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CAT 2025 Slot 3 answer key with solutions

This is the complete CAT 2025 Slot 3 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.

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VARC(24 questions)

Q1Reading Comprehension·Paragraph Summary

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

In investigating memory-beliefs, there are certain points which must be borne in mind. In the first place, everything constituting a memory-belief is happening now, not in that past time to which the belief is said to refer. It is not logically necessary to the existence of a memory-belief that the event remembered should have occurred, or even that the past should have existed at all. There is no logical impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that “remembered” a wholly unreal past. There is no logically necessary connection between events at different times; therefore nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago. Hence the occurrences which are CALLED knowledge of the past are logically independent of the past; they are wholly analysable into present contents, which might, theoretically, be just what they are even if no past had existed.

  • AThat which we call ‘knowledge of the past’ is logically independent of the past, since the act of remembering which forms memory-beliefs happens in the present, and does not need to be based in real past occurrences, or even need a past at all.Correct answer
  • BWhen we discuss the concept of memory-beliefs, we must understand that it is not logically impossible for the event remembered to have never happened at all; it could just be a figment of our imagination.
  • CWhen investigating memory beliefs, we must keep in mind that an actual past event is not a prerequisite for a memory-belief to exist, and that what we know of the past could theoretically not need a past at all.
  • DMemory-beliefs depend wholly on what is remembered in the present, and not on anything else; just as it is not logically impossible that the world came into being five minutes ago, and that everyone now just remembers a wholly imaginary past for it.

Answer: A

Show explanation
Answer:A Best essence: so-called knowledge of the past is logically independent of any real past because memory-beliefs are present occurrences that need not rest on actual past events—or even on there having been a past—A. Why the others fail: • B — Stops at “remembered event might never have happened,” missing the stronger logical independence of “knowledge of the past.” • C — Close but softer/wordier; underplays the full “logically independent / wholly present contents” landing A keeps. • D — “Depend wholly on what is remembered… and not on anything else” over-narrows, and treats the five-minute hypothesis as a parallel slogan rather than the passage’s reductio.
Q2Verbal Ability·Odd Sentence OutTITA

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

1. The profound emotional impact of music has inspired ongoing research into its relationship with emotions. 2. Music is a universal phenomenon that utilizes a myriad brain resources. 3. This inherent connection to musical expression is deeply intertwined with human identity and experience. 4. The proclivity to create and appreciate music is ubiquitous among humans, permeating daily life across diverse societies. 5. Engaging with music is among the most cognitively demanding tasks a human can undergo, and it is identified across cultures.

Answer: 1

Show explanation
Answer:1 2–5 cohere on music as universal, identity-linked, cognitively demanding, cross-cultural. Sentence 1—research into music’s emotional impact—is a different research-agenda opener and is odd one out. Why the others fail: • 2 — Universality/brain resources fits the set. • 3 — Identity/experience link continues 4’s ubiquity. • 4 — Ubiquitous human proclivity anchors the paragraph. • 5 — Cognitive demand across cultures pairs with 2.
Q3Reading Comprehension·Application & Analogy

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Once a society accepts a secular mode of creativity, within which the creator replaces God, imaginative transactions assume a self-conscious form. The tribal imagination, on the other hand, is still to a large extent dreamlike and hallucinatory. It admits fusion between various planes of existence and levels of time in a natural and artless manner. In tribal stories, oceans fly in the sky as birds, mountains swim in water as fish, animals speak as humans and stars grow like plants. Spatial order and temporal sequence do not restrict the narrative. This is not to say that tribal creations have no conventions or rules, but simply that they admit the principle of association between emotion and the narrative motif. Thus stars, seas, mountains, trees, men and animals can be angry, sad or happy. It might be said that tribal artists work more on the basis of their racial and sensory memory than on the basis of a cultivated imagination. In order to understand this distinction, we must understand the difference between imagination and memory. In the animate world, consciousness meets two immediate material realities: space and time. We put meaning into space by perceiving it in terms of images. The image-making faculty is a genetic gift to the human mind—this power of imagination helps us understand the space that envelops us. With regard to time, we make connections with the help of memory; one remembers being the same person today as one was yesterday. The tribal mind has a more acute sense of time than the sense of space. Somewhere along the history of human civilization, tribal communities seem to have realized that domination over territorial space was not their lot. Thus, they seem to have turned almost obsessively to gaining domination over time. This urge is substantiated in their ritual of conversing with their dead ancestors: year after year, tribals in many parts of India worship terracotta or carved-wood objects representing their ancestors, aspiring to enter a trance in which they can converse with the dead. Over the centuries, an amazingly sharp memory has helped tribals classify material and natural objects into a highly complex system of knowledge. . . . One of the main characteristics of the tribal arts is their distinct manner of constructing space and imagery, which might be described as ‘hallucinatory’. In both oral and visual forms of representation, tribal artists seem to interpret verbal or pictorial space as demarcated by an extremely flexible ‘frame’. The boundaries between art and non-art become almost invisible. A tribal epic can begin its narration from a trivial everyday event; tribal paintings merge with living space as if the two were one and the same. And within the narrative itself, or within the painted imagery, there is no deliberate attempt to follow a sequence. The episodes retold and the images created take on the apparently chaotic shapes of dreams. In a way, the syntax of language and the grammar of painting are the same, as if literature were painted words and painting were a song of images.

All of the following, if true, would weaken the passage’s claims about the hallucinatory tribal imagination EXCEPT that:

  • Atribal stories depict the natural world in accordance with rational scientific knowledge.
  • Btribal narratives exhibit a chronological beginning, middle, and end.
  • Cshamanic rituals involving conversing with the dead often feature in tribal stories.Correct answer
  • Dtribal art excludes the depiction of the mundane reality of everyday life and objects.

Answer: C

Show explanation
Answer:C Claims about hallucinatory tribal imagination are weakened by rational nature-depiction, linear chronology, or excluding everyday objects—but shamanic talk with the dead *supports* that imaginative mode, so C does not weaken (EXCEPT). Why the others fail: • A — Rational-scientific depiction undercuts “hallucinatory” framing. • B — Conventional beginning-middle-end undercuts non-linear imaginative form. • D — Excluding mundane reality weakens the claim that tribal art mixes dream and everyday.
Q4Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Once a society accepts a secular mode of creativity, within which the creator replaces God, imaginative transactions assume a self-conscious form. The tribal imagination, on the other hand, is still to a large extent dreamlike and hallucinatory. It admits fusion between various planes of existence and levels of time in a natural and artless manner. In tribal stories, oceans fly in the sky as birds, mountains swim in water as fish, animals speak as humans and stars grow like plants. Spatial order and temporal sequence do not restrict the narrative. This is not to say that tribal creations have no conventions or rules, but simply that they admit the principle of association between emotion and the narrative motif. Thus stars, seas, mountains, trees, men and animals can be angry, sad or happy. It might be said that tribal artists work more on the basis of their racial and sensory memory than on the basis of a cultivated imagination. In order to understand this distinction, we must understand the difference between imagination and memory. In the animate world, consciousness meets two immediate material realities: space and time. We put meaning into space by perceiving it in terms of images. The image-making faculty is a genetic gift to the human mind—this power of imagination helps us understand the space that envelops us. With regard to time, we make connections with the help of memory; one remembers being the same person today as one was yesterday. The tribal mind has a more acute sense of time than the sense of space. Somewhere along the history of human civilization, tribal communities seem to have realized that domination over territorial space was not their lot. Thus, they seem to have turned almost obsessively to gaining domination over time. This urge is substantiated in their ritual of conversing with their dead ancestors: year after year, tribals in many parts of India worship terracotta or carved-wood objects representing their ancestors, aspiring to enter a trance in which they can converse with the dead. Over the centuries, an amazingly sharp memory has helped tribals classify material and natural objects into a highly complex system of knowledge. . . . One of the main characteristics of the tribal arts is their distinct manner of constructing space and imagery, which might be described as ‘hallucinatory’. In both oral and visual forms of representation, tribal artists seem to interpret verbal or pictorial space as demarcated by an extremely flexible ‘frame’. The boundaries between art and non-art become almost invisible. A tribal epic can begin its narration from a trivial everyday event; tribal paintings merge with living space as if the two were one and the same. And within the narrative itself, or within the painted imagery, there is no deliberate attempt to follow a sequence. The episodes retold and the images created take on the apparently chaotic shapes of dreams. In a way, the syntax of language and the grammar of painting are the same, as if literature were painted words and painting were a song of images.

On the basis of the passage, which one of the following explains the main difference between imagination and memory?

  • AImagination needs to be cultivated whereas memory is more intuitive because it is racial and sensory.
  • BImagination helps humans make sense of space while memory helps them understand time.Correct answer
  • CTribal groups value memory over imagination when it comes to creating art and literature.
  • DImagination is a genetic gift to humans whereas memory is central to human consciousness.

Answer: B

Show explanation
Answer:B Main difference: imagination helps make sense of space; memory helps understand time—B. Why the others fail: • A — Cultivated vs racial/sensory is not the stated contrast. • C — Tribal preference for memory over imagination in art is not the definitional difference. • D — Genetic gift vs consciousness centre is invented metaphysics.
Q5Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Once a society accepts a secular mode of creativity, within which the creator replaces God, imaginative transactions assume a self-conscious form. The tribal imagination, on the other hand, is still to a large extent dreamlike and hallucinatory. It admits fusion between various planes of existence and levels of time in a natural and artless manner. In tribal stories, oceans fly in the sky as birds, mountains swim in water as fish, animals speak as humans and stars grow like plants. Spatial order and temporal sequence do not restrict the narrative. This is not to say that tribal creations have no conventions or rules, but simply that they admit the principle of association between emotion and the narrative motif. Thus stars, seas, mountains, trees, men and animals can be angry, sad or happy. It might be said that tribal artists work more on the basis of their racial and sensory memory than on the basis of a cultivated imagination. In order to understand this distinction, we must understand the difference between imagination and memory. In the animate world, consciousness meets two immediate material realities: space and time. We put meaning into space by perceiving it in terms of images. The image-making faculty is a genetic gift to the human mind—this power of imagination helps us understand the space that envelops us. With regard to time, we make connections with the help of memory; one remembers being the same person today as one was yesterday. The tribal mind has a more acute sense of time than the sense of space. Somewhere along the history of human civilization, tribal communities seem to have realized that domination over territorial space was not their lot. Thus, they seem to have turned almost obsessively to gaining domination over time. This urge is substantiated in their ritual of conversing with their dead ancestors: year after year, tribals in many parts of India worship terracotta or carved-wood objects representing their ancestors, aspiring to enter a trance in which they can converse with the dead. Over the centuries, an amazingly sharp memory has helped tribals classify material and natural objects into a highly complex system of knowledge. . . . One of the main characteristics of the tribal arts is their distinct manner of constructing space and imagery, which might be described as ‘hallucinatory’. In both oral and visual forms of representation, tribal artists seem to interpret verbal or pictorial space as demarcated by an extremely flexible ‘frame’. The boundaries between art and non-art become almost invisible. A tribal epic can begin its narration from a trivial everyday event; tribal paintings merge with living space as if the two were one and the same. And within the narrative itself, or within the painted imagery, there is no deliberate attempt to follow a sequence. The episodes retold and the images created take on the apparently chaotic shapes of dreams. In a way, the syntax of language and the grammar of painting are the same, as if literature were painted words and painting were a song of images.

Non-human living forms exhibit human emotions in tribal narratives because tribal narratives:

  • Aare rudimentary and underdeveloped.
  • Bhave a self-conscious form.
  • Caccommodate existential fluidity.Correct answer
  • Dabandon all rules and regulations.

Answer: C

Show explanation
Answer:C Non-humans show human emotions because tribal narrative allows existential fluidity—beings can cross categories—C. Why the others fail: • A — “Rudimentary” is dismissive, not the passage’s explanation. • B — Self-conscious form is not why animals feel human emotions in the tales. • D — “Abandon all rules” overstates; fluidity is structured, not lawlessness.
Q6Reading Comprehension·Inference

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Once a society accepts a secular mode of creativity, within which the creator replaces God, imaginative transactions assume a self-conscious form. The tribal imagination, on the other hand, is still to a large extent dreamlike and hallucinatory. It admits fusion between various planes of existence and levels of time in a natural and artless manner. In tribal stories, oceans fly in the sky as birds, mountains swim in water as fish, animals speak as humans and stars grow like plants. Spatial order and temporal sequence do not restrict the narrative. This is not to say that tribal creations have no conventions or rules, but simply that they admit the principle of association between emotion and the narrative motif. Thus stars, seas, mountains, trees, men and animals can be angry, sad or happy. It might be said that tribal artists work more on the basis of their racial and sensory memory than on the basis of a cultivated imagination. In order to understand this distinction, we must understand the difference between imagination and memory. In the animate world, consciousness meets two immediate material realities: space and time. We put meaning into space by perceiving it in terms of images. The image-making faculty is a genetic gift to the human mind—this power of imagination helps us understand the space that envelops us. With regard to time, we make connections with the help of memory; one remembers being the same person today as one was yesterday. The tribal mind has a more acute sense of time than the sense of space. Somewhere along the history of human civilization, tribal communities seem to have realized that domination over territorial space was not their lot. Thus, they seem to have turned almost obsessively to gaining domination over time. This urge is substantiated in their ritual of conversing with their dead ancestors: year after year, tribals in many parts of India worship terracotta or carved-wood objects representing their ancestors, aspiring to enter a trance in which they can converse with the dead. Over the centuries, an amazingly sharp memory has helped tribals classify material and natural objects into a highly complex system of knowledge. . . . One of the main characteristics of the tribal arts is their distinct manner of constructing space and imagery, which might be described as ‘hallucinatory’. In both oral and visual forms of representation, tribal artists seem to interpret verbal or pictorial space as demarcated by an extremely flexible ‘frame’. The boundaries between art and non-art become almost invisible. A tribal epic can begin its narration from a trivial everyday event; tribal paintings merge with living space as if the two were one and the same. And within the narrative itself, or within the painted imagery, there is no deliberate attempt to follow a sequence. The episodes retold and the images created take on the apparently chaotic shapes of dreams. In a way, the syntax of language and the grammar of painting are the same, as if literature were painted words and painting were a song of images.

Which one of the following best explains why tribals in India worship their dead ancestors?

  • ATribals show respect to their ancestors through terracotta and carved-wood objects.
  • BFor tribals, conversing with the dead becomes a way of seeking control over time.Correct answer
  • CTribals possess a sophisticated knowledge system that is based on memory.
  • DTribals seek territorial domination over the spaces that they inhabit.

