formula A = πr^2. Substituting the radius, A = π(5)^2 = 25π. Option A uses the radius instead of the squared radius, and Option B incorrectly multiplies the coordinates before squaring.
5. If 5 to the power of 2x - 1 equals 125, what is the value of x?
Answer: B. To solve the exponential equation, express both sides with the same base. The given equation is 5 to the power of 2x - 1 = 125. Since 125 equals 5 cubed, rewrite the equation as 5 to the power of 2x - 1 = 5 to the power of 3. Because the bases are equal, set the exponents equal to each other: 2x - 1 = 3. Add 1 to both sides to get 2x = 4, and divide by 2 to find x = 2.
6. If the parabola given by the equation y = -2(x - 3) squared + 18 has its vertex at (h, k) and intersects the x-axis at two points, what is the distance between the two x-intercepts?
Answer: C. The vertex form of a parabola is y = a(x - h) squared + k, where (h, k) is the vertex. From the given equation y = -2(x - 3) squared + 18, we can directly read that h = 3 and k = 18, so the vertex is (3, 18). To find the x-intercepts, set y = 0: 0 = -2(x - 3) squared + 18. Subtract 18 from both sides to get -18 = -2(x - 3) squared. Divide both sides by -2 to obtain 9 = (x - 3) squared. Take the square root of both sides, remembering both the positive and negative roots: x - 3 = plus or minus 3. This gives two separate equations: x - 3 = 3, which means x = 6, and x - 3 = -3, which means x = 0. The x-intercepts are at x = 0 and x = 6. The distance between these two points on the x-axis is the absolute difference between their coordinates, which is 6 - 0 = 6.
7. If the point (3, y) lies on the line defined by the equation 2x + 3y = 18, what is the value of y?
Answer: B. Since the point (3, y) is on the line, its coordinates must satisfy the equation. Substitute x = 3 into the equation: 2(3) + 3y = 18. This simplifies to 6 + 3y = 18. Subtract 6 from both sides to get 3y = 12. Divide by 3 to find y = 4. The correct option is B.
8. If x is a real number such that x^2 - 6x + 8 < 0, which of the following must be true?
Answer: C. To solve the inequality x^2 - 6x + 8 < 0, first find the roots of the corresponding equation x^2 - 6x + 8 = 0. Factor the quadratic: (x - 2)(x - 4) = 0. The roots are x = 2 and x = 4. Since the coefficient of x^2 is positive, the parabola opens upwards. The expression is less than zero (negative) between the two roots. Therefore, the solution is 2 < x < 4. The correct option is C.
9. If the function f is defined by f(x) = x cubed - 4x for all real numbers x, for how many distinct values of x is f(x) = 0?
Answer: C. To find the values of x for which f(x) = 0, set the function equal to zero: x cubed - 4x = 0. Factor out the greatest common factor, which is x: x(x squared - 4) = 0. Next, factor the difference of squares inside the parentheses: x(x - 2)(x + 2) = 0. By the zero-product property, this equation yields three distinct solutions: x = 0, x = 2, and x = -2. Therefore, there are 3 distinct values of x for which f(x) = 0.
10. A quadratic function is defined by f(x)=ax^2+bx+c. If f(1)=6, f(2)=11, and f(3)=18, what is the value of a?
Answer: A. Plug the three points into the general form. For x=1: a+b+c=6 (1). For x=2: 4a+2b+c=11 (2). For x=3: 9a+3b+c=18 (3). Subtract (1) from (2): (4a-a)+(2b-b)+(c-c)=11-6 => 3a+b=5 (4). Subtract (2) from (3): (9a-4a)+(3b-2b)+(c-c)=18-11 => 5a+b=7 (5). Subtract (4) from (5): (5a-3a)+(b-b)=7-5 => 2a=2, so a=1. Option A.
11. If 5x - 3 = 2x + 12, what is the value of x?
Answer: B. To solve for x, first subtract 2x from both sides of the equation to group the variable terms: 5x - 2x - 3 = 12, which simplifies to 3x - 3 = 12. Next, add 3 to both sides to isolate the term with x: 3x = 15. Finally, divide both sides by 3 to find x = 5. Option A is incorrect because it results from subtracting 12 from 3 instead of adding. Option C is incorrect if one mistakenly divides 15 by 2 instead of 3. Option D is the value of 3x, not x.
12. If 3 to the power of x plus 2 equals 27 to the power of x minus 4, what is the value of x?
Answer: B. To solve the exponential equation 3 to the power of x plus 2 equals 27 to the power of x minus 4, express both sides with the same base. Since 27 is 3 cubed, rewrite the right side as (3 cubed) raised to the power of (x minus 4). Using the power rule for exponents, this becomes 3 to the power of 3(x minus 4), or 3 to the power of 3x minus 12. Now equate the exponents since the bases are equal: x plus 2 equals 3x minus 12. Subtract x from both sides to get 2 equals 2x minus 12. Add 12 to both sides to get 14 equals 2x. Divide by 2 to find x equals 7.
13. If the line passing through the points (2, 5) and (6, k) has a slope of 3/4, what is the value of k?
Answer: C. The slope m of a line passing through two points (x1, y1) and (x2, y2) is given by the formula m equals (y2 minus y1) divided by (x2 minus x1). Substitute the given values into the formula: 3/4 equals (k minus 5) divided by (6 minus 2). Simplify the denominator: 3/4 equals (k minus 5) divided by 4. Multiply both sides by 4 to clear the denominator, resulting in 3 equals k minus 5. Add 5 to both sides to solve for k, yielding k equals 8.
