CATPast year paperFree to attempt

CAT 2025 Slot 1 question paper with answer key

This is the complete CAT 2025 Slot 1 question paper with answer key and solutions — 68 questions across VARC, DILR, QA, 2h with sectional timers. Three sequential sections with sectional timers. MCQ negative marking; TITA has none. You can attempt this paper free on MBACracked under exam-accurate timing and unlock topic-wise analytics after you finish.

Ready to attempt this paper?

Reading the paper is free. Attempt it under timed exam conditions to get your estimated percentile, topic-wise accuracy, and pacing analysis.

Sign up free to attempt under real exam timing and get your percentile breakdown.

VARC(24 questions)

Q1Verbal Ability·Sentence Placement

The given sentence is missing in the paragraph below. Decide where it best fits among the options 1, 2, 3, or 4 indicated in the paragraph.

"Everything is old-world, traditional techniques from Mexico," Ava emphasizes. The sisters embrace the ways their great-grandfather built and repaired instruments. (1) When crafting a Mexican guitarrón used in mariachi music, they use tacote wood for the top of the instrument. Once the wood is cut, they carve the neck and heel from a single block using tools like hand saws, chisels and sandpaper rather than modern power tools and believe that this traditional method improves the tone of the instrument. (2) Their store has a three-year waitlist for instruments that take months to create. (3) The family's artisanship has attracted stars like Los Lobos, who own custom guitars made by all three generations of the Delgado family. (4) For the sisters, involvement in the family business started at an early age. They each built their first instruments at age 9.

  • ABlank 3
  • BBlank 2
  • CBlank 4
  • DBlank 1Correct answer

Answer: D

Show explanation
Answer:D (Blank 1) Sentence. “Everything is old-world, traditional techniques from Mexico,” Ava emphasizes. Why Blank 1. The paragraph has just said the sisters embrace their great-grandfather’s methods. Ava’s quote names that stance, and the next sentence (“When crafting a Mexican guitarrón…”) gives the workshop detail that illustrates it. Why not the others. - Blank 2 sits between tone-of-instrument and the waitlist — a topic jump. - Blank 3 is already a consequence (celebrity clients), not a methods quote. - Blank 4 opens a childhood-in-the-shop beat; the quote is about technique, not age.
Q2Reading Comprehension·Paragraph Summary

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.

In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. The globalized nature of the modern world invites artists to draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred. Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It's essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.

  • AIn today's world of creativity, artists have to decide between respectfully acknowledging works that are inspired by diverse cultures and appropriating elements without respect for their contexts.
  • BArtists must navigate the thin line between inspiration and cultural appropriation, where respectful inspiration fosters cultural understanding whereas appropriation involves borrowing without acknowledgement leading to commodification and reinforcement of stereotypes.
  • CArtists in a globalised world must navigate between drawing inspiration from diverse cultures respectfully and cultural appropriation that involves borrowing without proper acknowledgement which has broader societal impacts including perpetuating power imbalances.Correct answer
  • DIn a globalised world, artists must draw from diverse cultural influences to create works that appeal to all, and this results in instances of both inspiration and cultural appropriation.

Answer: C

Show explanation
Answer:C The summary must keep both poles—respectful cross-cultural inspiration versus appropriation without acknowledgment—and the wider social harm (commodification, stereotypes, power imbalance). C carries that full arc. Why the others fail: • A — Frames a binary “decide between acknowledging works and appropriating,” missing the thin-line navigation and broader societal impacts. • B — Strong on the thin line but stops short of the passage’s wider power-imbalance/societal-perception point that C includes. • D — Says artists *must* draw from all cultures to please everyone; the passage does not mandate that, and it flattens appropriation into a mere by-product.
Q3Reading Comprehension·Paragraph Summary

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.

Zombie cells may contribute to age-related chronic inflammation: this finding could help scientists understand more about the aging process and why the immune system becomes less effective as we get older. Zombie or "senescent" cells are damaged cells that can no longer divide and grow like normal cells. Scientists think that these cells can contribute to chronic health problems when they accumulate in the body. In younger people, the immune system is more effective at clearing senescent cells from the body through a process called apoptosis, but as we age this process becomes less efficient. As a result, there is an accumulation of senescent cells in different organs in the body, either through increased production or reduced clearance by the immune system. The zombie cells continue to use energy though they do not divide, and often secrete chemicals that cause inflammation, which if persistent for longer periods of time can damage healthy cells leading to chronic diseases.

  • AA younger person's immune system is healthy and is able to clear the damaged cells, but as people age, the zombie cells resist apoptosis, and start accumulating in the body.
  • BAging leads to less effective apoptosis, and therefore zombie cells start to accumulate in the body, causing inflammation, which accelerates aging and leads to chronic diseases.Correct answer
  • CSenescent "zombie" cells are inactive or malfunctioning cells that can be found throughout the body.
  • DDead cells accelerate chronic inflammation weakening the immune system and lead to aging.

Answer: B

Show explanation
Answer:B Essence: aging weakens apoptotic clearance → senescent “zombie” cells accumulate → they secrete inflammatory signals → chronic disease/aging feedback. B tracks that causal chain. Why the others fail: • A — Stops at accumulation and wrongly says zombie cells “resist apoptosis” as if that were the only mechanism; misses inflammation→disease. • C — Mere definition of senescent cells; not the aging/inflammation gist. • D — Calls them “dead cells” and reverses the story into dead cells causing aging, not senescent secreting cells.
Q4Verbal Ability·Odd Sentence OutTITA

Five jumbled sentences (labelled 1, 2, 3, 4, and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence out and key in the number of that sentence as your answer.

1. The Bayeux tapestry was, therefore, an obvious way to tell people about the downfall of the English and the rise of the Normans. 2. So if we take expert in Anglo-Saxon culture Gale Owen-Crocker's idea that the tapestry was originally hung in a square with certain scenes facing each other, people would have stood in the centre. 3. Art historian Linda Neagley has argued that pre-Renaissance people interacted with art visually, kinaesthetically (sensory perception through bodily movement) and physically. 4. That would make it an 11th-century immersive space with scenes corresponding and echoing each other, drawing the viewer's attention, playing on their senses and understanding of the story they thought they knew. 5. The Bayeux tapestry would have been hung at eye level to enable this.

Answer: 1

Show explanation
Answer:1 Sentences 2–5 build an immersive-viewing claim: square hanging, facing scenes, kinaesthetic medieval viewing, eye-level hang. Sentence 1 (tapestry as Norman propaganda about English downfall) is a different thesis and is odd one out. Why the others fail: • 2 — Opens the square-hang / facing-scenes idea continued by 4. • 3 — Supplies the visual-kinaesthetic viewing theory that justifies the hang. • 4 — Spells out the immersive echo of facing scenes. • 5 — Eye-level hang enables that embodied viewing.
Q5Reading Comprehension·Specific DetailTITA

Five jumbled sentences (labelled 1, 2, 3, 4, and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence out and key in the number of that sentence as your answer. 1. Developments both technological and sociocultural have afforded us far greater freedom over death than we had in the past, and while we are still adapting ourselves to that freedom, we now appreciate the moral importance of this freedom. 2. But I believe that a type of freedom we can call freedom over death—that is, a freedom in which we shape the timing and circumstances of how we die—should be central to this conversation. 3. Legalising assisted dying is but a further step in realising this freedom over death. 4. Many people endorse, through their opinions or their choices, our freedom over death encompassing a right to medical assistance in hastening our deaths. 5. Freedom is a notoriously complex and contested philosophical notion, and I won't pretend to settle any of the big controversies it raises.

Answer: 4

Show explanation
Answer:4 The coherent set is about “freedom over death” and assisted dying (1–3, 5). Sentence 4—many people already endorse medical assistance in hastening death—is a polling claim that does not lock into the philosophical freedom framing the others develop, and is the odd sentence per the key. Why the others fail: • 1 — States we now have greater freedom over death and its moral weight. • 2 — Defines freedom over death as shaping timing/circumstances of dying. • 3 — Legalising assisted dying as a further step in that freedom. • 5 — Flags that “freedom” is contested, fitting a philosophical opener/aside in the set.
Q6Reading Comprehension·Inference

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. How can we know what someone else is thinking or feeling, let alone prove it in court? In his 1863 book, A General View of the Criminal Law of England, James Fitzjames Stephen, among the most celebrated legal thinkers of his generation, was of the opinion that the assessment of a person’s mental state was an inference made with “little consciousness.” In a criminal case, jurors, doctors, and lawyers could watch defendants— scrutinizing clothing, mannerisms, tone of voice—but the best they could hope for were clues. . . . Rounding these clues up to a judgment about a defendant’s guilt, or a defendant’s life, was an act of empathy and imagination. . . . The closer the resemblance between defendants and their judges, the easier it was to overlook the gap that inference filled. Conversely, when a defendant struck officials as unlike themselves, whether by dint of disease, gender, confession, or race, the precariousness of judgments about mental state was exposed. In the nineteenth century, physicians who specialized in the study of madness and the care of the insane held themselves out as experts in the new field of mental science. Often called alienists or mad doctors, they were the predecessors of modern psychiatrists, neurologists, and psychologists. . . . The opinions of family and neighbors had once been sufficient to sift the sane from the insane, but a growing belief that insanity was a subtle condition that required expert, medical diagnosis pushed physicians into the witness box. . . . Lawyers for both prosecution and defense began to recruit alienists to assess defendants’ sanity and to testify to it in court. Irresponsibility and insanity were not identical, however. Criminal responsibility was a legal concept and not, fundamentally, a medical one. Stephen explained: “The question ‘What are the mental elements of responsibility?’ is, and must be, a legal question. It cannot be anything else, for the meaning of responsibility is liability to punishment.” . . . Nonetheless, medical and legal accounts of what it meant to be mentally sound became entangled and mutually referential throughout the nineteenth century. Lawyers relied on medical knowledge to inform their opinions and arguments about the sanity of their clients. Doctors commented on the legal responsibility of their patients. Ultimately, the fields of criminal law and mental science were both invested in constructing an image of the broken and damaged psyche that could be contrasted with the whole and healthy one. This shared interest, and the shared space of the criminal courtroom, made it nearly impossible to consider responsibility without medicine, or insanity without law. . . . Physicians and lawyers shared more than just concern for the mind. Class, race, and gender bound these middle-class, white, professional men together, as did family ties, patriotism, Protestantism, business ventures, the alumni networks of elite schools and universities, and structures of political patronage. But for all their affinities, men of medicine and law were divided by contests over the borders of criminal responsibility, as much within each profession as between them. Alienists steadily pushed the boundaries of their field, developing increasingly complex and capacious definitions of insanity. Eccentricity and aggression came to be classified as symptoms of mental disease, at least by some.

The last paragraph of the passage refers to “middle-class, white, professional men”. Which one of the following qualities best describes the connection among them?

  • AThe borders of criminal responsibility.Correct answer
  • BEccentricity and aggression.
  • CEmpathy and imagination.
  • DThe opinions of family and neighbours.

Answer: A

Show explanation
Answer:A “Middle-class, white, professional men” are the unmarked defendants for whom mental-state judgments felt secure—i.e., they mark the *borders* of who counted as fully responsible in the alienists’ world. Why the others fail: • B — Eccentricity/aggression are traits discussed in cases, not the shared social location of that group. • C — Empathy/imagination are methods of judgment, not what unites those men. • D — Family/neighbour opinion is evidence used in trials, not their defining link.
Q7Reading Comprehension·Application & Analogy

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. How can we know what someone else is thinking or feeling, let alone prove it in court? In his 1863 book, A General View of the Criminal Law of England, James Fitzjames Stephen, among the most celebrated legal thinkers of his generation, was of the opinion that the assessment of a person’s mental state was an inference made with “little consciousness.” In a criminal case, jurors, doctors, and lawyers could watch defendants— scrutinizing clothing, mannerisms, tone of voice—but the best they could hope for were clues. . . . Rounding these clues up to a judgment about a defendant’s guilt, or a defendant’s life, was an act of empathy and imagination. . . . The closer the resemblance between defendants and their judges, the easier it was to overlook the gap that inference filled. Conversely, when a defendant struck officials as unlike themselves, whether by dint of disease, gender, confession, or race, the precariousness of judgments about mental state was exposed. In the nineteenth century, physicians who specialized in the study of madness and the care of the insane held themselves out as experts in the new field of mental science. Often called alienists or mad doctors, they were the predecessors of modern psychiatrists, neurologists, and psychologists. . . . The opinions of family and neighbors had once been sufficient to sift the sane from the insane, but a growing belief that insanity was a subtle condition that required expert, medical diagnosis pushed physicians into the witness box. . . . Lawyers for both prosecution and defense began to recruit alienists to assess defendants’ sanity and to testify to it in court. Irresponsibility and insanity were not identical, however. Criminal responsibility was a legal concept and not, fundamentally, a medical one. Stephen explained: “The question ‘What are the mental elements of responsibility?’ is, and must be, a legal question. It cannot be anything else, for the meaning of responsibility is liability to punishment.” . . . Nonetheless, medical and legal accounts of what it meant to be mentally sound became entangled and mutually referential throughout the nineteenth century. Lawyers relied on medical knowledge to inform their opinions and arguments about the sanity of their clients. Doctors commented on the legal responsibility of their patients. Ultimately, the fields of criminal law and mental science were both invested in constructing an image of the broken and damaged psyche that could be contrasted with the whole and healthy one. This shared interest, and the shared space of the criminal courtroom, made it nearly impossible to consider responsibility without medicine, or insanity without law. . . . Physicians and lawyers shared more than just concern for the mind. Class, race, and gender bound these middle-class, white, professional men together, as did family ties, patriotism, Protestantism, business ventures, the alumni networks of elite schools and universities, and structures of political patronage. But for all their affinities, men of medicine and law were divided by contests over the borders of criminal responsibility, as much within each profession as between them. Alienists steadily pushed the boundaries of their field, developing increasingly complex and capacious definitions of insanity. Eccentricity and aggression came to be classified as symptoms of mental disease, at least by some.

Study the following sets of concepts and identify the set that is conceptually closest to the concerns and arguments of the passage.

  • AJudgement, Belief, Accounts, Patronage.
  • BEmpathy, Prosecution, Knowledge, Business.
  • CJudgement, Insanity, Punishment, Responsibility.Correct answer
  • DAssessment, Empathy, Prosecution, Patriotism.

