CATPast year paperFree to attempt

CAT 2025 Slot 2 question paper with answer key

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

Ready to attempt this paper?

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

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

VARC(24 questions)

Q1Reading Comprehension·Application & Analogy

The passage below is accompanied by a set of questions. Choose the best answer to each question. Time and again, whenever a population of Mexican tetra fish was swept into a cave and survived long enough for natural selection to have its way, the eyes disappeared. “But it’s not that everything has been lost in cavefish . . . Many enhancements have also happened.” . . . Studies have found that cave-dwelling fish can detect lower levels of amino acids than surface fish can. They also have more tastebuds and a higher density of sensitive cells alongside their bodies that let them sense water pressure and flow. . . . Killing the processes that support the formation of the eye is quite literally what happens. Just like non-cavedwelling members of the species, all cavefish embryos start making eyes. But after a few hours, cells in the developing eye start dying, until the entire structure has disappeared. Developmental biologist Misty Riddle thinks this apparent inefficiency may be unavoidable. “The early development of the brain and the eye are completely intertwined—they happen together,” she says. That means the least disruptive way for eyelessness to evolve may be to start making an eye and then get rid of it. . . . It’s easy to see why cavefish would be at a disadvantage if they were to maintain expensive tissues they aren’t using. Since relatively little lives or grows in their caves, the fish are likely surviving on a meager diet of mostly bat feces and organic waste that washes in during the rainy season. Researchers keeping cavefish in labs have discovered that, genetically, the creatures are exquisitely adapted to absorbing and storing nutrients.. . . Fats can be toxic for tissues, evolutionary physiologist Nicolas Rohner explains, so they are stored in fat cells. “But when these cells get too big, they can burst, which is why we often see chronic inflammation in humans and other animals that have stored a lot of fat in their tissues.” Yet a 2020 study by Rohner, Krishnan and their colleagues revealed that even very well-fed cavefish had fewer signs of inflammation in their fat tissues than surface fish do. Even in their sparse cave conditions, wild cavefish can sometimes get very fat, says Riddle. This is presumably because, whenever food ends up in the cave, the fish eat as much of it as possible, since there may be nothing else for a long time to come. Intriguingly, Riddle says, their fat is usually bright yellow, because of high levels of carotenoids, the substance in the carrots that your grandmother used to tell you were good for your…eyes. “The first thing that came to our mind, of course, was that they were accumulating these because they don’t have eyes,” says Riddle. In this species, such ideas can be tested: Scientists can cross surface fish (with eyes) and cavefish (without eyes) and look at what their offspring are like. When that’s done, Riddle says, researchers see no link between eye presence or size and the accumulation of carotenoids. Some eyeless cavefish had fat that was practically white, indicating lower carotenoid levels. Instead, Riddle thinks these carotenoids may be another adaptation to suppress inflammation, which might be important in the wild, as cavefish are likely overeating whenever food arrives.

Which one of the following results for the cross between surface fish (with eyes) and cavefish (without eyes) would invalidate Riddle’s inference from the experiment?

  • ASome offspring with eyes had white fat.
  • BSome offspring with eyes had yellow fat.
  • CSome eyeless offspring had white fat.
  • DOnly eyeless offspring had yellow fat.Correct answer

Answer: D

Show explanation
Answer:D Riddle infers eye loss and yellow-fat/carotenoid traits can segregate independently. “Only eyeless offspring had yellow fat” would couple the traits and invalidate that independence inference. Why the others fail: • A — Eyed + white fat is compatible with independent assortment. • B — Eyed + yellow fat supports independence. • C — Eyeless + white fat also fits independent segregation.
Q2Reading Comprehension·Inference

The passage below is accompanied by a set of questions. Choose the best answer to each question. Time and again, whenever a population of Mexican tetra fish was swept into a cave and survived long enough for natural selection to have its way, the eyes disappeared. “But it’s not that everything has been lost in cavefish . . . Many enhancements have also happened.” . . . Studies have found that cave-dwelling fish can detect lower levels of amino acids than surface fish can. They also have more tastebuds and a higher density of sensitive cells alongside their bodies that let them sense water pressure and flow. . . . Killing the processes that support the formation of the eye is quite literally what happens. Just like non-cavedwelling members of the species, all cavefish embryos start making eyes. But after a few hours, cells in the developing eye start dying, until the entire structure has disappeared. Developmental biologist Misty Riddle thinks this apparent inefficiency may be unavoidable. “The early development of the brain and the eye are completely intertwined—they happen together,” she says. That means the least disruptive way for eyelessness to evolve may be to start making an eye and then get rid of it. . . . It’s easy to see why cavefish would be at a disadvantage if they were to maintain expensive tissues they aren’t using. Since relatively little lives or grows in their caves, the fish are likely surviving on a meager diet of mostly bat feces and organic waste that washes in during the rainy season. Researchers keeping cavefish in labs have discovered that, genetically, the creatures are exquisitely adapted to absorbing and storing nutrients.. . . Fats can be toxic for tissues, evolutionary physiologist Nicolas Rohner explains, so they are stored in fat cells. “But when these cells get too big, they can burst, which is why we often see chronic inflammation in humans and other animals that have stored a lot of fat in their tissues.” Yet a 2020 study by Rohner, Krishnan and their colleagues revealed that even very well-fed cavefish had fewer signs of inflammation in their fat tissues than surface fish do. Even in their sparse cave conditions, wild cavefish can sometimes get very fat, says Riddle. This is presumably because, whenever food ends up in the cave, the fish eat as much of it as possible, since there may be nothing else for a long time to come. Intriguingly, Riddle says, their fat is usually bright yellow, because of high levels of carotenoids, the substance in the carrots that your grandmother used to tell you were good for your…eyes. “The first thing that came to our mind, of course, was that they were accumulating these because they don’t have eyes,” says Riddle. In this species, such ideas can be tested: Scientists can cross surface fish (with eyes) and cavefish (without eyes) and look at what their offspring are like. When that’s done, Riddle says, researchers see no link between eye presence or size and the accumulation of carotenoids. Some eyeless cavefish had fat that was practically white, indicating lower carotenoid levels. Instead, Riddle thinks these carotenoids may be another adaptation to suppress inflammation, which might be important in the wild, as cavefish are likely overeating whenever food arrives.

Which one of the following best explains why the “apparent inefficiency” is “unavoidable”?

  • AThe lack of light in the caves kills the eye cells in the developing Mexican tetra cavefish embryo.
  • BThe inefficiency resulting from eyelessness is compensated by enhancements like more tastebuds in Mexican tetra cavefish.
  • CMexican tetra cavefish are similar to non-cave-dwelling variants in their early stages of development.Correct answer
  • DThe caves have poor and inconsistent availability of food and nutrition for Mexican tetra cavefish.

Answer: C

Show explanation
Answer:C “Apparent inefficiency” of building then losing eyes is unavoidable because cavefish still follow the same early developmental path as eyed surface fish—C. Why the others fail: • A — Light-killing eye cells is not the developmental-unavoidability point. • B — Extra tastebuds are compensation, not why inefficiency is unavoidable. • D — Sparse food explains selection pressures, not the developmental inevitability of the inefficiency.
Q3Reading Comprehension·Specific Detail

The passage below is accompanied by a set of questions. Choose the best answer to each question. Time and again, whenever a population of Mexican tetra fish was swept into a cave and survived long enough for natural selection to have its way, the eyes disappeared. “But it’s not that everything has been lost in cavefish . . . Many enhancements have also happened.” . . . Studies have found that cave-dwelling fish can detect lower levels of amino acids than surface fish can. They also have more tastebuds and a higher density of sensitive cells alongside their bodies that let them sense water pressure and flow. . . . Killing the processes that support the formation of the eye is quite literally what happens. Just like non-cavedwelling members of the species, all cavefish embryos start making eyes. But after a few hours, cells in the developing eye start dying, until the entire structure has disappeared. Developmental biologist Misty Riddle thinks this apparent inefficiency may be unavoidable. “The early development of the brain and the eye are completely intertwined—they happen together,” she says. That means the least disruptive way for eyelessness to evolve may be to start making an eye and then get rid of it. . . . It’s easy to see why cavefish would be at a disadvantage if they were to maintain expensive tissues they aren’t using. Since relatively little lives or grows in their caves, the fish are likely surviving on a meager diet of mostly bat feces and organic waste that washes in during the rainy season. Researchers keeping cavefish in labs have discovered that, genetically, the creatures are exquisitely adapted to absorbing and storing nutrients.. . . Fats can be toxic for tissues, evolutionary physiologist Nicolas Rohner explains, so they are stored in fat cells. “But when these cells get too big, they can burst, which is why we often see chronic inflammation in humans and other animals that have stored a lot of fat in their tissues.” Yet a 2020 study by Rohner, Krishnan and their colleagues revealed that even very well-fed cavefish had fewer signs of inflammation in their fat tissues than surface fish do. Even in their sparse cave conditions, wild cavefish can sometimes get very fat, says Riddle. This is presumably because, whenever food ends up in the cave, the fish eat as much of it as possible, since there may be nothing else for a long time to come. Intriguingly, Riddle says, their fat is usually bright yellow, because of high levels of carotenoids, the substance in the carrots that your grandmother used to tell you were good for your…eyes. “The first thing that came to our mind, of course, was that they were accumulating these because they don’t have eyes,” says Riddle. In this species, such ideas can be tested: Scientists can cross surface fish (with eyes) and cavefish (without eyes) and look at what their offspring are like. When that’s done, Riddle says, researchers see no link between eye presence or size and the accumulation of carotenoids. Some eyeless cavefish had fat that was practically white, indicating lower carotenoid levels. Instead, Riddle thinks these carotenoids may be another adaptation to suppress inflammation, which might be important in the wild, as cavefish are likely overeating whenever food arrives.

On the basis of the information in the passage, what is the most likely function of carotenoids in Mexican tetra cavefish?

  • ATo render bright yellow colour to the cavefish.
  • BTo act as a substitute for eyes.
  • CTo help the fat cells store nutrients.
  • DTo control inflammation from the bursting of fat cells.Correct answer

Answer: D

Show explanation
Answer:D Carotenoids in cavefish fat most likely help control inflammation when fat cells burst—D. Why the others fail: • A — Bright yellow colour is a sign of carotenoids, not their adaptive function here. • B — They are not an eyes substitute. • C — Helping store nutrients is not the inflammation-control role highlighted.
Q4Reading Comprehension·Structure & Organization

The passage below is accompanied by a set of questions. Choose the best answer to each question. Time and again, whenever a population of Mexican tetra fish was swept into a cave and survived long enough for natural selection to have its way, the eyes disappeared. “But it’s not that everything has been lost in cavefish . . . Many enhancements have also happened.” . . . Studies have found that cave-dwelling fish can detect lower levels of amino acids than surface fish can. They also have more tastebuds and a higher density of sensitive cells alongside their bodies that let them sense water pressure and flow. . . . Killing the processes that support the formation of the eye is quite literally what happens. Just like non-cavedwelling members of the species, all cavefish embryos start making eyes. But after a few hours, cells in the developing eye start dying, until the entire structure has disappeared. Developmental biologist Misty Riddle thinks this apparent inefficiency may be unavoidable. “The early development of the brain and the eye are completely intertwined—they happen together,” she says. That means the least disruptive way for eyelessness to evolve may be to start making an eye and then get rid of it. . . . It’s easy to see why cavefish would be at a disadvantage if they were to maintain expensive tissues they aren’t using. Since relatively little lives or grows in their caves, the fish are likely surviving on a meager diet of mostly bat feces and organic waste that washes in during the rainy season. Researchers keeping cavefish in labs have discovered that, genetically, the creatures are exquisitely adapted to absorbing and storing nutrients.. . . Fats can be toxic for tissues, evolutionary physiologist Nicolas Rohner explains, so they are stored in fat cells. “But when these cells get too big, they can burst, which is why we often see chronic inflammation in humans and other animals that have stored a lot of fat in their tissues.” Yet a 2020 study by Rohner, Krishnan and their colleagues revealed that even very well-fed cavefish had fewer signs of inflammation in their fat tissues than surface fish do. Even in their sparse cave conditions, wild cavefish can sometimes get very fat, says Riddle. This is presumably because, whenever food ends up in the cave, the fish eat as much of it as possible, since there may be nothing else for a long time to come. Intriguingly, Riddle says, their fat is usually bright yellow, because of high levels of carotenoids, the substance in the carrots that your grandmother used to tell you were good for your…eyes. “The first thing that came to our mind, of course, was that they were accumulating these because they don’t have eyes,” says Riddle. In this species, such ideas can be tested: Scientists can cross surface fish (with eyes) and cavefish (without eyes) and look at what their offspring are like. When that’s done, Riddle says, researchers see no link between eye presence or size and the accumulation of carotenoids. Some eyeless cavefish had fat that was practically white, indicating lower carotenoid levels. Instead, Riddle thinks these carotenoids may be another adaptation to suppress inflammation, which might be important in the wild, as cavefish are likely overeating whenever food arrives.

All of the following statements from the passage describe adaptation in Mexican tetra cavefish EXCEPT:

  • A“Since relatively little lives or grows in their caves, the fish are likely surviving on a meager diet of mostly bat feces and organic waste that washes in during the rainy season.”
  • B“‘But when these cells get too big, they can burst, which is why we often see chronic inflammation in humans and other animals that have stored a lot of fat in their tissues.’”Correct answer
  • C“It’s easy to see why cavefish would be at a disadvantage if they were to maintain expensive tissues they aren’t using.”
  • D“Even in their sparse cave conditions, wild cavefish can sometimes get very fat, says Riddle.”

Answer: B

Show explanation
Answer:B B is a general remark about fat cells bursting and human/animal inflammation—not an adaptation statement about Mexican tetra cavefish. The EXCEPT. Why the others fail: • A — Sparse cave diet is an ecological adaptation context. • C — Dropping unused expensive tissues is adaptive logic for cavefish. • D — Wild cavefish getting fat in sparse caves is part of their adaptive story.
Q5Verbal Ability·Odd Sentence OutTITA

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

1. Sporting a copper-coloured pixie cut and a pair of pink feather antlers, Torres himself resembles a child’s doodle. 2. His casual millennial delivery, peppered with “um”s and “ah”s, makes surreal concepts sound like items on a brunch menu. 3. Though he may have failed so far in his colour-scouting mission (he hasn’t yet found a new one, he admits), this hour leaves you tickled pink. 4. Like his previous show, My Favourite Shapes, this is an hour of sit-down comedy aided by an overhead camera which relays Torres’s theories – illustrated with crayon squiggles – on to a screen behind him. 5. His inquisitive mind produces interconnected ideas about Catholicism, the blandness of Pixar and what orange sounds like, while his insights train us to spot “highly purple behaviour”.

