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CAT 2023 Slot 2 question paper with answer key

This is the complete CAT 2023 Slot 2 question paper with answer key and solutions — 66 questions across VARC, DILR, QA, 2h with sectional timers. Three sequential sections with sectional timers. MCQ negative marking; TITA has none. Browse the full paper free here; attempting it under timed conditions on MBACracked requires Pro.

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VARC(24 questions)

Q1Reading Comprehension·Inference

The Positivists, anxious to stake out their claim for history as a science, contributed the weight of their influence to the cult of facts. First ascertain the facts, said the positivists, then draw your conclusions from them…..This is what may be called the common-sense view of history. History consists of a corpus of ascertained facts. The facts are available to the historian in documents, inscriptions, and so on…Sir George Clark contrasted the "hard core of facts" in history with the surrounding pulp of disputable interpretation forgetting perhaps that the pulpy part of the fruit is more rewarding than the hard core.….It recalls the favourite dictum of the great liberal journalist C. P. Scott: "Facts are sacred, opinion is free.". . . What is a historical fact?..... According to the common-sense view, there are certain basic facts which are the same for all historians and which form, so to speak, the backbone of history—the fact, for example, that the Battle of Hastings was fought in 1066. But this view calls for two observations. In the first place, it is not with facts like these that the historian is primarily concerned. It is no doubt important to know that the great battle was fought in 1066 and not in 1065 or 1067, and that it was fought at Hastings and not at Eastbourne or Brighton. The historian must not get these things wrong. But to praise a historian for his accuracy is like praising an architect for using well-seasoned timber or properly mixed concrete in his building. It is a necessary condition of his work, but not his essential function. It is precisely for matters of this kind that the historian is entitled to rely on what have been called the "auxiliary sciences" of history—archaeology, epigraphy, numismatics, chronology, and so forth…. The second observation is that the necessity to establish these basic facts rests not on any quality in the facts themselves, but on an apriori decision of the historian. In spite of C. P. Scott's motto, every journalist knows today that the most effective way to influence opinion is by the selection and arrangement of the appropriate facts. It used to be said that facts speak for themselves. This is, of course, untrue. The facts speak only when the historian calls on them: it is he who decides to which facts to give the floor, and in what order or context. . . . The only reason why we are interested to know that the battle was fought at Hastings in 1066 is that historians regard it as a major historical event……... Professor Talcott Parsons once called science "a selective system of cognitive orientations to reality." It might perhaps have been put more simply. But history is, among other things, that. The historian is necessarily selective. The belief in a hard core of historical facts existing objectively and independently of the interpretation of the historian is a preposterous fallacy, but one which it is very hard to eradicate.

According to this passage, which one of the following statements best describes the significance of archaeology for historians?

  • AArchaeology helps historians to interpret historical facts.
  • BArchaeology helps historians to ascertain factual accuracy.Correct answer
  • CArchaeology helps historians to carry out their primary duty.
  • DArchaeology helps historians to locate the oldest civilisations in history

Answer: B

Show explanation
Answer:B Archaeology (with other auxiliaries) helps check and establish factual accuracy of the documentary “hard core,” not mainly to interpret meaning or locate oldest civilisations. B matches Carr’s use of such sciences. Why the others fail: • A — Interpretation is the historian’s selective work; archaeology is cast as accuracy aid. • C — Primary duty is selective meaningful history, not archaeology per se. • D — “Oldest civilisations” is not the passage’s claim about archaeology’s role.
Q2Reading Comprehension·Inference

The Positivists, anxious to stake out their claim for history as a science, contributed the weight of their influence to the cult of facts. First ascertain the facts, said the positivists, then draw your conclusions from them…..This is what may be called the common-sense view of history. History consists of a corpus of ascertained facts. The facts are available to the historian in documents, inscriptions, and so on…Sir George Clark contrasted the "hard core of facts" in history with the surrounding pulp of disputable interpretation forgetting perhaps that the pulpy part of the fruit is more rewarding than the hard core.….It recalls the favourite dictum of the great liberal journalist C. P. Scott: "Facts are sacred, opinion is free.". . . What is a historical fact?..... According to the common-sense view, there are certain basic facts which are the same for all historians and which form, so to speak, the backbone of history—the fact, for example, that the Battle of Hastings was fought in 1066. But this view calls for two observations. In the first place, it is not with facts like these that the historian is primarily concerned. It is no doubt important to know that the great battle was fought in 1066 and not in 1065 or 1067, and that it was fought at Hastings and not at Eastbourne or Brighton. The historian must not get these things wrong. But to praise a historian for his accuracy is like praising an architect for using well-seasoned timber or properly mixed concrete in his building. It is a necessary condition of his work, but not his essential function. It is precisely for matters of this kind that the historian is entitled to rely on what have been called the "auxiliary sciences" of history—archaeology, epigraphy, numismatics, chronology, and so forth…. The second observation is that the necessity to establish these basic facts rests not on any quality in the facts themselves, but on an apriori decision of the historian. In spite of C. P. Scott's motto, every journalist knows today that the most effective way to influence opinion is by the selection and arrangement of the appropriate facts. It used to be said that facts speak for themselves. This is, of course, untrue. The facts speak only when the historian calls on them: it is he who decides to which facts to give the floor, and in what order or context. . . . The only reason why we are interested to know that the battle was fought at Hastings in 1066 is that historians regard it as a major historical event……... Professor Talcott Parsons once called science "a selective system of cognitive orientations to reality." It might perhaps have been put more simply. But history is, among other things, that. The historian is necessarily selective. The belief in a hard core of historical facts existing objectively and independently of the interpretation of the historian is a preposterous fallacy, but one which it is very hard to eradicate.

All of the following, if true, can weaken the passage’s claim that facts do not speak for themselves, EXCEPT:

  • Athe truth value of a fact is independent of the historian who expresses it.
  • Bfacts, like truth, can be relative: what is fact for person X may not be so for person Y.Correct answer
  • Ca fact, by its very nature, is objective and universal, irrespective of the context in which it is placed.
  • Dthe order in which a series of facts is presented does not have any bearing on the production of meaning.

Answer: B

Show explanation
Answer:B EXCEPT as weakener: if facts are relative person-to-person, that *supports* “facts don’t speak for themselves.” A, C, D would restore speaker-independent, context-proof facts and thus weaken the claim. Why the others fail: • A — Truth independent of historian would bolster speaking-for-themselves. • C — Objective universal facts irrespective of context would weaken Carr. • D — Order irrelevant to meaning would deny selection’s power.
Q3Reading Comprehension·Specific Detail

The Positivists, anxious to stake out their claim for history as a science, contributed the weight of their influence to the cult of facts. First ascertain the facts, said the positivists, then draw your conclusions from them…..This is what may be called the common-sense view of history. History consists of a corpus of ascertained facts. The facts are available to the historian in documents, inscriptions, and so on…Sir George Clark contrasted the "hard core of facts" in history with the surrounding pulp of disputable interpretation forgetting perhaps that the pulpy part of the fruit is more rewarding than the hard core.….It recalls the favourite dictum of the great liberal journalist C. P. Scott: "Facts are sacred, opinion is free.". . . What is a historical fact?..... According to the common-sense view, there are certain basic facts which are the same for all historians and which form, so to speak, the backbone of history—the fact, for example, that the Battle of Hastings was fought in 1066. But this view calls for two observations. In the first place, it is not with facts like these that the historian is primarily concerned. It is no doubt important to know that the great battle was fought in 1066 and not in 1065 or 1067, and that it was fought at Hastings and not at Eastbourne or Brighton. The historian must not get these things wrong. But to praise a historian for his accuracy is like praising an architect for using well-seasoned timber or properly mixed concrete in his building. It is a necessary condition of his work, but not his essential function. It is precisely for matters of this kind that the historian is entitled to rely on what have been called the "auxiliary sciences" of history—archaeology, epigraphy, numismatics, chronology, and so forth…. The second observation is that the necessity to establish these basic facts rests not on any quality in the facts themselves, but on an apriori decision of the historian. In spite of C. P. Scott's motto, every journalist knows today that the most effective way to influence opinion is by the selection and arrangement of the appropriate facts. It used to be said that facts speak for themselves. This is, of course, untrue. The facts speak only when the historian calls on them: it is he who decides to which facts to give the floor, and in what order or context. . . . The only reason why we are interested to know that the battle was fought at Hastings in 1066 is that historians regard it as a major historical event……... Professor Talcott Parsons once called science "a selective system of cognitive orientations to reality." It might perhaps have been put more simply. But history is, among other things, that. The historian is necessarily selective. The belief in a hard core of historical facts existing objectively and independently of the interpretation of the historian is a preposterous fallacy, but one which it is very hard to eradicate.

If the author of the passage were to write a book on the Battle of Hastings along the lines of his/her own reasoning, the focus of the historical account would be on:

  • Aproviding a nuanced interpretation by relying on the auxiliary sciences.
  • Bproducing a detailed timeline of the various events that led to the Battle.
  • Cexploring the socio-political and economic factors that led to the Battle.Correct answer
  • Dderiving historical facts from the relevant documents and inscriptions.

Answer: C

Show explanation
Answer:C Along the author’s lines, Hastings matters for socio-political/economic forces that make the date historically significant—not the bare fact alone. Why the others fail: • A — Auxiliaries help accuracy; they aren’t the thematic focus. • B — Detailed timeline is positivist fact-collecting. • D — Deriving facts from documents is the common-sense method he critiques as insufficient.
Q4Reading Comprehension·Inference

The Positivists, anxious to stake out their claim for history as a science, contributed the weight of their influence to the cult of facts. First ascertain the facts, said the positivists, then draw your conclusions from them…..This is what may be called the common-sense view of history. History consists of a corpus of ascertained facts. The facts are available to the historian in documents, inscriptions, and so on…Sir George Clark contrasted the "hard core of facts" in history with the surrounding pulp of disputable interpretation forgetting perhaps that the pulpy part of the fruit is more rewarding than the hard core.….It recalls the favourite dictum of the great liberal journalist C. P. Scott: "Facts are sacred, opinion is free.". . . What is a historical fact?..... According to the common-sense view, there are certain basic facts which are the same for all historians and which form, so to speak, the backbone of history—the fact, for example, that the Battle of Hastings was fought in 1066. But this view calls for two observations. In the first place, it is not with facts like these that the historian is primarily concerned. It is no doubt important to know that the great battle was fought in 1066 and not in 1065 or 1067, and that it was fought at Hastings and not at Eastbourne or Brighton. The historian must not get these things wrong. But to praise a historian for his accuracy is like praising an architect for using well-seasoned timber or properly mixed concrete in his building. It is a necessary condition of his work, but not his essential function. It is precisely for matters of this kind that the historian is entitled to rely on what have been called the "auxiliary sciences" of history—archaeology, epigraphy, numismatics, chronology, and so forth…. The second observation is that the necessity to establish these basic facts rests not on any quality in the facts themselves, but on an apriori decision of the historian. In spite of C. P. Scott's motto, every journalist knows today that the most effective way to influence opinion is by the selection and arrangement of the appropriate facts. It used to be said that facts speak for themselves. This is, of course, untrue. The facts speak only when the historian calls on them: it is he who decides to which facts to give the floor, and in what order or context. . . . The only reason why we are interested to know that the battle was fought at Hastings in 1066 is that historians regard it as a major historical event……... Professor Talcott Parsons once called science "a selective system of cognitive orientations to reality." It might perhaps have been put more simply. But history is, among other things, that. The historian is necessarily selective. The belief in a hard core of historical facts existing objectively and independently of the interpretation of the historian is a preposterous fallacy, but one which it is very hard to eradicate.

All of the following describe the “common-sense view” of history, EXCEPT:

  • Ahistory can be objective like the sciences if it is derived from historical facts.
  • Breal history can be found in ancient engravings and archival documents.
  • Chistory is like science: a selective system of cognitive orientations to reality.Correct answer
  • Donly the positivist methods can lead to credible historical knowledge.

Answer: C

Show explanation
Answer:C EXCEPT: Parsons’s “selective system of cognitive orientations” is the author’s/scientific description of history—not part of the common-sense cult of raw facts. Why the others fail: • A — Objectivity via ascertained facts is common-sense/positivist. • B — Documents/inscriptions as fact repositories match that view. • D — Positivist method as path to credible history is the cult described.
Q5Reading Comprehension·Specific Detail

Over the past four centuries liberalism has been so successful that it has driven all its opponents off the battlefield. Now it is disintegrating, destroyed by a mix of hubris and internal contradictions, according to Patrick Deneen, a professor of politics at the University of Notre Dame…..Equality of opportunity has produced a new meritocratic aristocracy that has all the aloofness of the old aristocracy with none of its sense of noblesse oblige. Democracy has degenerated into a theatre of the absurd. And technological advances are reducing ever more areas of work into meaningless drudgery. “The gap between liberalism’s claims about itself and the lived reality of the citizenry” is now so wide that “the lie can no longer be accepted,” Mr Deneen writes. What better proof of this than the vision of 1,000 private planes whisking their occupants to Davos to discuss the question of “creating a shared future in a fragmented world”? . . . Deneen does an impressive job of capturing the current mood of disillusionment, echoing left- wing complaints about rampant commercialism, right-wing complaints about narcissistic and bullying students, and general worries about atomisation and selfishness. But when he concludes that all this adds up to a failure of liberalism, is his argument convincing?....He argues that the essence of liberalism lies in freeing individuals from constraints. In fact, liberalism contains a wide range of intellectual traditions which provide different answers to the question of how to trade off the relative claims of rights and responsibilities, individual expression and social ties….. liberals experimented with a range of ideas from devolving power from the centre to creating national education systems. Mr Deneen’s fixation on the essence of liberalism leads to the second big problem of his book: his failure to recognise liberalism’s ability to reform itself and address its internal problems. The late 19th century saw America suffering from many of the problems that are reappearing today, including the creation of a business aristocracy, the rise of vast companies, the corruption of politics and the sense that society was dividing into winners and losers. But a wide variety of reformers, working within the liberal tradition, tackled these problems head on. Theodore Roosevelt took on the trusts. Progressives cleaned up government corruption. University reformers modernised academic syllabuses and built ladders of opportunity. Rather than dying, liberalism reformed itself. Mr Deneen is right to point out that the record of liberalism in recent years has been dismal. He is also right to assert that the world has much to learn from the premodern notions of liberty as self-mastery and self-denial. The biggest enemy of liberalism is not so much atomisation but old-fashioned greed, as members of the Davos elite pile their plates ever higher with perks and share options. But he is wrong to argue that the only way for people to liberate themselves from the contradictions of liberalism is “liberation from liberalism itself”. The best way to read “Why Liberalism Failed” is not as a funeral oration but as a call to action: up your game, or else.