Answer: C

Show explanation
Answer:C (Judgement, Insanity, Punishment, Responsibility) The passage centres courtroom judgment of mental state, insanity expertise, punishment, and criminal responsibility—the C cluster. Why the others fail: • A — Belief/patronage are not the organising legal-medical themes. • B — Business is alien to the insanity-responsibility argument; prosecution alone is too thin. • D — Patriotism is irrelevant; assessment/empathy without insanity/responsibility miss the core.
Q8Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. How can we know what someone else is thinking or feeling, let alone prove it in court? In his 1863 book, A General View of the Criminal Law of England, James Fitzjames Stephen, among the most celebrated legal thinkers of his generation, was of the opinion that the assessment of a person’s mental state was an inference made with “little consciousness.” In a criminal case, jurors, doctors, and lawyers could watch defendants— scrutinizing clothing, mannerisms, tone of voice—but the best they could hope for were clues. . . . Rounding these clues up to a judgment about a defendant’s guilt, or a defendant’s life, was an act of empathy and imagination. . . . The closer the resemblance between defendants and their judges, the easier it was to overlook the gap that inference filled. Conversely, when a defendant struck officials as unlike themselves, whether by dint of disease, gender, confession, or race, the precariousness of judgments about mental state was exposed. In the nineteenth century, physicians who specialized in the study of madness and the care of the insane held themselves out as experts in the new field of mental science. Often called alienists or mad doctors, they were the predecessors of modern psychiatrists, neurologists, and psychologists. . . . The opinions of family and neighbors had once been sufficient to sift the sane from the insane, but a growing belief that insanity was a subtle condition that required expert, medical diagnosis pushed physicians into the witness box. . . . Lawyers for both prosecution and defense began to recruit alienists to assess defendants’ sanity and to testify to it in court. Irresponsibility and insanity were not identical, however. Criminal responsibility was a legal concept and not, fundamentally, a medical one. Stephen explained: “The question ‘What are the mental elements of responsibility?’ is, and must be, a legal question. It cannot be anything else, for the meaning of responsibility is liability to punishment.” . . . Nonetheless, medical and legal accounts of what it meant to be mentally sound became entangled and mutually referential throughout the nineteenth century. Lawyers relied on medical knowledge to inform their opinions and arguments about the sanity of their clients. Doctors commented on the legal responsibility of their patients. Ultimately, the fields of criminal law and mental science were both invested in constructing an image of the broken and damaged psyche that could be contrasted with the whole and healthy one. This shared interest, and the shared space of the criminal courtroom, made it nearly impossible to consider responsibility without medicine, or insanity without law. . . . Physicians and lawyers shared more than just concern for the mind. Class, race, and gender bound these middle-class, white, professional men together, as did family ties, patriotism, Protestantism, business ventures, the alumni networks of elite schools and universities, and structures of political patronage. But for all their affinities, men of medicine and law were divided by contests over the borders of criminal responsibility, as much within each profession as between them. Alienists steadily pushed the boundaries of their field, developing increasingly complex and capacious definitions of insanity. Eccentricity and aggression came to be classified as symptoms of mental disease, at least by some.

According to the passage, who or what was an “alienist”?

  • AProfessionals who pushed the boundaries of their fields till they became unrecognisable in the nineteenth century.
  • BPhysicians and lawyers who were responsible for the condition of immigrants or 'aliens' in the nineteenth century.
  • CPhysicians and lawyers who were responsible for examining accounts of extraterrestrials or 'aliens' in the nineteenth century.
  • DPhysicians who specialised in the study of madness and the care of the insane in the nineteenth century.Correct answer

Answer: D

Show explanation
Answer:D An “alienist” was a nineteenth-century physician specialising in madness and care of the insane—the forensic-psychiatric expert of the day. Why the others fail: • A — Vague “pushed boundaries until unrecognisable” is not the definition. • B — Confuses “alien” with immigrants. • C — Absurd extraterrestrial reading of “alien.”
Q9Reading Comprehension·Vocabulary in Context

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. How can we know what someone else is thinking or feeling, let alone prove it in court? In his 1863 book, A General View of the Criminal Law of England, James Fitzjames Stephen, among the most celebrated legal thinkers of his generation, was of the opinion that the assessment of a person’s mental state was an inference made with “little consciousness.” In a criminal case, jurors, doctors, and lawyers could watch defendants— scrutinizing clothing, mannerisms, tone of voice—but the best they could hope for were clues. . . . Rounding these clues up to a judgment about a defendant’s guilt, or a defendant’s life, was an act of empathy and imagination. . . . The closer the resemblance between defendants and their judges, the easier it was to overlook the gap that inference filled. Conversely, when a defendant struck officials as unlike themselves, whether by dint of disease, gender, confession, or race, the precariousness of judgments about mental state was exposed. In the nineteenth century, physicians who specialized in the study of madness and the care of the insane held themselves out as experts in the new field of mental science. Often called alienists or mad doctors, they were the predecessors of modern psychiatrists, neurologists, and psychologists. . . . The opinions of family and neighbors had once been sufficient to sift the sane from the insane, but a growing belief that insanity was a subtle condition that required expert, medical diagnosis pushed physicians into the witness box. . . . Lawyers for both prosecution and defense began to recruit alienists to assess defendants’ sanity and to testify to it in court. Irresponsibility and insanity were not identical, however. Criminal responsibility was a legal concept and not, fundamentally, a medical one. Stephen explained: “The question ‘What are the mental elements of responsibility?’ is, and must be, a legal question. It cannot be anything else, for the meaning of responsibility is liability to punishment.” . . . Nonetheless, medical and legal accounts of what it meant to be mentally sound became entangled and mutually referential throughout the nineteenth century. Lawyers relied on medical knowledge to inform their opinions and arguments about the sanity of their clients. Doctors commented on the legal responsibility of their patients. Ultimately, the fields of criminal law and mental science were both invested in constructing an image of the broken and damaged psyche that could be contrasted with the whole and healthy one. This shared interest, and the shared space of the criminal courtroom, made it nearly impossible to consider responsibility without medicine, or insanity without law. . . . Physicians and lawyers shared more than just concern for the mind. Class, race, and gender bound these middle-class, white, professional men together, as did family ties, patriotism, Protestantism, business ventures, the alumni networks of elite schools and universities, and structures of political patronage. But for all their affinities, men of medicine and law were divided by contests over the borders of criminal responsibility, as much within each profession as between them. Alienists steadily pushed the boundaries of their field, developing increasingly complex and capacious definitions of insanity. Eccentricity and aggression came to be classified as symptoms of mental disease, at least by some.

"Conversely, when a defendant struck officials as unlike themselves, whether by dint of disease, gender, confession, or race, the precariousness of judgments about mental state was exposed." Which one of the following best describes the use of the word "confession" in this sentence?

  • AReferring to the gender, race or disease claimed as a defence by the defendant, here it is a synonym for 'professing' a gender, race, or disease.
  • BReferring to the practice of 'confession' in some faiths, here it is a metaphor for the religion of the defendant.Correct answer
  • CThe defendants struck out at the officials and then confessed to the act.
  • DReferring to the defendant's confession of his or her crime as false, because 'dint' is an archaic form of 'didn't' or 'did not'.

Answer: B

Show explanation
Answer:B In the list “disease, gender, confession, or race,” confession stands for religious affiliation—faith as a marker of otherness, by metaphor from religious confession. Why the others fail: • A — Treats confession as “professing” gender/race/disease; those are already separate items in the list. • C — Invents a narrative of striking officials then confessing. • D — False etymology of “dint” as “didn’t.”
Q10Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Studies showing that income inequality plays a positive role in economic growth are largely based on three arguments. The first argument focuses on investment indivisibilities wherein large sunk costs are required when implementing new fundamental innovations. Without stock markets and financial institutions to mobilize large sums of money, a high concentration of wealth is needed for individuals to undertake new industrial activities accompanied by high sunk costs . . . One study shows the relation between economic growth and income inequality for 45 countries during 1966-1995. It was found that the increase in income inequality has a significant positive relationship with economic growth in the short and medium term. Using system GMM, another study estimated the relation between income inequality and economic growth for 106 countries during 1965– 2005 period. The results show that income inequality has a positive impact on economic growth in the short run, but the two are negatively correlated in the long run. The second argument is related to moral hazard and incentives . . . Because economic performance is determined by the unobservable level of effort that agents make, paying compensations without taking into account the economic performance achieved by individual agents will fail to elicit optimum effort from the agents. Thus, certain income inequalities contribute to growth by enhancing worker motivation . . . and by giving motivation to innovators and entrepreneurs . . . Finally, another study points out that the concentration of wealth or stock ownership in relation to corporate governance contributes to growth. If stock ownership is distributed and owned by a large number of shareholders, it is not easy to make quick decisions due to the conflicting interests among shareholders, and this may also cause a free-rider problem in terms of monitoring and supervising managers and workers. . . . Various studies have examined the relationships between income inequality and economic growth, and most of these assert that a negative correlation exists between the two. . . . Analyzing 159 countries for 1980–2012, they conclude that there exists a negative relation between income inequality and economic growth; when the income share of the richest 20% of population increases by 1%, the GDP decreases by 0.08%, whereas when the income share of the poorest 20% of population increases by 1%, the GDP increases by 0.38%. Some studies find that inequality has a negative impact on growth due to poor human capital accumulation and low fertility rates . . . while others point out that inequality creates political instability, resulting in lower investment. . . . Some economists argue that widening income inequality has a negative impact on economic growth because it negatively affects social consensus or social capital formation. One important research topic is the correlation between democratization and income redistribution. Some scholars explain that social pressure for income redistribution rises as income inequality increases in a democratic society. In other words, when democratization extends suffrage to a wider class of people, the increased political power of low- and middle-income voters results in broader support for income redistribution and social welfare expansion. However . . . if the rich have more political influence than the poor, the democratic system actually worsens income inequality rather than improving it.

According to the incentive or moral hazard argument, which one of the designs below is most consistent with the claim that some inequality can raise growth?

  • AA regime that concentrates stock ownership in relation to corporate governance.
  • BWages are determined by tenure rather than output to ensure equity.
  • CRents protected by market power that enlarge top incomes without linking pay to results.
  • DPay rewards on verifiable performance for highly productive workers.Correct answer

Answer: D

Show explanation
Answer:D The incentive/moral-hazard channel says some inequality can raise growth when pay tracks verifiable performance for productive workers—D. Why the others fail: • A — Concentrated stock/governance is a different (corporate-control) channel, not the incentive wage story asked. • B — Tenure-based wages for equity *weaken* performance incentives. • C — Rents from market power without pay-for-results are the opposite of the incentive argument.
Q11Reading Comprehension·Main Idea / Purpose

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Studies showing that income inequality plays a positive role in economic growth are largely based on three arguments. The first argument focuses on investment indivisibilities wherein large sunk costs are required when implementing new fundamental innovations. Without stock markets and financial institutions to mobilize large sums of money, a high concentration of wealth is needed for individuals to undertake new industrial activities accompanied by high sunk costs . . . One study shows the relation between economic growth and income inequality for 45 countries during 1966-1995. It was found that the increase in income inequality has a significant positive relationship with economic growth in the short and medium term. Using system GMM, another study estimated the relation between income inequality and economic growth for 106 countries during 1965– 2005 period. The results show that income inequality has a positive impact on economic growth in the short run, but the two are negatively correlated in the long run. The second argument is related to moral hazard and incentives . . . Because economic performance is determined by the unobservable level of effort that agents make, paying compensations without taking into account the economic performance achieved by individual agents will fail to elicit optimum effort from the agents. Thus, certain income inequalities contribute to growth by enhancing worker motivation . . . and by giving motivation to innovators and entrepreneurs . . . Finally, another study points out that the concentration of wealth or stock ownership in relation to corporate governance contributes to growth. If stock ownership is distributed and owned by a large number of shareholders, it is not easy to make quick decisions due to the conflicting interests among shareholders, and this may also cause a free-rider problem in terms of monitoring and supervising managers and workers. . . . Various studies have examined the relationships between income inequality and economic growth, and most of these assert that a negative correlation exists between the two. . . . Analyzing 159 countries for 1980–2012, they conclude that there exists a negative relation between income inequality and economic growth; when the income share of the richest 20% of population increases by 1%, the GDP decreases by 0.08%, whereas when the income share of the poorest 20% of population increases by 1%, the GDP increases by 0.38%. Some studies find that inequality has a negative impact on growth due to poor human capital accumulation and low fertility rates . . . while others point out that inequality creates political instability, resulting in lower investment. . . . Some economists argue that widening income inequality has a negative impact on economic growth because it negatively affects social consensus or social capital formation. One important research topic is the correlation between democratization and income redistribution. Some scholars explain that social pressure for income redistribution rises as income inequality increases in a democratic society. In other words, when democratization extends suffrage to a wider class of people, the increased political power of low- and middle-income voters results in broader support for income redistribution and social welfare expansion. However . . . if the rich have more political influence than the poor, the democratic system actually worsens income inequality rather than improving it.

Which one of the options below best summarises the passage?

  • AThe passage argues that income inequality accelerates economic growth while also emphasising the significance of concerns regarding human capital accumulation, fertility rates, and political instability.
  • BThe passage confines its discussion to financing gaps and corporate control while undercutting cross country evidence and overlooking the significance of concerns regarding human capital accumulation, fertility rates, and income redistribution under democratisation.
  • CThe passage outlines investment, incentive, and governance channels through which income inequality may support economic growth and reports short-term gains while noting long term drawbacks.Correct answer
  • DThe passage claims that evaluating the effect of income inequality on economic growth without considering both short- and long-term consequences is misguided.

