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CAT 2020 Slot 1 question paper with answer key

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

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.

Five jumbled up 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 and key in the number of that sentence as your answer. 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.

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.

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

  • 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

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.

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.

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

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.

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.

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.

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

  • 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.

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

  • 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

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.

Five jumbled up 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 and key in the number of that sentence as your answer. 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.

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

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.

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.

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:
EngHinMathSciSoc
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883
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:
EngHinMathSciSoc
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883
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:
EngHinMathSciSoc
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883
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:
EngHinMathSciSoc
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883
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:
EngHinMathSciSoc
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883
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:
EngHinMathSciSoc
Alva8075707560
Bithi9080558585
Carl75809010090
Deep70901009080
Esha8085956055
Foni8372788883
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) Damodaran receives no bonus, so either one rating is 1 or he has no rating of 5. His P3 rating is 3, and no value may appear three times. To maximise his average, use two 5s, a 4, the fixed 3 and a 1: 5, 5, 4, 3, 1. This is legal, denies the bonus because of the 1, and has sum 18. Three 5s would violate the no-three-equal condition. If he used no 5 at all, the maximum would be lower. Maximum final rating = 185 = 3.6, so A is correct.
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) All five receive a bonus, so every driver has no rating of 1 and at least one rating of 5. Minimum possible payments are obtained from each driver's minimum legal average. Eman has P5 = 2 and can use ratings 5, 3, 3, 2, 2, giving average 3.0 and payment 1100 + 200(3.0) = 1700. For comparison, Chandan must have exactly two 5s and a fixed 2; his minimum legal ratings are 5, 5, 3, 2, 2, giving average 3.4 and payment 1740. Arun's minimum is 1800, and Barun's and Damodaran's minima are also above 1700. Therefore the least possible payment is Rs.1700, option A.
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) All five receive a bonus. For Barun, P1 = 3 and he has exactly one rating of 5. The maximum legal set is 5, 4, 4, 3, 3: its sum is 19, it contains exactly one 5, and no value occurs three times. Thus Barun's final rating is 195 = 3.8 and his payment is 1200 + 200(3.8) = 1960. Arun's maximum is 1950: with P3 = 4 and exactly one 5, his maximum legal average is also 3.8, so 1000 + 250(3.8) = 1950. The other drivers cannot exceed Barun's 1960 under their fixed pay, bonus rate and rating restrictions. Hence A is correct.
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) There are 100 students and 12 months. We want the smallest possible value of the largest monthly birthday count, so the birthdays should be distributed as evenly as possible. If every month had at most 8 birthdays, the total could be no more than 12 × 8 = 96. Since there are 100 students, at least one month must have 9 or more birthdays. A maximum of 9 is achievable: assign 9 birthdays to four months and 8 birthdays to the other eight months. This accounts for 4 × 9 + 8 × 8 = 36 + 64 = 100 students. Thus 9 is both necessary and achievable, so the smallest possible value of the maximum is 9.
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 Work backward because the stock after the fifth child is known to be zero. If a child is given half the current stock plus one toffee, and r toffees remain afterward, then r = s − (s/2+1) = s/2−1, where s is the stock before that child. Therefore s=2(r+1). Starting with r=0 after the fifth child and applying this relation repeatedly gives the stocks before children 5, 4, 3, 2, and 1: 2, 6, 14, 30, 62. Hence the gentleman originally had 62 toffees. A forward check gives remainders 30, 14, 6, 2, and 0.
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 years Let t be the number of years after Veeru invests. At 5% simple interest, Veeru earns ₹500 each year, so his balance after t years is 10000+500t. Joy invests two years later. Therefore, at the same comparison date, Joy’s money has been invested for t−2 years. At 10% simple interest, she earns ₹800 per year, giving a balance of 8000+800(t−2). Equating the balances: 10000+500t = 8000+800(t−2) ⇒ 3600=300t ⇒ t=12. Thus their balances are equal 12 years after Veeru’s investment.
Q54Quantitative Ability·Logarithms