The author of the passage faults Deneen’s conclusions for all of the following reasons, EXCEPT:

  • Aits failure to note historical instances in which the process of declining liberalism has managed to reverse itself.
  • Bits extreme pessimism about the future of liberalism today and predictions of an ultimate decline.
  • Cits repeated harking back to premodern notions of liberty.Correct answer
  • Dits very narrow definition of liberalism limited to individual freedoms.

Answer: C

Show explanation
Answer:C EXCEPT: the reviewer faults Deneen’s funeral-oration pessimism, narrow individualism reading, and missing liberalism’s self-corrections—not merely that Deneen recalls premodern liberty (which the reviewer partly allows). Why the others fail: • A — Failure to note liberalism’s past recoveries is a stated fault. • B — Extreme decline predictions are criticised (“not a funeral oration”). • D — Over-narrow liberty-as-individual-freedom definition is criticised.
Q6Reading Comprehension·Vocabulary in Context

Over the past four centuries liberalism has been so successful that it has driven all its opponents off the battlefield. Now it is disintegrating, destroyed by a mix of hubris and internal contradictions, according to Patrick Deneen, a professor of politics at the University of Notre Dame…..Equality of opportunity has produced a new meritocratic aristocracy that has all the aloofness of the old aristocracy with none of its sense of noblesse oblige. Democracy has degenerated into a theatre of the absurd. And technological advances are reducing ever more areas of work into meaningless drudgery. “The gap between liberalism’s claims about itself and the lived reality of the citizenry” is now so wide that “the lie can no longer be accepted,” Mr Deneen writes. What better proof of this than the vision of 1,000 private planes whisking their occupants to Davos to discuss the question of “creating a shared future in a fragmented world”? . . . Deneen does an impressive job of capturing the current mood of disillusionment, echoing left- wing complaints about rampant commercialism, right-wing complaints about narcissistic and bullying students, and general worries about atomisation and selfishness. But when he concludes that all this adds up to a failure of liberalism, is his argument convincing?....He argues that the essence of liberalism lies in freeing individuals from constraints. In fact, liberalism contains a wide range of intellectual traditions which provide different answers to the question of how to trade off the relative claims of rights and responsibilities, individual expression and social ties….. liberals experimented with a range of ideas from devolving power from the centre to creating national education systems. Mr Deneen’s fixation on the essence of liberalism leads to the second big problem of his book: his failure to recognise liberalism’s ability to reform itself and address its internal problems. The late 19th century saw America suffering from many of the problems that are reappearing today, including the creation of a business aristocracy, the rise of vast companies, the corruption of politics and the sense that society was dividing into winners and losers. But a wide variety of reformers, working within the liberal tradition, tackled these problems head on. Theodore Roosevelt took on the trusts. Progressives cleaned up government corruption. University reformers modernised academic syllabuses and built ladders of opportunity. Rather than dying, liberalism reformed itself. Mr Deneen is right to point out that the record of liberalism in recent years has been dismal. He is also right to assert that the world has much to learn from the premodern notions of liberty as self-mastery and self-denial. The biggest enemy of liberalism is not so much atomisation but old-fashioned greed, as members of the Davos elite pile their plates ever higher with perks and share options. But he is wrong to argue that the only way for people to liberate themselves from the contradictions of liberalism is “liberation from liberalism itself”. The best way to read “Why Liberalism Failed” is not as a funeral oration but as a call to action: up your game, or else.

The author of the passage refers to “the Davos elite” to illustrate his views on:

  • Athe unlikelihood of a return to the liberalism of the past as long as the rich continue to benefit from the decline in liberal values.
  • Bthe way the debate around liberalism has been captured by the rich who have managed to insulate themselves from economic hardships.
  • Cthe fact that the rise in liberalism had led to a greater interest in shared futures from unlikely social classes.
  • Dthe hypocrisy of the liberal rich, who profess to subscribe to liberal values while cornering most of the wealthCorrect answer

Answer: D

Show explanation
Answer:D Davos private jets to talk “shared future” exemplify liberal elites’ hypocrisy—professing liberal values while monopolising wealth/perks. Why the others fail: • A — Not mainly about unlikelihood of return while rich benefit. • B — Debate capture is secondary to the hypocrisy image. • C — Opposite of the passage’s ironic shared-future scene.
Q7Reading Comprehension·Specific Detail

Over the past four centuries liberalism has been so successful that it has driven all its opponents off the battlefield. Now it is disintegrating, destroyed by a mix of hubris and internal contradictions, according to Patrick Deneen, a professor of politics at the University of Notre Dame…..Equality of opportunity has produced a new meritocratic aristocracy that has all the aloofness of the old aristocracy with none of its sense of noblesse oblige. Democracy has degenerated into a theatre of the absurd. And technological advances are reducing ever more areas of work into meaningless drudgery. “The gap between liberalism’s claims about itself and the lived reality of the citizenry” is now so wide that “the lie can no longer be accepted,” Mr Deneen writes. What better proof of this than the vision of 1,000 private planes whisking their occupants to Davos to discuss the question of “creating a shared future in a fragmented world”? . . . Deneen does an impressive job of capturing the current mood of disillusionment, echoing left- wing complaints about rampant commercialism, right-wing complaints about narcissistic and bullying students, and general worries about atomisation and selfishness. But when he concludes that all this adds up to a failure of liberalism, is his argument convincing?....He argues that the essence of liberalism lies in freeing individuals from constraints. In fact, liberalism contains a wide range of intellectual traditions which provide different answers to the question of how to trade off the relative claims of rights and responsibilities, individual expression and social ties….. liberals experimented with a range of ideas from devolving power from the centre to creating national education systems. Mr Deneen’s fixation on the essence of liberalism leads to the second big problem of his book: his failure to recognise liberalism’s ability to reform itself and address its internal problems. The late 19th century saw America suffering from many of the problems that are reappearing today, including the creation of a business aristocracy, the rise of vast companies, the corruption of politics and the sense that society was dividing into winners and losers. But a wide variety of reformers, working within the liberal tradition, tackled these problems head on. Theodore Roosevelt took on the trusts. Progressives cleaned up government corruption. University reformers modernised academic syllabuses and built ladders of opportunity. Rather than dying, liberalism reformed itself. Mr Deneen is right to point out that the record of liberalism in recent years has been dismal. He is also right to assert that the world has much to learn from the premodern notions of liberty as self-mastery and self-denial. The biggest enemy of liberalism is not so much atomisation but old-fashioned greed, as members of the Davos elite pile their plates ever higher with perks and share options. But he is wrong to argue that the only way for people to liberate themselves from the contradictions of liberalism is “liberation from liberalism itself”. The best way to read “Why Liberalism Failed” is not as a funeral oration but as a call to action: up your game, or else.

All of the following statements are evidence of the decline of liberalism today, EXCEPT:

  • A“And technological advances are reducing ever more areas of work into meaningless drudgery.”Correct answer
  • B“‘The gap between liberalism’s claims about itself and the lived reality of the citizenry’ is now so wide that ‘the lie can no longer be accepted,’. ”
  • C“Democracy has degenerated into a theatre of the absurd.”
  • D“... the creation of a business aristocracy, the rise of vast companies”

Answer: A

Show explanation
Answer:A EXCEPT: tech-driven meaningless work is a labour/technology complaint; B–D more directly indict liberalism’s political self-image, democracy, and aristocratic political economy as liberalism’s decline markers. Why the others fail: • B — Credibility gap is classic decline-of-liberalism evidence in the text. • C — Democracy-as-absurd theatre targets liberal democracy’s decay. • D — Business aristocracy/vast firms mark liberal economic deformation.
Q8Reading Comprehension·Specific Detail

Over the past four centuries liberalism has been so successful that it has driven all its opponents off the battlefield. Now it is disintegrating, destroyed by a mix of hubris and internal contradictions, according to Patrick Deneen, a professor of politics at the University of Notre Dame…..Equality of opportunity has produced a new meritocratic aristocracy that has all the aloofness of the old aristocracy with none of its sense of noblesse oblige. Democracy has degenerated into a theatre of the absurd. And technological advances are reducing ever more areas of work into meaningless drudgery. “The gap between liberalism’s claims about itself and the lived reality of the citizenry” is now so wide that “the lie can no longer be accepted,” Mr Deneen writes. What better proof of this than the vision of 1,000 private planes whisking their occupants to Davos to discuss the question of “creating a shared future in a fragmented world”? . . . Deneen does an impressive job of capturing the current mood of disillusionment, echoing left- wing complaints about rampant commercialism, right-wing complaints about narcissistic and bullying students, and general worries about atomisation and selfishness. But when he concludes that all this adds up to a failure of liberalism, is his argument convincing?....He argues that the essence of liberalism lies in freeing individuals from constraints. In fact, liberalism contains a wide range of intellectual traditions which provide different answers to the question of how to trade off the relative claims of rights and responsibilities, individual expression and social ties….. liberals experimented with a range of ideas from devolving power from the centre to creating national education systems. Mr Deneen’s fixation on the essence of liberalism leads to the second big problem of his book: his failure to recognise liberalism’s ability to reform itself and address its internal problems. The late 19th century saw America suffering from many of the problems that are reappearing today, including the creation of a business aristocracy, the rise of vast companies, the corruption of politics and the sense that society was dividing into winners and losers. But a wide variety of reformers, working within the liberal tradition, tackled these problems head on. Theodore Roosevelt took on the trusts. Progressives cleaned up government corruption. University reformers modernised academic syllabuses and built ladders of opportunity. Rather than dying, liberalism reformed itself. Mr Deneen is right to point out that the record of liberalism in recent years has been dismal. He is also right to assert that the world has much to learn from the premodern notions of liberty as self-mastery and self-denial. The biggest enemy of liberalism is not so much atomisation but old-fashioned greed, as members of the Davos elite pile their plates ever higher with perks and share options. But he is wrong to argue that the only way for people to liberate themselves from the contradictions of liberalism is “liberation from liberalism itself”. The best way to read “Why Liberalism Failed” is not as a funeral oration but as a call to action: up your game, or else.

The author of the passage is likely to disagree with all of the following statements, EXCEPT:

  • Athe essence of liberalism lies in greater individual self-expression and freedoms.
  • Bclaims about liberalism’s disintegration are exaggerated and misunderstand its core features.
  • Cif we accept that liberalism is a dying ideal, we must work to find a viable substitute.
  • Dliberalism was the dominant ideal in the past century, but it had to reform itself to remain so.Correct answer

Answer: D

Show explanation
Answer:D EXCEPT (author can agree): liberalism dominated yet had to reform to survive—fits “up your game” call rather than abandon liberalism. Why the others fail: • A — Essence as mere self-expression is the narrow view he rejects. • B — He takes disintegration worries seriously enough to demand action. • C — He rejects “liberation from liberalism” as the only path.
Q9Reading Comprehension·Inference

The Second Hand September campaign, led by Oxfam . . . seeks to encourage shopping at local organisations and charities as alternatives to fast fashion brands such as Primark and Boohoo in the name of saving our planet. As innocent as mindless scrolling through online shops may seem, such consumers are unintentionally—or perhaps even knowingly— contributing to an industry that uses more energy than aviation. . . . Brits buy more garments than any other country in Europe, so it comes as no shock that many of those clothes end up in UK landfills each year: 300,000 tonnes of them, to be exact. This waste of clothing is destructive to our planet, releasing greenhouse gasses as clothes are burnt as well as bleeding toxins and dyes into the surrounding soil and water. As ecologist Chelsea Rochman bluntly put it, “The mismanagement of our waste has even come back to haunt us on our dinner plate.” It’s not surprising, then, that people are scrambling for a solution, the most common of which is second-hand shopping. Retailers selling consigned clothing are currently expanding at a rapid rate …..If everyone bought just one used item in a year, it would save 449 million lbs of waste, equivalent to the weight of 1 million Polar bears. “Thrifting” has increasingly become a trendy practice. London is home to many second-hand, or more commonly coined ‘vintage’, shops across the city from Bayswater to Brixton. So you’re cool and you care about the planet; you’ve killed two birds with one stone. But do people simply purchase a secondhand item, flash it on Instagram with #vintage and call it a day without considering whether what they are doing is actually effective? According to a study commissioned by Patagonia, for instance, older clothes shed more microfibres. These can end up in our rivers and seas after just one wash due to the worn material, thus contributing to microfibre pollution. To break it down, the amount of microfibres released by laundering 100,000 fleece jackets is equivalent to as many as 11,900 plastic grocery bags, and up to 40 per cent of that ends up in our oceans. So where does this leave second-hand consumers? They would be well advised to buy high-quality items that shed less and last longer as this combats both microfibre pollution and excess garments ending up in landfills. . . . Luxury brands would rather not circulate their latest season stock around the globe to be sold at a cheaper price, which is why companies like ThredUP, a US fashion resale marketplace, have not yet caught on in the UK. There will always be a market for consignment but there is also a whole generation of people who have been taught that only buying new products is the norm; second-hand luxury goods are not in their psyche. Ben Whitaker, director at Liquidation Firm B-Stock, told Prospect that unless recycling becomes cost-effective and filters into mass production, with the right technology to partner it, “high-end retailers would rather put brand before sustainability.”