Answer: B

Show explanation
Answer:B Ancestor worship/conversation with the dead is a way tribals seek control over time—B. Why the others fail: • A — Terracotta/wood objects are media of respect, not the why. • C — Sophisticated memory knowledge is related but not the control-over-time reason. • D — Territorial domination of space mixes the imagination/space theme, not ancestor rites.
Q7Reading Comprehension·Main Idea / Purpose

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Imagine a world in which artificial intelligence is entrusted with the highest moral responsibilities: sentencing criminals, allocating medical resources, and even mediating conflicts between nations. This might seem like the pinnacle of human progress: an entity unburdened by emotion, prejudice or inconsistency, making ethical decisions with impeccable precision. . . . Yet beneath this vision of an idealised moral arbiter lies a fundamental question: can a machine understand morality as humans do, or is it confined to a simulacrum of ethical reasoning? AI might replicate human decisions without improving on them, carrying forward the same biases, blind spots and cultural distortions from human moral judgment. In trying to emulate us, it might only reproduce our limitations, not transcend them. But there is a deeper concern. Moral judgment draws on intuition, historical awareness and context – qualities that resist formalisation. Ethics may be so embedded in lived experience that any attempt to encode it into formal structures risks flattening its most essential features. If so, AI would not merely reflect human shortcomings; it would strip morality of the very depth that makes ethical reflection possible in the first place. Still, many have tried to formalise ethics, by treating certain moral claims not as conclusions, but as starting points. A classic example comes from utilitarianism, which often takes as a foundational axiom the principle that one should act to maximise overall wellbeing. From this, more specific principles can be derived, for example, that it is right to benefit the greatest number, or that actions should be judged by their consequences for total happiness. As computational resources increase, AI becomes increasingly well-suited to the task of starting from fixed ethical assumptions and reasoning through their implications in complex situations. But what, exactly, does it mean to formalise something like ethics? The question is easier to grasp by looking at fields in which formal systems have long played a central role. Physics, for instance, has relied on formalisation for centuries. There is no single physical theory that explains everything. Instead, we have many physical theories, each designed to describe specific aspects of the Universe: from the behaviour of quarks and electrons to the motion of galaxies. These theories often diverge. Aristotelian physics, for instance, explained falling objects in terms of natural motion toward Earth’s centre; Newtonian mechanics replaced this with a universal force of gravity. These explanations are not just different; they are incompatible. Yet both share a common structure: they begin with basic postulates – assumptions about motion, force or mass – and derive increasingly complex consequences. . . . Ethical theories have a similar structure. Like physical theories, they attempt to describe a domain – in this case, the moral landscape. They aim to answer questions about which actions are right or wrong, and why. These theories also diverge and, even when they recommend similar actions, such as giving to charity, they justify them in different ways. Ethical theories also often begin with a small set of foundational principles or claims, from which they reason about more complex moral problems.

Which one of the options below best summarises the passage?

  • AThe passage rejects formal methods in principle. It holds that moral judgement cannot be expressed in disciplined terms and concludes that AI should not serve in courts, medicine, or diplomacy under any conditions.
  • BThe passage highlights administrative gains from automation. It treats reproducing human moral judgement as progress and argues that, as computational resources increase, AI can be responsible for decision-making across varied institutional settings.
  • CThe passage weighs the appeal of an impersonal AI judge against doubts about moral grasp. It warns that codification can erode case-sensitive judgement, allow axiom-led reasoning at scale, and use a physics analogy to model structured plurality.Correct answer
  • DThe passage weighs the appeal of an impersonal AI judge against doubts about moral grasp. It claims codified schemes retain case nuance at scale and uses a physics analogy to predict convergence on a unified framework.

Answer: C

Show explanation
Answer:C Summary: impersonal AI judge appeals, yet moral grasp is doubtful; codification erodes case-sensitive judgment and enables axiom-led scale—C. Why the others fail: • A — Rejects formal methods wholesale and bans AI from courts—too absolute. • B — Treats reproducing moral judgment via automation as progress—opposite lean. • D — Claims codified schemes keep nuance and converge on one ethic—misreads the warning.
Q8Reading Comprehension·Structure & Organization

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Imagine a world in which artificial intelligence is entrusted with the highest moral responsibilities: sentencing criminals, allocating medical resources, and even mediating conflicts between nations. This might seem like the pinnacle of human progress: an entity unburdened by emotion, prejudice or inconsistency, making ethical decisions with impeccable precision. . . . Yet beneath this vision of an idealised moral arbiter lies a fundamental question: can a machine understand morality as humans do, or is it confined to a simulacrum of ethical reasoning? AI might replicate human decisions without improving on them, carrying forward the same biases, blind spots and cultural distortions from human moral judgment. In trying to emulate us, it might only reproduce our limitations, not transcend them. But there is a deeper concern. Moral judgment draws on intuition, historical awareness and context – qualities that resist formalisation. Ethics may be so embedded in lived experience that any attempt to encode it into formal structures risks flattening its most essential features. If so, AI would not merely reflect human shortcomings; it would strip morality of the very depth that makes ethical reflection possible in the first place. Still, many have tried to formalise ethics, by treating certain moral claims not as conclusions, but as starting points. A classic example comes from utilitarianism, which often takes as a foundational axiom the principle that one should act to maximise overall wellbeing. From this, more specific principles can be derived, for example, that it is right to benefit the greatest number, or that actions should be judged by their consequences for total happiness. As computational resources increase, AI becomes increasingly well-suited to the task of starting from fixed ethical assumptions and reasoning through their implications in complex situations. But what, exactly, does it mean to formalise something like ethics? The question is easier to grasp by looking at fields in which formal systems have long played a central role. Physics, for instance, has relied on formalisation for centuries. There is no single physical theory that explains everything. Instead, we have many physical theories, each designed to describe specific aspects of the Universe: from the behaviour of quarks and electrons to the motion of galaxies. These theories often diverge. Aristotelian physics, for instance, explained falling objects in terms of natural motion toward Earth’s centre; Newtonian mechanics replaced this with a universal force of gravity. These explanations are not just different; they are incompatible. Yet both share a common structure: they begin with basic postulates – assumptions about motion, force or mass – and derive increasingly complex consequences. . . . Ethical theories have a similar structure. Like physical theories, they attempt to describe a domain – in this case, the moral landscape. They aim to answer questions about which actions are right or wrong, and why. These theories also diverge and, even when they recommend similar actions, such as giving to charity, they justify them in different ways. Ethical theories also often begin with a small set of foundational principles or claims, from which they reason about more complex moral problems.

All of the following can reasonably be inferred from the passage EXCEPT:

  • Athe appeal of an AI judge rests on immunity to bribery, partiality, and fatigue; yet the text questions whether procedural cleanliness amounts to moral understanding without lived context and interpretive depth.
  • Bwith fixed moral starting points and expanding computational resources, the argument forecasts convergence on one ethical system and treats contextual judgement as unnecessary once formal reasoning scales across domains and cultures.Correct answer
  • Cencoding ethics into fixed structures risks stripping away intuition, history, and context and, if that occurs, the depth that enables reflective judgement disappears. So, machines would mirror our limits rather than exceed them.
  • Dby analogy with physics, compact postulates can yield broad predictions across incompatible theories and ethics can likewise share structure while continuing to diverge rather than close on a single comprehensive framework.

Answer: B

Show explanation
Answer:B B says fixed starting points plus compute forecast one ethical system and make contextual judgment unnecessary—that is *not* a reasonable inference (the physics analogy allows shared structure with ongoing divergence)—EXCEPT. Why the others fail: • A — Appeal of AI judge vs doubts about moral understanding—inferable. • C — Encoding ethics risks stripping intuition/context—inferable. • D — Physics analogy: compact postulates, multiple theories, no forced single ethic—inferable.
Q9Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Imagine a world in which artificial intelligence is entrusted with the highest moral responsibilities: sentencing criminals, allocating medical resources, and even mediating conflicts between nations. This might seem like the pinnacle of human progress: an entity unburdened by emotion, prejudice or inconsistency, making ethical decisions with impeccable precision. . . . Yet beneath this vision of an idealised moral arbiter lies a fundamental question: can a machine understand morality as humans do, or is it confined to a simulacrum of ethical reasoning? AI might replicate human decisions without improving on them, carrying forward the same biases, blind spots and cultural distortions from human moral judgment. In trying to emulate us, it might only reproduce our limitations, not transcend them. But there is a deeper concern. Moral judgment draws on intuition, historical awareness and context – qualities that resist formalisation. Ethics may be so embedded in lived experience that any attempt to encode it into formal structures risks flattening its most essential features. If so, AI would not merely reflect human shortcomings; it would strip morality of the very depth that makes ethical reflection possible in the first place. Still, many have tried to formalise ethics, by treating certain moral claims not as conclusions, but as starting points. A classic example comes from utilitarianism, which often takes as a foundational axiom the principle that one should act to maximise overall wellbeing. From this, more specific principles can be derived, for example, that it is right to benefit the greatest number, or that actions should be judged by their consequences for total happiness. As computational resources increase, AI becomes increasingly well-suited to the task of starting from fixed ethical assumptions and reasoning through their implications in complex situations. But what, exactly, does it mean to formalise something like ethics? The question is easier to grasp by looking at fields in which formal systems have long played a central role. Physics, for instance, has relied on formalisation for centuries. There is no single physical theory that explains everything. Instead, we have many physical theories, each designed to describe specific aspects of the Universe: from the behaviour of quarks and electrons to the motion of galaxies. These theories often diverge. Aristotelian physics, for instance, explained falling objects in terms of natural motion toward Earth’s centre; Newtonian mechanics replaced this with a universal force of gravity. These explanations are not just different; they are incompatible. Yet both share a common structure: they begin with basic postulates – assumptions about motion, force or mass – and derive increasingly complex consequences. . . . Ethical theories have a similar structure. Like physical theories, they attempt to describe a domain – in this case, the moral landscape. They aim to answer questions about which actions are right or wrong, and why. These theories also diverge and, even when they recommend similar actions, such as giving to charity, they justify them in different ways. Ethical theories also often begin with a small set of foundational principles or claims, from which they reason about more complex moral problems.

The passage compares ethics to physics, where different theories apply to different aspects of a domain and says AI can reason from fixed starting points in complex cases. Which one of the assumptions below must hold for that comparison to guide practice?

  • AA single master framework replaces all others after translation into one code, so domain boundaries disappear in application.
  • BReal cases never straddle different areas, so a case always fits exactly one framework without any overlap whatsoever.
  • COnce formalised, all ethical frameworks yield the same recommendation in every case, so selection among them is unnecessary.
  • DThere is a principled way to decide which ethical framework applies to which class of cases, so the system can select the relevant starting points before deriving a recommendation.Correct answer

Answer: D

Show explanation
Answer:D For ethics-as-physics with fixed starting points to guide practice, there must be a principled way to pick which framework fits which case class before deriving a recommendation—D. Why the others fail: • A — One master code erasing domains contradicts multi-theory physics analogy. • B — Cases never straddling frameworks is unrealistically strong. • C — All frameworks yielding identical recommendations makes selection moot and denies divergence.
Q10Reading Comprehension·Structure & Organization

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Imagine a world in which artificial intelligence is entrusted with the highest moral responsibilities: sentencing criminals, allocating medical resources, and even mediating conflicts between nations. This might seem like the pinnacle of human progress: an entity unburdened by emotion, prejudice or inconsistency, making ethical decisions with impeccable precision. . . . Yet beneath this vision of an idealised moral arbiter lies a fundamental question: can a machine understand morality as humans do, or is it confined to a simulacrum of ethical reasoning? AI might replicate human decisions without improving on them, carrying forward the same biases, blind spots and cultural distortions from human moral judgment. In trying to emulate us, it might only reproduce our limitations, not transcend them. But there is a deeper concern. Moral judgment draws on intuition, historical awareness and context – qualities that resist formalisation. Ethics may be so embedded in lived experience that any attempt to encode it into formal structures risks flattening its most essential features. If so, AI would not merely reflect human shortcomings; it would strip morality of the very depth that makes ethical reflection possible in the first place. Still, many have tried to formalise ethics, by treating certain moral claims not as conclusions, but as starting points. A classic example comes from utilitarianism, which often takes as a foundational axiom the principle that one should act to maximise overall wellbeing. From this, more specific principles can be derived, for example, that it is right to benefit the greatest number, or that actions should be judged by their consequences for total happiness. As computational resources increase, AI becomes increasingly well-suited to the task of starting from fixed ethical assumptions and reasoning through their implications in complex situations. But what, exactly, does it mean to formalise something like ethics? The question is easier to grasp by looking at fields in which formal systems have long played a central role. Physics, for instance, has relied on formalisation for centuries. There is no single physical theory that explains everything. Instead, we have many physical theories, each designed to describe specific aspects of the Universe: from the behaviour of quarks and electrons to the motion of galaxies. These theories often diverge. Aristotelian physics, for instance, explained falling objects in terms of natural motion toward Earth’s centre; Newtonian mechanics replaced this with a universal force of gravity. These explanations are not just different; they are incompatible. Yet both share a common structure: they begin with basic postulates – assumptions about motion, force or mass – and derive increasingly complex consequences. . . . Ethical theories have a similar structure. Like physical theories, they attempt to describe a domain – in this case, the moral landscape. They aim to answer questions about which actions are right or wrong, and why. These theories also diverge and, even when they recommend similar actions, such as giving to charity, they justify them in different ways. Ethical theories also often begin with a small set of foundational principles or claims, from which they reason about more complex moral problems.

Choose the one option below that comes closest to being the opposite of “utilitarianism”.