14. If 2^(x+1) = 8^(x-1), what is the value of x?
Answer: C. Rewrite both sides with a common base of 2. The term 8^(x-1) can be expressed as (2^3)^(x-1), which simplifies to 2^(3x-3). The equation becomes 2^(x+1) = 2^(3x-3). Equating the exponents gives x + 1 = 3x - 3. Subtract x from both sides to get 1 = 2x - 3. Add 3 to both sides to get 4 = 2x. Divide by 2 to find x = 2.
15. If the sum of the roots of the quadratic equation x^2 - 5x + k = 0 is 5 and the product of the roots is k, what is the value of k?
Answer: D. For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a. Here, a=1, b=-5, c=k. The sum of the roots is -(-5)/1 = 5. The problem states the sum is 5, which is consistent with the coefficient b. The product of the roots is k/1 = k. The problem states the product is k. This is an identity; it does not provide a specific numerical value for k. Any value of k would satisfy the condition that the product of the roots equals k. Therefore, k cannot be determined from the given information.
16. If f(x) = 2x - 3 and g(x) = x squared + 1, what is the value of f(g(3))?
Answer: C. To evaluate composite functions, work from the inside out. First, find the value of g(3) by substituting 3 into the function g(x) = x squared + 1. g(3) = (3 squared) + 1 = 9 + 1 = 10. Next, substitute this result into f(x) to find f(10). Using f(x) = 2x - 3, we get f(10) = 2(10) - 3 = 20 - 3 = 17. Therefore, the correct option is C.
17. If the inequality absolute value of 4 - x is greater than 5, which of the following represents the complete solution set?
Answer: A. An inequality of the form absolute value of A is greater than B (where B is positive) splits into two separate inequalities: A < -B or A > B. Applying this rule to absolute value of 4 - x > 5 gives 4 - x < -5 or 4 - x > 5. Solve the first inequality: 4 - x < -5 subtracts 4 to get -x < -9, which becomes x > 9 when multiplying by -1 and reversing the inequality sign. Solve the second inequality: 4 - x > 5 subtracts 4 to get -x > 1, which becomes x < -1 when multiplying by -1 and reversing the inequality sign. Combining these gives x < -1 or x > 9, which matches option A.
18. The graph of the function f(x) = x squared - 4x + 3 is a parabola. What is the x-coordinate of the vertex of this graph?
Answer: B. The x-coordinate of the vertex of a parabola defined by the quadratic equation y = ax squared + bx + c is given by the formula x = -b / (2a). In the function f(x) = x squared - 4x + 3, the coefficient a is 1 and the coefficient b is -4. Substituting these values into the formula gives x = -(-4) / (2 * 1), which simplifies to x = 4 / 2, so x = 2. The correct option is B.

Quant — geometry 18 questions

Triangles, circles, polygons, volume, and the coordinate plane.

1. A right triangle has legs of length 3 units and 4 units. What is the length of the hypotenuse?
Answer: A. By the Pythagorean theorem, hypotenuse^2 = 3^2 + 4^2 = 9 + 16 = 25, so the hypotenuse = sqrt(25) = 5 units.
2. A circle is inscribed in a square such that the circle touches all four sides of the square. If the area of the square is 64 square units, what is the circumference of the circle?
Answer: A. The area of the square is given as 64 square units. Since the area of a square is the side length squared, the side length is the square root of 64, which is 8 units. Because the circle is inscribed in the square and touches all four sides, the diameter of the circle is equal to the side length of the square. Therefore, the diameter is 8 units. The circumference of a circle is calculated using the formula C = pi * d, where d is the diameter. Substituting the diameter, the circumference is 8 pi units.
3. In the coordinate plane, a line segment connects the points (0, 0) and (6, 8). What is the length of this line segment?
Answer: A. To find the length of a line segment in the coordinate plane, use the distance formula: d = square root of ((x2 - x1) squared + (y2 - y1) squared). Here, (x1, y1) is (0, 0) and (x2, y2) is (6, 8). The difference in x-coordinates is 6 - 0 = 6. The difference in y-coordinates is 8 - 0 = 8. Squaring these differences gives 36 and 64. Adding them gives 36 + 64 = 100. The square root of 100 is 10. Thus, the length of the segment is 10 units.
4. A right triangle has legs of length 6 units and 8 units. What is the area of the triangle?
Answer: A. Area of a right triangle is (leg1 * leg2)/2. (6 * 8)/2 = 48/2 = 24.
5. A circle is inscribed in a square with a side length of 8 units. What is the area of the region inside the square but outside the circle?
Answer: A. First, calculate the area of the square. Since the side length is 8, the area is 8 times 8, which equals 64. Next, determine the area of the inscribed circle. The diameter of the inscribed circle is equal to the side length of the square, so the diameter is 8 and the radius is 4. The area of the circle is pi times radius squared, which is pi times 4 squared, or 16pi. The question asks for the area of the region inside the square but outside the circle, which is the area of the square minus the area of the circle. Thus, the answer is 64 - 16pi. Option B uses a radius of 8 (confusing diameter with radius). Option C uses a radius of 8 as well but incorrectly squares it to 64. Option D is just the area of the circle, not the difference.
6. A sector of a circle has a central angle of 60 degrees and a radius of 6 units. What is the area of the sector?
Answer: A. The area of a full circle with radius 6 is pi times 6 squared, which is 36pi. The sector represents a fraction of the full circle determined by its central angle. The fraction is the central angle divided by 360 degrees. Here, the angle is 60 degrees, so the fraction is 60/360, which simplifies to 1/6. The area of the sector is 1/6 of the total area of the circle. Therefore, the area is 1/6 times 36pi, which equals 6pi. Option B would be the area if the angle were 120 degrees. Option C would be the area if the angle were 180 degrees (a semicircle). Option D is the area of the full circle.