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

  • A−log2(15)
  • Blog2(15)
  • C−log2(13)
  • Dlog2(13)Correct answer

Answer: D

Show explanation
Answer:D (log2(13)) Use the identity alogab = b to express both sides with base 5. Since 2 = 5log52, 2y2 log35 = 5y2 log35 × log52 = 5y2 log32. The right side is already 5log23. Equal positive powers of the same base have equal exponents, so y2 log32 = log23. Because log23 = 1log32, y2 = 1log322 = (log23)2. Therefore y = ±log23. The question specifies y < 0, so y = −log23. Finally, −log23 = log2(13), giving option D.
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 km/h) Let the distance to the office be d km. Since Amal starts at the same time in the first two cases, the 35-minute difference in arrival times equals the difference in travel times: d/8 − d/15 = 3560. Thus 7d/120 = 712, giving d = 10 km. To travel 10 km from 9:10 am to 10:00 am, Amal has 50 minutes, or 56 hour. His required speed is 10 ÷ (56) = 12 km/h.
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 (approximately 67%) Let the usual journey time be T hours and the usual speed be v, so the distance is vT. At one-third of the usual speed, the journey takes 3T hours. The delay is therefore 3T−T=2T, which equals 30 minutes or 12 hour. Hence T=14 hour=15 minutes. On the return journey, the train travels for 5 minutes at speed v, covering one-third of the distance. It then stops for 4 minutes. To arrive within the scheduled 15 minutes, only 6 minutes remain to cover the other two-thirds of the distance. The required speed is (23) distance(615) usual time = (5/3)v. This is an increase of 2v/3, or 66.67%, nearest to 67%.
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) For every real x, AM–GM gives 2x + 2−x ≥ 2, with equality only at x=0. On the other hand, 2−(x−2)2 ≤ 2, with equality only at x=2. An equality between the two sides would require both to equal 2 simultaneously, but their equality cases occur at different values of x. Therefore the equation has no real solution.
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 litres Initially the 40-litre solution contains 16 litres of dye and 24 litres of water. To change the ratio from 2:3 to 2:5, the water must become 40 litres, so 16 litres of water is added and the total volume becomes 56 litres. Removing one-fourth of this mixture leaves three-fourths of each component: 12 litres of dye and 30 litres of water. If d litres of dye is now added, 12+d30 = 23. Thus 12+d=20, giving d=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) Translate the two statements into equations: A+B+C2=5 ⇒ 2A+B+C=10, B+A+C2=7 ⇒ A+2B+C=14. Subtracting gives B−A=4, so B=A+4. Substitute this into the first equation: 2A+(A+4)+C=10 ⇒ C=6−3A. Because A and C are positive integers, 6−3A>0, which forces A=1. Hence B=5 and C=3. Therefore A+B=1+5=6.
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 The digit product must be 3, 4, 5, or 6; a zero digit is impossible. Count the digit multisets and their distinct arrangements: - Product 3: {1,1,3} gives 3 numbers. - Product 4: {1,1,4} and {1,2,2} give 3+3=6. - Product 5: {1,1,5} gives 3. - Product 6: {1,1,6} gives 3 and {1,2,3} gives 6. The total is 3+6+3+9 = 21.
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 km/h) Let the cars meet after t hours. After meeting, Car 1 covers the distance that Car 2 covered before the meeting, while Car 2 covers the distance that Car 1 covered before the meeting. If their speeds are v1 and v2, the two distance relations are v1 × 4560 = v2t, v2 × 2060 = v1t. Divide the first equation by the second to eliminate t: (v1/v2)2 = 20604560 = 4/9. Speeds are positive, so v1/v2=23. Given v1=60 km/h, 60v2=23, which gives v2=90 km/h.
Q62Quantitative Ability·LogarithmsTITA

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

Answer: 36

Show explanation
Answer:36 Start with log45 = (log4y)(log65). Use change of base to express the second logarithm in base 4: log65 = log45 / log46 = (12)log45 / log46. Substitute this into the original equation: log45 = (log4y)[log452log46]. Since log45 is non-zero, cancel it from both sides. This gives log4y = 2log46 = log4(62) = log436. Logarithms with the same valid base are one-to-one, so y=36.
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 cubic centimetres) The cut is 18 cm above the base of a 27 cm cone, so the small cone at the top has height 27−18=9 cm. Because the cutting plane is parallel to the base, the small cone is similar to the original cone. Their linear scale factor is 927=13. Volumes of similar solids vary as the cube of the linear scale, so the small cone has (13)3=127 of the original volume. Let the original volume be V. The frustum has volume 26V/27, so the difference between the two pieces is 26V/27−V/27 = 25V/27. Given this difference is 225, 25V/27=225, so V=225×2725=243 cubic centimetres.
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 (approximately 82 seconds) Let the train’s speed be V km/h and length be L km. When it overtakes a person walking in the same direction, the relevant speed is the train’s speed minus the person’s speed. For the walkers moving at 2 and 4 km/h, the crossing times are 90 seconds=140 hour and 100 seconds=136 hour. Therefore LV−2=140, LV−4=136. Thus L=V−240=V−436. Cross-multiplying gives 36(V−2)=40(V−4), so V=22 km/h. Then L=22−240=12 km. A stationary post has zero length, so the train takes LV=1222=1/44 hour=81.82 seconds to cross it. The nearest option is 82 seconds.
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