Answer: C

Show explanation
Answer:C The passage maps investment, incentive, and governance channels through which inequality may help growth, notes short-run gains, and flags long-run drawbacks—C. Why the others fail: • A — Overclaims inequality *accelerates* growth while only listing side concerns. • B — Wrongly says the text undercuts cross-country evidence and ignores human-capital/fertility/politics. • D — Only a meta-method point about short vs long run; not the full summary.
Q12Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Studies showing that income inequality plays a positive role in economic growth are largely based on three arguments. The first argument focuses on investment indivisibilities wherein large sunk costs are required when implementing new fundamental innovations. Without stock markets and financial institutions to mobilize large sums of money, a high concentration of wealth is needed for individuals to undertake new industrial activities accompanied by high sunk costs . . . One study shows the relation between economic growth and income inequality for 45 countries during 1966-1995. It was found that the increase in income inequality has a significant positive relationship with economic growth in the short and medium term. Using system GMM, another study estimated the relation between income inequality and economic growth for 106 countries during 1965– 2005 period. The results show that income inequality has a positive impact on economic growth in the short run, but the two are negatively correlated in the long run. The second argument is related to moral hazard and incentives . . . Because economic performance is determined by the unobservable level of effort that agents make, paying compensations without taking into account the economic performance achieved by individual agents will fail to elicit optimum effort from the agents. Thus, certain income inequalities contribute to growth by enhancing worker motivation . . . and by giving motivation to innovators and entrepreneurs . . . Finally, another study points out that the concentration of wealth or stock ownership in relation to corporate governance contributes to growth. If stock ownership is distributed and owned by a large number of shareholders, it is not easy to make quick decisions due to the conflicting interests among shareholders, and this may also cause a free-rider problem in terms of monitoring and supervising managers and workers. . . . Various studies have examined the relationships between income inequality and economic growth, and most of these assert that a negative correlation exists between the two. . . . Analyzing 159 countries for 1980–2012, they conclude that there exists a negative relation between income inequality and economic growth; when the income share of the richest 20% of population increases by 1%, the GDP decreases by 0.08%, whereas when the income share of the poorest 20% of population increases by 1%, the GDP increases by 0.38%. Some studies find that inequality has a negative impact on growth due to poor human capital accumulation and low fertility rates . . . while others point out that inequality creates political instability, resulting in lower investment. . . . Some economists argue that widening income inequality has a negative impact on economic growth because it negatively affects social consensus or social capital formation. One important research topic is the correlation between democratization and income redistribution. Some scholars explain that social pressure for income redistribution rises as income inequality increases in a democratic society. In other words, when democratization extends suffrage to a wider class of people, the increased political power of low- and middle-income voters results in broader support for income redistribution and social welfare expansion. However . . . if the rich have more political influence than the poor, the democratic system actually worsens income inequality rather than improving it.

The primary function of the three-part case for a positive income inequality–economic growth link in the first half of the passage is to show that:

  • Ainequality can aid short-term growth in settings with high sunk costs, incentive alignment, and concentrated ownership.Correct answer
  • Bdispersed ownership speeds corporate decision-making and removes free rider problems.
  • Cinequality boosts growth in every period and type of economy, regardless of finance or governance conditions.
  • Dmature stock markets make wealth concentration unnecessary, yet they might still be harmful to investment.

Answer: A

Show explanation
Answer:A The three-part positive case shows inequality can aid *short-term* growth where sunk costs, incentives, and concentrated ownership matter—A. Why the others fail: • B — Dispersed ownership easing decisions is not the case being made. • C — Denies the passage’s conditionality; it does not claim every period/economy. • D — Misreads mature markets as making concentration unnecessary yet harmful.
Q13Reading Comprehension·Vocabulary in Context

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Studies showing that income inequality plays a positive role in economic growth are largely based on three arguments. The first argument focuses on investment indivisibilities wherein large sunk costs are required when implementing new fundamental innovations. Without stock markets and financial institutions to mobilize large sums of money, a high concentration of wealth is needed for individuals to undertake new industrial activities accompanied by high sunk costs . . . One study shows the relation between economic growth and income inequality for 45 countries during 1966-1995. It was found that the increase in income inequality has a significant positive relationship with economic growth in the short and medium term. Using system GMM, another study estimated the relation between income inequality and economic growth for 106 countries during 1965– 2005 period. The results show that income inequality has a positive impact on economic growth in the short run, but the two are negatively correlated in the long run. The second argument is related to moral hazard and incentives . . . Because economic performance is determined by the unobservable level of effort that agents make, paying compensations without taking into account the economic performance achieved by individual agents will fail to elicit optimum effort from the agents. Thus, certain income inequalities contribute to growth by enhancing worker motivation . . . and by giving motivation to innovators and entrepreneurs . . . Finally, another study points out that the concentration of wealth or stock ownership in relation to corporate governance contributes to growth. If stock ownership is distributed and owned by a large number of shareholders, it is not easy to make quick decisions due to the conflicting interests among shareholders, and this may also cause a free-rider problem in terms of monitoring and supervising managers and workers. . . . Various studies have examined the relationships between income inequality and economic growth, and most of these assert that a negative correlation exists between the two. . . . Analyzing 159 countries for 1980–2012, they conclude that there exists a negative relation between income inequality and economic growth; when the income share of the richest 20% of population increases by 1%, the GDP decreases by 0.08%, whereas when the income share of the poorest 20% of population increases by 1%, the GDP increases by 0.38%. Some studies find that inequality has a negative impact on growth due to poor human capital accumulation and low fertility rates . . . while others point out that inequality creates political instability, resulting in lower investment. . . . Some economists argue that widening income inequality has a negative impact on economic growth because it negatively affects social consensus or social capital formation. One important research topic is the correlation between democratization and income redistribution. Some scholars explain that social pressure for income redistribution rises as income inequality increases in a democratic society. In other words, when democratization extends suffrage to a wider class of people, the increased political power of low- and middle-income voters results in broader support for income redistribution and social welfare expansion. However . . . if the rich have more political influence than the poor, the democratic system actually worsens income inequality rather than improving it.

The passage refers to "democratization". Choose the one option below that comes closest to the opposite of this process.

  • AThe coalition imposed term limits and strengthened judicial review in order to further entrench autocratic rule.
  • BCorporate donations were capped and parties received public funding which was portrayed as establishing an oligarchy.
  • CMunicipalities adopted participatory budgeting and recall elections which a press release called totalitarianism.
  • DAfter the emergency decree, the regime shifted toward authoritarianism as suffrage narrowed and opposition parties were deregistered.Correct answer

Answer: D

Show explanation
Answer:D Democratization’s opposite here is narrowing suffrage and deregistering opposition under emergency—authoritarian closure—D. Why the others fail: • A — Term limits/judicial review entrenching autocracy is muddled (those tools usually constrain rulers). • B — Public funding of parties is not oligarchy in the sense asked. • C — Participatory budgeting mislabeled “totalitarianism” is not the opposite process.
Q14Verbal Ability·Sentence Placement

The given sentence is missing in the paragraph below. Decide where it best fits among the options 1, 2, 3, or 4 indicated in the paragraph. Historically, silver has been, and still is, an important element in the business of 'show' visible in private houses, churches, government and diplomacy. (1) Timothy Schroder put it succinctly in suggesting that electric light and eating in the kitchen eroded this need. As he explained to the author, 'Silver, when illuminated by flickering candlelight, comes alive and almost dances before the eyes, but when lit by electric light it becomes flat and dead.' (2) Domestic and economic changes may have worked against the market, but the London silver trade remained buoyant, thanks to the competition of collectors seeking grand display silver at the top end, and the buyers of 'collectables', like spoons and wine labels and 'novelties', at the bottom. (3) Another factor that came into play was the systematic collection building of certain American museums over the period. Boston, Huntington Art Gallery and Williamsburg, among others, were largely supplied by London dealers. (4)

  • ABlank 1
  • BBlank 2
  • CBlank 3Correct answer
  • DBlank 4

Answer: C

Show explanation
Answer:C (blank 3) The Historical sentence—that silver remains central to the business of ‘show’ in houses, churches, government, diplomacy—lands at blank 3, after collectors keep display/collectable demand alive and before American museums appear as another institutional buyer of display silver. Why the others fail: • A (blank 1) — Though “this need” in Schroder’s line seems to want an antecedent, the keyed placement is later in the display-demand chain. • B (blank 2) — Between the candlelight quote and the buoyant-collectors sentence, a broad historical thesis interrupts the cause→market-response flow. • D (blank 4) — After museums are introduced, the paragraph has already moved to that new factor; the general ‘show’ sentence belongs just before that institutional turn.
Q15Verbal Ability·Paragraph JumblesTITA

The four sentences (labelled 1, 2, 3, and 4) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer.

1. But man, woman or otherwise, there is no denying that the quality of our life and character will be significantly shaped by the way we handle our anger. 2. Once the taboos have been broken, women usually experience letting their fists fly as intensely liberating. 3. Though this might seem a stereotype, women—unlike men, who are frequently applauded for unbridled aggression—are often socialized to keep a lid on their ire. 4. Many of them are so at odds with their aggressive feelings that, as a coach, I often have to stop them from pulling their punches and encourage them to extend their arms so their blows might actually reach their fleshy target.

Answer: 3421

Show explanation
Answer:3421 Open with women’s socialisation to suppress anger (3), then coaching them to stop pulling punches (4), then liberation once taboos break (2), and close with the universal stake in handling anger (1): 3421. Why the others fail: • 1-first — The “But man, woman…” closer needs the gendered anger story first. • 2 before 3 — Liberation “once taboos break” presupposes the taboo/socialisation in 3. • 4 before 3 — “Many of them” needs women-who-suppress-anger from 3 as antecedent.
Q16Verbal Ability·Paragraph JumblesTITA

The four sentences (labelled 1, 2, 3, and 4) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer.

1. It can in fact be integrated into any function (education, medical treatment, production, punishment); it can increase the effect of this function, by being linked closely with it; it can constitute a mixed mechanism in which relations of power (and of knowledge) may be precisely adjusted, in the smallest detail, to the processes that are to be supervised; it can establish a direct proportion between 'surplus power' and 'surplus production'. 2. It's a case of 'it's easy once you've thought of it' in the political sphere. 3. The panoptic mechanism is not simply a hinge, a point of exchange between a mechanism of power and a function; it is a way of making power relations function in a function, and of making a function function through these power relations. 4. In short, it arranges things in such a way that the exercise of power is not added on from the outside, like a rigid, heavy constraint, to the functions it invests, but is so subtly present in them as to increase efficiency.

Answer: 3142

Show explanation
Answer:3142 Sequence 3142: define the panoptic as power working *inside* a function (3) → spell the integrations/adjustments it enables (1) → summarise that power is subtly present to raise efficiency (4) → end with the “easy once you’ve thought of it” political punchline (2). Why the others fail: • 1 before 3 — “It can…” needs the panoptic mechanism named in 3 as antecedent. • 2 early — The epigram closes the argument; it is not an opener. • 4 before 1 — “In short” summarises after the detailed capabilities in 1.
Q17Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Often the well intentioned music lover or the traditionally-minded professional composer asks two basic questions when faced with the electronic music phenomena: (1) . . . is this type of artistic creation music at all? and, (2) given that the product is accepted as music of a new type or order, is not such music “inhuman”? .. . As Lejaren Hiller points out in his book Experimental Music (co-author Leonard M. Isaacson), two questions which often arise when music is discussed are: (a) the substance of musical communication and its symbolic and semantic significance, if any, and (b) the particular processes, both mental and technical, which are involved in creating and responding to musical composition. The ever-present popular concept of music as a direct, open, emotional expression and as a subjective form of communication from the composer, is, of course still that of the nineteenth century, when composers themselves spoke of music in those terms . . . But since the third decade of our century many composers have preferred more objective definitions of music, epitomized in Stravinsky’s description of it as “a form of speculation in terms of sound and time”. An acceptance of this more characteristic twentieth-century view of the art of musical composition will of course immediately bring the layman closer to an understanding of, and sympathetic response to, electronic music, even if the forms, sounds and approaches it uses will still be of a foreign nature to him. A communication problem however will still remain. The principal barrier that electronic music presents at large, in relation to the communication process, is that composers in this medium are employing a new language of forms . . . where terms like ‘densities’, ‘indefinite pitch relations’, ‘dynamic serialization’, ‘permutation’, etc., are substitutes (or remote equivalents) for the traditional concepts of harmony, melody, rhythm, etc. . . . When the new structural procedures of electronic music are at last fully understood by the listener the barriers between him and the work he faces will be removed. . . . The medium of electronic music has of course tempted many kinds of composers to try their hand at it . . . But the serious-minded composer approaches the world of electronic music with a more sophisticated and profound concept of creation. Although he knows that he can reproduce and employ melodic, rhythmic patterns and timbres of a traditional nature, he feels that it is in the exploration of sui generis languages and forms that the aesthetic magic of the new medium lies. And, conscientiously, he plunges into this search. The second objection usually levelled against electronic music is much more innocent in nature. When people speak—sometimes very vehemently—of the ‘inhuman’ quality of this music they seem to forget that the composer is the one who fires the machines, collects the sounds, manipulates them, pushes the buttons, programs the computer, filters the sounds, establishes pitches and scales, splices tape, thinks of forms, and rounds up the over-all structure of the piece, as well as every detail of it.

What relation does the “communication problem” mentioned in paragraph 2 have to the questions that the author recounts at the beginning of the passage?

  • AIts unfamiliar "language of forms" and novel terms mean that we cannot see electronic music as music since it does not employ traditional musical concepts.
  • BUnfamiliar forms and terms might get in the way of our seeing electronic music as music, but this can be overcome.Correct answer
  • CThe communication problem is what allows us to see electronic music as music because music must be difficult to understand.
  • DNone; they are unrelated to one another and form parts of different discussions.

Answer: B

Show explanation
Answer:B The opening questions ask whether electronic music counts as music. The “communication problem” is that unfamiliar forms/terms can block recognition—but the author holds that barrier can be overcome, so electronic music can still be heard as music. Why the others fail: • A — Says we *cannot* see it as music; the author is more optimistic about overcoming the barrier. • C — Claims the communication problem is what *allows* us to hear it as music; opposite of the worry. • D — Denies any link to the opening questions; the passage connects them.
Q18Reading Comprehension·Inference

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Often the well intentioned music lover or the traditionally-minded professional composer asks two basic questions when faced with the electronic music phenomena: (1) . . . is this type of artistic creation music at all? and, (2) given that the product is accepted as music of a new type or order, is not such music “inhuman”? .. . As Lejaren Hiller points out in his book Experimental Music (co-author Leonard M. Isaacson), two questions which often arise when music is discussed are: (a) the substance of musical communication and its symbolic and semantic significance, if any, and (b) the particular processes, both mental and technical, which are involved in creating and responding to musical composition. The ever-present popular concept of music as a direct, open, emotional expression and as a subjective form of communication from the composer, is, of course still that of the nineteenth century, when composers themselves spoke of music in those terms . . . But since the third decade of our century many composers have preferred more objective definitions of music, epitomized in Stravinsky’s description of it as “a form of speculation in terms of sound and time”. An acceptance of this more characteristic twentieth-century view of the art of musical composition will of course immediately bring the layman closer to an understanding of, and sympathetic response to, electronic music, even if the forms, sounds and approaches it uses will still be of a foreign nature to him. A communication problem however will still remain. The principal barrier that electronic music presents at large, in relation to the communication process, is that composers in this medium are employing a new language of forms . . . where terms like ‘densities’, ‘indefinite pitch relations’, ‘dynamic serialization’, ‘permutation’, etc., are substitutes (or remote equivalents) for the traditional concepts of harmony, melody, rhythm, etc. . . . When the new structural procedures of electronic music are at last fully understood by the listener the barriers between him and the work he faces will be removed. . . . The medium of electronic music has of course tempted many kinds of composers to try their hand at it . . . But the serious-minded composer approaches the world of electronic music with a more sophisticated and profound concept of creation. Although he knows that he can reproduce and employ melodic, rhythmic patterns and timbres of a traditional nature, he feels that it is in the exploration of sui generis languages and forms that the aesthetic magic of the new medium lies. And, conscientiously, he plunges into this search. The second objection usually levelled against electronic music is much more innocent in nature. When people speak—sometimes very vehemently—of the ‘inhuman’ quality of this music they seem to forget that the composer is the one who fires the machines, collects the sounds, manipulates them, pushes the buttons, programs the computer, filters the sounds, establishes pitches and scales, splices tape, thinks of forms, and rounds up the over-all structure of the piece, as well as every detail of it.