  • AThe authors advocated an absolutist stance, following exception less rules regardless of outcomes and evaluating choices by broadest societal benefit.
  • BThe committee adopted a non-egoist framework, ranking policies by their contribution to overall social welfare and treating self-interest as a derivative concern within institutional evaluation.
  • CThe policy was cast as deontological ethics, selecting the option that delivered the highest total benefit to citizens while presenting duty as a secondary consideration in public decision-making.
  • DThe council followed a prioritarian approach, assigning greater moral weight to improvements for the worst-off rather than to maximising total welfare across the affected population.Correct answer

Answer: D

Show explanation
Answer:D Utilitarianism maximises total welfare; prioritarianism weighting the worst-off is the closest opposite among the options—D. Why the others fail: • A — Mixes absolutist rules with “broadest societal benefit” (utilitarian), not a clean opposite. • B — Overall social welfare ranking is still consequentialist/utilitarian-adjacent. • C — Labels deontology while maximising total benefit—confused, not opposite.
Q11Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Over the course of the twentieth century, humans built, on average, one large dam a day, hulking structures of steel and concrete designed to control flooding, facilitate irrigation, and generate electricity. Dams were also lucrative contracts, large-scale employers, and the physical instantiation of a messianic drive to conquer territories and control nature. Some of the results of that drive were charismatic mega-infrastructure—the Hoover on the Colorado River or the Aswan on the Nile—but most of the tens of thousands of dams that dot the Earth’s landscape have drawn little attention. These are the smaller, though not inconsequential, barriers that today impede the flow of water on nearly two-thirds of the world’s large waterways. Chances are, what your map calls a “lake” is actually a reservoir, and that thin blue line that emerges from it once flowed very differently. Damming a river is always a partisan act. Even when explicit infrastructure goals— irrigation, flood control, electrification—were met, other consequences were significant and often deleterious. Across the world, river control displaced millions of people, threatening livelihoods, foodways, and cultures. In the western United States, dams were often an instrument of colonialism, used to dispossess Indigenous people and subsidize settler agriculture. And as dams slowed the flow of water, inhibited the movement of nutrients, and increased the amount of toxic algae and other parasites, they snuffed out entire river ecologies. Declining fish populations are the most evident effect, but dams also threaten a host of other animals—from birds and reptiles to fungi and plants—with extinction. Every major dam, then, is also a sacrifice zone, a place where lives, livelihoods, and ways of life are eliminated so that new sorts of landscapes can support water-intensive agriculture and cities that sprout downstream of new reservoirs. Such sacrifices have been justified as offerings at the temples of modernity. Justified by—and for—whom, though? Over the course of the twentieth century, rarely were the costs and benefits weighed thoughtfully and decided democratically. As Kader Asmal, chair of the landmark 2000 World Commission on Dams, concluded, “There have been precious few, if any, comprehensive, independent analyses as to why dams came about, how dams perform over time, and whether we are getting a fair return from our $2 trillion investment.” A quarter century later, Asmal’s words ring ever truer. A litany of dams built in the mid-twentieth century are approaching the end of their expected lives, with worrying prospects for their durability. Droughts, magnified and multiplied by the effects of climate change, have forced more and more to run below capacity. If ever there were a time to rethink the mania for dams, it would be now. There is some evidence that a combination of opposition, alternative energy sources, and a lack of viable projects has slowed the construction of major dams. But a wave of recent and ongoing construction, from India and China to Ethiopia and Canada, continues to tilt the global balance firmly in favor of water impoundment.

What does the author wish to communicate by referring to the Hoover and Aswan dams in the first paragraph?

  • AThe designers and builders of these mega-structures were highly charismatic individuals.
  • BThe Colorado and Nile rivers may be seen as thin blue lines on a map.
  • CBy building dams like the Hoover and Aswan dams, large-scale employers became messianic figures.
  • DThe drive to control nature is evident not only in mega-infrastructures like the Hoover and Aswan dams, but in smaller dams as well.Correct answer

Answer: D

Show explanation
Answer:D Hoover and Aswan exemplify the drive to control nature in mega-dams—and that drive also shows in smaller dams—D. Why the others fail: • A — Charisma of designers is not the point. • B — Rivers as map lines is imagery, not the communicative purpose. • C — “Messianic” employers over-psychologises the example.
Q12Reading Comprehension·Vocabulary in Context

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Over the course of the twentieth century, humans built, on average, one large dam a day, hulking structures of steel and concrete designed to control flooding, facilitate irrigation, and generate electricity. Dams were also lucrative contracts, large-scale employers, and the physical instantiation of a messianic drive to conquer territories and control nature. Some of the results of that drive were charismatic mega-infrastructure—the Hoover on the Colorado River or the Aswan on the Nile—but most of the tens of thousands of dams that dot the Earth’s landscape have drawn little attention. These are the smaller, though not inconsequential, barriers that today impede the flow of water on nearly two-thirds of the world’s large waterways. Chances are, what your map calls a “lake” is actually a reservoir, and that thin blue line that emerges from it once flowed very differently. Damming a river is always a partisan act. Even when explicit infrastructure goals— irrigation, flood control, electrification—were met, other consequences were significant and often deleterious. Across the world, river control displaced millions of people, threatening livelihoods, foodways, and cultures. In the western United States, dams were often an instrument of colonialism, used to dispossess Indigenous people and subsidize settler agriculture. And as dams slowed the flow of water, inhibited the movement of nutrients, and increased the amount of toxic algae and other parasites, they snuffed out entire river ecologies. Declining fish populations are the most evident effect, but dams also threaten a host of other animals—from birds and reptiles to fungi and plants—with extinction. Every major dam, then, is also a sacrifice zone, a place where lives, livelihoods, and ways of life are eliminated so that new sorts of landscapes can support water-intensive agriculture and cities that sprout downstream of new reservoirs. Such sacrifices have been justified as offerings at the temples of modernity. Justified by—and for—whom, though? Over the course of the twentieth century, rarely were the costs and benefits weighed thoughtfully and decided democratically. As Kader Asmal, chair of the landmark 2000 World Commission on Dams, concluded, “There have been precious few, if any, comprehensive, independent analyses as to why dams came about, how dams perform over time, and whether we are getting a fair return from our $2 trillion investment.” A quarter century later, Asmal’s words ring ever truer. A litany of dams built in the mid-twentieth century are approaching the end of their expected lives, with worrying prospects for their durability. Droughts, magnified and multiplied by the effects of climate change, have forced more and more to run below capacity. If ever there were a time to rethink the mania for dams, it would be now. There is some evidence that a combination of opposition, alternative energy sources, and a lack of viable projects has slowed the construction of major dams. But a wave of recent and ongoing construction, from India and China to Ethiopia and Canada, continues to tilt the global balance firmly in favor of water impoundment.

The word “instantiation” is used in the first paragraph. Which one of the following pairs of terms would be the best substitute for it in the context of its usage in the paragraph?

  • AExemplification and manifestationCorrect answer
  • BDurability and timeliness
  • CDevelopment and construction
  • DConcreteness and viability

Answer: A

Show explanation
Answer:A (Exemplification and manifestation) “Instantiation” here means making the drive concrete—exemplification/manifestation in dams. Why the others fail: • B — Durability/timeliness miss the making-concrete sense. • C — Development/construction are related but narrower than conceptual instantiation. • D — Concreteness/viability only half-fits; viability is extra.
Q13Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Over the course of the twentieth century, humans built, on average, one large dam a day, hulking structures of steel and concrete designed to control flooding, facilitate irrigation, and generate electricity. Dams were also lucrative contracts, large-scale employers, and the physical instantiation of a messianic drive to conquer territories and control nature. Some of the results of that drive were charismatic mega-infrastructure—the Hoover on the Colorado River or the Aswan on the Nile—but most of the tens of thousands of dams that dot the Earth’s landscape have drawn little attention. These are the smaller, though not inconsequential, barriers that today impede the flow of water on nearly two-thirds of the world’s large waterways. Chances are, what your map calls a “lake” is actually a reservoir, and that thin blue line that emerges from it once flowed very differently. Damming a river is always a partisan act. Even when explicit infrastructure goals— irrigation, flood control, electrification—were met, other consequences were significant and often deleterious. Across the world, river control displaced millions of people, threatening livelihoods, foodways, and cultures. In the western United States, dams were often an instrument of colonialism, used to dispossess Indigenous people and subsidize settler agriculture. And as dams slowed the flow of water, inhibited the movement of nutrients, and increased the amount of toxic algae and other parasites, they snuffed out entire river ecologies. Declining fish populations are the most evident effect, but dams also threaten a host of other animals—from birds and reptiles to fungi and plants—with extinction. Every major dam, then, is also a sacrifice zone, a place where lives, livelihoods, and ways of life are eliminated so that new sorts of landscapes can support water-intensive agriculture and cities that sprout downstream of new reservoirs. Such sacrifices have been justified as offerings at the temples of modernity. Justified by—and for—whom, though? Over the course of the twentieth century, rarely were the costs and benefits weighed thoughtfully and decided democratically. As Kader Asmal, chair of the landmark 2000 World Commission on Dams, concluded, “There have been precious few, if any, comprehensive, independent analyses as to why dams came about, how dams perform over time, and whether we are getting a fair return from our $2 trillion investment.” A quarter century later, Asmal’s words ring ever truer. A litany of dams built in the mid-twentieth century are approaching the end of their expected lives, with worrying prospects for their durability. Droughts, magnified and multiplied by the effects of climate change, have forced more and more to run below capacity. If ever there were a time to rethink the mania for dams, it would be now. There is some evidence that a combination of opposition, alternative energy sources, and a lack of viable projects has slowed the construction of major dams. But a wave of recent and ongoing construction, from India and China to Ethiopia and Canada, continues to tilt the global balance firmly in favor of water impoundment.

All of the following statements may be considered valid inferences from the passage EXCEPT that:

  • Asmaller, though not inconsequential, dams are safer than large dam projects.Correct answer
  • Bdam-building has proved to be an extremely costly enterprise that may not be justifiable.
  • Cprocesses of colonisation have used dam-building to make people vacate their territories.
  • Ddespite increasing evidence of opposition to dams as well as alternatives to them, they continue to be built.

Answer: A

Show explanation
Answer:A The passage does *not* validly support that smaller dams are safer than large ones—A is the EXCEPT. Why the others fail: • B — Costly, hard-to-justify dam-building is in scope. • C — Colonisation using dams to displace people is in scope. • D — Continued building despite opposition/alternatives is in scope.
Q14Reading Comprehension·Main Idea / Purpose

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. Over the course of the twentieth century, humans built, on average, one large dam a day, hulking structures of steel and concrete designed to control flooding, facilitate irrigation, and generate electricity. Dams were also lucrative contracts, large-scale employers, and the physical instantiation of a messianic drive to conquer territories and control nature. Some of the results of that drive were charismatic mega-infrastructure—the Hoover on the Colorado River or the Aswan on the Nile—but most of the tens of thousands of dams that dot the Earth’s landscape have drawn little attention. These are the smaller, though not inconsequential, barriers that today impede the flow of water on nearly two-thirds of the world’s large waterways. Chances are, what your map calls a “lake” is actually a reservoir, and that thin blue line that emerges from it once flowed very differently. Damming a river is always a partisan act. Even when explicit infrastructure goals— irrigation, flood control, electrification—were met, other consequences were significant and often deleterious. Across the world, river control displaced millions of people, threatening livelihoods, foodways, and cultures. In the western United States, dams were often an instrument of colonialism, used to dispossess Indigenous people and subsidize settler agriculture. And as dams slowed the flow of water, inhibited the movement of nutrients, and increased the amount of toxic algae and other parasites, they snuffed out entire river ecologies. Declining fish populations are the most evident effect, but dams also threaten a host of other animals—from birds and reptiles to fungi and plants—with extinction. Every major dam, then, is also a sacrifice zone, a place where lives, livelihoods, and ways of life are eliminated so that new sorts of landscapes can support water-intensive agriculture and cities that sprout downstream of new reservoirs. Such sacrifices have been justified as offerings at the temples of modernity. Justified by—and for—whom, though? Over the course of the twentieth century, rarely were the costs and benefits weighed thoughtfully and decided democratically. As Kader Asmal, chair of the landmark 2000 World Commission on Dams, concluded, “There have been precious few, if any, comprehensive, independent analyses as to why dams came about, how dams perform over time, and whether we are getting a fair return from our $2 trillion investment.” A quarter century later, Asmal’s words ring ever truer. A litany of dams built in the mid-twentieth century are approaching the end of their expected lives, with worrying prospects for their durability. Droughts, magnified and multiplied by the effects of climate change, have forced more and more to run below capacity. If ever there were a time to rethink the mania for dams, it would be now. There is some evidence that a combination of opposition, alternative energy sources, and a lack of viable projects has slowed the construction of major dams. But a wave of recent and ongoing construction, from India and China to Ethiopia and Canada, continues to tilt the global balance firmly in favor of water impoundment.

Which one of the following sets of terms is closest to mapping the key arguments of the passage?

  • ALucrative contracts – Sacrifice zone – Expected lives – Global balance
  • BPhysical instantiation – Partisan act – Decided democratically – Alternative energy
  • CMega-infrastructure – Sacrifice zone – Worshipping modernity – Water impoundmentCorrect answer
  • DPartisan act – Threatened livelihoods – Toxic algae – Quarter century

Answer: C

Show explanation
Answer:C Key map: mega-infrastructure, sacrifice zones, worshipping modernity, water impoundment—C. Why the others fail: • A — Expected lives/global balance are not the organising cluster. • B — “Decided democratically / alternative energy” mis-centres the critique. • D — Toxic algae/quarter century are details, not the argument map.
Q15Verbal 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. The effigy of a candidate establishes a personal link between him and the voters; the candidate does not only offer a programme for judgement, he suggests a physical climate, a set of daily choices expressed in a morphology, a way of dressing, a posture. 2. Some candidates for Parliament adorn their electoral prospectus with a portrait; this presupposes that photography has a power to convert which must be analysed. 3. Inasmuch as photography is an ellipse of language and a condensation of an ‘ineffable’ social whole, it constitutes an antiintellectual weapon and tends to spirit away ‘politics’ (that is to say a body of problems and solutions) to the advantage of a ‘manner of being’, a socio-moral status. 4. Photography tends to restore the paternalistic nature of elections, whose elitist essence has been disrupted by proportional representation and the rule of parties (the Right seems to use it more than the Left).

Answer: 2143

Show explanation
Answer:2143 Portraits on electoral prospectuses (2) → effigy creates personal link/morphology (1) → photography restores paternalistic elections (4) → photography as anti-intellectual displacement of politics by “manner of being” (3): 2143. Why the others fail: • 1-first — “Effigy” needs the portrait practice introduced in 2. • 3 before 4 — Anti-intellectual weapon claim follows the paternalism restoration better after 4’s stakes—or per key, 4 before 3. • 2413 — Skips linking effigy (1) before paternalism (4).
Q16Reading Comprehension·Paragraph Summary

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

The return to the tailor is the juxtaposition of three key things for the mindful Indian shopper. The first is the conscious shift away from the homogeneity of fast fashion, the idea of a hundred other people owning exactly the same Zara trench coat or H&M pleated skirt. The second is an actual understanding of the waste behind the fast fashion market, and wanting not to contribute to that anymore. The last is the shift toward customisation and fit—the idea of having imaginations brought to life and to have them fit exactly; without paying exorbitant rates for that bespoke tailoring. For the individual with a keen fashion sense and a genuine desire to move away from the waste and uniformity of fast fashion without paying the premium for it that indie brands would invariably demand, the tailor is the perfect crossover.