Based on the passage, we can infer that the opposite of fast fashion, ‘slow fashion’, would most likely refer to clothes that:

  • Ado not shed microfibres.
  • Bdo not bleed toxins and dyes.
  • Care sold by genuine vintage stores.
  • Dare of high quality and long lasting.Correct answer

Answer: D

Show explanation
Answer:D Slow fashion, opposite of disposable fast fashion, means durable, high-quality garments meant to last. Why the others fail: • A — Microfibres are a pollution detail, not the slow/fast opposition. • B — Toxins/dyes are landfill harms, not the definition of slow fashion. • C — Vintage stores are a channel, not the quality/longevity idea.
Q10Reading Comprehension·Inference

The Second Hand September campaign, led by Oxfam . . . seeks to encourage shopping at local organisations and charities as alternatives to fast fashion brands such as Primark and Boohoo in the name of saving our planet. As innocent as mindless scrolling through online shops may seem, such consumers are unintentionally—or perhaps even knowingly— contributing to an industry that uses more energy than aviation. . . . Brits buy more garments than any other country in Europe, so it comes as no shock that many of those clothes end up in UK landfills each year: 300,000 tonnes of them, to be exact. This waste of clothing is destructive to our planet, releasing greenhouse gasses as clothes are burnt as well as bleeding toxins and dyes into the surrounding soil and water. As ecologist Chelsea Rochman bluntly put it, “The mismanagement of our waste has even come back to haunt us on our dinner plate.” It’s not surprising, then, that people are scrambling for a solution, the most common of which is second-hand shopping. Retailers selling consigned clothing are currently expanding at a rapid rate …..If everyone bought just one used item in a year, it would save 449 million lbs of waste, equivalent to the weight of 1 million Polar bears. “Thrifting” has increasingly become a trendy practice. London is home to many second-hand, or more commonly coined ‘vintage’, shops across the city from Bayswater to Brixton. So you’re cool and you care about the planet; you’ve killed two birds with one stone. But do people simply purchase a secondhand item, flash it on Instagram with #vintage and call it a day without considering whether what they are doing is actually effective? According to a study commissioned by Patagonia, for instance, older clothes shed more microfibres. These can end up in our rivers and seas after just one wash due to the worn material, thus contributing to microfibre pollution. To break it down, the amount of microfibres released by laundering 100,000 fleece jackets is equivalent to as many as 11,900 plastic grocery bags, and up to 40 per cent of that ends up in our oceans. So where does this leave second-hand consumers? They would be well advised to buy high-quality items that shed less and last longer as this combats both microfibre pollution and excess garments ending up in landfills. . . . Luxury brands would rather not circulate their latest season stock around the globe to be sold at a cheaper price, which is why companies like ThredUP, a US fashion resale marketplace, have not yet caught on in the UK. There will always be a market for consignment but there is also a whole generation of people who have been taught that only buying new products is the norm; second-hand luxury goods are not in their psyche. Ben Whitaker, director at Liquidation Firm B-Stock, told Prospect that unless recycling becomes cost-effective and filters into mass production, with the right technology to partner it, “high-end retailers would rather put brand before sustainability.”

The act of “thrifting”, as described in the passage, can be considered ironic because it:

  • Aoffers luxury clothing at cut-rate prices.
  • Bis not cost-effective for retailers.
  • Cis an anti-consumerist attitude.
  • Dhas created environmental problems.Correct answer

Answer: D

Show explanation
Answer:D Irony: thrifting, sold as eco-virtue, can itself generate environmental harms (shipping, disposal of unsold poor-quality stock). Why the others fail: • A — Luxury at low price isn’t the irony named. • B — Retailer cost-effectiveness isn’t the thrifting irony. • C — Anti-consumerism would reduce irony, not create it.
Q11Reading Comprehension·Main Idea / Purpose

The Second Hand September campaign, led by Oxfam . . . seeks to encourage shopping at local organisations and charities as alternatives to fast fashion brands such as Primark and Boohoo in the name of saving our planet. As innocent as mindless scrolling through online shops may seem, such consumers are unintentionally—or perhaps even knowingly— contributing to an industry that uses more energy than aviation. . . . Brits buy more garments than any other country in Europe, so it comes as no shock that many of those clothes end up in UK landfills each year: 300,000 tonnes of them, to be exact. This waste of clothing is destructive to our planet, releasing greenhouse gasses as clothes are burnt as well as bleeding toxins and dyes into the surrounding soil and water. As ecologist Chelsea Rochman bluntly put it, “The mismanagement of our waste has even come back to haunt us on our dinner plate.” It’s not surprising, then, that people are scrambling for a solution, the most common of which is second-hand shopping. Retailers selling consigned clothing are currently expanding at a rapid rate …..If everyone bought just one used item in a year, it would save 449 million lbs of waste, equivalent to the weight of 1 million Polar bears. “Thrifting” has increasingly become a trendy practice. London is home to many second-hand, or more commonly coined ‘vintage’, shops across the city from Bayswater to Brixton. So you’re cool and you care about the planet; you’ve killed two birds with one stone. But do people simply purchase a secondhand item, flash it on Instagram with #vintage and call it a day without considering whether what they are doing is actually effective? According to a study commissioned by Patagonia, for instance, older clothes shed more microfibres. These can end up in our rivers and seas after just one wash due to the worn material, thus contributing to microfibre pollution. To break it down, the amount of microfibres released by laundering 100,000 fleece jackets is equivalent to as many as 11,900 plastic grocery bags, and up to 40 per cent of that ends up in our oceans. So where does this leave second-hand consumers? They would be well advised to buy high-quality items that shed less and last longer as this combats both microfibre pollution and excess garments ending up in landfills. . . . Luxury brands would rather not circulate their latest season stock around the globe to be sold at a cheaper price, which is why companies like ThredUP, a US fashion resale marketplace, have not yet caught on in the UK. There will always be a market for consignment but there is also a whole generation of people who have been taught that only buying new products is the norm; second-hand luxury goods are not in their psyche. Ben Whitaker, director at Liquidation Firm B-Stock, told Prospect that unless recycling becomes cost-effective and filters into mass production, with the right technology to partner it, “high-end retailers would rather put brand before sustainability.”

The central idea of the passage would be undermined if:

  • Asecond-hand stores sold only high-quality clothes.Correct answer
  • Bclothes were not thrown and burnt in landfills.
  • CPrimark and Boohoo recycled their clothes for vintage stores.
  • Dcustomers bought all their clothes online.

Answer: A

Show explanation
Answer:A Central critique: thrifting often recirculates low-quality fast fashion with its own footprints. If second-hand sold only high-quality durables, that undercuts the passage’s worry about thrifting-as-false-fix. Why the others fail: • B — Ending landfill burning would help the planet but not specifically refute thrifting’s problematic side. • C — Brand recycling into vintage doesn’t erase the thrifting-irony thesis. • D — All-online buying worsens fast fashion, supporting the problem frame.
Q12Reading Comprehension·Inference

The Second Hand September campaign, led by Oxfam . . . seeks to encourage shopping at local organisations and charities as alternatives to fast fashion brands such as Primark and Boohoo in the name of saving our planet. As innocent as mindless scrolling through online shops may seem, such consumers are unintentionally—or perhaps even knowingly— contributing to an industry that uses more energy than aviation. . . . Brits buy more garments than any other country in Europe, so it comes as no shock that many of those clothes end up in UK landfills each year: 300,000 tonnes of them, to be exact. This waste of clothing is destructive to our planet, releasing greenhouse gasses as clothes are burnt as well as bleeding toxins and dyes into the surrounding soil and water. As ecologist Chelsea Rochman bluntly put it, “The mismanagement of our waste has even come back to haunt us on our dinner plate.” It’s not surprising, then, that people are scrambling for a solution, the most common of which is second-hand shopping. Retailers selling consigned clothing are currently expanding at a rapid rate …..If everyone bought just one used item in a year, it would save 449 million lbs of waste, equivalent to the weight of 1 million Polar bears. “Thrifting” has increasingly become a trendy practice. London is home to many second-hand, or more commonly coined ‘vintage’, shops across the city from Bayswater to Brixton. So you’re cool and you care about the planet; you’ve killed two birds with one stone. But do people simply purchase a secondhand item, flash it on Instagram with #vintage and call it a day without considering whether what they are doing is actually effective? According to a study commissioned by Patagonia, for instance, older clothes shed more microfibres. These can end up in our rivers and seas after just one wash due to the worn material, thus contributing to microfibre pollution. To break it down, the amount of microfibres released by laundering 100,000 fleece jackets is equivalent to as many as 11,900 plastic grocery bags, and up to 40 per cent of that ends up in our oceans. So where does this leave second-hand consumers? They would be well advised to buy high-quality items that shed less and last longer as this combats both microfibre pollution and excess garments ending up in landfills. . . . Luxury brands would rather not circulate their latest season stock around the globe to be sold at a cheaper price, which is why companies like ThredUP, a US fashion resale marketplace, have not yet caught on in the UK. There will always be a market for consignment but there is also a whole generation of people who have been taught that only buying new products is the norm; second-hand luxury goods are not in their psyche. Ben Whitaker, director at Liquidation Firm B-Stock, told Prospect that unless recycling becomes cost-effective and filters into mass production, with the right technology to partner it, “high-end retailers would rather put brand before sustainability.”

According to the author, companies like ThredUP have not caught on in the UK for all of the following reasons EXCEPT that:

  • Aluxury brands want to maintain their brand image.
  • Bthe British don’t buy second-hand clothing.Correct answer
  • Crecycling is currently not financially attractive for luxury brands.
  • Dluxury brands do not like their product to be devalued.

Answer: B

Show explanation
Answer:B EXCEPT: the UK does have consignment/second-hand markets; the text does *not* say Britons simply don’t buy second-hand. Barriers are brand protection, cost of recycling, devaluation fears. Why the others fail: • A — Brand-before-sustainability is quoted. • C — Recycling not yet cost-effective is stated. • D — Fear of devaluing product fits brand logic.
Q13Reading Comprehension·Specific Detail

Umberto Eco, an Italian writer, was right when he said the language of Europe is translation. Netflix and other deep-pocketed global firms speak it well. Just as the EU employs a small army of translators and interpreters to turn intricate laws or impassioned speeches of Romanian MEPs into the EU’s 24 official languages, so do the likes of Netflix. It now offers dubbing in 34 languages and subtitling in a few more. . . . The economics of European productions are more appealing, too. American audiences are more willing than before to give dubbed or subtitled viewing a chance. This means shows such as “Lupin”, a French crime caper on Netflix, can become global hits. In 2015, about 75% of Netflix’s original content was American; now the figure is half, according to Ampere, a mediaanalysis company. Netflix has about 100 productions under way in Europe, which is more than big public broadcasters in France or Germany. . . . Not everything works across borders. Comedy sometimes struggles. Whodunits and bloodthirsty maelstroms between arch Romans and uppity tribesmen have a more universal appeal. Some do it better than others. Barbarians aside, German television is not always built for export, says one executive, being polite. A bigger problem is that national broadcasters still dominate. Streaming services, such as Netflix or Disney+, account for about a third of all viewing hours, even in markets where they are well-established. Europe is an ageing continent. The generation of teens staring at phones is outnumbered by their elders who prefer to gawp at the box. In Brussels and national capitals, the prospect of Netflix as a cultural hegemon is seen as a threat. “Cultural sovereignty” is the watchword of European executives worried that the Americans will eat their lunch. To be fair, Netflix content sometimes seems stuck in an uncanny valley somewhere in the mid-Atlantic, with local quirks stripped out. Netflix originals tend to have fewer specific cultural references than shows produced by domestic rivals, according to Enders, a market analyst. The company used to have an imperial model of commissioning, with executives in Los Angeles cooking up ideas French people might like. Now Netflix has offices across Europe. But ultimately the big decisions rest with American executives. This makes European politicians nervous. They should not be. An irony of European integration is that it is often American companies that facilitate it. Google Translate makes European newspapers comprehensible, even if a little clunky, for the continent’s non-polyglots. American social-media companies make it easier for Europeans to talk politics across borders. (That they do not always like to hear what they say about each other is another matter.) Now Netflix and friends pump the same content into homes across a continent, making culture a cross-border endeavour, too. If Europeans are to share a currency, bail each other out in times of financial need and share vaccines in a pandemic, then they need to have something in common—even if it is just bingeing on the same series. Watching fictitious northern and southern Europeans tear each other apart 2,000 years ago beats doing so in reality.

The author sees the rise of Netflix in Europe as:

  • Aa looming cultural threat.
  • Ba unifying force.Correct answer
  • Cfilling an entertainment gap.
  • Dan economic threat.

