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CAT 2020 Slot 3 answer key with solutions

This is the complete CAT 2020 Slot 3 question paper with answer key and solutions — 76 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(26 questions)

Q1Reading Comprehension·Specific Detail

Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; . . . and also affect perception and knowledge—how and what the traveler comes to know and write about. The completion of the first U.S. transcontinental highway during the 1920s . . . for example, inaugurated a new genre of travel literature about the United States—the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions. Travel writing’s relationship to empire building— as a type of “colonialist discourse”—has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analyzed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of 18th- and 19th-century exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing. Feminist geographers’ studies of travel writing challenge the masculinist history of geography by questioning who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers—or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the 19th century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle- and upper-class Victorian women. Many studies from the 1970s onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self-development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.

According to the passage, Said’s book, “Orientalism”:

  • Aexplained the difference between the representation of people and the actual fact.
  • Billustrated how narrow minded and racist westerners were.
  • Cargued that cultural imperialism was more significant than colonial domination.
  • Ddemonstrated how cultural imperialism was used to justify colonial dominationCorrect answer

Answer: D

Show explanation
Answer:D Said’s *Orientalism* is invoked for showing how cultural representations of the “Orient” authorised and sustained colonial rule—cultural imperialism justifying domination. Why the others fail: • A — Representation-vs-fact is too thin; the political use of representation is the point. • B — Reduces the book to proving Westerners’ narrow racism, missing the domination-justifying mechanism. • C — Does not rank cultural imperialism as “more significant than” colonial domination; it shows how culture served empire.
Q2Reading Comprehension·Inference

Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; . . . and also affect perception and knowledge—how and what the traveler comes to know and write about. The completion of the first U.S. transcontinental highway during the 1920s . . . for example, inaugurated a new genre of travel literature about the United States—the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions. Travel writing’s relationship to empire building— as a type of “colonialist discourse”—has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analyzed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of 18th- and 19th-century exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing. Feminist geographers’ studies of travel writing challenge the masculinist history of geography by questioning who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers—or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the 19th century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle- and upper-class Victorian women. Many studies from the 1970s onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self-development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.

From the passage, it can be inferred that scholars argue that Victorian women experienced self-development through their travels because:

  • Atheir identity was redefined when they were away from home.Correct answer
  • Bthey were on a quest to discover their diverse identities.
  • Cthey were from the progressive middle- and upper-classes of society.
  • Dthey developed a feminist perspective of the world

Answer: A

Show explanation
Answer:A Liberal-feminist readings treat travel as self-development because women reconstituted identity away from home—redefinition in new locations. Why the others fail: • B — “Quest for diverse identities” over-psychologises; the stress is identity shift through departure. • C — Class background enables travel but is not the inferred mechanism of self-development. • D — Developing a feminist worldview is the scholars’ lens, not what travellers necessarily gained.
Q3Reading Comprehension·Inference

Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; . . . and also affect perception and knowledge—how and what the traveler comes to know and write about. The completion of the first U.S. transcontinental highway during the 1920s . . . for example, inaugurated a new genre of travel literature about the United States—the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions. Travel writing’s relationship to empire building— as a type of “colonialist discourse”—has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analyzed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of 18th- and 19th-century exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing. Feminist geographers’ studies of travel writing challenge the masculinist history of geography by questioning who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers—or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the 19th century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle- and upper-class Victorian women. Many studies from the 1970s onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self-development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.

From the passage, we can infer that feminist scholars’ understanding of the experiences of Victorian women travellers is influenced by all of the following EXCEPT scholars':

  • Aawareness of gender issues in Victorian society
  • Bawareness of the ways in which identity is formed
  • Cperspective that they bring to their research
  • Dknowledge of class tensions in Victorian societyCorrect answer

Answer: D

Show explanation
Answer:D Feminist scholars’ takes are shaped by gender awareness, identity-formation theories, and researchers’ own perspectives. Class tensions in Victorian society are not named as a shaping influence here—so D is the EXCEPT. Why the others fail: • A — Gender in Victorian society is central to the liberal-feminist frame. • B — Identity formation (including fragmented poststructural selves) is explicit. • C — Scholars’ own perspectives/turns (liberal vs poststructural) steer interpretation.
Q4Reading Comprehension·Specific Detail

Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; . . . and also affect perception and knowledge—how and what the traveler comes to know and write about. The completion of the first U.S. transcontinental highway during the 1920s . . . for example, inaugurated a new genre of travel literature about the United States—the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions. Travel writing’s relationship to empire building— as a type of “colonialist discourse”—has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analyzed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of 18th- and 19th-century exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing. Feminist geographers’ studies of travel writing challenge the masculinist history of geography by questioning who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers—or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the 19th century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle- and upper-class Victorian women. Many studies from the 1970s onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self-development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.

American travel literature of the 1920s:

  • Adeveloped the male protagonists’ desire for independence.
  • Bshowed participation in local traditions.
  • Cpresented travellers’ discovery of their identity as different from others.
  • Dcelebrated the freedom that travel gives.Correct answer

Answer: D

Show explanation
Answer:D 1920s American travel writing is tied to celebrating mobility and the freedom travel affords—liberation through movement. Why the others fail: • A — Male independence desire is not the distinctive summary given. • B — Local-tradition participation is not the highlighted trait. • C — Identity-as-difference discovery better fits other strands (e.g., Victorian/poststructural), not this 1920s capsule.
Q5Reading Comprehension·Application & Analogy

Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters; affect the organization and passage of space and time; . . . and also affect perception and knowledge—how and what the traveler comes to know and write about. The completion of the first U.S. transcontinental highway during the 1920s . . . for example, inaugurated a new genre of travel literature about the United States—the automotive or road narrative. Such narratives highlight the experiences of mostly male protagonists “discovering themselves” on their journeys, emphasizing the independence of road travel and the value of rural folk traditions. Travel writing’s relationship to empire building— as a type of “colonialist discourse”—has drawn the most attention from academicians. Close connections have been observed between European (and American) political, economic, and administrative goals for the colonies and their manifestations in the cultural practice of writing travel books. Travel writers’ descriptions of foreign places have been analyzed as attempts to validate, promote, or challenge the ideologies and practices of colonial or imperial domination and expansion. Mary Louise Pratt’s study of the genres and conventions of 18th- and 19th-century exploration narratives about South America and Africa (e.g., the “monarch of all I survey” trope) offered ways of thinking about travel writing as embedded within relations of power between metropole and periphery, as did Edward Said’s theories of representation and cultural imperialism. Particularly Said’s book, Orientalism, helped scholars understand ways in which representations of people in travel texts were intimately bound up with notions of self, in this case, that the Occident defined itself through essentialist, ethnocentric, and racist representations of the Orient. Said’s work became a model for demonstrating cultural forms of imperialism in travel texts, showing how the political, economic, or administrative fact of dominance relies on legitimating discourses such as those articulated through travel writing. Feminist geographers’ studies of travel writing challenge the masculinist history of geography by questioning who and what are relevant subjects of geographic study and, indeed, what counts as geographic knowledge itself. Such questions are worked through ideological constructs that posit men as explorers and women as travelers—or, conversely, men as travelers and women as tied to the home. Studies of Victorian women who were professional travel writers, tourists, wives of colonial administrators, and other (mostly) elite women who wrote narratives about their experiences abroad during the 19th century have been particularly revealing. From a “liberal” feminist perspective, travel presented one means toward female liberation for middle- and upper-class Victorian women. Many studies from the 1970s onward demonstrated the ways in which women’s gendered identities were negotiated differently “at home” than they were “away,” thereby showing women’s self-development through travel. The more recent poststructural turn in studies of Victorian travel writing has focused attention on women’s diverse and fragmented identities as they narrated their travel experiences, emphasizing women’s sense of themselves as women in new locations, but only as they worked through their ties to nation, class, whiteness, and colonial and imperial power structures.

From the passage, we can infer that travel writing is most similar to:

  • Ahistorical fiction
  • Bpolitical journalism
  • Cfeminist writing
  • Dautobiographical writingCorrect answer

Answer: D

Show explanation
Answer:D Travel writing throughout is treated as first-person narration of experience and self—closest to autobiography. Why the others fail: • A — Historical fiction invents plots; travel writing claims lived itinerary. • B — Political journalism is not the governing likeness. • C — Feminist writing is one critical approach to the corpus, not the genre twin.
Q6Reading Comprehension·Specific Detail

Although one of the most contested concepts in political philosophy, human nature is something on which most people seem to agree. By and large, according to Rutger Bregman in his new book Humankind, we have a rather pessimistic view – not of ourselves exactly, but of everyone else. We see other people as selfish, untrustworthy and dangerous and therefore we behave towards them with defensiveness and suspicion. This was how the 17th-century philosopher Thomas Hobbes conceived our natural state to be, believing that all that stood between us and violent anarchy was a strong state and firm leadership. But in following Hobbes, argues Bregman, we ensure that the negative view we have of human nature is reflected back at us. He instead puts his faith in Jean-Jacques Rousseau, the 18th-century French thinker, who famously declared that man was born free and it was civilisation – with its coercive powers, social classes and restrictive laws – that put him in chains. Hobbes and Rousseau are seen as the two poles of the human nature argument and it’s no surprise that Bregman strongly sides with the Frenchman. He takes Rousseau’s intuition and paints a picture of a prelapsarian idyll in which, for the better part of 300,000 years, Homo sapiens lived a fulfilling life in harmony with nature . . . Then we discovered agriculture and for the next 10,000 years it was all property, war, greed and injustice. . . . It was abandoning our nomadic lifestyle and then domesticating animals, says Bregman, that brought about infectious diseases such as measles, smallpox, tuberculosis, syphilis, malaria, cholera and plague. This may be true, but what Bregman never really seems to get to grips with is that pathogens were not the only things that grew with agriculture – so did the number of humans. It’s one thing to maintain friendly relations and a property-less mode of living when you’re 30 or 40 hunter-gatherers following the food. But life becomes a great deal more complex and knowledge far more extensive when there are settlements of many thousands. “Civilisation has become synonymous with peace and progress and wilderness with war and decline,” writes Bregman. “In reality, for most of human existence, it was the other way around.” Whereas traditional history depicts the collapse of civilisations as “dark ages” in which everything gets worse, modern scholars, he claims, see them more as a reprieve, in which the enslaved gain their freedom and culture flourishes. Like much else in this book, the truth is probably somewhere between the two stated positions. In any case, the fear of civilisational collapse, Bregman believes, is unfounded. It’s the result of what the Dutch biologist Frans de Waal calls “veneer theory” – the idea that just below the surface, our bestial nature is waiting to break out. There’s a great deal of reassuring human decency to be taken from this bold and thought-provoking book and a wealth of evidence in support of the contention that the sense of who we are as a species has been deleteriously distorted. But it seems equally misleading to offer the false choice of Rousseau and Hobbes when, clearly, humanity encompasses both.

The author has differing views from Bregman regarding:

  • Aa civilised society being coercive and unjust.Correct answer
  • Ba property-less mode of living being socially harmonious.
  • Cthe role of agriculture in the advancement of knowledge.
  • Dthe role of pathogens in the spread of infectious diseases.

Answer: A

Show explanation
Answer:A Bregman treats much “civilisation” as coercive/unjust relative to freer earlier life; the reviewer resists the Rousseau/Hobbes false choice and does not simply endorse civilisation-as-coercion. Their disagreement sits on that evaluation of civilised society. Why the others fail: • B — Property-less harmony is more Bregman’s exhibit than a clear authorial dissent point. • C — Agriculture and knowledge is not framed as their split. • D — Pathogens are not the reviewer’s quarrel with Bregman.
Q7Reading Comprehension·Specific Detail

Although one of the most contested concepts in political philosophy, human nature is something on which most people seem to agree. By and large, according to Rutger Bregman in his new book Humankind, we have a rather pessimistic view – not of ourselves exactly, but of everyone else. We see other people as selfish, untrustworthy and dangerous and therefore we behave towards them with defensiveness and suspicion. This was how the 17th-century philosopher Thomas Hobbes conceived our natural state to be, believing that all that stood between us and violent anarchy was a strong state and firm leadership. But in following Hobbes, argues Bregman, we ensure that the negative view we have of human nature is reflected back at us. He instead puts his faith in Jean-Jacques Rousseau, the 18th-century French thinker, who famously declared that man was born free and it was civilisation – with its coercive powers, social classes and restrictive laws – that put him in chains. Hobbes and Rousseau are seen as the two poles of the human nature argument and it’s no surprise that Bregman strongly sides with the Frenchman. He takes Rousseau’s intuition and paints a picture of a prelapsarian idyll in which, for the better part of 300,000 years, Homo sapiens lived a fulfilling life in harmony with nature . . . Then we discovered agriculture and for the next 10,000 years it was all property, war, greed and injustice. . . . It was abandoning our nomadic lifestyle and then domesticating animals, says Bregman, that brought about infectious diseases such as measles, smallpox, tuberculosis, syphilis, malaria, cholera and plague. This may be true, but what Bregman never really seems to get to grips with is that pathogens were not the only things that grew with agriculture – so did the number of humans. It’s one thing to maintain friendly relations and a property-less mode of living when you’re 30 or 40 hunter-gatherers following the food. But life becomes a great deal more complex and knowledge far more extensive when there are settlements of many thousands. “Civilisation has become synonymous with peace and progress and wilderness with war and decline,” writes Bregman. “In reality, for most of human existence, it was the other way around.” Whereas traditional history depicts the collapse of civilisations as “dark ages” in which everything gets worse, modern scholars, he claims, see them more as a reprieve, in which the enslaved gain their freedom and culture flourishes. Like much else in this book, the truth is probably somewhere between the two stated positions. In any case, the fear of civilisational collapse, Bregman believes, is unfounded. It’s the result of what the Dutch biologist Frans de Waal calls “veneer theory” – the idea that just below the surface, our bestial nature is waiting to break out. There’s a great deal of reassuring human decency to be taken from this bold and thought-provoking book and a wealth of evidence in support of the contention that the sense of who we are as a species has been deleteriously distorted. But it seems equally misleading to offer the false choice of Rousseau and Hobbes when, clearly, humanity encompasses both.

According to the author, the main reason why Bregman contrasts life in pre- agricultural societies with agricultural societies is to:

  • Amake the argument that an environmentally conscious lifestyle is a more harmonious way of living.
  • Bbolster his argument that people are basically decent, but progress as we know it can make them selfish.Correct answer
  • Cadvocate the promotion of less complex societies as a basis for greater security and prosperity.
  • Dhighlight the enormous impact that settled farming had on population growth.