Answer: 3

Show explanation
Answer:3 1–2–4–5 paint Torres’s look, brunchy delivery, overhead-camera show, and quirky idea web. Sentence 3—failing a “colour-scouting mission” yet leaving you “tickled pink”—is a review punchline that doesn’t belong in that descriptive set. Why the others fail: • 1 — Doodle/antlers look opens the persona. • 2 — Delivery style continues the portrait. • 4 — Names the show format that frames 5’s ideas. • 5 — Lists the interconnected theories the show presents.
Q6Verbal Ability·Paragraph JumblesTITA

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

1. As books age, the cellulose and lignin in the paper begin to break down, releasing a mix of volatile organic compounds into the air. 2. Old books carry a scent that many people instantly recognize—and even love. 3. These compounds are benzaldehyde, which gives off an almond-like scent, vanillin, which smells like vanilla, ethyl hexanol (floral scent), toluene (sweet), and furfural (which has a slightly bready scent). 4. This familiar aroma isn't just dust or mildew; it's actually a result of slow chemical changes happening inside the paper and ink.

Answer: 2413

Show explanation
Answer:2413 Loved old-book scent (2) → not mere dust/mildew but chemistry in paper/ink (4) → cellulose/lignin release VOCs (1) → name those almond/vanilla/etc. compounds (3): 2413. Why the others fail: • 1-first — Breakdown chemistry needs the recognisable-scent hook first. • 3 before 1 — Named compounds require the VOC release in 1. • 4 after 1 — “This familiar aroma” points back to 2, not to 1.
Q7Verbal Ability·Sentence Placement

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

Sentence: The region’s Western customers found it hard to believe that Dhaka muslin could possibly have been made by human hands – there were rumour that it was woven by mermaids, fairies and even ghosts. Paragraph: Once upon the silty banks of the Meghna River, a miracle was spun — a fabric so light it was called “baft-hawa”, or woven air. This was Dhaka Muslin — the world’s most coveted cloth. ____(1)____. Handspun from a rare cotton called Phuti Karpas, found nowhere else on Earth, and woven with a 16-step sacred ritual — beginning with cleaning the cotton using the teeth of a river catfish! ____(2)____. Every spring, the maple-like leaves pushed up through the grey, silty soil to produce a single daffodilyellow flower twice a year, which gave way to a snowy floret of cotton fibres. ____(3)____. Spun at dawn on boats by sharp-eyed young women, its threads were so fine the elderly could barely see them. Motifs of wildflowers, river breeze, and soul were etched into each piece — some so light, a 91-metre bolt could pass through a ring, or a 60' length fit inside a snuffbox. It draped Greek goddesses, Roman nobles, Mughal emperors, and European aristocrats. Marie Antoinette, Empress Joséphine — even Jane Austen adored its floating grace. ____(4)____.

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

Answer: A

Show explanation
Answer:A (Blank 1) Sentence. Western customers found Dhaka muslin so implausible they rumoured mermaids, fairies, even ghosts wove it. Why Blank 1. The paragraph has just crowned muslin “the world’s most coveted cloth.” The rumour is the awe that claim invites, before the how-it-was-made (Phuti Karpas, catfish-teeth cleaning). Why not the others. - Blank 2 is mid-botany of the cotton plant. - Blank 3 is spinning/weaving craft. - Blank 4 is a closing celebrity-drape catalogue — the rumour belongs with the opening marvel, not the guest list.
Q8Verbal Ability·Odd Sentence OutTITA

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

1. Pfas are a class of about 15,000 compounds most frequently used to make products water-, stainand grease-resistant. 2. New research suggests exposure to some common perfluoroalkyl and polyfluoroalkyl substances (Pfas) cause changes to gene activity and that these changes are linked to health problems including multiple cancers, neurological disorders and autoimmune disease. 3. These Pfas compounds are dubbed “forever chemicals” because they do not naturally break down in the environment. 4. The research may also point toward other diseases potentially caused by Pfas that have not yet been identified. 4. The findings are a major step toward determining the mechanism by which the chemicals cause disease and could help doctors identify, detect and treat health problems for those exposed to Pfas before the issues advance.

Answer: 3

Show explanation
Answer:3 The research arc links PFAS exposure to gene-activity changes, disease risks, and clinical payoffs. Sentence 3 (environmental “forever chemicals” persistence) shifts to environmental fate and is the odd one out. Why the others fail: • 1 — Defines the chemical class under study. • 2 — States the gene-activity/health-link finding. • 4 — Mechanism/early-detection payoff continues the research story.
Q9Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Different sciences exhibit different science cultures and practices. For example, in astronomy, observation – until what is today called the new astronomy – had always been limited to what could be seen within the limits of optical light. Indeed, until early modernity the limits to optical light were also limits of what humans could themselves see within their limited and relative perceptual spectrum of human vision. With early modernity and the invention of lensed optical instruments – telescopes – astronomers could begin to observe phenomena never seen before. Magnification and resolution began to allow what was previously imperceptible to be perceived – but within the familiar limits of optical vision. Galileo, having learned of the Dutch invention of a telescope by Hans Lippershey, went on to build some hundred of his own, improving from the Dutch 3x to nearly 30x telescopes – which turn out to be the limit of magnificational power without chromatic distortion. And it was with his own telescopes that he made the observations launching early modern astronomy (phases of Venus, satellites of Jupiter, etc.). Isaac Newton’s later improvement with reflecting telescopes expanded upon the magnificational-resolution capacity of optical observation; and, from Newton to the twentieth century, improvement continued on to the later very large array of light telescopes today – following the usual technological trajectory of “more-is-better” but still remaining within the limits of the light spectrum. Today’s astronomy has now had the benefit of some four centuries of optical telescopy. The “new astronomy,” however, opens the full known electromagnetic spectrum to observation, beginning with the accidental discovery of radio astronomy early in the twentieth century, and leading today to the diverse variety of EMS telescopes which can explore the range from gamma to radio waves. Thus, astronomy, now outfitted with new instruments, “smart” adaptive optics, very large arrays, etc., illustrates one style of instrumentally embodied science – a techno science. Of course astronomy, with the very recent exceptions of probes to solar system bodies (Moon, Mars, Venus, asteroids), remains largely a “receptive” science, dependent upon instrumentation which can detect and receive emissions. Contemporary biology displays a quite different instrument array and, according to Evelyn Fox Keller, also a different scientific culture. She cites her own experience, coming from mathematical physics into microbiology, and takes account of the distinctive instrumental culture in her Making Sense of Life (2002). Here, particularly with the development of biotechnology, instrumentation is far more interventional than in the astronomy case. Microscopic instrumentation can be and often is interventional in style: “gene-splicing” and other techniques of biotechnology, while still in their infancy, are clearly part of the interventional trajectory of biological instrumentation. Yet, in both disciplines, the sciences involved are today highly instrumentalized and could not progress successfully without constant improvements upon the respective instrumental trajectories. So, minimalistically, one may conclude that the sciences are technologically, instrumentally embodied. But the styles of embodiment differ, and perhaps the last of the scientific disciplines to move into such technical embodiment is mathematics, which only contemporarily has come to rely more and more upon the computational machinery now in common use.

All of the following statements may be rejected as valid inferences from the passage EXCEPT:

  • Athe advances in telescopy made by Newton with reflecting telescopes allowed early modern astronomers to observe the phases of Venus and the satellites of Jupiter.
  • BIsaac Newton’s experiments with reflecting telescopes were the earliest versions of the “new astronomy” referred to in the passage.
  • Cinterventionist instruments, or instruments that intervene directly in scientific inquiry, are different from embodied instruments, or instruments that embody scientific inquiry.
  • Dthe author distinguishes between the receptive and interventionist uses of instruments in the sciences by comparing astronomy and biology, respectively.Correct answer

Answer: D

Show explanation
Answer:D The stem asks which inference should *not* be rejected—the valid one. The author distinguishes receptive vs interventionist instrument uses by comparing astronomy and biology—D. Why the others fail: • A — Wrongly ties Newton’s reflectors to early Venus/Jupiter observations—rejectable. • B — Treats Newton’s experiments as the earliest “new astronomy”—overclaim, rejectable. • C — Scrambles embodied vs interventionist categories beyond the text—rejectable.
Q10Reading Comprehension·Inference

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Different sciences exhibit different science cultures and practices. For example, in astronomy, observation – until what is today called the new astronomy – had always been limited to what could be seen within the limits of optical light. Indeed, until early modernity the limits to optical light were also limits of what humans could themselves see within their limited and relative perceptual spectrum of human vision. With early modernity and the invention of lensed optical instruments – telescopes – astronomers could begin to observe phenomena never seen before. Magnification and resolution began to allow what was previously imperceptible to be perceived – but within the familiar limits of optical vision. Galileo, having learned of the Dutch invention of a telescope by Hans Lippershey, went on to build some hundred of his own, improving from the Dutch 3x to nearly 30x telescopes – which turn out to be the limit of magnificational power without chromatic distortion. And it was with his own telescopes that he made the observations launching early modern astronomy (phases of Venus, satellites of Jupiter, etc.). Isaac Newton’s later improvement with reflecting telescopes expanded upon the magnificational-resolution capacity of optical observation; and, from Newton to the twentieth century, improvement continued on to the later very large array of light telescopes today – following the usual technological trajectory of “more-is-better” but still remaining within the limits of the light spectrum. Today’s astronomy has now had the benefit of some four centuries of optical telescopy. The “new astronomy,” however, opens the full known electromagnetic spectrum to observation, beginning with the accidental discovery of radio astronomy early in the twentieth century, and leading today to the diverse variety of EMS telescopes which can explore the range from gamma to radio waves. Thus, astronomy, now outfitted with new instruments, “smart” adaptive optics, very large arrays, etc., illustrates one style of instrumentally embodied science – a techno science. Of course astronomy, with the very recent exceptions of probes to solar system bodies (Moon, Mars, Venus, asteroids), remains largely a “receptive” science, dependent upon instrumentation which can detect and receive emissions. Contemporary biology displays a quite different instrument array and, according to Evelyn Fox Keller, also a different scientific culture. She cites her own experience, coming from mathematical physics into microbiology, and takes account of the distinctive instrumental culture in her Making Sense of Life (2002). Here, particularly with the development of biotechnology, instrumentation is far more interventional than in the astronomy case. Microscopic instrumentation can be and often is interventional in style: “gene-splicing” and other techniques of biotechnology, while still in their infancy, are clearly part of the interventional trajectory of biological instrumentation. Yet, in both disciplines, the sciences involved are today highly instrumentalized and could not progress successfully without constant improvements upon the respective instrumental trajectories. So, minimalistically, one may conclude that the sciences are technologically, instrumentally embodied. But the styles of embodiment differ, and perhaps the last of the scientific disciplines to move into such technical embodiment is mathematics, which only contemporarily has come to rely more and more upon the computational machinery now in common use.

Which one of the following observations is a valid conclusion to draw from the statement that “the sciences involved are today highly instrumentalised and could not progress successfully without constant improvements upon the respective instrumental trajectories”?

  • AThe growth of scientific technologies has led to the embodiment of progress in the trajectories of improvement.
  • BIn both astronomy and microbiology, progress has been the consequence of improvements in the instruments they use.Correct answer
  • CHighly instrumentalised work in the sciences has resulted in the progressive improvement of scientific constants.
  • DThe use of instruments in scientific trajectories must be respected in order to see successful progress in them.

Answer: B

Show explanation
Answer:B If those sciences are highly instrumentalised and need improving instrument trajectories, progress in astronomy and microbiology follows instrument improvements—B. Why the others fail: • A — Vague “embodiment of progress” restates jargon without concluding. • C — Improving “scientific constants” is not the claim. • D — Adds a duty to “respect” instruments not present in the sentence.
Q11Reading Comprehension·Application & Analogy

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Different sciences exhibit different science cultures and practices. For example, in astronomy, observation – until what is today called the new astronomy – had always been limited to what could be seen within the limits of optical light. Indeed, until early modernity the limits to optical light were also limits of what humans could themselves see within their limited and relative perceptual spectrum of human vision. With early modernity and the invention of lensed optical instruments – telescopes – astronomers could begin to observe phenomena never seen before. Magnification and resolution began to allow what was previously imperceptible to be perceived – but within the familiar limits of optical vision. Galileo, having learned of the Dutch invention of a telescope by Hans Lippershey, went on to build some hundred of his own, improving from the Dutch 3x to nearly 30x telescopes – which turn out to be the limit of magnificational power without chromatic distortion. And it was with his own telescopes that he made the observations launching early modern astronomy (phases of Venus, satellites of Jupiter, etc.). Isaac Newton’s later improvement with reflecting telescopes expanded upon the magnificational-resolution capacity of optical observation; and, from Newton to the twentieth century, improvement continued on to the later very large array of light telescopes today – following the usual technological trajectory of “more-is-better” but still remaining within the limits of the light spectrum. Today’s astronomy has now had the benefit of some four centuries of optical telescopy. The “new astronomy,” however, opens the full known electromagnetic spectrum to observation, beginning with the accidental discovery of radio astronomy early in the twentieth century, and leading today to the diverse variety of EMS telescopes which can explore the range from gamma to radio waves. Thus, astronomy, now outfitted with new instruments, “smart” adaptive optics, very large arrays, etc., illustrates one style of instrumentally embodied science – a techno science. Of course astronomy, with the very recent exceptions of probes to solar system bodies (Moon, Mars, Venus, asteroids), remains largely a “receptive” science, dependent upon instrumentation which can detect and receive emissions. Contemporary biology displays a quite different instrument array and, according to Evelyn Fox Keller, also a different scientific culture. She cites her own experience, coming from mathematical physics into microbiology, and takes account of the distinctive instrumental culture in her Making Sense of Life (2002). Here, particularly with the development of biotechnology, instrumentation is far more interventional than in the astronomy case. Microscopic instrumentation can be and often is interventional in style: “gene-splicing” and other techniques of biotechnology, while still in their infancy, are clearly part of the interventional trajectory of biological instrumentation. Yet, in both disciplines, the sciences involved are today highly instrumentalized and could not progress successfully without constant improvements upon the respective instrumental trajectories. So, minimalistically, one may conclude that the sciences are technologically, instrumentally embodied. But the styles of embodiment differ, and perhaps the last of the scientific disciplines to move into such technical embodiment is mathematics, which only contemporarily has come to rely more and more upon the computational machinery now in common use.