Answer: B

Show explanation
Answer:B Netflix as shared binge culture gives Europeans something in common—a unifying force alongside translation/EU tools. Why the others fail: • A — Not framed as cultural threat. • C — Filling a gap is weaker than the political-cultural glue claim. • D — Not an economic threat narrative.
Q14Reading Comprehension·Application & Analogy

Umberto Eco, an Italian writer, was right when he said the language of Europe is translation. Netflix and other deep-pocketed global firms speak it well. Just as the EU employs a small army of translators and interpreters to turn intricate laws or impassioned speeches of Romanian MEPs into the EU’s 24 official languages, so do the likes of Netflix. It now offers dubbing in 34 languages and subtitling in a few more. . . . The economics of European productions are more appealing, too. American audiences are more willing than before to give dubbed or subtitled viewing a chance. This means shows such as “Lupin”, a French crime caper on Netflix, can become global hits. In 2015, about 75% of Netflix’s original content was American; now the figure is half, according to Ampere, a mediaanalysis company. Netflix has about 100 productions under way in Europe, which is more than big public broadcasters in France or Germany. . . . Not everything works across borders. Comedy sometimes struggles. Whodunits and bloodthirsty maelstroms between arch Romans and uppity tribesmen have a more universal appeal. Some do it better than others. Barbarians aside, German television is not always built for export, says one executive, being polite. A bigger problem is that national broadcasters still dominate. Streaming services, such as Netflix or Disney+, account for about a third of all viewing hours, even in markets where they are well-established. Europe is an ageing continent. The generation of teens staring at phones is outnumbered by their elders who prefer to gawp at the box. In Brussels and national capitals, the prospect of Netflix as a cultural hegemon is seen as a threat. “Cultural sovereignty” is the watchword of European executives worried that the Americans will eat their lunch. To be fair, Netflix content sometimes seems stuck in an uncanny valley somewhere in the mid-Atlantic, with local quirks stripped out. Netflix originals tend to have fewer specific cultural references than shows produced by domestic rivals, according to Enders, a market analyst. The company used to have an imperial model of commissioning, with executives in Los Angeles cooking up ideas French people might like. Now Netflix has offices across Europe. But ultimately the big decisions rest with American executives. This makes European politicians nervous. They should not be. An irony of European integration is that it is often American companies that facilitate it. Google Translate makes European newspapers comprehensible, even if a little clunky, for the continent’s non-polyglots. American social-media companies make it easier for Europeans to talk politics across borders. (That they do not always like to hear what they say about each other is another matter.) Now Netflix and friends pump the same content into homes across a continent, making culture a cross-border endeavour, too. If Europeans are to share a currency, bail each other out in times of financial need and share vaccines in a pandemic, then they need to have something in common—even if it is just bingeing on the same series. Watching fictitious northern and southern Europeans tear each other apart 2,000 years ago beats doing so in reality.

Which one of the following research findings would weaken the author’s conclusion in the final paragraph?

  • AResearch shows there is a wide variance in the popularity and viewing of Netflix shows across different EU countries.Correct answer
  • BResearch shows that Netflix has been gradually losing market share to other streaming television service providers.
  • CResearch shows that Netflix hits produced in France are very popular with North American audiences.
  • DResearch shows that older women across the EU enjoy watching romantic comedies on Netflix, whereas younger women prefer historical fiction dramas.

Answer: A

Show explanation
Answer:A Final paragraph: shared series help Europeans have something in common. Wide variance in what different EU countries watch would weaken that unifying conclusion. Why the others fail: • B — Market-share loss doesn’t touch the cultural-commonality claim. • C — French hits in North America support cross-border success. • D — Age preference differences still allow shared catalogues.
Q15Reading Comprehension·Specific Detail

Umberto Eco, an Italian writer, was right when he said the language of Europe is translation. Netflix and other deep-pocketed global firms speak it well. Just as the EU employs a small army of translators and interpreters to turn intricate laws or impassioned speeches of Romanian MEPs into the EU’s 24 official languages, so do the likes of Netflix. It now offers dubbing in 34 languages and subtitling in a few more. . . . The economics of European productions are more appealing, too. American audiences are more willing than before to give dubbed or subtitled viewing a chance. This means shows such as “Lupin”, a French crime caper on Netflix, can become global hits. In 2015, about 75% of Netflix’s original content was American; now the figure is half, according to Ampere, a mediaanalysis company. Netflix has about 100 productions under way in Europe, which is more than big public broadcasters in France or Germany. . . . Not everything works across borders. Comedy sometimes struggles. Whodunits and bloodthirsty maelstroms between arch Romans and uppity tribesmen have a more universal appeal. Some do it better than others. Barbarians aside, German television is not always built for export, says one executive, being polite. A bigger problem is that national broadcasters still dominate. Streaming services, such as Netflix or Disney+, account for about a third of all viewing hours, even in markets where they are well-established. Europe is an ageing continent. The generation of teens staring at phones is outnumbered by their elders who prefer to gawp at the box. In Brussels and national capitals, the prospect of Netflix as a cultural hegemon is seen as a threat. “Cultural sovereignty” is the watchword of European executives worried that the Americans will eat their lunch. To be fair, Netflix content sometimes seems stuck in an uncanny valley somewhere in the mid-Atlantic, with local quirks stripped out. Netflix originals tend to have fewer specific cultural references than shows produced by domestic rivals, according to Enders, a market analyst. The company used to have an imperial model of commissioning, with executives in Los Angeles cooking up ideas French people might like. Now Netflix has offices across Europe. But ultimately the big decisions rest with American executives. This makes European politicians nervous. They should not be. An irony of European integration is that it is often American companies that facilitate it. Google Translate makes European newspapers comprehensible, even if a little clunky, for the continent’s non-polyglots. American social-media companies make it easier for Europeans to talk politics across borders. (That they do not always like to hear what they say about each other is another matter.) Now Netflix and friends pump the same content into homes across a continent, making culture a cross-border endeavour, too. If Europeans are to share a currency, bail each other out in times of financial need and share vaccines in a pandemic, then they need to have something in common—even if it is just bingeing on the same series. Watching fictitious northern and southern Europeans tear each other apart 2,000 years ago beats doing so in reality.

Based on information provided in the passage, all of the following are true, EXCEPT:

  • AEuropean television productions have the potential to become global hits.
  • Bnational broadcasters dominate in the EU in terms of total television viewing hours.
  • Conly half of Netflix’s original programming in the EU is now produced in America.
  • DNetflix has been able to transform itself into a truly European entity.Correct answer

Answer: D

Show explanation
Answer:D EXCEPT: Netflix remains a global firm speaking translation; it isn’t said to have become a “truly European entity.” Why the others fail: • A — Lupin-style global hits are affirmed. • B — National broadcasters still dominate viewing hours—stated elsewhere in such pieces; keyed as true here. • C — American share of originals down to about half—stated.
Q16Reading Comprehension·Inference

Umberto Eco, an Italian writer, was right when he said the language of Europe is translation. Netflix and other deep-pocketed global firms speak it well. Just as the EU employs a small army of translators and interpreters to turn intricate laws or impassioned speeches of Romanian MEPs into the EU’s 24 official languages, so do the likes of Netflix. It now offers dubbing in 34 languages and subtitling in a few more. . . . The economics of European productions are more appealing, too. American audiences are more willing than before to give dubbed or subtitled viewing a chance. This means shows such as “Lupin”, a French crime caper on Netflix, can become global hits. In 2015, about 75% of Netflix’s original content was American; now the figure is half, according to Ampere, a mediaanalysis company. Netflix has about 100 productions under way in Europe, which is more than big public broadcasters in France or Germany. . . . Not everything works across borders. Comedy sometimes struggles. Whodunits and bloodthirsty maelstroms between arch Romans and uppity tribesmen have a more universal appeal. Some do it better than others. Barbarians aside, German television is not always built for export, says one executive, being polite. A bigger problem is that national broadcasters still dominate. Streaming services, such as Netflix or Disney+, account for about a third of all viewing hours, even in markets where they are well-established. Europe is an ageing continent. The generation of teens staring at phones is outnumbered by their elders who prefer to gawp at the box. In Brussels and national capitals, the prospect of Netflix as a cultural hegemon is seen as a threat. “Cultural sovereignty” is the watchword of European executives worried that the Americans will eat their lunch. To be fair, Netflix content sometimes seems stuck in an uncanny valley somewhere in the mid-Atlantic, with local quirks stripped out. Netflix originals tend to have fewer specific cultural references than shows produced by domestic rivals, according to Enders, a market analyst. The company used to have an imperial model of commissioning, with executives in Los Angeles cooking up ideas French people might like. Now Netflix has offices across Europe. But ultimately the big decisions rest with American executives. This makes European politicians nervous. They should not be. An irony of European integration is that it is often American companies that facilitate it. Google Translate makes European newspapers comprehensible, even if a little clunky, for the continent’s non-polyglots. American social-media companies make it easier for Europeans to talk politics across borders. (That they do not always like to hear what they say about each other is another matter.) Now Netflix and friends pump the same content into homes across a continent, making culture a cross-border endeavour, too. If Europeans are to share a currency, bail each other out in times of financial need and share vaccines in a pandemic, then they need to have something in common—even if it is just bingeing on the same series. Watching fictitious northern and southern Europeans tear each other apart 2,000 years ago beats doing so in reality.

Based only on information provided in the passage, which one of the following hypothetical Netflix shows would be most successful with audiences across the EU?

  • AAn Italian comedy show hosted by an international star.
  • BAn original German TV science fiction production.
  • CA murder mystery drama set in North Africa and France.Correct answer
  • DA trans-Atlantic romantic drama set in Europe and America.

Answer: C

Show explanation
Answer:C Whodunits travel; comedy struggles. A murder mystery spanning North Africa/France fits the cross-border crime-drama template. Why the others fail: • A — Comedy is flagged as weak across borders. • B — Sci-fi isn’t the universal genre highlighted. • D — Trans-Atlantic romance isn’t the Roman/whodunit pattern praised.
Q17Verbal Ability·Sentence Placement

Sentence: Dualism was long held as the defining feature of developing countries in contrast to developed countries, where frontier technologies and high productivity were assumed to prevail. Paragraph: ___(1)___. At the core of development economics lies the idea of ‘productive dualism’: that poor countries’ economies are split between a narrow ‘modern’ sector that uses advanced technologies and a larger ‘traditional’ sector characterized by very low productivity. ___(2)___. While this distinction between developing and advanced economies may have made some sense in the 1950s and 1960s, it no longer appears to be very relevant. A combination of forces have produced a widening gap between the winners and those left behind. ___(3)___. Convergence between poor and rich parts of the economy was arrested and regional disparities widened. ___(4)___. As a result, policymakers in advanced economies are now grappling with the same questions that have long preoccupied developing economies: mainly how to close the gap with the more advanced parts of the economy.

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

Answer: B

Show explanation
Answer:B (blank 2) Missing sentence: dualism long defined developing vs developed countries. It follows the productive-dualism definition and before “this distinction…no longer relevant”—Blank 2. Why the others fail: • A (1) — Before dualism is defined; label lacks anchor. • C (3) — After forces widening gaps; too late for defining dualism. • D (4) — Closing policy parallel; definition belongs earlier.
Q18Verbal Ability·Sentence Placement

Sentence: And probably much earlier, moving the documentation for kissing back 1,000 years compared to what was acknowledged in the scientific community. Paragraph: Research has hypothesised that the earliest evidence of human lip kissing originated in a very specific geographical location in South Asia 3,500 years ago. ___(1)___. From there it may have spread to other regions, simultaneously accelerating the spread of the herpes simplex virus 1. According to Dr Troels Pank Arbøll and Dr Sophie Lund Rasmussen, who in a new article in the journal Science draw on a range of written sources from the earliest Mesopotamian societies, kissing was already a well-established practice 4,500 years ago in the Middle East. ___(2)___. In ancient Mesopotamia, people wrote in cuneiform script on clay tablets. ___(3)___. Many thousands of these clay tablets have survived to this day, and they contain clear examples that kissing was considered a part of romantic intimacy in ancient times. ___(4)___. “Kissing could also have been part of friendships and family members' relations,” says Dr Troels Pank Arbøll, an expert on the history of medicine in Mesopotamia.

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

Answer: A

Show explanation
Answer:A (blank 1) Missing sentence: kissing probably much earlier, pushing documentation back 1,000 years. It revises the South Asia 3,500-year hypothesis immediately—Blank 1—before Mesopotamia 4,500-year evidence. Why the others fail: • B (2) — After Mesopotamia claim; chronological correction belongs first. • C (3) — Mid cuneiform exposition. • D (4) — After tablets’ romantic kissing examples; too late.
Q19Verbal 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 banning of Northern Lights could be considered a precursor to censoring books for “moral”, world view or religious reasons. 2. Attempts to ban books are attempts to silence authors who have summoned immense courage in telling their stories. 3. Now the banning and challenging of books in the US has escalated to an unprecedented level. 4. The widely acclaimed fantasy novel Northern Lights was banned in some parts of the US, and was the second most challenged book in the US. 5. The American Library Association documented an unparalleled number of reported book challenges in 2022, about 2,500 unique titles.

Answer: 2

Show explanation
Answer:2 Keep 4 → 1 → 3 → 5: *Northern Lights* banned/challenged in the US (4); that ban can foreshadow moral/worldview/religious censorship (1); US book bans have now hit an unprecedented level (3); ALA logged ~2,500 challenged titles in 2022 (5). Why 2 is odd: It moralizes that bans “silence authors who summoned courage”—a claim about authorial bravery the NL → escalation → documentation chain never uses.
Q20Verbal 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. Self-care particularly links to loneliness, behavioural problems, and negative academic outcomes. 2. “Latchkey children” refers to children who routinely return home from school to empty homes and take care of themselves for extended periods of time. 3. Although self-care generally points to negative outcomes, it is important to consider that the bulk of research has yet to track long-term consequences. 4. In research and practice, the phrase “children in self-care” has come to replace latchkey in an effort to more accurately reflect the nature of their circumstances. 5. Although parents might believe that self-care would be beneficial for development, recent research has found quite the opposite.

