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CAT Mock Test- 3 - CAT MCQ


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66 Questions MCQ Test CAT Mock Test Series - CAT Mock Test- 3

CAT Mock Test- 3 for CAT 2024 is part of CAT Mock Test Series preparation. The CAT Mock Test- 3 questions and answers have been prepared according to the CAT exam syllabus.The CAT Mock Test- 3 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Mock Test- 3 below.
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CAT Mock Test- 3 - Question 1

According to the author, Deja vu is almost impossible to study because:

Detailed Solution for CAT Mock Test- 3 - Question 1

The author states that " Déjà vu is almost impossible to study — people are rarely hooked up to electrodes or undergoing internal scans when they experience it — so most information about the sensation comes from self-reports". Hence, it is not possible to conduct detailed laboratory studies, as the experience occurs randomly. As a result, most of the information about Deja-vu is based on anecdotal evidence. Option C aptly captures the point elucidated above (especially the part highlighting the unpredictability of the experience).

Option A is wrong. It talks about mental sensations - an idea that is irrelevant to the discussion.

Option B is not the reason. Instead, it serves to exemplify a potential outcome of Déjà vu being random. Because of the dearth of scientific information concerning this phenomenon, we largely depend on anecdotal evidence. Option B is incorrect.

Option D can be eliminated as it has not been implied in the passage.

Hence, Option C is the correct choice.

CAT Mock Test- 3 - Question 2

Which of the following statements CANNOT be inferred from the passage?

Detailed Solution for CAT Mock Test- 3 - Question 2

{Déjà vu — French for “already seen” — is a mental sensation of intense familiarity coupled with the awareness that the familiarity is mistaken. It’s a recognition we know is wrong, a memory we know doesn’t exist.} Option A can be inferred from these lines.

The third and fourth paragraphs discuss two theories that are backed by experimental findings. Option B can be inferred.

{Human memory is notoriously faulty and malleable.} Option C can be inferred as well.

Option D is a distortion; the author states that "déjà vu becomes more common when we are stressed and tired." However, the corollary may not necessarily true. It is not necessary that most people who experience are tired or stressed. Hence, option D cannot be inferred.

CAT Mock Test- 3 - Question 3

Which of the following is NOT one of the theories attempting to explain deja-vu?

Detailed Solution for CAT Mock Test- 3 - Question 3

In the passage, the author presents three theories that attempt to explain the occurrence of Deja-vu;

1)Deja-vu isn’t a sign of faulty memory, so much as it’s a sign of a well-functioning brain that actively fact-checks itself.

2)Our stored memories still influence our present perception even if we can’t consciously recall them.

3)Déjà vu occurs when a familiar object appears incongruously.

Options A, C and D are valid. 

Option B is close to the first theory but incorrect. The author does not say that the two regions have conflicting responses to the same stimuli. The second half of the option is out of the scope of the passage.

CAT Mock Test- 3 - Question 4

In the first paragraph, what is the "conflict" that the author refers to?

Detailed Solution for CAT Mock Test- 3 - Question 4

The author makes the following observation-"This conflict between what we know and what we remember is why déjà vu feels so eerie — almost paranormal or out-of-body." The person is aware that the memory doesn't exist but is still trying to discern if he remembers correctly and whether his awareness is indeed true. Option B conveys this inference and is the answer.

All other options are either tangential to the discussion or do not convey the above point.

Option C is wrong. The author does not mention the simultaneous nature of sensation and awareness.

Options A is extraneous to the discussion.

Option D is an exaggeration where it says that people doubt their sense of reality.

CAT Mock Test- 3 - Question 5

Authoritarian political systems echo monotheistic religions in that:

Detailed Solution for CAT Mock Test- 3 - Question 5

The following excerpt enables us to determine the correct choice: "...From this perspective, authoritarian political systems echo monotheistic religions. Like God himself, the leader is omniscient, omnipotent and omnibenevolent. His words define the horizons of reality. He must be praised and appeased, but never challenged. His enemies are, by definition, in league with the forces of evil..."

Option A: The author doesn't assert that authoritarian leaders exploit our vulnerabilities; nor does he label the followers as politically disillusioned. Hence, Option A is not implied.

Option B: The author does not mention any expectation, on the part of the followers, concerning deliverance from human helplessness. While he highlights how this facet forms the root of our vulnerabilities, he does not use this to correlate authoritarian systems and monotheistic religion. Thus, Option B can be rejected.

Option C: This aspect is presented as a belief of the followers and not as a true capability of the leader; the author does not assert that authoritarian leaders have the capacity to "define horizons of reality" (this is how the followers perceive them to be). The statement here appears to be definitive, and hence, goes beyond the scope of the discussion. Thus, Option C can be discarded.   

Option D: This highlights one of the points that the author mentions: "...He must be praised and appeased, but never challenged. His enemies are, by definition, in league with the forces of evil..."

Hence, Option D is the correct choice.