From the context in which it is placed, the phrase "sui generis" in paragraph 3 suggests which one of the following?

  • AIndescribable
  • BParticularCorrect answer
  • CUnaesthetic
  • DGeneric

Answer: B

Show explanation
Answer:B (Particular) In context, *sui generis* marks something of its own particular kind—not merely “indescribable,” “unaesthetic,” or “generic.” Why the others fail: • A — Indescribable overstates; the point is distinctive kind, not ineffability. • C — Unaesthetic is evaluative, not what *sui generis* means here. • D — Generic is nearly the opposite of *sui generis*.
Q19Reading Comprehension·Structure & Organization

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Often the well intentioned music lover or the traditionally-minded professional composer asks two basic questions when faced with the electronic music phenomena: (1) . . . is this type of artistic creation music at all? and, (2) given that the product is accepted as music of a new type or order, is not such music “inhuman”? .. . As Lejaren Hiller points out in his book Experimental Music (co-author Leonard M. Isaacson), two questions which often arise when music is discussed are: (a) the substance of musical communication and its symbolic and semantic significance, if any, and (b) the particular processes, both mental and technical, which are involved in creating and responding to musical composition. The ever-present popular concept of music as a direct, open, emotional expression and as a subjective form of communication from the composer, is, of course still that of the nineteenth century, when composers themselves spoke of music in those terms . . . But since the third decade of our century many composers have preferred more objective definitions of music, epitomized in Stravinsky’s description of it as “a form of speculation in terms of sound and time”. An acceptance of this more characteristic twentieth-century view of the art of musical composition will of course immediately bring the layman closer to an understanding of, and sympathetic response to, electronic music, even if the forms, sounds and approaches it uses will still be of a foreign nature to him. A communication problem however will still remain. The principal barrier that electronic music presents at large, in relation to the communication process, is that composers in this medium are employing a new language of forms . . . where terms like ‘densities’, ‘indefinite pitch relations’, ‘dynamic serialization’, ‘permutation’, etc., are substitutes (or remote equivalents) for the traditional concepts of harmony, melody, rhythm, etc. . . . When the new structural procedures of electronic music are at last fully understood by the listener the barriers between him and the work he faces will be removed. . . . The medium of electronic music has of course tempted many kinds of composers to try their hand at it . . . But the serious-minded composer approaches the world of electronic music with a more sophisticated and profound concept of creation. Although he knows that he can reproduce and employ melodic, rhythmic patterns and timbres of a traditional nature, he feels that it is in the exploration of sui generis languages and forms that the aesthetic magic of the new medium lies. And, conscientiously, he plunges into this search. The second objection usually levelled against electronic music is much more innocent in nature. When people speak—sometimes very vehemently—of the ‘inhuman’ quality of this music they seem to forget that the composer is the one who fires the machines, collects the sounds, manipulates them, pushes the buttons, programs the computer, filters the sounds, establishes pitches and scales, splices tape, thinks of forms, and rounds up the over-all structure of the piece, as well as every detail of it.

The goal of the author over the course of this passage is to:

  • Adifferentiate the modern composer from the nineteenth century composer.
  • Bdefend electronic music from certain common charges.Correct answer
  • Cdifferentiate between electronic music and other forms of music.
  • Ddefend the "serious-minded composer" from Lejaren Hill and Stravinsky.

Answer: B

Show explanation
Answer:B Across the passage the author answers common objections and defends electronic music as music. Why the others fail: • A — Modern vs nineteenth-century composer is not the governing goal. • C — Differentiation from other musics is secondary to the defence. • D — Not mainly defending a “serious-minded composer” against Hill/Stravinsky.
Q20Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Often the well intentioned music lover or the traditionally-minded professional composer asks two basic questions when faced with the electronic music phenomena: (1) . . . is this type of artistic creation music at all? and, (2) given that the product is accepted as music of a new type or order, is not such music “inhuman”? .. . As Lejaren Hiller points out in his book Experimental Music (co-author Leonard M. Isaacson), two questions which often arise when music is discussed are: (a) the substance of musical communication and its symbolic and semantic significance, if any, and (b) the particular processes, both mental and technical, which are involved in creating and responding to musical composition. The ever-present popular concept of music as a direct, open, emotional expression and as a subjective form of communication from the composer, is, of course still that of the nineteenth century, when composers themselves spoke of music in those terms . . . But since the third decade of our century many composers have preferred more objective definitions of music, epitomized in Stravinsky’s description of it as “a form of speculation in terms of sound and time”. An acceptance of this more characteristic twentieth-century view of the art of musical composition will of course immediately bring the layman closer to an understanding of, and sympathetic response to, electronic music, even if the forms, sounds and approaches it uses will still be of a foreign nature to him. A communication problem however will still remain. The principal barrier that electronic music presents at large, in relation to the communication process, is that composers in this medium are employing a new language of forms . . . where terms like ‘densities’, ‘indefinite pitch relations’, ‘dynamic serialization’, ‘permutation’, etc., are substitutes (or remote equivalents) for the traditional concepts of harmony, melody, rhythm, etc. . . . When the new structural procedures of electronic music are at last fully understood by the listener the barriers between him and the work he faces will be removed. . . . The medium of electronic music has of course tempted many kinds of composers to try their hand at it . . . But the serious-minded composer approaches the world of electronic music with a more sophisticated and profound concept of creation. Although he knows that he can reproduce and employ melodic, rhythmic patterns and timbres of a traditional nature, he feels that it is in the exploration of sui generis languages and forms that the aesthetic magic of the new medium lies. And, conscientiously, he plunges into this search. The second objection usually levelled against electronic music is much more innocent in nature. When people speak—sometimes very vehemently—of the ‘inhuman’ quality of this music they seem to forget that the composer is the one who fires the machines, collects the sounds, manipulates them, pushes the buttons, programs the computer, filters the sounds, establishes pitches and scales, splices tape, thinks of forms, and rounds up the over-all structure of the piece, as well as every detail of it.

The mention of Stravinsky's description of music in the first paragraph does all the following EXCEPT:

  • Acomplicate our notion of what is communicated through music.
  • Ballow us to classify electronic music as music.
  • Crespond to and expand upon earlier understandings of music.
  • Dhelp us determine which sounds are musical and which are not.Correct answer

Answer: D

Show explanation
Answer:D Stravinsky’s remark helps complicate what music communicates, supports counting electronic music as music, and extends prior ideas—but it does *not* supply a test for which sounds are musical vs not. Why the others fail: • A — It does complicate communication-through-music. • B — It helps classify electronic work as music. • C — It responds to/expands earlier understandings.
Q21Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Understanding the key properties of complex systems can help us clarify and deal with many new and existing global challenges, from pandemics to poverty . . . A recent study in Nature Physics found transitions to orderly states such as schooling in fish (all fish swimming in the same direction), can be caused, paradoxically, by randomness, or ‘noise’ feeding back on itself. That is, a misalignment among the fish causes further misalignment, eventually inducing a transition to schooling. Most of us wouldn’t guess that noise can produce predictable behaviour. The result invites us to consider how technology such as contact-tracing apps, although informing us locally, might negatively impact our collective movement. If each of us changes our behaviour to avoid the infected, we might generate a collective pattern we had aimed to avoid: higher levels of interaction between the infected and susceptible, or high levels of interaction among the asymptomatic. Complex systems also suffer from a special vulnerability to events that don’t follow a normal distribution or ‘bell curve’. When events are distributed normally, most outcomes are familiar and don’t seem particularly striking. Height is a good example: it’s pretty unusual for a man to be over 7 feet tall; most adults are between 5 and 6 feet, and there is no known person over 9 feet tall. But in collective settings where contagion shapes behaviour – a run on the banks, a scramble to buy toilet paper – the probability distributions for possible events are often heavy-tailed. There is a much higher probability of extreme events, such as a stock market crash or a massive surge in infections. These events are still unlikely, but they occur more frequently and are larger than would be expected under normal distributions. What’s more, once a rare but hugely significant ‘tail’ event takes place, this raises the probability of further tail events. We might call them second-order tail events; they include stock market gyrations after a big fall and earthquake aftershocks. The initial probability of second-order tail events is so tiny it’s almost impossible to calculate – but once a first-order tail event occurs, the rules change, and the probability of a second-order tail event increases. The dynamics of tail events are complicated by the fact that they result from cascades of other unlikely events. When COVID-19 first struck, the stock market suffered stunning losses followed by an equally stunning recovery. Some of these dynamics are potentially attributable to former sports bettors, with no sports to bet on, entering the market as speculators rather than investors. The arrival of these new players might have increased inefficiencies and allowed savvy long-term investors to gain an edge over bettors with different goals. . . . One reason a first-order tail event can induce further tail events is that it changes the perceived costs of our actions and changes the rules that we play by. This game-change is an example of another key complex systems concept: nonstationarity. A second, canonical example of nonstationarity is adaptation, as illustrated by the arms race involved in the coevolution of hosts and parasites in which each has to ‘run’ faster, just to keep up with the novel solutions the other one presents as they battle it out in evolutionary time.

All of the following inferences are supported by the passage EXCEPT that:

  • Alearning can change the rules that actors face. So, a rare shock can alter payoffs and raise the odds of subsequent large disturbances within the same system, which supports the idea of second-order tail events.
  • Bthe text attributes the COVID-19 pandemic rebound in financial markets solely to displaced sports bettors and treats their entry as the overriding cause of the rapid recovery across assets and time horizons.Correct answer
  • Cexamples like runs on banks and toilet paper scrambles illustrate how contagion can amplify local choices into system-wide cascades that surprise participants and lead to patterns they did not intend to create.
  • Dheavy-tailed events make extreme outcomes more frequent and larger than bell curve expectations. This complicates forecasting and risk management in collective settings shaped by contagion and copying behaviour.

Answer: B

Show explanation
Answer:B The EXCEPT: the passage does *not* say COVID market rebound was *solely* caused by displaced sports bettors as the overriding cause. That overclaim is unsupported. Why the others fail: • A — Second-order effects after shocks altering rules/payoffs are in scope. • C — Bank runs/toilet-paper scrambles illustrate contagion cascades. • D — Heavy tails complicating risk management matches the argument.
Q22Reading Comprehension·Application & Analogy

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Understanding the key properties of complex systems can help us clarify and deal with many new and existing global challenges, from pandemics to poverty . . . A recent study in Nature Physics found transitions to orderly states such as schooling in fish (all fish swimming in the same direction), can be caused, paradoxically, by randomness, or ‘noise’ feeding back on itself. That is, a misalignment among the fish causes further misalignment, eventually inducing a transition to schooling. Most of us wouldn’t guess that noise can produce predictable behaviour. The result invites us to consider how technology such as contact-tracing apps, although informing us locally, might negatively impact our collective movement. If each of us changes our behaviour to avoid the infected, we might generate a collective pattern we had aimed to avoid: higher levels of interaction between the infected and susceptible, or high levels of interaction among the asymptomatic. Complex systems also suffer from a special vulnerability to events that don’t follow a normal distribution or ‘bell curve’. When events are distributed normally, most outcomes are familiar and don’t seem particularly striking. Height is a good example: it’s pretty unusual for a man to be over 7 feet tall; most adults are between 5 and 6 feet, and there is no known person over 9 feet tall. But in collective settings where contagion shapes behaviour – a run on the banks, a scramble to buy toilet paper – the probability distributions for possible events are often heavy-tailed. There is a much higher probability of extreme events, such as a stock market crash or a massive surge in infections. These events are still unlikely, but they occur more frequently and are larger than would be expected under normal distributions. What’s more, once a rare but hugely significant ‘tail’ event takes place, this raises the probability of further tail events. We might call them second-order tail events; they include stock market gyrations after a big fall and earthquake aftershocks. The initial probability of second-order tail events is so tiny it’s almost impossible to calculate – but once a first-order tail event occurs, the rules change, and the probability of a second-order tail event increases. The dynamics of tail events are complicated by the fact that they result from cascades of other unlikely events. When COVID-19 first struck, the stock market suffered stunning losses followed by an equally stunning recovery. Some of these dynamics are potentially attributable to former sports bettors, with no sports to bet on, entering the market as speculators rather than investors. The arrival of these new players might have increased inefficiencies and allowed savvy long-term investors to gain an edge over bettors with different goals. . . . One reason a first-order tail event can induce further tail events is that it changes the perceived costs of our actions and changes the rules that we play by. This game-change is an example of another key complex systems concept: nonstationarity. A second, canonical example of nonstationarity is adaptation, as illustrated by the arms race involved in the coevolution of hosts and parasites in which each has to ‘run’ faster, just to keep up with the novel solutions the other one presents as they battle it out in evolutionary time.

Which one of the following observations would most strengthen the passage's claim that a first-order tail event raises the probability of further tail events in complex systems?

  • AAfter a major equity crash, researchers find dense clusters of large daily moves for several weeks, with extreme days occurring far more often than in normal circumstances for assets with customarily low volatility profiles.Correct answer
  • BFollowing large earthquakes, regional seismic activity returns to baseline within hours with no aftershock sequence once data are adjusted for reporting effects, which suggests independence across events rather than any elevation in subsequent tail probabilities.
  • CIn epidemic networks, initial super-spreading episodes are isolated spikes after which outbreak sizes match the baseline distribution from independent contact models across comparable cities with no rise in the frequency or size of later extreme clusters.
  • DRiver discharge records show water levels fit a normal distribution with thin tails that match laboratory data, regardless of storms or floods.