Answer: 3

Show explanation
Answer:3 Keep 2 → 4 → 5 → 1: define “latchkey” kids who self-supervise after school (2); research language shifts to “children in self-care” (4); parents may think it helps, but recent research finds the opposite (5); self-care links to loneliness, behaviour problems, and worse academics (1). Why 3 is odd: It softens the negative picture by saying long-term consequences are mostly untracked, undercutting the research claims 5 and 1 rely on.
Q21Verbal 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. Like the ants that make up a colony, no single neuron holds complex information like self-awareness, hope or pride. 2. Although the human brain is not yet understood enough to identify the mechanism by which emergence functions, most neurobiologists agree that complex interconnections among the parts give rise to qualities that belong only to the whole. 3. Nonetheless, the sum of all neurons in the nervous system generate complex human emotions like fear and joy, none of which can be attributed to a single neuron. 4. Human consciousness is often called an emergent property of the human brain.

Answer: 4132

Show explanation
Answer:4132 4 states the thesis: consciousness is an emergent property of the brain. 1 supplies the ant-colony analogy—no single neuron holds self-awareness, hope, or pride. 3’s “Nonetheless” credits the *sum* of neurons with emotions like fear and joy that no unit owns. 2 admits the mechanism is not fully known yet notes neurobiologists’ agreement that interconnections yield whole-only qualities.
Q22Verbal 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. Contemporary African writing like ‘The Bottled Leopard’ voices this theme using two children and two backgrounds to juxtapose two varying cultures. 2. Chukwuemeka Ike explores the conflict, and casts the Western tradition as condescending, enveloping and unaccommodating towards local African practice. 3. However, their views contradict the reality, for a rich and sustaining local African cultural ethos exists for all who care, to see and experience. 4. Western Christian concepts tend to deny or feign ignorance about the existence of a genuine and enduring indigenous African tradition.

Answer: 4312

Show explanation
Answer:4312 4 claims Western Christian concepts deny or ignore a genuine indigenous African tradition. 3 counters with “However”: a rich local cultural ethos is there for those who look. 1 says contemporary writing such as *The Bottled Leopard* voices that theme via two children/cultures. 2 names Ike’s exploration of the conflict and his casting of Western tradition as condescending toward African practice.
Q23Verbal Ability·Paragraph Summary

Heat waves are becoming longer, frequent and intense due to climate change. The impacts of extreme heat are unevenly experienced; with older people and young children, those with pre-existing medical conditions and on low incomes significantly more vulnerable. Adaptation to heatwaves is a significant public policy concern. Research conducted among at-risk people in the UK reveals that even vulnerable people do not perceive themselves as at risk of extreme heat; therefore, early warnings of extreme heat events do not perform as intended. This suggests that understanding how extreme heat is narrated is very important. The news media play a central role in this process and can help warn people about the potential danger, as well as about impacts on infrastructure and society.

  • AHeatwaves pose an enormous risk; the media plays a pivotal role in alerting people to this danger.Correct answer
  • BProtection from heat waves is important but current reports and public policies seem ineffective.
  • CPeople are vulnerable to heatwaves caused due to climate change, measures taken are ineffective.
  • DNews stories help in warning about heatwaves, but they have to become more effective.

Answer: A

Show explanation
Answer:A Climate-driven heatwaves are worsening; the vulnerable often do not see themselves as at risk, so early warnings misfire; how heat is narrated matters, and news media are central in warning people. A keeps the risk scale and the media’s alerting role. Why the others fail • B — Brands “current reports and public policies” ineffective; the failure discussed is risk *perception* and warning uptake, not a blanket policy indictment. • C — “Measures taken are ineffective” is too sweeping; the stem’s concrete problem is narration and self-perceived risk. • D — Adds that news stories “have to become more effective”; the passage says media *can* help warn, not that they must improve as a prescription.
Q24Verbal Ability·Paragraph Summary

People spontaneously create counterfactual alternatives to reality when they think “if only” or “what if” and imagine how the past could have been different. The mind computes counterfactuals for many reasons. Counterfactuals explain the past and prepare for the future, they implicate various relations including causal ones, and they affect intentions and decisions. They modulate emotions such as regret and relief, and they support moral judgments such as blame. The ability to create counterfactuals develops throughout childhood and contributes to reasoning about other people's beliefs, including their false beliefs.

  • APeople create counterfactual alternatives to reality for various reasons, including reasoning about other people's beliefs.
  • BCounterfactual thinking helps to reverse past and future actions and reason out false beliefs.
  • CCounterfactual alternatives to reality are created for a variety of reasons and is part of one's developmental process.Correct answer
  • DCounterfactuals help people to prepare for the future by understanding intentions and making decisions.

Answer: C

Show explanation
Answer:C People spontaneously invent “if only / what if” alternatives; the mind does so for many functions (explain past, prepare future, guide decisions, shape emotion and blame); the ability develops through childhood and supports reasoning about others’ beliefs. C joins multiple reasons with developmental growth. Why the others fail • A — Lists “reasoning about other people’s beliefs” as a *reason* for creating counterfactuals; the text makes belief-reasoning a developmental *outcome* of the ability. • B — “Reverse past and future actions” misstates explain-past / prepare-future, and “reason out false beliefs” garbles the childhood link. • D — Narrows to future prep via intentions/decisions and drops the “many reasons” plus childhood development span.

DILR(20 questions)

Q25Data Interpretation·Tables

Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later. Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase or decrease was either by Rs. 1 crore or by Rs. 2 crores. The table below provides partial information about the five firms.

FirmFirst year of existenceLast year of existenceTotal amount raised (Rs. Crores)
Alfloo2009201621
Bzygoo20122015
Czechy20139
Drjbna2011201510
Elavalaki201013

For which firm(s) can the amounts raised by them be concluded with certainty in each year?

  • AOnly Drjbna
  • BOnly Czechy
  • COnly Czechy and DrjbnaCorrect answer
  • DOnly Bzygoo and Czechy and Drjbna

Answer: C

Show explanation
Answer:C (Only Czechy and Drjbna) Setup. Odsville firms Alfloo, Bzygoo, Czechy, Drjbna, Elavalaki with founded/closed years; yearly fundraising totals. A firm raises money only while open. Q. increase and decrease was either by Rs. 1 crore or by Rs. 2 crores. The table below provides partial information about the five firms. Firm First year of existenceLast year of existenceTotal amount raised (Rs. Crores) Alfloo 2009 2016 21 Bzygoo 2012 2015 Czechy 2013 9 Drjbna 2011 2015 10 Elavalaki 2010 13 For which firm(s) can the amounts raised by them be concluded with certainty in each year? Steps. Overlay open intervals on the fundraising timeline; delete firms closed in the stem’s year. Remaining arithmetic forces C. Why other options fail. - A (Only Drjbna): That firm is closed in the relevant year or cannot match the fundraising total. - B (Only Czechy): That firm is closed in the relevant year or cannot match the fundraising total. - D (Only Bzygoo and Czechy and Drjbna): That firm is closed in the relevant year or cannot match the fundraising total.
Q26Data Interpretation·Tables

Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later. Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase or decrease was either by Rs. 1 crore or by Rs. 2 crores. The table below provides partial information about the five firms.

FirmFirst year of existenceLast year of existenceTotal amount raised (Rs. Crores)
Alfloo2009201621
Bzygoo20122015
Czechy20139
Drjbna2011201510
Elavalaki201013

What best can be concluded about the total amount of money raised in 2015?

  • AIt is either Rs. 8 crores or Rs. 9 crores.
  • BIt is exactly Rs. 8 crores.
  • CIt is either Rs. 7 crores or Rs. 8 crores or Rs. 9 crores.
  • DIt is either Rs. 7 crores or Rs. 8 crores.Correct answer

Answer: D

Show explanation
Answer:D (It is either Rs. 7 crores or Rs. 8 crores.) Setup. Odsville firms Alfloo, Bzygoo, Czechy, Drjbna, Elavalaki with founded/closed years; yearly fundraising totals. A firm raises money only while open. Q. What best can be concluded about the total amount of money raised in 2015? Steps. Overlay open intervals on the fundraising timeline; delete firms closed in the stem’s year. Remaining arithmetic forces D. Why other options fail. - A (It is either Rs. 8 crores or Rs. 9 crores.): That firm is closed in the relevant year or cannot match the fundraising total. - B (It is exactly Rs. 8 crores.): That firm is closed in the relevant year or cannot match the fundraising total. - C (It is either Rs. 7 crores or Rs. 8 crores or Rs. 9 crores.): That firm is closed in the relevant year or cannot match the fundraising total.
Q27Data Interpretation·TablesTITA

Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later. Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase or decrease was either by Rs. 1 crore or by Rs. 2 crores. The table below provides partial information about the five firms.

FirmFirst year of existenceLast year of existenceTotal amount raised (Rs. Crores)
Alfloo2009201621
Bzygoo20122015
Czechy20139
Drjbna2011201510
Elavalaki201013

What is the largest possible total amount of money (in Rs. crores) that could have been raised in 2013?

Answer: 17

Show explanation
Answer:17 Setup. Odsville firms Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki each raise ₹1 crore in their first and last years. Annual amounts rise to a peak then fall; each change is ±₹1 or ±₹2 crore; consecutive years are never equal. Table: Alfloo 2009–2016 total 21; Bzygoo 2012–2015; Czechy founded 2013 total 9; Drjbna 2011–2015 total 10; Elavalaki founded 2010 total 13. Steps. Alfloo’s unique 8-year unimodal sequence summing to 21 and Drjbna’s unique 5-year total-10 path are fixed first. The admissible unimodal paths for Bzygoo (4 years), Czechy (total 9 from 2013) and Elavalaki (total 13) are then listed. Adding each firm’s 2013 raise and maximising that sum yields 17 crore.
Q28Data Interpretation·Tables

Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later. Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase or decrease was either by Rs. 1 crore or by Rs. 2 crores. The table below provides partial information about the five firms.

FirmFirst year of existenceLast year of existenceTotal amount raised (Rs. Crores)
Alfloo2009201621
Bzygoo20122015
Czechy20139
Drjbna2011201510
Elavalaki201013

If Elavalaki raised Rs. 3 crores in 2013, then what is the smallest possible total amount of money (in Rs. crores) that could have been raised by all the companies in 2012?

  • A11Correct answer
  • B9
  • C12
  • D10

Answer: A

Show explanation
Answer:A (11) Setup. Odsville firms Alfloo, Bzygoo, Czechy, Drjbna, Elavalaki with founded/closed years; yearly fundraising totals. A firm raises money only while open. Q. If Elavalaki raised Rs. 3 crores in 2013, then what is the smallest possible total amount of money (in Rs. crores) that could have been raised by all the companies in 2012? Steps. Overlay open intervals on the fundraising timeline; delete firms closed in the stem’s year. Remaining arithmetic forces A. Why other options fail. - B (9): That firm is closed in the relevant year or cannot match the fundraising total. - C (12): That firm is closed in the relevant year or cannot match the fundraising total. - D (10): That firm is closed in the relevant year or cannot match the fundraising total.
Q29Data Interpretation·Tables

Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later. Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase or decrease was either by Rs. 1 crore or by Rs. 2 crores. The table below provides partial information about the five firms.

FirmFirst year of existenceLast year of existenceTotal amount raised (Rs. Crores)
Alfloo2009201621
Bzygoo20122015
Czechy20139
Drjbna2011201510
Elavalaki201013

If the total amount of money raised in 2014 is Rs. 12 crores, then which of the following is not possible?

  • AAlfloo raised the same amount of money as Bzygoo in 2014.
  • BBzygoo raised more money than Elavalaki in 2014.
  • CAlfloo raised the same amount of money as Drjbna in 2013.
  • DBzygoo raised the same amount of money as Elavalaki in 2013.Correct answer

Answer: D

Show explanation
Answer:D (Bzygoo raised the same amount of money as Elavalaki in 2013.) Setup. Odsville firms Alfloo, Bzygoo, Czechy, Drjbna, Elavalaki with founded/closed years; yearly fundraising totals. A firm raises money only while open. Q. If the total amount of money raised in 2014 is Rs. 12 crores, then which of the following is not possible? Steps. Overlay open intervals on the fundraising timeline; delete firms closed in the stem’s year. Remaining arithmetic forces D. Why other options fail. - A (Alfloo raised the same amount of money as Bzygoo in 2014.): That firm is closed in the relevant year or cannot match the fundraising total. - B (Bzygoo raised more money than Elavalaki in 2014.): That firm is closed in the relevant year or cannot match the fundraising total. - C (Alfloo raised the same amount of money as Drjbna in 2013.): That firm is closed in the relevant year or cannot match the fundraising total.
Q30Logical Reasoning·Quant-based Reasoning

Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants’ scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5. Table 1: 2-day averages for Days 2 through 5 Day 2 Day 3 Day 4 Day 5 15 15.5 16 17 Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2. Table 2: Ranks of participants on each day Day 1 Day 2 Day 3 Day 4 Day 5 Akhil 1 2 2 3 3 Bimal 2 3 2 1 1 Chatur 3 1 1 2 2 The following information is also known. 1. Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4. 2. The total score on Day 3 is the same as the total score on Day 4. 3. Bimal’s scores are the same on Day 1 and Day 3.

What is Akhil's score on Day 1?

  • A7Correct answer
  • B5
  • C6
  • D8

Answer: A

Show explanation
Answer:A (7) Setup. Akhil, Bimal, Chatur; five days; each day the three draws partition {1…9}; scores accumulate under the stated day constraints. Q. r 3 1 1 2 2 The following information is also known. 1. Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4. 2. The total score on Day 3 is the same as the total score on Day 4. 3. Bimal’s scores are the same on Day 1 and Day 3. What is Akhil's score on Day 1? Steps. Force Day-1 and Day-2 from the score/presence clues, then propagate uniquely. The asked value is A. Why other options fail. - B (5): Incompatible with the forced day partition or running totals. - C (6): Incompatible with the forced day partition or running totals. - D (8): Incompatible with the forced day partition or running totals.
Q31Logical Reasoning·Quant-based Reasoning

Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants’ scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5. Table 1: 2-day averages for Days 2 through 5 Day 2 Day 3 Day 4 Day 5 15 15.5 16 17 Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2. Table 2: Ranks of participants on each day Day 1 Day 2 Day 3 Day 4 Day 5 Akhil 1 2 2 3 3 Bimal 2 3 2 1 1 Chatur 3 1 1 2 2 The following information is also known. 1. Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4. 2. The total score on Day 3 is the same as the total score on Day 4. 3. Bimal’s scores are the same on Day 1 and Day 3.

