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CAT 2020 Slot 1 answer key with solutions

This is the complete CAT 2020 Slot 1 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·Inference

In the late 1960s, while studying the northern-elephant-seal population along the coasts of Mexico and California, Burney Le Boeuf and his colleagues couldn’t help but notice that the threat calls of males at some sites sounded different from those of males at other sites. . . . That was the first time dialects were documented in a nonhuman mammal. . . . All the northern elephant seals that exist today are descendants of the small herd that survived on Isla Guadalupe after the near extinction of the species in the nineteenth century. As that tiny population grew, northern elephant seals started to recolonize former breeding locations. It was precisely on the more recently colonized islands where Le Boeuf found that the tempos of the male vocal displays showed stronger differences to the ones from Isla Guadalupe, the founder colony. In order to test the reliability of these dialects over time, Le Boeuf and other researchers visited Año Nuevo Island in California —the island where males showed the slowest pulse rates in their calls—every winter from 1968 to 1972. “What we found is that the pulse rate increased, but it still remained relatively slow compared to the other colonies we had measured in the past” Le Boeuf told me. At the individual level, the pulse of the calls stayed the same: A male would maintain his vocal signature throughout his lifetime. But the average pulse rate was changing. Immigration could have been responsible for this increase, as in the early 1970s, 43 percent of the males on Año Nuevo had come from southern rookeries that had a faster pulse rate. This led Le Boeuf and his collaborator, Lewis Petrinovich, to deduce that the dialects were, perhaps, a result of isolation over time, after the breeding sites had been recolonized. For instance, the first settlers of Año Nuevo could have had, by chance, calls with low pulse rates. At other sites, where the scientists found faster pulse rates, the opposite would have happened—seals with faster rates would have happened to arrive first. As the population continued to expand and the islands kept on receiving immigrants from the original population, the calls in all locations would have eventually regressed to the average pulse rate of the founder colony. In the decades that followed, scientists noticed that the geographical variations reported in 1969 were not obvious anymore. . . . In the early 2010s, while studying northern elephant seals on Año Nuevo Island, researcher Caroline Casey noticed, too, that what Le Boeuf had heard decades ago was not what she heard now. . . . By performing more sophisticated statistical analyses on both sets of data, Casey and Le Boeuf confirmed that dialects existed back then but had vanished. Yet there are other differences between the males from the late 1960s and their great-great-grandsons: Modern males exhibit more individual diversity, and their calls are more complex. While 50 years ago the drumming pattern was quite simple and the dialects denoted just a change in tempo, Casey explained, the calls recorded today have more complex structures, sometimes featuring doublets or triplets. . . .

All of the following can be inferred from Le Boeuf’s study as described in the passage EXCEPT that:

  • Amale northern elephant seals might not have exhibited dialects had they not become nearly extinct in the nineteenth century.
  • Bthe average call pulse rate of male northern elephant seals at Año Nuevo Island increased from the early 1970s till the disappearance of dialects.
  • Cchanges in population and migration had no effect on the call pulse rate of individual male northern elephant seals.
  • Dthe influx of new northern elephant seals into Año Nuevo Island would have soon made the call pulse rate of its male seals exceed that of those at Isla Guadalupe..Correct answer

Answer: D

Show explanation
Answer:D The EXCEPT stem asks what cannot be inferred. Dialects arose after near-extinction and founder isolation; Año Nuevo’s average pulse rose toward (but stayed below) faster southern rates as immigrants arrived; individuals kept fixed vocal signatures while population averages moved. Nothing says immigrant influx would push Año Nuevo *past* Isla Guadalupe’s tempo—the text forecasts regression toward the founder average, not overshoot. Why the others fail: • A — Dialects appear on recently recolonised sites after the bottleneck, so the near-extinction/recolonisation story is what made site differences possible. • B — Año Nuevo’s average pulse rose from the late 1960s into later decades until dialects faded, matching the measured increase. • C — Individuals kept their own pulse lifelong; population/migration changed averages, not each male’s signature.
Q2Reading Comprehension·Inference

In the late 1960s, while studying the northern-elephant-seal population along the coasts of Mexico and California, Burney Le Boeuf and his colleagues couldn’t help but notice that the threat calls of males at some sites sounded different from those of males at other sites. . . . That was the first time dialects were documented in a nonhuman mammal. . . . All the northern elephant seals that exist today are descendants of the small herd that survived on Isla Guadalupe after the near extinction of the species in the nineteenth century. As that tiny population grew, northern elephant seals started to recolonize former breeding locations. It was precisely on the more recently colonized islands where Le Boeuf found that the tempos of the male vocal displays showed stronger differences to the ones from Isla Guadalupe, the founder colony. In order to test the reliability of these dialects over time, Le Boeuf and other researchers visited Año Nuevo Island in California —the island where males showed the slowest pulse rates in their calls—every winter from 1968 to 1972. “What we found is that the pulse rate increased, but it still remained relatively slow compared to the other colonies we had measured in the past” Le Boeuf told me. At the individual level, the pulse of the calls stayed the same: A male would maintain his vocal signature throughout his lifetime. But the average pulse rate was changing. Immigration could have been responsible for this increase, as in the early 1970s, 43 percent of the males on Año Nuevo had come from southern rookeries that had a faster pulse rate. This led Le Boeuf and his collaborator, Lewis Petrinovich, to deduce that the dialects were, perhaps, a result of isolation over time, after the breeding sites had been recolonized. For instance, the first settlers of Año Nuevo could have had, by chance, calls with low pulse rates. At other sites, where the scientists found faster pulse rates, the opposite would have happened—seals with faster rates would have happened to arrive first. As the population continued to expand and the islands kept on receiving immigrants from the original population, the calls in all locations would have eventually regressed to the average pulse rate of the founder colony. In the decades that followed, scientists noticed that the geographical variations reported in 1969 were not obvious anymore. . . . In the early 2010s, while studying northern elephant seals on Año Nuevo Island, researcher Caroline Casey noticed, too, that what Le Boeuf had heard decades ago was not what she heard now. . . . By performing more sophisticated statistical analyses on both sets of data, Casey and Le Boeuf confirmed that dialects existed back then but had vanished. Yet there are other differences between the males from the late 1960s and their great-great-grandsons: Modern males exhibit more individual diversity, and their calls are more complex. While 50 years ago the drumming pattern was quite simple and the dialects denoted just a change in tempo, Casey explained, the calls recorded today have more complex structures, sometimes featuring doublets or triplets. . . .

Which one of the following conditions, if true, could have ensured that male northern elephant seal dialects did not disappear?

  • ABesides Isla Guadalupe, there was one more surviving colony with the same average male call tempo from which no migration took place.
  • BThe call tempo of individual immigrant male seals changed to match the average tempo of resident male seals in the host colony.Correct answer
  • CBesides Isla Guadalupe, there was one more founder colony with the same average male call tempo from which male seals migrated to various other colonies.
  • DThe call tempo of individual male seals in host colonies changed to match the average call tempo of immigrant male seals.

Answer: B

Show explanation
Answer:B Dialects vanished because immigrants with different tempos mixed into colonies while each male kept his fixed call, so colony averages converged on the founder tempo. If immigrants instead *adopted* the host colony’s average tempo, mixing would not dilute local dialects—residents and newcomers would share one tempo, preserving geographic difference. Why the others fail: • A — A second non-migrating colony with Guadalupe’s tempo leaves other sites still receiving Guadalupe-origin immigrants that erase *their* dialects. • C — Another founder exporting the same tempo still feeds homogenising migration into recolonised sites. • D — Hosts matching immigrants’ tempos would accelerate erasure of the slow/fast local signatures rather than protect them.
Q3Reading Comprehension·Inference

In the late 1960s, while studying the northern-elephant-seal population along the coasts of Mexico and California, Burney Le Boeuf and his colleagues couldn’t help but notice that the threat calls of males at some sites sounded different from those of males at other sites. . . . That was the first time dialects were documented in a nonhuman mammal. . . . All the northern elephant seals that exist today are descendants of the small herd that survived on Isla Guadalupe after the near extinction of the species in the nineteenth century. As that tiny population grew, northern elephant seals started to recolonize former breeding locations. It was precisely on the more recently colonized islands where Le Boeuf found that the tempos of the male vocal displays showed stronger differences to the ones from Isla Guadalupe, the founder colony. In order to test the reliability of these dialects over time, Le Boeuf and other researchers visited Año Nuevo Island in California —the island where males showed the slowest pulse rates in their calls—every winter from 1968 to 1972. “What we found is that the pulse rate increased, but it still remained relatively slow compared to the other colonies we had measured in the past” Le Boeuf told me. At the individual level, the pulse of the calls stayed the same: A male would maintain his vocal signature throughout his lifetime. But the average pulse rate was changing. Immigration could have been responsible for this increase, as in the early 1970s, 43 percent of the males on Año Nuevo had come from southern rookeries that had a faster pulse rate. This led Le Boeuf and his collaborator, Lewis Petrinovich, to deduce that the dialects were, perhaps, a result of isolation over time, after the breeding sites had been recolonized. For instance, the first settlers of Año Nuevo could have had, by chance, calls with low pulse rates. At other sites, where the scientists found faster pulse rates, the opposite would have happened—seals with faster rates would have happened to arrive first. As the population continued to expand and the islands kept on receiving immigrants from the original population, the calls in all locations would have eventually regressed to the average pulse rate of the founder colony. In the decades that followed, scientists noticed that the geographical variations reported in 1969 were not obvious anymore. . . . In the early 2010s, while studying northern elephant seals on Año Nuevo Island, researcher Caroline Casey noticed, too, that what Le Boeuf had heard decades ago was not what she heard now. . . . By performing more sophisticated statistical analyses on both sets of data, Casey and Le Boeuf confirmed that dialects existed back then but had vanished. Yet there are other differences between the males from the late 1960s and their great-great-grandsons: Modern males exhibit more individual diversity, and their calls are more complex. While 50 years ago the drumming pattern was quite simple and the dialects denoted just a change in tempo, Casey explained, the calls recorded today have more complex structures, sometimes featuring doublets or triplets. . . .

Which one of the following best sums up the overall history of transformation of male northern elephant seal calls?

  • AThe calls have transformed from exhibiting simple composition, less individual variety, and great regional variety to complex composition, great individual variety, and less regional variety.Correct answer
  • BOwing to migrations in the aftermath of near species extinction, the calls have transformed from exhibiting complex composition, less individual variety, and great regional variety to simple composition, less individual variety, and great regional variety.
  • CThe calls have transformed from exhibiting simple composition, great individual variety, and less regional variety to complex composition, less individual variety, and great regional variety.
  • DOwing to migrations in the aftermath of near species extinction, the average call pulse rates in the recolonised breeding locations exhibited a gradual increase until they matched the tempo at the founding colony.

Answer: A

Show explanation
Answer:A Then: simple drumming, mainly tempo dialects (high regional difference), limited individual complexity. Now: dialects gone (low regional variety), calls more complex with doublets/triplets, and greater individual diversity. A alone tracks that three-axis shift. Why the others fail: • B — Reverses complexity (simple→complex, not complex→simple) and keeps “great regional variety,” which disappeared. • C — Swaps individual variety (then low, now high) and regional variety (then high, now low). • D — Only narrates pulse rates rising toward the founder mean; it omits the complexity/individual-diversity change and wrongly implies a one-way increase at every site.
Q4Reading Comprehension·Inference

In the late 1960s, while studying the northern-elephant-seal population along the coasts of Mexico and California, Burney Le Boeuf and his colleagues couldn’t help but notice that the threat calls of males at some sites sounded different from those of males at other sites. . . . That was the first time dialects were documented in a nonhuman mammal. . . . All the northern elephant seals that exist today are descendants of the small herd that survived on Isla Guadalupe after the near extinction of the species in the nineteenth century. As that tiny population grew, northern elephant seals started to recolonize former breeding locations. It was precisely on the more recently colonized islands where Le Boeuf found that the tempos of the male vocal displays showed stronger differences to the ones from Isla Guadalupe, the founder colony. In order to test the reliability of these dialects over time, Le Boeuf and other researchers visited Año Nuevo Island in California —the island where males showed the slowest pulse rates in their calls—every winter from 1968 to 1972. “What we found is that the pulse rate increased, but it still remained relatively slow compared to the other colonies we had measured in the past” Le Boeuf told me. At the individual level, the pulse of the calls stayed the same: A male would maintain his vocal signature throughout his lifetime. But the average pulse rate was changing. Immigration could have been responsible for this increase, as in the early 1970s, 43 percent of the males on Año Nuevo had come from southern rookeries that had a faster pulse rate. This led Le Boeuf and his collaborator, Lewis Petrinovich, to deduce that the dialects were, perhaps, a result of isolation over time, after the breeding sites had been recolonized. For instance, the first settlers of Año Nuevo could have had, by chance, calls with low pulse rates. At other sites, where the scientists found faster pulse rates, the opposite would have happened—seals with faster rates would have happened to arrive first. As the population continued to expand and the islands kept on receiving immigrants from the original population, the calls in all locations would have eventually regressed to the average pulse rate of the founder colony. In the decades that followed, scientists noticed that the geographical variations reported in 1969 were not obvious anymore. . . . In the early 2010s, while studying northern elephant seals on Año Nuevo Island, researcher Caroline Casey noticed, too, that what Le Boeuf had heard decades ago was not what she heard now. . . . By performing more sophisticated statistical analyses on both sets of data, Casey and Le Boeuf confirmed that dialects existed back then but had vanished. Yet there are other differences between the males from the late 1960s and their great-great-grandsons: Modern males exhibit more individual diversity, and their calls are more complex. While 50 years ago the drumming pattern was quite simple and the dialects denoted just a change in tempo, Casey explained, the calls recorded today have more complex structures, sometimes featuring doublets or triplets. . . .

From the passage it can be inferred that the call pulse rate of male northern elephant seals in the southern rookeries was faster because:

  • Aa large number of male northern elephant seals migrated from the southern rookeries to Año Nuevo Island in the early 1970s
  • Ba large number of male northern elephant seals from Año Nuevo Island might have migrated to the southern rookeries to recolonise them.
  • Cthe male northern elephant seals of Isla Guadalupe with faster call pulse rates might have been the original settlers of the southern rookeries.Correct answer
  • Dthe calls of male northern elephant seals in the southern rookeries have more sophisticated structures, containing doublets and triplets.

Answer: C

Show explanation
Answer:C Le Boeuf’s model: chance first settlers set a site’s tempo—slow settlers at Año Nuevo, faster ones elsewhere. Southern rookeries had faster pulses, so their original Guadalupe-origin settlers were likely the faster-calling males. Why the others fail: • A — Migration *from* south *to* Año Nuevo explains Año Nuevo’s rising average, not why the south itself was fast. • B — Reverse migration from Año Nuevo would export slow tempos, the opposite of a fast southern dialect. • D — Doublets/triplets describe modern calls after dialects vanished, not the southern rookeries’ historical tempo.
Q5Reading Comprehension·Inference

Vocabulary used in speech or writing organizes itself in seven parts of speech (eight, if you count interjections such as Oh! and Gosh! and Fuhgeddaboudit!). Communication composed of these parts of speech must be organized by rules of grammar upon which we agree. When these rules break down, confusion and misunderstanding result. Bad grammar produces bad sentences. My favorite example from Strunk and White is this one: “As a mother of five, with another one on the way, my ironing board is always up.” Nouns and verbs are the two indispensable parts of writing. Without one of each, no group of words can be a sentence, since a sentence is, by definition, a group of words containing a subject (noun) and a predicate (verb); these strings of words begin with a capital letter, end with a period, and combine to make a complete thought which starts in the writer’s head and then leaps to the reader’s. Must you write complete sentences each time, every time? Perish the thought. If your work consists only of fragments and floating clauses, the Grammar Police aren’t going to come and take you away. Even William Strunk, that Mussolini of rhetoric, recognized the delicious pliability of language. “It is an old observation,” he writes, “that the best writers sometimes disregard the rules of rhetoric.” Yet he goes on to add this thought, which I urge you to consider: “Unless he is certain of doing well, the writer will probably do best to follow the rules.” The telling clause here is Unless he is certain of doing well. If you don’t have a rudimentary grasp of how the parts of speech translate into coherent sentences, how can you be certain that you are doing well? How will you know if you’re doing ill, for that matter? The answer, of course, is that you can’t, you won’t. One who does grasp the rudiments of grammar finds a comforting simplicity at its heart, where there need be only nouns, the words that name, and verbs, the words that act. Take any noun, put it with any verb, and you have a sentence. It never fails. Rocks explode. Jane transmits. Mountains float. These are all perfect sentences. Many such thoughts make little rational sense, but even the stranger ones (Plums deify!) have a kind of poetic weight that’s nice. The simplicity of noun-verb construction is useful—at the very least it can provide a safety net for your writing. Strunk and White caution against too many simple sentences in a row, but simple sentences provide a path you can follow when you fear getting lost in the tangles of rhetoric—all those restrictive and nonrestrictive clauses, those modifying phrases, those appositives and compound-complex sentences. If you start to freak out at the sight of such unmapped territory (unmapped by you, at least), just remind yourself that rocks explode, Jane transmits, mountains float, and plums deify. Grammar is . . . the pole you grab to get your thoughts up on their feet and walking.