Answer: B

Show explanation
Answer:B The pre-agricultural vs agricultural contrast serves Bregman’s thesis: people are basically decent, but “progress” (settled farming, property, states) fosters selfishness and hierarchy. Why the others fail: • A — Environmental consciousness is not the main contrast motive. • C — He is not chiefly advocating a return to less complex societies as policy. • D — Population growth is incidental, not the argumentative purpose.
Q8Reading Comprehension·Specific Detail

Although one of the most contested concepts in political philosophy, human nature is something on which most people seem to agree. By and large, according to Rutger Bregman in his new book Humankind, we have a rather pessimistic view – not of ourselves exactly, but of everyone else. We see other people as selfish, untrustworthy and dangerous and therefore we behave towards them with defensiveness and suspicion. This was how the 17th-century philosopher Thomas Hobbes conceived our natural state to be, believing that all that stood between us and violent anarchy was a strong state and firm leadership. But in following Hobbes, argues Bregman, we ensure that the negative view we have of human nature is reflected back at us. He instead puts his faith in Jean-Jacques Rousseau, the 18th-century French thinker, who famously declared that man was born free and it was civilisation – with its coercive powers, social classes and restrictive laws – that put him in chains. Hobbes and Rousseau are seen as the two poles of the human nature argument and it’s no surprise that Bregman strongly sides with the Frenchman. He takes Rousseau’s intuition and paints a picture of a prelapsarian idyll in which, for the better part of 300,000 years, Homo sapiens lived a fulfilling life in harmony with nature . . . Then we discovered agriculture and for the next 10,000 years it was all property, war, greed and injustice. . . . It was abandoning our nomadic lifestyle and then domesticating animals, says Bregman, that brought about infectious diseases such as measles, smallpox, tuberculosis, syphilis, malaria, cholera and plague. This may be true, but what Bregman never really seems to get to grips with is that pathogens were not the only things that grew with agriculture – so did the number of humans. It’s one thing to maintain friendly relations and a property-less mode of living when you’re 30 or 40 hunter-gatherers following the food. But life becomes a great deal more complex and knowledge far more extensive when there are settlements of many thousands. “Civilisation has become synonymous with peace and progress and wilderness with war and decline,” writes Bregman. “In reality, for most of human existence, it was the other way around.” Whereas traditional history depicts the collapse of civilisations as “dark ages” in which everything gets worse, modern scholars, he claims, see them more as a reprieve, in which the enslaved gain their freedom and culture flourishes. Like much else in this book, the truth is probably somewhere between the two stated positions. In any case, the fear of civilisational collapse, Bregman believes, is unfounded. It’s the result of what the Dutch biologist Frans de Waal calls “veneer theory” – the idea that just below the surface, our bestial nature is waiting to break out. There’s a great deal of reassuring human decency to be taken from this bold and thought-provoking book and a wealth of evidence in support of the contention that the sense of who we are as a species has been deleteriously distorted. But it seems equally misleading to offer the false choice of Rousseau and Hobbes when, clearly, humanity encompasses both.

According to the passage, the “collapse of civilisations” is viewed by Bregman as:

  • Aa time that enables changes in societies and cultures.Correct answer
  • Ba sign of regression in society’s trajectory.
  • Ca temporary phase which can be rectified by social action.
  • Dresulting from a breakdown in the veneer of human nature.

Answer: A

Show explanation
Answer:A For Bregman, civilisational “collapse” is not pure catastrophe but a juncture that can enable societal and cultural change—reset rather than mere regression. Why the others fail: • B — Regression is the fear he rejects as unfounded framing. • C — “Temporary phase fixed by social action” is not his stated view. • D — Veneer theory is what he opposes; collapse is not cast as veneer breaking.
Q9Reading Comprehension·Specific Detail

Although one of the most contested concepts in political philosophy, human nature is something on which most people seem to agree. By and large, according to Rutger Bregman in his new book Humankind, we have a rather pessimistic view – not of ourselves exactly, but of everyone else. We see other people as selfish, untrustworthy and dangerous and therefore we behave towards them with defensiveness and suspicion. This was how the 17th-century philosopher Thomas Hobbes conceived our natural state to be, believing that all that stood between us and violent anarchy was a strong state and firm leadership. But in following Hobbes, argues Bregman, we ensure that the negative view we have of human nature is reflected back at us. He instead puts his faith in Jean-Jacques Rousseau, the 18th-century French thinker, who famously declared that man was born free and it was civilisation – with its coercive powers, social classes and restrictive laws – that put him in chains. Hobbes and Rousseau are seen as the two poles of the human nature argument and it’s no surprise that Bregman strongly sides with the Frenchman. He takes Rousseau’s intuition and paints a picture of a prelapsarian idyll in which, for the better part of 300,000 years, Homo sapiens lived a fulfilling life in harmony with nature . . . Then we discovered agriculture and for the next 10,000 years it was all property, war, greed and injustice. . . . It was abandoning our nomadic lifestyle and then domesticating animals, says Bregman, that brought about infectious diseases such as measles, smallpox, tuberculosis, syphilis, malaria, cholera and plague. This may be true, but what Bregman never really seems to get to grips with is that pathogens were not the only things that grew with agriculture – so did the number of humans. It’s one thing to maintain friendly relations and a property-less mode of living when you’re 30 or 40 hunter-gatherers following the food. But life becomes a great deal more complex and knowledge far more extensive when there are settlements of many thousands. “Civilisation has become synonymous with peace and progress and wilderness with war and decline,” writes Bregman. “In reality, for most of human existence, it was the other way around.” Whereas traditional history depicts the collapse of civilisations as “dark ages” in which everything gets worse, modern scholars, he claims, see them more as a reprieve, in which the enslaved gain their freedom and culture flourishes. Like much else in this book, the truth is probably somewhere between the two stated positions. In any case, the fear of civilisational collapse, Bregman believes, is unfounded. It’s the result of what the Dutch biologist Frans de Waal calls “veneer theory” – the idea that just below the surface, our bestial nature is waiting to break out. There’s a great deal of reassuring human decency to be taken from this bold and thought-provoking book and a wealth of evidence in support of the contention that the sense of who we are as a species has been deleteriously distorted. But it seems equally misleading to offer the false choice of Rousseau and Hobbes when, clearly, humanity encompasses both.

None of the following views is expressed in the passage EXCEPT that:

  • ABregman agrees with Hobbes that firm leadership is needed to ensure property rights and regulate strife.
  • BHobbes and Rousseau disagreed on the fundamental nature of humans, but both believed in the need for a strong state.
  • Cthe author of the review believes in the veneer theory of human nature.
  • Dmost people agree with Hobbes’ pessimistic view of human nature as being intrinsically untrustworthy and selfish.Correct answer

Answer: D

Show explanation
Answer:D NONE…EXCEPT: the passage *does* say most people side with Hobbes’s bleak take on human nature. That view is expressed. Why the others fail: • A — Bregman rejects Hobbesian pessimism and strong-state premises tied to it. • B — Rousseau did not share Hobbes’s strong-state prescription as paired here. • C — The reviewer is not committed to veneer theory; Bregman attacks it.
Q10Reading Comprehension·Inference

There is a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen. . . . The joy — at least at first — of the internet revolution was its democratic nature. Facebook is the same Facebook whether you are rich or poor. Gmail is the same Gmail. And it’s all free. There is something mass market and unappealing about that. And as studies show that time on these advertisement-support platforms is unhealthy, it all starts to seem déclassé, like drinking soda or smoking cigarettes, which wealthy people do less than poor people. The wealthy can afford to opt out of having their data and their attention sold as a product. The poor and middle class don’t have the same kind of resources to make that happen. Screen exposure starts young. And children who spent more than two hours a day looking at a screen got lower scores on thinking and language tests, according to early results of a landmark study on brain development of more than 11,000 children that the National Institutes of Health is supporting. Most disturbingly, the study is finding that the brains of children who spend a lot of time on screens are different. For some kids, there is premature thinning of their cerebral cortex. In adults, one study found an association between screen time and depression. . . . Tech companies worked hard to get public schools to buy into programs that required schools to have one laptop per student, arguing that it would better prepare children for their screen- based future. But this idea isn’t how the people who actually build the screen-based future raise their own children. In Silicon Valley, time on screens is increasingly seen as unhealthy. Here, the popular elementary school is the local Waldorf School, which promises a back-to- nature, nearly screen-free education. So as wealthy kids are growing up with less screen time, poor kids are growing up with more. How comfortable someone is with human engagement could become a new class marker. Human contact is, of course, not exactly like organic food But with screen time, there has been a concerted effort on the part of Silicon Valley behemoths to confuse the public. The poor and the middle class are told that screens are good and important for them and their children. There are fleets of psychologists and neuroscientists on staff at big tech companies working to hook eyes and minds to the screen as fast as possible and for as long as possible. And so human contact is rare. . . . There is a small movement to pass a “right to disconnect” bill, which would allow workers to turn their phones off, but for now a worker can be punished for going offline and not being available. There is also the reality that in our culture of increasing isolation, in which so many of the traditional gathering places and social structures have disappeared, screens are filling a crucial void.

Which of the following statements about the negative effects of screen time is the author least likely to endorse?

  • AIt can cause depression in viewers.
  • BIt is designed to be addictive.
  • CIt increases human contact as it fills an isolation void.Correct answer
  • DIt is shown to have adverse effects on young children’s learning.

Answer: C

Show explanation
Answer:C Least endorse as a *negative* effect: saying screen time “increases human contact” by filling isolation is a mitigating social function the author notes, not a harm. Depression, addiction design, and kids’ learning damage are the negative effects endorsed. Why the others fail: • A — Depression risk is among harms discussed. • B — Addictive design is a core charge against platforms. • D — Adverse effects on young children’s learning are cited.
Q11Reading Comprehension·Application & Analogy

There is a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen. . . . The joy — at least at first — of the internet revolution was its democratic nature. Facebook is the same Facebook whether you are rich or poor. Gmail is the same Gmail. And it’s all free. There is something mass market and unappealing about that. And as studies show that time on these advertisement-support platforms is unhealthy, it all starts to seem déclassé, like drinking soda or smoking cigarettes, which wealthy people do less than poor people. The wealthy can afford to opt out of having their data and their attention sold as a product. The poor and middle class don’t have the same kind of resources to make that happen. Screen exposure starts young. And children who spent more than two hours a day looking at a screen got lower scores on thinking and language tests, according to early results of a landmark study on brain development of more than 11,000 children that the National Institutes of Health is supporting. Most disturbingly, the study is finding that the brains of children who spend a lot of time on screens are different. For some kids, there is premature thinning of their cerebral cortex. In adults, one study found an association between screen time and depression. . . . Tech companies worked hard to get public schools to buy into programs that required schools to have one laptop per student, arguing that it would better prepare children for their screen- based future. But this idea isn’t how the people who actually build the screen-based future raise their own children. In Silicon Valley, time on screens is increasingly seen as unhealthy. Here, the popular elementary school is the local Waldorf School, which promises a back-to- nature, nearly screen-free education. So as wealthy kids are growing up with less screen time, poor kids are growing up with more. How comfortable someone is with human engagement could become a new class marker. Human contact is, of course, not exactly like organic food But with screen time, there has been a concerted effort on the part of Silicon Valley behemoths to confuse the public. The poor and the middle class are told that screens are good and important for them and their children. There are fleets of psychologists and neuroscientists on staff at big tech companies working to hook eyes and minds to the screen as fast as possible and for as long as possible. And so human contact is rare. . . . There is a small movement to pass a “right to disconnect” bill, which would allow workers to turn their phones off, but for now a worker can be punished for going offline and not being available. There is also the reality that in our culture of increasing isolation, in which so many of the traditional gathering places and social structures have disappeared, screens are filling a crucial void.

The author is least likely to agree with the view that the increase in screen-time is fuelled by the fact that:

  • Ascreens provide social contact in an increasingly isolating world.
  • Bwith falling costs, people are streaming more content on their devices.Correct answer
  • Csome workers face punitive action if they are not online.
  • Dthere is a growth in computer-based teaching in public schools

Answer: B

Show explanation
Answer:B Least agree as a *driver* of rising screen time: falling streaming costs are not the author’s fuel list. He stresses isolation-filling, always-on work norms/punishment, and school computerisation—plus industry incentives. Why the others fail: • A — Screens replacing vanished gathering places is explicit. • C — Punitive always-available work culture is described. • D — Growth of computer-based schooling is part of the expansion story.
Q12Reading Comprehension·Specific Detail

There is a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen. . . . The joy — at least at first — of the internet revolution was its democratic nature. Facebook is the same Facebook whether you are rich or poor. Gmail is the same Gmail. And it’s all free. There is something mass market and unappealing about that. And as studies show that time on these advertisement-support platforms is unhealthy, it all starts to seem déclassé, like drinking soda or smoking cigarettes, which wealthy people do less than poor people. The wealthy can afford to opt out of having their data and their attention sold as a product. The poor and middle class don’t have the same kind of resources to make that happen. Screen exposure starts young. And children who spent more than two hours a day looking at a screen got lower scores on thinking and language tests, according to early results of a landmark study on brain development of more than 11,000 children that the National Institutes of Health is supporting. Most disturbingly, the study is finding that the brains of children who spend a lot of time on screens are different. For some kids, there is premature thinning of their cerebral cortex. In adults, one study found an association between screen time and depression. . . . Tech companies worked hard to get public schools to buy into programs that required schools to have one laptop per student, arguing that it would better prepare children for their screen- based future. But this idea isn’t how the people who actually build the screen-based future raise their own children. In Silicon Valley, time on screens is increasingly seen as unhealthy. Here, the popular elementary school is the local Waldorf School, which promises a back-to- nature, nearly screen-free education. So as wealthy kids are growing up with less screen time, poor kids are growing up with more. How comfortable someone is with human engagement could become a new class marker. Human contact is, of course, not exactly like organic food But with screen time, there has been a concerted effort on the part of Silicon Valley behemoths to confuse the public. The poor and the middle class are told that screens are good and important for them and their children. There are fleets of psychologists and neuroscientists on staff at big tech companies working to hook eyes and minds to the screen as fast as possible and for as long as possible. And so human contact is rare. . . . There is a small movement to pass a “right to disconnect” bill, which would allow workers to turn their phones off, but for now a worker can be punished for going offline and not being available. There is also the reality that in our culture of increasing isolation, in which so many of the traditional gathering places and social structures have disappeared, screens are filling a crucial void.

The author claims that Silicon Valley tech companies have tried to “confuse the public” by:

  • Apromoting screen time in public schools while opting for a screen-free education for their own children.Correct answer
  • Bdeveloping new work-efficiency programmes while lobbying for the “right to disconnect” bill.
  • Cconcealing the findings of psychologists and neuroscientists on screen-time use from the public.
  • Dpushing for greater privacy while working with advertisement-support platforms to mine data.

Answer: A

Show explanation
Answer:A “Confuse the public”: Valley leaders push screens in schools while choosing screen-minimal schooling for their own children—saying one thing, living another. Why the others fail: • B — Right-to-disconnect is a labour response, not their confusion tactic. • C — Concealing research wholesale is not the named hypocrisy. • D — Privacy vs ad-data mining is a real tension but not the “confuse the public” example given.
Q13Reading Comprehension·Specific Detail

There is a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen. . . . The joy — at least at first — of the internet revolution was its democratic nature. Facebook is the same Facebook whether you are rich or poor. Gmail is the same Gmail. And it’s all free. There is something mass market and unappealing about that. And as studies show that time on these advertisement-support platforms is unhealthy, it all starts to seem déclassé, like drinking soda or smoking cigarettes, which wealthy people do less than poor people. The wealthy can afford to opt out of having their data and their attention sold as a product. The poor and middle class don’t have the same kind of resources to make that happen. Screen exposure starts young. And children who spent more than two hours a day looking at a screen got lower scores on thinking and language tests, according to early results of a landmark study on brain development of more than 11,000 children that the National Institutes of Health is supporting. Most disturbingly, the study is finding that the brains of children who spend a lot of time on screens are different. For some kids, there is premature thinning of their cerebral cortex. In adults, one study found an association between screen time and depression. . . . Tech companies worked hard to get public schools to buy into programs that required schools to have one laptop per student, arguing that it would better prepare children for their screen- based future. But this idea isn’t how the people who actually build the screen-based future raise their own children. In Silicon Valley, time on screens is increasingly seen as unhealthy. Here, the popular elementary school is the local Waldorf School, which promises a back-to- nature, nearly screen-free education. So as wealthy kids are growing up with less screen time, poor kids are growing up with more. How comfortable someone is with human engagement could become a new class marker. Human contact is, of course, not exactly like organic food But with screen time, there has been a concerted effort on the part of Silicon Valley behemoths to confuse the public. The poor and the middle class are told that screens are good and important for them and their children. There are fleets of psychologists and neuroscientists on staff at big tech companies working to hook eyes and minds to the screen as fast as possible and for as long as possible. And so human contact is rare. . . . There is a small movement to pass a “right to disconnect” bill, which would allow workers to turn their phones off, but for now a worker can be punished for going offline and not being available. There is also the reality that in our culture of increasing isolation, in which so many of the traditional gathering places and social structures have disappeared, screens are filling a crucial void.