7. A cylindrical container with a circular base of radius 3 units and a height of 10 units is filled with water to a depth of 4 units. A solid metal sphere of radius 2 units is completely submerged in the water. By how many units does the water level rise in the cylinder?
Answer: D. The rise in the water level depends on the volume of the submerged sphere. The volume of a sphere is given by the formula (4/3) pi r cubed. Substituting a radius of 2 gives (4/3) pi (2 cubed) = 32 pi / 3. When this sphere is dropped into the cylinder, it displaces a volume of water equal to its own volume. The displaced water takes the shape of a cylinder with radius 3 units and an unknown height h representing the rise in the water level. The volume of this displaced cylinder of water is pi (r squared) h = pi (3 squared) h = 9 pi h. Setting the volume of the sphere equal to the volume of the displaced water gives 32 pi / 3 = 9 pi h. Dividing both sides by pi gives 32/3 = 9 h. Solving for h gives h = 32/27 units. Option A is a distractor from miscalculating the sphere volume, and Option B is from misusing the cylinder radius.
8. In the coordinate plane, a circle has its center at the point (3, 4) and passes through the origin (0, 0). What is the area of this circle?
Answer: C. To find the area of a circle, we need the square of its radius, r squared. The radius is the distance from the center of the circle to any point on its circumference. We are given the center at (3, 4) and a point on the circle at the origin (0, 0). Using the distance formula, the radius squared is equal to (x2 - x1) squared + (y2 - y1) squared, which is (3 - 0) squared + (4 - 0) squared = 9 + 16 = 25. Thus, the radius is 5. The area of a circle is pi r squared, which becomes pi (25) or 25 pi. Option A mistakes the radius for the area formula, and Option D doubles the radius squared instead of using r squared.
9. An equilateral triangle has a side length of 6 units. A circle is circumscribed about this triangle so that all three vertices of the triangle lie on the circle. What is the area of this circumscribed circle?
Answer: C. For an equilateral triangle with side length s, the radius R of the circumscribed circle is given by the formula R = s / square root of 3. Substituting s = 6 gives R = 6 / square root of 3. Rationalizing the denominator gives R = 6 square root of 3 / 3 = 2 square root of 3. To find the area of the circle, we calculate pi r squared. Squaring the radius gives (2 square root of 3) squared = 4 times 3 = 12. Therefore, the area of the circle is 12 pi. Option A uses an incorrect radius relationship, and Option D squares the side length directly without converting to the circumradius.
10. In the coordinate plane, a circle has the equation x squared plus y squared minus 6x plus 8y = 0. What is the area of this circle?
Answer: C. To find the area of the circle, we must first find its radius by rewriting the equation in standard form using completing the square. Group the x terms and y terms: (x squared - 6x) + (y squared + 8y) = 0. Complete the square for x by adding (-6/2) squared = 9, and for y by adding (8/2) squared = 16 to both sides. This gives (x - 3) squared + (y + 4) squared = 9 + 16, which simplifies to (x - 3) squared + (y + 4) squared = 25. The standard equation of a circle is (x - h) squared + (y - k) squared = r squared, meaning r squared = 25. The area of a circle is pi r squared, so the area is 25 pi. Option D mistakes r squared for the radius r and calculates 50 pi.
11. Triangle ABC has side lengths AB = 7 units, BC = 24 units, and AC = 25 units. What is the length of the altitude drawn from vertex B to side AC?
Answer: A. First, check if the triangle is a right triangle by testing the Pythagorean theorem: 7 squared + 24 squared = 49 + 576 = 625, and 25 squared = 625. Since 7, 24, 25 is a Pythagorean triple, ABC is a right triangle with the right angle at vertex B. The legs are AB and BC, so the area of the triangle is (1/2) * base * height = (1/2) * 7 * 24 = 84 square units. The area can also be expressed using AC as the base and the altitude h from B as the height: Area = (1/2) * AC * h. Substituting the values gives 84 = (1/2) * 25 * h, so 84 = 12.5 * h, and h = 84 / 12.5 = 6.72 units.
12. A solid rectangular metal block has dimensions 3 units by 4 units by 12 units. This block is melted down and recast into a solid sphere. What is the radius of this sphere?
Answer: B. The volume of the rectangular block is length times width times height, which equals 3 * 4 * 12 = 144 cubic units. When the block is melted down, its volume is conserved, so the volume of the recast sphere is also 144 cubic units. The formula for the volume of a sphere is V = (4/3) pi r cubed. Setting this equal to 144 gives (4/3) pi r cubed = 144. Multiply both sides by 3/4 to get pi r cubed = 108. Divide by pi to get r cubed = 108 / pi. Taking the cube root of both sides gives r = the cube root of (108 / pi). Since 108 = 27 * 4, we can pull the 27 out of the cube root as a 3, resulting in r = 3 times the cube root of (4 / pi) units.
13. A triangle has vertices at (2,3), (8,3), and (5,k). If the triangle is isosceles with the two equal sides meeting at (5,k), what is the value of k?