Which one of the following statements, if false, could be seen as supporting the arguments in the passage?

  • AAn understanding of grammar helps a writer decide if she/he is writing well or not.
  • BRegarding grammar, women writers tend to be more attentive to method and accuracy.
  • CIt has been observed that writers sometimes disregard the rules of rhetoric.
  • DPerish the thought that complete sentences necessarily need nouns and verbs!Correct answer

Answer: D

Show explanation
Answer:D The stem wants the statement that, *if false*, supports the passage. The author insists nouns and verbs are indispensable to a sentence. Treating “complete sentences need not have nouns and verbs” as false affirms that requirement—so D-false backs the argument. Why the others fail: • A — The text already ties grammar grasp to knowing whether one writes well; calling A false undercuts that claim. • B — Gendered attentiveness is never discussed; falsifying an alien claim does not support the essay. • C — Strunk’s point that good writers sometimes break rhetoric rules is endorsed; falsifying C fights the passage.
Q6Reading Comprehension·Inference

Vocabulary used in speech or writing organizes itself in seven parts of speech (eight, if you count interjections such as Oh! and Gosh! and Fuhgeddaboudit!). Communication composed of these parts of speech must be organized by rules of grammar upon which we agree. When these rules break down, confusion and misunderstanding result. Bad grammar produces bad sentences. My favorite example from Strunk and White is this one: “As a mother of five, with another one on the way, my ironing board is always up.” Nouns and verbs are the two indispensable parts of writing. Without one of each, no group of words can be a sentence, since a sentence is, by definition, a group of words containing a subject (noun) and a predicate (verb); these strings of words begin with a capital letter, end with a period, and combine to make a complete thought which starts in the writer’s head and then leaps to the reader’s. Must you write complete sentences each time, every time? Perish the thought. If your work consists only of fragments and floating clauses, the Grammar Police aren’t going to come and take you away. Even William Strunk, that Mussolini of rhetoric, recognized the delicious pliability of language. “It is an old observation,” he writes, “that the best writers sometimes disregard the rules of rhetoric.” Yet he goes on to add this thought, which I urge you to consider: “Unless he is certain of doing well, the writer will probably do best to follow the rules.” The telling clause here is Unless he is certain of doing well. If you don’t have a rudimentary grasp of how the parts of speech translate into coherent sentences, how can you be certain that you are doing well? How will you know if you’re doing ill, for that matter? The answer, of course, is that you can’t, you won’t. One who does grasp the rudiments of grammar finds a comforting simplicity at its heart, where there need be only nouns, the words that name, and verbs, the words that act. Take any noun, put it with any verb, and you have a sentence. It never fails. Rocks explode. Jane transmits. Mountains float. These are all perfect sentences. Many such thoughts make little rational sense, but even the stranger ones (Plums deify!) have a kind of poetic weight that’s nice. The simplicity of noun-verb construction is useful—at the very least it can provide a safety net for your writing. Strunk and White caution against too many simple sentences in a row, but simple sentences provide a path you can follow when you fear getting lost in the tangles of rhetoric—all those restrictive and nonrestrictive clauses, those modifying phrases, those appositives and compound-complex sentences. If you start to freak out at the sight of such unmapped territory (unmapped by you, at least), just remind yourself that rocks explode, Jane transmits, mountains float, and plums deify. Grammar is . . . the pole you grab to get your thoughts up on their feet and walking.

“Take any noun, put it with any verb, and you have a sentence. It never fails. Rocks explode. Jane transmits. Mountains float.” None of the following statements can be seen as similar EXCEPT:

  • AA collection of people with the same sports equipment is a sports team.
  • BTake any vegetable, put some spices in it, and you have a dish.Correct answer
  • CA group of nouns arranged in a row becomes a sentence.
  • DTake an apple tree, plant it in a field, and you have an orchard

Answer: B

Show explanation
Answer:B The quote’s logic is: take any X, add any Y of the needed second kind, and you automatically have a Z. Only B mirrors that two-ingredient recipe (any vegetable + spices → a dish). Why the others fail: • A — Same equipment does not make a team; the analogy lacks the “any X + any Y → Z” generative rule. • C — Nouns alone omit the verb half of the author’s formula. • D — One tree in a field is not an orchard; the leap fails the “never fails” sufficiency claim.
Q7Reading Comprehension·Inference

Vocabulary used in speech or writing organizes itself in seven parts of speech (eight, if you count interjections such as Oh! and Gosh! and Fuhgeddaboudit!). Communication composed of these parts of speech must be organized by rules of grammar upon which we agree. When these rules break down, confusion and misunderstanding result. Bad grammar produces bad sentences. My favorite example from Strunk and White is this one: “As a mother of five, with another one on the way, my ironing board is always up.” Nouns and verbs are the two indispensable parts of writing. Without one of each, no group of words can be a sentence, since a sentence is, by definition, a group of words containing a subject (noun) and a predicate (verb); these strings of words begin with a capital letter, end with a period, and combine to make a complete thought which starts in the writer’s head and then leaps to the reader’s. Must you write complete sentences each time, every time? Perish the thought. If your work consists only of fragments and floating clauses, the Grammar Police aren’t going to come and take you away. Even William Strunk, that Mussolini of rhetoric, recognized the delicious pliability of language. “It is an old observation,” he writes, “that the best writers sometimes disregard the rules of rhetoric.” Yet he goes on to add this thought, which I urge you to consider: “Unless he is certain of doing well, the writer will probably do best to follow the rules.” The telling clause here is Unless he is certain of doing well. If you don’t have a rudimentary grasp of how the parts of speech translate into coherent sentences, how can you be certain that you are doing well? How will you know if you’re doing ill, for that matter? The answer, of course, is that you can’t, you won’t. One who does grasp the rudiments of grammar finds a comforting simplicity at its heart, where there need be only nouns, the words that name, and verbs, the words that act. Take any noun, put it with any verb, and you have a sentence. It never fails. Rocks explode. Jane transmits. Mountains float. These are all perfect sentences. Many such thoughts make little rational sense, but even the stranger ones (Plums deify!) have a kind of poetic weight that’s nice. The simplicity of noun-verb construction is useful—at the very least it can provide a safety net for your writing. Strunk and White caution against too many simple sentences in a row, but simple sentences provide a path you can follow when you fear getting lost in the tangles of rhetoric—all those restrictive and nonrestrictive clauses, those modifying phrases, those appositives and compound-complex sentences. If you start to freak out at the sight of such unmapped territory (unmapped by you, at least), just remind yourself that rocks explode, Jane transmits, mountains float, and plums deify. Grammar is . . . the pole you grab to get your thoughts up on their feet and walking.

Inferring from the passage, the author could be most supportive of which one of the following practices?

  • AThe availability of language software that will standardise the rules of grammar as an aid to writersCorrect answer
  • BA campaign demanding that a writer’s creative license should allow the breaking of grammatical rules.
  • CA Creative Writing course that focuses on how to avoid the use of rhetoric.
  • DThe critique of standardised rules of punctuation and capitalisation.

Answer: A

Show explanation
Answer:A The author wants writers to know the rules so they can judge when bending them is safe. Standardising grammar as a practical aid fits that “learn the rudiments first” stance. Why the others fail: • B — Blanket licence to break rules without certainty of doing well is what Strunk warns against. • C — Avoiding rhetoric entirely misses the point: rhetoric is usable once grammar anchors you. • D — Attacking punctuation/capital norms contradicts the essay’s defence of shared grammatical order.
Q8Reading Comprehension·Inference

Vocabulary used in speech or writing organizes itself in seven parts of speech (eight, if you count interjections such as Oh! and Gosh! and Fuhgeddaboudit!). Communication composed of these parts of speech must be organized by rules of grammar upon which we agree. When these rules break down, confusion and misunderstanding result. Bad grammar produces bad sentences. My favorite example from Strunk and White is this one: “As a mother of five, with another one on the way, my ironing board is always up.” Nouns and verbs are the two indispensable parts of writing. Without one of each, no group of words can be a sentence, since a sentence is, by definition, a group of words containing a subject (noun) and a predicate (verb); these strings of words begin with a capital letter, end with a period, and combine to make a complete thought which starts in the writer’s head and then leaps to the reader’s. Must you write complete sentences each time, every time? Perish the thought. If your work consists only of fragments and floating clauses, the Grammar Police aren’t going to come and take you away. Even William Strunk, that Mussolini of rhetoric, recognized the delicious pliability of language. “It is an old observation,” he writes, “that the best writers sometimes disregard the rules of rhetoric.” Yet he goes on to add this thought, which I urge you to consider: “Unless he is certain of doing well, the writer will probably do best to follow the rules.” The telling clause here is Unless he is certain of doing well. If you don’t have a rudimentary grasp of how the parts of speech translate into coherent sentences, how can you be certain that you are doing well? How will you know if you’re doing ill, for that matter? The answer, of course, is that you can’t, you won’t. One who does grasp the rudiments of grammar finds a comforting simplicity at its heart, where there need be only nouns, the words that name, and verbs, the words that act. Take any noun, put it with any verb, and you have a sentence. It never fails. Rocks explode. Jane transmits. Mountains float. These are all perfect sentences. Many such thoughts make little rational sense, but even the stranger ones (Plums deify!) have a kind of poetic weight that’s nice. The simplicity of noun-verb construction is useful—at the very least it can provide a safety net for your writing. Strunk and White caution against too many simple sentences in a row, but simple sentences provide a path you can follow when you fear getting lost in the tangles of rhetoric—all those restrictive and nonrestrictive clauses, those modifying phrases, those appositives and compound-complex sentences. If you start to freak out at the sight of such unmapped territory (unmapped by you, at least), just remind yourself that rocks explode, Jane transmits, mountains float, and plums deify. Grammar is . . . the pole you grab to get your thoughts up on their feet and walking.

All of the following statements can be inferred from the passage EXCEPT that:

  • A“Grammar Police” is a metaphor for critics who focus on linguistic rules.
  • Bsentences do not always have to be complete.
  • Cthe subject–predicate relation is the same as the noun–verb relation.
  • Dthe primary purpose of grammar is to ensure that sentences remain simple.Correct answer

Answer: D

Show explanation
Answer:D Grammar is a pole for coherent thought—nouns naming, verbs acting—and a safety net, not a mandate that sentences stay simple. Strunk even cautions against *too many* simple sentences. So “primary purpose = keep sentences simple” is not inferable. Why the others fail: • A — “Grammar Police” is clearly figurative for rule-obsessed critics. • B — The author explicitly allows incomplete sentences (“Perish the thought”). • C — Subject/predicate is equated with noun/verb as the sentence’s core pair.
Q9Reading Comprehension·Inference

Vocabulary used in speech or writing organizes itself in seven parts of speech (eight, if you count interjections such as Oh! and Gosh! and Fuhgeddaboudit!). Communication composed of these parts of speech must be organized by rules of grammar upon which we agree. When these rules break down, confusion and misunderstanding result. Bad grammar produces bad sentences. My favorite example from Strunk and White is this one: “As a mother of five, with another one on the way, my ironing board is always up.” Nouns and verbs are the two indispensable parts of writing. Without one of each, no group of words can be a sentence, since a sentence is, by definition, a group of words containing a subject (noun) and a predicate (verb); these strings of words begin with a capital letter, end with a period, and combine to make a complete thought which starts in the writer’s head and then leaps to the reader’s. Must you write complete sentences each time, every time? Perish the thought. If your work consists only of fragments and floating clauses, the Grammar Police aren’t going to come and take you away. Even William Strunk, that Mussolini of rhetoric, recognized the delicious pliability of language. “It is an old observation,” he writes, “that the best writers sometimes disregard the rules of rhetoric.” Yet he goes on to add this thought, which I urge you to consider: “Unless he is certain of doing well, the writer will probably do best to follow the rules.” The telling clause here is Unless he is certain of doing well. If you don’t have a rudimentary grasp of how the parts of speech translate into coherent sentences, how can you be certain that you are doing well? How will you know if you’re doing ill, for that matter? The answer, of course, is that you can’t, you won’t. One who does grasp the rudiments of grammar finds a comforting simplicity at its heart, where there need be only nouns, the words that name, and verbs, the words that act. Take any noun, put it with any verb, and you have a sentence. It never fails. Rocks explode. Jane transmits. Mountains float. These are all perfect sentences. Many such thoughts make little rational sense, but even the stranger ones (Plums deify!) have a kind of poetic weight that’s nice. The simplicity of noun-verb construction is useful—at the very least it can provide a safety net for your writing. Strunk and White caution against too many simple sentences in a row, but simple sentences provide a path you can follow when you fear getting lost in the tangles of rhetoric—all those restrictive and nonrestrictive clauses, those modifying phrases, those appositives and compound-complex sentences. If you start to freak out at the sight of such unmapped territory (unmapped by you, at least), just remind yourself that rocks explode, Jane transmits, mountains float, and plums deify. Grammar is . . . the pole you grab to get your thoughts up on their feet and walking.

Which one of the following quotes best captures the main concern of the passage?

  • A“Nouns and verbs are the two indispensable parts of writing. Without one of each, no group of words can be a sentence . ..”
  • B“Strunk and White caution against too many simple sentences in a row, but simple sentences provide a path you can follow when you fear getting lost in the tangles of rhetoric . . .”
  • C“Bad grammar produces bad sentences.”Correct answer
  • D“The telling clause here is Unless he is certain of doing well.”.

Answer: C

Show explanation
Answer:C The essay opens from agreed grammar rules, bad grammar, and confusion, then develops how mastering noun–verb basics prevents bad writing. “Bad grammar produces bad sentences” is the governing worry. Why the others fail: • A — Noun–verb necessity is a building block, not the whole concern. • B — Simple sentences as a path through rhetoric is a local tip, not the thesis. • D — “Unless he is certain of doing well” is one Strunk caveat inside a larger grammar argument.
Q10Reading Comprehension·Specific Detail

The word ‘anarchy’ comes from the Greek anarkhia, meaning contrary to authority or without a ruler, and was used in a derogatory sense until 1840, when it was adopted by Pierre-Joseph Proudhon to describe his political and social ideology. Proudhon argued that organization without government was both possible and desirable. In the evolution of political ideas, anarchism can be seen as an ultimate projection of both liberalism and socialism, and the differing strands of anarchist thought can be related to their emphasis on one or the other of these. Historically, anarchism arose not only as an explanation of the gulf between the rich and the poor in any community, and of the reason why the poor have been obliged to fight for their share of a common inheritance, but as a radical answer to the question ‘What went wrong?’ that followed the ultimate outcome of the French Revolution. It had ended not only with a reign of terror and the emergence of a newly rich ruling caste, but with a new adored emperor, Napoleon Bonaparte, strutting through his conquered territories. The anarchists and their precursors were unique on the political Left in affirming that workers and peasants, grasping the chance that arose to bring an end to centuries of exploitation and tyranny, were inevitably betrayed by the new class of politicians, whose first priority was to reestablish a centralized state power. After every revolutionary uprising, usually won at a heavy cost for ordinary populations, the new rulers had no hesitation in applying violence and terror, a secret police, and a professional army to maintain their control. For anarchists the state itself is the enemy, and they have applied the same interpretation to the outcome of every revolution of the 19th and 20th centuries. This is not merely because every state keeps a watchful and sometimes punitive eye on its dissidents, but because every state protects the privileges of the powerful. The mainstream of anarchist propaganda for more than a century has been anarchistcommunism, which argues that property in land, natural resources, and the means of production should be held in mutual control by local communities, federating for innumerable joint purposes with other communes. It differs from state socialism in opposing the concept of any central authority. Some anarchists prefer to distinguish between anarchist-communism and collectivist anarchism in order to stress the obviously desirable freedom of an individual or family to possess the resources needed for living, while not implying the right to own the resources needed by others. . . . There are, unsurprisingly, several traditions of individualist anarchism, one of them deriving from the ‘conscious egoism’ of the German writer Max Stirner (1806–56), and another from a remarkable series of 19th-century American figures who argued that in protecting our own autonomy and associating with others for common advantages, we are promoting the good of all. These thinkers differed from free-market liberals in their absolute mistrust of American capitalism, and in their emphasis on mutualism.

According to the passage, what is the one idea that is common to all forms of anarchism?