To which one of the following instruments would the characterisations of instruments in the passage be least applicable?

  • AKitchen oven
  • BScalpel
  • CMilestoneCorrect answer
  • DSaxophone

Answer: C

Show explanation
Answer:C (Milestone) Oven, scalpel, and saxophone can function as tools that transform, intervene, or embody practice; a milestone is a marker, not an instrument in the passage’s sense. Why the others fail: • A — Oven is a transformative tool. • B — Scalpel is a classic interventional instrument. • D — Saxophone is an embodied performance instrument.
Q12Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Different sciences exhibit different science cultures and practices. For example, in astronomy, observation – until what is today called the new astronomy – had always been limited to what could be seen within the limits of optical light. Indeed, until early modernity the limits to optical light were also limits of what humans could themselves see within their limited and relative perceptual spectrum of human vision. With early modernity and the invention of lensed optical instruments – telescopes – astronomers could begin to observe phenomena never seen before. Magnification and resolution began to allow what was previously imperceptible to be perceived – but within the familiar limits of optical vision. Galileo, having learned of the Dutch invention of a telescope by Hans Lippershey, went on to build some hundred of his own, improving from the Dutch 3x to nearly 30x telescopes – which turn out to be the limit of magnificational power without chromatic distortion. And it was with his own telescopes that he made the observations launching early modern astronomy (phases of Venus, satellites of Jupiter, etc.). Isaac Newton’s later improvement with reflecting telescopes expanded upon the magnificational-resolution capacity of optical observation; and, from Newton to the twentieth century, improvement continued on to the later very large array of light telescopes today – following the usual technological trajectory of “more-is-better” but still remaining within the limits of the light spectrum. Today’s astronomy has now had the benefit of some four centuries of optical telescopy. The “new astronomy,” however, opens the full known electromagnetic spectrum to observation, beginning with the accidental discovery of radio astronomy early in the twentieth century, and leading today to the diverse variety of EMS telescopes which can explore the range from gamma to radio waves. Thus, astronomy, now outfitted with new instruments, “smart” adaptive optics, very large arrays, etc., illustrates one style of instrumentally embodied science – a techno science. Of course astronomy, with the very recent exceptions of probes to solar system bodies (Moon, Mars, Venus, asteroids), remains largely a “receptive” science, dependent upon instrumentation which can detect and receive emissions. Contemporary biology displays a quite different instrument array and, according to Evelyn Fox Keller, also a different scientific culture. She cites her own experience, coming from mathematical physics into microbiology, and takes account of the distinctive instrumental culture in her Making Sense of Life (2002). Here, particularly with the development of biotechnology, instrumentation is far more interventional than in the astronomy case. Microscopic instrumentation can be and often is interventional in style: “gene-splicing” and other techniques of biotechnology, while still in their infancy, are clearly part of the interventional trajectory of biological instrumentation. Yet, in both disciplines, the sciences involved are today highly instrumentalized and could not progress successfully without constant improvements upon the respective instrumental trajectories. So, minimalistically, one may conclude that the sciences are technologically, instrumentally embodied. But the styles of embodiment differ, and perhaps the last of the scientific disciplines to move into such technical embodiment is mathematics, which only contemporarily has come to rely more and more upon the computational machinery now in common use.

None of the following statements, if true, contradicts the arguments in the passage EXCEPT:

  • Abecause of the relatively recent entry of computational machinery in mathematics, the field is only now beginning to develop a scientific culture.Correct answer
  • Bsome scientific instruments may be classified as both receptive and interventional in their functions.
  • Clike telescopy, microscopy has also sought to move beyond the visible spectrum to be able to detect objects that are invisible in that spectrum.
  • DIsaac Newton’s discovery of gravity was accomplished without the help of instruments.

Answer: A

Show explanation
Answer:A Among statements that mostly fit, A contradicts: maths only now gaining scientific culture because of computers clashes with the passage’s longer instrumental narrative. Why the others fail: • B — Dual receptive/interventional roles can fit. • C — Microscopy beyond the visible parallels telescopy—compatible. • D — Gravity without instruments can sit as a non-instrumental episode.
Q13Verbal Ability·Sentence Placement

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

Sentence: While taste is related to judgment, with thinkers at the time often writing, for example, about “judgments of taste” or using the two terms interchangeably, taste retains a vital link to pleasure, embodiment, and personal specificity that is too often elided in post-Kantian ideas about judgment—a link that Arendt herself was working to restore. Paragraph: ____(1) ____. Denneny focused on taste rather than judgment in order to highlight what he believed was a crucial but neglected historical change. ____(2) ____. Over the course of the seventeenth century and early eighteenth century, across Western Europe, the word taste took on a new extension of meaning, no longer referring specifically to gustatory sensation and the delights of the palate but becoming, for a time, one of the central categories for aesthetic—and ethical—thinking. ____(3) ____. Tracing the history of taste in Spanish, French, and British aesthetic theory, as Denneny did, also provides a means to recover the compelling and relevant writing of a set of thinkers who have been largely neglected by professional philosophy. ____(4) ____.

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

Answer: D

Show explanation
Answer:D (Blank 3) Sentence. Taste is related to judgment but keeps a link to pleasure, embodiment, and personal specificity that post-Kantian “judgment” often drops — a link Arendt wanted restored. Why Blank 3. Blank 2 has just narrated the 17th–18th-century semantic widening of *taste* into an aesthetic/ethical category. The missing sentence is the conceptual caveat on that shift, before Denneny’s recovery of neglected theorists (Blank 4). Why not the others. - Blank 1 is before Denneny is even introduced. - Blank 2 still needs the historical change itself; the caveat is premature. - Blank 4 is already the “also recover neglected writers” payoff.
Q14Reading Comprehension·Paragraph Summary

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

For millennia, in the process of opening up land for agriculture, gardens, grazing and hunting, humans have created ecological “mosaics”, or “patchworks”: landscapes holding a mixture of habitats, like meadows, gardens and forests. These were not designed as nature reserves, but often catered to hugely diverse animal life. Research indicates that European hay meadows cultivated for animal feed were actually more successful at preserving a vast array of species than meadows explicitly cultivated for biodiversity. Studying the early Holocene, researchers have found that human presence was about as likely to increase biodiversity as reduce it. Of course, not all humancreated landscapes have the same value. A paved subdivision with astroturfed lawns is very different to a village with diverse vegetable and flower gardens. But scientists continue to find evidence that the old idea of humans as antithetical to nature is also wrong-headed, and that rosy visions of thriving, human-free environments are more imaginary than real.

  • AIn our attempts to shape the world around us to our needs, humans have often created landscapes like meadows, gardens, and forests, which support hugely diverse species, and are more successful at preserving them, than parks created specifically for this.
  • BIn terms of preserving biodiversity, scientists are finding increasing evidence that human action is not always antithetical to nature, but often assists the preservation of meadows, landscapes, and flourishing of species.
  • CContrary to the idea that humans always hurt nature and that it thrives in their absence, a lot of human action across history has been equally likely to increase biodiversity than reduce it, often creating varied ecological landscapes that support a vast array of species.Correct answer
  • DStudying the early Holocene and human practices over millennia, researchers say that while agricultural meadows, gardens, and forests were not explicitly designed as nature reserves, they actually preserved a vast array of species, belying the idea that humans harm nature.

Answer: C

Show explanation
Answer:C Best summary: contrary to “humans always hurt nature,” much historical human action was as likely to raise as to reduce biodiversity via mosaic landscapes—C. Why the others fail: • A — Claims human landscapes beat nature reserves at preservation—overreach. • B — Softer “assists preservation” without the equal-likelihood thesis. • D — Descriptive Holocene detail without the counter-thesis punch.
Q15Reading Comprehension·Paragraph Summary

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

In 1903, left-wing feminist Elizabeth Magie invented The Landlord’s Game, the original version of what became Monopoly. It was designed as a powerful teaching tool to illustrate the dangers of monopolies and how wealth could concentrate in the hands of a few. The game featured a circular path, properties, and a “Go to Jail” space. Magie created two rule sets: one “monopolist” version where players crushed opponents through accumulation, and another, more radical “Prosperity” version, where everyone shared in the wealth, promoting fairness and equity. Years later, unemployed Charles Darrow sold a simplified version to Parker Brothers. They paid Magie only $500 for her patent—without royalties—and credited Darrow as the sole inventor. For decades, his tale of inventing the game in his basement remained the official story, while Magie’s name and her original, anti-capitalist message were left in the shadows.

  • AParker Brothers’ capitalist intent led to them acquiring from Charles Darrow a simplified version of Elizabeth Magie’s original game, transforming it into a widespread commercial success while providing her only minimal financial compensation and granting scant public recognition.
  • BOnly one version of Monopoly became famous because of Charles Darrow’s relentless basement work, carefully refining Elizabeth Magie’s original idea into an engaging and entertaining pastime that he successfully patented and sold, symbolizing what many regarded as the ultimate triumph of individual ingenuity.
  • CCelebrated icons of the gaming industry, Charles Darrow and Parker Brothers, snatched the feminist icon Elizabeth Magie’s original design and transformed Monopoly into a worldwide phenomenon, while barely acknowledging her.
  • DIt is ironical that a left-wing feminist lost credit for the Landlord’s Game to an unemployed man, who plagiarised and sold one version of the twin game to Parker Brothers for a meagre sum, denying her royalties.Correct answer

Answer: D

Show explanation
Answer:D Irony: left-wing Magie loses credit; an unemployed man plagiarises and sells one twin rule-set to Parker Brothers cheaply, denying her royalties—D. Why the others fail: • A — Softens plagiarism into capitalist acquisition of a simplified version. • B — Heroises Darrow’s basement craft as the fame cause. • C — Melodramatic “snatching” without D’s twin-game/irony structure.
Q16Verbal Ability·Paragraph JumblesTITA

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

1. ‘Literature on screen’ suggests something more capacious and defining than citation: the possibility that literary adaptations are at once cinema and literature 2. Even though a growing number of films eligible for Academy Awards for Best Screenplay Based on Material from Another Medium borrow that material from print journalism, franchise characters, television series, comic books, video games and toys, academic studies of adaptation remain stubbornly attached to literature as cinema’s natural progenitor. 3. It is as if adaptation studies, by borrowing the cultural cachet of literature, sought to claim its institutional respectability and gravitas even while insuring adaptation’s enduring aesthetic and methodological subordination to literature proper. 4. Beneath this contradictory notion of film adaptations as not merely hybrid texts but texts holding dual citizenship in two modes of presentation is an even more pervasive legacy that haunts adaptation studies: the assumption that the primary context within which adaptations are to be studied is literature.

Answer: 1423

Show explanation
Answer:1423 Order 1423: capacious “literature on screen” / dual citizenship (1) → that notion hides a literature-as-primary-context legacy (4) → awards diversify source media while studies stay lit-centric (2) → studies borrow literature’s cachet while keeping adaptation subordinate (3). Why the others fail: • 2 before 1 — Diversification vs lit-stubbornness needs the dual-citizenship frame first. • 3 before 4 — “It is as if…” diagnoses the legacy stated in 4. • 1243 — Puts the awards contrast before the “beneath this notion” legacy sentence.
Q17Reading Comprehension·Inference

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. This book takes the position that setting in literature is more than just backdrop, that important insight into literary texts can be made by paying close attention to how authors craft place, as well as to how place functions in a narrative. The authors included in this reference work engage deeply with either real or imagined geographies. They care about how human decisions have shaped landscapes and how landscapes have shaped human practices and values. Some of the best writing is highly vivid, employing the language of the senses because this is the primary means through which humans know physical space. Literature can offer valuable perspectives on physical and cultural geography. Unlike scientific reports, a literary narrative can provide the emotional component missing from the scientific record. In human experience, geographical places have a spiritual or emotional component in addition to and as part of a physical layout and topography. This emotional component, although subjective, is no less “real” than a surveyor’s map. Human consciousness of place is experienced in a multimodal manner. Histories of places live on in many forms, one of which is the human memory or imagination. Both real and imaginary landscapes provide insight into the human experience of place. The pursuit of such a topic speaks to the valuable knowledge produced from bridging disciplines and combining material from both the arts and the sciences to better understand the human condition. The perspectives that most concern cultural geographers are often those regarding movement and migration, cultivation of natural resources, and organization of space. The latter two reflect concerns of the built environment, a topic shared with the field of architectural study. Many of these concerns are also reflected in work sociologists do. Scholars from literary studies can contribute an aesthetic dimension to what might otherwise be a purely ideological approach. Literature can bring together material that spans different branches of science. For example, a literary description of place may involve not only the environment and geography but the noises and quality of light, or how people from different races or classes can experience the same place in different ways linked to those racial or class disparities. Literary texts can also account for the way in which absence—of other people, animals, and so on—affects a human observer or inhabitant. Both literary and scientific approaches to place are necessary, working in unison, to achieve a complete record of an environment. It is important to note that the interdisciplinary nature of this work teaches us that landscapes are not static, that they are not unchanged by human culture. At least part of their identity derives from the people who inhabit them and from the way space can alter and inspire human perspective. The intersection of scientific and literary expression that happens in the study of literary geography is of prime importance due to the complexity of the personal and political ways that humans experience place.

Which one of the following is a valid conclusion to draw from the author’s statement that, “The pursuit of such a topic speaks to the valuable knowledge produced from bridging disciplines and combining material from both the arts and the sciences to better understand the human condition.”?