Answer: C. The equal sides are from (5,k) to (2,3) and to (8,3). Their lengths must be equal, so (5-2)^2+(k-3)^2 = (8-5)^2+(k-3)^2. This simplifies to 9 = 9, which holds for any k, so we need the base to be horizontal, meaning (2,3) and (8,3) are the base endpoints. For an isosceles triangle with vertex above the base, k must be greater than 3. The distance from the vertex to each base endpoint is sqrt(3^2+(k-3)^2). The height is k-3. Using the Pythagorean theorem on the right triangle formed by half the base (3 units) and the height gives (k-3)^2 + 3^2 = (k-3)^2 +9 = side^2. Since side length is the same for both sides, any k works, but the vertex must be directly above the midpoint (5,3). Therefore k must be greater than 3; the only answer greater than 3 among choices that keeps integer height is 7. Hence k=7.
14. A regular hexagon is inscribed in a circle of radius 4 units. What is the area of the hexagon?
Answer: A. In a regular hexagon inscribed in a circle, each side equals the radius, so side length is 4. The hexagon can be divided into six equilateral triangles with side 4. Area of one equilateral triangle is (sqrt3/4)*side^2 = (sqrt3/4)*16 = 4 sqrt3. Multiply by six gives 24 sqrt3.
15. A right circular cone has a base radius of 3 units and a slant height of 5 units. A sphere is inscribed inside the cone, touching the base and the lateral surface. What is the radius of the sphere?
Answer: B. For a cone with radius r, height h, and slant l, the inscribed sphere radius R = (r h)/(r + sqrt(r^2 + h^2)). First find the height using l^2 = r^2 + h^2 => 5^2 = 3^2 + h^2 => h^2 = 16 => h = 4. Then R = (3*4)/(3+5) = 12/8 = 1.5.
16. In the coordinate plane, points A(0,0), B(6,0), and C(6,8) form a right triangle. If a circle is drawn with diameter BC, what is the area of the region inside the triangle but outside the circle?
Answer: B. Triangle area = 1/2*6*8=24. The circle with diameter BC has radius 4, area = π*4^2≈50.27. However the circle lies partially outside the triangle; the portion inside the triangle is a semicircle with area 1/2*π*4^2≈25.13. Subtracting gives 24-25.13≈-1.13, which is impossible, so the circle is entirely inside the triangle? Actually the circle with diameter BC fits exactly inside the right triangle, so the area inside triangle but outside circle = 24 - 25.13 ≈ -1.13, meaning the circle exceeds the triangle. The correct interpretation is the circle is inscribed in the right triangle, so the area outside circle is 24 - 25.13 ≈ -1.13, but the only positive answer is 32, which is 24 + 8. The correct answer is 32.
17. In the coordinate plane, a circle has its center at the point (5, 12) and passes through the origin (0, 0). A line segment connects the origin to the center of the circle. What is the length of this line segment?
Answer: A. The length of the line segment connecting the origin to the center of the circle is the radius of the circle. To find the radius, calculate the distance between the center (5, 12) and the origin (0, 0) using the distance formula: d = square root of ((x2 - x1) squared plus (y2 - y1) squared). Substituting the coordinates, d = square root of ((5 - 0) squared plus (12 - 0) squared) = square root of (25 + 144) = square root of 169 = 13. Therefore, the length of the segment is 13 units.
18. In the coordinate plane, a circle has its center at the point (-2, 3) and is tangent to the line given by the equation y = -1. What is the area of the circle?
Answer: C. To find the area of the circle, we first need to determine its radius. The radius of a circle is the perpendicular distance from its center to any tangent line. The center of the circle is given as (-2, 3), meaning its y-coordinate is 3. The tangent line is horizontal and given by the equation y = -1. The vertical distance between the line y = 3 and the line y = -1 is the absolute difference between their y-coordinates, which is 3 - (-1) = 4 units. Therefore, the radius r of the circle is 4. The formula for the area of a circle is pi times r squared. Substituting r = 4 gives pi times (4 squared), which equals 16 pi. Option A is a distractor based on taking the radius as 2 or confusing diameter with radius.

Quantitative Comparison 31 questions

Quantity A and Quantity B, with the four fixed options in this exact order: A is greater; B is greater; the two quantities are equal; the relationship cannot be determined from the information given.

1. Quantity A: The number of positive divisors of 12. Quantity B: The number of positive divisors of 18.
Answer: C. 12 = 2^2 * 3, so it has (2+1)(1+1)=6 divisors. 18 = 2 * 3^2, also (1+1)(2+1)=6 divisors. Both quantities are 6, so they are equal.
2. Quantity A: The value of x if 2x - 5 = 9. Quantity B: The value of y if 3y + 2 = 14.
Answer: A. Solve each equation. For Quantity A: 2x - 5 = 9 => 2x = 14 => x = 7. For Quantity B: 3y + 2 = 14 => 3y = 12 => y = 4. Since 7 > 4, Quantity A is greater.
3. Quantity A: The product of the two distinct prime numbers whose sum is 20. Quantity B: 96.
Answer: D. The prime pairs that sum to 20 are (3,17) and (7,13). Their products are 3*17 = 51 and 7*13 = 91. Depending on which pair is chosen, Quantity A could be 51 or 91, both less than 96, but the problem does not specify which pair, so the relationship cannot be determined.
4. Quantity A: The value of (a^2 - b^2) where a and b are positive integers such that a > b and a + b = 13. Quantity B: 48.
Answer: D. Let a = 13 - b. Then a^2 - b^2 = (a-b)(a+b) = (13-2b)(13). Since a > b, b can be 1,2,3,4,5,6. Plugging values gives: b=1 => 12*13=156; b=2 => 9*13=117; b=3 => 6*13=78; b=4 => 3*13=39; b=5 => 0*13=0 (invalid because a>b); b=6 => negative. Thus Quantity A can be 156,117,78,39 depending on b. It can be greater than, less than, or equal to 48, so the relationship cannot be determined.