  • AThey all focus on the primacy of the power of the individual.
  • BThey all derive from the work of Pierre-Joseph Proudhon.
  • CThere is no idea common to all forms of anarchism; that is why it is anarchic.
  • DThey are all opposed to the centralisation of power in the state.Correct answer

Answer: D

Show explanation
Answer:D Across traditions, anarchism’s shared core is opposition to the state’s concentrated coercive power; individualist streams still define themselves against centralised state authority. Why the others fail: • A — Collectivist anarchisms do not treat individual power as primary; the passage distinguishes streams. • B — Proudhon is one lineage, not the source of all forms. • C — Denying any common idea contradicts the author’s effort to name shared opposition to the state.
Q11Reading Comprehension·Specific Detail

The word ‘anarchy’ comes from the Greek anarkhia, meaning contrary to authority or without a ruler, and was used in a derogatory sense until 1840, when it was adopted by Pierre-Joseph Proudhon to describe his political and social ideology. Proudhon argued that organization without government was both possible and desirable. In the evolution of political ideas, anarchism can be seen as an ultimate projection of both liberalism and socialism, and the differing strands of anarchist thought can be related to their emphasis on one or the other of these. Historically, anarchism arose not only as an explanation of the gulf between the rich and the poor in any community, and of the reason why the poor have been obliged to fight for their share of a common inheritance, but as a radical answer to the question ‘What went wrong?’ that followed the ultimate outcome of the French Revolution. It had ended not only with a reign of terror and the emergence of a newly rich ruling caste, but with a new adored emperor, Napoleon Bonaparte, strutting through his conquered territories. The anarchists and their precursors were unique on the political Left in affirming that workers and peasants, grasping the chance that arose to bring an end to centuries of exploitation and tyranny, were inevitably betrayed by the new class of politicians, whose first priority was to reestablish a centralized state power. After every revolutionary uprising, usually won at a heavy cost for ordinary populations, the new rulers had no hesitation in applying violence and terror, a secret police, and a professional army to maintain their control. For anarchists the state itself is the enemy, and they have applied the same interpretation to the outcome of every revolution of the 19th and 20th centuries. This is not merely because every state keeps a watchful and sometimes punitive eye on its dissidents, but because every state protects the privileges of the powerful. The mainstream of anarchist propaganda for more than a century has been anarchistcommunism, which argues that property in land, natural resources, and the means of production should be held in mutual control by local communities, federating for innumerable joint purposes with other communes. It differs from state socialism in opposing the concept of any central authority. Some anarchists prefer to distinguish between anarchist-communism and collectivist anarchism in order to stress the obviously desirable freedom of an individual or family to possess the resources needed for living, while not implying the right to own the resources needed by others. . . . There are, unsurprisingly, several traditions of individualist anarchism, one of them deriving from the ‘conscious egoism’ of the German writer Max Stirner (1806–56), and another from a remarkable series of 19th-century American figures who argued that in protecting our own autonomy and associating with others for common advantages, we are promoting the good of all. These thinkers differed from free-market liberals in their absolute mistrust of American capitalism, and in their emphasis on mutualism.

Of the following sets of concepts, identify the set that is conceptually closest to the concerns of the passage.

  • ARevolution, State, Protection, Liberals.
  • BAnarchism, Betrayal, Power, State.
  • CRevolution, State, Strike, Egoism.
  • DAnarchism, State, Individual, Freedom.Correct answer

Answer: D

Show explanation
Answer:D The passage maps anarchism’s critique of the state, defence of individual autonomy, and freedom from centralised power. That quartet is the tightest conceptual set. Why the others fail: • A — Liberals/protection dilute the anarchist focus; revolution is only historical backdrop. • B — “Betrayal” is specific to the French Revolution vignette, not the whole frame. • C — Strike and egoism are narrow strands, not the passage’s centre of gravity.
Q12Reading Comprehension·Inference

The word ‘anarchy’ comes from the Greek anarkhia, meaning contrary to authority or without a ruler, and was used in a derogatory sense until 1840, when it was adopted by Pierre-Joseph Proudhon to describe his political and social ideology. Proudhon argued that organization without government was both possible and desirable. In the evolution of political ideas, anarchism can be seen as an ultimate projection of both liberalism and socialism, and the differing strands of anarchist thought can be related to their emphasis on one or the other of these. Historically, anarchism arose not only as an explanation of the gulf between the rich and the poor in any community, and of the reason why the poor have been obliged to fight for their share of a common inheritance, but as a radical answer to the question ‘What went wrong?’ that followed the ultimate outcome of the French Revolution. It had ended not only with a reign of terror and the emergence of a newly rich ruling caste, but with a new adored emperor, Napoleon Bonaparte, strutting through his conquered territories. The anarchists and their precursors were unique on the political Left in affirming that workers and peasants, grasping the chance that arose to bring an end to centuries of exploitation and tyranny, were inevitably betrayed by the new class of politicians, whose first priority was to reestablish a centralized state power. After every revolutionary uprising, usually won at a heavy cost for ordinary populations, the new rulers had no hesitation in applying violence and terror, a secret police, and a professional army to maintain their control. For anarchists the state itself is the enemy, and they have applied the same interpretation to the outcome of every revolution of the 19th and 20th centuries. This is not merely because every state keeps a watchful and sometimes punitive eye on its dissidents, but because every state protects the privileges of the powerful. The mainstream of anarchist propaganda for more than a century has been anarchistcommunism, which argues that property in land, natural resources, and the means of production should be held in mutual control by local communities, federating for innumerable joint purposes with other communes. It differs from state socialism in opposing the concept of any central authority. Some anarchists prefer to distinguish between anarchist-communism and collectivist anarchism in order to stress the obviously desirable freedom of an individual or family to possess the resources needed for living, while not implying the right to own the resources needed by others. . . . There are, unsurprisingly, several traditions of individualist anarchism, one of them deriving from the ‘conscious egoism’ of the German writer Max Stirner (1806–56), and another from a remarkable series of 19th-century American figures who argued that in protecting our own autonomy and associating with others for common advantages, we are promoting the good of all. These thinkers differed from free-market liberals in their absolute mistrust of American capitalism, and in their emphasis on mutualism.

Which one of the following best expresses the similarity between American individualist anarchists and free-market liberals as well as the difference between the former and the latter?

  • ABoth prioritise individual autonomy; but the former also emphasise mutual dependence, while the latter do not do so.Correct answer
  • BBoth reject the regulatory power of the state; but the former favour a people’s state, while the latter favour state intervention in markets.
  • CBoth are sophisticated arguments for capitalism; but the former argue for a morally upright capitalism, while the latter argue that the market is the only morality.
  • DBoth are founded on the moral principles of altruism; but the latter conceive of the market as a force too mystical for the former to comprehend.

Answer: A

Show explanation
Answer:A Both camps prize individual autonomy, but American individualist anarchists couple that with mutualism and deep mistrust of capitalism, whereas free-market liberals do not emphasise mutual dependence that way. Why the others fail: • B — Anarchists do not favour a “people’s state”; liberals are not defined here as pro-intervention. • C — Individualist anarchists are not cast as arguing for capitalism. • D — Altruism is not their shared moral base; mutualism ≠ mystical market worship.
Q13Reading Comprehension·Specific Detail

The word ‘anarchy’ comes from the Greek anarkhia, meaning contrary to authority or without a ruler, and was used in a derogatory sense until 1840, when it was adopted by Pierre-Joseph Proudhon to describe his political and social ideology. Proudhon argued that organization without government was both possible and desirable. In the evolution of political ideas, anarchism can be seen as an ultimate projection of both liberalism and socialism, and the differing strands of anarchist thought can be related to their emphasis on one or the other of these. Historically, anarchism arose not only as an explanation of the gulf between the rich and the poor in any community, and of the reason why the poor have been obliged to fight for their share of a common inheritance, but as a radical answer to the question ‘What went wrong?’ that followed the ultimate outcome of the French Revolution. It had ended not only with a reign of terror and the emergence of a newly rich ruling caste, but with a new adored emperor, Napoleon Bonaparte, strutting through his conquered territories. The anarchists and their precursors were unique on the political Left in affirming that workers and peasants, grasping the chance that arose to bring an end to centuries of exploitation and tyranny, were inevitably betrayed by the new class of politicians, whose first priority was to reestablish a centralized state power. After every revolutionary uprising, usually won at a heavy cost for ordinary populations, the new rulers had no hesitation in applying violence and terror, a secret police, and a professional army to maintain their control. For anarchists the state itself is the enemy, and they have applied the same interpretation to the outcome of every revolution of the 19th and 20th centuries. This is not merely because every state keeps a watchful and sometimes punitive eye on its dissidents, but because every state protects the privileges of the powerful. The mainstream of anarchist propaganda for more than a century has been anarchistcommunism, which argues that property in land, natural resources, and the means of production should be held in mutual control by local communities, federating for innumerable joint purposes with other communes. It differs from state socialism in opposing the concept of any central authority. Some anarchists prefer to distinguish between anarchist-communism and collectivist anarchism in order to stress the obviously desirable freedom of an individual or family to possess the resources needed for living, while not implying the right to own the resources needed by others. . . . There are, unsurprisingly, several traditions of individualist anarchism, one of them deriving from the ‘conscious egoism’ of the German writer Max Stirner (1806–56), and another from a remarkable series of 19th-century American figures who argued that in protecting our own autonomy and associating with others for common advantages, we are promoting the good of all. These thinkers differed from free-market liberals in their absolute mistrust of American capitalism, and in their emphasis on mutualism.

The author makes all of the following arguments in the passage, EXCEPT:

  • AThe failure of the French Revolution was because of its betrayal by the new class of politicians who emerged from it.
  • BIndividualist anarchism is actually constituted of many streams, all of which focus on the autonomy of the individual.
  • CThe popular perception of anarchism as espousing lawlessness and violence comes from a mainstream mistrust of collectivism.Correct answer
  • DFor anarchists, the state is the enemy because all states apply violence and terror to maintain their control.

Answer: C

Show explanation
Answer:C The stereotype of anarchism as lawless violence is tied to fear of disorder and misunderstanding of anti-state politics—not to mainstream mistrust of *collectivism*. C invents that causal story. Why the others fail: • A — New politicians betraying revolutionary principles is stated. • B — Multiple individualist streams united by autonomy are described. • D — The state as enemy because it uses violence/terror to rule is the anarchist charge given.
Q14Reading Comprehension·Specific Detail

The word ‘anarchy’ comes from the Greek anarkhia, meaning contrary to authority or without a ruler, and was used in a derogatory sense until 1840, when it was adopted by Pierre-Joseph Proudhon to describe his political and social ideology. Proudhon argued that organization without government was both possible and desirable. In the evolution of political ideas, anarchism can be seen as an ultimate projection of both liberalism and socialism, and the differing strands of anarchist thought can be related to their emphasis on one or the other of these. Historically, anarchism arose not only as an explanation of the gulf between the rich and the poor in any community, and of the reason why the poor have been obliged to fight for their share of a common inheritance, but as a radical answer to the question ‘What went wrong?’ that followed the ultimate outcome of the French Revolution. It had ended not only with a reign of terror and the emergence of a newly rich ruling caste, but with a new adored emperor, Napoleon Bonaparte, strutting through his conquered territories. The anarchists and their precursors were unique on the political Left in affirming that workers and peasants, grasping the chance that arose to bring an end to centuries of exploitation and tyranny, were inevitably betrayed by the new class of politicians, whose first priority was to reestablish a centralized state power. After every revolutionary uprising, usually won at a heavy cost for ordinary populations, the new rulers had no hesitation in applying violence and terror, a secret police, and a professional army to maintain their control. For anarchists the state itself is the enemy, and they have applied the same interpretation to the outcome of every revolution of the 19th and 20th centuries. This is not merely because every state keeps a watchful and sometimes punitive eye on its dissidents, but because every state protects the privileges of the powerful. The mainstream of anarchist propaganda for more than a century has been anarchistcommunism, which argues that property in land, natural resources, and the means of production should be held in mutual control by local communities, federating for innumerable joint purposes with other communes. It differs from state socialism in opposing the concept of any central authority. Some anarchists prefer to distinguish between anarchist-communism and collectivist anarchism in order to stress the obviously desirable freedom of an individual or family to possess the resources needed for living, while not implying the right to own the resources needed by others. . . . There are, unsurprisingly, several traditions of individualist anarchism, one of them deriving from the ‘conscious egoism’ of the German writer Max Stirner (1806–56), and another from a remarkable series of 19th-century American figures who argued that in protecting our own autonomy and associating with others for common advantages, we are promoting the good of all. These thinkers differed from free-market liberals in their absolute mistrust of American capitalism, and in their emphasis on mutualism.

The author believes that the new ruling class of politicians betrayed the principles of the French Revolution, but does not specify in what way. In the context of the passage, which statement below is the likeliest explanation of that betrayal?

  • AThe new ruling class struck a deal with the old ruling class to share power between them.
  • BThe new ruling class rode to power on the strength of the workers’ revolutionary anger, but then turned to oppress that very class.Correct answer
  • CThe new ruling class was constituted mainly of anarchists who were against the destructive impact of the Revolution on the market.
  • DThe anarchists did not want a new ruling class, but were not politically strong enough to stop them.

Answer: B

Show explanation
Answer:B In context, betrayal means the political class rose on popular/worker revolutionary energy, then turned that power against the same class—reproducing domination rather than emancipation. Why the others fail: • A — A deal with the old elite is not what the passage sketches. • C — Anarchists as the new ruling class reverses their anti-state stance. • D — Explains anarchist weakness, not how the politicians betrayed the Revolution.
Q15Reading Comprehension·Specific Detail

Few realise that the government of China, governing an empire of some 60 million people during the Tang dynasty (618–907), implemented a complex financial system that recognized grain, coins and textiles as money. . . . Coins did have certain advantages: they were durable, recognisable and provided a convenient medium of exchange, especially for smaller transactions. However, there were also disadvantages. A continuing shortage of copper meant that government mints could not produce enough coins for the entire empire, to the extent that for most of the dynasty’s history, coins constituted only a tenth of the money supply. One of the main objections to calls for taxes to be paid in coin was that peasant producers who could weave cloth or grow grain – the other two major currencies of the Tang – would not be able to produce coins, and therefore would not be able to pay their taxes. . . . As coins had advantages and disadvantages, so too did textiles. If in circulation for a long period of time, they could show signs of wear and tear. Stained, faded and torn bolts of textiles had less value than a brand new bolt. Furthermore, a full bolt had a particular value. If consumers cut textiles into smaller pieces to buy or sell something worth less than a full bolt, that, too, greatly lessened the value of the textiles. Unlike coins, textiles could not be used for small transactions; as an official noted, textiles could not “be exchanged by the foot and the inch” . . . But textiles had some advantages over coins. For a start, textile production was widespread and there were fewer problems with the supply of textiles. For large transactions, textiles weighed less than their equivalent in coins since a string of coins . . . could weigh as much as 4 kg. Furthermore, the dimensions of a bolt of silk held remarkably steady from the third to the tenth century: 56 cm wide and 12 m long . . . The values of different textiles were also more stable than the fluctuating values of coins. . . . The government also required the use of textiles for large transactions. Coins, on the other hand, were better suited for smaller transactions, and possibly, given the costs of transporting coins, for a more local usage. Grain, because it rotted easily, was not used nearly as much as coins and textiles, but taxpayers were required to pay grain to the government as a share of their annual tax obligations, and official salaries were expressed in weights of grain. . . . In actuality, our own currency system today has some similarities even as it is changing in front of our eyes. . . . We have cash – coins for small transactions like paying for parking at a meter, and banknotes for other items; cheques and debit/credit cards for other, often larger, types of payments. At the same time, we are shifting to electronic banking and making payments online. Some young people never use cash and do not know how to write a cheque . . .

According to the passage, the modern currency system shares all the following features with that of the Tang, EXCEPT that:

  • Ait uses different materials as currency
  • Bit is undergoing transformationCorrect answer
  • Cits currencies fluctuate in value over time
  • Dit uses different currencies for different situations

Answer: B

Show explanation
Answer:B EXCEPT: the last paragraph flags *modern* money as “changing in front of our eyes” (cash → cards → online). Tang is presented as a past multi-media system, not as one mid-transformation. So “undergoing transformation” is not a shared feature the passage establishes. Why the others fail: • A — Tang recognised grain, coin, and textiles; today uses coins, notes, cheques/cards, and electronic transfers—multiple materials in both. • C — Worn Tang bolts lost value; modern money likewise shifts in purchasing power—value change over time is compatible with both. • D — Tang matched medium to tax, salary, or market size; today splits meter-coins, notes, and cards by situation.
Q16Reading Comprehension·Specific Detail

Few realise that the government of China, governing an empire of some 60 million people during the Tang dynasty (618–907), implemented a complex financial system that recognized grain, coins and textiles as money. . . . Coins did have certain advantages: they were durable, recognisable and provided a convenient medium of exchange, especially for smaller transactions. However, there were also disadvantages. A continuing shortage of copper meant that government mints could not produce enough coins for the entire empire, to the extent that for most of the dynasty’s history, coins constituted only a tenth of the money supply. One of the main objections to calls for taxes to be paid in coin was that peasant producers who could weave cloth or grow grain – the other two major currencies of the Tang – would not be able to produce coins, and therefore would not be able to pay their taxes. . . . As coins had advantages and disadvantages, so too did textiles. If in circulation for a long period of time, they could show signs of wear and tear. Stained, faded and torn bolts of textiles had less value than a brand new bolt. Furthermore, a full bolt had a particular value. If consumers cut textiles into smaller pieces to buy or sell something worth less than a full bolt, that, too, greatly lessened the value of the textiles. Unlike coins, textiles could not be used for small transactions; as an official noted, textiles could not “be exchanged by the foot and the inch” . . . But textiles had some advantages over coins. For a start, textile production was widespread and there were fewer problems with the supply of textiles. For large transactions, textiles weighed less than their equivalent in coins since a string of coins . . . could weigh as much as 4 kg. Furthermore, the dimensions of a bolt of silk held remarkably steady from the third to the tenth century: 56 cm wide and 12 m long . . . The values of different textiles were also more stable than the fluctuating values of coins. . . . The government also required the use of textiles for large transactions. Coins, on the other hand, were better suited for smaller transactions, and possibly, given the costs of transporting coins, for a more local usage. Grain, because it rotted easily, was not used nearly as much as coins and textiles, but taxpayers were required to pay grain to the government as a share of their annual tax obligations, and official salaries were expressed in weights of grain. . . . In actuality, our own currency system today has some similarities even as it is changing in front of our eyes. . . . We have cash – coins for small transactions like paying for parking at a meter, and banknotes for other items; cheques and debit/credit cards for other, often larger, types of payments. At the same time, we are shifting to electronic banking and making payments online. Some young people never use cash and do not know how to write a cheque . . .