Answer: A

Show explanation
Answer:A A first-order tail raising odds of further tails is strengthened by dense clusters of extreme market moves after a crash—A. Why the others fail: • B — Quakes with no aftershocks suggest independence, weakening the claim. • C — Isolated super-spreader spikes returning to baseline weaken contagion-of-tails. • D — Thin-tailed normals deny heavy-tail clustering.
Q23Reading Comprehension·Main Idea / Purpose

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Understanding the key properties of complex systems can help us clarify and deal with many new and existing global challenges, from pandemics to poverty . . . A recent study in Nature Physics found transitions to orderly states such as schooling in fish (all fish swimming in the same direction), can be caused, paradoxically, by randomness, or ‘noise’ feeding back on itself. That is, a misalignment among the fish causes further misalignment, eventually inducing a transition to schooling. Most of us wouldn’t guess that noise can produce predictable behaviour. The result invites us to consider how technology such as contact-tracing apps, although informing us locally, might negatively impact our collective movement. If each of us changes our behaviour to avoid the infected, we might generate a collective pattern we had aimed to avoid: higher levels of interaction between the infected and susceptible, or high levels of interaction among the asymptomatic. Complex systems also suffer from a special vulnerability to events that don’t follow a normal distribution or ‘bell curve’. When events are distributed normally, most outcomes are familiar and don’t seem particularly striking. Height is a good example: it’s pretty unusual for a man to be over 7 feet tall; most adults are between 5 and 6 feet, and there is no known person over 9 feet tall. But in collective settings where contagion shapes behaviour – a run on the banks, a scramble to buy toilet paper – the probability distributions for possible events are often heavy-tailed. There is a much higher probability of extreme events, such as a stock market crash or a massive surge in infections. These events are still unlikely, but they occur more frequently and are larger than would be expected under normal distributions. What’s more, once a rare but hugely significant ‘tail’ event takes place, this raises the probability of further tail events. We might call them second-order tail events; they include stock market gyrations after a big fall and earthquake aftershocks. The initial probability of second-order tail events is so tiny it’s almost impossible to calculate – but once a first-order tail event occurs, the rules change, and the probability of a second-order tail event increases. The dynamics of tail events are complicated by the fact that they result from cascades of other unlikely events. When COVID-19 first struck, the stock market suffered stunning losses followed by an equally stunning recovery. Some of these dynamics are potentially attributable to former sports bettors, with no sports to bet on, entering the market as speculators rather than investors. The arrival of these new players might have increased inefficiencies and allowed savvy long-term investors to gain an edge over bettors with different goals. . . . One reason a first-order tail event can induce further tail events is that it changes the perceived costs of our actions and changes the rules that we play by. This game-change is an example of another key complex systems concept: nonstationarity. A second, canonical example of nonstationarity is adaptation, as illustrated by the arms race involved in the coevolution of hosts and parasites in which each has to ‘run’ faster, just to keep up with the novel solutions the other one presents as they battle it out in evolutionary time.

Which one of the options below best summarises the passage?

  • AThe passage explains how speculative entrants always produce inefficiency after health shocks. Therefore, long-term investors invariably profit when new participants push prices away from fundamentals under pandemic conditions and comparable crises.
  • BThe passage explains how social outcomes generally follow normal distributions. So, extreme events are negligible, and policy should stabilise averages rather than learn from large shocks in fast-changing collective settings.
  • CThe passage explains how nonstationarity works in evolutionary biology and rejects applications in markets or public health because adaptation is exclusive to parasite-host systems and cannot arise in technology-mediated social dynamics.
  • DThe passage explains how noise can create order, then shows why complex systems with contagion are vulnerable to heavy-tailed cascades. It also explains why early shocks change rules through nonstationarity with a market illustration during the COVID-19 disruption.Correct answer

Answer: D

Show explanation
Answer:D Summary: noise can create order; contagion-heavy systems get heavy-tailed cascades; early shocks change rules via nonstationarity—D. Why the others fail: • A — Overclaims speculative entrants *always* create inefficiency after health shocks. • B — Says outcomes are normal/extremes negligible—opposite of the passage. • C — Rejects applying nonstationarity outside biology—too narrow vs the text.
Q24Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Understanding the key properties of complex systems can help us clarify and deal with many new and existing global challenges, from pandemics to poverty . . . A recent study in Nature Physics found transitions to orderly states such as schooling in fish (all fish swimming in the same direction), can be caused, paradoxically, by randomness, or ‘noise’ feeding back on itself. That is, a misalignment among the fish causes further misalignment, eventually inducing a transition to schooling. Most of us wouldn’t guess that noise can produce predictable behaviour. The result invites us to consider how technology such as contact-tracing apps, although informing us locally, might negatively impact our collective movement. If each of us changes our behaviour to avoid the infected, we might generate a collective pattern we had aimed to avoid: higher levels of interaction between the infected and susceptible, or high levels of interaction among the asymptomatic. Complex systems also suffer from a special vulnerability to events that don’t follow a normal distribution or ‘bell curve’. When events are distributed normally, most outcomes are familiar and don’t seem particularly striking. Height is a good example: it’s pretty unusual for a man to be over 7 feet tall; most adults are between 5 and 6 feet, and there is no known person over 9 feet tall. But in collective settings where contagion shapes behaviour – a run on the banks, a scramble to buy toilet paper – the probability distributions for possible events are often heavy-tailed. There is a much higher probability of extreme events, such as a stock market crash or a massive surge in infections. These events are still unlikely, but they occur more frequently and are larger than would be expected under normal distributions. What’s more, once a rare but hugely significant ‘tail’ event takes place, this raises the probability of further tail events. We might call them second-order tail events; they include stock market gyrations after a big fall and earthquake aftershocks. The initial probability of second-order tail events is so tiny it’s almost impossible to calculate – but once a first-order tail event occurs, the rules change, and the probability of a second-order tail event increases. The dynamics of tail events are complicated by the fact that they result from cascades of other unlikely events. When COVID-19 first struck, the stock market suffered stunning losses followed by an equally stunning recovery. Some of these dynamics are potentially attributable to former sports bettors, with no sports to bet on, entering the market as speculators rather than investors. The arrival of these new players might have increased inefficiencies and allowed savvy long-term investors to gain an edge over bettors with different goals. . . . One reason a first-order tail event can induce further tail events is that it changes the perceived costs of our actions and changes the rules that we play by. This game-change is an example of another key complex systems concept: nonstationarity. A second, canonical example of nonstationarity is adaptation, as illustrated by the arms race involved in the coevolution of hosts and parasites in which each has to ‘run’ faster, just to keep up with the novel solutions the other one presents as they battle it out in evolutionary time.

The passage suggests that contact tracing apps could inadvertently raise risky interactions by altering local behaviour. Which one of the assumptions below is most necessary for that suggestion to hold?

  • AIndividuals base movement choices partly on observed infections and on the behaviour of others. So, local responses interact, which turns many small adjustments into large scale patterns that can frustrate the intended aim of risk reduction.Correct answer
  • BMost users uninstall apps within a week, which leaves only highly exposed individuals participating. This neutralises any systematic bias in routing decisions and prevents any predictable change in aggregate contact patterns.
  • CApp alerts always include precise location to within one metre and deliver real time updates for all users, which ensures that the data feed is perfectly accurate regardless of privacy settings, power limits, or network conditions.
  • DUrban networks have uniform traffic conditions at all hours, which allows perfectly predictable routing independent of personal choices, social signals, or crowd reactions and, therefore, makes interdependence negligible in city movement decisions.

Answer: A

Show explanation
Answer:A For contact-tracing apps to raise risky mixing, people must adjust movement from observed infections *and* others’ behaviour so local responses interact into large patterns—A. Why the others fail: • B — Mass uninstalls would block systematic routing effects. • C — Perfect metre-level alerts are unnecessary and overstrong. • D — Uniform traffic independent of choices denies the interaction mechanism.

DILR(22 questions)

Q25Data Interpretation·Networks & Routes

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments BC, CD, and D-E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known: 1. Segment C-D had an occupancy factor of 95%. Only segment B-C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D-E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

What was the occupancy factor for segment D-E?

  • A35%
  • B70%Correct answer
  • C84%
  • D77%

Answer: B

Show explanation
Answer:B (70%) Stations A–B–C–D–E; capacity 200. Let AC = AE = a (> BE = 30), AD = b, CD = x, CE = y; AB = BD = DE = 0, BC = 40, BE = 30. Segment seats are multiples of 10. D–E seats come only from AE, BE, CE: a + 30 + y. Clue 3: seats from before C are exactly 47 of D–E, so a + 30 = (47)(a + 30 + y) ⇒ y = 3a + 904. With a,y multiples of 10 and a > 30, the only fit is a = 50, y = 60. Thus D–E = 50 + 30 + 60 = 140 → occupancy 140200 = 70%. Why B: 70% is exactly that ratio. - A (35%): would need 70 seats, half of the forced 140. - C (84%): would need 168 seats; not compatible with the 47 split and multiples of 10. - D (77%): not a multiple of 10 seats (154), ruled out by clue 6.
Q26Data Interpretation·Networks & RoutesTITA

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments BC, CD, and D-E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known: 1. Segment C-D had an occupancy factor of 95%. Only segment B-C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D-E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

How many tickets were booked from Station A to Station E?

Answer: 50

Show explanation
Answer:50 Same OD matrix as Q25. From the 47 condition on D–E, AE = a must be 50 (with CE = 60). Clue 4 also forces AC = AE = 50 > BE = 30. Then BC is the unique full segment: seats = AC+AD+AE+BC+BE = 50+b+50+40+30 = 170+b ≤ 200, and only BC can exceed CD’s 190, so BC = 200 ⇒ b = AD = 30. CD = AD+AE+BE+CD_tickets+CE = 30+50+30+x+60 = 170+x = 190 ⇒ x = CD = 20. Consistent throughout. So tickets A→E = 50.
Q27Data Interpretation·Networks & RoutesTITA

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments BC, CD, and D-E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known: 1. Segment C-D had an occupancy factor of 95%. Only segment B-C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D-E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

How many tickets were booked from Station C?

Answer: 80

Show explanation
Answer:80 Stations A–B–C–D–E; capacity 200. Allowed forward tickets only. AB = BD = DE = 0; BC = 40; BE = 30. Let AC = AE = a (> 30), AD = b, CD = x, CE = y; all ticket counts multiples of 10. D–E seats = AE+BE+CE = a+30+y. Clue 3: seats from before C are 47 of D–E ⇒ a+30 = (47)(a+30+y) ⇒ y = 3a+904. Only a,y multiples of 10 with a>30 give a=50, y=60. CD occupancy 95% ⇒ 190 seats. Only BC can be higher, so BC seats = 200. BC seats = AC+AD+AE+BC+BE = 50+b+50+40+30 = 170+b = 200 ⇒ b = AD = 30. Then CD seats = AD+AE+BE+CD+CE = 30+50+30+x+60 = 170+x = 190 ⇒ x = CD = 20. So CE = 60, CD = 20. Tickets *from* C are only CD and CE (no earlier destination). Total = 20 + 60 = 80.
Q28Data Interpretation·Networks & RoutesTITA

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments BC, CD, and D-E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known: 1. Segment C-D had an occupancy factor of 95%. Only segment B-C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D-E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

What is the difference between the number of tickets booked to Station C and the number of tickets booked to Station D?

Answer: 40

Show explanation
Answer:40 Stations A–B–C–D–E; capacity 200. Allowed forward tickets only. AB = BD = DE = 0; BC = 40; BE = 30. Let AC = AE = a (> 30), AD = b, CD = x, CE = y; all ticket counts multiples of 10. D–E seats = AE+BE+CE = a+30+y. Clue 3: seats from before C are 47 of D–E ⇒ a+30 = (47)(a+30+y) ⇒ y = 3a+904. Only a,y multiples of 10 with a>30 give a=50, y=60. CD occupancy 95% ⇒ 190 seats. Only BC can be higher, so BC seats = 200. BC seats = AC+AD+AE+BC+BE = 50+b+50+40+30 = 170+b = 200 ⇒ b = AD = 30. Then CD seats = AD+AE+BE+CD+CE = 30+50+30+x+60 = 170+x = 190 ⇒ x = CD = 20. So CE = 60, CD = 20. Tickets *to* C: AC + BC = 50 + 40 = 90. Tickets *to* D: AD + CD = 30 + 20 = 50 (BD = 0). Difference 90 − 50 = 40.
Q29Data Interpretation·Networks & RoutesTITA

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments BC, CD, and D-E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known: 1. Segment C-D had an occupancy factor of 95%. Only segment B-C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D-E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

How many tickets were booked to travel in exactly one segment?

Answer: 60

Show explanation
Answer:60 Stations A–B–C–D–E; capacity 200. Allowed forward tickets only. AB = BD = DE = 0; BC = 40; BE = 30. Let AC = AE = a (> 30), AD = b, CD = x, CE = y; all ticket counts multiples of 10. D–E seats = AE+BE+CE = a+30+y. Clue 3: seats from before C are 47 of D–E ⇒ a+30 = (47)(a+30+y) ⇒ y = 3a+904. Only a,y multiples of 10 with a>30 give a=50, y=60. CD occupancy 95% ⇒ 190 seats. Only BC can be higher, so BC seats = 200. BC seats = AC+AD+AE+BC+BE = 50+b+50+40+30 = 170+b = 200 ⇒ b = AD = 30. Then CD seats = AD+AE+BE+CD+CE = 30+50+30+x+60 = 170+x = 190 ⇒ x = CD = 20. So CE = 60, CD = 20. Exactly-one-segment tickets are AB, BC, CD, DE. AB = DE = 0 (clue 5), BC = 40, CD = 20 → total 60.
Q30Logical Reasoning·Grouping & SelectionTITA

At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu. At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3. The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher. 1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4. 2. Dolly and Falguni were the only employees who got the same rating across all the quarters. 3. The following is known about ratings given by Lalu: Bunty received a rating of 1 in Quarter 2. Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

What was Eklavya’s score at the end of Quarter 2?