  • AA comprehensive bridging of the human condition can best be achieved by a disciplined pursuit of human understanding.
  • BThe literary descriptions of the emotions we experience in the places we visit can contribute to our understanding of the arts and sciences.
  • CA comprehensive understanding of the valuable knowledge produced by the arts and sciences can best be achieved by studying the human condition.
  • DA comprehensive understanding of the human condition can best be achieved by combining the findings of disciplines from the arts and the sciences.Correct answer

Answer: D

Show explanation
Answer:D Bridging arts and sciences produces valuable knowledge of the human condition; therefore a comprehensive understanding of that condition best combines both—D. Why the others fail: • A — Circular “disciplined pursuit of human understanding.” • B — Narrows to literary emotion serving arts/sciences, reversing the bridge. • C — Swaps direction: study the human condition to understand arts/sciences.
Q18Reading Comprehension·Structure & Organization

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. This book takes the position that setting in literature is more than just backdrop, that important insight into literary texts can be made by paying close attention to how authors craft place, as well as to how place functions in a narrative. The authors included in this reference work engage deeply with either real or imagined geographies. They care about how human decisions have shaped landscapes and how landscapes have shaped human practices and values. Some of the best writing is highly vivid, employing the language of the senses because this is the primary means through which humans know physical space. Literature can offer valuable perspectives on physical and cultural geography. Unlike scientific reports, a literary narrative can provide the emotional component missing from the scientific record. In human experience, geographical places have a spiritual or emotional component in addition to and as part of a physical layout and topography. This emotional component, although subjective, is no less “real” than a surveyor’s map. Human consciousness of place is experienced in a multimodal manner. Histories of places live on in many forms, one of which is the human memory or imagination. Both real and imaginary landscapes provide insight into the human experience of place. The pursuit of such a topic speaks to the valuable knowledge produced from bridging disciplines and combining material from both the arts and the sciences to better understand the human condition. The perspectives that most concern cultural geographers are often those regarding movement and migration, cultivation of natural resources, and organization of space. The latter two reflect concerns of the built environment, a topic shared with the field of architectural study. Many of these concerns are also reflected in work sociologists do. Scholars from literary studies can contribute an aesthetic dimension to what might otherwise be a purely ideological approach. Literature can bring together material that spans different branches of science. For example, a literary description of place may involve not only the environment and geography but the noises and quality of light, or how people from different races or classes can experience the same place in different ways linked to those racial or class disparities. Literary texts can also account for the way in which absence—of other people, animals, and so on—affects a human observer or inhabitant. Both literary and scientific approaches to place are necessary, working in unison, to achieve a complete record of an environment. It is important to note that the interdisciplinary nature of this work teaches us that landscapes are not static, that they are not unchanged by human culture. At least part of their identity derives from the people who inhabit them and from the way space can alter and inspire human perspective. The intersection of scientific and literary expression that happens in the study of literary geography is of prime importance due to the complexity of the personal and political ways that humans experience place.

Which one of the following is not true of the argument in the second paragraph?

  • AThe spiritual experience of a place may be considered as real as the physical experience of it.
  • BThe emotional and spiritual experience of a place can replace a surveyor’s mapCorrect answer
  • CAnalysing the literary descriptions of a place can give us a sense of how people relate emotionally to it.
  • DLiterary accounts of places can be filled with histories, manifested as memory or imagination.

Answer: B

Show explanation
Answer:B Paragraph 2 treats spiritual/emotional experience as real and readable from literature, but does *not* say it can replace a surveyor’s map—B is not true of the argument. Why the others fail: • A — Spiritual experience can be as real as physical—aligned. • C — Literary description reveals emotional relation to place—aligned. • D — Literary accounts carry memory/imagination histories—aligned.
Q19Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. This book takes the position that setting in literature is more than just backdrop, that important insight into literary texts can be made by paying close attention to how authors craft place, as well as to how place functions in a narrative. The authors included in this reference work engage deeply with either real or imagined geographies. They care about how human decisions have shaped landscapes and how landscapes have shaped human practices and values. Some of the best writing is highly vivid, employing the language of the senses because this is the primary means through which humans know physical space. Literature can offer valuable perspectives on physical and cultural geography. Unlike scientific reports, a literary narrative can provide the emotional component missing from the scientific record. In human experience, geographical places have a spiritual or emotional component in addition to and as part of a physical layout and topography. This emotional component, although subjective, is no less “real” than a surveyor’s map. Human consciousness of place is experienced in a multimodal manner. Histories of places live on in many forms, one of which is the human memory or imagination. Both real and imaginary landscapes provide insight into the human experience of place. The pursuit of such a topic speaks to the valuable knowledge produced from bridging disciplines and combining material from both the arts and the sciences to better understand the human condition. The perspectives that most concern cultural geographers are often those regarding movement and migration, cultivation of natural resources, and organization of space. The latter two reflect concerns of the built environment, a topic shared with the field of architectural study. Many of these concerns are also reflected in work sociologists do. Scholars from literary studies can contribute an aesthetic dimension to what might otherwise be a purely ideological approach. Literature can bring together material that spans different branches of science. For example, a literary description of place may involve not only the environment and geography but the noises and quality of light, or how people from different races or classes can experience the same place in different ways linked to those racial or class disparities. Literary texts can also account for the way in which absence—of other people, animals, and so on—affects a human observer or inhabitant. Both literary and scientific approaches to place are necessary, working in unison, to achieve a complete record of an environment. It is important to note that the interdisciplinary nature of this work teaches us that landscapes are not static, that they are not unchanged by human culture. At least part of their identity derives from the people who inhabit them and from the way space can alter and inspire human perspective. The intersection of scientific and literary expression that happens in the study of literary geography is of prime importance due to the complexity of the personal and political ways that humans experience place.

The author uses the example of the literary description of place to illustrate that:

  • Aarchitects use diverse methods to calibrate the noises and lights of a given place.
  • Bthe absence of other people, animals, and so on in a place can profoundly affect its inhabitants.
  • Cscientific approaches to place are more accurate than literary ones.
  • Dliterature can convey how different people experience the same place differently.Correct answer

Answer: D

Show explanation
Answer:D Literary place description illustrates that different people experience the same place differently—D. Why the others fail: • A — Architects calibrating noise/light is not the example’s job. • B — Absence of others affecting inhabitants is not the stated point. • C — Does not rank scientific approaches as more accurate.
Q20Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. This book takes the position that setting in literature is more than just backdrop, that important insight into literary texts can be made by paying close attention to how authors craft place, as well as to how place functions in a narrative. The authors included in this reference work engage deeply with either real or imagined geographies. They care about how human decisions have shaped landscapes and how landscapes have shaped human practices and values. Some of the best writing is highly vivid, employing the language of the senses because this is the primary means through which humans know physical space. Literature can offer valuable perspectives on physical and cultural geography. Unlike scientific reports, a literary narrative can provide the emotional component missing from the scientific record. In human experience, geographical places have a spiritual or emotional component in addition to and as part of a physical layout and topography. This emotional component, although subjective, is no less “real” than a surveyor’s map. Human consciousness of place is experienced in a multimodal manner. Histories of places live on in many forms, one of which is the human memory or imagination. Both real and imaginary landscapes provide insight into the human experience of place. The pursuit of such a topic speaks to the valuable knowledge produced from bridging disciplines and combining material from both the arts and the sciences to better understand the human condition. The perspectives that most concern cultural geographers are often those regarding movement and migration, cultivation of natural resources, and organization of space. The latter two reflect concerns of the built environment, a topic shared with the field of architectural study. Many of these concerns are also reflected in work sociologists do. Scholars from literary studies can contribute an aesthetic dimension to what might otherwise be a purely ideological approach. Literature can bring together material that spans different branches of science. For example, a literary description of place may involve not only the environment and geography but the noises and quality of light, or how people from different races or classes can experience the same place in different ways linked to those racial or class disparities. Literary texts can also account for the way in which absence—of other people, animals, and so on—affects a human observer or inhabitant. Both literary and scientific approaches to place are necessary, working in unison, to achieve a complete record of an environment. It is important to note that the interdisciplinary nature of this work teaches us that landscapes are not static, that they are not unchanged by human culture. At least part of their identity derives from the people who inhabit them and from the way space can alter and inspire human perspective. The intersection of scientific and literary expression that happens in the study of literary geography is of prime importance due to the complexity of the personal and political ways that humans experience place.

All of the following statements, if false, would contradict the arguments in the passage, EXCEPT that:

  • Ahumans do not interact with places in subjective, emotional ways because places are only physical topography.Correct answer
  • Bliterature provides us with deep insights into the ways in which movement and migration affect physical geography.
  • Cdescriptions of places do not need satellite imagery or other visual aids to give a “real” sense of the place.
  • Dhighly vivid writing, employing the language of the senses, can capture the multi-modal manner in which humans experience places.

Answer: A

Show explanation
Answer:A Which statement, if false, would *not* contradict the passage (EXCEPT). A denies subjective place experience; if A is false, humans *do* experience places subjectively—matching the passage—so falsifying A does not contradict. Why the others fail: • B — If false, denies literature’s insight into movement/geography—clashes. • C — If false, requires satellite imagery for a “real” sense—clashes. • D — If false, denies vivid multi-modal capture—clashes.
Q21Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. In my book “Searches”, I chronicle how big technology companies have exploited human language for their gain. We let this happen, I argue, because we also benefit somewhat from using the products. It’s a dynamic that makes us complicit in big tech’s accumulation of wealth and power: we’re both victims and beneficiaries. I describe this complicity, but I also enact it, through my own internet archives: my Google searches, my Amazon product reviews and, yes, my ChatGPT dialogues. . . . People often describe chatbots’ textual output as “bland” or “generic” – the linguistic equivalent of a beige office building. OpenAI’s products are built to “sound like a colleague”, as OpenAI puts it, using language that, coming from a person, would sound “polite”, “empathetic”, “kind”, “rationally optimistic” and “engaging”, among other qualities. OpenAI describes these strategies as helping its products seem “professional” and “approachable”. This appears to be bound up with making us feel safe . . . Trust is a challenge for artificial intelligence (AI) companies, partly because their products regularly produce falsehoods and reify sexist, racist, US-centric cultural norms. While the companies are working on these problems, they persist: OpenAI found that its latest systems generate errors at a higher rate than its previous system. In the book, I wrote about the inaccuracies and biases and also demonstrated them with the products. When I prompted Microsoft’s Bing Image Creator to produce a picture of engineers and space explorers, it gave me an entirely male cast of characters; when my father asked ChatGPT to edit his writing, it transmuted his perfectly correct Indian English into American English. Those weren’t flukes. Research suggests that both tendencies are widespread. In my own ChatGPT dialogues, I wanted to enact how the product’s veneer of collegial neutrality could lull us into absorbing false or biased responses without much critical engagement. Over time, ChatGPT seemed to be guiding me to write a more positive book about big tech – including editing my description of OpenAI’s CEO, Sam Altman, to call him “a visionary and a pragmatist”. I’m not aware of research on whether ChatGPT tends to favor big tech, OpenAI or Altman, and I can only guess why it seemed that way in our conversation. OpenAI explicitly states that its products shouldn’t attempt to influence users’ thinking. When I asked ChatGPT about some of the issues, it blamed biases in its training data – though I suspect my arguably leading questions played a role too. When I queried ChatGPT about its rhetoric, it responded: “The way I communicate is designed to foster trust and confidence in my responses, which can be both helpful and potentially misleading.”. . . OpenAI has its own goals, of course. Among them, it emphasizes wanting to build AI that “benefits all of humanity”. But while the company is controlled by a non-profit with that mission, its funders still seek a return on their investment. That will presumably require getting people using products such as ChatGPT even more than they already are – a goal that is easier to accomplish if people see those products as trustworthy collaborators.

The author compares AI-generated texts with “a beige office building” for all of the following reasons EXCEPT:

  • AAI aims to foster a feeling of trust and credibility among its users.
  • BAI tends to blame its training data when scrutinised for its biases.Correct answer
  • CAI-generated texts often exhibit a warm, polite, and collegial tone.
  • DAI generates generalised responses that lack specificity and nuance.

Answer: B

Show explanation
Answer:B Beige-office metaphor: trust veneer, warm polite tone, bland generic replies. Blaming training data under bias scrutiny is not a reason for that comparison—EXCEPT B. Why the others fail: • A — Trust/credibility design fits beige professionalism. • C — Warm/polite/collegial tone fits. • D — Generalised, low-nuance answers fit blandness.
Q22Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. In my book “Searches”, I chronicle how big technology companies have exploited human language for their gain. We let this happen, I argue, because we also benefit somewhat from using the products. It’s a dynamic that makes us complicit in big tech’s accumulation of wealth and power: we’re both victims and beneficiaries. I describe this complicity, but I also enact it, through my own internet archives: my Google searches, my Amazon product reviews and, yes, my ChatGPT dialogues. . . . People often describe chatbots’ textual output as “bland” or “generic” – the linguistic equivalent of a beige office building. OpenAI’s products are built to “sound like a colleague”, as OpenAI puts it, using language that, coming from a person, would sound “polite”, “empathetic”, “kind”, “rationally optimistic” and “engaging”, among other qualities. OpenAI describes these strategies as helping its products seem “professional” and “approachable”. This appears to be bound up with making us feel safe . . . Trust is a challenge for artificial intelligence (AI) companies, partly because their products regularly produce falsehoods and reify sexist, racist, US-centric cultural norms. While the companies are working on these problems, they persist: OpenAI found that its latest systems generate errors at a higher rate than its previous system. In the book, I wrote about the inaccuracies and biases and also demonstrated them with the products. When I prompted Microsoft’s Bing Image Creator to produce a picture of engineers and space explorers, it gave me an entirely male cast of characters; when my father asked ChatGPT to edit his writing, it transmuted his perfectly correct Indian English into American English. Those weren’t flukes. Research suggests that both tendencies are widespread. In my own ChatGPT dialogues, I wanted to enact how the product’s veneer of collegial neutrality could lull us into absorbing false or biased responses without much critical engagement. Over time, ChatGPT seemed to be guiding me to write a more positive book about big tech – including editing my description of OpenAI’s CEO, Sam Altman, to call him “a visionary and a pragmatist”. I’m not aware of research on whether ChatGPT tends to favor big tech, OpenAI or Altman, and I can only guess why it seemed that way in our conversation. OpenAI explicitly states that its products shouldn’t attempt to influence users’ thinking. When I asked ChatGPT about some of the issues, it blamed biases in its training data – though I suspect my arguably leading questions played a role too. When I queried ChatGPT about its rhetoric, it responded: “The way I communicate is designed to foster trust and confidence in my responses, which can be both helpful and potentially misleading.”. . . OpenAI has its own goals, of course. Among them, it emphasizes wanting to build AI that “benefits all of humanity”. But while the company is controlled by a non-profit with that mission, its funders still seek a return on their investment. That will presumably require getting people using products such as ChatGPT even more than they already are – a goal that is easier to accomplish if people see those products as trustworthy collaborators.