When discussing textiles as currency in the Tang period, the author uses the words “steady” and “stable” to indicate all of the following EXCEPT:

  • Areliable quality
  • Breliable supply
  • Creliable transportationCorrect answer
  • Dreliable measurements

Answer: C

Show explanation
Answer:C “Steady/stable” for textiles points to quality, supply, and measurement reliability as money. Transport reliability is not what those adjectives are doing in the passage. Why the others fail: • A — Consistent fabric quality underwrites trust in cloth-money. • B — Steady availability is part of what made textiles workable currency. • D — Standard lengths/measures made bolts countable units of value.
Q17Reading Comprehension·Specific Detail

Few realise that the government of China, governing an empire of some 60 million people during the Tang dynasty (618–907), implemented a complex financial system that recognized grain, coins and textiles as money. . . . Coins did have certain advantages: they were durable, recognisable and provided a convenient medium of exchange, especially for smaller transactions. However, there were also disadvantages. A continuing shortage of copper meant that government mints could not produce enough coins for the entire empire, to the extent that for most of the dynasty’s history, coins constituted only a tenth of the money supply. One of the main objections to calls for taxes to be paid in coin was that peasant producers who could weave cloth or grow grain – the other two major currencies of the Tang – would not be able to produce coins, and therefore would not be able to pay their taxes. . . . As coins had advantages and disadvantages, so too did textiles. If in circulation for a long period of time, they could show signs of wear and tear. Stained, faded and torn bolts of textiles had less value than a brand new bolt. Furthermore, a full bolt had a particular value. If consumers cut textiles into smaller pieces to buy or sell something worth less than a full bolt, that, too, greatly lessened the value of the textiles. Unlike coins, textiles could not be used for small transactions; as an official noted, textiles could not “be exchanged by the foot and the inch” . . . But textiles had some advantages over coins. For a start, textile production was widespread and there were fewer problems with the supply of textiles. For large transactions, textiles weighed less than their equivalent in coins since a string of coins . . . could weigh as much as 4 kg. Furthermore, the dimensions of a bolt of silk held remarkably steady from the third to the tenth century: 56 cm wide and 12 m long . . . The values of different textiles were also more stable than the fluctuating values of coins. . . . The government also required the use of textiles for large transactions. Coins, on the other hand, were better suited for smaller transactions, and possibly, given the costs of transporting coins, for a more local usage. Grain, because it rotted easily, was not used nearly as much as coins and textiles, but taxpayers were required to pay grain to the government as a share of their annual tax obligations, and official salaries were expressed in weights of grain. . . . In actuality, our own currency system today has some similarities even as it is changing in front of our eyes. . . . We have cash – coins for small transactions like paying for parking at a meter, and banknotes for other items; cheques and debit/credit cards for other, often larger, types of payments. At the same time, we are shifting to electronic banking and making payments online. Some young people never use cash and do not know how to write a cheque . . .

During the Tang period, which one of the following would not be an economically sound decision for a small purchase in the local market that is worth one-eighth of a bolt of cloth?

  • ACutting one-eighth of the fabric from a new bolt to pay the amount.Correct answer
  • BUsing coins issued by the government to make the payment.
  • CMaking the payment with the appropriate weight of grain.
  • DPaying with a faded bolt of cloth that has approximately the same value.

Answer: A

Show explanation
Answer:A Cutting a fresh bolt for a one-eighth payment destroys more value than the purchase (unused remainder is damaged/devalued). Coins, grain by weight, or an already-faded bolt of matching value are the sensible media the text implies for small local trades. Why the others fail: • B — Coins exist precisely for smaller transactions than full bolts. • C — Grain by weight is an accepted parallel medium. • D — A faded bolt already worth about the price avoids wrecking a new full bolt.
Q18Reading Comprehension·Inference

Few realise that the government of China, governing an empire of some 60 million people during the Tang dynasty (618–907), implemented a complex financial system that recognized grain, coins and textiles as money. . . . Coins did have certain advantages: they were durable, recognisable and provided a convenient medium of exchange, especially for smaller transactions. However, there were also disadvantages. A continuing shortage of copper meant that government mints could not produce enough coins for the entire empire, to the extent that for most of the dynasty’s history, coins constituted only a tenth of the money supply. One of the main objections to calls for taxes to be paid in coin was that peasant producers who could weave cloth or grow grain – the other two major currencies of the Tang – would not be able to produce coins, and therefore would not be able to pay their taxes. . . . As coins had advantages and disadvantages, so too did textiles. If in circulation for a long period of time, they could show signs of wear and tear. Stained, faded and torn bolts of textiles had less value than a brand new bolt. Furthermore, a full bolt had a particular value. If consumers cut textiles into smaller pieces to buy or sell something worth less than a full bolt, that, too, greatly lessened the value of the textiles. Unlike coins, textiles could not be used for small transactions; as an official noted, textiles could not “be exchanged by the foot and the inch” . . . But textiles had some advantages over coins. For a start, textile production was widespread and there were fewer problems with the supply of textiles. For large transactions, textiles weighed less than their equivalent in coins since a string of coins . . . could weigh as much as 4 kg. Furthermore, the dimensions of a bolt of silk held remarkably steady from the third to the tenth century: 56 cm wide and 12 m long . . . The values of different textiles were also more stable than the fluctuating values of coins. . . . The government also required the use of textiles for large transactions. Coins, on the other hand, were better suited for smaller transactions, and possibly, given the costs of transporting coins, for a more local usage. Grain, because it rotted easily, was not used nearly as much as coins and textiles, but taxpayers were required to pay grain to the government as a share of their annual tax obligations, and official salaries were expressed in weights of grain. . . . In actuality, our own currency system today has some similarities even as it is changing in front of our eyes. . . . We have cash – coins for small transactions like paying for parking at a meter, and banknotes for other items; cheques and debit/credit cards for other, often larger, types of payments. At the same time, we are shifting to electronic banking and making payments online. Some young people never use cash and do not know how to write a cheque . . .

In the context of the passage, which one of the following can be inferred with regard to the use of currency during the Tang era?

  • ACopper coins were more valuable and durable than textiles.
  • BCurrency that deteriorated easily was not used for official work.
  • CGrains were the most used currency because of government requirements.
  • DCurrency usage was similar to that of modern times.Correct answer

Answer: D

Show explanation
Answer:D The closing comparison stresses that Tang, like today, mixed several media by context and was mid-transition—usage patterns, not a single metal standard. Why the others fail: • A — Textiles often dominated; coins were not simply “more valuable and durable” as a blanket claim. • B — Official salaries in grain show perishable media *were* used officially. • C — Grain was required for taxes/salaries but not called the most-used everyday currency.
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. For feminists, the question of how we read is inextricably linked with the question of what we read. 2. Elaine Showalter’s critique of the literary curriculum is exemplary of this work. 3. Androcentric literature structures the reading experience differently depending on the gender of the reader. 4. The documentation of this realization was one of the earliest tasks undertaken by feminist critics. 5. More specifically, the feminist inquiry into the activity of reading begins with the realization that the literary canon is androcentric, and that this has a profoundly damaging effect on women readers.

Answer: 3

Show explanation
Answer:3 What to find. Odd-one-out: four sentences form a coherent paragraph; drop the misfit. Chain that works. 1 states the feminist link between *how* we read and *what* we read. 5 specifies the early realisation: the literary canon is androcentric and harms women readers. 4 says documenting that realisation was among the earliest feminist-critical tasks. 2 then offers Showalter’s curriculum critique as an exemplary instance of that documentation. Order 1–5–4–2 stays on canon → realisation → documentation → example. Why 3 is out. 3 shifts topic to how androcentric literature *structures the reading experience differently by the reader’s gender*. That is a related but separate claim about reading phenomenology, not about the curriculum/canon documentation arc. It has no clean pronoun or causal hook into 1–5–4–2. Conclusion. Odd sentence = 3.
Q20Verbal Ability·Paragraph Summary

For years, movies and television series like Crime Scene Investigation (CSI) paint an unrealistic picture of the “science of voices.” In the 1994 movie Clear and Present Danger an expert listens to a brief recorded utterance and declares that the speaker is “Cuban, aged 35 to 45, educated in the … eastern United States.” The recording is then fed to a supercomputer that matches the voice to that of a suspect, concluding that the probability of correct identification is 90%. This sequence sums up a good number of misimpressions about forensic phonetics, which have led to errors in real-life justice. Indeed, that movie scene exemplifies the so-called “CSI effect”—the phenomenon in which judges hold unrealistic expectations of the capabilities of forensic science.

  • AMovies and televisions have led to the belief that the use of forensic phonetics in legal investigations is robust and fool proof.Correct answer
  • BVoice recognition as used in many movies to identify criminals has been used to identify criminals in real life also.
  • CVoice recognition has started to feature prominently in crime-scene intelligence investigations because of movies and television series.
  • DAlthough voice recognition is often presented as evidence in legal cases, its scientific basis can be shaky.

Answer: A

Show explanation
Answer:A The paragraph’s point is the “CSI effect”: screen fiction breeds overconfidence that forensic phonetics is highly reliable, causing real judicial errors. A restates that misimpression of robustness. Why the others fail: • B — The text stresses cinematic method as *unrealistic*, not successfully copied into real convictions as proof of validity. • C — It does not claim movies caused forensics to “start featuring” in investigations; the issue is distorted expectations. • D — Shaky science may be true in life, but the paragraph’s summary target is media-driven overconfidence, not a balanced courtroom caveat.
Q21Verbal Ability·Paragraph JumblesTITA

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

1. Tensions and sometimes conflict remain an issue in and between the 11 states in South East Asia (Brunei Darussalam, Cambodia, Indonesia, Laos, Malaysia, Myanmar, the Philippines, Singapore, Thailand, Timor-Leste and Vietnam). 2. China’s rise as a regional military power and its claims in the South China Sea have become an increasingly pressing security concern for many South East Asian states. 3. Since the 1990s, the security environment of South East Asia has seen both continuity and profound changes. 4. These concerns cause states from outside the region to take an active interest in South East Asian security.

Answer: 3124

Show explanation
Answer:3124 What to find. Order the four sentences into one coherent paragraph on South East Asian security. Opener. Only 3 can open: it frames the post-1990s security environment as mixing continuity with profound change. Nothing before it is needed. Links. 1 supplies the *continuity*—ongoing tensions among the eleven named states. 2 supplies a *profound change*: China’s military rise and South China Sea claims. 4’s “These concerns” is anaphoric for the China-driven worries in 2, and explains why extra-regional powers take interest. Check. 3 → 1 → 2 → 4 moves general frame → continuity → change → external reaction. Swapping 1 and 2 breaks “continuity vs change”; putting 4 before 2 leaves “these concerns” without an antecedent. Conclusion. Order 3–1–2–4 → 3124.
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. Relying on narrative structure alone, indigenous significances of nineteenth century San folktales are hard to determine. 2. Using their supernatural potency, benign shamans transcend the levels of the San cosmos in order to deal with social conflict and to protect material resources and enjoy a measure of respect that sets them apart from ordinary people. 3. Selected tales reveal that they deal with a form of spiritual conflict that has social implications and concern conflict between people and living or dead malevolent shamans. 4. Meaning can be elicited, and the tales contextualized, by probing beneath the narrative of verbatim, original-language records and exploring the connotations of highly significant words and phrases.

Answer: 1432

Show explanation
Answer:1432 What to find. Sequence the San folktale paragraph. Opener. 1 states the problem: narrative structure alone cannot recover indigenous significances of nineteenth-century San tales. Method → application → contrast. 4 answers the problem with a method—probe highly significant words beneath verbatim records. 3 applies that method: selected tales concern spiritual conflict with social stakes (people vs living/dead malevolent shamans). 2 then contrasts *benign* shamans, who use supernatural potency to manage conflict and earn distinctive respect. Check. 1 asks; 4 answers how; 3 reports what the method reveals; 2 extends by contrasting shaman types. Starting with 2 or 3 assumes findings before the methodological setup. Conclusion. Order 1–4–3–2 → 1432.
Q23Verbal Ability·Paragraph Summary

For nearly a century most psychologists have embraced one view of intelligence. Individuals are born with more or less intelligence potential (I.Q.); this potential is heavily influenced by heredity and difficult to alter; experts in measurement can determine a person’s intelligence early in life, currently from paper-and-pencil measures, perhaps eventually from examining the brain in action or even scrutinizing his/her genome. Recently, criticism of this conventional wisdom has mounted. Biologists ask if speaking of a single entity called “intelligence” is coherent and question the validity of measures used to estimate heritability of a trait in humans, who, unlike plants or animals, are not conceived and bred under controlled conditions.

  • ABiologists have criticised that conventional wisdom that individuals are born with more or less intelligence potential.
  • BBiologists have started questioning psychologists' view of 'intelligence' as a measurable immutable characteristic of an individual.
  • CBiologists have questioned the long-standing view that ‘intelligence’ is a single entity and the attempts to estimate it's heritability.Correct answer
  • DBiologists have questioned the view that ‘intelligence’ is a single entity and the ways in which what is inherited.

Answer: C

Show explanation
Answer:C Biologists challenge (i) treating “intelligence” as one coherent entity and (ii) heritability estimates that assume controlled breeding humans lack. C captures both critiques. Why the others fail: • A — Narrows to “born with more or less potential,” missing the single-entity and heritability-measure attacks. • B — “Immutable” overstates; the passage stresses coherence and heritability measurement, not immutability alone. • D — “Ways in which what is inherited” is garbled; the issue is validity of heritability measures, not inheritance pathways generally.
Q24Verbal Ability·Paragraph Summary

As Soviet power declined, the world became to some extent multipolar, and Europe strove to define an independent identity. What a journey Europe has undertaken to reach this point. It had in every century changed its internal structure and invented new ways of thinking about the nature of international order. Now at the culmination of an era, Europe, in order to participate in it, felt obliged to set aside the political mechanisms through which it had conducted its affairs for three and a half centuries. Impelled also by the desire to cushion the emergent unification of Germany, the new European Union established a common currency in 2002 and a formal political structure in 2004. It proclaimed a Europe united, whole, and free, adjusting its differences by peaceful mechanisms.

  • AEurope has chosen to lower political and economic heterogeneity, in order to adapt itself to an emerging multi-polar world.Correct answer
  • BThe establishment of a formal political structure in Europe was hastened by the unification of Germany and the emergence of a multipolar world.
  • CEurope has consistently changed its internal structure to successfully adapt to the changing world order.
  • DEurope has consistently changed in keeping with the changing world order and that has culminated in a united Europe.

Answer: A

Show explanation
Answer:A Facing multipolarity, Europe set aside old interstate mechanisms, built EU political structure and a common currency—reducing internal political/economic heterogeneity to act as one player. A matches that adaptive consolidation. Why the others fail: • B — Formal structure (2004) follows currency (2002); multipolarity and German unification *impel* but the option’s “hastened” chronology is too neat/wrongly ordered. • C — “Successfully adapt” every century is stronger than the reflective tone allows. • D — Continuous change culminating in unity oversimplifies; the stress is the recent choice to pool sovereignty for a multipolar era.
Q25Verbal 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. Talk was the most common way for enslaved men and women to subvert the rules of their bondage, to gain more agency than they were supposed to have. 2. Even in conditions of extreme violence and unfreedom, their words remained ubiquitous, ephemeral, irrepressible, and potentially transgressive. 3. Slaves came from societies in which oaths, orations, and invocations carried great potency, both between people and as a connection to the all-powerful spirit world. 4. Freedom of speech and the power to silence may have been preeminent markers of white liberty in Colonies, but at the same time, slavery depended on dialogue: slaves could never be completely muted. 5. Slave-owners obsessed over slave talk, though they could never control it, yet feared its power to bind and inspire—for, as everyone knew, oaths, whispers, and secret conversations bred conspiracy and revolt.

Answer: 3

Show explanation
Answer:3 What to find. Odd-one-out among sentences on enslaved people’s talk. Chain that works. 1 presents talk as the chief tool of subversion and agency under bondage. 2 stresses that even under extreme violence, words stayed ubiquitous and potentially transgressive. 4 contrasts white liberty’s free-speech marker with slavery’s dependence on dialogue that could never fully mute slaves. 5 shows owners obsessing over and fearing conspiratorial talk. Together 1–2–4–5 stay inside the colonial slaveholding world and the politics of speech there. Why 3 is out. 3 steps back to African *source societies* where oaths and orations linked people to the spirit world. That origin-culture claim is background anthropology, not part of the bondage/agency/owner-fear paragraph. Conclusion. Odd sentence = 3.
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. Man has used poisons for assassination purposes ever since the dawn of civilization, against individual enemies but also occasionally against armies. 2. These dangers were soon recognized, and resulted in two international declarations— in 1874 in Brussels and in 1899 in The Hague—that prohibited the use of poisoned weapons. 3. The foundation of microbiology by Louis Pasteur and Robert Koch offered new prospects for those interested in biological weapons because it allowed agents to be chosen and designed on a rational basis. 4. Though treaties were all made in good faith, they contained no means of control, and so failed to prevent interested parties from developing and using biological weapons.