Answer: 4

Show explanation
Answer:4 Elite Q1 = {{Asha, Bunty, Chintu}}; Novice Q1 = {{Dolly, Eklavya, Falguni}}. Dolly and Falguni alone keep a constant rating all year. Lalu’s Q3 ratings (Asha = 1, Dolly = 2) and Bunty’s Q2 = 1 force Dolly ≡ 2 and Falguni ≡ 3 every quarter, so Eklavya’s leftover Q1 Novice rating is 1. End-Q1: Bunty (Elite min, rating 1) demotes; Falguni (Novice max, score 3) promotes. Q2 Elite = {{Asha, Chintu, Falguni}}; Q2 Novice = {{Bunty, Dolly, Eklavya}}. With Bunty = 1 given, Dolly = 2, Eklavya = 3. After Q2, Asha (Elite min with rating 1) demotes; Eklavya promotes. Q3 Novice = {{Asha, Bunty, Dolly}} with ratings 1, 3, 2 respectively. Eklavya’s score after Q2 = Q1 rating 1 + Q2 rating 3 = 4.
Q31Logical Reasoning·Grouping & SelectionTITA

At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu. At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3. The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher. 1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4. 2. Dolly and Falguni were the only employees who got the same rating across all the quarters. 3. The following is known about ratings given by Lalu: Bunty received a rating of 1 in Quarter 2. Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

How many employees changed groups more than once up to the beginning of Quarter 4?

Answer: 0

Show explanation
Answer:0 Elite Q1 = {{Asha, Bunty, Chintu}}; Novice Q1 = {{Dolly, Eklavya, Falguni}}. Dolly and Falguni alone keep a constant rating all year. Lalu’s Q3 ratings (Asha = 1, Dolly = 2) and Bunty’s Q2 = 1 force Dolly ≡ 2 and Falguni ≡ 3 every quarter, so Eklavya’s leftover Q1 Novice rating is 1. End-Q1: Bunty (Elite min, rating 1) demotes; Falguni (Novice max, score 3) promotes. Q2 Elite = {{Asha, Chintu, Falguni}}; Q2 Novice = {{Bunty, Dolly, Eklavya}}. With Bunty = 1 given, Dolly = 2, Eklavya = 3. After Q2, Asha (Elite min with rating 1) demotes; Eklavya promotes. Q3 Novice = {{Asha, Bunty, Dolly}} with ratings 1, 3, 2 respectively. Forced group paths to start of Q4 (one swap per quarter-end): Asha Elite→Elite→Novice→Novice; Bunty Elite→Novice→Novice→Novice; Chintu Elite→Elite→Elite→Novice; Dolly stays Novice until at most one late move; Eklavya and Falguni each cross Elite↔Novice once. No one changes groups more than once before Q4, so the count is 0.
Q32Logical Reasoning·Grouping & SelectionTITA

At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu. At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3. The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher. 1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4. 2. Dolly and Falguni were the only employees who got the same rating across all the quarters. 3. The following is known about ratings given by Lalu: Bunty received a rating of 1 in Quarter 2. Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

What was Bunty’s score at the end of Quarter 3?

Answer: 5

Show explanation
Answer:5 Elite Q1 = {{Asha, Bunty, Chintu}}; Novice Q1 = {{Dolly, Eklavya, Falguni}}. Dolly and Falguni alone keep a constant rating all year. Lalu’s Q3 ratings (Asha = 1, Dolly = 2) and Bunty’s Q2 = 1 force Dolly ≡ 2 and Falguni ≡ 3 every quarter, so Eklavya’s leftover Q1 Novice rating is 1. End-Q1: Bunty (Elite min, rating 1) demotes; Falguni (Novice max, score 3) promotes. Q2 Elite = {{Asha, Chintu, Falguni}}; Q2 Novice = {{Bunty, Dolly, Eklavya}}. With Bunty = 1 given, Dolly = 2, Eklavya = 3. After Q2, Asha (Elite min with rating 1) demotes; Eklavya promotes. Q3 Novice = {{Asha, Bunty, Dolly}} with ratings 1, 3, 2 respectively. Bunty’s ratings: Q1 Elite = 1 (must be Elite-min to demote while Asha/Chintu stay), Q2 = 1 (given), Q3 Novice = 3 (leftover vs Asha 1, Dolly 2). Score end Q3 = 1 + 1 + 3 = 5.
Q33Logical Reasoning·Grouping & SelectionTITA

At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu. At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3. The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher. 1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4. 2. Dolly and Falguni were the only employees who got the same rating across all the quarters. 3. The following is known about ratings given by Lalu: Bunty received a rating of 1 in Quarter 2. Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

For how many employees can the scores at the end of Quarter 3 be determined with certainty?

Answer: 4

Show explanation
Answer:4 Elite Q1 = {{Asha, Bunty, Chintu}}; Novice Q1 = {{Dolly, Eklavya, Falguni}}. Dolly and Falguni alone keep a constant rating all year. Lalu’s Q3 ratings (Asha = 1, Dolly = 2) and Bunty’s Q2 = 1 force Dolly ≡ 2 and Falguni ≡ 3 every quarter, so Eklavya’s leftover Q1 Novice rating is 1. End-Q1: Bunty (Elite min, rating 1) demotes; Falguni (Novice max, score 3) promotes. Q2 Elite = {{Asha, Chintu, Falguni}}; Q2 Novice = {{Bunty, Dolly, Eklavya}}. With Bunty = 1 given, Dolly = 2, Eklavya = 3. After Q2, Asha (Elite min with rating 1) demotes; Eklavya promotes. Q3 Novice = {{Asha, Bunty, Dolly}} with ratings 1, 3, 2 respectively. Certain end-Q3 scores: Dolly = 2+2+2 = 6; Falguni = 3+3+3 = 9; Bunty = 1+1+3 = 5; Eklavya = 1+3+2 = 6. Asha’s and Chintu’s Q1 Elite ratings can still be {2,3} swapped without breaking promotions, so their totals stay ambiguous. Exactly 4 employees have determined Q3 scores.
Q34Logical Reasoning·Grouping & Selection

At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu. At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3. The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher. 1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4. 2. Dolly and Falguni were the only employees who got the same rating across all the quarters. 3. The following is known about ratings given by Lalu: Bunty received a rating of 1 in Quarter 2. Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

Which of the following statements is/are NECESSARILY true? I. Asha received a rating of 2 in Quarter 1. II. Asha received a rating of 1 in Quarter 2.

  • AOnly IICorrect answer
  • BOnly I
  • CBoth I and II
  • DNeither I nor II

Answer: A

Show explanation
Answer:A (Only II) I. Asha’s Q1 Elite rating can be 2 or 3 (swap with Chintu) — not necessary. II. After Q1, Asha stays Elite; Q2 Elite = {Asha, Chintu, Falguni}. Falguni constant 3, and the demotion into Novice after Q2 must be Asha (she is in Novice by Q3 with Lalu rating 1). The only way Asha is Elite-min after Q2 is rating 1 in Q2. So only II is necessary → A. - B: claims only I, but I is optional. - C: both — I fails. - D: neither — II is forced.
Q35Logical Reasoning·Seating ArrangementsTITA

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on. The friends take turns moving either clockwise or counter clockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively). The following information is known. 1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6. 2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2

What is the number of the chair initially occupied by Bashir?

Answer: 4

Show explanation
Answer:4 Initial: A–C adjacent; Bashir and Davies each have empty chairs on both sides. Davies is still on chair 2 after Turn 1 and Chhavi on 7 after Turn 2, so those are their starting seats. The unique start is Davies 2, Bashir 4, Aslam 6, Chhavi 7 (empties 1,3,5). Forced moves (adjacent block only after Turns 2 and 6; Davies on 4 after Turn 5): Turn1 Aslam → 1; Turn2 Bashir → 3 (adjacent on 1–2–3–7); Turn3 Chhavi → 6 (chair 4 kept free); Turn4 Davies → 4; Turn5 Aslam → 7; Turn6 Bashir → 5. Bashir’s initial chair is therefore 4.
Q36Logical Reasoning·Seating Arrangements

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on. The friends take turns moving either clockwise or counter clockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively). The following information is known. 1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6. 2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2

Who sits on the chair numbered 4 at the end of Turn 3?

  • ABashir
  • BChhavi
  • CDavies
  • DNo oneCorrect answer

Answer: D

Show explanation
Answer:D (No one) Forced moves for adjacency only after Turns 2 and 6, and Davies on 4 after Turn 5: Turn1 Aslam → chair 1; Turn2 Bashir → 3 (four become adjacent on 1–2–3–7…); Turn3 Chhavi must go to 6 (not 4 — chair 4 must stay free for Davies); Turn4 Davies → 4. After Turn 3, chair 4 is still empty → No one. - A Bashir: he is on 3 after Turn 2 and does not move on Turn 3. - B Chhavi: she took 6, not 4. - C Davies: he only reaches 4 on Turn 4.
Q37Logical Reasoning·Seating Arrangements

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on. The friends take turns moving either clockwise or counter clockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively). The following information is known. 1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6. 2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2

Which of the chairs are occupied at the end of Turn 6?

  • AChairs numbered 1, 2, 6, and 7
  • BChairs numbered 2, 3, 4, and 5
  • CChairs numbered 1, 2, 3, and 4
  • DChairs numbered 4, 5, 6, and 7Correct answer

Answer: D

Show explanation
Answer:D (Chairs numbered 4, 5, 6, and 7) Initial: A–C adjacent; Bashir and Davies each have empty chairs on both sides. Davies is still on chair 2 after Turn 1 and Chhavi on 7 after Turn 2, so those are their starting seats. The unique start is Davies 2, Bashir 4, Aslam 6, Chhavi 7 (empties 1,3,5). Forced moves (adjacent block only after Turns 2 and 6; Davies on 4 after Turn 5): Turn1 Aslam → 1; Turn2 Bashir → 3 (adjacent on 1–2–3–7); Turn3 Chhavi → 6 (chair 4 kept free); Turn4 Davies → 4; Turn5 Aslam → 7; Turn6 Bashir → 5. End of Turn 6: Davies 4, Bashir 5, Chhavi 6, Aslam 7 → occupied {4,5,6,7}. - A {1,2,6,7}: includes early chairs already vacated. - B {2,3,4,5}: Bashir left 3; Aslam left the low numbers. - C {1,2,3,4}: that is the Turn-2 block, not Turn 6.
Q38Logical Reasoning·Seating Arrangements

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on. The friends take turns moving either clockwise or counter clockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively). The following information is known. 1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6. 2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2

Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?

  • ADavies onlyCorrect answer
  • BChhavi and Davies
  • CAslam and Chhavi
  • DChhavi only

Answer: A

Show explanation
Answer:A (Davies only) Initial: A–C adjacent; Bashir and Davies each have empty chairs on both sides. Davies is still on chair 2 after Turn 1 and Chhavi on 7 after Turn 2, so those are their starting seats. The unique start is Davies 2, Bashir 4, Aslam 6, Chhavi 7 (empties 1,3,5). Forced moves (adjacent block only after Turns 2 and 6; Davies on 4 after Turn 5): Turn1 Aslam → 1; Turn2 Bashir → 3 (adjacent on 1–2–3–7); Turn3 Chhavi → 6 (chair 4 kept free); Turn4 Davies → 4; Turn5 Aslam → 7; Turn6 Bashir → 5. After Turn 6 Bashir sits on 5 beside Davies (4) and Chhavi (6). Turn7 Chhavi leaves chair 6 either way, so one neighbor empties while Davies stays on 4. The only occupied neighbor of Bashir is Davies. - B Chhavi and Davies: Chhavi has just left an adjacent seat. - C Aslam and Chhavi: Aslam is on 7, not next to 5. - D Chhavi only: Davies remains on 4 beside Bashir.
Q39Logical Reasoning·Binary LogicTITA

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”. A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.” The following information is known. 1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan. 2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal. 3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions. 4. No one responded “Yes” more than twice. 5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan. 6. Clive tapped more times in total than Badal.

How many taps did Clive receive for his question?

Answer: 7

Show explanation
Answer:7 Total taps 40; Alia 6, Dilshan 11, Ehsaan 9 ⇒ Badal + Clive = 14. Clive > Badal and each person answers 4 questions with ≤2 Yes (1-tap), so minimum taps/person = 1+1+2+2 = 6. Only feasible split: Badal 6, Clive 8. Alia Yes to Clive & Dilshan; with total 6 and ≤2 Yes, her answers to Badal & Ehsaan are both No (2). Dilshan’s remaining three answers must all be Maybe (3) to reach 11. Badal/Dilshan/Ehsaan each receive the same total a; filling the response grid with “each question has ≥1 Yes, No, Maybe” forces Badal’s received total a = 8, then Alia’s received 9 + three 8’s + Clive’s received = 40 ⇒ Clive received 7.
Q40Logical Reasoning·Binary LogicTITA

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”. A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.” The following information is known. 1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan. 2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal. 3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions. 4. No one responded “Yes” more than twice. 5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan. 6. Clive tapped more times in total than Badal.

Which two people tapped an equal number of times in total?

Answer: Alia and Badal

Show explanation
Answer:Alia and Badal Total taps 40; Alia 6, Dilshan 11, Ehsaan 9 ⇒ Badal + Clive = 14. Clive > Badal; each answers 4 questions with ≤2 Yes, so min taps/person = 6. Only split: Badal 6, Clive 8. Alia Yes to Clive & Dilshan; with total 6 and ≤2 Yes, her answers to Badal & Ehsaan are both No. Dilshan’s other three answers are all Maybe (to reach 11). Badal/Dilshan/Ehsaan receive equal totals a; the Yes/No/Maybe-per-question and Alia/Ehsaan mismatch rules force a = 8 and Clive received 7. The unique response grid then follows. Outgoing tap totals: Alia 6, Badal 6, Clive 8, Dilshan 11, Ehsaan 9. The equal pair is Alia and Badal.
Q41Logical Reasoning·Binary Logic

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”. A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.” The following information is known. 1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan. 2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal. 3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions. 4. No one responded “Yes” more than twice. 5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan. 6. Clive tapped more times in total than Badal.

What was Clive’s response to Ehsaan’s question?

  • AYes
  • BMaybe
  • CCannot be determined
  • DNoCorrect answer

Answer: D

Show explanation
Answer:D (No) Total taps 40; Alia 6, Dilshan 11, Ehsaan 9 ⇒ Badal + Clive = 14. Clive > Badal; each answers 4 questions with ≤2 Yes, so min taps/person = 6. Only split: Badal 6, Clive 8. Alia Yes to Clive & Dilshan; with total 6 and ≤2 Yes, her answers to Badal & Ehsaan are both No. Dilshan’s other three answers are all Maybe (to reach 11). Badal/Dilshan/Ehsaan receive equal totals a; the Yes/No/Maybe-per-question and Alia/Ehsaan mismatch rules force a = 8 and Clive received 7. The unique response grid then follows. In that unique grid, Clive’s answer to Ehsaan is No (2 taps). - A Yes: would give Clive a third Yes or break Ehsaan’s mismatch/tap total. - B Maybe: Dilshan is already Maybe to Ehsaan; another Maybe leaves Ehsaan’s question without a No once other cells are fixed. - C Cannot be determined: the grid closes uniquely.
Q42Logical Reasoning·Binary LogicTITA

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”. A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.” The following information is known. 1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan. 2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal. 3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions. 4. No one responded “Yes” more than twice. 5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan. 6. Clive tapped more times in total than Badal.