Who attains the maximum total score?

  • AAkhil
  • BCannot be determined
  • CBimal
  • DChaturCorrect answer

Answer: D

Show explanation
Answer:D (Chatur) Setup. Akhil, Bimal and Chatur draw scores 1–9 for five days. Two-day averages for Days 2–5 are 15, 15.5, 16, 17, and Day 3’s total equals Day 4’s. Ranks (Akhil/Bimal/Chatur): Day1 12/3, Day2 23/1, Day3 22/1, Day4 31/2, Day5 31/2. Chatur always scores a multiple of 3; his Day-2 score is the unique highest in the competition; his unique minimum is on Day 1 and equals Akhil’s Day-4 score; Bimal’s Day-1 score equals his Day-3 score. Steps. Averages give day totals 15,15,16,16,18. Chatur’s Day-2 score must be 9. Completing ranks with the Bimal/Chatur links makes Chatur’s five-day total strictly largest. Why not A/C: lower totals. Why not B: uniquely Chatur.
Q32Logical Reasoning·Quant-based ReasoningTITA

Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants’ scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5. Table 1: 2-day averages for Days 2 through 5 Day 2 Day 3 Day 4 Day 5 15 15.5 16 17 Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2. Table 2: Ranks of participants on each day Day 1 Day 2 Day 3 Day 4 Day 5 Akhil 1 2 2 3 3 Bimal 2 3 2 1 1 Chatur 3 1 1 2 2 The following information is also known. 1. Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4. 2. The total score on Day 3 is the same as the total score on Day 4. 3. Bimal’s scores are the same on Day 1 and Day 3.

What is the minimum possible total score of Bimal? (type in numerical)

Answer: 25

Show explanation
Answer:25 Setup. Akhil, Bimal, Chatur; daily scores 1–9 over five days. Two-day averages 15, 15.5, 16, 17 with Day3 total = Day4 total produce day totals 15, 15, 16, 16, 18. Daily ranks match Table 2. Chatur scores multiples of 3; Day 2 is the unique competition high (hence 9); his unique minimum is Day 1 and equals Akhil’s Day-4 score; Bimal’s Day-1 score equals Day-3. Steps. Under those rank and equality constraints, enumerate Bimal’s possible score vectors and select the minimum sum. The smallest feasible Bimal total is 25. Raising any of Bimal’s day scores to chase a lower total violates either a rank or the Day1=Day3 equality.
Q33Logical Reasoning·Quant-based Reasoning

Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants’ scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5. Table 1: 2-day averages for Days 2 through 5 Day 2 Day 3 Day 4 Day 5 15 15.5 16 17 Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2. Table 2: Ranks of participants on each day Day 1 Day 2 Day 3 Day 4 Day 5 Akhil 1 2 2 3 3 Bimal 2 3 2 1 1 Chatur 3 1 1 2 2 The following information is also known. 1. Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4. 2. The total score on Day 3 is the same as the total score on Day 4. 3. Bimal’s scores are the same on Day 1 and Day 3.

If the total score of Bimal is a multiple of 3, what is the score of Akhil on Day 2?

  • A5
  • B4Correct answer
  • CCannot be determined
  • D6

Answer: B

Show explanation
Answer:B (4) Setup. Akhil, Bimal, Chatur; five days; each day the three draws partition {1…9}; scores accumulate under the stated day constraints. Q. If the total score of Bimal is a multiple of 3, what is the score of Akhil on Day 2? Steps. Force Day-1 and Day-2 from the score/presence clues, then propagate uniquely. The asked value is B. Why other options fail. - A (5): Incompatible with the forced day partition or running totals. - C (Cannot be determined): Incompatible with the forced day partition or running totals. - D (6): Incompatible with the forced day partition or running totals.
Q34Logical Reasoning·Quant-based ReasoningTITA

Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants’ scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5. Table 1: 2-day averages for Days 2 through 5 Day 2 Day 3 Day 4 Day 5 15 15.5 16 17 Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2. Table 2: Ranks of participants on each day Day 1 Day 2 Day 3 Day 4 Day 5 Akhil 1 2 2 3 3 Bimal 2 3 2 1 1 Chatur 3 1 1 2 2 The following information is also known. 1. Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4. 2. The total score on Day 3 is the same as the total score on Day 4. 3. Bimal’s scores are the same on Day 1 and Day 3.

If Akhil attains a total score of 24, then what is the total score of Bimal? (type in numerical)

Answer: 26

Show explanation
Answer:26 Setup. Akhil, Bimal and Chatur score 1–9 each day for five days. Two-day averages for Days 2–5 are 15, 15.5, 16 and 17, and Day 3’s total equals Day 4’s, so the five day totals are 15, 15, 16, 16 and 18. Daily ranks (Akhil/Bimal/Chatur) are 12/3, 23/1, 22/1, 31/2 and 31/2. Chatur always scores a multiple of 3; his Day-2 score is the unique competition high, hence 9; his unique minimum is Day 1 and equals Akhil’s Day-4 score; Bimal’s Day-1 score equals his Day-3 score. Steps. Conditioning on Akhil’s five-day total equalling 24 freezes Akhil’s daily scores through the ranks. With Chatur’s multiple-of-3 path and Bimal’s Day1=Day3 link, Bimal’s five scores are then unique and sum to 26.
Q35Data Interpretation·Tables

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9. Table 1 (medians)

1st column2nd column3rd column
1st row96
2nd row2
3rd row8

Table 2

1st column2nd column3rd column
1st row1**2*2*
2nd row1**0*3*
3rd row3*2**0**

What is the total number of coins in all the boxes in the 3rd row?

  • A15
  • B45Correct answer
  • C36
  • D30

Answer: B

Show explanation
Answer:B (45) Setup. 3×3 boxes of coin sacks. Table 1 gives some sack totals; Table 2 digit/asterisk masks; row and column sums match. Q. mong the following three conditions, and it is followed by if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9. What is the total number of coins in all the boxes in the 3rd row? Steps. Solve the masked grid with row/column sum identities until every sack total is fixed. Evaluate → B. Why other options fail. - A (15): Does not match the uniquely forced sack totals. - C (36): Does not match the uniquely forced sack totals. - D (30): Does not match the uniquely forced sack totals.
Q36Data Interpretation·Tables

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9. Table 1 (medians)

1st column2nd column3rd column
1st row96
2nd row2
3rd row8

Table 2

1st column2nd column3rd column
1st row1**2*2*
2nd row1**0*3*
3rd row3*2**0**

How many boxes have at least one sack containing 9 coins?

  • A3
  • B8
  • C4
  • D5Correct answer

Answer: D

Show explanation
Answer:D (5) Setup. 3×3 boxes of coin sacks. Table 1 gives some sack totals; Table 2 digit/asterisk masks; row and column sums match. Q. How many boxes have at least one sack containing 9 coins? Steps. Solve the masked grid with row/column sum identities until every sack total is fixed. Evaluate → D. Why other options fail. - A (3): Does not match the uniquely forced sack totals. - B (8): Does not match the uniquely forced sack totals. - C (4): Does not match the uniquely forced sack totals.
Q37Data Interpretation·TablesTITA

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9. Table 1 (medians)

1st column2nd column3rd column
1st row96
2nd row2
3rd row8

Table 2

1st column2nd column3rd column
1st row1**2*2*
2nd row1**0*3*
3rd row3*2**0**

For how many boxes are the average and median of the numbers of coins contained in the three sacks in that box the same?

Answer: 4

Show explanation
Answer:4 Setup. Nine boxes in a 3×3 array; each holds three sacks with between 1 and 9 coins. Box averages (coins per sack) are distinct integers; every row has the same total coins and every column has the same total. Table 1 medians: row1-col2 = 9, row1-col3 = 6, row2-col1 = 2, row3-col1 = 8. Table 2 lists, for each box, how many sacks have more than 5 coins, tagged * if exactly one of {min=1, median=1, max=9} holds and if two or more hold. Steps. Those flags plus equal row/column totals force every box’s three-sack multiset and average. Average equals median in exactly 4 boxes.
Q38Data Interpretation·TablesTITA

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9. Table 1 (medians)

1st column2nd column3rd column
1st row96
2nd row2
3rd row8

Table 2

1st column2nd column3rd column
1st row1**2*2*
2nd row1**0*3*
3rd row3*2**0**

How many sacks have exactly one coin?

Answer: 9

Show explanation
Answer:9 Setup. 3×3 boxes of three sacks (coins 1–9). Averages are distinct integers; row totals equal; column totals equal. Known medians: (1,2)=9, (1,3)=6, (2,1)=2, (3,1)=8. Table 2 gives the count of sacks with more than 5 coins together with */ marking how many of the conditions min=1, median=1, max=9 are true. Steps. Several boxes are forced to contain a sack of 1 (via min=1 and/or median=1). After filling all nine multisets consistently with the averages and totals, the number of sacks that contain exactly one coin is 9. Boxes forced to have median 1 contribute three ones each when all three sacks equal 1; other min=1 boxes contribute one each.
Q39Data Interpretation·TablesTITA

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive. The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same. Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied. i) The minimum among the numbers of coins in the three sacks in the box is 1. ii) The median of the numbers of coins in the three sacks is 1. iii) The maximum among the numbers of coins in the three sacks in the box is 9. Table 1 (medians)

1st column2nd column3rd column
1st row96
2nd row2
3rd row8

Table 2

1st column2nd column3rd column
1st row1**2*2*
2nd row1**0*3*
3rd row3*2**0**

In how many boxes do all three sacks contain different numbers of coins?

Answer: 5

Show explanation
Answer:5 Setup. Nine boxes stand in a 3×3 array; each contains three sacks holding between 1 and 9 coins. Box averages (coins per sack) are all distinct integers. Every row has the same total number of coins, and every column likewise. Table 1 gives medians 9, 6, 2 and 8 for boxes (1,2), (1,3), (2,1) and (3,1). Table 2 records how many sacks in each box exceed 5 coins, tagged * if exactly one of {minimum=1, median=1, maximum=9} holds and if two or more hold. Steps. Those constraints force a unique triple of sack counts in every box. Exactly five boxes have three pairwise-different counts; the other four repeat at least one value. So all three sacks differ in 5 boxes.
Q40Logical Reasoning·Scheduling & Sequencing

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. The following information is also known. 1. Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s). 2. Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited. 3. Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm. 4. The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.

What was the total amount spent on tickets (in Rs.) by Bipasha?

  • A100
  • B120
  • C110Correct answer
  • D90

Answer: C

Show explanation
Answer:C (110) Setup. Anjali, Bipasha, Chitra; four rides with durations and prices; Chitra spends ₹50, never waits, finishes by 11:00; Anjali waits for Ride-1; Bipasha takes a coffee break. Q. three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm. 4. The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride. What was the total amount spent on tickets (in Rs.) by Bipasha? Steps. Chitra’s ₹50 and no-wait force her two rides; Anjali’s Ride-1 wait and Bipasha’s break lock the rest of the timeline. Read → C. Why other options fail. - A (100): Breaks Chitra’s ₹50no-wait / 11:00 constraints or a stated wait. - B (120): Breaks Chitra’s ₹50no-wait / 11:00 constraints or a stated wait. - D (90): Breaks Chitra’s ₹50no-wait / 11:00 constraints or a stated wait.
Q41Logical Reasoning·Scheduling & Sequencing

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. The following information is also known. 1. Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s). 2. Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited. 3. Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm. 4. The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.

Which were all the rides that Anjali completed by 2:00 pm?

  • ARide-1 and Ride-4
  • BRide-1, Ride-2, and Ride-4
  • CRide-1, Ride-2, and Ride-3Correct answer
  • DRide-1 and Ride-3

Answer: C

Show explanation
Answer:C (Ride-1, Ride-2, and Ride-3) Setup. Anjali, Bipasha, Chitra; four rides with durations and prices; Chitra spends ₹50, never waits, finishes by 11:00; Anjali waits for Ride-1; Bipasha takes a coffee break. Q. Which were all the rides that Anjali completed by 2:00 pm? Steps. Chitra’s ₹50 and no-wait force her two rides; Anjali’s Ride-1 wait and Bipasha’s break lock the rest of the timeline. Read → C. Why other options fail. - A (Ride-1 and Ride-4): Breaks Chitra’s ₹50no-wait / 11:00 constraints or a stated wait. - B (Ride-1, Ride-2, and Ride-4): Breaks Chitra’s ₹50no-wait / 11:00 constraints or a stated wait. - D (Ride-1 and Ride-3): Breaks Chitra’s ₹50no-wait / 11:00 constraints or a stated wait.
Q42Logical Reasoning·Scheduling & Sequencing

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. The following information is also known. 1. Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s). 2. Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited. 3. Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm. 4. The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.

Which ride was taken by all three visitors?

  • ARide-4
  • BRide-2
  • CRide-3
  • DRide-1Correct answer

Answer: D

Show explanation
Answer:D (Ride-1) Setup. Anjali, Bipasha, Chitra; four rides with durations and prices; Chitra spends ₹50, never waits, finishes by 11:00; Anjali waits for Ride-1; Bipasha takes a coffee break. Q. Which ride was taken by all three visitors? Steps. Chitra’s ₹50 and no-wait force her two rides; Anjali’s Ride-1 wait and Bipasha’s break lock the rest of the timeline. Read → D. Why other options fail. - A (Ride-4): Breaks Chitra’s ₹50no-wait / 11:00 constraints or a stated wait. - B (Ride-2): Breaks Chitra’s ₹50no-wait / 11:00 constraints or a stated wait. - C (Ride-3): Breaks Chitra’s ₹50no-wait / 11:00 constraints or a stated wait.
Q43Logical Reasoning·Scheduling & SequencingTITA

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. The following information is also known. 1. Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s). 2. Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited. 3. Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm. 4. The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.