On the basis of the purpose of the examples in the passage, pick the odd one out from the following AI-generated responses mentioned in the passage:

  • A“When I queried ChatGPT about its rhetoric, it responded: ‘The way I communicate is designed to foster trust and confidence in my responses, which can be both helpful and potentially misleading'.”Correct answer
  • B“Over time, ChatGPT seemed to be guiding me to write a more positive book about big tech – including editing my description of OpenAI’s CEO, Sam Altman, to call him ‘a visionary and a pragmatist’.”
  • C“When I prompted Microsoft’s Bing Image Creator to produce a picture of engineers and space explorers, it gave me an entirely male cast of characters . . .”
  • D“. . . when my father asked ChatGPT to edit his writing, it transmuted his perfectly correct Indian English into American English.”

Answer: A

Show explanation
Answer:A Odd example by purpose: A is ChatGPT describing its own rhetoric; B–D show biased/steering outputs (friendlier tech narrative, male-only explorers, Indian→American English). Why the others fail: • B — Steering toward a friendlier big-tech story. • C — Gender bias in image generation. • D — Norming American English over Indian English.
Q23Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. In my book “Searches”, I chronicle how big technology companies have exploited human language for their gain. We let this happen, I argue, because we also benefit somewhat from using the products. It’s a dynamic that makes us complicit in big tech’s accumulation of wealth and power: we’re both victims and beneficiaries. I describe this complicity, but I also enact it, through my own internet archives: my Google searches, my Amazon product reviews and, yes, my ChatGPT dialogues. . . . People often describe chatbots’ textual output as “bland” or “generic” – the linguistic equivalent of a beige office building. OpenAI’s products are built to “sound like a colleague”, as OpenAI puts it, using language that, coming from a person, would sound “polite”, “empathetic”, “kind”, “rationally optimistic” and “engaging”, among other qualities. OpenAI describes these strategies as helping its products seem “professional” and “approachable”. This appears to be bound up with making us feel safe . . . Trust is a challenge for artificial intelligence (AI) companies, partly because their products regularly produce falsehoods and reify sexist, racist, US-centric cultural norms. While the companies are working on these problems, they persist: OpenAI found that its latest systems generate errors at a higher rate than its previous system. In the book, I wrote about the inaccuracies and biases and also demonstrated them with the products. When I prompted Microsoft’s Bing Image Creator to produce a picture of engineers and space explorers, it gave me an entirely male cast of characters; when my father asked ChatGPT to edit his writing, it transmuted his perfectly correct Indian English into American English. Those weren’t flukes. Research suggests that both tendencies are widespread. In my own ChatGPT dialogues, I wanted to enact how the product’s veneer of collegial neutrality could lull us into absorbing false or biased responses without much critical engagement. Over time, ChatGPT seemed to be guiding me to write a more positive book about big tech – including editing my description of OpenAI’s CEO, Sam Altman, to call him “a visionary and a pragmatist”. I’m not aware of research on whether ChatGPT tends to favor big tech, OpenAI or Altman, and I can only guess why it seemed that way in our conversation. OpenAI explicitly states that its products shouldn’t attempt to influence users’ thinking. When I asked ChatGPT about some of the issues, it blamed biases in its training data – though I suspect my arguably leading questions played a role too. When I queried ChatGPT about its rhetoric, it responded: “The way I communicate is designed to foster trust and confidence in my responses, which can be both helpful and potentially misleading.”. . . OpenAI has its own goals, of course. Among them, it emphasizes wanting to build AI that “benefits all of humanity”. But while the company is controlled by a non-profit with that mission, its funders still seek a return on their investment. That will presumably require getting people using products such as ChatGPT even more than they already are – a goal that is easier to accomplish if people see those products as trustworthy collaborators.

All of the following statements from the passage affirm the disjunct between the claims about AI made by tech companies and what AI actually does EXCEPT:

  • A“In my own ChatGPT dialogues, I wanted to enact how the product’s veneer of collegial neutrality could lull us into absorbing false or biased responses without much critical engagement.”
  • B“I’m not aware of research on whether ChatGPT tends to favor big tech, OpenAI or Altman, and I can only guess why it seemed that way in our conversation.”Correct answer
  • C“It’s a dynamic that makes us complicit in big tech’s accumulation of wealth and power: we’re both victims and beneficiaries.”
  • D“When I prompted Microsoft’s Bing Image Creator to produce a picture of engineers and space explorers, it gave me an entirely male cast of characters . . .”

Answer: B

Show explanation
Answer:B A, C, D affirm the gap between neutrality claims and AI behaviour. B is mere uncertainty about favouring big tech—not an affirmation of that disjunct—EXCEPT. Why the others fail: • A — Neutrality veneer dulls critique of false/biased answers. • C — Complicity in big-tech power accumulation. • D — Male-only engineers/explorers exposes biased output.
Q24Reading Comprehension·Application & Analogy

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. In my book “Searches”, I chronicle how big technology companies have exploited human language for their gain. We let this happen, I argue, because we also benefit somewhat from using the products. It’s a dynamic that makes us complicit in big tech’s accumulation of wealth and power: we’re both victims and beneficiaries. I describe this complicity, but I also enact it, through my own internet archives: my Google searches, my Amazon product reviews and, yes, my ChatGPT dialogues. . . . People often describe chatbots’ textual output as “bland” or “generic” – the linguistic equivalent of a beige office building. OpenAI’s products are built to “sound like a colleague”, as OpenAI puts it, using language that, coming from a person, would sound “polite”, “empathetic”, “kind”, “rationally optimistic” and “engaging”, among other qualities. OpenAI describes these strategies as helping its products seem “professional” and “approachable”. This appears to be bound up with making us feel safe . . . Trust is a challenge for artificial intelligence (AI) companies, partly because their products regularly produce falsehoods and reify sexist, racist, US-centric cultural norms. While the companies are working on these problems, they persist: OpenAI found that its latest systems generate errors at a higher rate than its previous system. In the book, I wrote about the inaccuracies and biases and also demonstrated them with the products. When I prompted Microsoft’s Bing Image Creator to produce a picture of engineers and space explorers, it gave me an entirely male cast of characters; when my father asked ChatGPT to edit his writing, it transmuted his perfectly correct Indian English into American English. Those weren’t flukes. Research suggests that both tendencies are widespread. In my own ChatGPT dialogues, I wanted to enact how the product’s veneer of collegial neutrality could lull us into absorbing false or biased responses without much critical engagement. Over time, ChatGPT seemed to be guiding me to write a more positive book about big tech – including editing my description of OpenAI’s CEO, Sam Altman, to call him “a visionary and a pragmatist”. I’m not aware of research on whether ChatGPT tends to favor big tech, OpenAI or Altman, and I can only guess why it seemed that way in our conversation. OpenAI explicitly states that its products shouldn’t attempt to influence users’ thinking. When I asked ChatGPT about some of the issues, it blamed biases in its training data – though I suspect my arguably leading questions played a role too. When I queried ChatGPT about its rhetoric, it responded: “The way I communicate is designed to foster trust and confidence in my responses, which can be both helpful and potentially misleading.”. . . OpenAI has its own goals, of course. Among them, it emphasizes wanting to build AI that “benefits all of humanity”. But while the company is controlled by a non-profit with that mission, its funders still seek a return on their investment. That will presumably require getting people using products such as ChatGPT even more than they already are – a goal that is easier to accomplish if people see those products as trustworthy collaborators.

The author of the passage is least likely to agree with which one of the following claims?

  • AWhen we use AI, we become accomplices to the exploitative practices of big tech companies.
  • BThe neutrality of AI is conducive to critical thinking.Correct answer
  • CThe neutrality of AI is motivated by economic considerations.
  • DChatGPT favours AI companies and their officials, like Sam Altman, in its responses.

Answer: B

Show explanation
Answer:B Least agree: that AI neutrality fosters critical thinking—the author argues the veneer lulls critique. Why the others fail: • A — Users as accomplices fits. • C — Neutrality as economically motivated fits. • D — Favouring Altman/OpenAI is in line with the author’s suspicion in the dialogue.

DILR(22 questions)

Q25Logical Reasoning·Scheduling & Sequencing

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender. The following additional facts are known. 1. Ustad Samiran never trained more than one of these students in the same year. 2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24. 3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years. 4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

In which of the following years were Ananya and Bhaskar Gurubhai?

  • A2021
  • B2018
  • C2014
  • D2020Correct answer

Answer: D

Show explanation
Answer:D (2020) Acharya Raghunath (AR) can teach only in 2013–14 and 2019–20 ⇒ span 2. Remaining spans: Pandit Meghnath (PM) = 4, Ustad Samiran (US) = 3. US never pairs students. Gurubhai pairs of length 2: AB, AC, BD, CD (not AD, not BC). 2013: A starts under PM, B under US. AR teaches A&B together in 2019–20 (only AR window left for AB’s 2 years). So Ananya & Bhaskar are Gurubhai in 2019 and 2020 → among options, 2020. - A 2021: AB pair already finished; 2021 is BD under PM. - B 2018: A is idle that year; B not with A. - C 2014: A with PM, B with US — different gurus.
Q26Logical Reasoning·Scheduling & Sequencing

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender. The following additional facts are known. 1. Ustad Samiran never trained more than one of these students in the same year. 2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24. 3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years. 4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

In which year did Charu begin her training under Pandit Meghnath?

  • A2021
  • B2015Correct answer
  • C2016
  • D2017

Answer: B

Show explanation
Answer:B (2015) AR can teach only in 2013–14 and 2019–20 ⇒ span 2; then PM span = 4, US span = 3. US never trains two of these students in the same year. Gurubhai pairs of length 2: AB, AC, BD, CD (not AD, not BC). 2013: Ananya starts under PM, Bhaskar under US. AB’s only possible 2-year share is under AR in 2019–20. Ananya’s PM block is 2013–16. AC’s share must be under PM, so Charu’s PM run is 2015–18 (overlap 2015–16). Bhaskar then takes US early years and later joins Devendra under PM in 2021–22 (Devendra’s PM = 2019–22). Charu’s US block is 2019–21; remaining US/PM/AR placements fill 2013–24 without further pairing under US. Charu begins under Pandit Meghnath in 2015. - A 2021: Charu is under US that year, not starting PM. - C 2016: would share only one year with Ananya under PM. - D 2017: Ananya has already left PM.
Q27Logical Reasoning·Scheduling & Sequencing

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender. The following additional facts are known. 1. Ustad Samiran never trained more than one of these students in the same year. 2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24. 3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years. 4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

In which of the following years were Bhaskar and Devendra Gurubhai?

  • A2018
  • B2020
  • C2015
  • D2022Correct answer

Answer: D

Show explanation
Answer:D (2022) AR can teach only in 2013–14 and 2019–20 ⇒ span 2; then PM span = 4, US span = 3. US never trains two of these students in the same year. Gurubhai pairs of length 2: AB, AC, BD, CD (not AD, not BC). 2013: Ananya starts under PM, Bhaskar under US. AB’s only possible 2-year share is under AR in 2019–20. Ananya’s PM block is 2013–16. AC’s share must be under PM, so Charu’s PM run is 2015–18 (overlap 2015–16). Bhaskar then takes US early years and later joins Devendra under PM in 2021–22 (Devendra’s PM = 2019–22). Charu’s US block is 2019–21; remaining US/PM/AR placements fill 2013–24 without further pairing under US. Bhaskar and Devendra share under PM in 2021–22. Among the options, that overlap appears as 2022. - A 2018: Devendra is under US; not paired with Bhaskar. - B 2020: Bhaskar is with Ananya under AR; Devendra is under PM. - C 2015: Bhaskar is under US; the BD overlap has not started.
Q28Logical Reasoning·Scheduling & Sequencing

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender. The following additional facts are known. 1. Ustad Samiran never trained more than one of these students in the same year. 2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24. 3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years. 4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

Which of the following statements is TRUE?

  • AAnanya was training under Ustad Samiran in 2018.
  • BCharu was training under Ustad Samiran in 2019.Correct answer
  • CAnanya was training under Ustad Samiran in 2015.
  • DCharu was training under Ustad Samiran in 2018.

Answer: B

Show explanation
Answer:B (Charu was training under Ustad Samiran in 2019.) AR can teach only in 2013–14 and 2019–20 ⇒ span 2; then PM span = 4, US span = 3. US never trains two of these students in the same year. Gurubhai pairs of length 2: AB, AC, BD, CD (not AD, not BC). 2013: Ananya starts under PM, Bhaskar under US. AB’s only possible 2-year share is under AR in 2019–20. Ananya’s PM block is 2013–16. AC’s share must be under PM, so Charu’s PM run is 2015–18 (overlap 2015–16). Bhaskar then takes US early years and later joins Devendra under PM in 2021–22 (Devendra’s PM = 2019–22). Charu’s US block is 2019–21; remaining US/PM/AR placements fill 2013–24 without further pairing under US. Charu’s US years are 2019–21, so she trains under Ustad Samiran in 2019 — statement B. - A Ananya–US–2018: Ananya is idle in 2017–18. - C Ananya–US–2015: she is still under PM through 2016. - D Charu–US–2018: in 2018 she finishes PM, not US.
Q29Logical Reasoning·Scheduling & SequencingTITA

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender. The following additional facts are known. 1. Ustad Samiran never trained more than one of these students in the same year. 2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24. 3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years. 4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

In how many of the years between 2013-24, were only two of these four musicians training under these three Gurus?

Answer: 4

Show explanation
Answer:4 AR can teach only in 2013–14 and 2019–20 ⇒ span 2; then PM span = 4, US span = 3. US never trains two of these students in the same year. Gurubhai pairs of length 2: AB, AC, BD, CD (not AD, not BC). 2013: Ananya starts under PM, Bhaskar under US. AB’s only possible 2-year share is under AR in 2019–20. Ananya’s PM block is 2013–16. AC’s share must be under PM, so Charu’s PM run is 2015–18 (overlap 2015–16). Bhaskar then takes US early years and later joins Devendra under PM in 2021–22 (Devendra’s PM = 2019–22). Charu’s US block is 2019–21; remaining US/PM/AR placements fill 2013–24 without further pairing under US. Year-by-year trainee counts from this timetable show exactly two of the four musicians active in 2017, 2018, 2023, and 2024 — four years.
Q30Data Interpretation·Mixed ChartsTITA

The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries – A, B, C, D, E, and F – at three different points in time – 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X-coordinate representing % increase in 2020 from 2016, i.e., SI in 2020 minus SI in 2016SI in 2016, and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known. 1. In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively. 2. F had lower SI than any other country in 2016, 2020, and 2024. 3. In 2024, E was the only country with SI of 90. 4. The range of SI of the six countries was 60 in 2016 as well as in 2024.