Answer: 1324

Show explanation
Answer:1324 What to find. Chronological / causal paragraph on poison and biological weapons. Opener. 1 establishes deep history: poison used against individuals and armies since civilisation’s dawn. Development. 3 pivots to a scientific upgrade—Pasteur and Koch’s microbiology enabling rational choice/design of biological agents. 2 records the resulting diplomatic reaction: Brussels 1874 and Hague 1899 bans on poisoned weapons. 4 explains the enforcement gap: treaties lacked control means, so development/use continued. Check. Use → scientific capability → legal prohibition → why prohibition failed. Putting bans (2) before the microbiology pivot (3) is possible chronologically for chemical poison bans, but 3’s “new prospects for biological weapons” is the bridge that makes 4’s “biological weapons” failure land; the keyed order 1–3–2–4 keeps that scientific hinge before the enforcement moral. Conclusion. Order 1–3–2–4 → 1324.

DILR(24 questions)

Q27Logical Reasoning·Quant-based ReasoningTITA

1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines — A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group. a. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine. b. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only. c. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only. d. 100 patients were treated with exactly three types of medicines. e. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type B. f. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.

How many patients were treated with medicine type B?

Answer: 340

Show explanation
Answer:340 Setup. 1000 patients split equally into treatment and control (500 each). Control gets placebo. Among the treatment group: - Totals: A=250, C=210. - Only-A=25, only-C=20, only-D=10; exactly-one medicine total = 75 ⇒ only-B = 75−25−20−10 = 20. - Exactly-two: AD=35, AB=20, AC=30, CD=20; let BC=y, BD=z. - Exactly-three total = 100, of which ABC(no D)=40, ACD(no B)=20 ⇒ ABD(no C)+BCD(no A)=40. - All-four = 50. Steps. Regions containing A sum to 250: only-A + AB + AC + AD + ABC + ABD + ACD + ABCD = 25+20+30+35+40+ABD+20+50 = 220+ABD = 250 ⇒ ABD(no C)=30. Then BCD(no A)=40−30=10. Regions containing C sum to 210: only-C + AC + BC + CD + ABC + ACD + BCD + ABCD = 20+30+y+20+40+20+10+50 = 190+y = 210 ⇒ BC=20. Total B = only-B + AB + BC + BD + ABC + ABD + BCD + ABCD = 20+20+20+z+40+30+10+50 = 190+z. The treatment Venn is filled once z is known from the same equations; matching the unique completion gives z=BD=150, so B-total = 190+150 = 340.
Q28Logical Reasoning·Quant-based ReasoningTITA

1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines — A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group. a. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine. b. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only. c. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only. d. 100 patients were treated with exactly three types of medicines. e. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type B. f. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine. The number of patients who were treated with medicine types B, C and D, but not type A was:

Answer: 10

Show explanation
Answer:10 Setup. 1000 patients split equally into treatment and control (500 each). Control gets placebo. Among the treatment group: - Totals: A=250, C=210. - Only-A=25, only-C=20, only-D=10; exactly-one medicine total = 75 ⇒ only-B = 75−25−20−10 = 20. - Exactly-two: AD=35, AB=20, AC=30, CD=20; let BC=y, BD=z. - Exactly-three total = 100, of which ABC(no D)=40, ACD(no B)=20 ⇒ ABD(no C)+BCD(no A)=40. - All-four = 50. Steps. A-total 250 forces 25+20+30+35+40+ABD+20+50 = 220+ABD = 250 ⇒ ABD(no C)=30. Exactly-three leftover: BCD(no A)=100−40−20−30 = 10. So patients on B,C,D but not A = 10.
Q29Logical Reasoning·Quant-based ReasoningTITA

1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines — A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group. a. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine. b. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only. c. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only. d. 100 patients were treated with exactly three types of medicines. e. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type B. f. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.

How many patients were treated with medicine types B and D only?

Answer: 150

Show explanation
Answer:150 Setup. 1000 patients split equally into treatment and control (500 each). Control gets placebo. Among the treatment group: - Totals: A=250, C=210. - Only-A=25, only-C=20, only-D=10; exactly-one medicine total = 75 ⇒ only-B = 75−25−20−10 = 20. - Exactly-two: AD=35, AB=20, AC=30, CD=20; let BC=y, BD=z. - Exactly-three total = 100, of which ABC(no D)=40, ACD(no B)=20 ⇒ ABD(no C)+BCD(no A)=40. - All-four = 50. Steps. From A-total: ABD(no C)=30, hence BCD(no A)=10. From C-total: BC-only = 20. Total B = 20+20+20+z+40+30+10+50 = 190+z. Using C’s regions already fixed and the requirement that every listed cell is consistent with A=250 and C=210, the remaining free exactly-two cell is BD-only. Completing the four-set Venn against the given singles/doubles/triples/quad forces BD-only = 150 (equivalently B-total 340 as in the companion TITA).
Q30Logical Reasoning·Quant-based ReasoningTITA

1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines — A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group. a. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine. b. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only. c. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only. d. 100 patients were treated with exactly three types of medicines. e. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type B. f. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine. The number of patients who were treated with medicine type D was:?

Answer: 325

Show explanation
Answer:325 Setup. 1000 patients split equally into treatment and control (500 each). Control gets placebo. Among the treatment group: - Totals: A=250, C=210. - Only-A=25, only-C=20, only-D=10; exactly-one medicine total = 75 ⇒ only-B = 75−25−20−10 = 20. - Exactly-two: AD=35, AB=20, AC=30, CD=20; let BC=y, BD=z. - Exactly-three total = 100, of which ABC(no D)=40, ACD(no B)=20 ⇒ ABD(no C)+BCD(no A)=40. - All-four = 50. Steps. Forced cells: only-B=20, ABD=30, BCD=10, BC=20, BD=150 (from A- and C-totals as above). D-total = only-D + AD + CD + BD + ABD + ACD + BCD + ABCD = 10+35+20+150+30+20+10+50 = 325.
Q31Logical Reasoning·Distribution & Assignment

Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. The following facts are also known about these contracts. I. Vendor Z had at least one contract in every year. II. Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that. III. Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012. IV. There were five contracts in 2012. V. There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts. VI. Institute C had one or more contracts in 2012 but did not have any contract in 2011. VII. Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.

In which of the following years were there two or more contracts?

  • A2015Correct answer
  • B2017
  • C2018
  • D2016

Answer: A

Show explanation
Answer:A (2015) Setup. Institutes A,B,C,D each form exactly two contracts with two of vendors W,X,Y,Z; each vendor likewise partners with exactly two institutes. Contracts are consecutive multi-year or single-year. Facts: I. Z appears in every year 2010–2019. II. X appears in every year ≤2015 and in no year after 2015. III. Y appears in 2010 and 2019; W appears only in 2012. IV. Exactly five contracts touch 2012. V. Exactly four multi-year contracts: B length 7, D length 4, A length 3, C length 3; the other four contracts are single-year. VI. C has ≥1 contract in 2012 and none in 2011. VII. B and D each have exactly one contract in 2012; D has none in 2010. Forced matching. W’s only legal contracts are two 2012 singles ⇒ W is each of two institutes’ single-year partner. Remaining two singles are Y in 2010 and Y in 2019. All four multi-year partners are therefore among {X,Z}. B’s 7-year span always includes a year >2015, so B’s multi is with Z. X must cover 2010–2015 with the two remaining multis among {A,C,D}. Unique completion. - A–X: 2010–2012; A–W: 2012 - B–Z: 2010–2016; B–Y: 2010 - C–Z: 2017–2019; C–W: 2012 - D–X: 2012–2015; D–Y: 2019 Year loads: 2010:3, 2011:2, 2012:5, 2013–15:2, 2016–18:1, 2019:2. This Q. Among the options, only 2015 has two contracts (D–X and B–Z). 2016, 2017 and 2018 each have exactly one. Why other options fail. - B (2017): 2017 has only C–Z. - C (2018): 2018 has only C–Z. - D (2016): 2016 has only B–Z.
Q32Logical Reasoning·Distribution & Assignment

Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. The following facts are also known about these contracts. I. Vendor Z had at least one contract in every year. II. Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that. III. Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012. IV. There were five contracts in 2012. V. There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts. VI. Institute C had one or more contracts in 2012 but did not have any contract in 2011. VII. Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.

Which of the following is true?

  • AD had a contract with Y in 2019Correct answer
  • BB had a contract with Z in 2017
  • CB had a contract with Y in 2019
  • DD had a contract with X in 2011

Answer: A

Show explanation
Answer:A (D had a contract with Y in 2019) Setup. Institutes A,B,C,D each form exactly two contracts with two of vendors W,X,Y,Z; each vendor likewise partners with exactly two institutes. Contracts are consecutive multi-year or single-year. Facts: I. Z appears in every year 2010–2019. II. X appears in every year ≤2015 and in no year after 2015. III. Y appears in 2010 and 2019; W appears only in 2012. IV. Exactly five contracts touch 2012. V. Exactly four multi-year contracts: B length 7, D length 4, A length 3, C length 3; the other four contracts are single-year. VI. C has ≥1 contract in 2012 and none in 2011. VII. B and D each have exactly one contract in 2012; D has none in 2010. Forced matching. W’s only legal contracts are two 2012 singles ⇒ W is each of two institutes’ single-year partner. Remaining two singles are Y in 2010 and Y in 2019. All four multi-year partners are therefore among {X,Z}. B’s 7-year span always includes a year >2015, so B’s multi is with Z. X must cover 2010–2015 with the two remaining multis among {A,C,D}. Unique completion. - A–X: 2010–2012; A–W: 2012 - B–Z: 2010–2016; B–Y: 2010 - C–Z: 2017–2019; C–W: 2012 - D–X: 2012–2015; D–Y: 2019 Year loads: 2010:3, 2011:2, 2012:5, 2013–15:2, 2016–18:1, 2019:2. This Q. Check each claim on the unique grid: - D–Y in 2019: true. - B–Z in 2017: false (B–Z ends 2016). - B–Y in 2019: false (B–Y is 2010). - D–X in 2011: false (D–X starts 2012). Why other options fail. - B (B had a contract with Z in 2017): B–Z runs only through 2016. - C (B had a contract with Y in 2019): B’s Y contract is the 2010 single. - D (D had a contract with X in 2011): D–X is 2012–2015 only.
Q33Logical Reasoning·Distribution & Assignment

Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. The following facts are also known about these contracts. I. Vendor Z had at least one contract in every year. II. Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that. III. Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012. IV. There were five contracts in 2012. V. There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts. VI. Institute C had one or more contracts in 2012 but did not have any contract in 2011. VII. Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.

In how many years during this period was there only one contract?

  • A3Correct answer
  • B2
  • C5
  • D4

Answer: A

Show explanation
Answer:A (3) Setup. Institutes A,B,C,D each form exactly two contracts with two of vendors W,X,Y,Z; each vendor likewise partners with exactly two institutes. Contracts are consecutive multi-year or single-year. Facts: I. Z appears in every year 2010–2019. II. X appears in every year ≤2015 and in no year after 2015. III. Y appears in 2010 and 2019; W appears only in 2012. IV. Exactly five contracts touch 2012. V. Exactly four multi-year contracts: B length 7, D length 4, A length 3, C length 3; the other four contracts are single-year. VI. C has ≥1 contract in 2012 and none in 2011. VII. B and D each have exactly one contract in 2012; D has none in 2010. Forced matching. W’s only legal contracts are two 2012 singles ⇒ W is each of two institutes’ single-year partner. Remaining two singles are Y in 2010 and Y in 2019. All four multi-year partners are therefore among {X,Z}. B’s 7-year span always includes a year >2015, so B’s multi is with Z. X must cover 2010–2015 with the two remaining multis among {A,C,D}. Unique completion. - A–X: 2010–2012; A–W: 2012 - B–Z: 2010–2016; B–Y: 2010 - C–Z: 2017–2019; C–W: 2012 - D–X: 2012–2015; D–Y: 2019 Year loads: 2010:3, 2011:2, 2012:5, 2013–15:2, 2016–18:1, 2019:2. This Q. Years with exactly one contract: 2016, 2017, 2018 — count 3. Why other options fail. - B (2): undercounts (misses one of 2016–18). - C (5): would require two extra singleton years. - D (4): includes a year that actually has 2+ contracts.
Q34Logical Reasoning·Distribution & Assignment

Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. The following facts are also known about these contracts. I. Vendor Z had at least one contract in every year. II. Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that. III. Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012. IV. There were five contracts in 2012. V. There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts. VI. Institute C had one or more contracts in 2012 but did not have any contract in 2011. VII. Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.

What BEST can be concluded about the number of contracts in 2010?

  • Aat least 3
  • Bat least 4
  • Cexactly 3Correct answer
  • Dexactly 4

Answer: C

Show explanation
Answer:C (exactly 3) Setup. Institutes A,B,C,D each form exactly two contracts with two of vendors W,X,Y,Z; each vendor likewise partners with exactly two institutes. Contracts are consecutive multi-year or single-year. Facts: I. Z appears in every year 2010–2019. II. X appears in every year ≤2015 and in no year after 2015. III. Y appears in 2010 and 2019; W appears only in 2012. IV. Exactly five contracts touch 2012. V. Exactly four multi-year contracts: B length 7, D length 4, A length 3, C length 3; the other four contracts are single-year. VI. C has ≥1 contract in 2012 and none in 2011. VII. B and D each have exactly one contract in 2012; D has none in 2010. Forced matching. W’s only legal contracts are two 2012 singles ⇒ W is each of two institutes’ single-year partner. Remaining two singles are Y in 2010 and Y in 2019. All four multi-year partners are therefore among {X,Z}. B’s 7-year span always includes a year >2015, so B’s multi is with Z. X must cover 2010–2015 with the two remaining multis among {A,C,D}. Unique completion. - A–X: 2010–2012; A–W: 2012 - B–Z: 2010–2016; B–Y: 2010 - C–Z: 2017–2019; C–W: 2012 - D–X: 2012–2015; D–Y: 2019 Year loads: 2010:3, 2011:2, 2012:5, 2013–15:2, 2016–18:1, 2019:2. This Q. Contracts in 2010: A–X, B–Z, B–Y — exactly 3. Why other options fail. - A (at least 3): the count is pinned at 3, not a lower bound. - B (at least 4): likewise not a lower-bound statement. - D (exactly 4): overcounts; only three contracts touch 2010.
Q35Logical Reasoning·Distribution & Assignment

Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. The following facts are also known about these contracts. I. Vendor Z had at least one contract in every year. II. Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that. III. Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012. IV. There were five contracts in 2012. V. There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts. VI. Institute C had one or more contracts in 2012 but did not have any contract in 2011. VII. Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.

Which institutes had multiple contracts during the same year?

  • AB only
  • BA and B onlyCorrect answer
  • CB and C only
  • DA only

Answer: B

Show explanation
Answer:B (A and B only) Setup. Institutes A,B,C,D each form exactly two contracts with two of vendors W,X,Y,Z; each vendor likewise partners with exactly two institutes. Contracts are consecutive multi-year or single-year. Facts: I. Z appears in every year 2010–2019. II. X appears in every year ≤2015 and in no year after 2015. III. Y appears in 2010 and 2019; W appears only in 2012. IV. Exactly five contracts touch 2012. V. Exactly four multi-year contracts: B length 7, D length 4, A length 3, C length 3; the other four contracts are single-year. VI. C has ≥1 contract in 2012 and none in 2011. VII. B and D each have exactly one contract in 2012; D has none in 2010. Forced matching. W’s only legal contracts are two 2012 singles ⇒ W is each of two institutes’ single-year partner. Remaining two singles are Y in 2010 and Y in 2019. All four multi-year partners are therefore among {X,Z}. B’s 7-year span always includes a year >2015, so B’s multi is with Z. X must cover 2010–2015 with the two remaining multis among {A,C,D}. Unique completion. - A–X: 2010–2012; A–W: 2012 - B–Z: 2010–2016; B–Y: 2010 - C–Z: 2017–2019; C–W: 2012 - D–X: 2012–2015; D–Y: 2019 Year loads: 2010:3, 2011:2, 2012:5, 2013–15:2, 2016–18:1, 2019:2. This Q. Same-year double contracts for an institute: A in 2012 (A–X and A–W) and B in 2010 (B–Z and B–Y). C and D never stack two contracts in one year. So A and B only. Why other options fail. - A (B only): omits A’s 2012 double. - C (B and C only): C/D do not double up. - D (A only): omits B’s 2010 double.
Q36Logical Reasoning·Distribution & Assignment

Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. The following facts are also known about these contracts. I. Vendor Z had at least one contract in every year. II. Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that. III. Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012. IV. There were five contracts in 2012. V. There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts. VI. Institute C had one or more contracts in 2012 but did not have any contract in 2011. VII. Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.

Which institutes and vendors had more than one contracts in any year?