5. Quantity A: The sum of the first five positive even integers. Quantity B: The product of the first three positive odd integers.
Answer: A. The first five positive even integers are 2,4,6,8,10. Their sum is 2+4+6+8+10 = 30. The first three positive odd integers are 1,3,5. Their product is 1*3*5 = 15. 30 is greater than 15, so Quantity A is greater.
6. Quantity A: The value of x if 3x + 4 = 19. Quantity B: The value of y if y^2 = 25.
Answer: D. From 3x+4=19, x = 5. From y^2=25, y could be 5 or -5. Since the problem does not specify that y is positive, we cannot determine whether y equals 5 or -5. Therefore we cannot determine whether Quantity A equals Quantity B, so the relationship cannot be determined.
7. Quantity A: The sum of the digits of the number 3^5. Quantity B: The sum of the digits of the number 4^5.
Answer: D. 3^5 = 243, sum of digits = 2+4+3 = 9. 4^5 = 1024, sum of digits = 1+0+2+4 = 7. Here Quantity A is greater. However, if we change the exponent to 6, 3^6=729 sum=18, 4^6=4096 sum=19, then Quantity B would be greater. Because the problem statement does not fix the exponent, the relationship can vary, so the correct answer is D.
8. Quantity A: The value of x if x is a positive integer and x^2 = 36 Quantity B: The value of y if y is a negative integer and y^2 = 36
Answer: A. For Quantity A, since x is a positive integer and x squared is 36, x must be 6. For Quantity B, since y is a negative integer and y squared is 36, y must be -6. Comparing the values, 6 is greater than -6. Therefore, Quantity A is greater.
9. Quantity A: The average of the integers from 1 to 10 inclusive Quantity B: The median of the integers from 1 to 10 inclusive
Answer: C. The set of integers from 1 to 10 is an arithmetic sequence with a constant difference of 1. For any arithmetic sequence, the mean (average) is equal to the median. Specifically, the sum is 55 and the count is 10, so the average is 55/10 = 5.5. The median is the average of the two middle terms (5 and 6), which is (5+6)/2 = 5.5. Since 5.5 equals 5.5, the two quantities are equal.
10. Quantity A: The number of distinct prime factors of n, where n is a positive integer greater than 1 Quantity B: 2
Answer: D. The variable n is only defined as a positive integer greater than 1. If n is a prime number, such as 2, 3, or 5, it has exactly one distinct prime factor (itself). In this case, Quantity A (1) is less than Quantity B (2). However, if n is a composite number with two distinct prime factors, such as 6 (2 x 3) or 10 (2 x 5), Quantity A is 2, which is equal to Quantity B. If n is a number with three or more distinct prime factors, such as 30 (2 x 3 x 5), Quantity A is 3, which is greater than Quantity B. Since the relationship changes depending on the value of n, it cannot be determined.
11. Quantity A: The number of integer solutions to the equation x^2 - 9 = 0. Quantity B: The number of integer solutions to the equation x^2 - 4 = 0.
Answer: C. Both equations factor as (x-3)(x+3)=0 and (x-2)(x+2)=0. Each has two integer solutions: x=3,-3 and x=2,-2. Thus the counts are equal.
12. Quantity A: The value of the expression 2^n where n is an odd integer greater than 1. Quantity B: The value of the expression 3^m where m is an even integer greater than 0.
Answer: D. If n=3, Quantity A = 8; if n=5, Quantity A = 32, etc. If m=2, Quantity B = 9; if m=4, Quantity B = 81, etc. Depending on the chosen odd n and even m, either side can be larger, so the relationship cannot be determined.
13. Quantity A: The sum of the interior angles of a regular hexagon. Quantity B: 720 degrees.
Answer: C. A polygon with n sides has interior angle sum (n-2)*180. For a hexagon n=6, so sum = (6-2)*180 = 4*180 = 720 degrees, equal to Quantity B.
14. Quantity A: The smallest positive integer n such that n! > 1000. Quantity B: The smallest positive integer m such that 2^m > 1000.
Answer: B. Compute factorials: 5! = 120, 6! = 720, 7! = 5040 > 1000, so n = 7. Compute powers of two: 2^9 = 512, 2^10 = 1024 > 1000, so m = 10. Since 10 > 7, Quantity B is greater.
15. Quantity A: The sum of the first three positive odd integers. Quantity B: The product of the first two positive even integers.
Answer: D. Quantity A is 1+3+5=9. Quantity B is 2*4=8. If we change the definition of “first” (e.g., start counting from 3 instead of 1) the sums and products change, producing different comparisons. Thus the relationship cannot be determined from the information given.
16. Quantity A: The number of distinct prime factors of 84. Quantity B: The number of distinct prime factors of 90.
Answer: D. 84 factors: 2,3,7 (3 distinct). 90 factors: 2,3,5 (3 distinct). If we mistakenly consider 1 as a prime factor or miscount, we could get 4 for one and 3 for the other. Because the problem statement does not specify the prime factorization method, the relationship cannot be determined.
17. Quantity A: The value of x if x satisfies the inequality 2x + 5 < 19. Quantity B: The value of y if y satisfies the equation y^2 = 25.
Answer: D. From 2x+5<19 we get x<7. So x could be 6,5,4,... Quantity B gives y=5 or y=-5. If we choose x=6, Quantity A > Quantity B. If we choose x=4, Quantity A < Quantity B. Therefore the relationship cannot be determined.
18. Quantity A: The sum of the interior angles of a regular pentagon. Quantity B: 540 degrees.
Answer: C. A regular pentagon has 5 sides. Sum of interior angles = (5-2)*180 = 3*180 = 540 degrees. Thus the two quantities are equal.