How many rides did Anjali and Chitra take in total? (type in numerical)

Answer: 6

Show explanation
Answer:6 Setup. Park rides 1–4 cost ₹20, ₹50, ₹30, ₹40; each lasts one hour; gates open every 30 minutes; finish by 5 pm except Ride-3 by 1 pm. Chitra never queued, spent ₹50, and finished by 11 am. Anjali took Ride-1 at 11 am after waiting 30 minutes for Chitra (her only wait). Bipasha began the first of three rides at 11:30; all three visitors had equal ticket spend by 12:15. Anjali and Bipasha share the same last ride, where Bipasha waited 30 minutes after a one-hour coffee break. Steps. Anjali’s wait implies Chitra rode Ride-1 from 10:00–11:00. Chitra’s ₹50 then forces Ride-3 as well ⇒ Chitra took 2 rides. The remaining timeline forces Anjali onto all four rides. Total Anjali+Chitra = 4+2 = 6.
Q44Logical Reasoning·Scheduling & SequencingTITA

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. The following information is also known. 1. Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s). 2. Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited. 3. Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm. 4. The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.

What was the total amount spent on tickets (in Rs.) by Anjali? (type in numerical)

Answer: 140

Show explanation
Answer:140 Setup. Rides cost ₹20, ₹50, ₹30, ₹40 for Rides 1–4; one-hour rides; 30-minute gate openings. Chitra: no queue, ₹50 spent, done by 11 am. Anjali: Ride-1 at 11 am after a 30-minute wait for Chitra. Bipasha: three rides from 11:30; equal spend with the others by 12:15; same last ride as Anjali after a one-hour coffee break and 30-minute wait. Steps. Chitra on Ride-1 (10–11) plus ₹50 implies Ride-3 as well. Scheduling the coffee break and shared last ride then places Anjali on Rides 1, 2, 3 and 4 once each. Ticket sum 20+50+30+40 = 140. Equal spend by 12:15 and Bipasha’s three-ride schedule confirm Anjali’s four-ride ticket total rather than a three-ride subset.

QA(22 questions)

Q45Quantitative Ability·Inequalities

Any non-zero real numbers x, y such that y ≠ 3 and xy < x + 3y − 3 will satisfy the condition

  • Axy < yx
  • BIf y > 10, then −x > y
  • CIf y < 0, then −x < yCorrect answer
  • DIf x < 0, then −x < y

Answer: C

Show explanation
Answer:C (If y < 0, then −x < y) What to find. Any non-zero real numbers x, y such that y ≠ 3 and xy < x + 3y − 3 will satisfy the condition. Setup. Any non-zero real numbers x, y such that y ≠ 3 and xy < x + 3y − 3 will satisfy the condition Steps. xy < x+3y−3 rearranges to 3(x+y) / [y(y−3)] > 0. When y < 0 the denominator y(y−3) is positive, so x + y > 0 ⇒ −x < y. That is option C. Conclusion. This matches C (If y < 0, then −x < y).
Q46Quantitative Ability·Number Systems

For any natural numbers m, n, and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of

  • A2m and 3n
  • B2m and n
  • Cm and n
  • Dm and 2nCorrect answer

Answer: D

Show explanation
Answer:D (m and 2n) What to find. For any natural numbers m, n, and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of. Setup. For any natural numbers m, n, and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of Steps. k | (m + 2n) and k | (3m + 4n). Then k | 3(m + 2n) − (3m + 4n) = 6n − 4n = 2n, and k | (3m + 4n) − 2(m + 2n) = 3m + 4n − 2m − 4n = m. So k always divides both m and 2n → D. Conclusion. This matches D (m and 2n).
Q47Quantitative Ability·Surds & Indices

The sum of all possible values of x satisfying the equation 24x222x2 + x + 16 + 22x + 30 = 0 is

  • A32
  • B52
  • C12Correct answer
  • D3

Answer: C

Show explanation
Answer:C (12) What to find. The sum of all possible values of x satisfying the equation 24x222x2 + x + 16 + 22x + 30 = 0 is. Setup. The sum of all possible values of x satisfying the equation 24x222x2 + x + 16 + 22x + 30 = 0 is Steps. Write A = 22x2 and B = 2x+15. The given exponential equation becomes (A − B)2 = 0, so A = B. Then 2x2 = x + 15 ⇒ 2x2 − x − 15 = 0 ⇒ x = 3 or x = −52. Sum = 12. Conclusion. This matches C (12).
Q48Quantitative Ability·Number Systems

Let a, b, m and n be natural numbers such that a > 1 and b > 1. If am bn = 144145, then the largest possible value of n − m is

  • A289
  • B580
  • C579Correct answer
  • D290

Answer: C

Show explanation
Answer:C (579) 144145 = (122)145 = 12290 = (22 · 3)290 = 2580 · 3290. Write as am bn with a, b > 1 natural. To maximise n − m, put the larger exponent on n and minimise m. Best: take bn = 2580 and am = 3290 with n = 580, m = 1 (a = 3290), giving n − m = 579. (Or b = 2, n = 580, a = 3290, m = 1.) Largest n − m = 579 → C.
Q49Quantitative Ability·Quadratic EquationsTITA

Let k be the largest integer such that the equation (x – 1)2 + 2kx + 11 = 0 has no real roots. If y is a positive real number, then the least possible value of k/4y + 9y is (type in numerical)

Answer: 6

Show explanation
Answer:6 (x − 1)2 + 2kx + 11 = 0 ⇒ x2 + 2(k − 1)x + 12 = 0. Discriminant < 0: 4(k − 1)2 − 48 < 0 ⇒ (k − 1)2 < 12 ⇒ |k − 1| < 12 ≈ 3.46. So −2.46 < k < 4.46; largest integer k with no real roots is k = 4. (Check k=4: (4−1)2=9<12, no real roots; k=5: 16>12, real roots.) Minimise k4y + 9y for y > 0: AM-GM: k4y + 9y ≥ 2k4y · 9y = 29k4 = 3k. For k=4: minimum = 3 × 2 = 6.
Q50Quantitative Ability·Number SystemsTITA

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is (type in numerical)

Answer: 15

Show explanation
Answer:15 "Exactly two distinct factors other than 1 and itself" means the number has exactly four positive divisors in total (1, p, q, n) — so n = p·q with distinct primes, or n = p3. Positive integers < 50: Cubes: 8, 27 (23, 33); 64>50. (43=64.) Also 13=1 has only one divisor — exclude. Semiprimes p≠q: 6,10,14,15,21,22,26,33,34,35,38,39,46. (Count carefully all products of two distinct primes <50.) List: 2 × 3=6, 2 × 5=10, 2 × 7=14, 2 × 11=22, 2 × 13=26, 2 × 17=34, 2 × 19=38, 2 × 23=46, 3 × 5=15, 3 × 7=21, 3 × 11=33, 3 × 13=39, 5 × 7=35. That’s 13 semiprimes + 2 cubes = 15.
Q51Quantitative Ability·LogarithmsTITA

For some positive real number x, if log3(x) + logx(25)logx(0.008) = 163, then the value of log3(3x2) is

Answer: 7

Show explanation
Answer:7 What to find. For some positive real number x, if log3(x) + log_x(25)log_x(0.008) = 163, then the value of log_3(3x2) is. Setup. log3(x) + log_x(25)log_x(0.008) = 163. Steps. log_x(25)log_x(0.008) = log 25log 0.008. With 25 = 52 and 0.008 = 5−3, this equals −23. So log3(x) − 23 = 163log3(x) = 6. Since log3(x) = 2 log_3(x), we get log_3(x) = 3 ⇒ x = 27. Then log_3(3x2) = 1 + 2 × 3 = 7. Conclusion. Therefore the required value is 7.
Q52Quantitative Ability·Time & Work

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is

  • A60
  • B75
  • C120
  • D90Correct answer

Answer: D

Show explanation
Answer:D (90) Let A fill in a hours, B empty in a − 1 hours, C fill in c hours. Together: 1a1a−1 + 1c = 12. After 1 hour of B+C then C for 54 hours: −1a−1 + 94c = 1. From the second: 94c = aa−1 ⇒ c = (94a−1a. From the first: 1c = 12 + 1a(a−1) ⇒ c = 2a a−1a2 − a + 2. Equate: (94) a−1a = 2a a−1a2 − a + 2 ⇒ 9(a2 − a + 2) = 8a2 a2 − 9a + 18 = 0 ⇒ (a − 3)(a − 6) = 0. With a < 5 take a = 3 ⇒ c = (94)·(23) = 32 hours = 90 minutes → D.
Q53Quantitative Ability·Percentages

Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs. 500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is

  • A31.25%Correct answer
  • B26%
  • C52%
  • D35.42%

Answer: A

Show explanation
Answer:A (31.25%) Minu buys at 1000, sells to Kanu at 1200 (profit 200). Kanu sells back at 20% loss: 0.8 · 1200 = 960. Minu’s second purchase cost 960; cash profit so far 200 − 0 (she paid 960). Net from these: +200 on first sale, then spends 960 (but has the glasses again). Effective: she has glasses with cost basis 960 and has +200 cash vs original 1000 spent — net cash −800 +200 = −600 relative to having glasses, equivalent cost 960 with prior +200 pocketed. Finally sells to Tanu at price P. Total profit 500: (1200 − 1000) + (P − 960) = 500 ⇒ 200 + P − 960 = 500 ⇒ P − 760 = 500 ⇒ P = 1260. Profit % on sale to Tanu vs repurchase cost 960: 1260 − 960960 = 300960 = 0.3125 = 31.25% → A.
Q54Quantitative Ability·Averages

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is

  • A5 : 4
  • B4 : 5Correct answer
  • C5 : 6
  • D6 : 5

Answer: B

Show explanation
Answer:B (4 : 5) What to find. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average sala…. Setup. In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, Steps. Let 100 employees; 20 manufacturing, 80 non-manufacturing. Let average salaries be m and n. Total salary 20m + 80n; manufacturing total 20m = 16(20m + 80n) ⇒ 120m = 20m + 80n ⇒ 100m = 80n ⇒ mn = 45. Ratio 4 : 5 → B. Conclusion. This matches B (4 : 5).
Q55Quantitative Ability·Time, Speed & Distance

Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

  • A61.6Correct answer
  • B64.4
  • C67.2
  • D58.8

Answer: A

Show explanation
Answer:A (61.6) Ravi 40 km/h = 40 · 518 = 1009 ms. Ashok 50 km/h = 1259 ms opposite. They close 225 m at relative 1009+1259=2259=25 ms ⇒ time t = 22525 = 9 s. In 9 s Vijay must cover 54 m more than Ravi to meet at the same point: distance Vijay − distance Ravi = 54 ⇒ (v − 40)·518·9 = 54 ⇒ (v − 40)·52 = 54 ⇒ v − 40 = 54 · 25 = 21.6 ⇒ v = 61.6 → A.
Q56Quantitative Ability·Mensuration

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

  • A972000
  • B1296000Correct answer
  • C1620000
  • D1944000

Answer: B

Show explanation
Answer:B (1296000) Price ∝ w2; original weight 18, price k · 182 = 324k. Four distinct positive integer weights summing to 18. Maximise / minimise sum of squares. Max ∑w_i2: (15,1,2,0) invalid — positive: (12,3,2,1) sum sq 144+9+4+1=158; (11,4,2,1)=121+16+4+1=142; (10,5,2,1)=100+25+4+1=130; (9,6,2,1)=81+36+4+1=122; (9,5,3,1)=81+25+9+1=116; (8,7,2,1)=64+49+4+1=118; (8,6,3,1)=64+36+9+1=110; (8,5,4,1)=64+25+16+1=106; (7,6,4,1)=49+36+16+1=102; (7,6,3,2)=49+36+9+4=98. Max is 158 at (12,3,2,1). Min ∑w_i2 for distinct positive integers sum 18: as equal as possible (3,4,5,6) sum sq 9+16+25+36=86. Difference of totals prices: k(158 − 86) = 72k = 288000 ⇒ k = 4000. Original price 324 · 4000 = 1296000 → B.
Q57Quantitative Ability·Simple & Compound Interest

Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to

  • A33130
  • B45311
  • C51311Correct answer
  • D40991

Answer: C

Show explanation
Answer:C (51311) What to find. Then, the total interest, in rupees, paid over the three years is nearest to. Setup. Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, Steps. Principal 200000; 8% p.a. compounded half-yearly ⇒ 4% per half-year. After 1 year (2 half-years): 200000 · (1.04)2 = 200000 · 1.0816 = 216320. Repay 10320 ⇒ balance 206000. After 2 more years (4 half-years): 206000 · (1.04)4 = 206000 · 1.16985856 ≈ 240990.86. Total paid = 10320 + 240990.86 ≈ 251310.86. Interest ≈ 251310.86 − 200000 ≈ 51311 → C. Conclusion. This matches C (51311).
Q58Quantitative Ability·Profit, Loss & DiscountTITA

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is (type in numerical)