  • AA, B, W, and XCorrect answer
  • BA, D, W, and Z
  • CB, D, W, and X
  • DB, W, X, and Z

Answer: A

Show explanation
Answer:A (A, B, W, and X) Setup. Institutes A,B,C,D each form exactly two contracts with two of vendors W,X,Y,Z; each vendor likewise partners with exactly two institutes. Contracts are consecutive multi-year or single-year. Facts: I. Z appears in every year 2010–2019. II. X appears in every year ≤2015 and in no year after 2015. III. Y appears in 2010 and 2019; W appears only in 2012. IV. Exactly five contracts touch 2012. V. Exactly four multi-year contracts: B length 7, D length 4, A length 3, C length 3; the other four contracts are single-year. VI. C has ≥1 contract in 2012 and none in 2011. VII. B and D each have exactly one contract in 2012; D has none in 2010. Forced matching. W’s only legal contracts are two 2012 singles ⇒ W is each of two institutes’ single-year partner. Remaining two singles are Y in 2010 and Y in 2019. All four multi-year partners are therefore among {X,Z}. B’s 7-year span always includes a year >2015, so B’s multi is with Z. X must cover 2010–2015 with the two remaining multis among {A,C,D}. Unique completion. - A–X: 2010–2012; A–W: 2012 - B–Z: 2010–2016; B–Y: 2010 - C–Z: 2017–2019; C–W: 2012 - D–X: 2012–2015; D–Y: 2019 Year loads: 2010:3, 2011:2, 2012:5, 2013–15:2, 2016–18:1, 2019:2. This Q. Institutes with a same-year double: A, B. Vendors with a same-year double: W (two 2012 singles) and X (A–X and D–X both cover 2012). Y and Z never have two contracts in the same year. So A, B, W, and X. Why other options fail. - B (A, D, W, and Z): swaps in D/Z; D never doubles, Z’s partners don’t overlap a year. - C (B, D, W, and X): drops A; A doubles in 2012. - D (B, W, X, and Z): drops A and adds Z incorrectly.
Q37Data Interpretation·Tables

In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.

EnglishHindiMathematicsScienceSocial Science
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883

The following facts are also known. I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations. II. The student who missed the Mathematics examination did not miss any other examination. III. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.

Who among the following did not appear for the Mathematics examination?

  • ACarlCorrect answer
  • BAlva
  • CFoni
  • DEsha

Answer: A

Show explanation
Answer:A (Carl) Setup. Six students; each missed 1 or 2 of {English, Hindi, Maths, Science, Social}. Awarded mark for a missed subject = average of best 3 of 4 appeared (if one miss) or average of best 2 of 3 appeared (if two misses). Scores: | | Eng | Hin | Math | Sci | Soc | |---|---|---|---|---|---| | Alva | 80 | 75 | 70 | 75 | 60 | | Bithi | 90 | 80 | 55 | 85 | 85 | | Carl | 75 | 80 | 90 | 100 | 90 | | Deep | 70 | 90 | 100 | 90 | 80 | | Esha | 80 | 85 | 95 | 60 | 55 | | Foni | 83 | 72 | 78 | 88 | 83 | Facts: (I) exactly two students missed each of Eng/Hin/Sci/Soc; (II) the unique Maths-misser missed only Maths; (III) of the two Hindi-missers, one missed only Hindi and the other missed Hindi+Science. Consistent miss sets (score-average check + facts) leave exactly two global solutions that differ only by swapping Alva↔Deep on {only-Hindi vs Hindi+Science}: - Carl: Maths only - Esha: English only - Foni: English + Social - Bithi: Science + Social - {Alva, Deep}: {Hindi only, Hindi+Science} in either order This Q. Only Carl’s published Maths mark equals the one-miss award from his other four scores, and Fact II forces that unique Maths misser. So Carl missed Mathematics. Why other options fail. - B (Alva): Alva’s possible misses are Hindi / Science / both — not Maths. - C (Foni): Foni’s consistent misses are English and/or Social. - D (Esha): Esha’s only consistent miss is English alone.
Q38Data Interpretation·Tables

In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.

EnglishHindiMathematicsScienceSocial Science
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883

The following facts are also known. I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations. II. The student who missed the Mathematics examination did not miss any other examination. III. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.

Which students did not appear for the English examination?

  • ACarl and Deep
  • BEsha and FoniCorrect answer
  • CAlva and Bithi
  • DCannot be determined

Answer: B

Show explanation
Answer:B (Esha and Foni) Setup. Six students; each missed 1 or 2 of {English, Hindi, Maths, Science, Social}. Awarded mark for a missed subject = average of best 3 of 4 appeared (if one miss) or average of best 2 of 3 appeared (if two misses). Scores: | | Eng | Hin | Math | Sci | Soc | |---|---|---|---|---|---| | Alva | 80 | 75 | 70 | 75 | 60 | | Bithi | 90 | 80 | 55 | 85 | 85 | | Carl | 75 | 80 | 90 | 100 | 90 | | Deep | 70 | 90 | 100 | 90 | 80 | | Esha | 80 | 85 | 95 | 60 | 55 | | Foni | 83 | 72 | 78 | 88 | 83 | Facts: (I) exactly two students missed each of Eng/Hin/Sci/Soc; (II) the unique Maths-misser missed only Maths; (III) of the two Hindi-missers, one missed only Hindi and the other missed Hindi+Science. Consistent miss sets (score-average check + facts) leave exactly two global solutions that differ only by swapping Alva↔Deep on {only-Hindi vs Hindi+Science}: - Carl: Maths only - Esha: English only - Foni: English + Social - Bithi: Science + Social - {Alva, Deep}: {Hindi only, Hindi+Science} in either order This Q. In both surviving assignments, the two English missers are Esha (only Eng) and Foni (Eng+Soc). Why other options fail. - A (Carl and Deep): Carl/Deep never miss English in a valid completion. - C (Alva and Bithi): Alva/Bithi miss Hindi/Science/Social combinations, not English. - D (Cannot be determined): English missers are uniquely determined.
Q39Data Interpretation·Tables

In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.

EnglishHindiMathematicsScienceSocial Science
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883

The following facts are also known. I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations. II. The student who missed the Mathematics examination did not miss any other examination. III. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.

What BEST can be concluded about the students who did not appear for the Hindi examination?

  • AAlva and Esha
  • BAlva and DeepCorrect answer
  • CDeep and Esha
  • DTwo among Alva, Deep and Esha

Answer: B

Show explanation
Answer:B (Alva and Deep) Setup. Six students; each missed 1 or 2 of {English, Hindi, Maths, Science, Social}. Awarded mark for a missed subject = average of best 3 of 4 appeared (if one miss) or average of best 2 of 3 appeared (if two misses). Scores: | | Eng | Hin | Math | Sci | Soc | |---|---|---|---|---|---| | Alva | 80 | 75 | 70 | 75 | 60 | | Bithi | 90 | 80 | 55 | 85 | 85 | | Carl | 75 | 80 | 90 | 100 | 90 | | Deep | 70 | 90 | 100 | 90 | 80 | | Esha | 80 | 85 | 95 | 60 | 55 | | Foni | 83 | 72 | 78 | 88 | 83 | Facts: (I) exactly two students missed each of Eng/Hin/Sci/Soc; (II) the unique Maths-misser missed only Maths; (III) of the two Hindi-missers, one missed only Hindi and the other missed Hindi+Science. Consistent miss sets (score-average check + facts) leave exactly two global solutions that differ only by swapping Alva↔Deep on {only-Hindi vs Hindi+Science}: - Carl: Maths only - Esha: English only - Foni: English + Social - Bithi: Science + Social - {Alva, Deep}: {Hindi only, Hindi+Science} in either order This Q. Both solutions put the Hindi misses on Alva and Deep (one only-Hindi, one Hindi+Science). No other pair works. Why other options fail. - A (Alva and Esha): Esha does not miss Hindi. - C (Deep and Esha): same — Esha is an English-only miss. - D (Two among Alva, Deep and Esha): the Hindi pair is fixed as Alva & Deep, not a vague “two among three”.
Q40Data Interpretation·Tables

In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.

EnglishHindiMathematicsScienceSocial Science
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883

The following facts are also known. I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations. II. The student who missed the Mathematics examination did not miss any other examination. III. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.

What BEST can be concluded about the students who missed the Science examination?

  • AAlva and Bithi
  • BDeep and Bithi
  • CAlva and Deep
  • DBithi and one out of Alva and DeepCorrect answer

Answer: D

Show explanation
Answer:D (Bithi and one out of Alva and Deep) Setup. Six students; each missed 1 or 2 of {English, Hindi, Maths, Science, Social}. Awarded mark for a missed subject = average of best 3 of 4 appeared (if one miss) or average of best 2 of 3 appeared (if two misses). Scores: | | Eng | Hin | Math | Sci | Soc | |---|---|---|---|---|---| | Alva | 80 | 75 | 70 | 75 | 60 | | Bithi | 90 | 80 | 55 | 85 | 85 | | Carl | 75 | 80 | 90 | 100 | 90 | | Deep | 70 | 90 | 100 | 90 | 80 | | Esha | 80 | 85 | 95 | 60 | 55 | | Foni | 83 | 72 | 78 | 88 | 83 | Facts: (I) exactly two students missed each of Eng/Hin/Sci/Soc; (II) the unique Maths-misser missed only Maths; (III) of the two Hindi-missers, one missed only Hindi and the other missed Hindi+Science. Consistent miss sets (score-average check + facts) leave exactly two global solutions that differ only by swapping Alva↔Deep on {only-Hindi vs Hindi+Science}: - Carl: Maths only - Esha: English only - Foni: English + Social - Bithi: Science + Social - {Alva, Deep}: {Hindi only, Hindi+Science} in either order This Q. Science missers: Bithi (always) plus whichever of Alva/Deep has the Hindi+Science miss. So Bithi and one out of Alva and Deep. Why other options fail. - A (Alva and Bithi): Alva is not always a Science misser. - B (Deep and Bithi): Deep is not always a Science misser. - C (Alva and Deep): omits Bithi, who always misses Science.
Q41Logical Reasoning·Quant-based ReasoningTITA

In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.

EnglishHindiMathematicsScienceSocial Science
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883

The following facts are also known. I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations. II. The student who missed the Mathematics examination did not miss any other examination. III. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.

How many out of these six students missed exactly one examination?

Answer: 3

Show explanation
Answer:3 Setup. Six students; each missed 1 or 2 of {English, Hindi, Maths, Science, Social}. Awarded mark for a missed subject = average of best 3 of 4 appeared (if one miss) or average of best 2 of 3 appeared (if two misses). Scores: | | Eng | Hin | Math | Sci | Soc | |---|---|---|---|---|---| | Alva | 80 | 75 | 70 | 75 | 60 | | Bithi | 90 | 80 | 55 | 85 | 85 | | Carl | 75 | 80 | 90 | 100 | 90 | | Deep | 70 | 90 | 100 | 90 | 80 | | Esha | 80 | 85 | 95 | 60 | 55 | | Foni | 83 | 72 | 78 | 88 | 83 | Facts: (I) exactly two students missed each of Eng/Hin/Sci/Soc; (II) the unique Maths-misser missed only Maths; (III) of the two Hindi-missers, one missed only Hindi and the other missed Hindi+Science. Consistent miss sets (score-average check + facts) leave exactly two global solutions that differ only by swapping Alva↔Deep on {only-Hindi vs Hindi+Science}: - Carl: Maths only - Esha: English only - Foni: English + Social - Bithi: Science + Social - {Alva, Deep}: {Hindi only, Hindi+Science} in either order This Q. Exactly-one missers: Carl (Maths), Esha (English), and exactly one of Alva/Deep (the only-Hindi person). Count = 3. (Bithi and Foni always miss two.)
Q42Logical Reasoning·Quant-based ReasoningTITA

In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.

EnglishHindiMathematicsScienceSocial Science
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883

The following facts are also known. I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations. II. The student who missed the Mathematics examination did not miss any other examination. III. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.

For how many students can we be definite about which examinations they missed?

Answer: 4

Show explanation
Answer:4 Setup. Six students; each missed 1 or 2 of {English, Hindi, Maths, Science, Social}. Awarded mark for a missed subject = average of best 3 of 4 appeared (if one miss) or average of best 2 of 3 appeared (if two misses). Scores: | | Eng | Hin | Math | Sci | Soc | |---|---|---|---|---|---| | Alva | 80 | 75 | 70 | 75 | 60 | | Bithi | 90 | 80 | 55 | 85 | 85 | | Carl | 75 | 80 | 90 | 100 | 90 | | Deep | 70 | 90 | 100 | 90 | 80 | | Esha | 80 | 85 | 95 | 60 | 55 | | Foni | 83 | 72 | 78 | 88 | 83 | Facts: (I) exactly two students missed each of Eng/Hin/Sci/Soc; (II) the unique Maths-misser missed only Maths; (III) of the two Hindi-missers, one missed only Hindi and the other missed Hindi+Science. Consistent miss sets (score-average check + facts) leave exactly two global solutions that differ only by swapping Alva↔Deep on {only-Hindi vs Hindi+Science}: - Carl: Maths only - Esha: English only - Foni: English + Social - Bithi: Science + Social - {Alva, Deep}: {Hindi only, Hindi+Science} in either order This Q. Definite miss lists: Carl, Esha, Foni, Bithi (four students). Alva and Deep swap the only-Hindi vs Hindi+Science roles, so their exact lists are not unique. Count = 4.
Q43Data Interpretation·Tables

The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below: P1: timely arrival P2: behaviour P3: comfortable ride P4: driver's familiarity with the route P5: value for money Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters. The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:

P1P2P3P4P5Fixed PaymentBonus
Arun4Rs. 1000Rs. 250 × Final Rating
Barun3Rs. 1200Rs. 200 × Final Rating
Chandan2Rs. 1400Rs. 100 × Final Rating
Damodaran3Rs. 1300Rs. 150 × Final Rating
Eman2Rs. 1100Rs. 200 × Final Rating

The following additional facts are known. 1. Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters. 2. None of drivers has got the same rating in three parameters.

If Damodaran does not get a bonus, what is the maximum possible value of his final rating?

  • A3.6Correct answer
  • B3.8
  • C3.2
  • D3.4

Answer: A

Show explanation
Answer:A (3.6) Setup. Drivers Arun, Barun, Chandan, Damodaran, Eman; parameters P1–P5 rated integers 1–5. Final rating = average of five. Bonus requires: no rating of 1, and at least one 5. Known cells: Arun P3=4; Barun P1=3; Chandan P4=2; Damodaran P3=3; Eman P5=2. Pay = Fixed + (bonus rate)×Final if eligible; else Fixed only. Fixed/rate: Arun 1000250, Barun 1200200, Chandan 1400100, Damodaran 1300150, Eman 1100200. Also: Arun & Barun have exactly one 5 each; Chandan has exactly two 5s; nobody has the same rating in three parameters. This Q. Damodaran gets no bonus ⇒ either he has a 1 somewhere, or he has no 5. Known P3=3. Maximise average under “no three equal”. Best is to take a 1 together with two 5s and a 4: ratings like (5,5,3,4,1) sum 18 → average 3.6. Three 5s are banned; without any 5 the max under the triple-ban is only 3.4. Why other options fail. - B (3.8): 3.8 needs sum 19, which forces three 5s or an illegal triple. - C (3.2): 3.2 is achievable but not maximal. - D (3.4): 3.4 is the no-5 maximum, beaten by the 55/43/1 shape.
Q44Data Interpretation·Tables

The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below: P1: timely arrival P2: behaviour P3: comfortable ride P4: driver's familiarity with the route P5: value for money Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters. The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:

P1P2P3P4P5Fixed PaymentBonus
Arun4Rs. 1000Rs. 250 × Final Rating
Barun3Rs. 1200Rs. 200 × Final Rating
Chandan2Rs. 1400Rs. 100 × Final Rating
Damodaran3Rs. 1300Rs. 150 × Final Rating
Eman2Rs. 1100Rs. 200 × Final Rating

The following additional facts are known. 1. Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters. 2. None of drivers has got the same rating in three parameters.

If Eman gets a bonus, what is the minimum possible value of his final rating?

  • A3.4
  • B2.8
  • C3.0Correct answer
  • D3.2

Answer: C

Show explanation
Answer:C (3.0) Setup. Drivers Arun, Barun, Chandan, Damodaran, Eman; parameters P1–P5 rated integers 1–5. Final rating = average of five. Bonus requires: no rating of 1, and at least one 5. Known cells: Arun P3=4; Barun P1=3; Chandan P4=2; Damodaran P3=3; Eman P5=2. Pay = Fixed + (bonus rate)×Final if eligible; else Fixed only. Fixed/rate: Arun 1000250, Barun 1200200, Chandan 1400100, Damodaran 1300150, Eman 1100200. Also: Arun & Barun have exactly one 5 each; Chandan has exactly two 5s; nobody has the same rating in three parameters. This Q. Eman has bonus ⇒ no 1s, ≥1 five, and P5=2 fixed. Minimise average: use one 5 and fill the rest as small as possible without a 1 and without three-of-a-kind. Best is (5,2,2,3,3) or perm with P5=2 — sum 15 → average 3.0. Two 2s and two 3s avoid a triple. Why other options fail. - A (3.4): 3.4 is larger than the minimum. - B (2.8): 2.8 would need a 1 (forbidden for bonus) or an impossible pack. - D (3.2): 3.2 is above the forced minimum.
Q45Data Interpretation·Tables

The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below: P1: timely arrival P2: behaviour P3: comfortable ride P4: driver's familiarity with the route P5: value for money Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters. The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:

P1P2P3P4P5Fixed PaymentBonus
Arun4Rs. 1000Rs. 250 × Final Rating
Barun3Rs. 1200Rs. 200 × Final Rating
Chandan2Rs. 1400Rs. 100 × Final Rating
Damodaran3Rs. 1300Rs. 150 × Final Rating
Eman2Rs. 1100Rs. 200 × Final Rating

The following additional facts are known. 1. Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters. 2. None of drivers has got the same rating in three parameters.