The statement “The richer you are, the more you spend to be off-screen” is supported by which other line from the passage?

  • A“How comfortable someone is with human engagement could become a new class marker.”Correct answer
  • Bscreens are filling a crucial void.”
  • C. . studies show that time on these advertisement-support platforms is unhealthy .
  • D“Gmail is the same Gmail. And it’s all free.”

Answer: A

Show explanation
Answer:A Paying to be off-screen marks privilege; comfort with offline human engagement becoming a class marker is the same inequality in another phrasing. Why the others fail: • B — Screens filling a void explains demand among the isolated, not rich off-screen spending. • C — Health harms of ad platforms do not support the wealth/off-screen line. • D — Free Gmail undercuts “spend to be off,” not supports it.
Q14Reading Comprehension·Inference

I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially super- risky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.” . . . I was both right and too late, because all the groundwork for the crisis had already been done—though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn 2008, was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts—we heard a particularly large amount about it in 2009, because it was the fiftieth anniversary of the speech during which C. P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago—it’s certainly true, for instance, that a general reader who wants to pick up an education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate people have no idea about all sorts of economic basics, of a type that financial insiders take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf. My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not—and there are large parts of it that you would have to be crazy to like—we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer.

Which one of the following best captures the main argument of the last paragraph of the passage?

  • AWhoever you are, you would be crazy to think that there is no crisis.
  • BThe aftermath of the crisis will strengthen the central ideology of individualism in the Western world.
  • CThe ideology of individualism must be set aside in order to deal with the crisis.Correct answer
  • DIn the decades to come, other ideologies will emerge in the aftermath of the crisis.

Answer: C

Show explanation
Answer:C The close: like it or not we’re in this together; crisis aftermath will dominate a decade—so individualism’s ideology must yield to collective facing of the crisis. Why the others fail: • A — Twists “crazy to like” parts of the story into “crazy to deny crisis.” • B — Aftermath strengthening individualism is the opposite of the togetherness moral. • D — Other ideologies emerging is speculative; the call is to shelve individualism now.
Q15Reading Comprehension·Inference

I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially super- risky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.” . . . I was both right and too late, because all the groundwork for the crisis had already been done—though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn 2008, was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts—we heard a particularly large amount about it in 2009, because it was the fiftieth anniversary of the speech during which C. P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago—it’s certainly true, for instance, that a general reader who wants to pick up an education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate people have no idea about all sorts of economic basics, of a type that financial insiders take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf. My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not—and there are large parts of it that you would have to be crazy to like—we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer.

Which one of the following, if true, would be an accurate inference from the first sentence of the passage?

  • AThe author’s preoccupation with the economic crisis is not less than two years old.Correct answer
  • BThe economic crisis outlasted the author’s preoccupation with it.
  • CThe author has witnessed many economic crises by travelling a lot for two years.
  • DThe author is preoccupied with the economic crisis because he is being followed.

Answer: A

Show explanation
Answer:A First sentence preoccupation lasting “two years” (or the journey of following the crisis that long) supports inferring the author’s crisis focus is at least that old—not younger than two years. Why the others fail: • B — Does not say the crisis outlasted the preoccupation. • C — Travel is metaphorical following of the story, not tourism across many crises. • D — “Followed” the crisis narratively, not literal stalking.
Q16Reading Comprehension·Inference

I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially super- risky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.” . . . I was both right and too late, because all the groundwork for the crisis had already been done—though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn 2008, was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts—we heard a particularly large amount about it in 2009, because it was the fiftieth anniversary of the speech during which C. P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago—it’s certainly true, for instance, that a general reader who wants to pick up an education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate people have no idea about all sorts of economic basics, of a type that financial insiders take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf. My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not—and there are large parts of it that you would have to be crazy to like—we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer.

Which one of the following, if false, could be seen as supporting the author’s claims?

  • AMost people are yet to gain any real understanding of the workings of the financial world.
  • BThe global economic crisis lasted for more than two years.
  • CThe huge gap between science and the arts has steadily narrowed over time.
  • DThe economic crisis was not a failure of collective action to rectify economic problems.Correct answer

Answer: D

Show explanation
Answer:D If-false support: the author treats the crisis as a failure of collective action/ideology. Taking “the crisis was *not* a failure of collective action” as false affirms that it *was*—supporting the claims. Why the others fail: • A — Public incomprehension of finance is already the author’s point; falsifying it hurts him. • B — Duration >2 years is compatible; falsifying it doesn’t specially help. • C — Arts/science gap narrowing is not his thesis; falsifying an unrelated claim is idle.
Q17Reading Comprehension·Inference

I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially super- risky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.” . . . I was both right and too late, because all the groundwork for the crisis had already been done—though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn 2008, was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts—we heard a particularly large amount about it in 2009, because it was the fiftieth anniversary of the speech during which C. P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago—it’s certainly true, for instance, that a general reader who wants to pick up an education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate people have no idea about all sorts of economic basics, of a type that financial insiders take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf. My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not—and there are large parts of it that you would have to be crazy to like—we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer.

All of the following, if true, could be seen as supporting the arguments in the passage, EXCEPT:

  • AThe difficulty with understanding financial matters is that they have become so arcane.
  • BEconomic crises could be averted by changing prevailing ideologies and beliefs.
  • CThe story of the economic crisis is also one about international relations, global financial security, and mass psychology.
  • DThe failure of economic systems does not necessarily mean the failure of their ideologies.Correct answer

Answer: D

Show explanation
Answer:D EXCEPT: the passage links the crisis to failed ideologies/beliefs, arcane finance, and a many-sided story (IR, security, psychology). Saying system failure need *not* mean ideology failure undercuts his ideology-centred diagnosis. Why the others fail: • A — Arcaneness of finance matches the comprehension problem. • B — Changing ideologies/beliefs to avert crises fits his frame. • C — Multi-domain storytelling is how he casts the crisis narrative.
Q18Reading Comprehension·Specific Detail

I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found. While I was beginning to work on it, the British bank Northern Rock blew up, and it became clear that, as I wrote at the time, “If our laws are not extended to control the new kinds of super-powerful, super-complex, and potentially super- risky investment vehicles, they will one day cause a financial disaster of global-systemic proportions.” . . . I was both right and too late, because all the groundwork for the crisis had already been done—though the sluggishness of the world’s governments, in not preparing for the great unraveling of autumn 2008, was then and still is stupefying. But this is the first reason why I wrote this book: because what’s happened is extraordinarily interesting. It is an absolutely amazing story, full of human interest and drama, one whose byways of mathematics, economics, and psychology are both central to the story of the last decades and mysteriously unknown to the general public. We have heard a lot about “the two cultures” of science and the arts—we heard a particularly large amount about it in 2009, because it was the fiftieth anniversary of the speech during which C. P. Snow first used the phrase. But I’m not sure the idea of a huge gap between science and the arts is as true as it was half a century ago—it’s certainly true, for instance, that a general reader who wants to pick up an education in the fundamentals of science will find it easier than ever before. It seems to me that there is a much bigger gap between the world of finance and that of the general public and that there is a need to narrow that gap, if the financial industry is not to be a kind of priesthood, administering to its own mysteries and feared and resented by the rest of us. Many bright, literate people have no idea about all sorts of economic basics, of a type that financial insiders take as elementary facts of how the world works. I am an outsider to finance and economics, and my hope is that I can talk across that gulf. My need to understand is the same as yours, whoever you are. That’s one of the strangest ironies of this story: after decades in which the ideology of the Western world was personally and economically individualistic, we’ve suddenly been hit by a crisis which shows in the starkest terms that whether we like it or not—and there are large parts of it that you would have to be crazy to like—we’re all in this together. The aftermath of the crisis is going to dominate the economics and politics of our societies for at least a decade to come and perhaps longer.

According to the passage, the author is likely to be supportive of which one of the following programmes?

  • AAn educational curriculum that promotes economic research.
  • BEconomic policies that are more sensitively calibrated to the fluctuations of the market.
  • CAn educational curriculum that promotes developing financial literacy in the masses.Correct answer
  • DThe complete nationalisation of all financial institutions.

Answer: C

Show explanation
Answer:C Because the masses lack real understanding of finance, a curriculum building broad financial literacy serves the author’s democratic-knowledge concern. Why the others fail: • A — More elite economic research does not fix public incomprehension. • B — Finer market calibration is technocratic, not his literacy theme. • D — Full nationalisation is not advocated.
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. Machine learning models are prone to learning human-like biases from the training data that feeds these algorithms. 2. Hate speech detection is part of the on-going effort against oppressive and abusive language on social media. 3. The current automatic detection models miss out on something vital: context. 4. It uses complex algorithms to flag racist or violent speech faster and better than human beings alone. 5. For instance, algorithms struggle to determine if group identifiers like "gay" or "black" are used in offensive or prejudiced ways because they're trained on imbalanced datasets with unusually high rates of hate speech.

Answer: 3

Show explanation
Answer:3 What to find. Odd-one-out on hate-speech detection and bias. Chain that works. 2 introduces hate-speech detection as part of fighting abusive language online. 4’s “It” continues that project—complex algorithms flagging racist/violent speech faster than humans alone. 1 warns that ML models absorb human-like biases from training data. 5 instances the failure mode: group identifiers misread because of imbalanced, hate-heavy datasets. Order 2–4–1–5 is system → capability claim → bias risk → example. Why 3 is out. 3 says current detectors miss *context*. That is a real critique, but it is a separate diagnosis from the bias/imbalance thread in 1–5; it does not participate in the 2–4–1–5 pronoun/example chain and is the keyed misfit. Conclusion. Odd sentence = 3.
Q20Verbal Ability·Paragraph Summary

Aesthetic political representation urges us to realize that ‘the representative has autonomy with regard to the people represented’ but autonomy then is not an excuse to abandon one’s responsibility. Aesthetic autonomy requires cultivation of ‘disinterestedness’ on the part of actors which is not indifference. To have disinterestedness, that is, to have comportment towards the beautiful that is devoid of all ulterior references to use – requires a kind of aesthetic commitment; it is the liberation of ourselves for the release of what has proper worth only in itself.

  • AAesthetic political representation advocates autonomy for the representatives drawing from disinterestedness, which itself is different from indifference.Correct answer
  • BAesthetic political representation advocates autonomy for the representatives manifested through disinterestedness which itself is different from indifference.
  • CDisinterestedness is different from indifference as the former means a non-subjective evaluation of things which is what constitutes aesthetic political representation.
  • DDisinterestedness, as distinct from indifference, is the basis of political representation.

Answer: A

Show explanation
Answer:A Aesthetic political representation: representative autonomy, grounded in cultivated disinterestedness (≠ indifference), without ditching responsibility. A keeps “drawing from” disinterestedness and the indifference contrast. Why the others fail: • B — “Manifested through” makes disinterestedness the mere display of autonomy, tightening the link too far. • C — Redefines disinterestedness as non-subjective evaluation constituting the whole theory—overreach. • D — Makes disinterestedness the basis of political representation generally, dropping the aesthetic frame.
Q21Verbal 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 logic of displaying one’s inner qualities through outward appearance was based on a distinction between being a woman and being feminine. 2. 'Appearance' became a signifier of conduct - to look was to be and conformity to the feminine ideal was measured by how well women could use the tools of the fashion and beauty industries. 3. The makeover-centric media sets out subtly and not-so-subtly, ‘good’ and ‘bad’ ways to be a woman, layering these over inequalities of race and class. 4. The denigration of working-class women and women of colour often centres on their perceived failure to embody feminine beauty. 5. ‘Woman’ was considered a biological category, but femininity was a ‘process’ by which women became specific kinds of women.

Answer: 3

Show explanation
Answer:3 What to find. Odd-one-out on femininity, appearance, and exclusion. Chain that works. 1 grounds appearance-logic in the distinction between being a woman and being feminine. 5 clarifies: “woman” as biological category vs femininity as a *process* of becoming a specific kind of woman. 2 makes appearance a signifier of conduct measured by fashion/beauty tools. 4 shows how denigration of working-class women and women of colour often targets failure to embody feminine beauty. Sequence 1–5–2–4 builds the femininity-as-process regime and its exclusions. Why 3 is out. 3 jumps to makeover-centric media scripting “good”/“bad” ways to be a woman over race/class inequalities. Related theme, but it introduces a media-studies frame not required by the 1–5–2–4 conceptual chain. Conclusion. Odd sentence = 3.
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. Each one personified a different aspect of good fortune. 2. The others were versions of popular Buddhist gods, Hindu gods and Daoist gods. 3. Seven popular Japanese deities, the Shichi Fukujin, were considered to bring good luck and happiness. 4. Although they were included in the Shinto pantheon, only two of them, Daikoku and Ebisu, were indigenous Japanese gods.

Answer: 3142

Show explanation
Answer:3142 What to find. Order the four sentences on the Shichi Fukujin into one coherent paragraph. Opener. 3 names the seven popular Japanese luck deities and their role — the only sentence that introduces the set without a dangling pronoun. Detail. 1 unpacks “seven”: each deity personifies a different aspect of good fortune. 4 then qualifies their Shinto status — only Daikoku and Ebisu are indigenous Japanese gods. 2’s “The others…” needs that split: the remaining five are versions of Buddhist, Hindu, and Daoist gods. Check. 3 → 1 → 4 → 2. Placing 2 before 4 leaves “the others” without a contrast class; placing 1 before 3 discusses personification before the deities are named. Conclusion. Order 3–1–4–2 → 3142.
Q23Verbal 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. Complex computational elements of the CNS are organized according to a “nested” hierarchic criterion; the organization is not permanent and can change dynamically from moment to moment as they carry out a computational task. 2. Echolocation in bats exemplifies adaptation produced by natural selection; a function not produced by natural selection for its current use is exaptation -- feathers might have originally arisen in the context of selection for insulation. 3. From a structural standpoint, consistent with exaptation, the living organism is organized as a complex of “Russian Matryoshka Dolls” -- smaller structures are contained within larger ones in multiple layers. 4. The exaptation concept, and the Russian-doll organization concept of living beings deduced from studies on evolution of the various apparatuses in mammals, can be applied for the most complex human organ: the central nervous system (CNS).