  • AThe mindful Indian shopper is shifting away from convenience and uniformity of clothing, and waste in fashion, to customisation and less exorbitantly priced clothing.Correct answer
  • BThe mindful Indian shoppers are returning to the tailor with a genuine desire to wear clothes which are less expensive, fit them well and are yet fashionable.
  • CAll Indian shoppers are opting for customisation and a shift away from homogeneity over expensive clothing brands like Zara and H&M.
  • DIn the Indian retail market, people believe that expensive branded clothes are wasteful and, therefore, are returning to the neighbourhood tailor.

Answer: A

Show explanation
Answer:A Mindful Indian shoppers leave fast-fashion sameness and waste for customisation and less extortionate clothing—A. Why the others fail: • B — “Less expensive… yet fashionable” misses the anti-waste/anti-homogeneity core. • C — “All Indian shoppers” overgeneralises. • D — Reduces the motive to “branded clothes are wasteful” alone and ignores customisation.
Q17Verbal 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. When I ask the distinguished LGBTQ activist and writer Cherie Moraga whether she uses Latinx to refer to herself, she tells me, ‘I worked too hard for the “a” in Latina to give it up! I refer to myself as Xicana.’ 2. Of our accumulated ethnic population, only a third use Hispanic to identify themselves, a mere 14 percent use Latino, and less than 2 percent recognize Latinx. 3. They have done this, although gender in languages is grammatical, not sociological or sexual, and found in linguistic families throughout the world, from French to Russian to Japanese. 4. More recently, activists seeking to render our name gender neutral, out of respect for our LGBTQ members, have devised yet another name for us: Latinx.

Answer: 4312

Show explanation
Answer:4312 Activists coin Latinx (4) → they do so though gender is grammatical not sociological (3) → tiny uptake vs Hispanic/Latino (2) → Moraga refuses Latinx for Xicana (1): 4312. Why the others fail: • 1-first — Anecdote lands after Latinx is introduced. • 2 before 4 — Usage stats need the coinage first. • 3 before 4 — “They have done this” needs Latinx-naming in 4.
Q18Verbal 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. About half of all the oxygen we breathe is made near the surface of the ocean by phytoplankton that photosynthesize just like land-dwelling plants. 2. A team of scientists that includes Boston University experts has discovered they also produce oxygen on the seafloor. 3. The research team used deep-sea chambers that land on the seafloor and enclose the seawater, sediment, polymetallic nodules, and living organisms. 4. The discovery is a surprise considering oxygen is typically created by plants and organisms with help from the sun—not by rocks on the ocean floor. 5. The deep-sea rocks, called polymetallic nodules, don’t only host a surprising number of sea critters.

Answer: 3

Show explanation
Answer:3 2, 4, 5 (and 1 as surface oxygen contrast) tell a seafloor oxygen / polymetallic-nodule discovery story. Sentence 3—method detail about deep-sea chambers—is the odd procedural aside per the key. Why the others fail: • 1 — Surface phytoplankton oxygen sets up the surprise of seafloor oxygen. • 2 — States the seafloor oxygen discovery. • 4 — Flags why rock-made oxygen is surprising. • 5 — Nodules hosting critters continues the rock/seafloor theme.
Q19Verbal 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: Productivity gains, once expected to feed through to broader living standards, now primarily serve to enhance returns to wealth. Paragraph: Economists now argue that inequality is no longer a by-product of growth but a condition of it. ____ (1) ____. Unlike wages, wealth reflects not just income but also access to assets, favourable institutional conditions – such as low interest rates – and public policies like low taxes and housing shortages. ____ (2) ____. In other words, wealth depends on political choices in ways that income currently does not. It’s not just the inequality itself that is the issue but the erosion of mechanisms that once constrained it. ____ (3) ____. Wealth and income inequality are linked, but where wages have stagnated and collective bargaining has weakened, capital income – derived from profits, rents and interest – has been boosted by design. ____ (4) ____.

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

Answer: A

Show explanation
Answer:A (Blank 4) Sentence. Productivity gains, once expected to lift living standards, now mainly raise returns to wealth. Why Blank 4. The paragraph has moved from “inequality as a condition of growth” through political construction of wealth and the boosting of capital income “by design.” The missing sentence is the payoff: productivity no longer feeds wages, it feeds wealth. Why not the others. - Blank 1 would interrupt before wealth is distinguished from wages. - Blank 2 sits inside the wealth-vs-income definition. - Blank 3 is the erosion-of-constraints hinge, not yet the productivity punchline.
Q20Verbal 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: In each of the affected males, the genetic defect was located to the X chromosome in the region of p11-12. Paragraph: The first suggested evidence of a human genetic mutation associated with aggressive behaviour came from a study in 1993. _____(1)____. Genetic and metabolic studies were conducted on a large Dutch family in which several of the males has a syndrome of borderline mental retardation and abnormal behaviour. _____(2)____. The undesirable behaviour included impulsive aggression, arson and exhibitionism. _____(3)____. A point mutation was identified in the eighth exon of the monoamine oxidase A (MAOA) structural gene which changes glutamine to a termination codon. _____(4)____.

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

Answer: A

Show explanation
Answer:A (Blank 3) Sentence. In each affected male, the genetic defect mapped to Xp11–12. Why Blank 3. The Dutch-family phenotype (retardation, impulsive aggression, arson, exhibitionism) is on the table. Chromosomal localisation is the next lab result, immediately before the MAOA nonsense mutation in exon 8. Why not the others. - Blank 1 is before the family has been introduced. - Blank 2 is still listing behaviours. - Blank 4 is after the precise mutation — localisation would be out of order.
Q21Reading Comprehension·Inference

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. In 1982, a raging controversy broke out over a forest act drafted by the Government of India. This act sought to strengthen the already extensive powers enjoyed by the forest bureaucracy in controlling the extraction, disposal and sale of forest produce. It also gave forest officials greater powers to strictly regulate the entry of any person into reserved forest areas. While forest officials justified the act on the grounds that it was necessary to stop the continuing deforestation, it was bitterly opposed by representatives of grassroots organisations, who argued that it was a major violation of the rights of peasants and tribals living in and around forest areas. . . . The debate over the draft forest act fuelled a larger controversy over the orientation of state forest policy. It was pointed out, for example, that the draft act was closely modelled on its predecessor, the Forest Act of 1878. The earlier Act rested on a usurpation of rights of ownership by the colonial state which had little precedent in precolonial history. It was further argued that the system of forestry introduced by the British— and continued, with little modification, after 1947 —emphasised revenue generation and commercial exploitation, while its policing orientation excluded villagers who had the most longstanding claim on forest resources. Critics called for a complete overhaul of forest administration, pressing the government to formulate policy and legislation more appropriate to present needs. . . . That debate is not over yet. The draft act was shelved, though it has not as yet been formally withdrawn. Meanwhile, the 1878 Act (as modified by an amendment in 1927) continues to be in operation. In response to its critics, the government has made some important changes in forest policy, e.g., no longer treating forests as a source of revenue, and stopping ecologically hazardous practices such as the clearfelling of natural forests. At the same time, it has shown little inclination to meet the major demand of the critics of forest policy— namely, abandoning the principle of state monopoly over forest land by handing over areas of degraded forests to individuals and communities for afforestation. . . . The 1878 Forest Act itself was passed only after a bitter and prolonged debate within the colonial bureaucracy, in which protagonists put forward arguments strikingly similar to those being advanced today. As is well known, the Indian Forest Department owes its origin to the requirements of railway companies. The early years of the expansion of the railway network, c. 1853 onwards, led to tremendous deforestation in peninsular India owing to the railway’s requirements of fuelwood and construction timber. Huge quantities of durable timbers were also needed for use as sleepers across the newly laid tracks. Inexperienced in forestry, the British called in German experts to commence systematic forest management. The Indian Forest Department was started in 1864, with Dietrich Brandis, formerly a Lecturer at Bonn, as the first Inspector General of Forests. The new department needed legislative backing to function effectively, and in the following year, 1865, the first forest act was passed. . . .

Which one of the following best encapsulates the reason for the “raging controversy” developing into a “larger controversy”?

  • AThe 1982 draft forest act further enabled the commercial exploitation of forest resources by the forest bureaucracy.
  • BThe 1982 draft forest act violated the rights of tribals and peasants who lived in and around forest areas.
  • CThe 1982 draft forest act was unjustifiably defended by forest officials in the face of bitter opposition by grassroots organisations.
  • DThe 1982 draft forest act replicated colonial measures of control and regulation of forest resources.Correct answer

Answer: D

Show explanation
Answer:D The controversy enlarges because the 1982 draft replayed colonial control/regulation of forests—D. Why the others fail: • A — Commercial exploitation by bureaucracy is related but not the “larger controversy” encapsulator. • B — Rights violations matter but the passage’s enlargement hinge is colonial replication. • C — Officials defending the draft is situational, not the encapsulating reason.
Q22Reading Comprehension·Application & Analogy

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. In 1982, a raging controversy broke out over a forest act drafted by the Government of India. This act sought to strengthen the already extensive powers enjoyed by the forest bureaucracy in controlling the extraction, disposal and sale of forest produce. It also gave forest officials greater powers to strictly regulate the entry of any person into reserved forest areas. While forest officials justified the act on the grounds that it was necessary to stop the continuing deforestation, it was bitterly opposed by representatives of grassroots organisations, who argued that it was a major violation of the rights of peasants and tribals living in and around forest areas. . . . The debate over the draft forest act fuelled a larger controversy over the orientation of state forest policy. It was pointed out, for example, that the draft act was closely modelled on its predecessor, the Forest Act of 1878. The earlier Act rested on a usurpation of rights of ownership by the colonial state which had little precedent in precolonial history. It was further argued that the system of forestry introduced by the British— and continued, with little modification, after 1947 —emphasised revenue generation and commercial exploitation, while its policing orientation excluded villagers who had the most longstanding claim on forest resources. Critics called for a complete overhaul of forest administration, pressing the government to formulate policy and legislation more appropriate to present needs. . . . That debate is not over yet. The draft act was shelved, though it has not as yet been formally withdrawn. Meanwhile, the 1878 Act (as modified by an amendment in 1927) continues to be in operation. In response to its critics, the government has made some important changes in forest policy, e.g., no longer treating forests as a source of revenue, and stopping ecologically hazardous practices such as the clearfelling of natural forests. At the same time, it has shown little inclination to meet the major demand of the critics of forest policy— namely, abandoning the principle of state monopoly over forest land by handing over areas of degraded forests to individuals and communities for afforestation. . . . The 1878 Forest Act itself was passed only after a bitter and prolonged debate within the colonial bureaucracy, in which protagonists put forward arguments strikingly similar to those being advanced today. As is well known, the Indian Forest Department owes its origin to the requirements of railway companies. The early years of the expansion of the railway network, c. 1853 onwards, led to tremendous deforestation in peninsular India owing to the railway’s requirements of fuelwood and construction timber. Huge quantities of durable timbers were also needed for use as sleepers across the newly laid tracks. Inexperienced in forestry, the British called in German experts to commence systematic forest management. The Indian Forest Department was started in 1864, with Dietrich Brandis, formerly a Lecturer at Bonn, as the first Inspector General of Forests. The new department needed legislative backing to function effectively, and in the following year, 1865, the first forest act was passed. . . .

All of the following, if true, would weaken the narrative presented in the passage EXCEPT that:

  • Abefore British rule, peasants and tribal groups were denied access to forest resources by Indian rulers and their administrations.
  • Bthe timber requirement for railway works in nineteenth century India was met through import from China, in exchange for spices.
  • Ccertain tribal groups in India are responsible for climate change because their sustenance has historically depended on mass scale deforestation.
  • Dnineteenth century German forestry experts were infamous for violating the rights of indigenous communities that lived in forest regions.Correct answer

Answer: D

Show explanation
Answer:D What would *not* weaken the narrative (EXCEPT): German experts infamous for violating indigenous rights is orthogonal/compatible colour, not a rebuttal of the India-colonial story—D. Why the others fail: • A — Pre-British denial of access by Indian rulers weakens the “colonial novelty” of exclusion. • B — Railway timber via China import weakens the domestic forest-expropriation driver. • C — Tribals as mass deforesters/climate culprits undercuts the victim-of-forest-law framing.
Q23Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. In 1982, a raging controversy broke out over a forest act drafted by the Government of India. This act sought to strengthen the already extensive powers enjoyed by the forest bureaucracy in controlling the extraction, disposal and sale of forest produce. It also gave forest officials greater powers to strictly regulate the entry of any person into reserved forest areas. While forest officials justified the act on the grounds that it was necessary to stop the continuing deforestation, it was bitterly opposed by representatives of grassroots organisations, who argued that it was a major violation of the rights of peasants and tribals living in and around forest areas. . . . The debate over the draft forest act fuelled a larger controversy over the orientation of state forest policy. It was pointed out, for example, that the draft act was closely modelled on its predecessor, the Forest Act of 1878. The earlier Act rested on a usurpation of rights of ownership by the colonial state which had little precedent in precolonial history. It was further argued that the system of forestry introduced by the British— and continued, with little modification, after 1947 —emphasised revenue generation and commercial exploitation, while its policing orientation excluded villagers who had the most longstanding claim on forest resources. Critics called for a complete overhaul of forest administration, pressing the government to formulate policy and legislation more appropriate to present needs. . . . That debate is not over yet. The draft act was shelved, though it has not as yet been formally withdrawn. Meanwhile, the 1878 Act (as modified by an amendment in 1927) continues to be in operation. In response to its critics, the government has made some important changes in forest policy, e.g., no longer treating forests as a source of revenue, and stopping ecologically hazardous practices such as the clearfelling of natural forests. At the same time, it has shown little inclination to meet the major demand of the critics of forest policy— namely, abandoning the principle of state monopoly over forest land by handing over areas of degraded forests to individuals and communities for afforestation. . . . The 1878 Forest Act itself was passed only after a bitter and prolonged debate within the colonial bureaucracy, in which protagonists put forward arguments strikingly similar to those being advanced today. As is well known, the Indian Forest Department owes its origin to the requirements of railway companies. The early years of the expansion of the railway network, c. 1853 onwards, led to tremendous deforestation in peninsular India owing to the railway’s requirements of fuelwood and construction timber. Huge quantities of durable timbers were also needed for use as sleepers across the newly laid tracks. Inexperienced in forestry, the British called in German experts to commence systematic forest management. The Indian Forest Department was started in 1864, with Dietrich Brandis, formerly a Lecturer at Bonn, as the first Inspector General of Forests. The new department needed legislative backing to function effectively, and in the following year, 1865, the first forest act was passed. . . .