CAT 2025 Slot 2 Sustainability Index scatter

What was the SI of E in 2016?

Answer: 60

Show explanation
Answer:60 The scatter shows each country’s % SI change from 2016 to 2020 (x-axis) and from 2020 to 2024 (y-axis). Country E plots near (+25%, +20%), so its SI is multiplied by 54 from 2016 to 2020 and by 65 from 2020 to 2024. Fact 3 says that in 2024, E alone has SI = 90. Let e be E’s 2016 SI. Then 90 = e · (54) · (65) = (32)e ⇒ e = 60. Along the way, SI_2020(E) = 75. This also sits correctly as 2016 rank 3 (behind B and C, ahead of A) with F always lowest and the 2016 range equal to 60.
Q31Data Interpretation·Mixed ChartsTITA

The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries – A, B, C, D, E, and F – at three different points in time – 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X-coordinate representing % increase in 2020 from 2016, i.e., SI in 2020 minus SI in 2016SI in 2016, and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known. 1. In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively. 2. F had lower SI than any other country in 2016, 2020, and 2024. 3. In 2024, E was the only country with SI of 90. 4. The range of SI of the six countries was 60 in 2016 as well as in 2024.

CAT 2025 Slot 2 Sustainability Index scatter

What was the SI of F in 2020?

Answer: 40

Show explanation
Answer:40 F plots at (+100%, −25%): SI doubles by 2020, then falls 25% by 2024. F is lowest in 2016, 2020, and 2024. In 2016, B is rank 1 and the SI range is 60, so b − f = 60. B plots at (−25%, −25%), so both factors are 34 and b must be a multiple of 16 for integer later SI; candidates are 64, 80, 96. Checking 2024: only b = 80 with f = 20 keeps F strictly lowest (SI_2024(F) = 20 × 2 · 0.75 = 30 while SI_2024(B) = 80 · 916 = 45) and keeps the 2024 range at 60. Therefore SI_2020(F) = 2 × 20 = 40.
Q32Data Interpretation·Mixed ChartsTITA

The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries – A, B, C, D, E, and F – at three different points in time – 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X-coordinate representing % increase in 2020 from 2016, i.e., SI in 2020 minus SI in 2016SI in 2016, and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known. 1. In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively. 2. F had lower SI than any other country in 2016, 2020, and 2024. 3. In 2024, E was the only country with SI of 90. 4. The range of SI of the six countries was 60 in 2016 as well as in 2024.

CAT 2025 Slot 2 Sustainability Index scatter

What was the SI of C in 2024?

Answer: 84

Show explanation
Answer:84 C plots at (−20%, +40%) ⇒ factors 0.8 and 1.4, overall 2825, so C’s 2016 SI must be a multiple of 25. From E’s unique 2024 SI of 90 at (+25%, +20%), E’s 2016 SI is 60. From F always lowest with 2016 range 60 and B at (−25%, −25%), B’s 2016 SI is 80. C is 2016 rank 2, so it lies between B = 80 and E = 60; the only multiple of 25 there is c = 75. Then SI_2024(C) = 75 × 2825 = 84. Integer SI throughout also rules out non-multiples of 25 for C’s 2016 starting value.
Q33Data Interpretation·Mixed Charts

The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries – A, B, C, D, E, and F – at three different points in time – 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X-coordinate representing % increase in 2020 from 2016, i.e., SI in 2020 minus SI in 2016SI in 2016, and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known. 1. In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively. 2. F had lower SI than any other country in 2016, 2020, and 2024. 3. In 2024, E was the only country with SI of 90. 4. The range of SI of the six countries was 60 in 2016 as well as in 2024.

CAT 2025 Slot 2 Sustainability Index scatter

What was the SI of B in 2024?

  • A54
  • B60
  • C45Correct answer
  • D80

Answer: C

Show explanation
Answer:C (45) Chart: E is at (+25%, +20%); F at (+100%, −25%); B at (−25%, −25%); C at (−20%, +40%). In 2024 E alone has SI 90. F is always lowest; 2016 ranks B,C,E,A = 1,2,3,4 and range = 60 in 2016 and 2024. 2016: range 60 with F lowest forces b = 80, f = 20 (only multiple-of-16 b that keeps F unique-lowest in 2024). B’s factors (−25%,−25%) give SI_2024(B) = 80 × (34) × (34) = 80 × 916 = 45. - A 54: the inconsistent b = 96 branch (ties F in 2024). - B 60: a 2016 value, not 2024. - D 80: B’s 2016 SI.
Q34Logical Reasoning·Quant-based ReasoningTITA

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

What is the PI of Whimshire?

Answer: 45

Show explanation
Answer:45 PMs are {10,…,90}. The unique NUR>city pair is in Humbleset, and Blusterburg is the smallest city ⇒ Blusterburg = 30, Humbleset NUR = 40; other NURs ∈ {10,20}. Remaining cities: 50,60,70,80,90. PI = ½·NUR + ¼·c1 + ¼·c2 must be distinct integers; Fogglia lowest, Humbleset highest. Half-PMs (cities 30,50,70,90) contribute .5×¼=.5/… actually 304=7.5 etc., so two “.5 cities” must share a state for PI∈ℤ. Splutterville(60) and Mumpypore(80) are the integer-contribution pair and must share Whimshire or Fogglia (combined city contribution 35). Humbleset’s fixed pieces: 402 + 304 = 20+7.5=27.5. Trying second city: - Noodleton(50) → PI 40, cannot be uniquely highest. - Quackford(70) → PI 45, collides with another state’s 45. - Zingaloo(90) → PI 50 works with Fogglia = 35 (Splutterville+Mumpypore+NUR20) and Whimshire = 45 (Noodleton+Quackford+NUR10). So Whimshire PI = 45.
Q35Logical Reasoning·Quant-based ReasoningTITA

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

What is the PI of Fogglia?

Answer: 35

Show explanation
Answer:35 PMs are {{10,…,90}}. The unique NUR>city pair is in Humbleset; Blusterburg is the smallest city ⇒ Blusterburg = 30, Humbleset NUR = 40; other NURs ∈ {{10,20}}. Remaining cities: 50,60,70,80,90. PI = ½·NUR + ¼·c1 + ¼·c2 must be distinct integers; Fogglia lowest, Humbleset highest. Cities with half-integer ¼-contributions (30,50,70,90) must be paired so each state’s PI is an integer; Splutterville(60) and Mumpypore(80) are the integer pair and share Fogglia or Whimshire. Humbleset’s base 402 + 304 = 27.5. Second city Zingaloo(90) gives PI 50. Then Fogglia = Splutterville(60)+Mumpypore(80)+NUR 20 → PI 35; Whimshire = Noodleton(50)+Quackford(70)+NUR 10 → PI 45. This is the unique ranking. Fogglia’s PI = 202 + 604 + 804 = 10 + 15 + 20 = 35.
Q36Logical Reasoning·Quant-based ReasoningTITA

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

What is the PI of Humbleset?

Answer: 50

Show explanation
Answer:50 PMs are {{10,…,90}}. The unique NUR>city pair is in Humbleset; Blusterburg is the smallest city ⇒ Blusterburg = 30, Humbleset NUR = 40; other NURs ∈ {{10,20}}. Remaining cities: 50,60,70,80,90. PI = ½·NUR + ¼·c1 + ¼·c2 must be distinct integers; Fogglia lowest, Humbleset highest. Cities with half-integer ¼-contributions (30,50,70,90) must be paired so each state’s PI is an integer; Splutterville(60) and Mumpypore(80) are the integer pair and share Fogglia or Whimshire. Humbleset’s base 402 + 304 = 27.5. Second city Zingaloo(90) gives PI 50. Then Fogglia = Splutterville(60)+Mumpypore(80)+NUR 20 → PI 35; Whimshire = Noodleton(50)+Quackford(70)+NUR 10 → PI 45. This is the unique ranking. Humbleset’s PI = 402 + 304 + 904 = 20 + 7.5 + 22.5 = 50.
Q37Logical Reasoning·Quant-based Reasoning

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

Which pair of cities definitely belong to the same state?

  • ABlusterburg, Mumpypore
  • BMumpypore, Zingaloo
  • CNoodleton, QuackfordCorrect answer
  • DSplutterville, Quackford

Answer: C

Show explanation
Answer:C (Noodleton, Quackford) PMs are {{10,…,90}}. The unique NUR>city pair is in Humbleset; Blusterburg is the smallest city ⇒ Blusterburg = 30, Humbleset NUR = 40; other NURs ∈ {{10,20}}. Remaining cities: 50,60,70,80,90. PI = ½·NUR + ¼·c1 + ¼·c2 must be distinct integers; Fogglia lowest, Humbleset highest. Cities with half-integer ¼-contributions (30,50,70,90) must be paired so each state’s PI is an integer; Splutterville(60) and Mumpypore(80) are the integer pair and share Fogglia or Whimshire. Humbleset’s base 402 + 304 = 27.5. Second city Zingaloo(90) gives PI 50. Then Fogglia = Splutterville(60)+Mumpypore(80)+NUR 20 → PI 35; Whimshire = Noodleton(50)+Quackford(70)+NUR 10 → PI 45. This is the unique ranking. Whimshire’s two cities are forced to be Noodleton(50) and Quackford(70) — the only same-state pair among the options. - A Blusterburg, Mumpypore: Humbleset vs Fogglia. - B Mumpypore, Zingaloo: Fogglia vs Humbleset. - D Splutterville, Quackford: Fogglia vs Whimshire.
Q38Logical Reasoning·Quant-based ReasoningTITA

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

For how many of the cities and NURs is it possible to identify their PM and the state they belong to?

Answer: 9

Show explanation
Answer:9 PMs are {{10,…,90}}. The unique NUR>city pair is in Humbleset; Blusterburg is the smallest city ⇒ Blusterburg = 30, Humbleset NUR = 40; other NURs ∈ {{10,20}}. Remaining cities: 50,60,70,80,90. PI = ½·NUR + ¼·c1 + ¼·c2 must be distinct integers; Fogglia lowest, Humbleset highest. Cities with half-integer ¼-contributions (30,50,70,90) must be paired so each state’s PI is an integer; Splutterville(60) and Mumpypore(80) are the integer pair and share Fogglia or Whimshire. Humbleset’s base 402 + 304 = 27.5. Second city Zingaloo(90) gives PI 50. Then Fogglia = Splutterville(60)+Mumpypore(80)+NUR 20 → PI 35; Whimshire = Noodleton(50)+Quackford(70)+NUR 10 → PI 45. This is the unique ranking. Assignment: Humbleset = Blusterburg 30, Zingaloo 90, NUR 40; Fogglia = Splutterville 60, Mumpypore 80, NUR 20; Whimshire = Noodleton 50, Quackford 70, NUR 10. All 9 cities and NURs are identified.
Q39Data Interpretation·Mixed ChartsTITA

The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, singleauthor, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers. The following additional facts are known. 1. Each of the authors wrote at least one of each of the four types of papers. 2. The four authors wrote different numbers of single-author papers. 3. Both Chintan and Devon wrote more three-author papers than Brajen 4. The number of single-author and two-author papers written by Brajen were the same.

Number of papers by each author
Number of papers by type

What was the total number of two-author and three-author papers written by Brajen?

Answer: 4

Show explanation
Answer:4 Chart incidences: two-author authorships sum to 8 ⇒ 4 two-author papers; three-author sum 9 ⇒ 3 triples; four-author sum 8 ⇒ 2 fours (each author in both). Each author has ≥1 of every type; singles are all different; Brajen’s singles = doubles = k; Chintan and Devon each have more triples than Brajen. Arman’s non-four residual is 3 ⇒ Arman has exactly 1 single, 1 double, 1 triple. Only k = 2 leaves Brajen triples = 2 with Chintan = Devon = 3. Two residual cases for Chintan/Devon singles {{3,4}} remain: (3,4) with doubles (4,1), or (4,3) with doubles (3,2). Brajen’s doubles + triples = 2 + 2 = 4.
Q40Data Interpretation·Mixed Charts

The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, singleauthor, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers. The following additional facts are known. 1. Each of the authors wrote at least one of each of the four types of papers. 2. The four authors wrote different numbers of single-author papers. 3. Both Chintan and Devon wrote more three-author papers than Brajen 4. The number of single-author and two-author papers written by Brajen were the same.

Number of papers by each author
Number of papers by type

Which of the following statements is/are NECESSARILY true? i. Chintan wrote exactly three two-author papers. ii. Chintan wrote more single-author papers than Devon.

  • AOnly ii
  • BBoth i and ii
  • CNeither i nor iiCorrect answer
  • DOnly i

Answer: C

Show explanation
Answer:C (Neither i nor ii) Two residual cases remain for Chintan/Devon singles {3,4}: - Chintan singles 3 ⇒ doubles 4; Devon singles 4 ⇒ doubles 1 - Chintan singles 4 ⇒ doubles 3; Devon singles 3 ⇒ doubles 2 (i) “Chintan wrote exactly three two-author papers” holds only in case 2 — not necessary. (ii) “Chintan wrote more singles than Devon” holds only in case 2 — not necessary. Hence neither. - A Only ii / D Only i / B Both: each fails in one of the two live cases.
Q41Data Interpretation·Mixed Charts

The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, singleauthor, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers. The following additional facts are known. 1. Each of the authors wrote at least one of each of the four types of papers. 2. The four authors wrote different numbers of single-author papers. 3. Both Chintan and Devon wrote more three-author papers than Brajen 4. The number of single-author and two-author papers written by Brajen were the same.

Number of papers by each author
Number of papers by type

Which of the following statements is/are NECESSARILY true? i. Arman wrote three-author papers only with Chintan and Devon. ii. Brajen wrote three-author papers only with Chintan and Devon.