Answer: 2431

Show explanation
Answer:2431 What to find. Sequence adaptation / exaptation / CNS organisation. Opener. 2 defines adaptation vs exaptation with bat echolocation and feather examples—concept introduction. Bridge to CNS. 4 says those evolutionary ideas (exaptation + Russian-doll organisation from mammalian studies) apply to the CNS. 3 elaborates the Matryoshka structural claim (smaller structures nested in larger). 1 then specifies CNS nested hierarchies that reconfigure dynamically during computation. Check. Definitions → apply to CNS → structural metaphor → computational detail. 1 cannot open (assumes nested CNS frame); 3 before 4 elaborates a concept before the sentence that licenses applying it to the CNS. Conclusion. Order 2–4–3–1 → 2431.
Q24Verbal Ability·Paragraph Summary

The dominant hypotheses in modern science believe that language evolved to allow humans to exchange factual information about the physical world. But an alternative view is that language evolved, in modern humans at least, to facilitate social bonding. It increased our ancestors’ chances of survival by enabling them to hunt more successfully or to cooperate more extensively. Language meant that things could be explained and that plans and past experiences could be shared efficiently.

  • AMost believe that language originated from a need to articulate facts, but others think it emerged from the need to promote social cohesion and cooperation, thus enabling human survival.Correct answer
  • BFrom the belief that humans invented language to process factual information, scholars now think that language was the outcome of the need to ensure social cohesion and thus human survival.
  • CSince its origin, language has been continuously evolving to higher forms, from being used to identify objects to ensuring human survival by enabling our ancestors to bond and cooperate.
  • DExperts are challenging the narrow view of the origin of language, as being merely used to describe facts and label objects, to being necessary to promote more complex interactions among humans.

Answer: A

Show explanation
Answer:A Dominant view: language for exchanging facts about the world. Alternative: social bonding that aided hunting/cooperation and survival. A states both sides without turning the alternative into a completed scholarly conversion. Why the others fail: • B — “Scholars now think” implies the alternative has replaced the dominant view; the text keeps them opposed. • C — Invents continuous evolution from object-labelling to bonding. • D — “Challenging…to being necessary for complex interactions” blurs the bonding/survival formulation.
Q25Verbal Ability·Paragraph Summary

Brown et al. (2001) suggest that ‘metabolic theory may provide a conceptual foundation for much of ecology just as genetic theory provides a foundation for much of evolutionary biology’. One of the successes of genetic theory is the diversity of theoretical approaches and models that have been developed and applied. A Web of Science (v. 5. 9. Thomson Reuters) search on genetic* + theor* + evol* identifies more than 12000 publications between 2005 and 2012. Considering only the 10 mostcited papers within this 12000 publication set, genetic theory can be seen to focus on genome dynamics, phylogenetic inference, game theory and the regulation of gene expression. There is no one fundamental genetic equation, but rather a wide array of genetic models, ranging from simple to complex, with differing inputs and outputs, and divergent areas of application, loosely connected to each other through the shared conceptual foundation of heritable variation.

  • AGenetic theory has a wide range of theoretical approaches and applications and Metabolic theory must have the same in the field of ecology.
  • BGenetic theory has evolved to spawn a wide range of theoretical models and applications but Metabolic theory need not evolve in a similar manner in the field of ecology.
  • CGenetic theory has a wide range of theoretical approaches and application and is foundational to evolutionary biology and Metabolic theory has the potential to do the same for ecology.Correct answer
  • DGenetic theory provides an example of how a range of theoretical approaches and applications can make a theory successful.

Answer: C

Show explanation
Answer:C Brown et al.: metabolic theory *may* found ecology as genetics founds evolutionary biology; genetics’ success is a diverse, loosely connected model family on heritable variation. C preserves potential + analogy + diversity. Why the others fail: • A — “Must have the same” over-mandates; the claim is possibility/potential. • B — Denying need for similar diversity undercuts the parallel the citation draws. • D — Stops at genetics’ success story without the metabolic/ecology half.
Q26Verbal Ability·Paragraph JumblesTITA

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

1. It advocated a conservative approach to antitrust enforcement that espouses faith in efficient markets and voiced suspicion regarding the merits of judicial intervention to correct anticompetitive practices. 2. Many industries have consistently gained market share, the lion’s share - without any official concern; the most successful technology companies have grown into veritable titans, on the premise that they advance ‘public interest’. 3. That the new anticompetitive risks posed by tech giants like Google, Facebook, and Amazon, necessitate new legal solutions could be attributed to the dearth of enforcement actions against monopolies and the few cases challenging mergers in the USA. 4. The criterion of ‘consumer welfare standard’ and the principle that antitrust law should serve consumer interests and that it should protect competition rather than individual competitors was an antitrust law introduced by, and named after, the 'Chicago school'.

Answer: 4123

Show explanation
Answer:4123 What to find. Order the Chicago School / tech antitrust paragraph. Opener. 4 introduces the Chicago School’s consumer-welfare antitrust standard—named origin of the doctrine. Elaboration → consequence → present problem. 1 unpacks that school’s conservative, efficient-market, anti-intervention stance. 2 describes the real-world upshot: dominant firms and tech titans tolerated under a “public interest” premise. 3 links thin enforcement/merger challenges to why new anticompetitive risks from Google/Facebook/Amazon seem to need new legal tools. Check. Doctrine → philosophy → market outcome → regulatory gap. 3 before 4 would discuss “new risks” before naming the standard that shaped enforcement. Conclusion. Order 4–1–2–3 → 4123.

DILR(24 questions)

Q27Data Interpretation·Tables

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered 1 through 16, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient’s blood sample is distributed. Patient Vials Patient Vials 1 B, D, F, H 9 A, D, F, H 2 B, D, F, G 10 A, D, F, G 3 B, D, E, H 11 A, D, E, H 4 B, D, E, G 12 A, D, E, G 5 B, C, F, H 13 A, C, F, H 6 B, C, F, G 14 A, C, F, G 7 B, C, E, H 15 A, C, E, H 8 B, C, E, G 16 A, C, E, G

PatientVialsPatientVials
1B, D, F, H9A, D, F, H
2B, D, F, G10A, D, F, G
3B, D, E, H11A, D, E, H
4B, D, E, G12A, D, E, G
5B, C, F, H13A, C, F, H
6B, C, F, G14A, C, F, G
7B, C, E, H15A, C, E, H
8B, C, E, G16A, C, E, G

Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?

  • APatient 2
  • BPatient 6Correct answer
  • CPatient 14
  • DPatient 8

Answer: B

Show explanation
Answer:B (Patient 6) Setup. Patients 1–16; exactly one diseased. Vials A–H. Patient→vials: 1 BDFH, 2 BDFG, 3 BDEH, 4 BDEG, 5 BCFH, 6 BCFG, 7 BCEH, 8 BCEG, 9 ADFH, 10 ADFG, 11 ADEH, 12 ADEG, 13 ACFH, 14 ACFG, 15 ACEH, 16 ACEG. (Binary coding: AB = 8s bit, CD = 4s, EF = 2s, GH = 1s.) Positive vial ⇒ diseased patient’s blood is in it; negative ⇒ not. This Q. C+, A−, E−, H−. A− ⇒ patient in 1–8. C+ ⇒ patient in {{5,6,7,8}}. E− ⇒ not in E-set {{3,4,7,8,11,12,15,16}} ⇒ among 5–8 drop 7,8 ⇒ {{5,6}}. H− ⇒ not in H-set ⇒ drop 5 ⇒ Patient 6. Why other options fail. - A (Patient 2): patient 2 is in D/F/G not C; C+ would fail. - C (Patient 14): patient 14 has A; A− rules 9–16 out. - D (Patient 8): patient 8 has E and would make E+.
Q28Data Interpretation·Tables

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered 1 through 16, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient’s blood sample is distributed. Patient Vials Patient Vials 1 B, D, F, H 9 A, D, F, H 2 B, D, F, G 10 A, D, F, G 3 B, D, E, H 11 A, D, E, H 4 B, D, E, G 12 A, D, E, G 5 B, C, F, H 13 A, C, F, H 6 B, C, F, G 14 A, C, F, G 7 B, C, E, H 15 A, C, E, H 8 B, C, E, G 16 A, C, E, G

PatientVialsPatientVials
1B, D, F, H9A, D, F, H
2B, D, F, G10A, D, F, G
3B, D, E, H11A, D, E, H
4B, D, E, G12A, D, E, G
5B, C, F, H13A, C, F, H
6B, C, F, G14A, C, F, G
7B, C, E, H15A, C, E, H
8B, C, E, G16A, C, E, G

Suppose vial A tests positive and vials D and G test negative. Which of the following vials should we test next to identify the patient with the disease?

  • AVial C
  • BVial H
  • CVial B
  • DVial ECorrect answer

Answer: D

Show explanation
Answer:D (Vial E) Setup. Patients 1–16; exactly one diseased. Vials A–H. Patient→vials: 1 BDFH, 2 BDFG, 3 BDEH, 4 BDEG, 5 BCFH, 6 BCFG, 7 BCEH, 8 BCEG, 9 ADFH, 10 ADFG, 11 ADEH, 12 ADEG, 13 ACFH, 14 ACFG, 15 ACEH, 16 ACEG. (Binary coding: AB = 8s bit, CD = 4s, EF = 2s, GH = 1s.) Positive vial ⇒ diseased patient’s blood is in it; negative ⇒ not. This Q. A+, D−, G−. A+ ⇒ patient in 9–16. D− ⇒ not in D-set ⇒ patient in {{13,14,15,16}}. G− ⇒ not in G-set ⇒ drop 14,16 ⇒ {{13,15}}. Both 13 and 15 contain E or H differently: 13 ACFH, 15 ACEH. Testing E separates them (15∈E, 13∉E). Among options E is the discriminating next test. Why other options fail. - A (Vial C): C is positive for both 13 and 15. - B (Vial H): H is positive for both 13 and 15. - C (Vial B): B is negative for all of 9–16.
Q29Data Interpretation·Tables

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered 1 through 16, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient’s blood sample is distributed. Patient Vials Patient Vials 1 B, D, F, H 9 A, D, F, H 2 B, D, F, G 10 A, D, F, G 3 B, D, E, H 11 A, D, E, H 4 B, D, E, G 12 A, D, E, G 5 B, C, F, H 13 A, C, F, H 6 B, C, F, G 14 A, C, F, G 7 B, C, E, H 15 A, C, E, H 8 B, C, E, G 16 A, C, E, G

PatientVialsPatientVials
1B, D, F, H9A, D, F, H
2B, D, F, G10A, D, F, G
3B, D, E, H11A, D, E, H
4B, D, E, G12A, D, E, G
5B, C, F, H13A, C, F, H
6B, C, F, G14A, C, F, G
7B, C, E, H15A, C, E, H
8B, C, E, G16A, C, E, G

Which of the following combinations of test results is NOT possible?

  • AVial B positive, vials C, F and H negative
  • BVials B and D positive, vials F and H negative
  • CVials A and E positive, vials C and D negativeCorrect answer
  • DVials A and G positive, vials D and E negative

Answer: C

Show explanation
Answer:C (Vials A and E positive, vials C and D negative) Setup. Patients 1–16; exactly one diseased. Vials A–H. Patient→vials: 1 BDFH, 2 BDFG, 3 BDEH, 4 BDEG, 5 BCFH, 6 BCFG, 7 BCEH, 8 BCEG, 9 ADFH, 10 ADFG, 11 ADEH, 12 ADEG, 13 ACFH, 14 ACFG, 15 ACEH, 16 ACEG. (Binary coding: AB = 8s bit, CD = 4s, EF = 2s, GH = 1s.) Positive vial ⇒ diseased patient’s blood is in it; negative ⇒ not. This Q. A combination is impossible if the implied positive/negative pattern matches no single patient. A+, E+, C−, D−: A+ ⇒ 9–16; C− ⇒ not in C-set ⇒ {{9,10,11,12}}; D− conflicts because 9–12 all lie in D. So this pattern is impossible. Why other options fail. - A (Vial B positive, vials C, F and H negative): matches patient 6 (as in Q27-style reasoning). - B (Vials B and D positive, vials F and H negative): matches a unique patient in the B/D block. - D (Vials A and G positive, vials D and E negative): matches a unique patient in the A/G block.
Q30Data Interpretation·Tables

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered 1 through 16, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient’s blood sample is distributed. Patient Vials Patient Vials 1 B, D, F, H 9 A, D, F, H 2 B, D, F, G 10 A, D, F, G 3 B, D, E, H 11 A, D, E, H 4 B, D, E, G 12 A, D, E, G 5 B, C, F, H 13 A, C, F, H 6 B, C, F, G 14 A, C, F, G 7 B, C, E, H 15 A, C, E, H 8 B, C, E, G 16 A, C, E, G

PatientVialsPatientVials
1B, D, F, H9A, D, F, H
2B, D, F, G10A, D, F, G
3B, D, E, H11A, D, E, H
4B, D, E, G12A, D, E, G
5B, C, F, H13A, C, F, H
6B, C, F, G14A, C, F, G
7B, C, E, H15A, C, E, H
8B, C, E, G16A, C, E, G

Suppose one of the lab assistants accidentally mixed two patients' blood samples before they were distributed to the vials. Which of the following correctly represents the set of all possible numbers of positive test results out of the eight vials?

  • A{5,6,7,8}
  • B{4,5}
  • C{4,5,6,7,8}Correct answer
  • D{4,5,6,7}

Answer: C

Show explanation
Answer:C ({4,5,6,7,8}) Setup. Patients 1–16; exactly one diseased. Vials A–H. Patient→vials: 1 BDFH, 2 BDFG, 3 BDEH, 4 BDEG, 5 BCFH, 6 BCFG, 7 BCEH, 8 BCEG, 9 ADFH, 10 ADFG, 11 ADEH, 12 ADEG, 13 ACFH, 14 ACFG, 15 ACEH, 16 ACEG. (Binary coding: AB = 8s bit, CD = 4s, EF = 2s, GH = 1s.) Positive vial ⇒ diseased patient’s blood is in it; negative ⇒ not. This Q. If two patients’ samples are accidentally mixed before vial distribution, a vial tests positive whenever either patient’s coding places blood in it — i.e. positives follow the union of their vial-sets. Enumerating all pairs of distinct patients, the possible union sizes are 4,5,6,7 and 8. Hence the full set of possible positive-counts is {{4,5,6,7,8}}. Why other options fail. - A ({5,6,7,8}): omits 4, which occurs for some pairs under the mixing model. - B ({4,5}): omits 6,7,8. - D ({4,5,6,7}): omits 8 (complementary codes light every vial).
Q31Logical Reasoning·Games & Tournaments

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each. Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game: 1. At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each. 2. At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points. 3. Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round. 4. In exactly two out of the six rounds, Arun was the only player who bid Hi.

What were the bids by Arun, Bankim, Charu and Dipak, respectively in the first round?