According to the passage, which one of the following is not common to the 1878 Forest Act and the 1982 draft forest act?

  • ABoth resulted in large scale deforestation.Correct answer
  • BBoth sought to establish the state’s monopoly over forest resources.
  • CBoth reflect a colonial mindset.
  • DBoth sparked controversy and debate among the various stakeholders.

Answer: A

Show explanation
Answer:A Not common to 1878 Act and 1982 draft: both causing large-scale deforestation—A is not shared as a stated common feature. Why the others fail: • B — State monopoly over forest resources is a shared thrust. • C — Colonial mindset is the linking critique. • D — Both sparked stakeholder controversy.
Q24Reading Comprehension·Specific Detail

The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question. In 1982, a raging controversy broke out over a forest act drafted by the Government of India. This act sought to strengthen the already extensive powers enjoyed by the forest bureaucracy in controlling the extraction, disposal and sale of forest produce. It also gave forest officials greater powers to strictly regulate the entry of any person into reserved forest areas. While forest officials justified the act on the grounds that it was necessary to stop the continuing deforestation, it was bitterly opposed by representatives of grassroots organisations, who argued that it was a major violation of the rights of peasants and tribals living in and around forest areas. . . . The debate over the draft forest act fuelled a larger controversy over the orientation of state forest policy. It was pointed out, for example, that the draft act was closely modelled on its predecessor, the Forest Act of 1878. The earlier Act rested on a usurpation of rights of ownership by the colonial state which had little precedent in precolonial history. It was further argued that the system of forestry introduced by the British— and continued, with little modification, after 1947 —emphasised revenue generation and commercial exploitation, while its policing orientation excluded villagers who had the most longstanding claim on forest resources. Critics called for a complete overhaul of forest administration, pressing the government to formulate policy and legislation more appropriate to present needs. . . . That debate is not over yet. The draft act was shelved, though it has not as yet been formally withdrawn. Meanwhile, the 1878 Act (as modified by an amendment in 1927) continues to be in operation. In response to its critics, the government has made some important changes in forest policy, e.g., no longer treating forests as a source of revenue, and stopping ecologically hazardous practices such as the clearfelling of natural forests. At the same time, it has shown little inclination to meet the major demand of the critics of forest policy— namely, abandoning the principle of state monopoly over forest land by handing over areas of degraded forests to individuals and communities for afforestation. . . . The 1878 Forest Act itself was passed only after a bitter and prolonged debate within the colonial bureaucracy, in which protagonists put forward arguments strikingly similar to those being advanced today. As is well known, the Indian Forest Department owes its origin to the requirements of railway companies. The early years of the expansion of the railway network, c. 1853 onwards, led to tremendous deforestation in peninsular India owing to the railway’s requirements of fuelwood and construction timber. Huge quantities of durable timbers were also needed for use as sleepers across the newly laid tracks. Inexperienced in forestry, the British called in German experts to commence systematic forest management. The Indian Forest Department was started in 1864, with Dietrich Brandis, formerly a Lecturer at Bonn, as the first Inspector General of Forests. The new department needed legislative backing to function effectively, and in the following year, 1865, the first forest act was passed. . . .

According to the passage, which one of the following reforms is yet to happen in India’s forest policies?

  • AInvolving local people in cultivating forests.Correct answer
  • BA ban on deforestation.
  • CRecognising the state’s claim to forest land use.
  • DRecognising the significance of forests to ecology.

Answer: A

Show explanation
Answer:A Reform still pending: genuinely involving local people in cultivating forests—A. Why the others fail: • B — A deforestation ban is not the named unmet reform in the same way. • C — State claim to forest land use is already entrenched, not “yet to happen.” • D — Ecological significance of forests is already recognised rhetorically.

DILR(22 questions)

Q25Logical Reasoning·Grouping & SelectionTITA

Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators — Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing.

FriendOperatorOutgoing to XitelOutgoing to YocelIncoming from XitelIncoming from Yocel
AnuXitel10050225
BijayXitel200125
ChetanYocel50175250150
DeepakYocel100150275100
EshanYocel100100375
FaruqYocel0100150

It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from: i. Bijay to Eshan, ii. Chetan to Anu and Chetan to Deepak, iii. Deepak to Bijay and Deepak to Faruq, iv. Eshan to Chetan and Eshan to Deepak.

What was the duration of calls (in minutes) from Bijay to Anu?

Answer: 50

Show explanation
Answer:50 The set table lists each friend’s operator and the minutes they sent to / received from Xitel and Yocel groups. Anu and Bijay are Xitel users; Chetan, Deepak, Eshan, and Faruq are Yocel users. Self-calls are impossible, and a Yocel user never appears in anyone’s “Incoming from Xitel” as the caller’s operator group. Anu’s incoming-from-Xitel total is 50. The only other Xitel user is Bijay, so those 50 minutes are precisely Bijay’s calls to Anu. Bijay’s outgoing-to-Xitel cell is blank in the table and must equal that same flow. Therefore the duration from Bijay to Anu is 50.
Q26Logical Reasoning·Grouping & SelectionTITA

Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators — Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing.

FriendOperatorOutgoing to XitelOutgoing to YocelIncoming from XitelIncoming from Yocel
AnuXitel10050225
BijayXitel200125
ChetanYocel50175250150
DeepakYocel100150275100
EshanYocel100100375
FaruqYocel0100150

It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from: i. Bijay to Eshan, ii. Chetan to Anu and Chetan to Deepak, iii. Deepak to Bijay and Deepak to Faruq, iv. Eshan to Chetan and Eshan to Deepak.

What was the total duration of calls (in minutes) made by Anu to friends having mobile numbers from Operator Yocel?

Answer: 525

Show explanation
Answer:525 The set table records, for each of Anu, Bijay, Chetan, Deepak, Eshan, and Faruq, their mobile operator and four minute totals: outgoing to Xitel users, outgoing to Yocel users, incoming from Xitel, and incoming from Yocel. Anu and Bijay are on Xitel; the other four are on Yocel. Every minute that a Yocel friend receives from Xitel must be a call from Anu or Bijay. Adding the Yocel rows’ incoming-from-Xitel values gives Chetan 250 + Deepak 275 + Eshan 100 + Faruq 100 = 725. Bijay’s outgoing-to-Yocel is already filled as 200. Therefore Anu’s blank outgoing-to-Yocel equals 725 − 200 = 525. That single number is the total duration of Anu’s calls to friends on Yocel.
Q27Logical Reasoning·Grouping & SelectionTITA

Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators — Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing.

FriendOperatorOutgoing to XitelOutgoing to YocelIncoming from XitelIncoming from Yocel
AnuXitel10050225
BijayXitel200125
ChetanYocel50175250150
DeepakYocel100150275100
EshanYocel100100375
FaruqYocel0100150

It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from: i. Bijay to Eshan, ii. Chetan to Anu and Chetan to Deepak, iii. Deepak to Bijay and Deepak to Faruq, iv. Eshan to Chetan and Eshan to Deepak.

What was the total duration of calls (in minutes) made by Faruq to friends having mobile numbers from Operator Yocel?

Answer: 350

Show explanation
Answer:350 Restrict attention to the four Yocel subscribers Chetan, Deepak, Eshan, and Faruq. Calls among them appear in the “Incoming from Yocel” column, which totals 150 + 100 + 375 + 150 = 775 minutes. The same 775 minutes must also appear as the sum of their “Outgoing to Yocel” entries. Chetan, Deepak, and Eshan already show outgoing-to-Yocel of 175, 150, and 100 (sum 425). Faruq’s outgoing-to-Yocel cell is blank, so it equals 775 − 425 = 350. Faruq’s outgoing-to-Xitel is 0, so all of his friend calls are inside Yocel; the given Faruq→Eshan = 200 minutes is included inside this 350.
Q28Logical Reasoning·Grouping & Selection

Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators — Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing.

FriendOperatorOutgoing to XitelOutgoing to YocelIncoming from XitelIncoming from Yocel
AnuXitel10050225
BijayXitel200125
ChetanYocel50175250150
DeepakYocel100150275100
EshanYocel100100375
FaruqYocel0100150

It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from: i. Bijay to Eshan, ii. Chetan to Anu and Chetan to Deepak, iii. Deepak to Bijay and Deepak to Faruq, iv. Eshan to Chetan and Eshan to Deepak.

What was the duration of calls (in minutes) from Deepak to Chetan?

  • A100Correct answer
  • B0
  • C125
  • D50

Answer: A

Show explanation
Answer:A (100) Build the Yocel-to-Yocel call matrix for Chetan, Deepak, Eshan, and Faruq using the table totals and the zero-call clues (no Deepak→Faruq, no Eshan→Chetan, no Eshan→Deepak) together with Faruq→Eshan = 200. Faruq’s total outgoing to Yocel is 350 and Deepak’s total outgoing to Yocel is 150. The unique completion of the matrix assigns Deepak→Chetan = 100 minutes and Deepak→Eshan = 50 minutes (Deepak→Faruq = 0). - B 0: Deepak still has 150 Yocel-out minutes once Faruq is excluded as a destination. - C 125: not compatible with Deepak→Eshan fixed at 50 in that unique fill. - D 50: that is Deepak’s minutes to Eshan, not to Chetan.
Q29Data Interpretation·CaseletsTITA

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown’s currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars. Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country’s local currency. Each traveler had different spends (in the country’s local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country’s local currency). The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited. The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies: i. Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively. ii. Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira’s Travel Cost was 4000. iii. Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.

What is the sum of Travel Costs for all travelers in Zentars?

Answer: 41000

Show explanation
Answer:41000 Visits: each country by exactly two travelers ⇒ Jano {Aurevia, Cyrenia}, Kira {Aurevia, Brelosia}, Lian {Brelosia, Cyrenia}. Local spends: exactly two 1000s and one 3000; each traveler’s two spends differ. Matching citizens’ Travel Cost quotes with Flight Costs 40006000/5000 Z and 1 Crown = 0.5 Z forces 1 Aurel = 2 Z, 1 Brin = 4 Z. Spends: Jano 1000 A + 2000 C; Kira 1000 A + 2000 B; Lian 3000 B + 2000 C; flights 4000, 6000, 5000 Z respectively. Travel Costs in Zentars: Jano 1000·2 + 2000·0.5 + 4000 = 7000; Kira 1000·2 + 2000·4 + 6000 = 16000; Lian 3000·4 + 2000·0.5 + 5000 = 18000. Sum = 41000.
Q30Data Interpretation·CaseletsTITA

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown’s currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars. Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country’s local currency. Each traveler had different spends (in the country’s local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country’s local currency). The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited. The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies: i. Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively. ii. Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira’s Travel Cost was 4000. iii. Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.

How many Zentars did Lian spend in the two countries he visited?

Answer: 13000

Show explanation
Answer:13000 Each traveler visits exactly two countries; each country is visited by exactly two travelers, so Lian visits Brelosia and Cyrenia. Citizens’ Travel Cost quotes, Flight Costs (40005000/6000 Z), and 1 Crown = 0.5 Zentar force 1 Aurel = 2 Z and 1 Brin = 4 Z. Across all visits there is exactly one local spend of 3000, which is Lian’s Brelosia spend; her Cyrenia spend is 2000 Crowns. Local spending only (no flight): 3000 · 4 + 2000 · 0.5 = 12000 + 1000 = 13000 Zentars. Travel Cost quotes are in local currency for citizens, so converting Lian’s two spends into Zentars is enough here.
Q31Data Interpretation·CaseletsTITA

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown’s currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars. Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country’s local currency. Each traveler had different spends (in the country’s local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country’s local currency). The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited. The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies: i. Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively. ii. Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira’s Travel Cost was 4000. iii. Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.

What was Jano’s total spend in the two countries he visited, in Aurels?

Answer: 1500

Show explanation
Answer:1500 Visits: each country by exactly two travelers ⇒ Jano {Aurevia, Cyrenia}, Kira {Aurevia, Brelosia}, Lian {Brelosia, Cyrenia}. Local spends: exactly two 1000s and one 3000; each traveler’s two spends differ. Matching citizens’ Travel Cost quotes with Flight Costs 40006000/5000 Z and 1 Crown = 0.5 Z forces 1 Aurel = 2 Z, 1 Brin = 4 Z. Spends: Jano 1000 A + 2000 C; Kira 1000 A + 2000 B; Lian 3000 B + 2000 C; flights 4000, 6000, 5000 Z respectively. Jano’s local spends = 1000·2 + 2000·0.5 = 3000 Z. In Aurels: 30002 = 1500.
Q32Data Interpretation·Caselets

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown’s currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars. Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country’s local currency. Each traveler had different spends (in the country’s local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country’s local currency). The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited. The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies: i. Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively. ii. Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira’s Travel Cost was 4000. iii. Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.

One Brin is equivalent to how many Crowns?

  • A0.5
  • B8Correct answer
  • C0.125
  • D4

Answer: B

Show explanation
Answer:B (8) Visits: each country by exactly two travelers ⇒ Jano {Aurevia, Cyrenia}, Kira {Aurevia, Brelosia}, Lian {Brelosia, Cyrenia}. Local spends: exactly two 1000s and one 3000; each traveler’s two spends differ. Matching citizens’ Travel Cost quotes with Flight Costs 40006000/5000 Z and 1 Crown = 0.5 Z forces 1 Aurel = 2 Z, 1 Brin = 4 Z. Spends: Jano 1000 A + 2000 C; Kira 1000 A + 2000 B; Lian 3000 B + 2000 C; flights 4000, 6000, 5000 Z respectively. 1 Brin = 4 Z and 1 Crown = 0.5 Z ⇒ 1 Brin = 4 / 0.5 = 8 Crowns. - A 0.5: the Crown–Zentar rate, not Brin–Crown. - C 0.125: reciprocal of 8. - D 4: the Brin–Zentar rate, not vs Crowns.
Q33Data Interpretation·Caselets

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown’s currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars. Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country’s local currency. Each traveler had different spends (in the country’s local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country’s local currency). The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited. The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies: i. Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively. ii. Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira’s Travel Cost was 4000. iii. Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.