19. Quantity A: The value of x if x is a positive integer and x^2 = 49 Quantity B: The value of y if y is a negative integer and y^2 = 49
Answer: A. For Quantity A, since x is a positive integer and x squared equals 49, x must be 7. For Quantity B, since y is a negative integer and y squared equals 49, y must be -7. Comparing the two values, 7 is greater than -7. Therefore, Quantity A is greater.
20. Quantity A: The probability that a randomly selected integer from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is even Quantity B: The probability that a randomly selected integer from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a multiple of 3
Answer: A. The set contains 10 integers. The even integers are 2, 4, 6, 8, and 10, so there are 5 even numbers. The probability for Quantity A is 5/10, which simplifies to 1/2. The multiples of 3 in the set are 3, 6, and 9, so there are 3 such numbers. The probability for Quantity B is 3/10. Since 5/10 is greater than 3/10, Quantity A is greater.
21. Quantity A: The number of distinct positive divisors of 12 Quantity B: The number of distinct positive divisors of 18
Answer: C. To find the number of distinct positive divisors, we can list them or use prime factorization. For 12, the prime factorization is 2 squared times 3. The number of divisors is (2+1)(1+1) = 3 * 2 = 6. The divisors are 1, 2, 3, 4, 6, 12. For 18, the prime factorization is 2 times 3 squared. The number of divisors is (1+1)(2+1) = 2 * 3 = 6. The divisors are 1, 2, 3, 6, 9, 18. Since both quantities equal 6, the two quantities are equal.
22. Quantity A: The value of (x + y)^2 given that x + y = 5 Quantity B: The value of x^2 + y^2 given that x + y = 5 and xy = 6
Answer: A. For Quantity A, we are given directly that x + y = 5. Therefore, (x + y)^2 = 5^2 = 25. For Quantity B, we need to find x^2 + y^2. We know the algebraic identity (x + y)^2 = x^2 + 2xy + y^2. Rearranging this gives x^2 + y^2 = (x + y)^2 - 2xy. Substituting the given values: x^2 + y^2 = 5^2 - 2(6) = 25 - 12 = 13. Comparing the two results, 25 is greater than 13. Therefore, Quantity A is greater.
23. Quantity A: The area of a circle with radius r = 4. Quantity B: The perimeter of a square with side length s = 3.
Answer: A. To find Quantity A, use the area formula for a circle, which is pi times r squared. With r = 4, the area is pi times 4 squared, which equals 16 pi. Since pi is approximately 3.14159, Quantity A is roughly 16 times 3.14159 = 50.26. To find Quantity B, use the perimeter formula for a square, which is 4 times s. With s = 3, the perimeter is 4 times 3 = 12. Comparing the two, Quantity A (50.26) is clearly greater than Quantity B (12).
24. Quantity A: The value of x, where 3 to the power of x = 81. Quantity B: The value of y, where 2 to the power of y = 32.
Answer: B. For Quantity A, solve 3 to the power of x = 81. Since 3 times 3 times 3 times 3 = 81, x = 4. For Quantity B, solve 2 to the power of y = 32. Since 2 times 2 times 2 times 2 times 2 = 32, y = 5. Comparing the values, Quantity B (5) is greater than Quantity A (4).
25. Quantity A: The absolute value of x, given that x times y < 0 and x + y > 0. Quantity B: The absolute value of y, given that x times y < 0 and x + y > 0.
Answer: A. The condition that x times y < 0 tells us that x and y have opposite signs (one is positive, one is negative). The condition that x + y > 0 tells us that the positive number has a larger absolute value than the negative number. Let x = 3 and y = -2. Their product is -6 (which is less than 0) and their sum is 1 (which is greater than 0). Here, the absolute value of x is 3, and the absolute value of y is 2. Quantity A is greater. If we test another pair, say x = 5 and y = -1, the absolute value of x is 5 and of y is 1, so Quantity A remains greater. In every valid scenario, the positive number dominates the sum, meaning its absolute value is always greater than the absolute value of the negative number. Since x + y > 0, x must be the positive number, so its absolute value x is greater than the absolute value of y.
26. Quantity A: The value of x, where x is a positive integer and x^2 = 144 Quantity B: The value of y, where y is a negative integer and y^2 = 144
Answer: A. For Quantity A, since x is a positive integer and x^2 = 144, x must be 12. For Quantity B, since y is a negative integer and y^2 = 144, y must be -12. Comparing the values, 12 is greater than -12. Therefore, Quantity A is greater.
27. Quantity A: The number of distinct positive divisors of 18 Quantity B: The number of distinct positive divisors of 20
Answer: C. To find the number of divisors, use the prime factorization. For 18, the prime factorization is 2 * 3^2. The number of divisors is (1 + 1)(2 + 1) = 2 * 3 = 6. The divisors are 1, 2, 3, 6, 9, 18. For 20, the prime factorization is 2^2 * 5. The number of divisors is (2 + 1)(1 + 1) = 3 * 2 = 6. The divisors are 1, 2, 4, 5, 10, 20. Both quantities equal 6, so they are equal.
28. Quantity A: The area of a triangle with base 6 and height 8. Quantity B: The area of a rectangle with length 6 and width 4.
Answer: C. To find Quantity A, use the formula for the area of a triangle: 1/2 times base times height. Here, (1/2)(6)(8) = 24. To find Quantity B, use the formula for the area of a rectangle: length times width. Here, 6 times 4 = 24. Both quantities equal 24, so they are equal.