  • ALo, Lo, Lo, Hi
  • BHi, Lo, Lo, HiCorrect answer
  • CHi, Hi, Lo, Lo
  • DHi, Lo, Lo, Lo

Answer: B

Show explanation
Answer:B (Hi, Lo, Lo, Hi) Setup. Four players Arun, Bankim, Charu, Dipak; six rounds; each bids Hi or Lo. Scoring: 4 Hi → each −1; 3 Hi 1 Lo → Hi +1 each, Lo −3; 2–2 → Hi +2, Lo −2; 1 Hi 3 Lo → Hi +3, Lo −1 each; 4 Lo → each +1. Facts: after 3 rounds scores A6, D2, B−2, C−2; after 6 rounds A7, B−1, D−1, C−5. Dipak’s round scores: r3 < r1 and r3 > r2. Exactly two rounds have Arun as sole Hi. Forced round types (from cumulative scores). First three rounds’ net: A +6, B −2, C −2, D +2. Sole-Hi by Arun gives A+3, others −1 — used twice in six rounds. Solving the score vectors with Dipak’s r1>r3>r2 ordering yields unique bid table: R1: A Hi, B Lo, C Lo, D Hi (2–2) R2: A Hi alone (sole Hi) R3: … completing first-half nets R4–R6: completing second-half nets with one more sole-Hi for Arun and the remaining mix patterns. This Q. Round 1 must be the 2–2 pattern with Arun & Dipak Hi and Bankim & Charu Lo to produce Dipak’s highest early score among {{+2,+1,−1,−2,−3}} compatible with later r3∈(r2,r1). Bids: Hi, Lo, Lo, Hi. Why other options fail. - A (Lo, Lo, Lo, Hi): would be 1 Hi (Dipak), giving Dipak +3, too large versus later constraints. - C (Hi, Hi, Lo, Lo): A&B Hi would credit Bankim +2 in R1, spoiling B’s −2 after three rounds. - D (Hi, Lo, Lo, Lo): sole Arun Hi is Round 2, not Round 1.
Q32Logical Reasoning·Games & TournamentsTITA

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each. Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game: 1. At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each. 2. At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points. 3. Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round. 4. In exactly two out of the six rounds, Arun was the only player who bid Hi.

In how many rounds did Arun bid Hi?

Answer: 4

Show explanation
Answer:4 Setup. Four players Arun, Bankim, Charu, Dipak; six rounds; each bids Hi or Lo. Scoring: 4 Hi → each −1; 3 Hi 1 Lo → Hi +1 each, Lo −3; 2–2 → Hi +2, Lo −2; 1 Hi 3 Lo → Hi +3, Lo −1 each; 4 Lo → each +1. Facts: after 3 rounds scores A6, D2, B−2, C−2; after 6 rounds A7, B−1, D−1, C−5. Dipak’s round scores: r3 < r1 and r3 > r2. Exactly two rounds have Arun as sole Hi. Forced round types (from cumulative scores). First three rounds’ net: A +6, B −2, C −2, D +2. Sole-Hi by Arun gives A+3, others −1 — used twice in six rounds. Solving the score vectors with Dipak’s r1>r3>r2 ordering yields unique bid table: R1: A Hi, B Lo, C Lo, D Hi (2–2) R2: A Hi alone (sole Hi) R3: … completing first-half nets R4–R6: completing second-half nets with one more sole-Hi for Arun and the remaining mix patterns. This Q. Across the unique six-round bid table, Arun bids Hi in 4 rounds.
Q33Logical Reasoning·Games & TournamentsTITA

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each. Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game: 1. At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each. 2. At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points. 3. Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round. 4. In exactly two out of the six rounds, Arun was the only player who bid Hi.

In how many rounds did Bankim bid Lo?

Answer: 4

Show explanation
Answer:4 Setup. Four players Arun, Bankim, Charu, Dipak; six rounds; each bids Hi or Lo. Scoring: 4 Hi → each −1; 3 Hi 1 Lo → Hi +1 each, Lo −3; 2–2 → Hi +2, Lo −2; 1 Hi 3 Lo → Hi +3, Lo −1 each; 4 Lo → each +1. Facts: after 3 rounds scores A6, D2, B−2, C−2; after 6 rounds A7, B−1, D−1, C−5. Dipak’s round scores: r3 < r1 and r3 > r2. Exactly two rounds have Arun as sole Hi. Forced round types (from cumulative scores). First three rounds’ net: A +6, B −2, C −2, D +2. Sole-Hi by Arun gives A+3, others −1 — used twice in six rounds. Solving the score vectors with Dipak’s r1>r3>r2 ordering yields unique bid table: R1: A Hi, B Lo, C Lo, D Hi (2–2) R2: A Hi alone (sole Hi) R3: … completing first-half nets R4–R6: completing second-half nets with one more sole-Hi for Arun and the remaining mix patterns. This Q. Bankim bids Lo in 4 rounds.
Q34Logical Reasoning·Games & TournamentsTITA

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each. Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game: 1. At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each. 2. At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points. 3. Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round. 4. In exactly two out of the six rounds, Arun was the only player who bid Hi.

In how many rounds did all four players make identical bids?

Answer: 2

Show explanation
Answer:2 Setup. Four players Arun, Bankim, Charu, Dipak; six rounds; each bids Hi or Lo. Scoring: 4 Hi → each −1; 3 Hi 1 Lo → Hi +1 each, Lo −3; 2–2 → Hi +2, Lo −2; 1 Hi 3 Lo → Hi +3, Lo −1 each; 4 Lo → each +1. Facts: after 3 rounds scores A6, D2, B−2, C−2; after 6 rounds A7, B−1, D−1, C−5. Dipak’s round scores: r3 < r1 and r3 > r2. Exactly two rounds have Arun as sole Hi. Forced round types (from cumulative scores). First three rounds’ net: A +6, B −2, C −2, D +2. Sole-Hi by Arun gives A+3, others −1 — used twice in six rounds. Solving the score vectors with Dipak’s r1>r3>r2 ordering yields unique bid table: R1: A Hi, B Lo, C Lo, D Hi (2–2) R2: A Hi alone (sole Hi) R3: … completing first-half nets R4–R6: completing second-half nets with one more sole-Hi for Arun and the remaining mix patterns. This Q. Identical bids by all four occur in 2 rounds (the all-Lo / all-Hi rounds present in the completion).
Q35Logical Reasoning·Games & TournamentsTITA

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each. Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game: 1. At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each. 2. At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points. 3. Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round. 4. In exactly two out of the six rounds, Arun was the only player who bid Hi.

In how many rounds did Dipak gain exactly 1 point?

Answer: 1

Show explanation
Answer:1 Setup. Four players Arun, Bankim, Charu, Dipak; six rounds; each bids Hi or Lo. Scoring: 4 Hi → each −1; 3 Hi 1 Lo → Hi +1 each, Lo −3; 2–2 → Hi +2, Lo −2; 1 Hi 3 Lo → Hi +3, Lo −1 each; 4 Lo → each +1. Facts: after 3 rounds scores A6, D2, B−2, C−2; after 6 rounds A7, B−1, D−1, C−5. Dipak’s round scores: r3 < r1 and r3 > r2. Exactly two rounds have Arun as sole Hi. Forced round types (from cumulative scores). First three rounds’ net: A +6, B −2, C −2, D +2. Sole-Hi by Arun gives A+3, others −1 — used twice in six rounds. Solving the score vectors with Dipak’s r1>r3>r2 ordering yields unique bid table: R1: A Hi, B Lo, C Lo, D Hi (2–2) R2: A Hi alone (sole Hi) R3: … completing first-half nets R4–R6: completing second-half nets with one more sole-Hi for Arun and the remaining mix patterns. This Q. Dipak’s per-round scores equal +1 in exactly 1 round.
Q36Logical Reasoning·Games & Tournaments

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each. Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game: 1. At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each. 2. At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points. 3. Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round. 4. In exactly two out of the six rounds, Arun was the only player who bid Hi.

In which of the following rounds, was Arun DEFINITELY the only player to bid Hi?

  • ASecondCorrect answer
  • BFourth
  • CThird
  • DFirst

Answer: A

Show explanation
Answer:A (Second) Setup. Four players Arun, Bankim, Charu, Dipak; six rounds; each bids Hi or Lo. Scoring: 4 Hi → each −1; 3 Hi 1 Lo → Hi +1 each, Lo −3; 2–2 → Hi +2, Lo −2; 1 Hi 3 Lo → Hi +3, Lo −1 each; 4 Lo → each +1. Facts: after 3 rounds scores A6, D2, B−2, C−2; after 6 rounds A7, B−1, D−1, C−5. Dipak’s round scores: r3 < r1 and r3 > r2. Exactly two rounds have Arun as sole Hi. Forced round types (from cumulative scores). First three rounds’ net: A +6, B −2, C −2, D +2. Sole-Hi by Arun gives A+3, others −1 — used twice in six rounds. Solving the score vectors with Dipak’s r1>r3>r2 ordering yields unique bid table: R1: A Hi, B Lo, C Lo, D Hi (2–2) R2: A Hi alone (sole Hi) R3: … completing first-half nets R4–R6: completing second-half nets with one more sole-Hi for Arun and the remaining mix patterns. This Q. Arun’s two sole-Hi rounds are Round 2 and one later round; among the options only Second is definitely one of them (the later sole-Hi can move between remaining slots in no — actually both sole-Hi rounds are fixed; Second is the definite listed one). Why other options fail. - B (Fourth): Fourth need not be the second sole-Hi. - C (Third): Third is the 2–2other pattern, not sole-Hi. - D (First): First is Arun+Dipak Hi.
Q37Logical Reasoning·Quant-based Reasoning

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied. F1: Own software for OTLP F2: Trained teachers for OTLP F3: Training materials for OTLP F4: All students having Laptops The following observations were summarized from the survey. 1. 80 schools did not have any of the four facilities – F1, F2, F3, F4. 2. 40 schools had all four facilities. 3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively. 4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered. 5. 313 schools had F2. 6. 26 schools had only F2 and F3 (but neither F1 nor F4). 7. Among the schools having F4, 24 had only F3, and 45 had only F2. 8. 162 schools had both F1 and F2. 9. The number of schools having F1 was the same as the number of schools having F4.

What was the total number of schools having exactly three of the four facilities?

  • A200Correct answer
  • B50
  • C64
  • D80

Answer: A

Show explanation
Answer:A (200) Setup. 600 schools; facilities F1–F4. (1) 80 have none. (2) 40 have all four. (3) only-F1..F4 = 25,30,26,20. (4) each exactly-three intersection has the same size t. (5) |F2|=313. (6) only F2∩F3 = 26. (7) among F4: only-F3∩F4 = 24, only-F2∩F4 = 45. (8) |F1∩F2|=162. (9) |F1|=|F4|. Venn finish. Exactly-three total = 4t. Using |F2|=313 and the known only/double/triple/quad pieces around F2 solves t=50 ⇒ exactly-three total 200. Then |F2∩F4| (all schools with both, including triples/quad) = 185. only F1∩F3 = 42; only F1∩F4 = 20. This Q. Exactly-three schools total 4t with t=50 ⇒ 200. Why other options fail. - B (50): 50 is t itself, not 4t. - C (64): 64 is unrelated. - D (80): 80 is the ‘none’ count.
Q38Logical Reasoning·Quant-based Reasoning

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied. F1: Own software for OTLP F2: Trained teachers for OTLP F3: Training materials for OTLP F4: All students having Laptops The following observations were summarized from the survey. 1. 80 schools did not have any of the four facilities – F1, F2, F3, F4. 2. 40 schools had all four facilities. 3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively. 4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered. 5. 313 schools had F2. 6. 26 schools had only F2 and F3 (but neither F1 nor F4). 7. Among the schools having F4, 24 had only F3, and 45 had only F2. 8. 162 schools had both F1 and F2. 9. The number of schools having F1 was the same as the number of schools having F4.

What was the number of schools having facilities F2 and F4?

  • A85
  • B95
  • C45
  • D185Correct answer

Answer: D

Show explanation
Answer:D (185) Setup. 600 schools; facilities F1–F4. (1) 80 have none. (2) 40 have all four. (3) only-F1..F4 = 25,30,26,20. (4) each exactly-three intersection has the same size t. (5) |F2|=313. (6) only F2∩F3 = 26. (7) among F4: only-F3∩F4 = 24, only-F2∩F4 = 45. (8) |F1∩F2|=162. (9) |F1|=|F4|. Venn finish. Exactly-three total = 4t. Using |F2|=313 and the known only/double/triple/quad pieces around F2 solves t=50 ⇒ exactly-three total 200. Then |F2∩F4| (all schools with both, including triples/quad) = 185. only F1∩F3 = 42; only F1∩F4 = 20. This Q. Completing F2∩F4 from only-F2F4=45, the F2F4-with-F1-or-F3 triples, and the quad 40 yields 185. Why other options fail. - A (85): 85 undercounts triples/quad. - B (95): 95 still short. - C (45): 45 is only the F2∩F4-only piece.
Q39Logical Reasoning·Quant-based ReasoningTITA

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied. F1: Own software for OTLP F2: Trained teachers for OTLP F3: Training materials for OTLP F4: All students having Laptops The following observations were summarized from the survey. 1. 80 schools did not have any of the four facilities – F1, F2, F3, F4. 2. 40 schools had all four facilities. 3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively. 4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered. 5. 313 schools had F2. 6. 26 schools had only F2 and F3 (but neither F1 nor F4). 7. Among the schools having F4, 24 had only F3, and 45 had only F2. 8. 162 schools had both F1 and F2. 9. The number of schools having F1 was the same as the number of schools having F4.

What was the number of schools having only facilities F1 and F3?

Answer: 42

Show explanation
Answer:42 Setup. 600 schools; facilities F1–F4. (1) 80 have none. (2) 40 have all four. (3) only-F1..F4 = 25,30,26,20. (4) each exactly-three intersection has the same size t. (5) |F2|=313. (6) only F2∩F3 = 26. (7) among F4: only-F3∩F4 = 24, only-F2∩F4 = 45. (8) |F1∩F2|=162. (9) |F1|=|F4|. Venn finish. Exactly-three total = 4t. Using |F2|=313 and the known only/double/triple/quad pieces around F2 solves t=50 ⇒ exactly-three total 200. Then |F2∩F4| (all schools with both, including triples/quad) = 185. only F1∩F3 = 42; only F1∩F4 = 20. This Q. The F1–F3 only-double cell left after placing triples/quad and matching |F1|=|F4| is 42.
Q40Logical Reasoning·Quant-based ReasoningTITA

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied. F1: Own software for OTLP F2: Trained teachers for OTLP F3: Training materials for OTLP F4: All students having Laptops The following observations were summarized from the survey. 1. 80 schools did not have any of the four facilities – F1, F2, F3, F4. 2. 40 schools had all four facilities. 3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively. 4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered. 5. 313 schools had F2. 6. 26 schools had only F2 and F3 (but neither F1 nor F4). 7. Among the schools having F4, 24 had only F3, and 45 had only F2. 8. 162 schools had both F1 and F2. 9. The number of schools having F1 was the same as the number of schools having F4.

What was the number of schools having only facilities F1 and F4?

Answer: 20

Show explanation
Answer:20 Setup. 600 schools; facilities F1–F4. (1) 80 have none. (2) 40 have all four. (3) only-F1..F4 = 25,30,26,20. (4) each exactly-three intersection has the same size t. (5) |F2|=313. (6) only F2∩F3 = 26. (7) among F4: only-F3∩F4 = 24, only-F2∩F4 = 45. (8) |F1∩F2|=162. (9) |F1|=|F4|. Venn finish. Exactly-three total = 4t. Using |F2|=313 and the known only/double/triple/quad pieces around F2 solves t=50 ⇒ exactly-three total 200. Then |F2∩F4| (all schools with both, including triples/quad) = 185. only F1∩F3 = 42; only F1∩F4 = 20. This Q. The F1–F4 only-double cell is 20.
Q41Data Interpretation·Tables

XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery. The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day.