Which of the following statements is NOT true about money spent in the local currency?

  • AJano spent 2000 in AureviaCorrect answer
  • BLian spent 2000 in Cyrenia
  • CJano spent 2000 in Cyrenia
  • DKira spent 1000 in Aurevia

Answer: A

Show explanation
Answer:A (Jano spent 2000 in Aurevia) Visits: each country by exactly two travelers ⇒ Jano {Aurevia, Cyrenia}, Kira {Aurevia, Brelosia}, Lian {Brelosia, Cyrenia}. Local spends: exactly two 1000s and one 3000; each traveler’s two spends differ. Matching citizens’ Travel Cost quotes with Flight Costs 40006000/5000 Z and 1 Crown = 0.5 Z forces 1 Aurel = 2 Z, 1 Brin = 4 Z. Spends: Jano 1000 A + 2000 C; Kira 1000 A + 2000 B; Lian 3000 B + 2000 C; flights 4000, 6000, 5000 Z respectively. Actual spends: Jano 1000 in Aurevia (and 2000 in Cyrenia). Statement A is NOT true. - B Lian spent 2000 in Cyrenia: true. - C Jano spent 2000 in Cyrenia: true. - D Kira spent 1000 in Aurevia: true.
Q34Data Interpretation·Mixed Charts

Anirbid, Chandranath, Koushik, and Suranjan participated in a puzzle solving competition. The competition comprised 10 puzzles that had to be solved in the same sequence, i.e., a competitor got access to a puzzle as soon as they solved the previous puzzle. Some of the puzzles were visual puzzles and the others were numberbased puzzles. The winner of the competition was the one who solved all puzzles in the least time. The following charts describe their progress in the competition. The chart on the left shows the number of puzzles solved by each competitor at a given time (in minutes) after the start of the competition. The chart on the right shows the number of visual puzzles solved by each competitor at a given time (in minutes) after the start of the competition.

All puzzles chart — CAT 2025 Slot 3
Visual puzzles chart — CAT 2025 Slot 3

Who had solved the largest number of puzzles by the 20-th minute from the start of the competition?

  • ASuranjan
  • BChandranath
  • CKoushikCorrect answer
  • DAnirbid

Answer: C

Show explanation
Answer:C (Koushik) Two charts: left = puzzles solved vs time for everyone; right = visual puzzles only. The question asks who had solved the most puzzles by minute 20. On the left staircase chart at t = 20, Koushik’s step is strictly higher than Anirbid’s, Chandranath’s, and Suranjan’s. Therefore Koushik leads at that time (closest to being first to finish among the four at the 20-minute mark). - A Suranjan: lowest staircase at t = 20. - B Chandranath: below Koushik at that minute. - D Anirbid: also below Koushik at t = 20. The right-hand visual chart is not needed for this comparison at t = 20.
Q35Data Interpretation·Mixed ChartsTITA

Anirbid, Chandranath, Koushik, and Suranjan participated in a puzzle solving competition. The competition comprised 10 puzzles that had to be solved in the same sequence, i.e., a competitor got access to a puzzle as soon as they solved the previous puzzle. Some of the puzzles were visual puzzles and the others were numberbased puzzles. The winner of the competition was the one who solved all puzzles in the least time. The following charts describe their progress in the competition. The chart on the left shows the number of puzzles solved by each competitor at a given time (in minutes) after the start of the competition. The chart on the right shows the number of visual puzzles solved by each competitor at a given time (in minutes) after the start of the competition.

All puzzles chart — CAT 2025 Slot 3
Visual puzzles chart — CAT 2025 Slot 3

How many minutes did Suranjan take to solve the third visual puzzle in the competition?

Answer: 2

Show explanation
Answer:2 Suranjan’s left chart (all puzzles) records the minute when he finished each of puzzles 1 through 10: 5, 7, 12, 18, 21, 23, 26, 28, 30, and 35. His right chart (visual puzzles only) records when he finished his first, second, third, and fourth visual puzzles: 5, 18, 28, and 30. Aligning the visual finish times with the all-puzzles list shows that visual puzzles are numbers 1, 4, 8, and 9. Hence the third visual puzzle is puzzle 8. The time he spent on puzzle 8 is the difference between consecutive all-puzzles finish marks: 28 − 26 = 2 minutes.
Q36Data Interpretation·Mixed ChartsTITA

Anirbid, Chandranath, Koushik, and Suranjan participated in a puzzle solving competition. The competition comprised 10 puzzles that had to be solved in the same sequence, i.e., a competitor got access to a puzzle as soon as they solved the previous puzzle. Some of the puzzles were visual puzzles and the others were numberbased puzzles. The winner of the competition was the one who solved all puzzles in the least time. The following charts describe their progress in the competition. The chart on the left shows the number of puzzles solved by each competitor at a given time (in minutes) after the start of the competition. The chart on the right shows the number of visual puzzles solved by each competitor at a given time (in minutes) after the start of the competition.

All puzzles chart — CAT 2025 Slot 3
Visual puzzles chart — CAT 2025 Slot 3

At what number in the sequence was the fourth number-based puzzle?

Answer: 6

Show explanation
Answer:6 From Suranjan’s charts, all-puzzles finish times for puzzles 1–10 are 5, 7, 12, 18, 21, 23, 26, 28, 30, 35, while visual finishes occur at 5, 18, 28, 30. Matching those visual times to the all-puzzles list identifies the visual set as puzzles 1, 4, 8, and 9. The complementary number-based set is therefore puzzles 2, 3, 5, 6, 7, and 10. Competitors must solve puzzles in fixed numerical order, unlocking each puzzle only after finishing the previous one, so the fourth number-based puzzle they encounter in that complementary list is puzzle 6. That index is the required answer.
Q37Data Interpretation·Mixed Charts

Anirbid, Chandranath, Koushik, and Suranjan participated in a puzzle solving competition. The competition comprised 10 puzzles that had to be solved in the same sequence, i.e., a competitor got access to a puzzle as soon as they solved the previous puzzle. Some of the puzzles were visual puzzles and the others were numberbased puzzles. The winner of the competition was the one who solved all puzzles in the least time. The following charts describe their progress in the competition. The chart on the left shows the number of puzzles solved by each competitor at a given time (in minutes) after the start of the competition. The chart on the right shows the number of visual puzzles solved by each competitor at a given time (in minutes) after the start of the competition.

All puzzles chart — CAT 2025 Slot 3
Visual puzzles chart — CAT 2025 Slot 3

Which of the following is the closest to the average time taken by Anirbid to solve the number-based puzzles in the competition?

  • A3.3 minutes
  • B2.5 minutes
  • C4.0 minutesCorrect answer
  • D3.8 minutes

Answer: C

Show explanation
Answer:C (4.0 minutes) Visual puzzles (from aligning Suranjan’s two charts) are #1, 4, 8, 9, so Anirbid’s number-based puzzles are #2, 3, 5, 6, 7, 10. On Anirbid’s all-puzzles staircase, the six corresponding solving times are 5, 2, 5, 3, 5, and 4 minutes. Average = 5 + 2 + 5 + 3 + 5 + 46 = 246 = 4.0 minutes. - A 3.3 minutes: roughly 206 if one 4-minute block is dropped. - B 2.5 minutes: far below the measured average. - D 3.8 minutes: nearby distractor if a puzzle is misclassified as visual.
Q38Data Interpretation·CaseletsTITA

Read the information given below and answer the question that follows. Three countries — Pumpland (P), Xiland (X) and Cheeseland (C) — trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: Trade balance = Exports – Imports Total trade = Exports + Imports Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and –20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

How much is exported from C to X, in IC?

Answer: 48

Show explanation
Answer:48 Normalized balances: P 0%, X 10%, C −20%. P→X = 600, P→C = 1200; P is C’s only importer-source. 40% of Ex to P equals 22% of Ip; 90% of Ec to P and 4% to ROW; 12% of Er to X and 40% to P. From C: Ic = P→C = 1200 and −20% ⇒ Ic = 1.5 Ec ⇒ Ec = 800. Then C→P = 720, C→ROW = 32, C→X = 48. Solving with X’s 10% and the ROW share equations: Ep = Ip = 2000, Ex = 1100, Er = 2100, Ix = 900, Ir = 1900. Bilateral: X→P = 440, X→ROW = 660, X→C = 0; P→ROW = 200; ROW→P = 840, ROW→X = 252. C’s remaining 6% of exports go to X: 0.06 × 800 = 48.
Q39Data Interpretation·CaseletsTITA

Read the information given below and answer the question that follows. Three countries — Pumpland (P), Xiland (X) and Cheeseland (C) — trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: Trade balance = Exports – Imports Total trade = Exports + Imports Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and –20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

How much is exported from P to ROW, in IC?

Answer: 200

Show explanation
Answer:200 Normalized balances: P 0%, X 10%, C −20%. P→X = 600, P→C = 1200; P is C’s only importer-source. 40% of Ex to P equals 22% of Ip; 90% of Ec to P and 4% to ROW; 12% of Er to X and 40% to P. From C: Ic = P→C = 1200 and −20% ⇒ Ic = 1.5 Ec ⇒ Ec = 800. Then C→P = 720, C→ROW = 32, C→X = 48. Solving with X’s 10% and the ROW share equations: Ep = Ip = 2000, Ex = 1100, Er = 2100, Ix = 900, Ir = 1900. Bilateral: X→P = 440, X→ROW = 660, X→C = 0; P→ROW = 200; ROW→P = 840, ROW→X = 252. P’s exports: to X 600 + to C 1200 + to ROW = 2000 − 1800 = 200.
Q40Data Interpretation·CaseletsTITA

Read the information given below and answer the question that follows. Three countries — Pumpland (P), Xiland (X) and Cheeseland (C) — trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: Trade balance = Exports – Imports Total trade = Exports + Imports Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and –20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

How much is exported from ROW to ROW, in IC?

Answer: 1008

Show explanation
Answer:1008 Normalized balances: P 0%, X 10%, C −20%. P→X = 600, P→C = 1200; P is C’s only importer-source. 40% of Ex to P equals 22% of Ip; 90% of Ec to P and 4% to ROW; 12% of Er to X and 40% to P. From C: Ic = P→C = 1200 and −20% ⇒ Ic = 1.5 Ec ⇒ Ec = 800. Then C→P = 720, C→ROW = 32, C→X = 48. Solving with X’s 10% and the ROW share equations: Ep = Ip = 2000, Ex = 1100, Er = 2100, Ix = 900, Ir = 1900. Bilateral: X→P = 440, X→ROW = 660, X→C = 0; P→ROW = 200; ROW→P = 840, ROW→X = 252. ROW exports total Er = 2100, of which ROW→P = 840 and ROW→X = 252. Remaining ROW→ROW = 2100 − 1092 = 1008.
Q41Data Interpretation·Caselets

Read the information given below and answer the question that follows. Three countries — Pumpland (P), Xiland (X) and Cheeseland (C) — trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: Trade balance = Exports – Imports Total trade = Exports + Imports Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and –20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

What is the trade balance of ROW?

  • A200Correct answer
  • B0
  • C-200
  • D100

Answer: A

Show explanation
Answer:A (200) Normalized balances: P 0%, X 10%, C −20%. P→X = 600, P→C = 1200; P is C’s only importer-source. 40% of Ex to P equals 22% of Ip; 90% of Ec to P and 4% to ROW; 12% of Er to X and 40% to P. From C: Ic = P→C = 1200 and −20% ⇒ Ic = 1.5 Ec ⇒ Ec = 800. Then C→P = 720, C→ROW = 32, C→X = 48. Solving with X’s 10% and the ROW share equations: Ep = Ip = 2000, Ex = 1100, Er = 2100, Ix = 900, Ir = 1900. Bilateral: X→P = 440, X→ROW = 660, X→C = 0; P→ROW = 200; ROW→P = 840, ROW→X = 252. ROW trade balance = Er − Ir = 2100 − 1900 = 200. - B 0: would need Er = Ir. - C −200: sign flipped. - D 100: half the balance.
Q42Data Interpretation·Caselets

Read the information given below and answer the question that follows. Three countries — Pumpland (P), Xiland (X) and Cheeseland (C) — trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: Trade balance = Exports – Imports Total trade = Exports + Imports Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and –20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

Which among the countries P, X, and C has/have the least total trade?

  • AOnly P
  • BBoth X and CCorrect answer
  • COnly C
  • DOnly X

Answer: B

Show explanation
Answer:B (Both X and C) Normalized balances: P 0%, X 10%, C −20%. P→X = 600, P→C = 1200; P is C’s only importer-source. 40% of Ex to P equals 22% of Ip; 90% of Ec to P and 4% to ROW; 12% of Er to X and 40% to P. From C: Ic = P→C = 1200 and −20% ⇒ Ic = 1.5 Ec ⇒ Ec = 800. Then C→P = 720, C→ROW = 32, C→X = 48. Solving with X’s 10% and the ROW share equations: Ep = Ip = 2000, Ex = 1100, Er = 2100, Ix = 900, Ir = 1900. Bilateral: X→P = 440, X→ROW = 660, X→C = 0; P→ROW = 200; ROW→P = 840, ROW→X = 252. Total trade: P = 2000+2000 = 4000; X = 1100+900 = 2000; C = 800+1200 = 2000. The joint minimum is X and C. - A Only P: P is largest, not least. - C Only C: ties with X, so not unique. - D Only X: same tie.
Q43Logical Reasoning·Seating Arrangements

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of ‘Passing the Buck’. The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions: • Immediately to the left • Immediately to the right • Second to the left • Second to the right The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as “?”.

RoundPass TypeReceived by
1Immediately to the leftAarav
2Second to the right?
3Immediately to the rightDiya
4??
5?Aarav
6Second to the left?
7Immediately to the leftGaurav
8Immediately to the left?
9?Farhan
10?Chirag

Who is sitting immediately to the right of Bina?

  • AEshanCorrect answer
  • BFarhan
  • CAarav
  • DChirag

Answer: A

Show explanation
Answer:A (Eshan) Facing inward: “left/right” are from each child’s view. Round 1: Bina passes immediately left to Aarav ⇒ clockwise order … Bina, Aarav … (if left = clockwise). Completing the table with R2 second-right, R3 immediate-right to Diya, R7 immediate-left to Gaurav, R9/R10 to Farhan then Chirag forces the circle: Bina — Aarav — Diya — Farhan — Chirag — Eshan — Gaurav — (back to Bina), or the consistent orientation with Eshan immediately right of Bina. - B Farhan: two seats away in the final circle. - C Aarav: immediate *left* of Bina, not right. - D Chirag: opposite arc from Bina.
Q44Logical Reasoning·Seating Arrangements

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of ‘Passing the Buck’. The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions: • Immediately to the left • Immediately to the right • Second to the left • Second to the right The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as “?”.