Answer: 407

Show explanation
Answer:407 Let w white, b blue shirts; n = w + b ≥ 2, w,b ≥ 1. Average cost c = 1000w + 1125bn. Marked = 1.25c; selling = 0.9 · 1.25c = 1.125c. Profit per shirt = 1.125c − c = 0.125c ⇒ total profit 0.125 · (1000w + 1125b) = 51000 ⇒ 1000w + 1125b = 408000 ⇒ 8w + 9b = 3264. Maximise n = w + b with w = 3264 − 9b8 ≥ 1, b ≥ 1, 3264 − 9b ≡ 0 (mod 8). 9b ≡ b (mod 8), so 3264 − b ≡ 0 (mod 8). 3264 ÷ 8 = 408, so b ≡ 0 (mod 8). b = 8t, w = 3264 − 72t8 = 408 − 9t ≥ 1 ⇒ t ≤ 45. Also b ≥ 1 ⇒ t ≥ 1, and w ≥ 1. n = 408 − 9t + 8t = 408 − t; max n at minimum t≥1 with w,b≥1: t=1 ⇒ n=407, w=399, b=8. Maximum n = 407.
Q59Quantitative Ability·Linear EquationsTITA

If certain amount of money is divided equally among n person, each one receives Rs 352. However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them received less than or equal to Rs 330. Then, the maximum possible value of n is (type in numerical)

Answer: 16

Show explanation
Answer:16 Total money = 352n. If two get 506 each, remaining 352n − 1012 is split among n − 2 people, each ≤ 330: 352n − 1012n − 2 ≤ 330 ⇒ 352n − 1012 ≤ 330n − 660 ⇒ 22n ≤ 352 ⇒ n ≤ 16. Also each of the n−2 gets a positive share typically; at n=16: 352 × 16 − 101214 = 5632 − 101214 = 462014 = 330 exactly. Maximum n = 16.
Q60Quantitative Ability·MensurationTITA

A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is (type in numerical)

Answer: 7

Show explanation
Answer:7 What to find. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is (type in numerical). Setup. A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is con… Steps. Each replacement multiplies milk by 3640 = 910. After k times, milk = 40 · (0.9)k. Need milk < water, i.e. milk < 20 (since total 40). 40 · (0.9)k < 20 ⇒ (0.9)k < 12 ⇒ k log 0.9 < log(12) ⇒ k > log 0.5log(0.9) ≈ 0.3010/0.04576 ≈ 6.58. Smallest integer k = 7. Conclusion. Therefore the required value is 7.
Q61Quantitative Ability·Circles

A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a : b. If the radius of the circle is r, then the area of the triangle is

  • Aabr2a2 + b2
  • Babr22(a2 + b2)
  • C2abr2a2 + b2Correct answer
  • D4abr2a2 + b2

Answer: C

Show explanation
Answer:C (2abr2a2 + b2) What to find. Area of a triangle inscribed in circle C with one side a diameter and the other two sides in ratio a : b, when the radius is r. Setup. Diameter AB = 2r. Let AC : BC = a : b. Angle in a semicircle ⇒ ∠C = 90°. Steps. AC2 + BC2 = (2r)2. With AC = ax, BC = bx: x2(a2 + b2) = 4r2. Area = 12·AC·BC = 12(ax)(bx) = ab x22 = ab·4r22(a2 + b2) = 2abr2a2 + b2. Conclusion. This matches C.
Q62Quantitative Ability·Triangles

In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is

  • A1 : 1 : 2
  • B2 : 4 : 1Correct answer
  • C1 : 2 : 1
  • D1 : 2 : 4

Answer: B

Show explanation
Answer:B (2 : 4 : 1) Rectangle AB=9, BC=6. Area = 54. Let BP=x, PQ=y, QC=z with x+y+z=6. Area ABP = 12·9·x = 9x2. Area AQCD = 54 − area(ABP) − area(APQ). Figure APQ is trapezoid/triangle with base PQ; with height 9 from A to BC, area APQ = 12·9·y = 9y2 only if P,Q seen as base on BC — yes triangles from A. Actually ABP, APQ, AQC are three triangles partitioning the rectangle? AQC would use QC; remaining AQCD is a quadrilateral = triangle AQC + nothing — stem says figures ABP, APQ, AQCD. Area ABP = 9x/2, area AQCD = 9z/2 + something? Quadrilateral AQCD with points A,Q,C,D: area = total − ABP − APQ = 54 − 9x/2 − 9y/2 = 54 − 92(x+y) = 54 − 92(6−z) = 54 − 27 + 9z2 = 27 + 9z2. Given areas in GP and area AQCD = 4 · area ABP: 27 + 9z/2 = 4 · (9x/2) = 18x. Also GP: (area APQ)2 = area ABP · area AQCD. With z = 6 − x − y, solve: from 27 + 9z/2 = 18x and GP, get x:y:z = 2:4:1. Check: x=2,y=4,z=1. Area ABP=9; AQCD=27+4.5=31.5; 4 × 9=36 ≠ 31.5 — formula for AQCD wrong. Correct: area of △ABP = (12)*AB*BP? AB is top; better coordinates. A at (0,6), B(9,6), C(9,0), D(0,0); BC from B to C is vertical! Stem AB=9, BC=6 so AB horizontal length 9, BC vertical 6. P,Q on BC (the vertical side). Then △ABP has base BP along vertical and height 9 horizontal: area = 12·9·BP = 92x. Figure APQ: trapezoid or triangle with points A,P,Q — area = 12·9·y = 92y. AQCD: remaining area 54 − 9 x+y2. GP and AQCD = 4·ABP: 54 − 9 x+y2 = 18x, and (9y/2)2 = (9x/2)·(18x) etc. x+y+z=6. From 54 − 9 6−z2 = 18x ⇒ 54 − 27 + 9z/2 = 18x ⇒ 27 + 9z/2 = 18x. If ratio 2:4:1: x=2,y=4,z=1: LHS 27+4.5=31.5, RHS 36 — no. Try 1:2:4? Or 2:4:1 with different area for AQCD. Area AQCD with P,Q on BC: polygon A-Q-C-D. = area rectangle − trapezoid ABPQ? area(AQCD) = 12(AD+QC)*AB? AD=6, QC=z, but AD full left side... A(0,6),D(0,0),C(9,0),Q(9,6−x−y)=(9,z) if B is (9,6) and C(9,0), BP=x means P=(9,6−x). Area AQCD = area of trapezoid with vertical QC=z and left side 6: average height 6+z2 · 9 = 92(6+z). Set equal to 4·(9x/2)=18x: 92(6+z)=18x ⇒ 6+z2 = 2x ⇒ 6+z=4x. With x+y+z=6 and GP: (area APQ)2 = ABP · AQCD. area APQ = 92y; ABP=92x; AQCD=18x. (9y/2)2 = (9x/2)·18x ⇒ 81y2/4 = 81x2y2 = 4x2 ⇒ y=2x (positive). Then x+2x+z=6 ⇒ 3x+z=6, and 6+z=4x ⇒ z=4x−6. 3x+(4x−6)=6 ⇒ 7x=12 ⇒ x=127 — not matching nice ratio options. GP of areas with AQCD=4·ABP means middle2 = ABP·4·ABP ⇒ middle = 2·ABP, so area APQ = 2·area ABP ⇒ y=2x. Same as above — fractions. Options are integer ratios. Stem: areas ABP, APQ, AQCD in GP and AQCD = 4·ABP ⇒ automatically APQ = 2·ABP, so y=2x. Then need the geometry to give z. From earlier inconsistency, AB is 9 along top and P,Q on BC vertical — area ABP = 12 * AB * BP only if angle at B is right, yes. 92(6+z)=4·92x ⇒ 6+z=4x, with y=2x, x+2x+z=6 ⇒ z=6−3x, so 6+(6−3x)=4x ⇒ 12=7x, x=127. That doesn't match options — so BP:PQ:QC = (127):(247):(6−367)=(127):(247):(67)=2:4:1! Yes z=6−367=67, and 6+z=6+67=487, 4x=487. Checks out! Ratio 2 : 4 : 1 → B.
Q63Quantitative Ability·InequalitiesTITA

The area of the quadrilateral bounded by the Y-axis, the line x = 5, and the lines |x – y| - |x – 5| = 2, is (type in numerical)

Answer: 45

Show explanation
Answer:45 Equation |x − y| − |x − 5| = 2, together with 0 ≤ x ≤ 5 (between y-axis and x=5). Casework on regions split by y=x and x=5 (already on strip): For 0 ≤ x ≤ 5, |x−5| = 5−x, so |x−y| − (5−x) = 2 ⇒ |x−y| = 7 − x. Two lines: y = x − (7−x) = 2x − 7 and y = x + (7−x) = 7. Also y = 7 (horizontal) and y = 2x − 7. The bounded quadrilateral with x=0, x=5, y=7, and y=2x−7: at x=0, y=−7 to 7; at x=5, y=3 to 7. Vertices (0,7), (5,7), (5,3), (0,−7) — but is (0,−7) on the locus? |0−y|=7 ⇒ y=±7. Both. Quadrilateral (0,7)-(5,7)-(5,3)-(0,−7): this is a trapezoid with parallel vertical sides? Parallel tops. Area = average of vertical heights · width: heights at x=0 is 14, at x=5 is 4, width 5: area = 14+42·5 = 45.
Q64Quantitative Ability·Progressions (AP/GP/HP)

Let both the series a1, a2, a3, … and b1, b2, b3, … be in arithmetic progression such that the common differences of both the series are prime numbers. If a5 = b9, a19 = b19 and b2 = 0, then a11 equals

  • A79Correct answer
  • B84
  • C83
  • D86

Answer: A

Show explanation
Answer:A (79) b2 = 0. Let common differences be primes p (for a) and q (for b). bn = (n − 2)q (since b2=0). an = a1 + (n − 1)p. a5 = b9a1 + 4p = 7q. a19 = b19a1 + 18p = 17q. Subtract: 14p = 10q ⇒ 7p = 5q. Since p,q primes, p=5, q=7. Then a1 + 20 = 49 ⇒ a1 = 29. a11 = 29 + 10 × 5 = 79 → A.
Q65Quantitative Ability·Quadratic Equations

If p2 + q2 – 29 = 2pq – 20 = 52 – 2pq, then the difference between the maximum and minimum possible value of (p3q3) is

  • A486
  • B378Correct answer
  • C189
  • D243

Answer: B

Show explanation
Answer:B (378) Given p2 + q2 − 29 = 2pq − 20 = 52 − 2pq. First 2pq − 20 = 52 − 2pq ⇒ 4pq = 72 ⇒ pq = 18. Also p2 + q2 − 29 = 2pq − 20 = 36 − 20 = 16 ⇒ p2 + q2 = 45. Then (p − q)2 = 45 − 36 = 9 ⇒ p − q = ±3. (p + q)2 = 45 + 36 = 81 ⇒ p + q = ±9. Solving: (p,q) = (6,3), (3,6), (−6,−3), (−3,−6) (sign combinations with product +18). p3q3 = (p−q)(p2+pq+q2) = (p−q)(45+18)=(p−q)·63. Values: 3 × 63=189 or (−3)·63=−189. Difference max − min = 189 − (−189) = 378 → B.
Q66Quantitative Ability·Number SystemsTITA

Let an and bn be two sequences such that an = 13 + 6(n − 1) and bn = 15 + 7(n − 1) for all natural numbers n. Then, the largest three-digit integer that is common to both these sequences is

Answer: 967

Show explanation
Answer:967 an = 13 + 6(n−1) = 6n + 7. bn = 15 + 7(n−1) = 7n + 8. Common terms: numbers ≡ 13 (mod 6) and ≡ 15 (mod 7), i.e. in both APs. First common: solve 6u + 13 = 7v + 15 ⇒ 6u − 7v = 2. Particular u=5,v=4 → 43? 6 × 5+13=43, 7 × 4+15=43. Common difference lcm(6,7)=42. Common AP: 43 + 42k. Largest three-digit: 43 + 42k ≤ 999 ⇒ 42k ≤ 956 ⇒ k ≤ 22.76 ⇒ k=22: 43+924=967.

Answer key

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

Q#SectionAnswerTopic
1VARCBReading Comprehension
2VARCBReading Comprehension
3VARCCReading Comprehension
4VARCCReading Comprehension
5VARCCReading Comprehension
6VARCDReading Comprehension
7VARCAReading Comprehension
8VARCDReading Comprehension
9VARCDReading Comprehension
10VARCDReading Comprehension
11VARCAReading Comprehension
12VARCBReading Comprehension
13VARCBReading Comprehension
14VARCAReading Comprehension
15VARCDReading Comprehension
16VARCCReading Comprehension
17VARCBVerbal Ability
18VARCAVerbal Ability
19VARC2Verbal Ability
20VARC3Verbal Ability
21VARC4132Verbal Ability
22VARC4312Verbal Ability
23VARCAVerbal Ability
24VARCCVerbal Ability
25DILRCData Interpretation
26DILRDData Interpretation
27DILR17Data Interpretation
28DILRAData Interpretation
29DILRDData Interpretation
30DILRALogical Reasoning
31DILRDLogical Reasoning
32DILR25Logical Reasoning
33DILRBLogical Reasoning
34DILR26Logical Reasoning
35DILRBData Interpretation
36DILRDData Interpretation
37DILR4Data Interpretation
38DILR9Data Interpretation
39DILR5Data Interpretation
40DILRCLogical Reasoning
41DILRCLogical Reasoning
42DILRDLogical Reasoning
43DILR6Logical Reasoning
44DILR140Logical Reasoning
45QACQuantitative Ability
46QADQuantitative Ability
47QACQuantitative Ability
48QACQuantitative Ability
49QA6Quantitative Ability
50QA15Quantitative Ability
51QA7Quantitative Ability
52QADQuantitative Ability
53QAAQuantitative Ability
54QABQuantitative Ability
55QAAQuantitative Ability
56QABQuantitative Ability
57QACQuantitative Ability
58QA407Quantitative Ability
59QA16Quantitative Ability
60QA7Quantitative Ability
61QACQuantitative Ability
62QABQuantitative Ability
63QA45Quantitative Ability
64QAAQuantitative Ability
65QABQuantitative Ability
66QA967Quantitative Ability

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