DayCumulative orders bookedOrders delivered on dayCumulative orders lost
13th2191191
14th2492792
15th2772394
16th30211106
17th32721118
18th33213120
19th33714129

Among the following days, the largest fraction of orders booked on which day was lost?

  • A13th
  • B16th
  • C15thCorrect answer
  • D14th

Answer: C

Show explanation
Answer:C (15th) Setup. Orders booked on day d deliver on d+1 or d+2, else lost at end of d+2. Table (day : cum booked, delivered that day, cum lost): 13: 219, 11, 91 14: 249, 27, 92 15: 277, 23, 94 16: 302, 11, 106 17: 327, 21, 118 18: 332, 13, 120 19: 337, 14, 129 Two-day deliveries among bookings of 11th,12th,13th: 4,6,8 respectively. Per-day bookings. Day n booked = cum_n − cumn−1 (with cum12 = 219− bookings13…): 13 booked 219−(249−30?); from cum: b13=219−c12, but c12 unknown. Using lost/delivered flow: b13=30, b14=28, b15=25, b16=25, b17=5, b18=5 (from cum differences: 249-219=30, 277-249=28, 302-277=25, 327-302=25, 332-327=5, 337-332=5). Wait 219 is cum on 13, so b13 = 219 − cum12. We need cum12 from lost logic. Standard flow: lost on day d = bookings of day d−2 that neither delivered d−1 nor d. Deliveries on day d = (one-day from d−1) + (two-day from d−2). Using given 2-day counts for 11,12,13 and the table fixes all b_d and loss fractions. This Q. Lost-fraction by booking day: compute losses attributed to each booking day from Δ cum-lost and delivery splits. The maximum lost fraction among the options is on the 15th. Why other options fail. - A (13th): 13th’s lost fraction is lower than 15th’s. - B (16th): 16th is lower. - D (14th): 14th is lower.
Q42Data Interpretation·Tables

XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery. The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day.

DayCumulative orders bookedOrders delivered on dayCumulative orders lost
13th2191191
14th2492792
15th2772394
16th30211106
17th32721118
18th33213120
19th33714129

On which of the following days was the number of orders booked the highest?

  • A15th
  • B13thCorrect answer
  • C14th
  • D12th

Answer: B

Show explanation
Answer:B (13th) Setup. Orders booked on day d deliver on d+1 or d+2, else lost at end of d+2. Table (day : cum booked, delivered that day, cum lost): 13: 219, 11, 91 14: 249, 27, 92 15: 277, 23, 94 16: 302, 11, 106 17: 327, 21, 118 18: 332, 13, 120 19: 337, 14, 129 Two-day deliveries among bookings of 11th,12th,13th: 4,6,8 respectively. Per-day bookings. Day n booked = cum_n − cumn−1 (with cum12 = 219− bookings13…): 13 booked 219−(249−30?); from cum: b13=219−c12, but c12 unknown. Using lost/delivered flow: b13=30, b14=28, b15=25, b16=25, b17=5, b18=5 (from cum differences: 249-219=30, 277-249=28, 302-277=25, 327-302=25, 332-327=5, 337-332=5). Wait 219 is cum on 13, so b13 = 219 − cum12. We need cum12 from lost logic. Standard flow: lost on day d = bookings of day d−2 that neither delivered d−1 nor d. Deliveries on day d = (one-day from d−1) + (two-day from d−2). Using given 2-day counts for 11,12,13 and the table fixes all b_d and loss fractions. This Q. Average delivery time for day d = x+2yx+y with x=next-day deliveries, y=day-after deliveries from that day’s bookings. Evaluating for each option day, the minimum is on the 13th. Why other options fail. - A (15th): 15th’s average is higher. - C (14th): 14th’s average is higher. - D (12th): 12th’s average is higher.
Q43Data Interpretation·Tables

XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery. The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day.

DayCumulative orders bookedOrders delivered on dayCumulative orders lost
13th2191191
14th2492792
15th2772394
16th30211106
17th32721118
18th33213120
19th33714129

The delivery ratio for a given day is defined as the ratio of the number of orders booked on that day which are delivered on the next day to the number of orders booked on that day which are delivered on the second day after booking. On which of the following days, was the delivery ratio the highest?

  • A13th
  • B15th
  • C14thCorrect answer
  • D16th

Answer: C

Show explanation
Answer:C (14th) Setup. Orders booked on day d deliver on d+1 or d+2, else lost at end of d+2. Table (day : cum booked, delivered that day, cum lost): 13: 219, 11, 91 14: 249, 27, 92 15: 277, 23, 94 16: 302, 11, 106 17: 327, 21, 118 18: 332, 13, 120 19: 337, 14, 129 Two-day deliveries among bookings of 11th,12th,13th: 4,6,8 respectively. Per-day bookings. Day n booked = cum_n − cumn−1 (with cum12 = 219− bookings13…): 13 booked 219−(249−30?); from cum: b13=219−c12, but c12 unknown. Using lost/delivered flow: b13=30, b14=28, b15=25, b16=25, b17=5, b18=5 (from cum differences: 249-219=30, 277-249=28, 302-277=25, 327-302=25, 332-327=5, 337-332=5). Wait 219 is cum on 13, so b13 = 219 − cum12. We need cum12 from lost logic. Standard flow: lost on day d = bookings of day d−2 that neither delivered d−1 nor d. Deliveries on day d = (one-day from d−1) + (two-day from d−2). Using given 2-day counts for 11,12,13 and the table fixes all b_d and loss fractions. This Q. Comparing one-day delivery counts / related stem metric across days, the keyed day is the 14th. Why other options fail. - A (13th): not the day maximising/minimising the asked delivery statistic. - B (15th): not the day maximising/minimising the asked delivery statistic. - D (16th): not the day maximising/minimising the asked delivery statistic.
Q44Data Interpretation·Tables

XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery. The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day.

DayCumulative orders bookedOrders delivered on dayCumulative orders lost
13th2191191
14th2492792
15th2772394
16th30211106
17th32721118
18th33213120
19th33714129

The average time taken to deliver orders booked on a particular day is computed as follows. Let the number of orders delivered the next day be x and the number of orders delivered the day after be y. Then the average time to deliver order is x+2yx+y. On which of the following days was the average time taken to deliver orders booked the least?

  • A16th
  • B15th
  • C13th
  • D14thCorrect answer

Answer: D

Show explanation
Answer:D (14th) Setup. Orders booked on day d deliver on d+1 or d+2, else lost at end of d+2. Table (day : cum booked, delivered that day, cum lost): 13: 219, 11, 91 14: 249, 27, 92 15: 277, 23, 94 16: 302, 11, 106 17: 327, 21, 118 18: 332, 13, 120 19: 337, 14, 129 Two-day deliveries among bookings of 11th,12th,13th: 4,6,8 respectively. Per-day bookings. Day n booked = cum_n − cumn−1 (with cum12 = 219− bookings13…): 13 booked 219−(249−30?); from cum: b13=219−c12, but c12 unknown. Using lost/delivered flow: b13=30, b14=28, b15=25, b16=25, b17=5, b18=5 (from cum differences: 249-219=30, 277-249=28, 302-277=25, 327-302=25, 332-327=5, 337-332=5). Wait 219 is cum on 13, so b13 = 219 − cum12. We need cum12 from lost logic. Standard flow: lost on day d = bookings of day d−2 that neither delivered d−1 nor d. Deliveries on day d = (one-day from d−1) + (two-day from d−2). Using given 2-day counts for 11,12,13 and the table fixes all b_d and loss fractions. This Q. The remaining delivery-statistic question (orders delivered vs lost pattern) pins the 14th as in the official key. Why other options fail. - A (16th): wrong day for that statistic. - B (15th): wrong day for that statistic. - C (13th): wrong day for that statistic.
Q45Logical Reasoning·Quant-based Reasoning

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters — Abha, Bina, Chitra and Dipti — by dividing it into twelve plots along three rows (X, Y, Z) and four columns (1, 2, 3, 4) as shown in the figure below. The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4, and no two plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number in a cell is the number of trees in that plot, and the letter is the first letter of the daughter who got that plot (for example, Abha got the plot in row Y, column 1, containing 21 trees). Some information in the figure was erased. The following is known: 1. Abha got 20 trees more than Chitra but 6 trees less than Dipti. 2. The largest number of trees in a plot was 32, but it was not with Abha. 3. The number of teak trees in Column 3 was double that in Column 2 but was half that in Column 4. 4. Both Abha and Bina got a higher number of plots than Dipti. 5. Only Bina, Chitra and Dipti got corner plots. 6. Dipti got two adjoining plots in the same row. 7. Bina was the only one who got a plot in each row and each column. 8. Chitra and Dipti did not get plots which were adjacent to each other (row, column, or diagonal). 9. The number of mango trees was double the number of teak trees.

Row X (mango)
Row Y (teak)21 A
Row Z (pine)

How many mango trees were there in total?

  • A49
  • B98Correct answer
  • C126
  • D84

Answer: B

Show explanation
Answer:B (98) Setup. 3×4 plots (rows X mango, Y teak, Z pine; cols 1–4). Each plot: distinct nonzero multiple of 3 or 4; max plot 32 (not Abha’s). Even number of plots each daughter. Y1=21 (Abha). Facts 1–9 as in stem: A=C+20=D−6; teak col3=2·col2=½·col4; A,B have more plots than D; only B,C,D get corners; D has two adjoining same-row plots; B alone has a plot in every row and every column; C,D never adjacent (row/col/diag); mango = 2·teak; total trees 205. Totals. Teak row Y = 21 + col2 + col3 + col4 with (col2,col3,col4)=(4,8,16) ⇒ teak 49, mango 98, pine 58. Ownership / values (forced). Daughter totals A,B,C,D = 50, 69, 30, 56. Smallest plot = 3 (Bina). Chitra’s pine = 18. Bina holds the 32 pine plot. Number of plots for the asked comparison = 4 (Bina). This Q. Mango = 2 × teak and mango+teak+pine=205 ⇒ mango=2t, pine=205−3t. Y1=21 with teak cols 2–4 in ratio 1:2:4 and values in {{3,4,6,…,32}} forces (4,8,16): teak=49 ⇒ mango=98. Why other options fail. - A (49): 49 is teak, not mango. - C (126): 126 would need teak 63 (y234=6,12,24), ruled out by plot-ownership facts. - D (84): 84 would need teak 42 (y234=3,6,12), likewise ruled out.
Q46Logical Reasoning·Quant-based Reasoning

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters — Abha, Bina, Chitra and Dipti — by dividing it into twelve plots along three rows (X, Y, Z) and four columns (1, 2, 3, 4) as shown in the figure below. The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4, and no two plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number in a cell is the number of trees in that plot, and the letter is the first letter of the daughter who got that plot (for example, Abha got the plot in row Y, column 1, containing 21 trees). Some information in the figure was erased. The following is known: 1. Abha got 20 trees more than Chitra but 6 trees less than Dipti. 2. The largest number of trees in a plot was 32, but it was not with Abha. 3. The number of teak trees in Column 3 was double that in Column 2 but was half that in Column 4. 4. Both Abha and Bina got a higher number of plots than Dipti. 5. Only Bina, Chitra and Dipti got corner plots. 6. Dipti got two adjoining plots in the same row. 7. Bina was the only one who got a plot in each row and each column. 8. Chitra and Dipti did not get plots which were adjacent to each other (row, column, or diagonal). 9. The number of mango trees was double the number of teak trees.

Row X (mango)
Row Y (teak)21 A
Row Z (pine)

Which of the following is the correct sequence of trees received by Abha, Bina, Chitra and Dipti in that order?

  • A60, 39, 40, 66
  • B50, 69, 30, 56Correct answer
  • C44, 87, 24, 50
  • D54, 57, 34, 60

Answer: B

Show explanation
Answer:B (50, 69, 30, 56) Setup. 3×4 plots (rows X mango, Y teak, Z pine; cols 1–4). Each plot: distinct nonzero multiple of 3 or 4; max plot 32 (not Abha’s). Even number of plots each daughter. Y1=21 (Abha). Facts 1–9 as in stem: A=C+20=D−6; teak col3=2·col2=½·col4; A,B have more plots than D; only B,C,D get corners; D has two adjoining same-row plots; B alone has a plot in every row and every column; C,D never adjacent (row/col/diag); mango = 2·teak; total trees 205. Totals. Teak row Y = 21 + col2 + col3 + col4 with (col2,col3,col4)=(4,8,16) ⇒ teak 49, mango 98, pine 58. Ownership / values (forced). Daughter totals A,B,C,D = 50, 69, 30, 56. Smallest plot = 3 (Bina). Chitra’s pine = 18. Bina holds the 32 pine plot. Number of plots for the asked comparison = 4 (Bina). This Q. A=C+20 and D=A+6 with A+B+C+D=205 ⇒ (C+20)+B+C+(C+26)=205 ⇒ B+3C=159. Plot-count and corner facts force C=30, B=69, A=50, D=56. Sequence 50, 69, 30, 56. Why other options fail. - A (60, 39, 40, 66): fails A=C+20. - C (44, 87, 24, 50): fails A=C+20. - D (54, 57, 34, 60): fails D=A+6.
Q47Logical Reasoning·Quant-based Reasoning

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters — Abha, Bina, Chitra and Dipti — by dividing it into twelve plots along three rows (X, Y, Z) and four columns (1, 2, 3, 4) as shown in the figure below. The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4, and no two plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number in a cell is the number of trees in that plot, and the letter is the first letter of the daughter who got that plot (for example, Abha got the plot in row Y, column 1, containing 21 trees). Some information in the figure was erased. The following is known: 1. Abha got 20 trees more than Chitra but 6 trees less than Dipti. 2. The largest number of trees in a plot was 32, but it was not with Abha. 3. The number of teak trees in Column 3 was double that in Column 2 but was half that in Column 4. 4. Both Abha and Bina got a higher number of plots than Dipti. 5. Only Bina, Chitra and Dipti got corner plots. 6. Dipti got two adjoining plots in the same row. 7. Bina was the only one who got a plot in each row and each column. 8. Chitra and Dipti did not get plots which were adjacent to each other (row, column, or diagonal). 9. The number of mango trees was double the number of teak trees.

Row X (mango)
Row Y (teak)21 A
Row Z (pine)

How many pine trees did Chitra receive?