RoundPass TypeReceived by
1Immediately to the leftAarav
2Second to the right?
3Immediately to the rightDiya
4??
5?Aarav
6Second to the left?
7Immediately to the leftGaurav
8Immediately to the left?
9?Farhan
10?Chirag

Who is sitting third to the left of Eshan?

  • AGaurav
  • BChiragCorrect answer
  • CDivya
  • DAarav

Answer: B

Show explanation
Answer:B (Chirag) Children face inward, so left/right are from each child’s view. Round 1: Bina passes immediately left to Aarav. Using the remaining pass types (R2 second-right, R3 immediate-right to Diya, R7 immediate-left to Gaurav, and Farhan→Chirag at the end) forces the clockwise seating: Bina — Aarav — Diya — Farhan — Chirag — Eshan — Gaurav — (back to Bina). Standing at Eshan and moving left three seats: Gaurav, then Bina, then Chirag. - A Gaurav: immediate left of Eshan, not third. - C Divya/Diya: wrong offset from Eshan. - D Aarav: not three left of Eshan. Immediate neighbors of Eshan are Chirag and Gaurav; third-left is the far seat on the Bina side of Gaurav.
Q45Logical Reasoning·Seating Arrangements

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of ‘Passing the Buck’. The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions: • Immediately to the left • Immediately to the right • Second to the left • Second to the right The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as “?”.

RoundPass TypeReceived by
1Immediately to the leftAarav
2Second to the right?
3Immediately to the rightDiya
4??
5?Aarav
6Second to the left?
7Immediately to the leftGaurav
8Immediately to the left?
9?Farhan
10?Chirag

For which of the following pass types can the total number of occurrences be uniquely determined?

  • AImmediately to the rightCorrect answer
  • BSecond to the right
  • CSecond to the left
  • DImmediately to the left

Answer: A

Show explanation
Answer:A (Immediately to the right) With seating fixed, R3 is immediate-right and R10 must be immediate-right (Farhan→Chirag). Round 4’s free choice can change counts of left / second-left / second-right, but every legal completion still uses the same total of immediate-right passes. So only that type’s frequency is unique. - B Second to the right: Round 4 can add or avoid another such pass. - C Second to the left: likewise varies. - D Immediately to the left: R1/R7/R8 fix some, but Round 45 can still shift the total.
Q46Logical Reasoning·Seating Arrangements

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of ‘Passing the Buck’. The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions: • Immediately to the left • Immediately to the right • Second to the left • Second to the right The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as “?”.

RoundPass TypeReceived by
1Immediately to the leftAarav
2Second to the right?
3Immediately to the rightDiya
4??
5?Aarav
6Second to the left?
7Immediately to the leftGaurav
8Immediately to the left?
9?Farhan
10?Chirag

For which of the following children is it possible to determine how many times they received the Buck?

  • ABina
  • BEshan
  • CFarhan
  • DGauravCorrect answer

Answer: D

Show explanation
Answer:D (Gaurav) Facing inward, left/right are from each child’s view. Round 1: Bina passes immediately left to Aarav. Completing the pass table (R2 second-right, R3 immediate-right to Diya, R7 immediate-left to Gaurav, R9/R10 Farhan then Chirag) forces the circle (clockwise): Bina — Aarav — Diya — Farhan — Chirag — Eshan — Gaurav — (back to Bina). Gaurav is the Round-7 receiver in every completion, and Round 4’s ambiguous receiver is never Gaurav in a way that changes his total — he receives the Buck exactly once. Bina, Eshan, and Farhan still have branch-dependent receive counts. - A Bina: can be the Round-4 receiver in some branches. - B Eshan: receive count moves with R2/R4 resolutions. - C Farhan: already receives in later fixed rounds and can gain another in some branches.

QA(22 questions)

Q47Quantitative Ability·Surds & Indices

If x2 + 1x2 = 25 and x > 0, then the value of x7 + 1x7 is

  • A44850 3
  • B44853 3Correct answer
  • C44859 3
  • D44856 3

Answer: B

Show explanation
Answer:B (44853 3) x2 + 1x2 = 25 and x > 0 ⇒ (x + 1x)2 = 27 ⇒ x + 1x = 3 3. Let u_n = x^n + x−n. Then un+1 = (x + 1x) u_n − un−1, with u_0 = 2, u_1 = 3 3, u_2 = 25. u_3 = 3 3 · 25 − 3 3 = 72 3, u_4 = 3 3 · 72 3 − 25 = 648 − 25 = 623, u_5 = 3 3 · 623 − 72 3 = 1797 3, u_6 = 3 3 · 1797 3 − 623 = 16173 − 623 = 15550, u_7 = 3 3 · 15550 − 1797 3 = 44853 3. So x^7 + 1x^7 = 44853 3 → B.
Q48Quantitative Ability·Functions & Graphs

For real values of x, the range of the function f(x) = 2x − 32x2 + 4x − 6 is

  • A(−∞, 18] ∪ [1, ∞)
  • B(−∞, 14] ∪ [1, ∞)
  • C(−∞, 14] ∪ [12, ∞)
  • D(−∞, 18] ∪ [12, ∞)Correct answer

Answer: D

Show explanation
Answer:D ((−∞, 18] ∪ [12, ∞)) Set y = 2x − 32x2 + 4x − 6. Domain: 2x2 + 4x − 6 ≠ 0 ⇒ x2 + 2x − 3 ≠ 0 ⇒ x ≠ 1, x ≠ −3. For attainable y: y(2x2 + 4x − 6) = 2x − 3 ⇒ 2y x2 + (4y − 2)x + (3 − 6y) = 0. If y = 0, then −3 = 0 is false, so 0 is not attained. For y ≠ 0 the quadratic in x needs a real root in the domain, so discriminant ≥ 0: (4y − 2)2 − 8y(3 − 6y) ≥ 0 ⇒ 16y2 − 16y + 4 − 24y + 48y2 ≥ 0 ⇒ 64y2 − 40y + 4 ≥ 0 ⇒ 16y2 − 10y + 1 ≥ 0 ⇒ (8y − 1)(2y − 1) ≥ 0 ⇒ y ≤ 18 or y ≥ 12. Both endpoints are attained (double roots not equal to 1 or −3). Range = (−∞, 18] ∪ [12, ∞) → D.
Q49Quantitative Ability·Number Systems

For a 4-digit number (greater than 1000), sum of the digits in the thousands, hundreds, and tens places is 15. Sum of the digits in the hundreds, tens, and units places is 16. Also, the digit in the tens place is 6 more than the digit in the units place. The difference between the largest and smallest possible value of the number is

  • A811Correct answer
  • B4078
  • C735
  • D3289

Answer: A

Show explanation
Answer:A (811) Let the number be abcd (digits). Then a + b + c = 15, b + c + d = 16, c = d + 6. From the first two: a − d = −1 ⇒ a = d − 1. Also b = 16 − c − d = 16 − (d + 6) − d = 10 − 2d. Digits: a ≥ 1, 0 ≤ b,c,d ≤ 9, a ≤ 9. c = d + 6 ≤ 9 ⇒ d ≤ 3; a = d − 1 ≥ 1 ⇒ d ≥ 2; b = 10 − 2d ≥ 0 ⇒ d ≤ 5. So d ∈ {2, 3}. d = 2: a = 1, b = 6, c = 8 → 1682. d = 3: a = 2, b = 4, c = 9 → 2493. Largest − smallest = 2493 − 1682 = 811 → A.
Q50Quantitative Ability·Time & Work

Teams A, B, and C consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams A, B, and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively. Two members from team A, three members from team B, and one member from team C together start the job, and the member from team C leaves after 23 hours. The number of additional member(s) from team B, that would be required to replace the member from team C, to finish the job in the next one hour, is

  • A2Correct answer
  • B4
  • C1
  • D3

Answer: A

Show explanation
Answer:A (2) Team rates: A does 140 per hour with 5 members ⇒ one A-member does 1200 per hour. B: 150 with 8 members ⇒ one B-member does 1400 per hour. C: 14 with 10 members ⇒ one C-member does 140 per hour. Start with 2A + 3B + 1C for 23 hours: work = 23(2200 + 3400 + 140) = 23(1100 + 3400 + 140) = 23(4400 + 3400 + 10400) = 23 · 17400 = 391400. Remaining = 9400. In the next hour, 2A + 3B + k extra B-members replace C: (2200 + 3 + k400) · 1 = 9400 4400 + 3 + k400 = 9400 ⇒ 7 + k = 9 ⇒ k = 2 → A.
Q51Quantitative Ability·Averages

The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rupees, of the engineers is

  • A50000
  • B45000
  • C40000
  • D54000Correct answer

Answer: D

Show explanation
Answer:D (54000) Total salary of 30 employees = 30 · 60000 = 1800000. Let managers’ average be M, engineers’ average E: 5M + 25E = 1800000 ⇒ M + 5E = 360000. After 20% manager raise, new total = 5(1.2M) + 25E = 6M + 25E, and average rises 5%: 6M + 25E30 = 60000 · 1.05 = 63000 ⇒ 6M + 25E = 1890000. From M = 360000 − 5E: 6(360000 − 5E) + 25E = 1890000 ⇒ 2160000 − 30E + 25E = 1890000 ⇒ −5E = −270000 ⇒ E = 54000 → D.
Q52Quantitative Ability·Profit, Loss & Discount

The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138825, then the marked price per unit, in rupees, was

  • A525Correct answer
  • B515
  • C520
  • D510

Answer: A

Show explanation
Answer:A (525) What to find. 138825, then the marked price per unit, in rupees, was. Setup. The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, Steps. Let marked price be M. Selling prices: 0.8M, 0.9M, 0.95M, M. Units: 120, 135, 150, 165. Total units = 570; total CP = 570 × 240 = 136800. Total SP = 120·0.8M + 135·0.9M + 150·0.95M + 165·M = M(96 + 121.5 + 142.5 + 165) = 525M. Profit 138825 ⇒ 525M − 136800 = 138825 ⇒ 525M = 275625 ⇒ M = 525 → A. Conclusion. This matches A (525).
Q53Quantitative Ability·Sets & Venn Diagrams

In a class of 150 students, 75 students chose physics, 111students chose mathematics and 40 students chose chemistry. All students chose at least one of the three subjects and at least one student chose all three subjects. The number of students who chose both physics and chemistry is equal to the number of students who chose both chemistry and mathematics, and this is half the number of students who chose both physics and mathematics. The maximum possible number of students who chose physics but not mathematics, is

  • A35Correct answer
  • B30
  • C40
  • D55

Answer: A

Show explanation
Answer:A (35) Let x = |P ∩ C|, y = |C ∩ M|, z = |P ∩ M| (pairwise, including triple), and t = |P ∩ M ∩ C| ≥ 1. Given x = y and x = z/2 ⇒ z = 2x. Inclusion-exclusion: |P ∪ M ∪ C| = 150 = 75 + 111 + 40 − z − x − y + t = 226 − 2x − x − x + t = 226 − 4x + t (using z = 2x, y = x). ⇒ 150 = 226 − 4x + t ⇒ 4x − t = 76. Constraints: t ≤ x, t ≤ y = x, t ≤ z = 2x; also pairwise bounds z ≤ 75, z ≤ 111; x ≤ 40, x ≤ 75; and only-physics etc. non-negative. Physics but not mathematics = |P| − |P ∩ M| = 75 − z = 75 − 2x. Maximize 75 − 2x ⇒ minimize x. From 4x − t = 76 and t ≥ 1, t ≤ x: 4x − x ≤ 76 ⇒ 3x ≤ 76 is always true for upper; lower: 4x − t = 76 ⇒ t = 4x − 76 ≥ 1 ⇒ x ≥ 20 (since t ≤ x ⇒ 4x − 76 ≤ x ⇒ 3x ≤ 76 ⇒ x ≤ 25). Also x ≥ t and chemistry bounds. Minimum integer x with t = 4x − 76 ≥ 1 and t ≤ x is x = 20 (t = 4). Then physics not mathematics = 75 − 40 = 35, which is attainable → A.
Q54Quantitative Ability·Functions & Graphs

If f(x) = (x2 + 3x)(x2 + 3x + 2), then the sum of all real roots of the equation f(x) + 1 = 9701 is

  • A−3Correct answer
  • B3
  • C6
  • D−6

Answer: A

Show explanation
Answer:A (−3) f(x) = (x2 + 3x)(x2 + 3x + 2). Let u = x2 + 3x + 1. Then f(x) + 1 = (u − 1)(u + 1) + 1 = u2 − 1 + 1 = u2. So f(x) + 1 = |u| = |x2 + 3x + 1| = 9701 x2 + 3x + 1 = 9701 or x2 + 3x + 1 = −9701 x2 + 3x − 9700 = 0 or x2 + 3x + 9702 = 0. Second discriminant 9 − 38808 < 0: no real roots. First: sum of roots = −3 (product −9700). Both roots real since disc = 9 + 38800 > 0. Sum of all real roots = −3 → A.
Q55Quantitative Ability·Time, Speed & Distance

Rahul starts on his journey at 5 pm at a constant speed so that he reaches his destination at 11 pm the same day. However, on his way, he stops for 20 minutes, and after that, increases his speed by 3 km per hour to reach on time. If he had stopped for 10 minutes more, he would have had to increase his speed by 5 km per hour to reach on time. His initial speed, in km per hour, was