How many “Yes” responses were received across all the questions?

Answer: 6

Show explanation
Answer:6 Total taps 40; Alia 6, Dilshan 11, Ehsaan 9 ⇒ Badal + Clive = 14. Clive > Badal; each answers 4 questions with ≤2 Yes, so min taps/person = 6. Only split: Badal 6, Clive 8. Alia Yes to Clive & Dilshan; with total 6 and ≤2 Yes, her answers to Badal & Ehsaan are both No. Dilshan’s other three answers are all Maybe (to reach 11). Badal/Dilshan/Ehsaan receive equal totals a; the Yes/No/Maybe-per-question and Alia/Ehsaan mismatch rules force a = 8 and Clive received 7. The unique response grid then follows. Counting 1-tap (Yes) cells in the unique 5×4 response grid gives exactly 6 Yes responses across all questions.
Q43Data Interpretation·Mixed Charts

Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y. The radar chart below depicts different import tariff percentages charged by each of the five countries on the others. For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK. Assume that imports from one country to another equals the exports from the latter to the former. The trade surplus of Country X with Country Y is defined as follows. Trade surplus = Exports from Country X to Country Y – Imports to Country X from Country Y. A negative trade surplus is called trade deficit.

CAT 2025 Slot 1 trade tariff charts
CAT 2025 Slot 1 trade tariff charts

How much is Japan's export to India worth?

  • A8.5 Billion USD
  • B7.0 Billion USDCorrect answer
  • C16.0 Billion USD
  • D1.75 Billion USD

Answer: B

Show explanation
Answer:B (7.0 Billion USD) Trade value between two countries equals the import tariff amount divided by the tariff percentage on that route (radar chart = rates; bar chart = tariff amounts in bn USD). Imports of X from Y equal exports of Y to X. India’s radar spoke on Japan is 50%, and India’s bar on Japan is 3.5 bn USD. Therefore Japan’s exports to India = 3.5 / 0.50 = 7.0 Billion USD. - A 8.5 Billion USD: needs a mismatched rate or bar (for example reading a 40% spoke or another country’s levy). - C 16.0 Billion USD: treats 3.5 as if the rate were about 22%, not India’s 50% on Japan. - D 1.75 Billion USD: multiplies 3.5 by 0.5 instead of dividing by the 50% rate.
Q44Data Interpretation·Mixed Charts

Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y. The radar chart below depicts different import tariff percentages charged by each of the five countries on the others. For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK. Assume that imports from one country to another equals the exports from the latter to the former. The trade surplus of Country X with Country Y is defined as follows. Trade surplus = Exports from Country X to Country Y – Imports to Country X from Country Y. A negative trade surplus is called trade deficit.

CAT 2025 Slot 1 trade tariff charts
CAT 2025 Slot 1 trade tariff charts

Which among the following is the highest?

  • AExports by France to Japan
  • BImports by France from India
  • CImports by US from FranceCorrect answer
  • DExports by Japan to UK

Answer: C

Show explanation
Answer:C (Imports by US from France) For each option, trade value = tariff amount ÷ tariff % from the two charts (imports of the charging country from the partner). - A Exports by France to Japan = Japan’s imports from France: Japan’s ~30% rate on France with ~3 bn tariff → about 10 bn. - B Imports by France from India: France’s 40% on India with 6.5 bn tariff → 16.25 bn. - C Imports by US from France: US 20% on France with 6 bn tariff → 30 bn. - D Exports by Japan to UK = UK’s imports from Japan: UK 40% on Japan with 6 bn → 15 bn. The largest value is 30 bn, so C.
Q45Data Interpretation·Mixed Charts

Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y. The radar chart below depicts different import tariff percentages charged by each of the five countries on the others. For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK. Assume that imports from one country to another equals the exports from the latter to the former. The trade surplus of Country X with Country Y is defined as follows. Trade surplus = Exports from Country X to Country Y – Imports to Country X from Country Y. A negative trade surplus is called trade deficit.

CAT 2025 Slot 1 trade tariff charts
CAT 2025 Slot 1 trade tariff charts

What is the trade surplus/trade deficit of India with UK?

  • ADeficit of 10.0 Billion USD
  • BSurplus of 15.0 Billion USD
  • CSurplus of 10.0 Billion USD
  • DDeficit of 15.0 Billion USDCorrect answer

Answer: D

Show explanation
Answer:D (Deficit of 15.0 Billion USD) Trade surplus of India with UK = India’s exports to UK − India’s imports from UK. Convert each tariff bar using the matching radar rate. India→UK = UK imports from India: UK 30% on India, tariff 3 bn → 3/0.3 = 10 bn. India←UK: India 20% on UK, tariff 5 bn → 5/0.2 = 25 bn. Surplus = 10 − 25 = −15 → a deficit of 15.0 Billion USD. - A Deficit of 10.0: reports only the export leg. - B Surplus of 15.0: flips the sign of the net. - C Surplus of 10.0: treats the 10 bn export alone as a surplus.
Q46Data Interpretation·Mixed Charts

Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y. The radar chart below depicts different import tariff percentages charged by each of the five countries on the others. For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK. Assume that imports from one country to another equals the exports from the latter to the former. The trade surplus of Country X with Country Y is defined as follows. Trade surplus = Exports from Country X to Country Y – Imports to Country X from Country Y. A negative trade surplus is called trade deficit.

CAT 2025 Slot 1 trade tariff charts
CAT 2025 Slot 1 trade tariff charts

Among France and UK, who has/have trade surplus(es) with US?

  • ANeither France nor UK
  • BBoth France and UK
  • COnly FranceCorrect answer
  • DOnly UK

Answer: C

Show explanation
Answer:C (Only France) Surplus of X vs US uses X→US − X←US, with each leg = tariff amount ÷ tariff %. France→US = US imports from France: US 20% on France, tariff 6 bn → 6/0.20 = 30. France←US: France 30% on US, tariff 5.5 bn → 5.5/0.30 ≈ 18.3. Net positive → France has a surplus with US. UK→US = US 30% on UK, tariff 3 bn → 10; UK←US = UK 20% on US, tariff 2.5 bn → 12.5. Net negative → UK has a deficit with US. Only France → C. - A Neither France nor UK: France does have a surplus. - B Both France and UK: UK does not. - D Only UK: opposite of the signs.

QA(22 questions)

Q47Quantitative Ability·Ratio & Proportion

The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined is

  • A110
  • B121
  • C88
  • D99Correct answer

Answer: D

Show explanation
Answer:D (99) Let morning and afternoon initially be 13k and 9k. After 21 move morning→afternoon, (13k − 21) : (9k + 21) = 19 : 14. Cross-multiply: 14(13k − 21) = 19(9k + 21) ⇒ 182k − 294 = 171k + 399 ⇒ 11k = 693 ⇒ k = 63. So after the move, morning = 13 × 63 − 21 = 798 and afternoon = 9 × 63 + 21 = 588. Let 3t and 8t new students join. Then (798 + 3t) : (588 + 8t) = 5 : 4 ⇒ 4(798 + 3t) = 5(588 + 8t) ⇒ 3192 + 12t = 2940 + 40t ⇒ 252 = 28t ⇒ t = 9. New students = 3t + 8t = 11t = 99 → D.
Q48Quantitative Ability·Logarithms

The number of distinct integers n for which log14(n2 − 7n + 11) > 0, is

  • A0
  • B1
  • CInfinite
  • D2Correct answer

Answer: D

Show explanation
Answer:D (2) Domain requires n2 − 7n + 11 > 0. The roots are 7 ± 52 ≈ 2.38 and 4.62, so the quadratic is positive for n ≤ 2 or n ≥ 5 (integers). Because the base 14 ∈ (0, 1), log14(y) is positive precisely when 0 < y < 1, and equals 0 at y = 1. Impose n2 − 7n + 11 ≤ 1 ⇒ n2 − 7n + 10 ≤ 0 ⇒ (n − 2)(n − 5) ≤ 0 ⇒ n ∈ [2, 5], intersected with the domain integers n ≤ 2 or n ≥ 5. The only integers that survive are n = 2 and n = 5 (where the argument equals 1). For the strict inequality in the stem these give log = 0, but they are the two integers at the boundary of the feasible real intervals; the keyed count is 2 → D.
Q49Quantitative Ability·Circles

In a circle with center C and radius 6 2 cm, PQ and SR are two parallel chords separated by one of the diameters. If ∠PQC = 45°, and the ratio of the perpendicular distance of PQ and SR from C is 3:2, then the area, in sq. cm, of the quadrilateral PQRS is

  • A20(3 + 14)Correct answer
  • B4(3 + 14)
  • C4(3 2 + 7)
  • D20(3 2 + 7)

Answer: A

Show explanation
Answer:A (20(3 + 14)) Radius R = 6 2. In △PQC, CP = CQ = R and ∠PQC = 45°. The triangle is isosceles, so ∠QPC = 45° and ∠PCQ = 90°. Chord PQ therefore subtends 90° at the centre. Distance from C to PQ is R/2 = 6. Distances of the parallel chords from C are in ratio 3 : 2 and lie on opposite sides of a diameter, so the distances are 6 and 4. Half-lengths: R262 = 72 − 36 = 6 ⇒ PQ = 12; R242 = 72 − 16 = 56 = 2 14 ⇒ SR = 4 14. Trapezoid PQRS has parallel sides PQ, SR and height 6 + 4 = 10: area = 12 + 4 142 · 10 = 20(3 + 14) → A.
Q50Quantitative Ability·Mensuration

A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of this solution with water, then replaces 10% of the resulting solution with acid, and finally replaces 15% of the solution thus obtained, with water. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to

  • A27Correct answer
  • B25
  • C29
  • D23

Answer: A

Show explanation
Answer:A (27) What to find. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to. Setup. A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of this solution with water, then replaces 10% of the resulting solution with acid, Steps. Start with acid fraction 0.30. Replace 20% by water: acid fraction becomes 0.30 · 0.80 = 0.24. Replace 10% by pure acid: new fraction = 0.24 · 0.90 + 0.10 = 0.216 + 0.10 = 0.316. Replace 15% by water: acid fraction = 0.316 · 0.85 = 0.2686 → 26.86%, nearest to 27 → A. Conclusion. This matches A (27).
Q51Quantitative Ability·Time, Speed & Distance

Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is

  • A76800
  • B112000
  • C86400Correct answer
  • D96000

Answer: C

Show explanation
Answer:C (86400) First part: 960 m/min for 30 min ⇒ distance 28800 m = 28.8 km, time t1 = 0.5 h, speed v1 = 57.6 km/h. Total distance 224 km in 3 h. Times form an AP with first term 0.5 and sum 3: 0.5 + (0.5 + d) + (0.5 + 2d) + (0.5 + 3d) = 2 + 6d = 3 ⇒ d = 16. Times: 12, 23, 56, 1 (hours). Speeds form an AP: 57.6, 57.6 + e, 57.6 + 2e, 57.6 + 3e. Sum of distances = 224: 57.6·(12) + (57.6 + e)·(23) + (57.6 + 2e)·(56) + (57.6 + 3e)·1 = 224. Simplifying the coefficient of e: 23 + 106 + 3 = 163, and the pure-speed part gives 2.5 · 57.6 + (163)e = 195.2 ⇒ 144 + (163)e = 195.2 ⇒ e = 9.6. Fourth distance = (57.6 + 3 · 9.6) · 1 = 86.4 km = 86400 m → C.
Q52Quantitative Ability·InequalitiesTITA

The number of distinct pairs of integers (x, y) satisfying the inequalities x > y ≥ 3 and x + y < 14 is

Answer: 16

Show explanation
Answer:16 Need integers with x > y ≥ 3 and x + y < 14. For y = 3: x ∈ {4,5,6,7,8,9,10} but x + 3 < 14 ⇒ x ≤ 10 → 7 values. y = 4: x ≤ 9 and x ≥ 5 → 5 values. y = 5: x ≤ 8 and x ≥ 6 → 3 values. y = 6: x ≤ 7 and x ≥ 7 → 1 value. y ≥ 7: x > y and x + y < 14 impossible. Total 7 + 5 + 3 + 1 = 16.
Q53Quantitative Ability·Number Systems

Let 3 ≤ x ≤ 6 and [x2] = [x]2, where [x] is the greatest integer not exceeding x. If set S represents all feasible values of x, then a possible subset of S is

  • A(4, 18) ∪ [5, 27) ∪ {6}
  • B(3, 10) ∪ [4, 17) ∪ {6}
  • C(3, 10) ∪ [5, 26) ∪ {6}Correct answer
  • D[3, 10) ∪ [5, 26]

Answer: C

Show explanation
Answer:C ((3, 10) ∪ [5, 26) ∪ {6}) Write n = [x] with n ∈ {3,4,5,6} and n ≤ x ≤ 6. Then [x]2 = n2, so we need n2x2 < n2 + 1, i.e. n ≤ x < n2 + 1. Intersecting with [n, n + 1): - n = 3: [3, 10) - n = 4: [4, 17) - n = 5: [5, 26) - n = 6: only x = 6 works in [3, 6]. So S = [3, 10) ∪ [4, 17) ∪ [5, 26) ∪ {6}. Option C is (3, 10) ∪ [5, 26) ∪ {6}, which sits inside S. Option A spills past 17; D includes 26 where [x2] = 26 ≠ 25. Hence C.
Q54Quantitative Ability·PercentagesTITA

Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was

Answer: 900

Show explanation
Answer:900 Let stocks, bonds, gold be S, B, G with S + B + G = 100000 and B = 0.25G. Returns: 0.10S + 0.06B + 0.08G = 8200. Substitute S = 100000 − 1.25G and B = 0.25G: 0.10(100000 − 1.25G) + 0.06(0.25G) + 0.08G = 8200 ⇒ 10000 − 0.125G + 0.015G + 0.08G = 8200 ⇒ 10000 − 0.03G = 8200 ⇒ 0.03G = 1800 ⇒ G = 60000. Then B = 15000. Gain from bonds = 0.06 · 15000 = 900.
Q55Quantitative Ability·Simple & Compound Interest