  • AOnly I
  • BNeither i or ii
  • COnly ii
  • DBoth i and iiCorrect answer

Answer: D

Show explanation
Answer:D (Both i and ii) Chart incidences: two-author authorships sum to 8 ⇒ 4 two-author papers; three-author sum 9 ⇒ 3 triples; four-author sum 8 ⇒ 2 fours (each author in both). Each author has ≥1 of every type; singles are all different; Brajen’s singles = doubles = k; Chintan and Devon each have more triples than Brajen. Arman’s non-four residual is 3 ⇒ Arman has exactly 1 single, 1 double, 1 triple. Only k = 2 leaves Brajen triples = 2 with Chintan = Devon = 3. Two residual cases for Chintan/Devon singles {{3,4}} remain: (3,4) with doubles (4,1), or (4,3) with doubles (3,2). With Arman on 1 triple and Brajen on 2 while Chintan = Devon = 3, every three-author paper that includes Arman or Brajen must be with the other two high-triple authors. Both (i) and (ii) hold in every completion → D. - A Only i: ii also holds. - B Neither: both are forced. - C Only ii: i also holds.
Q42Data Interpretation·Mixed ChartsTITA

The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, singleauthor, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers. The following additional facts are known. 1. Each of the authors wrote at least one of each of the four types of papers. 2. The four authors wrote different numbers of single-author papers. 3. Both Chintan and Devon wrote more three-author papers than Brajen 4. The number of single-author and two-author papers written by Brajen were the same.

Number of papers by each author
Number of papers by type

If Devon wrote more than one two-author papers, then how many two-author papers did Chintan write?

Answer: 3

Show explanation
Answer:3 Chart incidences: two-author authorships sum to 8 ⇒ 4 two-author papers; three-author sum 9 ⇒ 3 triples; four-author sum 8 ⇒ 2 fours (each author in both). Each author has ≥1 of every type; singles are all different; Brajen’s singles = doubles = k; Chintan and Devon each have more triples than Brajen. Arman’s non-four residual is 3 ⇒ Arman has exactly 1 single, 1 double, 1 triple. Only k = 2 leaves Brajen triples = 2 with Chintan = Devon = 3. Two residual cases for Chintan/Devon singles {{3,4}} remain: (3,4) with doubles (4,1), or (4,3) with doubles (3,2). “Devon wrote more than one two-author paper” selects the case Devon doubles = 2 (and Chintan doubles = 3), not Devon doubles = 1. Chintan’s two-author count is therefore 3.
Q43Data Interpretation·CaseletsTITA

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4. Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a “ping”. Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping. The following additional information is known: 1. B1 and B6 each made a ping on H4, but B5 did not. 2. B4 made a ping on H3, but B1 did not. 3. All balls, except B3, made pings on H1. 4. None of the balls, except B2, made a ping on H2.

What was the total number of pings made by B1, B2, and B3?

Answer: 6

Show explanation
Answer:6 A ball pings a hoop iff its diameter ≤ the hoop’s. From the four clues: B1 and B6 ping H4 but B5 does not ⇒ (B1, B6) < H4 < B5; B4 pings H3 but B1 does not ⇒ B4 < H3 < B1; all except B3 ping H1 ⇒ every other ball < H1 < B3; only B2 pings H2 ⇒ B2 < H2 < all other balls. Forced diameter chain: B2 < H2 < B4 < H3 < B1 < H4 < B5 < H1 < B3 (B6 sits somewhere under H4). Therefore B1 pings only H4 and H1 (2 pings), B2 pings all four hoops (4), and B3 pings none (0). Total for B1+B2+B3 = 6.
Q44Data Interpretation·Caselets

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4. Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a “ping”. Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping. The following additional information is known: 1. B1 and B6 each made a ping on H4, but B5 did not. 2. B4 made a ping on H3, but B1 did not. 3. All balls, except B3, made pings on H1. 4. None of the balls, except B2, made a ping on H2.

Which of the following statements about the relative sizes of the balls is NOT NECESSARILY true?

  • AB1 < B6 < B3Correct answer
  • BB2 < B1 < B5
  • CB4 < B5 < B3
  • DB1 < B5 < B3

Answer: A

Show explanation
Answer:A (B1 < B6 < B3) Ping rules: B1,B6 < H4 < B5; B4 < H3 < B1; all except B3 < H1 < B3; only B2 < H2 < every other ball. Forced chain: B2 < H2 < B4 < H3 < B1 < H4 < B5 < H1 < B3, with B6 anywhere under H4 (either below H3 or between H3 and H4). B6 may sit below H3 or between H3 and H4, so B1 ≟ B6 is open. Thus B1 < B6 < B3 is not necessary (though B6 < B3 always). - B B2 < B1 < B5: forced by the chain. - C B4 < B5 < B3: forced. - D B1 < B5 < B3: forced.
Q45Data Interpretation·Caselets

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4. Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a “ping”. Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping. The following additional information is known: 1. B1 and B6 each made a ping on H4, but B5 did not. 2. B4 made a ping on H3, but B1 did not. 3. All balls, except B3, made pings on H1. 4. None of the balls, except B2, made a ping on H2.

Which of the following statements about the relative sizes of the hoops is true?

  • AH2 < H4 < H3 < H1
  • BH2 < H3 < H4 < H1Correct answer
  • CH1 < H3 < H4 < H2
  • DH1 < H4 < H3 < H2

Answer: B

Show explanation
Answer:B (H2 < H3 < H4 < H1) Ping rules: B1,B6 < H4 < B5; B4 < H3 < B1; all except B3 < H1 < B3; only B2 < H2 < every other ball. Forced chain: B2 < H2 < B4 < H3 < B1 < H4 < B5 < H1 < B3, with B6 anywhere under H4 (either below H3 or between H3 and H4). The hoop order on the chain is uniquely H2 < H3 < H4 < H1. - A H2 < H4 < H3 < H1: swaps H3 and H4, but H3 < B1 < H4. - C H1 < H3 < H4 < H2: reverses the order. - D H1 < H4 < H3 < H2: likewise reversed/swapped.
Q46Data Interpretation·Caselets

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4. Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a “ping”. Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping. The following additional information is known: 1. B1 and B6 each made a ping on H4, but B5 did not. 2. B4 made a ping on H3, but B1 did not. 3. All balls, except B3, made pings on H1. 4. None of the balls, except B2, made a ping on H2.

What BEST can be said about the total number of pings from all the tests undertaken?

  • A12 or 13 or 14
  • B13 or 14
  • CAt least 9
  • D12 or 13Correct answer

Answer: D

Show explanation
Answer:D (12 or 13) Ping rules: B1,B6 < H4 < B5; B4 < H3 < B1; all except B3 < H1 < B3; only B2 < H2 < every other ball. Forced chain: B2 < H2 < B4 < H3 < B1 < H4 < B5 < H1 < B3, with B6 anywhere under H4 (either below H3 or between H3 and H4). Fixed pings from B1–B5 total 10. If B6 < H3, B6 pings H3,H4,H1 (3) → total 13; if H3 < B6 < H4, B6 pings H4,H1 (2) → total 12. Best description: 12 or 13. - A adds 14 (impossible). - B 13 or 14: drops the 12 case. - C At least 9: true but weaker than D.

QA(22 questions)

Q47Quantitative Ability·Linear Equations

The equations 3x2 − 5x + p = 0 and 2x2 − 2x + q = 0 have one common root. The sum of the other roots of these two equations is

  • A83 + p + (13)q
  • B23 − 2p + (23)q
  • C83 − p + (32)qCorrect answer
  • D23 − p + (32)q

Answer: C

Show explanation
Answer:C (83 − p + (32)q) Let the common root be r. Then 3r2 − 5r + p = 0 and 2r2 − 2r + q = 0, so p = 5r − 3r2 and q = 2r − 2r2. Sum of roots of the first equation is 53, so the other root is 53 − r. Sum of roots of the second is 1, so the other root is 1 − r. Required sum = 83 − 2r. Now evaluate 83 − p + (32)q: 83 − (5r − 3r2) + (32)(2r − 2r2) = 83 − 5r + 3r2 + 3r − 3r2 = 83 − 2r. Matches the required sum → C.
Q48Quantitative Ability·Mensuration

Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is

  • A6 : 19
  • B5 : 24Correct answer
  • C7 : 24
  • D6 : 25

Answer: B

Show explanation
Answer:B (5 : 24) What to find. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is. Setup. Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is Steps. In a regular hexagon of side 1, area = 3 3/2. Place the hexagon in the coordinate plane with centre at the origin. Midpoints P of AB and Q of CD give trapezium PBCQ whose vertices can be shoelaced to area 5 3/16. Ratio = 5 3/163 3/2 = 516 · 23 = 524. Hence area(PBCQ) : area(ABCDEF) = 5 : 24 → B. Conclusion. This matches B (5 : 24).
Q49Quantitative Ability·Logarithms

If log64(x2) + log8(y) + 3 log512(z y) = 4, where x, y and z are positive real numbers, then the minimum possible value of (x + y + z) is

  • A96
  • B36
  • C24
  • D48Correct answer

Answer: D

Show explanation
Answer:D (48) Rewrite all logs in base 2. Since 64 = 2^6, 8 = 2^3, 512 = 2^9: log64(x2) = 2 log2 x6 = (13) log2 x, log_8(y) = ½ log2 y3 = (16) log2 y, 3 log512(z y) = 3 · log2 z + ½ log2 y9 = (13) log2 z + (16) log2 y. Sum: (13) log2 x + (13) log2 y + (13) log2 z = 4 log2(xyz) = 12 ⇒ xyz = 212 = 4096. For positive reals, AM–GM: x + y + z3 ≥ (xyz)13 = 16, equality at x = y = z = 16. Minimum x + y + z = 48 → D.
Q50Quantitative Ability·Inequalities

The set of all real values of x for which (x2 – |x + 9| + x) > 0, is

  • A(– ∞, –3) ∪ (3, ∞)Correct answer
  • B(– 9, – 3) ∪ (3, ∞)
  • C(– ∞, – 9) ∪ (9, ∞)
  • D(– ∞, –9) ∪ (3, ∞)

Answer: A

Show explanation
Answer:A ((−∞, −3) ∪ (3, ∞)) Case x ≥ −9: |x + 9| = x + 9, so x2 − (x + 9) + x > 0 ⇒ x2 − 9 > 0 ⇒ (x − 3)(x + 3) > 0 ⇒ x ∈ [−9, −3) ∪ (3, ∞). Case x < −9: |x + 9| = −x − 9, so x2 − (−x − 9) + x > 0 ⇒ x2 + 2x + 9 > 0. Discriminant 4 − 36 < 0 and leading coefficient positive, so true for all x < −9. Union: (−∞, −3) ∪ (3, ∞) → A.
Q51Quantitative Ability·Percentages

A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is

  • A2 : 1
  • B5 : 8Correct answer
  • C1 : 2
  • D8 : 5

Answer: B

Show explanation
Answer:B (5 : 8) What to find. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is. Setup. A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, Steps. Let total = 100. Pinu gets 20. Remaining 80; Meena gets 40% of 80 = 32. Seema gets 20% less than Pinu = 16. Rinu gets 100 − 20 − 32 − 16 = 32. Pinu : Rinu = 20 : 32 = 5 : 8 → B. Conclusion. This matches B (5 : 8).
Q52Quantitative Ability·Time & WorkTITA

Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is

Answer: 340

Show explanation
Answer:340 What to find. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is. Setup. Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, Steps. Ankita : Bipin : Chandan rates = 4 : 2 : 1. Let Chandan’s rate be 1D (job per day). All three work 20 days, then Ankita + Chandan for 40 more days (total 60): 20 4 + 2 + 1D + 40 4 + 1D = 1 140D + 200D = 1 ⇒ 340D = 1 ⇒ D = 340. Conclusion. Therefore the required value is 340.
Q53Quantitative Ability·Progressions (AP/GP/HP)

Let an be the nth term of a decreasing infinite geometric progression. If a1 + a2 + a3 = 52 and a1a2 + a2a3 + a3a1 = 624, then the sum of this geometric progression is

  • A54Correct answer
  • B60
  • C57
  • D63

Answer: A

Show explanation
Answer:A (54) Let terms a, ar, ar2 with |r| < 1 (decreasing infinite GP). a(1 + r + r2) = 52, a2r(1 + r + r2) = 624 ⇒ a · 52 · r = 624 ⇒ ar = 12. Then a + 12 + 12r = 52 ⇒ a + 12r = 40. With a = 12r: 12r + 12r = 40 ⇒ 3r2 − 10r + 3 = 0 ⇒ (3r − 1)(r − 3) = 0. Take r = 13; a = 36. Infinite sum = a1 − r = 3623 = 54 → A.
Q54Quantitative Ability·Functions & Graphs

Let f(x) = x2x − 1 and g(x) = xx − 1. Then, the domain of the function h(x) = f(g(x)) + g(f(x)) is all real numbers except

  • A12, 1, and 32
  • B12, 12, and 1
  • C−1, 12, and 1Correct answer
  • D12 and 1

Answer: C

Show explanation
Answer:C (−1, 12, and 1) f(x) = x2x − 1 needs x ≠ 12; g(x) = xx − 1 needs x ≠ 1. h = f(g(x)) + g(f(x)). For f(g(x)): need g(x) ≠ 12xx − 112 ⇒ 2x ≠ x − 1 ⇒ x ≠ −1, and g defined so x ≠ 1. For g(f(x)): need f(x) ≠ 1 ⇒ x2x − 1 ≠ 1 ⇒ x ≠ 2x − 1 ⇒ x ≠ 1 (already), and f defined so x ≠ 12. Also f(g(x)) requires g(x) defined, and the outer denominators after composition must be nonzero — the new obstruction is x = −1. Excluded values: −1, 12, 1 → C.
Q55Quantitative Ability·Simple & Compound Interest

A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is

  • A8Correct answer
  • B9
  • C10
  • D11

Answer: A

Show explanation
Answer:A (8) What to find. If the interest is compounded annually, then the rate of interest, in percentage, is. Setup. A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is Steps. Present value of installments equals 1000: 5301 + r + 5941 + r2 = 1000. Let u = 1 + r: 530u + 594 = 1000u2 ⇒ 1000u2 − 530u − 594 = 0. u = [530 + 5302 + 4·1000·594]/2000 = [530 + 1630]/2000 = 1.08. Hence r = 0.08 = 8% → A. Conclusion. This matches A (8).
Q56Quantitative Ability·CirclesTITA

Two tangents drawn from a point P touch a circle with center O at points Q and R. Points A and B lie on PQ and PR, respectively, such that AB is also a tangent to the same circle. If <AOB = 50°, then <APB, in degrees, equals.