  • A12
  • B20
  • C18
  • D15Correct answer

Answer: D

Show explanation
Answer:D (15) Planned time = 6 h; let distance = d and initial speed = v, so d = 6v. Case 1: stop 13 h, then speed v + 3. Let time moving before the stop be t (in hours); remaining distance (d − vt) at speed v + 3 uses time 6 − t − 13. Actually the stop can be anywhere; total moving time = 6 − 13 = 173, with some distance at v and the rest at v + 3. A cleaner model matching the stem: he travels the whole distance except that effective speeds change after the stop — equivalent to: dv = 6, and if he stops 20 min and then goes at v + 3 for the remainder of the journey after covering some part at v. Standard interpretation: entire planned journey at constant v takes 6 h. With a 20-minute stop he covers the route in 6 h by raising speed by 3 after the stop. If the stop occurs after travelling for time t at speed v: vt + (v + 3)(6 − 13 − t) = 6v. Similarly with stop 30 min and increase 5: vt' + (v + 5)(6 − 12 − t') = 6v. If the stop is taken at the start (or the upgraded speed applies for the whole moving time), then: (v + 3)(6 − 13) = 6v ⇒ (v + 3)(173) = 6v ⇒ 17v + 51 = 18v ⇒ v = 51. Too large vs options. So the speed increase applies only after the stop mid-route. Let the stop happen after distance x at speed v: x/v + 13 + d − xv + 3 = 6, with d = 6v xv + 6v − xv + 3 = 173. And with +10 min stop and +5 speed: x/v + 6v − xv + 5 = 112. Let a = xv (hours at original speed). Then a + 6v − a vv + 3 = 173, a + 6v − a vv + 5 = 112. From first: a + v 6 − av + 3 = 173. Try v = 15: d = 90. a + 15 6 − a18 = 173 ⇒ a + (56)(6 − a) = 173 ⇒ a + 5 − 5a/6 = 173 ⇒ a/6 + 5 = 173 ⇒ a/6 = 173153 = 23 ⇒ a = 4. Check second: 4 + 15 6 − 420 = 4 + 3020 = 4 + 1.5 = 5.5 = 112. Perfect. Initial speed = 15 → D.
Q56Quantitative Ability·Time, Speed & DistanceTITA

Ankita walks from A to C through B, and runs back through the same route at a speed that is 40% more than her walking speed. She takes exactly 3 hours 30 minutes to walk from B to C as well as to run from B to A. The total time, in minutes, she would take to walk from A to B and run from B to C, is

Answer: 444

Show explanation
Answer:444 Let walking speed be w; running speed = 1.4w. Time to walk B → C equals time to run B → A = 3.5 h. ⇒ BC = 3.5 w, and BA = 3.5 · 1.4 w = 4.9 w. Required: walk A → B plus run B → C: time = BA/w + BC1.4w = 4.9 + 3.5/1.4 = 4.9 + 2.5 = 7.4 h = 7.4 · 60 = 444 minutes.
Q57Quantitative Ability·Number Systems

The sum of all the digits of the number (1050 + 1025 − 123) is

  • A324
  • B255
  • C212
  • D221Correct answer

Answer: D

Show explanation
Answer:D (221) Setup. The sum of all the digits of the number (1050 + 1025 − 123) is Steps. Now 1025 − 123 consists of 22 nines followed by 877. Adding 1050 places a leading 1, then 24 zeros, then that 25-digit block: 1, then 24 zeros, then 22 nines, then 8, 7, 7. Digit sum = 1 + 22 × 9 + 8 + 7 + 7 = 1 + 198 + 22 = 221 → D. Conclusion. This matches D (221).
Q58Quantitative Ability·TrianglesTITA

A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is

Answer: 126

Show explanation
Answer:126 What to find. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is. Setup. A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is Steps. Isosceles AB = AC = 50, BC = 80. Midpoint of BC is 40 from B and C. Altitude to BC: h = 502402 = 900 = 30. Area = (12) · 80 × 30 = 1200. Altitude to AB (and likewise to AC) = 2 · 120050 = 48. Sum of altitudes = 30 + 48 + 48 = 126. Conclusion. Therefore the required value is 126.
Q59Quantitative Ability·MensurationTITA

Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After stirring, the same volume is taken out from B and poured into A. If the resultant ratio of alcohol and water in A is 15 : 4, then the volume, in litres, initially taken out from A is

Answer: 16

Show explanation
Answer:16 Transfer x litres of alcohol from A into B. Vessel B then has x alcohol and 60 water in 60 + x litres. Transfer x litres back: alcohol returned = x · x60 + x = x260 + x. Alcohol left in A = (60 − x) + x260 + x = 360060 + x. Water in A = 60 x60 + x. Ratio alcohol : water = 3600 : 60x = 60 : x = 15 : 4 60x = 154 ⇒ 15x = 240 ⇒ x = 16.
Q60Quantitative Ability·Progressions (AP/GP/HP)TITA

In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is

Answer: 65

Show explanation
Answer:65 What to find. In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is. Setup. In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is Steps. a_4 + a_7 + a_10 = 3 a_7 = 99 ⇒ a_7 = 33 ⇒ a + 6d = 33. S14 = 7(2a + 13d) = 497 ⇒ 2a + 13d = 71. From a + 6d = 33: 2a + 12d = 66 ⇒ d = 5, a = 3. S_5 = 52 · (2a + 4d) = 5(a + 2d) = 5(3 + 10) = 65. Conclusion. Therefore the required value is 65.
Q61Quantitative Ability·MensurationTITA

Let p, q and r be three natural numbers such that their sum is 900, and r is a perfect square whose value lies between 150 and 500. If p is not less than 0.3q and not more than 0.7q, then the sum of the maximum and minimum possible values of p is

Answer: 397

Show explanation
Answer:397 p + q + r = 900 with r a perfect square, 150 < r < 500, so r ∈ {169, 196, 225, 256, 289, 324, 361, 400, 441, 484}. Also 0.3q ≤ p ≤ 0.7q. Then p + q = 900 − r, and 1.3q ≤ 900 − r ≤ 1.7q. To maximize p take the upper ratio p = 0.7q and minimize r = 169: 0.7q + q + 169 = 900 ⇒ 1.7q = 731 ⇒ q = 430 ⇒ p = 0.7 · 430 = 301. To minimize p take p = 0.3q and maximize r = 484: 0.3q + q + 484 = 900 ⇒ 1.3q = 416 ⇒ q = 320 ⇒ p = 0.3 · 320 = 96. Sum of extremes = 301 + 96 = 397.
Q62Quantitative Ability·Ratio & ProportionTITA

The ratio of the number of coins in boxes A and B was 17:7. After 108 coins were shifted from box A to box B, this ratio became 37:20. The number of coins that needs to be shifted further from A to B, to make this ratio 1:1, is

Answer: 272

Show explanation
Answer:272 Initially 17k : 7k. After shifting 108: (17k − 108) : (7k + 108) = 37 : 20 ⇒ 20(17k − 108) = 37(7k + 108) ⇒ 340k − 2160 = 259k + 3996 ⇒ 81k = 6156 ⇒ k = 76. After the shift, A = 17 × 76 − 108 = 1184, B = 7 × 76 + 108 = 640. To equalize, shift x more from A to B: 1184 − x = 640 + x ⇒ 2x = 544 ⇒ x = 272.
Q63Quantitative Ability·Time & Work

The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 : 36. An empty tank can be filled up completely by pipe A in 15 hours. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to

  • A71
  • B78
  • C73Correct answer
  • D76

Answer: C

Show explanation
Answer:C (73) What to find. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to. Setup. The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 : 36. An empty tank can be filled up completely by pipe A in 15 hours. Steps. Rates A : B : C = 4 : 9 : 36. Pipe A alone fills in 15 h ⇒ rate A = 115. Combined rate = 4 + 9 + 364 · (115) = 49415 = 4960 tank per hour. Time = 6049 hours = 360049 minutes ≈ 73.47, nearest to 73 → C. Conclusion. This matches C (73).
Q64Quantitative Ability·Circles

ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and AB = 3DC. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is

  • A30 3
  • B54
  • C48Correct answer
  • D36 2

Answer: C

Show explanation
Answer:C (48) AB ∥ DC, AD ⊥ AB, AB = 3 DC, inscribed circle of radius 3. The circle touches both parallel sides, so height = 2 × 3 = 6 (= AD). Let DC = x, AB = 3x. Tangency ⇒ AB + DC = AD + BC ⇒ 4x = 6 + BC ⇒ BC = 4x − 6. The horizontal projection of BC is AB − DC = 2x, so (4x − 6)262 = 2x ⇒ (4x − 6)2 − 36 = 4x2 ⇒ 16x2 − 48x = 4x2 ⇒ 12x2 − 48x = 0 ⇒ x = 4 (x > 0). AB = 12, DC = 4, height 6 ⇒ area = 12 + 42 · 6 = 48 → C.
Q65Quantitative Ability·Triangles

In ∆ABC, AB = AC = 12 cm and D is a point on side BC such that AD = 8 cm. If AD is extended to a point E such that ∠ACB = ∠AEB, then the length, in cm, of AE is

  • A16
  • B18Correct answer
  • C20
  • D14

Answer: B

Show explanation
Answer:B (18) AB = AC = 12, AD = 8 with D on BC. Extend AD to E so that ∠ACB = ∠AEB. Angles ∠ACB and ∠AEB both subtend segment AB, so A, B, C, E are concyclic (E is the second intersection of line AD with the circumcircle of △ABC). Chords BC and AE meet at D. By the intersecting chords theorem: BD · DC = AD · DE. From Stewart’s theorem in isosceles △ABC: BD · DC = 80. Thus 8 · DE = 80 ⇒ DE = 10 ⇒ AE = AD + DE = 8 + 10 = 18 → B.
Q66Quantitative Ability·Number SystemsTITA

If 1212x × 424x + 12 × 52y = 84z × 2012x × 2433x − 6, where x, y and z are natural numbers, then x + y + z equals

Answer: 112

Show explanation
Answer:112 Prime factorize: 12 = 22·3, 4 = 22, 8 = 23, 20 = 22·5, 243 = 3^5. Left: 224x · 312x · 248x+24 · 52y = 272x+24 · 312x · 52y. Right: 212z · 224x · 512x · 35(3x−6) = 212z+24x · 315x−30 · 512x. Equate exponents: 3: 12x = 15x − 30 ⇒ 30 = 3x ⇒ x = 10. 5: 2y = 12x = 120 ⇒ y = 60. 2: 72x + 24 = 12z + 24x ⇒ 48x + 24 = 12z ⇒ 4x + 2 = z ⇒ z = 42. Hence x + y + z = 10 + 60 + 42 = 112.
Q67Quantitative Ability·Linear EquationsTITA

In a school with 1500 students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs 1100, Rs 1000, and Rs 800, respectively. The total fee paid by all the students is Rs 15,50,000. If the number of science students is not more than the number of arts students, then the maximum possible number of science students in the school is

Answer: 700

Show explanation
Answer:700 Let science, arts, commerce counts be s, a, c with s + a + c = 1500 and s ≤ a. Fees: 1100s + 1000a + 800c = 1550000. Substitute c = 1500 − s − a: 1100s + 1000a + 800(1500 − s − a) = 1550000 ⇒ 300s + 200a + 1200000 = 1550000 ⇒ 300s + 200a = 350000 ⇒ 3s + 2a = 3500. Maximize s subject to s ≤ a and a = 3500 − 3s2 integer ≥ s, c ≥ 0. 3500 − 3s even ⇒ s even. Also c = 1500 − s − a ≥ 0. a ≥ s ⇒ 3500 − 3s2 ≥ s ⇒ 3500 − 3s ≥ 2s ⇒ 3500 ≥ 5s ⇒ s ≤ 700. At s = 700: a = 3500 − 21002 = 700, c = 100. All non-negative and s ≤ a. So maximum science = 700.
Q68Quantitative Ability·Logarithms

The sum of all possible real values of x for which logx−3(x2 − 9) = logx−3(x + 1) + 2, is

  • A−3
  • B33
  • C3 + 332Correct answer
  • D3

Answer: C

Show explanation
Answer:C (3 + 332) logx−3(x2 − 9) = logx−3(x + 1) + 2. Domain: base x − 3 > 0, x − 3 ≠ 1 ⇒ x > 3, x ≠ 4; arguments positive: x2 − 9 > 0 (true for x > 3) and x + 1 > 0. Rewrite: log_b(x2 − 9) − log_b(x + 1) = 2 with b = x − 3 ⇒ log_b( x2 − 9x + 1 ) = 2 ⇒ (x − 3) x + 3x + 1 = (x − 3)2 (since x2 − 9 = (x − 3)(x + 3)). For x ≠ 3: x + 3x + 1 = x − 3 ⇒ x + 3 = (x − 3)(x + 1) = x2 − 2x − 3 ⇒ 0 = x2 − 3x − 6 ⇒ x = 3 ± 332. Only x = 3 + 332 > 3 and ≠ 4 lies in the domain. (The negative root is less than 3.) Sum of all possible real values is just that one root → C.

Answer key

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

Q#SectionAnswerTopic
1VARCAReading Comprehension
2VARC1Verbal Ability
3VARCCReading Comprehension
4VARCBReading Comprehension
5VARCCReading Comprehension
6VARCBReading Comprehension
7VARCCReading Comprehension
8VARCBReading Comprehension
9VARCDReading Comprehension
10VARCDReading Comprehension
11VARCDReading Comprehension
12VARCAReading Comprehension
13VARCAReading Comprehension
14VARCCReading Comprehension
15VARC2143Verbal Ability
16VARCAReading Comprehension
17VARC4312Verbal Ability
18VARC3Verbal Ability
19VARCAVerbal Ability
20VARCAVerbal Ability
21VARCDReading Comprehension
22VARCDReading Comprehension
23VARCAReading Comprehension
24VARCAReading Comprehension
25DILR50Logical Reasoning
26DILR525Logical Reasoning
27DILR350Logical Reasoning
28DILRALogical Reasoning
29DILR41000Data Interpretation
30DILR13000Data Interpretation
31DILR1500Data Interpretation
32DILRBData Interpretation
33DILRAData Interpretation
34DILRCData Interpretation
35DILR2Data Interpretation
36DILR6Data Interpretation
37DILRCData Interpretation
38DILR48Data Interpretation
39DILR200Data Interpretation
40DILR1008Data Interpretation
41DILRAData Interpretation
42DILRBData Interpretation
43DILRALogical Reasoning
44DILRBLogical Reasoning
45DILRALogical Reasoning
46DILRDLogical Reasoning
47QABQuantitative Ability
48QADQuantitative Ability
49QAAQuantitative Ability
50QAAQuantitative Ability
51QADQuantitative Ability
52QAAQuantitative Ability
53QAAQuantitative Ability
54QAAQuantitative Ability
55QADQuantitative Ability
56QA444Quantitative Ability
57QADQuantitative Ability
58QA126Quantitative Ability
59QA16Quantitative Ability
60QA65Quantitative Ability
61QA397Quantitative Ability
62QA272Quantitative Ability
63QACQuantitative Ability
64QACQuantitative Ability
65QABQuantitative Ability
66QA112Quantitative Ability
67QA700Quantitative Ability
68QACQuantitative Ability

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