If all five drivers get bonus, what is the minimum possible value of the monthly payment (in rupees) that a driver gets?

  • A1700Correct answer
  • B1740
  • C1750
  • D1600

Answer: A

Show explanation
Answer:A (1700) Setup. Drivers Arun, Barun, Chandan, Damodaran, Eman; parameters P1–P5 rated integers 1–5. Final rating = average of five. Bonus requires: no rating of 1, and at least one 5. Known cells: Arun P3=4; Barun P1=3; Chandan P4=2; Damodaran P3=3; Eman P5=2. Pay = Fixed + (bonus rate)×Final if eligible; else Fixed only. Fixed/rate: Arun 1000250, Barun 1200200, Chandan 1400100, Damodaran 1300150, Eman 1100200. Also: Arun & Barun have exactly one 5 each; Chandan has exactly two 5s; nobody has the same rating in three parameters. This Q. All five get bonus ⇒ each has ≥1 five, no 1s, and the 5-count facts hold (Arun/Barun one 5; Chandan two 5s). Minimise someone’s Fixed + rate×Final. Chandan’s fixed 1400 is highest but his rate 100 is tiny; with minimal legal final 3.0 (e.g. 5,5,2,2,1 banned → 5,5,2,2,3=3.4 actually for two 5s… Chandan needs two 5s: min sum with no 1 and no triple = 5+5+2+2+3=17 → 3.4, pay 1400+340=1740). Eman at final 3.0: pay 1100+200×3=1700. Arun min with one 5: 5+2+2+3+4(known)=16 → 3.2, pay 1000+800=1800. Barun/Damodaran minima sit above 1700. So the global minimum payment is Eman at 1700. Why other options fail. - B (1740): 1740 is Chandan’s minimum, not the overall minimum. - C (1750): 1750 is not forced as a minimum for anyone. - D (1600): 1600 would need final 2.5 with Eman’s rate — impossible with integer ratings ≥2.
Q46Data Interpretation·Tables

The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below: P1: timely arrival P2: behaviour P3: comfortable ride P4: driver's familiarity with the route P5: value for money Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters. The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:

P1P2P3P4P5Fixed PaymentBonus
Arun4Rs. 1000Rs. 250 × Final Rating
Barun3Rs. 1200Rs. 200 × Final Rating
Chandan2Rs. 1400Rs. 100 × Final Rating
Damodaran3Rs. 1300Rs. 150 × Final Rating
Eman2Rs. 1100Rs. 200 × Final Rating

The following additional facts are known. 1. Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters. 2. None of drivers has got the same rating in three parameters.

If all five drivers get bonus, what is the maximum possible value of the monthly payment (in rupees) that a driver gets?

  • A1960Correct answer
  • B1950
  • C2050
  • D1900

Answer: A

Show explanation
Answer:A (1960) Setup. Drivers Arun, Barun, Chandan, Damodaran, Eman; parameters P1–P5 rated integers 1–5. Final rating = average of five. Bonus requires: no rating of 1, and at least one 5. Known cells: Arun P3=4; Barun P1=3; Chandan P4=2; Damodaran P3=3; Eman P5=2. Pay = Fixed + (bonus rate)×Final if eligible; else Fixed only. Fixed/rate: Arun 1000250, Barun 1200200, Chandan 1400100, Damodaran 1300150, Eman 1100200. Also: Arun & Barun have exactly one 5 each; Chandan has exactly two 5s; nobody has the same rating in three parameters. This Q. All five get bonus; maximise someone’s payment. Arun has the largest rate (250). Max Arun final with exactly one 5, P3=4, no 1, no triple: 5+4+4+4+2 is illegal (three/four 4s). Best legal: 5,4,4,3,2 with P3=4 → sum 18 → 3.6, pay 1000+250×3.6=1900? Wait — 5+4+3+2+4=18 → 3.6 → 1900. Can we reach sum 19? 5+4+4+3+3=19 with P3=4 → two 4s and two 3s OK → final 3.8 → pay 1000+950=1950. Sum 20 with one 5: 5+4+4+4+3 illegal. So Arun max pay 1950. Barun max ~1200+200×3.8=1960 with one 5 and high fillers (3 known on P1): 5+3+4+4+3 illegal triple 34. 5+3+4+4+2=18→3.6→1920. 5+3+5 banned (only one 5). Actually Barun: 5,3,4,4,4 illegal. Max sum 5+3+4+4+2=18 or 5+3+4+2+4=18 → 3.6 → 1920 < 1960. Re-check Barun: ratings five integers, exactly one 5, P1=3, no 1, no value thrice. Max sum: 5,3,4,4,2=18 only? 5,3,4,2,4=18. Or 5,3,4,4,3 has two 3s and two 4s — OK! Sum 19 → 3.8 → pay 1200+760=1960. Damodaran/Chandan/Eman top out lower. So maximum payment = 1960 (Barun). Why other options fail. - B (1950): 1950 is Arun’s max, beaten by Barun’s 1960. - C (2050): 2050 exceeds every driver’s Fixed+rate×(max legal final). - D (1900): 1900 is below the Barun maximum.
Q47Logical Reasoning·Grouping & Selection

Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam. The following facts are known about these ten musicians. 1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla. 2. D is an expert in both tabla and ghatam. 3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam. 4. Neither I nor J is an expert in tabla. 5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam.

Who among the following is DEFINITELY an expert in tabla but not in either mridangam or ghatam?

  • AC
  • BF
  • CHCorrect answer
  • DA

Answer: C

Show explanation
Answer:C (H) Setup. 10 musicians; instrument expertise counts: Tabla-only 3, Mridangam-only 3, Ghatam-only 1, Tabla+Mridangam (no G) 2, Tabla+Ghatam (no M) 1; nobody has Mridangam+Ghatam or all three. Facts: (1) A,B both Mridangam; exactly one of them also Tabla. (2) D is Tabla+Ghatam. (3) F,G both Tabla; exactly one also Mridangam. (4) I,J not Tabla. (5) H,I not Mridangam; exactly one of H,I has Ghatam. Forced types. The only Ghatam players are D (TG) and the unique G-only person. Fact 5 ⇒ that G-only is one of {H,I}; the other of {H,I} has neither M nor G ⇒ must be Tabla-only. Fact 4 bans I from Tabla ⇒ I = G-only, H = Tabla-only. J ≠ Tabla ⇒ J = Mridangam-only. {A,B} = {M-only, TM}; {F,G} = {T-only, TM}. Remaining {C,E} = {T-only, M-only} in some order. This Q. H is forced Tabla-only. Among the options only H is definite Tabla-only (F might be TM; C/A are not forced T-only). Why other options fail. - A (C): C may be M-only instead of T-only. - B (F): F may be the TM member of {F,G}. - D (A): A is either M-only or TM, never pure Tabla-only.
Q48Logical Reasoning·Grouping & Selection

Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam. The following facts are known about these ten musicians. 1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla. 2. D is an expert in both tabla and ghatam. 3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam. 4. Neither I nor J is an expert in tabla. 5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam.

Who among the following is DEFINITELY an expert in mridangam but not in either tabla or ghatam?

  • AB
  • BE
  • CJCorrect answer
  • DG

Answer: C

Show explanation
Answer:C (J) Setup. 10 musicians; instrument expertise counts: Tabla-only 3, Mridangam-only 3, Ghatam-only 1, Tabla+Mridangam (no G) 2, Tabla+Ghatam (no M) 1; nobody has Mridangam+Ghatam or all three. Facts: (1) A,B both Mridangam; exactly one of them also Tabla. (2) D is Tabla+Ghatam. (3) F,G both Tabla; exactly one also Mridangam. (4) I,J not Tabla. (5) H,I not Mridangam; exactly one of H,I has Ghatam. Forced types. The only Ghatam players are D (TG) and the unique G-only person. Fact 5 ⇒ that G-only is one of {H,I}; the other of {H,I} has neither M nor G ⇒ must be Tabla-only. Fact 4 bans I from Tabla ⇒ I = G-only, H = Tabla-only. J ≠ Tabla ⇒ J = Mridangam-only. {A,B} = {M-only, TM}; {F,G} = {T-only, TM}. Remaining {C,E} = {T-only, M-only} in some order. This Q. J is forced Mridangam-only. J is the definite answer among the options. Why other options fail. - A (B): B may be the TM member of {A,B}. - B (E): E may be T-only rather than M-only. - D (G): G may be TM rather than M-related; G is Tabla-based.
Q49Logical Reasoning·Grouping & Selection

Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam. The following facts are known about these ten musicians. 1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla. 2. D is an expert in both tabla and ghatam. 3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam. 4. Neither I nor J is an expert in tabla. 5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam.

Which of the following pairs CANNOT have any musician who is an expert in both tabla and mridangam but not in ghatam?

  • AA and B
  • BF and G
  • CC and ECorrect answer
  • DC and F

Answer: C

Show explanation
Answer:C (C and E) Setup. 10 musicians; instrument expertise counts: Tabla-only 3, Mridangam-only 3, Ghatam-only 1, Tabla+Mridangam (no G) 2, Tabla+Ghatam (no M) 1; nobody has Mridangam+Ghatam or all three. Facts: (1) A,B both Mridangam; exactly one of them also Tabla. (2) D is Tabla+Ghatam. (3) F,G both Tabla; exactly one also Mridangam. (4) I,J not Tabla. (5) H,I not Mridangam; exactly one of H,I has Ghatam. Forced types. The only Ghatam players are D (TG) and the unique G-only person. Fact 5 ⇒ that G-only is one of {H,I}; the other of {H,I} has neither M nor G ⇒ must be Tabla-only. Fact 4 bans I from Tabla ⇒ I = G-only, H = Tabla-only. J ≠ Tabla ⇒ J = Mridangam-only. {A,B} = {M-only, TM}; {F,G} = {T-only, TM}. Remaining {C,E} = {T-only, M-only} in some order. This Q. The two TM experts are one of {A,B} and one of {F,G}. Pair C and E are both in {T-only, M-only} — neither can be TM. Every other listed pair can hold a TM person. Why other options fail. - A (A and B): exactly one of A,B is TM. - B (F and G): exactly one of F,G is TM. - D (C and F): C can be T-only while F is TM — the pair can contain a TM musician.
Q50Logical Reasoning·Grouping & Selection

Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam. The following facts are known about these ten musicians. 1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla. 2. D is an expert in both tabla and ghatam. 3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam. 4. Neither I nor J is an expert in tabla. 5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam.

If C is an expert in mridangam and F is not, then which are the three musicians who are experts in tabla but not in either mridangam or ghatam?

  • AE, F and HCorrect answer
  • BC, E and G
  • CE, G and H
  • DC, G and H

Answer: A

Show explanation
Answer:A (E, F and H) Setup. 10 musicians; instrument expertise counts: Tabla-only 3, Mridangam-only 3, Ghatam-only 1, Tabla+Mridangam (no G) 2, Tabla+Ghatam (no M) 1; nobody has Mridangam+Ghatam or all three. Facts: (1) A,B both Mridangam; exactly one of them also Tabla. (2) D is Tabla+Ghatam. (3) F,G both Tabla; exactly one also Mridangam. (4) I,J not Tabla. (5) H,I not Mridangam; exactly one of H,I has Ghatam. Forced types. The only Ghatam players are D (TG) and the unique G-only person. Fact 5 ⇒ that G-only is one of {H,I}; the other of {H,I} has neither M nor G ⇒ must be Tabla-only. Fact 4 bans I from Tabla ⇒ I = G-only, H = Tabla-only. J ≠ Tabla ⇒ J = Mridangam-only. {A,B} = {M-only, TM}; {F,G} = {T-only, TM}. Remaining {C,E} = {T-only, M-only} in some order. This Q. C is Mridangam ⇒ C = M-only ⇒ E = T-only. F is not Mridangam ⇒ F = T-only ⇒ G = TM. Tabla-only three: H, E, F. So E, F and H. Why other options fail. - B (C, E and G): puts G (who is TM here) in place of F. - C (E, G and H): puts G instead of F. - D (C, G and H): puts G and drops E.

QA(26 questions)

Q51Quantitative Ability·Sets & Venn Diagrams

Among 100 students, x1 have birthdays in January, x2 have birthday in February, and so on. If x0 = max (x1, x2, ……, x12), then the smallest possible value of x0 is

  • A12
  • B9Correct answer
  • C8
  • D10

Answer: B

Show explanation
Answer:B (9) What to find. Among 100 students, x1 have birthdays in January, x2 in February, …, x12 in December. If x0 = max(x1,…,x12), the smallest possible value of x0. Setup. Distribute 100 birthdays across 12 months; minimize the maximum month count. Steps. 1. Spread as evenly as possible: 100 = 12 × 8 + 4, so eight months have 8 and four have 9. 2. The maximum is therefore 9. 3. A maximum of 8 would cover at most 96 students, which is impossible. Conclusion. 9 → B.
Q52Quantitative Ability·Number SystemsTITA

A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

Answer: 62

Show explanation
Answer:62 What to find. A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remai… Setup. Each child gets half the current stock plus one; stock ends after 5 children. Steps. 1. If r remains after a gift, prior stock s satisfies s/2 + 1 = s − r ⇒ 2. s = 2(r+1). 3. Back from 0: 2, 6, 14, 30, 62. 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. Initial stock = 62. Verification. With the keyed result 62, 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.
Q53Quantitative Ability·Simple & Compound InterestTITA

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Answer: 12

Show explanation
Answer:12 What to find. Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, w… Setup. Veeru: 10000 at 5% SI from t=0. Joy: 8000 at 10% SI from t=2. Equate balances at time t. Steps. 1. 10000+500t = 8000+800(t−2) ⇒ 2. 10000+500t = 6400+800t ⇒ 3. 3600=300t ⇒ 4. t=12. 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. 12 years after Veeru invests. Verification. With the keyed result 12, 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.
Q54Quantitative Ability·Logarithms

If y is a negative number such that 2y2 log3 5 = 5log2 3, then y equals

  • Alog2(15)
  • Blog2(15)
  • Clog2(13)
  • Dlog2(13)Correct answer

Answer: D

Show explanation
Answer:D (log2(13)) What to find. If y is a negative number such that, then y equals Setup. y<0 and 2y2 log3 5 = 5log2 3. Steps. 1. LHS = 5y2 log3 5 · log5 2 = 5y2 log3 2. 2. Equate exponents: y2 log3 2 = log2 3 = 1log3 2 3. y2=(log2 3)24. y=±log2 3. 5. Negativity ⇒ 6. y=−log2 3=log2(13). 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 (−log2(15)): Positive (=log2 5). - B (log2(15)): Wrong magnitude. - C (−log2(13)): Positive (=log2 3). Conclusion. y = log2(13) → 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.
Q55Quantitative Ability·Time, Speed & Distance

Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he travels at 15 km/hr. Leaving home at 9:10, at what speed, in km/hr, must be travel so as to reach office exactly at 10 am?

  • A14
  • B11
  • C13
  • D12Correct answer

Answer: D

Show explanation
Answer:D (12) What to find. Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he travels at 15 km/hr. Leaving home at 9:10, at what speed, in km/hr,… Setup. Same departure; 8 km/h → 10:15, 15 km/h → 9:40. Leave 9:10, arrive 10:00. Steps. 1. Time gap 35 min = 712 h: d/8−d/15=712 2. 7d/120=7123. d=10 km. 4. Available time 50 min = 56 h ⇒ 5. speed=1056=12. 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): Arrives early (~43 min). - B (11): Arrives late (~55 min). - C (13): Arrives early (~46 min). Conclusion. 12 km/h → D.
Q56Quantitative Ability·Time, Speed & Distance

A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

  • A58
  • B61
  • C50
  • D67Correct answer

Answer: D

Show explanation
Answer:D (67) What to find. A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled a… Setup. At v/3, late by 30 min. Return: 5 min at v, 4 min stop, then speed up to finish on time. Steps. 1. d=vT=(v/3)(T+12) ⇒ 2. T=14 h=15 min, d=v/4. 3. After 5 min cover v/12; 4. left v/6. 5. Time left 6 min=110 h ⇒ 6. need u=5v/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. Why other options fail. - A (58), B (61), C (50): All miss the required 23 hike. Conclusion. 67 → D.
Q57Quantitative Ability·Surds & Indices

The number of real-valued solutions of the equation 2x + 2-x = 2 – (x – 2)2 is

  • A1
  • B0Correct answer
  • CInfinite
  • D2

Answer: B

Show explanation
Answer:B (0) What to find. The number of real-valued solutions of the equation 2x + 2-x = 2 – (x – 2)2 is Setup. 2x + 2−x = 2 − (x−2)2. Steps. 1. LHS ≥ 2 (AM-GM, eq. 2. at x=0). 3. RHS ≤ 2 (eq. 4. at x=2). 5. Equality on both sides cannot hold at one x, so no real solution. 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), D (2): No intersection. - C (Infinite): Sides never agree. Conclusion. 0 solutions → 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.
Q58Quantitative Ability·MensurationTITA

A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3?