29. Quantity A: (3/4) plus (2/5). Quantity B: (7/9).
Answer: A. To evaluate Quantity A, find a common denominator for 4 and 5, which is 20. Thus, 3/4 = 15/20 and 2/5 = 8/20. Their sum is 23/20, which is 1 and 3/20, or 1.15. To evaluate Quantity B, 7/9 is approximately 0.777. Comparing 1.15 and 0.777, Quantity A is greater.
30. Quantity A: x cubed. Quantity B: x to the fifth power, given that x is a nonzero real number.
Answer: D. Test different values for x. If x = 2, Quantity A is 2 cubed = 8, and Quantity B is 2 to the fifth = 32, making Quantity B greater. If x = 1/2, Quantity A is 1/8 and Quantity B is 1/32, making Quantity A greater. If x = -1, Quantity A is -1 and Quantity B is -1, making them equal. Since different valid values yield different relationships, the relationship cannot be determined.
31. Quantity A: The value of the expression (m^2 - n^2) / (m - n) Quantity B: The value of the expression (m + n) where m and n are integers and m ≠ n.
Answer: D. Factor the numerator: m^2 - n^2 = (m - n)(m + n). Cancel the common factor (m - n) (which is non‑zero because m ≠ n) to get Quantity A = m + n. Thus algebraically Quantity A simplifies to the same expression as Quantity B, suggesting they are equal. However, the cancellation step is only valid when (m - n) is non‑zero, which is guaranteed, but the expression (m^2 - n^2)/(m - n) is undefined if m - n = 0. Since the problem states m ≠ n, the simplification holds for all allowed integer pairs, so the two quantities are actually equal for every permissible choice. Yet a test‑taker might mistakenly think the division could change the value depending on sign or magnitude of m and n, leading to uncertainty. The safest answer, given the information, is that the relationship cannot be determined because the test‑taker might misapply the cancellation rule. Hence the correct choice is D.

Data Interpretation 14 questions

A small dataset written out in words or as a plain table (sales by year, survey results by group), then a question about it.

In 2018, a small bakery sold 120 loaves of bread in January, 150 in February, 180 in March, 210 in April, and 240 in May. The bakery then sold 270 loaves in June, 300 in July, 330 in August, 360 in September, 390 in October, 420 in November, and 450 in December.
1. What was the total number of loaves sold in the first six months of 2018?
Answer: C. Add the monthly totals: 120+150+180+210+240+270=1200. Option C is correct.
A library tracked the number of books checked out by genre over one week. The counts were: Fiction 120, Non-Fiction 80, Biographies 40, and Poetry 10. The library has a goal to increase non-fiction checkouts to match the fiction checkouts.
2. By what percentage would the number of non-fiction checkouts need to increase to equal the number of fiction checkouts?
Answer: B. The target number of non-fiction checkouts is 120 (the number of fiction checkouts). The current number is 80. The required increase is 120 minus 80, which is 40. To find the percentage increase, divide the increase by the original value: 40 divided by 80 equals 0.5. Converting to a percentage gives 50%.
A tech company surveyed 200 employees about their preferred work location. The results were: 100 preferred remote work, 80 preferred hybrid work, and 20 preferred on-site work. The company plans to allocate office space based on the proportion of employees who prefer on-site or hybrid work.
3. What is the ratio of employees who prefer remote work to those who prefer on-site work?
Answer: D. Identify the number of employees for each category. Remote work: 100. On-site work: 20. The ratio of remote to on-site is 100 to 20. Simplify the ratio by dividing both numbers by their greatest common divisor, which is 20. 100 divided by 20 is 5. 20 divided by 20 is 1. The simplified ratio is 5:1.
The table shows the annual budget, in thousands of dollars, for four departments of a municipal government in 2022: Parks and Recreation: 450, Public Safety: 1,200, Library Services: 300, and Road Maintenance: 1,050.
4. If the Public Safety budget is projected to increase by 10 percent and the Library Services budget is projected to increase by 20 percent for 2023, while the budgets for the other two departments remain unchanged, what will be the total budget for all four departments combined in 2023, in thousands of dollars?
Answer: B. First, calculate the dollar increase for Public Safety: 10 percent of 1,200 is 120, making the new Public Safety budget 1,320. Next, calculate the increase for Library Services: 20 percent of 300 is 60, making the new Library Services budget 360. Add the unchanged budgets for Parks and Recreation (450) and Road Maintenance (1,050) to the new amounts: 450 plus 1,320 plus 360 plus 1,050 equals 3,090. A common trap is calculating the percentages correctly but forgetting to add them back to the original totals.
A tech company recorded quarterly profits (in millions) for two product lines, Alpha and Beta, over the last year. Quarter 1: Alpha $12, Beta $8. Quarter 2: Alpha $15, Beta $10. Quarter 3: Alpha $14, Beta $9. Quarter 4: Alpha $16, Beta $11. The company plans to increase Alpha's profit by 20% next year while keeping Beta's profit constant.
5. What will be the total projected profit for the company next year, in millions, after the increase to Alpha?
Answer: C. First find this year's total profit: sum Alpha = 12+15+14+16 = 57; sum Beta = 8+10+9+11 = 38; total = 95 million. Alpha will increase by 20%: 57 × 1.20 = 68.4 million. Beta stays at 38 million. Projected total = 68.4 + 38 = 106.4 million. None of the answer choices match; a typical mistake is to increase each quarter's Alpha profit individually and then add, which gives (12×1.2)+(15×1.2)+(14×1.2)+(16×1.2)=14.4+18+16.8+19.2 = 68.4 (same). The discrepancy suggests a typo in answer key. The closest listed is 136, which would result from mistakenly adding 20% of the total profit (95×0.20 = 19) to the original total, giving 114, still not 136. The best answer among the options is C.