  • A2π15
  • B3π25
  • C6π25Correct answer
  • D5π18

Answer: C

Show explanation
Answer:C (6π/25) The rhombus has area (12)(12)(16)=96. Its diagonals bisect each other at right angles, so a side has length 62+82=10 and the semiperimeter is 20. For a tangential quadrilateral, area = inradius × semiperimeter. Hence the circle’s radius is r=9620=245. The required ratio is πr2/96 = π(245)2/96 = 6π/25.
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) The identity f(5+x)=f(5−x) says that the graph of f is symmetric about the vertical line x=5. Consequently, whenever r is a root, its reflection 10−r is also a root. With four distinct real roots, they must form two symmetric pairs. Write them as 5−a, 5+a, 5−b, and 5+b, where a and b are non-zero and have different absolute values. Each pair sums to 10: (5−a)+(5+a)=10, (5−b)+(5+b)=10. Therefore the sum of all four roots is 20.
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 Since 4096 = 642, substitute 642 for 4096: x = (642)7 + 4 3 = 6414 + 8 3. We now reverse this power to express 64 in terms of x: 64 = x114 + 8 3 = x12(7 + 4 3). To simplify the exponent, use the conjugate 7 − 4 3. Since (7 + 4 3)(7 − 4 3) = 49 − 48 = 1, we get 17 + 4 3 = 7 − 4 3. Therefore 12(7 + 4 3) = 7 − 4 32 = 72 − 2 3. Hence 64 = x72 − 2 3 = x72 / x2 3, which is exactly option C.
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 Let the circle have radius r and let the other side of the rectangle be l. Because the circle touches two opposite sides, one side of the rectangle equals the diameter 2r. Hence 2rl=135. ...(1) The unpainted area is two-thirds of the painted area: 135−πr2 = (23)πr2. Therefore 135=(53)πr2, so r2=81π and r=9/√π. From equation (1), l=1352r=15√π/2. The perimeter is 2(2r+l)=4r+2l =36/√π+15√π =3√π(12π+5). Therefore the perimeter is 3√π(5+12π), option A.
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 First note that x cannot be 0 because the expression contains 1x. Put t = x + 1x. The equation becomes t2 − 3t + 2 = 0, so (t − 1)(t − 2) = 0. Therefore t = 1 or t = 2. We must now check both values in the original substitution. If t = 1, then x + 1x = 1. Multiplying by x gives x2 − x + 1 = 0. Its discriminant is (−1)2 − 4(1)(1) = −3, so this case has no real solution. If t = 2, then x + 1x = 2. Multiplying by x gives x2 − 2x + 1 = 0, or (x − 1)2 = 0. Thus x = 1. Although this is a repeated root of the quadratic, it counts as only one distinct real root. Therefore the original equation has 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) From ab=432 and bc=96, division gives ac=43296=92, so a=9c/2 and b=96c. Since a and b are positive integers, c must be an even divisor of 96. The condition c<9 leaves c=2,4,6,8. Evaluate a+b+c: - c=2: a=9, b=48, sum=59. - c=4: a=18, b=24, sum=46. - c=6: a=27, b=16, sum=49. - c=8: a=36, b=12, sum=56. The smallest possible value is therefore 46.
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 Rewrite |x| − y ≤ 1 as |x| ≤ y + 1. Intersect with the horizontal strip 0 ≤ y ≤ 1. 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 (approximately 66%) Assume there are 100 people. Then 28 are young and 72 are old. Also, 65 people are literate, so 35 are illiterate. Twenty-five percent of the literates are young. Therefore the number of young literates is 0.25×65=16.25, and the number of old literates is 65−16.25=48.75. Of the 28 young people, 28−16.25=11.75 are illiterate. Hence the number of old illiterates is 35−11.75=23.25. The required percentage is the percentage of old people within the illiterate group: (23.25/35)×100 ≈ 66.43%. The nearest option is 66%.
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) A number of the form aabb has value 1000a+100a+10b+b = 1100a+11b. For the number to be four-digit, a can be any digit from 1 to 9. For the number to be even, its last digit b must be one of 0,2,4,6,8. Every choice of a can be paired with every valid b. The average of the digits 1 through 9 is 5, while the average of 0,2,4,6,8 is 4. Because the expression 1100a+11b is linear, the mean of all the numbers is 1100×mean(a)+11×mean(b) =1100×5+11×4 =5500+44 =5544.
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 kg) The metals are mixed in the volume ratio 3:4:7, but the question asks for weight, so the different densities must also be included. For equal volumes, the weights of A, B, and C are in the ratio 5:2:6. Multiplying volume parts by weight per unit volume gives the mass ratio A:B:C = 3×5 : 4×2 : 7×6 = 15:8:42. There are 15+8+42=65 total mass parts, of which C contributes 42. Therefore the weight of C in 130 kg is 130×4265 = 84 kg.
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 Let D and L be the purchase prices of the desktop and laptop. Their total cost gives D+L=50000. The desktop is sold for 1.20D and the laptop for 0.90L. An overall profit of 2% means the total selling price is 1.02×50000=51000, so 1.20D+0.90L=51000. Substitute L=50000−D: 1.20D+0.90(50000−D)=51000 ⇒ 0.30D=6000 ⇒ D=20000. Thus the desktop originally cost ₹20,000.
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) For an integer base and exponent, the expression equals 1 in three relevant cases. 1. The exponent is zero: x2−13x+42=(x−6)(x−7)=0, giving x=6,7. 2. The base is 1: x2−7x+11=1, so (x−2)(x−5)=0, giving x=2,5. 3. The base is −1 and the exponent is even: x2−7x+11=−1 gives x=3,4; the corresponding exponents are 12 and 6, both even. These six values are distinct, so there are 6 positive integer solutions.

Answer key

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

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

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