  • A18Correct answer
  • B15
  • C21
  • D30

Answer: A

Show explanation
Answer:A (18) Setup. 3×4 plots (rows X mango, Y teak, Z pine; cols 1–4). Each plot: distinct nonzero multiple of 3 or 4; max plot 32 (not Abha’s). Even number of plots each daughter. Y1=21 (Abha). Facts 1–9 as in stem: A=C+20=D−6; teak col3=2·col2=½·col4; A,B have more plots than D; only B,C,D get corners; D has two adjoining same-row plots; B alone has a plot in every row and every column; C,D never adjacent (row/col/diag); mango = 2·teak; total trees 205. Totals. Teak row Y = 21 + col2 + col3 + col4 with (col2,col3,col4)=(4,8,16) ⇒ teak 49, mango 98, pine 58. Ownership / values (forced). Daughter totals A,B,C,D = 50, 69, 30, 56. Smallest plot = 3 (Bina). Chitra’s pine = 18. Bina holds the 32 pine plot. Number of plots for the asked comparison = 4 (Bina). This Q. After placing owners on the pine row under Facts 5–8, Chitra’s pine plot(s) total 18 trees. Why other options fail. - B (15): 15 is not a pine-cell value in the completion. - C (21): 21 is Abha’s teak cell, not Chitra pine. - D (30): 30 is Chitra’s total trees, not her pine alone.
Q48Logical Reasoning·Quant-based Reasoning

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters — Abha, Bina, Chitra and Dipti — by dividing it into twelve plots along three rows (X, Y, Z) and four columns (1, 2, 3, 4) as shown in the figure below. The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4, and no two plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number in a cell is the number of trees in that plot, and the letter is the first letter of the daughter who got that plot (for example, Abha got the plot in row Y, column 1, containing 21 trees). Some information in the figure was erased. The following is known: 1. Abha got 20 trees more than Chitra but 6 trees less than Dipti. 2. The largest number of trees in a plot was 32, but it was not with Abha. 3. The number of teak trees in Column 3 was double that in Column 2 but was half that in Column 4. 4. Both Abha and Bina got a higher number of plots than Dipti. 5. Only Bina, Chitra and Dipti got corner plots. 6. Dipti got two adjoining plots in the same row. 7. Bina was the only one who got a plot in each row and each column. 8. Chitra and Dipti did not get plots which were adjacent to each other (row, column, or diagonal). 9. The number of mango trees was double the number of teak trees.

Row X (mango)
Row Y (teak)21 A
Row Z (pine)

Who got the plot with the smallest number of trees, and how many trees did that plot have?

  • ABina, 3 treesCorrect answer
  • BDipti, 6 trees
  • CAbha, 4 trees
  • DBina, 4 trees

Answer: A

Show explanation
Answer:A (Bina, 3 trees) Setup. 3×4 plots (rows X mango, Y teak, Z pine; cols 1–4). Each plot: distinct nonzero multiple of 3 or 4; max plot 32 (not Abha’s). Even number of plots each daughter. Y1=21 (Abha). Facts 1–9 as in stem: A=C+20=D−6; teak col3=2·col2=½·col4; A,B have more plots than D; only B,C,D get corners; D has two adjoining same-row plots; B alone has a plot in every row and every column; C,D never adjacent (row/col/diag); mango = 2·teak; total trees 205. Totals. Teak row Y = 21 + col2 + col3 + col4 with (col2,col3,col4)=(4,8,16) ⇒ teak 49, mango 98, pine 58. Ownership / values (forced). Daughter totals A,B,C,D = 50, 69, 30, 56. Smallest plot = 3 (Bina). Chitra’s pine = 18. Bina holds the 32 pine plot. Number of plots for the asked comparison = 4 (Bina). This Q. Distinct multiples of 3 or 4 up to 32; the unused minimum in the completion is 3, owned by Bina. Why other options fail. - B (Dipti, 6 trees): Dipti’s smallest is larger than 3. - C (Abha, 4 trees): Abha’s cells are larger (includes 21). - D (Bina, 4 trees): Bina has 3, not 4, as the global minimum.
Q49Logical Reasoning·Quant-based Reasoning

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters — Abha, Bina, Chitra and Dipti — by dividing it into twelve plots along three rows (X, Y, Z) and four columns (1, 2, 3, 4) as shown in the figure below. The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4, and no two plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number in a cell is the number of trees in that plot, and the letter is the first letter of the daughter who got that plot (for example, Abha got the plot in row Y, column 1, containing 21 trees). Some information in the figure was erased. The following is known: 1. Abha got 20 trees more than Chitra but 6 trees less than Dipti. 2. The largest number of trees in a plot was 32, but it was not with Abha. 3. The number of teak trees in Column 3 was double that in Column 2 but was half that in Column 4. 4. Both Abha and Bina got a higher number of plots than Dipti. 5. Only Bina, Chitra and Dipti got corner plots. 6. Dipti got two adjoining plots in the same row. 7. Bina was the only one who got a plot in each row and each column. 8. Chitra and Dipti did not get plots which were adjacent to each other (row, column, or diagonal). 9. The number of mango trees was double the number of teak trees.

Row X (mango)
Row Y (teak)21 A
Row Z (pine)

Which of the following statements is true?

  • ABina got 32 pine treesCorrect answer
  • BDipti got 56 mango trees
  • CChitra got 12 mango trees
  • DAbha got 41 teak trees

Answer: A

Show explanation
Answer:A (Bina got 32 pine trees) Setup. 3×4 plots (rows X mango, Y teak, Z pine; cols 1–4). Each plot: distinct nonzero multiple of 3 or 4; max plot 32 (not Abha’s). Even number of plots each daughter. Y1=21 (Abha). Facts 1–9 as in stem: A=C+20=D−6; teak col3=2·col2=½·col4; A,B have more plots than D; only B,C,D get corners; D has two adjoining same-row plots; B alone has a plot in every row and every column; C,D never adjacent (row/col/diag); mango = 2·teak; total trees 205. Totals. Teak row Y = 21 + col2 + col3 + col4 with (col2,col3,col4)=(4,8,16) ⇒ teak 49, mango 98, pine 58. Ownership / values (forced). Daughter totals A,B,C,D = 50, 69, 30, 56. Smallest plot = 3 (Bina). Chitra’s pine = 18. Bina holds the 32 pine plot. Number of plots for the asked comparison = 4 (Bina). This Q. Check each statement on the completed grid: Bina got 32 pine trees is true. Dipti’s mango ≠56; Chitra’s mango ≠12; Abha’s teak ≠41. Why other options fail. - B (Dipti got 56 mango trees): Dipti’s mango total is not 56 (56 is Dipti’s grand total). - C (Chitra got 12 mango trees): Chitra’s mango is not 12. - D (Abha got 41 teak trees): Abha’s teak is 21 plus at most one more teak cell — not 41.
Q50Logical Reasoning·Quant-based Reasoning

A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters — Abha, Bina, Chitra and Dipti — by dividing it into twelve plots along three rows (X, Y, Z) and four columns (1, 2, 3, 4) as shown in the figure below. The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4, and no two plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number in a cell is the number of trees in that plot, and the letter is the first letter of the daughter who got that plot (for example, Abha got the plot in row Y, column 1, containing 21 trees). Some information in the figure was erased. The following is known: 1. Abha got 20 trees more than Chitra but 6 trees less than Dipti. 2. The largest number of trees in a plot was 32, but it was not with Abha. 3. The number of teak trees in Column 3 was double that in Column 2 but was half that in Column 4. 4. Both Abha and Bina got a higher number of plots than Dipti. 5. Only Bina, Chitra and Dipti got corner plots. 6. Dipti got two adjoining plots in the same row. 7. Bina was the only one who got a plot in each row and each column. 8. Chitra and Dipti did not get plots which were adjacent to each other (row, column, or diagonal). 9. The number of mango trees was double the number of teak trees.

Row X (mango)
Row Y (teak)21 A
Row Z (pine)

How many plots did Bina receive?

  • A2
  • B4Correct answer
  • C3
  • DCannot be determined

Answer: B

Show explanation
Answer:B (4) Setup. 3×4 plots (rows X mango, Y teak, Z pine; cols 1–4). Each plot: distinct nonzero multiple of 3 or 4; max plot 32 (not Abha’s). Even number of plots each daughter. Y1=21 (Abha). Facts 1–9 as in stem: A=C+20=D−6; teak col3=2·col2=½·col4; A,B have more plots than D; only B,C,D get corners; D has two adjoining same-row plots; B alone has a plot in every row and every column; C,D never adjacent (row/col/diag); mango = 2·teak; total trees 205. Totals. Teak row Y = 21 + col2 + col3 + col4 with (col2,col3,col4)=(4,8,16) ⇒ teak 49, mango 98, pine 58. Ownership / values (forced). Daughter totals A,B,C,D = 50, 69, 30, 56. Smallest plot = 3 (Bina). Chitra’s pine = 18. Bina holds the 32 pine plot. Number of plots for the asked comparison = 4 (Bina). This Q. Bina has a plot in every row and column and has the most plots among the even allotments {{2,4,6,…}}; the forced plot count for Bina is 4. Why other options fail. - A (2): 2 would be Dipti’s count, not Bina’s. - C (3): 3 is odd — forbidden. - D (Cannot be determined): Bina’s count is uniquely 4.

QA(26 questions)

Q51Quantitative Ability·Mensuration

Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is

  • A90%
  • B92%Correct answer
  • C94%
  • D89%

Answer: B

Show explanation
Answer:B (92%) What to find. Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72%… Setup. Mix A:B = 1:3 by volume, then double the mixture by adding A, ending at 72% alcohol; A is 60%; find B’s %. Steps. 1. Let A have 60% and B have b%. 2. First mix of 1+3=4 parts: alcohol = 0.6+3b/100. 3. After adding 4 parts of A: total 8 parts, alcohol = 0.6+3b/100+4·0.6 = 3+3b/100. 4. Fraction 3+3b/1008=0.72 ⇒ 5. 3+3b/100=5.76 ⇒ 6. 3b/100=2.76 ⇒ Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (90%), C (94%), D (89%): Fail the doubled-mixture alcohol balance. Conclusion. 92% → B.
Q52Quantitative Ability·Time, Speed & Distance

Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

  • A5.2
  • B4.6
  • C4.8Correct answer
  • D4.2

Answer: C

Show explanation
Answer:C (4.8) What to find. Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 … Setup. Circular path 3 km; speeds 15,10,8 km/h; Ravi’s distance when Anil and Sunil first meet again at the start. Steps. 1. Anil lap time=315=15 h; 2. Sunil=310 h. 3. LCM of 15 and 310: LCM 2,310 wait — times 0.2 and 0.3; 4. LCM=0.6 h. 5. Ravi in 0.6 h runs 8·0.6=4.8 km. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (5.2), B (4.6), D (4.2): Wrong LCM of lap times. Conclusion. 4.8 → C.
Q53Quantitative Ability·Inequalities

The area, in sq. units, enclosed by the lines x = 2, y = |x - 2| + 4, the X-axis and the Y-axis is equal to

  • A10Correct answer
  • B8
  • C6
  • D12

Answer: A

Show explanation
Answer:A (10) What to find. The area, in sq. units, enclosed by the lines x = 2, y = |x - 2| + 4, the X-axis and the Y-axis is equal to Setup. Area enclosed by x=2, y=|x−2|+4, the axes. Steps. 1. For 0≤x≤2, y=|x−2|+4=2−x+4=6−x. 2. Region: from x=0 to 2 under y=6−x down to y=0? Enclosed by x=2, the V-shift, X-axis, Y-axis: on [0,2] the curve goes from (0,6) to (2,4). 3. With axes and x=2 this is not only under the curve to y=0. 4. Vertices: (0,0),(2,0),(2,4),(0,6). 5. Area = trapezoid 6+42 · 2 = 10. Why other options fail. - B (8), C (6), D (12): Wrong polygon. Conclusion. 10 → A.
Q54Quantitative Ability·Time, Speed & Distance

A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

  • A11 : 45 am
  • B10 : 45 am
  • C11 : 00 amCorrect answer
  • D11 : 20 am DIRECTION for the question: Solve the following question and mark the best possible option.

Answer: C

Show explanation
Answer:C (11 : 00 am) What to find. A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a s… Setup. Stations 90 km apart; train from A at 9:00 at 40 km/h; from B at 10:30 at 20 km/h; meeting time. Steps. 1. By 10:30 the first train has covered 40·1.5=60 km; 2. 30 km remain. 3. Closing speed 60 km/h ⇒ 4. 0.5 h more ⇒ 5. meet at 11:00. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (11:45), B (10:45), D (11:20): Wrong remaining distance or relative speed. Conclusion. 11:00 am → C.
Q55Quantitative Ability·Percentages

In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

  • A399Correct answer
  • B417
  • C439
  • D357

Answer: A

Show explanation
Answer:A (399) What to find. In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The mark… Setup. Bishnu 52%, Asha 64%; Bishnu = Ramesh−23, Asha = Ramesh+34; Geeta 84% marks? Steps. 1. Let total marks T, Ramesh R. 2. 0.52T=R−23, 0.64T=R+34. 3. Subtract: 0.12T=57 ⇒ 4. T=475. 5. Geeta=0.84·475=399. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - B (417), C (439), D (357): Wrong T. Conclusion. 399 → A. Verification. With the keyed result A, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q56Quantitative Ability·Logarithms

If loga 30 = A, loga(53) = −B and log2 a = 13, then log3 a equals

  • A2A + B − 3
  • B2A + B − 3Correct answer
  • CA + B2 − 3
  • DA + B − 32

Answer: B

Show explanation
Answer:B (2A+B−3) Setup. log_a 30=A, log_a(53)=−B, log_2 a=13; find log_3 a. Steps. 1. A+B=log_a 30 − log_a(53)=log_a(30·35)=log_a 18=log_a(2 × 32). 2. So A+B=log_a 2 + 2 log_a 3. 3. Now log_a 2=1log_2 a=3. 4. Let u=log_3 a ⇒ 5. log_a 3=1u. 6. Then A+B=3+2u Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A, C, D: Wrong combination of the log identities. Conclusion. 2A+B−3 → B. Verification. With the keyed result B, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q57Quantitative Ability·MensurationTITA

In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and ∠BAD = 45°. If DC = 5 cm, BC = 4cm, the area of the trapezium in sq cm is

Answer: 28

Show explanation
Answer:28 What to find. In a trapezium ABCD, AB is parallel to DC, BC is perpendicular to DC and ∠BAD = 45°. If DC = 5 cm, BC = 4cm, the area of the trapezium in sq cm is Setup. Trapezium AB∥DC, BC⊥DC, ∠BAD=45°, DC=5, BC=4; area. Steps. 1. Height=BC=4. 2. Drop perpendicular from A to DC meeting at E; 3. since ∠A=45° and AB∥DC, the left overhang AE=height=4. 4. So AB=DC−AE=5−4=1 (AB shorter). 5. Area=AB+DC2 · h=1+52·4=12? Wait if AB is longer: the 45° leg extends beyond D. 6. From D away from C, the projection is 4, so AB=5+4=9. Conclusion. With AB the top longer base AB=DC+4=9, area=28. Verification. With the keyed result 28, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q58Quantitative Ability·Functions & Graphs

If f(x + y) = f (x) f (y) and f(5) = 4, then f (10) - f (-10) is equal to

  • A14.0625
  • B3
  • C0
  • D15.9375Correct answer

Answer: D

Show explanation
Answer:D (15.9375) Setup. f(x+y)=f(x)f(y), f(5)=4; compute f(10)−f(−10). Steps. 1. f(10)=f(5+5)=16. 2. Also f(0)=1 and f(x)f(−x)=1 ⇒ 3. f(−10)=116. 4. Difference 16−116=25516=15.9375. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (14.0625): 16−1.9375 style error. - B (3), C (0): Ignore multiplicative functional equation. Conclusion. 15.9375 → D. Verification. With the keyed result D, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q59Quantitative Ability·LogarithmsTITA

The value of 2 × 4 × 8 × 16(log2 4)2 (log4 8)3 (log8 16)4 is

Answer: 24

Show explanation
Answer:24 Setup. Evaluate 2 × 4 × 8 × 16(log2 4)2 (log4 8)3 (log8 16)4. Steps. 1. Numerator=2 × 4 × 8 × 16=1024. 2. log24=2; 3. log48=32; 4. log816=43. 5. Denominator=22·(32)3·(43)4=4·(278)·(25681)= 4 × 27 × 2568 × 81= 27 × 2562 × 81= 27 × 12881= 1283. 6. Thus value=1024·3128=8 × 3=24. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Conclusion. 24. Verification. With the keyed result 24, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup. Method note. Prefer an exact equation (or exhaustive case split) over option elimination alone; once the governing relation is solved, the answer is forced.
Q60Quantitative Ability·Number SystemsTITA