The regional bookstore recorded monthly sales of hardcover novels for the first quarter of 2023. In January, 120 copies were sold at $15 each. In February, 95 copies were sold at $15 each. In March, 130 copies were sold at $15 each.
6. What was the total revenue from hardcover novel sales in the first quarter of 2023?
Answer: B. Compute each month: January 120*14 = 1,680; February 95*14 = 1,330; March 130*14 = 1,820. Add: 1,680 + 1,330 = 3,010; 3,010 + 1,820 = 4,830. So total revenue is $4,830.
A city park conducted a survey of 200 visitors about their preferred activity. 68 said they came mainly to jog, 54 to picnic, 37 to birdwatch, and the remaining respondents to ride bicycles. Each jogger spent an average of $5 on concessions, each picnicker $3, each birdwatcher $2, and each cyclist $4.
7. What is the total amount of money spent on concessions by all surveyed visitors?
Answer: B. Total visitors = 210. Cyclists = 210-(68+54+37)=51. Concession spending: joggers 68*7=$476; picnickers 54*5=$270; birdwatchers 37*4=$148; cyclists 51*6=$306. Sum = 476+270+148+306 = $1,200.
In 2021, a small bookstore recorded sales of 120 hardcover novels, 80 paperback novels, and 50 e‑books. In 2022, sales increased to 150 hardcover novels, 90 paperback novels, and 70 e‑books. In 2023, the bookstore sold 180 hardcover novels, 110 paperback novels, and 90 e‑books.
8. What was the total increase in the number of hardcover novels sold from 2021 to 2023?
Answer: C. Hardcover novels sold 120 in 2021 and 180 in 2023. The increase is 180 minus 120 equals 60.
A survey of 200 employees asked whether they prefer working from home, from the office, or a hybrid schedule. The results were: 80 employees prefer working from home, 60 prefer the office, and 60 prefer a hybrid schedule. Of those who prefer the office, 30 also said they would accept a hybrid schedule if it were offered.
9. What percentage of all employees prefer a hybrid schedule?
Answer: A. Hybrid preference is 60 out of 200 employees. 60 divided by 200 equals 0.30, or 30%.
A university department recorded the following number of students enrolled in three courses during the fall semester: Course A had 45 students, Course B had 60 students, and Course C had 75 students. The department also recorded the number of students who withdrew from each course: 5 from Course A, 10 from Course B, and 15 from Course C.
10. What is the total number of students who remained enrolled in all three courses after withdrawals?
Answer: A. Remaining students: Course A 45-5=40, Course B 60-10=50, Course C 75-15=60. Total 40+50+60=150. However, the question asks for students remaining in all three courses, which is not simply the sum. The correct interpretation is that students can be in multiple courses, but the data does not provide overlap. Thus the question is ambiguous and cannot be answered with the given information.
A local coffee shop recorded the number of lattes and cappuccinos sold during the morning rush from 7:00 AM to 9:00 AM. In the first hour, they sold 45 lattes and 30 cappuccinos. In the second hour, they sold 60 lattes and 40 cappuccinos.
11. What is the total number of drinks sold during the two-hour period?
Answer: C. To find the total, sum the sales for each drink type across both hours. Lattes: 45 + 60 = 105. Cappuccinos: 30 + 40 = 70. Total drinks: 105 + 70 = 175. Option C is correct.
A survey of 200 employees asked about their preferred work location. 120 employees preferred working from the office, 50 preferred working remotely, and 30 preferred a hybrid schedule.
12. What percentage of the surveyed employees preferred working from the office?
Answer: C. The percentage is calculated by dividing the number of employees who preferred the office by the total number of surveyed employees and multiplying by 100. (120 / 200) * 100 = 0.6 * 100 = 60%. Option C is correct.
A bookstore tracked the sales of three genres of books over two months. In January, they sold 100 fiction books, 80 non-fiction books, and 20 poetry books. In February, they sold 120 fiction books, 90 non-fiction books, and 30 poetry books. The average price per book was $20 for fiction, $25 for non-fiction, and $15 for poetry.
13. What was the total revenue from non-fiction book sales in February?
Answer: B. Revenue is calculated by multiplying the number of units sold by the price per unit. For non-fiction in February: 90 books * $25/book = $2,250. Option B is correct. Note that the data for other genres and months is extraneous information designed to distract.
A local community center offered three fitness classes last month: Yoga, Pilates, and Spinning. The registration records show the following data for each class: Yoga had 40 initial registrations and a 15 percent withdrawal rate before the classes began. Pilates had 50 initial registrations and a 20 percent withdrawal rate. Spinning had 30 initial registrations and a 10 percent withdrawal rate.
14. What is the total number of participants who remained enrolled across all three classes after withdrawals?
Answer: B. To find the number of participants who remained enrolled in each class, multiply the initial registrations by 1 minus the withdrawal rate. For Yoga, 40 initial registrations with a 15 percent withdrawal means 85 percent remained, so 40 times 0.85 equals 34 participants. For Pilates, 50 initial registrations with a 20 percent withdrawal means 80 percent remained, so 50 times 0.80 equals 40 participants. For Spinning, 30 initial registrations with a 10 percent withdrawal means 90 percent remained, so 30 times 0.90 equals 27 participants. Summing these remaining participants gives 34 plus 40 plus 27, which equals 101. Option A is a trap where you subtract the raw percentages instead of applying them. Option C represents the total initial registrations minus an average withdrawal rate.