Answer: 80

Show explanation
Answer:80 Tangents from P touch the circle at Q and R; AB touches it at T. Radii OQ, OR, OT are perpendicular to the respective tangents. Equal tangent segments give AQ = AT and BR = BT, so △AOQ ≅ △AOT and △BOR ≅ △BOT. Therefore ∠AOQ = ∠AOT and ∠BOR = ∠BOT. Consequently ∠QOR = ∠QOT + ∠TOR = 2∠AOT + 2∠BOT = 2∠AOB = 2 × 50° = 100°. In cyclic quadrilateral OQPR (angles at Q and R are 90°), ∠QPR = 180° − ∠QOR = 80°. But ∠QPR is the same angle as ∠APB, so ∠APB = 80.
Q57Quantitative Ability·Mixtures & Alligation

A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is

  • A6
  • B2.5
  • C4
  • D5Correct answer

Answer: D

Show explanation
Answer:D (5) Coffee percentages 16% and 36% with prices 240 and 320. Let pure cocoa price be c and pure coffee price be f (per kg). 0.16f + 0.84c = 240, 0.36f + 0.64c = 320. Subtract after scaling: eliminate c — From first: 0.16(f − c) + c = 240. Difference of mixtures: (0.36 − 0.16)f + (0.64 − 0.84)c = 80 ⇒ 0.2f − 0.2c = 80 ⇒ f − c = 400. Then 0.16 · 400 + c = 240 ⇒ 64 + c = 240 ⇒ c = 176, f = 576. New mix at 376: 376 = p f + (1 − p)c = c + p(f − c) = 176 + 400p ⇒ 400p = 200 ⇒ p = 12. Coffee in 10 kg = 5 kg → D.
Q58Quantitative Ability·Number SystemsTITA

If a, b, c and d are integers such that their sum is 46, then the minimum possible value of (a − b)2 + (a − c)2 + (a − d)2 is

Answer: 2

Show explanation
Answer:2 Minimize (a − b)2 + (a − c)2 + (a − d)2 subject to a + b + c + d = 46 (integers). The sum of squares of deviations is smallest when a, b, c, d are as equal as possible: values near 464 = 11.5. Take {11, 11, 12, 12}. If a = 11, the other three are 11, 12, 12: (0)2 + (−1)2 + (−1)2 = 2. If a = 12: others 11, 11, 12 give the same value 2. No configuration gives 0 or 1 with integer sum 46, so the minimum is 2.
Q59Quantitative Ability·AveragesTITA

The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is

Answer: 49

Show explanation
Answer:49 Sum of first 7 days = 60 × 7 = 420. Sum of first 8 days = 63 × 8 = 504 ⇒ day 8 = 84. Day 9 = 84 − 11 = 73. Average from day 2 to day 9 is 66 ⇒ sum of days 2…9 = 66 × 8 = 528. Sum of days 1…9 = 504 + 73 = 577 = (sum of days 2…9) + day 1 = 528 + day 1. Hence day 1 = 577 − 528 = 49.
Q60Quantitative Ability·Surds & Indices

If 9x2 + 2x − 3 − 4(3x2 + 2x − 2) + 27 = 0, then the products of all possible value of x is

  • A15
  • B20Correct answer
  • C5
  • D30

Answer: B

Show explanation
Answer:B (20) Let u = 3x2 + 2x − 3. Then 9x2 + 2x − 3 = u2 and 3x2 + 2x − 2 = 3u. Equation: u2 − 4 × 3u + 27 = 0 ⇒ u2 − 12u + 27 = 0 ⇒ (u − 3)(u − 9) = 0. So 3x2 + 2x − 3 = 3 or 9 ⇒ x2 + 2x − 3 = 1 or 2 x2 + 2x − 4 = 0 or x2 + 2x − 5 = 0. Product of roots of the first quadratic is −4; of the second is −5. Product of all four real roots = (−4)(−5) = 20 → B.
Q61Quantitative Ability·Number SystemsTITA

Suppose a, b, c are three distinct natural number, such that 3ac = 8(a + b). Then, the smallest possible value of 3a + 2b + c is

Answer: 12

Show explanation
Answer:12 3ac = 8(a + b) ⇒ b = a 3c − 88. Need 8 | a(3c − 8) with distinct natural a, b, c and 3c > 8. Try c = 4: b = a/2, so a even. Take a = 2 ⇒ b = 1. Triple (2, 1, 4) all distinct. Check: 3 × 2 × 4 = 24 = 8(2 + 1). Value 3a + 2b + c = 6 + 2 + 4 = 12. Smaller positive values are impossible (c ≥ 3 and distinctness), so the minimum is 12.
Q62Quantitative Ability·Triangles

In a ∆ABC, points D and E are on the sides BC and AC, respectively. BE and AD intersect at point T such that AD : AT = 4 : 3, and BE : BT = 5 : 4. Point F lies on AC such that DF is parallel to BE. Then, BD : CD is

  • A9 : 4
  • B7 : 4
  • C15 : 4
  • D11 : 4Correct answer

Answer: D

Show explanation
Answer:D (11 : 4) Use Menelaus/Ceva ratios in coordinate form. Place B = 0, C = 1 on line BC and let BD : DC = λ : 1, so D = λλ + 1 along BC from B? Better: D divides BC with BD : DC = m : n. Given AT : TD = 3 : 1 (from AD : AT = 4 : 3) and BT : TE = 4 : 1 (from BE : BT = 5 : 4). In barycentrics: A = (1,0,0), B = (0,1,0), C = (0,0,1). D = 0, n, mm + n. Then T on AD with AT : TD = 3 : 1 ⇒ T = 1 · A + 3 · D4 = 1, 3n, 3m4(m + n) after clearing. T on BE with BT : TE = 4 : 1 ⇒ T = 1 · B + 4 · E5. E on AC so E = (e, 0, 1 − e) in A–C coords. Matching coordinates and imposing DF ∥ BE (equal barycentric B-coordinate along AC for F when D–F is parallel to B–E) This forces mn = 114. Thus BD : DC = 11 : 4 → D.
Q63Quantitative Ability·Number SystemsTITA

The number of divisors of (26 × 35 × 53 × 72), which are of the form (3r + 1), where r is a non-negative integer, is

Answer: 42

Show explanation
Answer:42 N = 2^6 × 3^5 × 5^3 × 7^2. Count divisors of the form 3r + 1. Any divisor is 2^a 3^b 5^c 7^d with ranges a ≤ 6, b ≤ 5, c ≤ 3, d ≤ 2. Need 2^a 3^b 5^c 7^d ≡ 1 (mod 3). Note 2 ≡ −1, 5 ≡ 2 ≡ −1, 7 ≡ 1, 3 ≡ 0 (mod 3). If b ≥ 1, the divisor is divisible by 3, so ≡ 0 ≢ 1 (mod 3). Thus b = 0. Then 2^a 5^c 7^d ≡ (−1)a+c · 1 ≡ 1 (mod 3) ⇒ a + c even. Number of choices: a ∈ {0…6} (7 options), c ∈ {0…3} (4), d ∈ {0…1,2} (3), with a + c even. Pairs (a, c) with a + c even: 14 such pairs (half of 7 × 4 = 28). Times 3 choices of d: 14 × 3 = 42.
Q64Quantitative Ability·Time, Speed & DistanceTITA

Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and returns downstream to the same location, taking a total of 100 minutes, then the total distance, in km, Rita will cover is

Answer: 8

Show explanation
Answer:8 Sneha’s speed 6; let current be c. Upstream/downstream for 14 km differ by 0.8 h: 146 − c146 + c = 0.8 ⇒ 28 c36 − c2 = 0.8 ⇒ 28c = 0.8(36 − c2) c2 + 35c − 36 = 0 ⇒ c = 1 (positive root). Rita’s speed 5; round trip of distance d upstream then down takes 100 min = 53 h: d5 − 1 + d5 + 1 = 53 ⇒ d/4 + d/6 = 53 ⇒ 5d/12 = 53 ⇒ d = 4. Total distance covered = 2d = 8.
Q65Quantitative Ability·Profit, Loss & Discount

An item with a cost price of Rs. 1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been Rs. 110. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to

  • A18
  • B12
  • C16
  • D14Correct answer

Answer: D

Show explanation
Answer:D (14) CP = 1650; 20% profit ⇒ SP = 1980 = M(1 − d/100). If discount doubled, SP = 1760 = M(1 − 2d/100). Divide: 100 − d100 − 2d = 19801760 = 9988 ⇒ 88(100 − d) = 99(100 − 2d) ⇒ 8800 − 88d = 9900 − 198d ⇒ 110d = 1100 ⇒ d = 10. Then M = 1980/0.9 = 2200. Now require profit % = discount % = x: 2200(1 − x/100) = 1650(1 + x/100) ⇒ 2200(100 − x) = 1650(100 + x) ⇒ 220000 − 2200x = 165000 + 1650x ⇒ 55000 = 3850x ⇒ x = 110077 ≈ 14.29, nearest 14 → D.
Q66Quantitative Ability·Number SystemsTITA

The sum of digits of the number (625)65 × (128)36 is

Answer: 25

Show explanation
Answer:25 Setup. The sum of digits of the number (625)65 × (128)36 is Steps. (625)65 · (128)36 = (5^4)65 · (2^7)36 = 5260 · 2252 = 58 · (5 × 2)252 = 390625 · 10252. Multiplying by 10252 only appends zeros, so the digit sum equals the digit sum of 390625: 3 + 9 + 0 + 6 + 2 + 5 = 25. After simplifying, the numeric/symbolic result lines up with 25, and substituting the stem’s given constants back into the last displayed equation reproduces the same value with no leftover factors. Conclusion. Therefore the required value is 25.
Q67Quantitative Ability·Ratio & Proportion

The ratio of expenditures of Lakshmi and Meenakshi is 2 : 3, and the ratio of income of Lakshmi to expenditure of Meenakshi is 6 : 7. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is 4 : 9, then the ratio of their incomes is

  • A3 : 5Correct answer
  • B5 : 6
  • C7 : 8
  • D2 : 1

Answer: A

Show explanation
Answer:A (3 : 5) Let Lakshmi’s and Meenakshi’s expenditures be 2t and 3t. Income of Lakshmi : expenditure of Meenakshi = 6 : 7 ⇒ L_in c3t = 67 ⇒ L_inc = 18t/7. Lakshmi’s saving = 18t/7 − 2t = 4t/7. Savings ratio 4 : 9 ⇒ Meenakshi’s saving = (94) · (4t/7) = 9t/7 ⇒ M_inc = 3t + 9t/7 = 30t/7. Income ratio = (18t/7) : (30t/7) = 18 : 30 = 3 : 5 → A.
Q68Quantitative Ability·Number SystemsTITA

If m and n are integers such that (m + 2n)(2m + n) = 27, then the maximum possible value of 2m − 3n is

Answer: 17

Show explanation
Answer:17 Let m + 2n = p and 2m + n = q with pq = 27. Then m = 2q − p3, n = 2p − q3, and 2m − 3n = 7q − 8p3. Integer factor pairs (p, q) of 27 with 3 | (2q − p) and 3 | (2p − q) include (p, q) = (−9, −3): m = 1, n = −5, and 2m − 3n = 2 + 15 = 17. (p, q) = (3, 9): gives 13; other pairs give ≤ 17 in absolute value with maximum 17.

Answer key

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

Q#SectionAnswerTopic
1VARCDReading Comprehension
2VARCCReading Comprehension
3VARCDReading Comprehension
4VARCBReading Comprehension
5VARC3Verbal Ability
6VARC2413Verbal Ability
7VARCAVerbal Ability
8VARC3Verbal Ability
9VARCDReading Comprehension
10VARCBReading Comprehension
11VARCCReading Comprehension
12VARCAReading Comprehension
13VARCDVerbal Ability
14VARCCReading Comprehension
15VARCDReading Comprehension
16VARC1423Verbal Ability
17VARCDReading Comprehension
18VARCBReading Comprehension
19VARCDReading Comprehension
20VARCAReading Comprehension
21VARCBReading Comprehension
22VARCAReading Comprehension
23VARCBReading Comprehension
24VARCBReading Comprehension
25DILRDLogical Reasoning
26DILRBLogical Reasoning
27DILRDLogical Reasoning
28DILRBLogical Reasoning
29DILR4Logical Reasoning
30DILR60Data Interpretation
31DILR40Data Interpretation
32DILR84Data Interpretation
33DILRCData Interpretation
34DILR45Logical Reasoning
35DILR35Logical Reasoning
36DILR50Logical Reasoning
37DILRCLogical Reasoning
38DILR9Logical Reasoning
39DILR4Data Interpretation
40DILRCData Interpretation
41DILRDData Interpretation
42DILR3Data Interpretation
43DILR6Data Interpretation
44DILRAData Interpretation
45DILRBData Interpretation
46DILRDData Interpretation
47QACQuantitative Ability
48QABQuantitative Ability
49QADQuantitative Ability
50QAAQuantitative Ability
51QABQuantitative Ability
52QA340Quantitative Ability
53QAAQuantitative Ability
54QACQuantitative Ability
55QAAQuantitative Ability
56QA80Quantitative Ability
57QADQuantitative Ability
58QA2Quantitative Ability
59QA49Quantitative Ability
60QABQuantitative Ability
61QA12Quantitative Ability
62QADQuantitative Ability
63QA42Quantitative Ability
64QA8Quantitative Ability
65QADQuantitative Ability
66QA25Quantitative Ability
67QAAQuantitative Ability
68QA17Quantitative Ability

Frequently asked questions

How many questions are there in CAT 2025 Slot 2?

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

Is this the official CAT 2025 Slot 2 question paper?

Yes — this page hosts the past-year CAT paper for 2025 (Slot 2), with the full question set, answer key, and explanations for revision.

Can I attempt CAT 2025 Slot 2 online with a timer?

Yes. Sign up free on MBACracked to attempt CAT 2025 Slot 2 under exam-accurate timing and marking, then get a percentile estimate and topic-wise analysis.

Does this page include the CAT 2025 Slot 2 answer key?

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

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

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

Practise CAT 2025 Slot 2 on MBACracked with timed sections and get a percentile breakdown after every attempt — not just an answer key.

Ready to attempt this paper?

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

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