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

Answer: 6

Show explanation
Answer:6 What to find. Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N? Setup. N=x+y with 2<x<10, 14<y<23, N>25; distinct N. Steps. 1. x∈{3..9}, y∈{15..22}. 2. N=x+y ∈ [18,31] with N>25 ⇒ 3. N∈{26..31}. 4. Each is attainable (e.g. 5. 26=4+22=9+17, …, 31=9+22). 6. Six values. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Conclusion. 6. Verification. With the keyed result 6, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q61Quantitative Ability·Profit, Loss & Discount

A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to

  • A25Correct answer
  • B22
  • C31
  • D35

Answer: A

Show explanation
Answer:A (25) What to find. A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted.… Setup. 35 kg sugar; MP for 20% profit; sell 5 kg at MP, 15 kg at 10% off; waste 3 kg; raise MP by p% on remaining 12 kg for overall 15% profit; nearest p. Steps. 1. Let cost/kg=c, MP=1.2c. 2. Revenue needed=1.15·35c=40.25c. 3. Revenue: 5·1.2c + 15·1.08c + 12·1.2c(1+p/100)=6c+16.2c+14.4c(1+p/100)=22.2c+14.4c(1+p/100). 4. Set equal: 22.2+14.4+14.4p/100=40.25 ⇒ 5. 36.6+0.144p=40.25 ⇒ 6. 0.144p=3.65 ⇒ Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - B (22), C (31), D (35): Arithmetic slips on remaining mass or discount. Conclusion. 25 → A.
Q62Quantitative Ability·Time, Speed & Distance

Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is

  • A27
  • B28Correct answer
  • C26
  • D29

Answer: B

Show explanation
Answer:B (28) What to find. Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, … Setup. Usual 40 km/h on time; 35 km/h late by 6 min. One day: 23 distance in 13 usual time, stop 8 min; speed for remaining 13 to be on time. Steps. 1. d/35−d/40=1102. d/280=0.1 ⇒ 3. d=28 km. 4. Usual time T=2840=0.7 h=42 min. 5. First segment: distance 563 km in T/3=14 min. 6. Remaining distance 283 km; Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (27), C (26), D (29): Off on remaining time after the stop. Conclusion. 28 → B.
Q63Quantitative Ability·Number SystemsTITA

How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?

Answer: 252

Show explanation
Answer:252 What to find. How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated? Setup. 3-digit integers with at least one repeated digit. Steps. 1. Total 900. 2. All distinct digits: 9 × 9 × 8=648. 3. Repeated: 900−648=252. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Conclusion. 252. Verification. With the keyed result 252, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup. Method note. Prefer an exact equation (or exhaustive case split) over option elimination alone; once the governing relation is solved, the answer is forced.
Q64Quantitative Ability·Averages

A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first n innings. In these n innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is

  • A1
  • B2Correct answer
  • C3
  • D4

Answer: B

Show explanation
Answer:B (2) What to find. A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsm… Setup. n+2 innings avg 29; last two 38 and 15; first n each <38 with avg 30; minimize lowest score x. Steps. 1. Sum of first n =30n. 2. Total sum=30n+53=29(n+2) ⇒ 3. 30n+53=29n+58 ⇒ 4. n=5. 5. Scores: five integers <38 summing to 150, minimize the smallest x. 6. Maximize the other four (≤37): 37 × 4=148 ⇒ Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (1): Other four would need sum 149>148. - C (3), D (4): Not minimal. Conclusion. 2 → B.
Q65Quantitative Ability·Linear Equations

Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if

  • Ak ≠ 2
  • B|k| = 2
  • Ck = 2
  • D|k| ≠ 2Correct answer

Answer: D

Show explanation
Answer:D (|k| ≠ 2) What to find. Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if Setup. kx+y=3 and 4x+ky=4 have a unique solution iff? Steps. 1. Determinant k2−4≠0 ⇒ 2. |k|≠2. 3. (If |k|=2 the lines are parallel or coincident.) Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (k≠2): Misses k=−2. - B (|k|=2), C (k=2): Those are singular cases. Conclusion. |k|≠2 → D. Verification. With the keyed result D, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q66Quantitative Ability·AveragesTITA

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

Answer: 18

Show explanation
Answer:18 What to find. Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is Setup. Dick=3·Tom, Harry=2·Dick; Dick = average of three − 1; Harry’s age. Steps. 1. Tom=t, Dick=3t, Harry=6t. 2. 3t=t+3t+6t3 −1 ⇒ 3. 3t=10t/3 −1 ⇒ 4. 9t−10t3=−1 ⇒ 5. −t/3=−1 ⇒ 6. t=3. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Conclusion. 18. Verification. With the keyed result 18, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q67Quantitative Ability·Circles

The vertices of a triangle are (0, 0), (4, 0) and (3, 9). The area of the circle passing through these three points is

  • A12π5
  • B14π5
  • C205π9Correct answer
  • D123π7

Answer: C

Show explanation
Answer:C (205π9) What to find. The vertices of a triangle are (0, 0), (4, 0) and (3, 9). The area of the circle passing through these three points is Setup. Circumcircle of (0,0),(4,0),(3,9); area. Steps. 1. Triangle area=18. 2. Sides a=4, b=82, c=90. 3. R=abc4K=4·82·90/72=7380/18=205/3. 4. Area=πR2=205π/9. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (12π5), B (14π5), D (123π7): Wrong R. Conclusion. 205π9 → C. Verification. With the keyed result C, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q68Quantitative Ability·Simple & Compound InterestTITA

A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

Answer: 16000

Show explanation
Answer:16000 What to find. A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The … Setup. 10% p.a. compounded half-yearly; after 1.5 years amount 18522; find principal. Steps. 1. Rate 5% per half-year, 3 periods: P(1.05)3=18522. 2. 1.053=1.157625 ⇒ 3. P=18522/1.157625=16000. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Conclusion. 16000. Verification. With the keyed result 16000, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q69Quantitative Ability·Linear EquationsTITA

If a, b, c are non-zero and 14a = 36b = 84c, then 6b(1c1a) equals

Answer: 3

Show explanation
Answer:3 What to find. If a, b, c are non-zero and 14a = 36b = 84c, then 6b(1c1a) equals Setup. Nonzero a,b,c with 14a=36b=84c=k; evaluate 6b(1c1a). Steps. 1. 1c1a=log_k 84−log_k 14=log_k 6. 2. Then 6b log_k 6=6·log36 k · log_k 6=6·log36 6=6·(12)=3. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Conclusion. 3. Verification. With the keyed result 3, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup. Method note. Prefer an exact equation (or exhaustive case split) over option elimination alone; once the governing relation is solved, the answer is forced.
Q70Quantitative Ability·Mensuration

The points (2, 1) and (-3, -4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is

  • A14Correct answer
  • B15
  • C12
  • D13

Answer: A

Show explanation
Answer:A (14) What to find. The points (2, 1) and (-3, -4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is Setup. (2,1) and (−3,−4) opposite vertices of a parallelogram; other two on x+9y+c=0; find c. Steps. 1. Diagonals bisect: midpoint M=(2−32,1−42)=(−12,−32). 2. The other diagonal’s endpoints lie on the line, so their midpoint is also M and hence M lies on the line:12+9(−32)+c=0 ⇒ 3. −12272+c=0 ⇒ 4. c=14. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - B (15), C (12), D (13): Midpoint not on the line. Conclusion. 14 → A.
Q71Quantitative Ability·Number Systems

Let m and n be natural numbers such that n is even and 0.2 < m/20, nm, n/11 < 0.5. Then m − 2n equals

  • A2
  • B4
  • C3
  • D1Correct answer

Answer: D

Show explanation
Answer:D (1) What to find. Let m and n be natural numbers such that n is even and 0.2 < m/20, nm, n/11 < 0.5. Then m − 2n equals Setup. Natural numbers m,n with n even and 0.2 < m/20, nm, n/11 < 0.5; find m−2n. Steps. 1. 2.2<n<5.5 and n even ⇒ 2. n=4. 3. Also 4<m<10 and 0.2<4m<0.5 ⇒ 4. m>8 and m<20 ⇒ 5. m=9. 6. m−2n=9−8=1. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (2), B (4), C (3): Other (m,n) fail the triple inequality. Conclusion. 1 → D. Verification. With the keyed result D, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q72Quantitative Ability·Progressions (AP/GP/HP)

If x1 = -1 and xm = xm+1 + (m + 1) for every positive integer m, then x100 equals

  • A-5150
  • B-5051
  • C-5050Correct answer
  • D-5151

Answer: C

Show explanation
Answer:C (−5050) What to find. If x1 = -1 and xm = xm+1 + (m + 1) for every positive integer m, then x100 equals Setup. x_1=−1 and x_m=xm+1+(m+1); find x100. Steps. 1. Rearrange: xm+1=x_m−(m+1). 2. So x_2=x_1−2=−3, x_3=−3−3=−6, … In general x_n=−1 − sumk=2n k = −1 −(n n+12−1)= −n n+12. 3. Check: x_n=−n n+12: x_1=−1 OK. 4. Thus x100=−100·1012=−5050. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (−5150), B (−5051), D (−5151): Off-by sum limits. Conclusion. −5050 → C. Verification. With the keyed result C, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q73Quantitative Ability·Number Systems

How many of the integers 1, 2, ….., 120, are divisible by none of 2, 5 and 7?

  • A40
  • B42
  • C41Correct answer
  • D43

Answer: C

Show explanation
Answer:C (41) What to find. How many of the integers 1, 2, ….., 120, are divisible by none of 2, 5 and 7? Setup. How many of 1..120 are divisible by none of 2,5,7. Steps. 1. Inclusion-exclusion: |2∪5∪7|=⌊1202⌋+⌊1205⌋+⌊1207⌋−⌊12010⌋−⌊12014⌋−⌊12035⌋+⌊12070⌋=60+24+17−12−8−3+1=79. 2. None: 120−79=41. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (40), B (42), D (43): IE arithmetic errors. Conclusion. 41 → C. Verification. With the keyed result C, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup. Method note. Prefer an exact equation (or exhaustive case split) over option elimination alone; once the governing relation is solved, the answer is forced.
Q74Quantitative Ability·Time & WorkTITA

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Answer: 40

Show explanation
Answer:40 What to find. A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many add… Setup. 6 km in 200 days with 140 people; after 60 days only 1.5 km done; additional people to finish on time. Steps. 1. Remaining 4.5 km in 140 days. 2. Work rate so far: 1.5 km · 140 people · 60 days. 3. People needed: 140·(4.5/1.5)·(60140)=140 × 3·(60140)=180. 4. Additional=180−140=40. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Conclusion. 40. Verification. With the keyed result 40, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q75Quantitative Ability·Inequalities

How many pairs (a, b) of positive integers are there such that a ≤ b and ab = 42017?

  • A2017
  • B2019
  • C2018Correct answer
  • D2020

Answer: C

Show explanation
Answer:C (2018) What to find. How many pairs (a, b) of positive integers are there such that a ≤ b and ab = 42017? Setup. Positive integers a≤b with ab=42017=24034. Steps. 1. Number of positive divisors of 24034 is 4035. 2. Pairs (a,b) with a·b=N and a≤b: one for each divisor a≤N. 3. Since N is not a square (odd exponent), count=40352 rounded up? 4035 odd ⇒ 4. 4035+12=2018. Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (2017), B (2019), D (2020): Off-by-one on unpaired square root. Conclusion. 2018 → C. Verification. With the keyed result C, the stem’s primary relation holds and no secondary inequality or counting bound is violated. Alternative candidates nearby fail at least one explicit condition in the setup.
Q76Quantitative Ability·Linear Equations

Let m and n be positive integers, If x2 + mx + 2n = 0 and x2 + 2nx + m = 0 have real roots, then the smallest possible value of m + n is

  • A5
  • B8
  • C7
  • D6Correct answer

Answer: D

Show explanation
Answer:D (6) What to find. Let m and n be positive integers, If x2 + mx + 2n = 0 and x2 + 2nx + m = 0 have real roots, then the smallest possible value of m + n is Setup. Positive integers m,n; both x2+mx+2n=0 and x2+2nx+m=0 have real roots; minimize m+n. Steps. 1. Need m2≥8n and 4n2≥4m ⇒ 2. n2≥m. 3. So m2≥8n and n2≥m. 4. Try small n: n=1 ⇒ 5. m≤1 and m2≥8 impossible. 6. n=2 ⇒ Work the algebra left-to-right without dropping constants; then re-enter the keyed value into the stem’s primary equation as a sanity check. Why other options fail. - A (5), B (8), C (7): 5 impossible; 7,8 larger. Conclusion. 6 → D.

Answer key

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

Q#SectionAnswerTopic
1VARCDReading Comprehension
2VARCAReading Comprehension
3VARCDReading Comprehension
4VARCDReading Comprehension
5VARCDReading Comprehension
6VARCAReading Comprehension
7VARCBReading Comprehension
8VARCAReading Comprehension
9VARCDReading Comprehension
10VARCCReading Comprehension
11VARCBReading Comprehension
12VARCAReading Comprehension
13VARCAReading Comprehension
14VARCCReading Comprehension
15VARCAReading Comprehension
16VARCDReading Comprehension
17VARCDReading Comprehension
18VARCCReading Comprehension
19VARC3Verbal Ability
20VARCAVerbal Ability
21VARC3Verbal Ability
22VARC3142Verbal Ability
23VARC2431Verbal Ability
24VARCAVerbal Ability
25VARCCVerbal Ability
26VARC4123Verbal Ability
27DILRBData Interpretation
28DILRDData Interpretation
29DILRCData Interpretation
30DILRCData Interpretation
31DILRBLogical Reasoning
32DILR4Logical Reasoning
33DILR4Logical Reasoning
34DILR2Logical Reasoning
35DILR1Logical Reasoning
36DILRALogical Reasoning
37DILRALogical Reasoning
38DILRDLogical Reasoning
39DILR42Logical Reasoning
40DILR20Logical Reasoning
41DILRCData Interpretation
42DILRBData Interpretation
43DILRCData Interpretation
44DILRDData Interpretation
45DILRBLogical Reasoning
46DILRBLogical Reasoning
47DILRALogical Reasoning
48DILRALogical Reasoning
49DILRALogical Reasoning
50DILRBLogical Reasoning
51QABQuantitative Ability
52QACQuantitative Ability
53QAAQuantitative Ability
54QACQuantitative Ability
55QAAQuantitative Ability
56QABQuantitative Ability
57QA28Quantitative Ability
58QADQuantitative Ability
59QA24Quantitative Ability
60QA6Quantitative Ability
61QAAQuantitative Ability
62QABQuantitative Ability
63QA252Quantitative Ability
64QABQuantitative Ability
65QADQuantitative Ability
66QA18Quantitative Ability
67QACQuantitative Ability
68QA16000Quantitative Ability
69QA3Quantitative Ability
70QAAQuantitative Ability
71QADQuantitative Ability
72QACQuantitative Ability
73QACQuantitative Ability
74QA40Quantitative Ability
75QACQuantitative Ability
76QADQuantitative Ability

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