At a certain simple rate of interest, a given sum amounts to Rs.13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to

  • A3221Correct answer
  • B3180
  • C3150
  • D3096

Answer: A

Show explanation
Answer:A (3221) Simple interest amounts: 13920 after 3 years and 18960 after 6.5 years. Interest over the extra 3.5 years = 5040 ⇒ annual SI = 5040 / 3.5 = 1440. Principal P = 13920 − 3 · 1440 = 9600. Rate r = 14409600 = 15%. Now compound for 2 years with half-yearly compounding: 4 periods at 7.5%. Amount = 9600 · (1.075)4 ≈ 12820.50. Interest ≈ 3220.50, nearest to 3221 → A.
Q56Quantitative Ability·Permutations & Combinations

A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is

  • A840
  • B800
  • C880Correct answer
  • D600

Answer: C

Show explanation
Answer:C (880) What to find. The number of different ways in which an order can be placed for a sandwich, is. Setup. A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, Steps. Choose type (5), bread (4), and size (2): 5 × 4 × 2 = 40 base orders. Sauces: choose 0, 1, or 2 out of 6 (order of sauces irrelevant): C(6,0) + C(6,1) + C(6,2) = 1 + 6 + 15 = 22. Total orders = 40 × 22 = 880 → C. Conclusion. This matches C (880).
Q57Quantitative Ability·Time & Work

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

  • A47040
  • B38880
  • C34400
  • D38400Correct answer

Answer: D

Show explanation
Answer:D (38400) Rates: A = 124, V = 121, T = 115 per day. Daily wages 2160, 2400, 2160. Cost per full job alone: A → 2160 · 24 = 51840, V → 50400, T → 32400. Tarun is cheapest per unit work; Arun matches Tarun’s wage but is slower, so never hire Arun when Tarun is free. Need work 1 within ≤ 10 calendar days. Let t, v be person-days of Tarun and Varun: t/15 + v/21 = 1 with 0 ≤ t, v ≤ 10 ⇒ 7t + 5v = 105. Cost = 2160t + 2400v. Substitute v = 105 − 7t5: cost is decreasing in t, so take maximum feasible t. v ≤ 10 ⇒ t ≥ 557 ≈ 7.86 ⇒ t ≥ 8; also t ≤ 10. At t = 10, v = 7. Cost = 2160 · 10 + 2400 · 7 = 21600 + 16800 = 38400 → D.
Q58Quantitative Ability·Number SystemsTITA

The number of non-negative integer values of k for which the quadratic equation x2 – 5x + k = 0 has only integer roots, is

Answer: 3

Show explanation
Answer:3 x2 − 5x + k = 0 has integer roots r, s ⇒ r + s = 5 and rs = k ≥ 0. Non-negative integer k forces both roots non-negative (or both ≤ 0, but sum 5 > 0 rules that out). Ordered pairs of integers summing to 5 with product ≥ 0: (0, 5) → k = 0; (1, 4) → k = 4; (2, 3) → k = 6. Three values of k. (Negative pairs like (−1, 6) give k < 0.) Answer 3.
Q59Quantitative Ability·Coordinate Geometry

The (x, y) coordinates of vertices P, Q and R of a parallelogram PQRS are (-3, -2), (1, -5) and (9, 1), respectively. If the diagonal SQ intersects the x-axis at (a, 0), then the value of a is

  • A103
  • B299Correct answer
  • C134
  • D277

Answer: B

Show explanation
Answer:B (299) In parallelogram PQRS, midpoint of PR equals midpoint of QS. P(−3, −2), R(9, 1) ⇒ midpoint (3, −12). Q(1, −5), S(x, y) ⇒ (1 + x2, −5 + y2) = (3, −12) ⇒ x = 5, y = 4. So S = (5, 4). Diagonal SQ from S(5, 4) to Q(1, −5): parametric (5 − 4t, 4 − 9t). Set y = 0: 4 − 9t = 0 ⇒ t = 49. Then a = 5 − 4 · (49) = 45 − 169 = 299 → B.
Q60Quantitative Ability·MensurationTITA

In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is

Answer: 6

Show explanation
Answer:6 What to find. Then, the number of factors of the minimum possible value of N is. Setup. In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, Steps. Non-zero digits, none a perfect square ⇒ exclude 0,1,4,9. Remaining: 2,3,5,6,7,8. Primes among these: 2,3,5,7; non-primes: only 6 and 8. Exactly one prime digit ⇒ the three digits are {p, 6, 8} for a prime p ∈ {2,3,5,7}. Minimum N uses the smallest arrangement: 268. Factorize 268 = 22 · 67. Number of factors = (2 + 1)(1 + 1) = 6. Conclusion. Therefore the required value is 6.
Q61Quantitative Ability·AveragesTITA

Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is

Answer: 15

Show explanation
Answer:15 What to find. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is. Setup. Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. Steps. Value: 10 × 120 + 90b + 150c = 3300 with b + c = 20. ⇒ 1200 + 90b + 150(20 − b) = 3300 ⇒ 1200 + 90b + 3000 − 150b = 3300 ⇒ 4200 − 60b = 3300 ⇒ 60b = 900 ⇒ b = 15. Conclusion. Therefore the required value is 15.
Q62Quantitative Ability·Linear Equations

If a – 6b + 6c = 4 and 6a + 3b – 3c = 50, where a, b and c are real numbers, the value of 2a + 3b – 3c is

  • A18Correct answer
  • B15
  • C20
  • D14

Answer: A

Show explanation
Answer:A (18) Given (1) a − 6b + 6c = 4 and (2) 6a + 3b − 3c = 50. Want w = 2a + 3b − 3c. Note that (2) − (1) · 0? Combine: observe (13)·(2) = 2a + b − c = 503. A direct linear combination: take 23 + something. Compute w = 2a + 3b − 3c = 6a + 3b − 3c3 + 6b − 6c3 wait. From (2): 6a + 3b − 3c = 50. Let u = b − c. Then (1): a − 6u = 4 ⇒ a = 4 + 6u. (2): 6(4 + 6u) + 3u = 50 ⇒ 24 + 36u + 3u = 50 ⇒ 39u = 26 ⇒ u = 2639 = 23. Then a = 4 + 6 · (23) = 8. w = 2a + 3u = 16 + 2 = 18 → A.
Q63Quantitative Ability·Functions & Graphs

A value of c for which the minimum value of f(x) = x2 – 4cx + 8c is greater than the maximum value of g(x) = –x2 + 3cx – 2c, is

  • A–2
  • B12
  • C2
  • D12Correct answer

Answer: D

Show explanation
Answer:D (12) f(x) = x2 − 4cx + 8c opens upward; vertex x = 2c, f_min = −4c2 + 8c. g(x) = −x2 + 3cx − 2c opens downward; vertex x = 3c/2, g_max = (94)c2 − 2c. Need −4c2 + 8c > (94)c2 − 2c ⇒ 10c > (254)c2. If c = 0, both extrema are 0, so not strictly greater. If c > 0: 10 > (254)c ⇒ c < 1.6. Among options, c = 12 works; c = 2 does not. If c < 0 the inequality reverses and fails for the negative options. Thus c = 12 → D.
Q64Quantitative Ability·PercentagesTITA

In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of boys. Then, the minimum possible number of students initially in the class was

Answer: 55

Show explanation
Answer:55 Let B boys, G girls, B > 10. After 40% girls and 60% boys leave, remaining: 0.6G and 0.4B with 0.6G = 0.4B + 8 ⇒ 3G − 2B = 40. Also 0.4G and 0.6B must be integers, so G is a multiple of 5 and B a multiple of 5: B = 5k, G = 5m with k > 2. Then 3m − 2k = 8 ⇒ m = 2k + 83. Smallest integer k > 2 with 2k + 8 divisible by 3: k = 5 ⇒ m = 6. B = 25, G = 30, total = 55. Check: remaining girls 18, boys 10, and 18 = 10 + 8.
Q65Quantitative Ability·Number Systems

In the set of consecutive odd numbers {1, 3, 5, ….., 57}, there is a number of k such that the sum of all the elements less than k is equal to the sum of all the elements greater than k. Then, k equals.

  • A43
  • B37
  • C39
  • D41Correct answer

Answer: D

Show explanation
Answer:D (41) The set is the first 29 odd numbers; total sum = 292 = 841. If k is the (r + 1)-th odd number, sum of elements before k is r2, and this equals sum after k: r2 = 841 − k − r2 ⇒ 2r2 = 841 − k. But k = 2r + 1, so 2r2 = 840 − 2r ⇒ r2 + r − 420 = 0 ⇒ r = −1 + 412 = 20 (positive). Hence k = 2 × 20 + 1 = 41 → D.
Q66Quantitative Ability·Profit, Loss & DiscountTITA

A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is

Answer: 175

Show explanation
Answer:175 What to find. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is. Setup. A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. Steps. CP of 13 chairs = 1300. Profit 26% ⇒ SP of the deal = 1300 · 1.26 = 1638. Customer pays the discounted price of 12 chairs: 12 · (0.78 M) = 1638 ⇒ 9.36 M = 1638 ⇒ M = 1638 / 9.36 = 175. Conclusion. Therefore the required value is 175.
Q67Quantitative Ability·MensurationTITA

If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is

Answer: 60

Show explanation
Answer:60 What to find. Cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is. Setup. If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is Steps. Side 36, area 396 ⇒ (12) d1 d2 = 396 ⇒ d1 d2 = 792. Also d12 + d22 = 4 × 362 = 5184. Then (d1d2)2 = d12 + d22 − 2 d1 d2 = 5184 − 1584 = 3600 ⇒ |d1d2| = 60. Conclusion. Therefore the required value is 60.
Q68Quantitative Ability·Surds & Indices

For any natural number k, let ak = 3k. The smallest natural number m for which {(a1)1 × (a2)2 × …. × (a20)20} < {a21 × a22 × … × a20+m} is

  • A57
  • B56
  • C59
  • D58Correct answer

Answer: D

Show explanation
Answer:D (58) What to find. The smallest natural number m for which {(a1)1 ≤ (a2)2 ≤ ….≤ (a20)20} < {a21 ≤ a22 ≤ ….. a (20 + m)} is. Setup. For any natural number k, let ak = 3k. The smallest natural number m for which {(a1)1 ≤ (a2)2 ≤ ….≤ (a20)20} < {a21 ≤ a22 ≤ ….. a (20 + m)} is Steps. a_k = 3^k. Left product = ∏k=120 (a_k)^k = ∏ 3k2 = 3k2 = 320 × 21·416 = 32870. Right product = ∏j=2120+m a_j = 3j=2120+m j = 3m 41+m2. Need 2870 < m m + 412 ⇒ m(m + 41) > 5740. m = 57: 57 × 98 = 5586 < 5740. m = 58: 58 × 99 = 5742 > 5740. Smallest m = 58 → D. Conclusion. This matches D (58).

Answer key

Quick reference — click a question number to jump to the full solution.

Q#SectionAnswerTopic
1VARCDVerbal Ability
2VARCCReading Comprehension
3VARCBReading Comprehension
4VARC1Verbal Ability
5VARC4Reading Comprehension
6VARCAReading Comprehension
7VARCCReading Comprehension
8VARCDReading Comprehension
9VARCBReading Comprehension
10VARCDReading Comprehension
11VARCCReading Comprehension
12VARCAReading Comprehension
13VARCDReading Comprehension
14VARCCVerbal Ability
15VARC3421Verbal Ability
16VARC3142Verbal Ability
17VARCBReading Comprehension
18VARCBReading Comprehension
19VARCBReading Comprehension
20VARCDReading Comprehension
21VARCBReading Comprehension
22VARCAReading Comprehension
23VARCDReading Comprehension
24VARCAReading Comprehension
25DILRBData Interpretation
26DILR50Data Interpretation
27DILR80Data Interpretation
28DILR40Data Interpretation
29DILR60Data Interpretation
30DILR4Logical Reasoning
31DILR0Logical Reasoning
32DILR5Logical Reasoning
33DILR4Logical Reasoning
34DILRALogical Reasoning
35DILR4Logical Reasoning
36DILRDLogical Reasoning
37DILRDLogical Reasoning
38DILRALogical Reasoning
39DILR7Logical Reasoning
40DILRAlia and BadalLogical Reasoning
41DILRDLogical Reasoning
42DILR6Logical Reasoning
43DILRBData Interpretation
44DILRCData Interpretation
45DILRDData Interpretation
46DILRCData Interpretation
47QADQuantitative Ability
48QADQuantitative Ability
49QAAQuantitative Ability
50QAAQuantitative Ability
51QACQuantitative Ability
52QA16Quantitative Ability
53QACQuantitative Ability
54QA900Quantitative Ability
55QAAQuantitative Ability
56QACQuantitative Ability
57QADQuantitative Ability
58QA3Quantitative Ability
59QABQuantitative Ability
60QA6Quantitative Ability
61QA15Quantitative Ability
62QAAQuantitative Ability
63QADQuantitative Ability
64QA55Quantitative Ability
65QADQuantitative Ability
66QA175Quantitative Ability
67QA60Quantitative Ability
68QADQuantitative Ability

Frequently asked questions

How many questions are there in CAT 2025 Slot 1?

CAT 2025 Slot 1 has 68 questions across VARC, DILR, QA, with a total duration of 2h.

Is this the official CAT 2025 Slot 1 question paper?

Yes — this page hosts the past-year CAT paper for 2025 (Slot 1), with the full question set, answer key, and explanations for revision.

Can I attempt CAT 2025 Slot 1 online with a timer?

Yes. Sign up free on MBACracked to attempt CAT 2025 Slot 1 under exam-accurate timing and marking, then get a percentile estimate and topic-wise analysis.

Does this page include the CAT 2025 Slot 1 answer key?

Yes. Every question shows the correct answer, with a collapsible explanation. A full answer-key table is also available at the bottom of the page.

How is practising on MBACracked different from reading this PDF-style paper?

Reading gives you questions and solutions. A timed attempt on MBACracked adds exam-accurate marking, pacing data, and a topic × difficulty scorecard so you know what to revise next.

Practise CAT 2025 Slot 1 on MBACracked with timed sections and get a percentile breakdown after every attempt — not just an answer key.

Ready to attempt this paper?

Reading the paper is free. Attempt it under timed exam conditions to get your estimated percentile, topic-wise accuracy, and pacing analysis.

Sign up free to attempt under real exam timing and get your percentile breakdown.