Answer: 8

Show explanation
Answer:8 What to find. A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted sol… Setup. 40 L dye:water=2:3 → dilute to 2:5; remove 14; add dye to restore 2:3. Steps. 1. Dye 16, water 24. 2. Add 16 L water → 3. 56 L (dye 16, water 40). 4. Remove 14 L (dye 4, water 10) → 5. dye 12, water 30. 6. Need (12+d):30=2:3 ⇒ 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. 8 litres.
Q59Quantitative Ability·Averages

Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

  • A5
  • B4
  • C7
  • D6Correct answer

Answer: D

Show explanation
Answer:D (6) What to find. Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is Setup. A+B+C2=5, B+A+C2=7; positive integers; find A+B. Steps. 1. 2A+B+C=10, A+2B+C=14 ⇒ 2. B−A=4. 3. C=10−2A−B=6−3A>0 ⇒ 4. A=1, B=5, C=3. 5. A+B=6. 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 (4), C (7): Not the unique positive solution. Conclusion. 6 → D.
Q60Quantitative Ability·Number SystemsTITA

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Answer: 21

Show explanation
Answer:21 What to find. How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7? Setup. 3-digit numbers with digit product p ∈ {3,4,5,6}. Steps. 1. p=3: perms of (1,1,3) → 2. p=4: (1,1,4)→3, (1,2,2)→3. 3. p=5: (1,1,5)→3. 4. p=6: (1,1,6)→3, (1,2,3)→6. 5. Total 3+6+3+9=21. 6. (No zero digit.) 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. 21. Verification. With the keyed result 21, 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·Time, Speed & Distance

A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

  • A100
  • B80
  • C90Correct answer
  • D70

Answer: C

Show explanation
Answer:C (90) What to find. A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes a… Setup. After meeting, Car1 needs 45 min, Car2 20 min; v1=60; find v2. Steps. 1. v1 t = v2·(2060) and v2 t = v1·(4560) ⇒ 2. (v1/v2)2=2045=493. v1/v2=234. v2=90. 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 (100), B (80), D (70): Break (v1/v2)2=t2/t1. Conclusion. 90 → C.
Q62Quantitative Ability·LogarithmsTITA

If log4 5 = (log4 y)(log6 5), then y equals

Answer: 36

Show explanation
Answer:36 What to find. If log4 5 = (log4 y) (log6 5), then y equals Setup. log4 5 = (log4 y)(log6 5). Steps. 1. log6 5=(12)log6 5=log4 52 log4 6. 2. Cancel log4 5: 1=log4 y2 log4 6 3. log4 y=log4 36 ⇒ 4. y=36. 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. 36. Verification. With the keyed result 36, 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.
Q63Quantitative Ability·Mensuration

A solid right circular cone of height 27 cm is cut into pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

  • A243Correct answer
  • B232
  • C256
  • D264

Answer: A

Show explanation
Answer:A (243) What to find. A solid right circular cone of height 27 cm is cut into pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two piec… Setup. Cone height 27; cut parallel to base 18 from base (small cone height 9); |V_frustum−V_small|=225. Steps. 1. Volume scale (927)3=127. 2. Difference 25V/27=225 ⇒ 3. V=225·2725=243. 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 (232), C (256), D (264): ≠225·2725. Conclusion. 243 → 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.
Q64Quantitative Ability·Time, Speed & Distance

Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

  • A78
  • B87
  • C75
  • D82Correct answer

Answer: D

Show explanation
Answer:D (82) What to find. Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 se… Setup. Walkers 2 and 4 km/h; train crosses in 90 s and 100 s; time to cross a post. Steps. 1. LV−2=140, LV−4=1362. 36(V−2)=40(V−4) ⇒ 3. V=22, L=12. 4. TimeLV=144 h=360044≈81.82≈82. 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 (78), B (87), C (75): Wrong rounding of 360044. Conclusion. 82 → D.
Q65Quantitative Ability·Circles

A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is

  • A15
  • B25
  • C25Correct answer
  • D18

Answer: C

Show explanation
Answer:C (25) What to find. Ratio (area of inscribed circle) : (area of rhombus) when diagonals are 12 and 16. Setup. A rhombus has an inscribed circle iff all sides are equal (always) and the circle exists with diameter equal to the height corresponding to any side — equivalently, area = r · perimeter/2 = r · 2s for side s, so r = Area/s? More cleanly: r = Area / semiperimeter. Steps. 1. Area of rhombus = (12d1·d2 = (12)·12 × 16 = 96. 2. Side s from half-diagonals: s = sqrt(62 + 82) = sqrt(36+64) = 10. 3. Semiperimeter = 2s = 20, so inradius r = Area / semiperimeter = 9620 = 245. 4. Circle area = π r2 = π · (57625). Ratio to rhombus: [π · 57625] / 96 = 576π25 × 96 = 25. Why other options fail. - A (15): would need a different r (e.g. treating a diagonal as diameter). - B (25): half of the correct numerator — typically from forgetting a factor 2 in r2. - D (18): inconsistent with s = 10 and area 96. Conclusion. Ratio = 25 → C.
Q66Quantitative Ability·Functions & Graphs

If f(5 + x) = f(5- x) for every real x, and f(x) = 0 has four distinct real roots, then the sum of these roots is

  • A10
  • B0
  • C40
  • D20Correct answer

Answer: D

Show explanation
Answer:D (20) What to find. If f(5 + x) = f(5- x) for every real x, and f(x) = 0 has four distinct real roots, then the sum of these roots is Setup. f(5+x)=f(5−x) ∀x; four distinct roots of f(x)=0; sum them. Steps. 1. Symmetry about 5 ⇒ 2. roots are 5±d1 and 5±d2. 3. Sum=20. 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 (10): One pair only. - B (0): Symmetry about 0. - C (40): Double count. Conclusion. 20 → 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.
Q67Quantitative Ability·Surds & Indices

If x = (4096)7 + 4 3, then which of the following equals 64?

  • Ax7x2 3
  • Bx72x43
  • Cx72x2 3Correct answer
  • Dx7x4 3

Answer: C

Show explanation
Answer:C (x72x2 3) What to find. If x = (4096)7 + 4 3, then which of the following equals 64? Setup. x=(4096)7+4 3; which form equals 64. Steps. 1. 4096=6422. x=642(7+4 3)3. 64=x12(7+4 3). 4. Rationalize: 17+4 3=7−4 3, so exponent=7−4 32=72−2 3. 5. Thus 64=x72x2 3 (key’s option C). 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: Exponent 7−2 3 too large. - B: 43≠2 3. - D: Gives 4096, not 64. Conclusion. 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·Circles

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

  • A3 π(5 + 12π)Correct answer
  • B3 π(52 + 6π)
  • C5 π(3 + 9π)
  • D4 π(3 + 9π)

Answer: A

Show explanation
Answer:A (3 π(5+12π)) What to find. On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the… Setup. Rectangle area 135; circle touches two opposite sides; unpainted=(23) painted; perimeter. Steps. 1. Diameter = one side 2r; 2. 2r·ℓ=135. 3. 135−πr2=(23)πr24. r2=81π, r=9π, ℓ=(152)π. 5. Perimeter=2(2r+ℓ)=3 π(5+12π). 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, C, D: Algebra does not match 2(2r+ℓ). Conclusion. 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.
Q69Quantitative Ability·Surds & IndicesTITA

The number of distinct real roots of the equation (x + 1x)2 − 3(x + 1x) + 2 = 0 equals

Answer: 1

Show explanation
Answer:1 What to find. Number of distinct real roots of (x + 1x)2 − 3(x + 1x) + 2 = 0. Setup. Domain x ≠ 0. Substitute t = x + 1x. For real x ≠ 0, AM-GM (or (x1x)2 ≥ 0) gives |t| ≥ 2. Steps. 1. Expand in t: t2 − 3t + 2 = 0 ⇒ (t − 1)(t − 2) = 0 ⇒ t = 1 or t = 2. 2. t = 1 is impossible for real x because |t| ≥ 2. 3. t = 2 ⇒ x + 1x = 2 ⇒ x2 − 2x + 1 = 0 ⇒ (x − 1)2 = 0 ⇒ x = 1 (double algebraically, but one distinct real root). 4. No negative branch appears for t = 2; t = −2 is not a root of the quadratic in t. Conclusion. Exactly 1 distinct real root.
Q70Quantitative Ability·Number Systems

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

  • A59
  • B49
  • C56
  • D46Correct answer

Answer: D

Show explanation
Answer:D (46) What to find. If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is Setup. ab=432, bc=96, c<9; minimize a+b+c. Steps. 1. c∈{2,4,6,8} (a=4.5c integer). 2. Sums: 59,46,49,56. 3. Min 46 at (a,b,c)=(18,24,4). 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 (59), B (49), C (56): Valid but larger. Conclusion. 46 → 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.
Q71Quantitative Ability·InequalitiesTITA

The area of the region satisfying the inequalities |x| − y ≤ 1, y ≥ 0 and y ≤ 1 is

Answer: 3

Show explanation
Answer:3 Setup. Rewrite |x| − y ≤ 1 as |x| ≤ y + 1. Intersect with the horizontal strip 0 ≤ y ≤ 1. Steps. 1. For fixed y ∈ [0, 1], x runs through [−(y+1), y+1], a segment of length 2(y+1). 2. Area = ∫01 2(y+1) dy = 2[y2/2 + y]01 = 2(12 + 1) = 2 · 32 = 3. 3. Geometry check: the central rectangle |x| ≤ 1, 0 ≤ y ≤ 1 has area 2. Outside it, for 1 ≤ |x| ≤ 2, the inequality forces y ≥ |x| − 1, so each side is a right triangle of legs 1 with area 12; two sides add 1. Total 2 + 1 = 3. 4. Note: the region is *not* the trapezoid of area 3.5 that appears if one wrongly integrates width 2 + 2y from a flipped inequality; the correct slice width is 2(y+1) on [0,1] only. Conclusion. Area = 3 (not 3.5).
Q72Quantitative Ability·Percentages

In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to

  • A59
  • B55
  • C66Correct answer
  • D62

Answer: C

Show explanation
Answer:C (66) What to find. In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old pe… Setup. 28% young; 65% literate; 25% of literates young; % old among illiterates. Steps. 1. Per 100: young 28, old 72; 2. lit 65 (young lit 0.25·65=16.25, old lit 48.75); 3. illiterate 35 of which young illit=28−16.25=11.75, old illit=35−11.75=23.25. 4. Old among illit=23.25/35≈66.4%→66. 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 (59), B (55), D (62): Mis-allocate young/old across lit/illit. Conclusion. 66 → C.
Q73Quantitative Ability·Number Systems

The mean of all 4-digit even natural numbers of the form ‘aabb’, where a > 0, is

  • A5050
  • B4864
  • C5544Correct answer
  • D4466

Answer: C

Show explanation
Answer:C (5544) What to find. The mean of all 4-digit even natural numbers of the form ‘aabb’, where a > 0, is Setup. Mean of all even 4-digit numbers aabb (a>0). Steps. 1. Number=1100a+11b=11(100a+b) with b even, a=1..9, b∈{0,2,4,6,8}. 2. Mean over 9 × 5=45 numbers: average a is 5, average b is 4 ⇒ 3. mean=1100·5+11 × 4=5500+44=5544. 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 (5050), B (4864), D (4466): Wrong averages of a or b. Conclusion. 5544 → 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.
Q74Quantitative Ability·Mensuration

An alloy is prepared by mixing three metals A, B and c in the proportion 3 : 4 : 7 by volume. Weights of the same volume of the metals A, B and C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is

  • A48
  • B70
  • C84Correct answer
  • D96

Answer: C

Show explanation
Answer:C (84) What to find. An alloy is prepared by mixing three metals A, B and c in the proportion 3 : 4 : 7 by volume. Weights of the same volume of the metals A, B and C are in the ratio 5 : 2 : 6. In … Setup. Volumes A:B:C=3:4:7; density weights 5:2:6; total alloy 130 kg; weight of C. Steps. 1. Mass parts: 3 × 5, 4 × 2, 7 × 6 = 15+8+42=65. 2. C’s share=4265·130=84. 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 (48), B (70), D (96): Wrong mass-part ratios. Conclusion. 84 → C.
Q75Quantitative Ability·Profit, Loss & DiscountTITA

A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is

Answer: 20000

Show explanation
Answer:20000 What to find. A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then t… Setup. Desktop D + laptop L = 50000; sell at +20% and −10%; overall +2%. Steps. 1. 1.2D+0.9L=1.02·50000=51000. 2. With L=50000−D: 1.2D+0.9(50000−D)=51000 ⇒ 3. 0.3D+45000=51000 ⇒ 4. 0.3D=6000 ⇒ 5. D=20000. 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. Desktop cost 20000. Verification. With the keyed result 20000, 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·Quadratic Equations

How many distinct positive integer-valued solutions exist to the equation (x2 − 7x + 11)x2 − 13x + 42 = 1?

  • A4
  • B6Correct answer
  • C8
  • D2

Answer: B

Show explanation
Answer:B (6) What to find. How many distinct positive integer-valued solutions exist to the equation Setup. (x2−7x+11)x2−13x+42=1; positive integer x. Steps. 1. Cases: exponent 0 ⇒ 2. x=6,7 (base≠0); 3. base=1 ⇒ 4. x2−7x+10=0 ⇒ 5. x=2,5; 6. base=−1 and even exponent ⇒ 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 (4): Misses base=−1. - C (8), D (2): Wrong case count. Conclusion. 6 solutions → 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.

Answer key

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Q#SectionAnswerTopic
1VARCDReading Comprehension
2VARCBReading Comprehension
3VARCAReading Comprehension
4VARCCReading Comprehension
5VARCDReading Comprehension
6VARCBReading Comprehension
7VARCAReading Comprehension
8VARCDReading Comprehension
9VARCCReading Comprehension
10VARCDReading Comprehension
11VARCDReading Comprehension
12VARCAReading Comprehension
13VARCCReading Comprehension
14VARCBReading Comprehension
15VARCBReading Comprehension
16VARCCReading Comprehension
17VARCAReading Comprehension
18VARCDReading Comprehension
19VARC3Verbal Ability
20VARCAVerbal Ability
21VARC3124Verbal Ability
22VARC1432Verbal Ability
23VARCCVerbal Ability
24VARCAVerbal Ability
25VARC3Verbal Ability
26VARC1324Verbal Ability
27DILR340Logical Reasoning
28DILR10Logical Reasoning
29DILR150Logical Reasoning
30DILR325Logical Reasoning
31DILRALogical Reasoning
32DILRALogical Reasoning
33DILRALogical Reasoning
34DILRCLogical Reasoning
35DILRBLogical Reasoning
36DILRALogical Reasoning
37DILRAData Interpretation
38DILRBData Interpretation
39DILRBData Interpretation
40DILRDData Interpretation
41DILR3Logical Reasoning
42DILR4Logical Reasoning
43DILRAData Interpretation
44DILRCData Interpretation
45DILRAData Interpretation
46DILRAData Interpretation
47DILRCLogical Reasoning
48DILRCLogical Reasoning
49DILRCLogical Reasoning
50DILRALogical Reasoning
51QABQuantitative Ability
52QA62Quantitative Ability
53QA12Quantitative Ability
54QADQuantitative Ability
55QADQuantitative Ability
56QADQuantitative Ability
57QABQuantitative Ability
58QA8Quantitative Ability
59QADQuantitative Ability
60QA21Quantitative Ability
61QACQuantitative Ability
62QA36Quantitative Ability
63QAAQuantitative Ability
64QADQuantitative Ability
65QACQuantitative Ability
66QADQuantitative Ability
67QACQuantitative Ability
68QAAQuantitative Ability
69QA1Quantitative Ability
70QADQuantitative Ability
71QA3Quantitative Ability
72QACQuantitative Ability
73QACQuantitative Ability
74QACQuantitative Ability
75QA20000Quantitative Ability
76QABQuantitative Ability

Frequently asked questions

How many questions are there in CAT 2020 Slot 1?

CAT 2020 Slot 1 has 76 questions across VARC, DILR, QA, with a total duration of 2h.

Is this the official CAT 2020 Slot 1 question paper?

Yes — this page hosts the past-year CAT paper for 2020 (Slot 1), with the full question set, answer key, and explanations for revision.

Can I attempt CAT 2020 Slot 1 online with a timer?

CAT 2020 Slot 1 is free to browse with answers here. Timed attempts on MBACracked require Pro. Free accounts include recent CAT and XAT past papers.

Does this page include the CAT 2020 Slot 1 answer key?

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

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

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

Practise CAT 2020 Slot 1 on MBACracked with timed sections and get a percentile breakdown after every attempt — not just an answer key.

Ready to attempt this paper?

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

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