CAT Mock Test- 3 - Question 6

The purpose of the first three paragraphs is to

Detailed Solution for CAT Mock Test- 3 - Question 6

The author highlights how Plato was one of the first eminent thinkers to deliberate on the concept of tyranny. His opinion on this topic is discussed briefly in the first paragraph. This is followed by Weber's version of the same subject in the second paragraph. The author mentions the idea of a 'charismatic leader' and relates it to the underlying beliefs of the followers of a tyrant. Subsequently, the author discusses two main ideas stemming from Freud's study of the psychological dynamics of followership. The ideas are briefly presented in the third paragraph, followed by their implications (in the fourth paragraph). Thus, the author intends to describe the manner in which different eminent thinkers have conceptualised the idea of tyranny and followership. Option B aptly captures this point.

Option A: The author does not attempt to contrast 'a modern take' on tyranny and an 'earlier/older version'. Neither of these categories has been understandably identified in the passage. Hence, Option A can be eliminated. 

Option C: The statement here has subtle distortions and differs in the intended meaning. Plato has been labelled as "one of the first and most influential thinkers to address the problem of tyranny". Additionally, the claim in C implies that he is followed by Weber and Freud as perhaps the second and third individuals who worked on the idea of followership - a point that is not backed by any information. Thus, Option C can be rejected.

Option D: We cannot perceive the author's attitude as alarmed or concerned, nor does he attribute the establishment of authoritarian regimes to deluded followers. Hence, Option D can be discarded as the potential choice.

 Hence, Option B is the correct answer.

CAT Mock Test- 3 - Question 7

All of the following have not been discussed in the passage except:

Detailed Solution for CAT Mock Test- 3 - Question 7

Option A: The statement here coincide with the discussion undertaken in the following excerpt: "...There are clear links between Freud’s analysis of the religious impulse, and psychological forces at play in the political sphere. Politics is, explicitly, a response to human vulnerability. Our deepest hopes and fears permeate the political arena, and this makes us susceptible to political illusions, which are often clung to with such impassioned tenacity, and so refractory to reasoned argument, that they fit Freud’s characterisation of delusions..." Hence, Option A has been discussed in the passage.

Option B: The author mentions that: "Charismatic leaders inspire devotion, and are regarded as prophetic figures by their followers." However, we notice no cause-effect relationship presented; nor does the author shed light on the claim made in the latter half of Option B. Thus, we can reject B as the potential answer. 

Option C: The author makes the following comments: "...Religious convictions are Freud’s prime examples of delusions. They are, he wrote, ‘fulfillments of the oldest, strongest, and most urgent wishes of mankind. The wishes that underpin religious belief have to do with deliverance from human helplessness..." However, he does not contrast political convictions with the aforementioned idea; they are not presented as opposing elements but instead have similar underlying drivers. Hence, the comparison is C is not presented, and hence, we can eliminate it.

Option D: No such assertion has been made in the passage and thus, we can eliminate D.

Hence, Option A is the correct choice.

CAT Mock Test- 3 - Question 8

Which of the following cannot be said to be true based on the passage?

I. Submission of personal objectives for a greater collective cause is an essential feature of authoritarian regimes. 

II. According to the author, oppositions of the authoritarian leader are allies of evil.

III. Followers of monotheistic religions are highly supportive of authoritarian political systems.

Detailed Solution for CAT Mock Test- 3 - Question 8

Statement I: We observe that the author has discussed this point in the passage: "This intoxicating sense of unity, and the subordination of personal self-interest to a greater cause, is a very important component of authoritarian systems.". Hence, Statement I is true. 

Statement II: "He must be praised and appeased, but never challenged. His enemies are, by definition, in league with the forces of evil." The above lines from the passage covey a general idea/perception concerning similarities between an authoritarian government and monotheistic religion; it does not reflect the author's opinion. The author is simply describing the common underlying beliefs. 

Statement III: "From this perspective, authoritarian political systems echo monotheistic religions." The author draws a parallel between these two setups. However, it has not been implied that followers of monotheistic religions would be highly supportive of authoritarian political systems; we do not have sufficient information to substantiate this claim.

Hence, Option C is the correct choice.

CAT Mock Test- 3 - Question 9

Which of the following best describes the reason why the author terms the concept 'performative authenticity' paradoxical?

Detailed Solution for CAT Mock Test- 3 - Question 9

In the second and third paragraphs, the author advances the point that authenticity is intricately linked with self-realisation and self-appraisal, i.e., staying true to oneself. Hence, when someone 'performs' or 'builds' an authentic self that conforms to expectations, it is simply not authentic because authenticity is a natural state of being, not a manufactured one.

Comparing the options, only option B conveys this point.

Options A and D have not been implied in the passage. Option C is not incorrect but does not convey the larger point. 

Option B is the answer.

CAT Mock Test- 3 - Question 10

According to Charles Guignon, finding one's true self involves all of the following, EXCEPT:

Detailed Solution for CAT Mock Test- 3 - Question 10

{Finding your true self means self-reflection, engaging in candid self-appraisal and seeking ‘genuine self-knowledge’, in the words of the American philosopher Charles Guignon."}. So, self-reflection, self-appraisal and seeking self-knowledge are the three activities associated with finding one's true self, according to Charles Guignon.

Options A, B and C convey these activities. Option D has not been implied explicitly in the passage. Hence, option D is the answer. 

Option A talks about bonafide knowledge of one's characteristics, which is the same as, genuine self-knowledge.

Option B discusses introspection, part of self-realisation.

Self-appraisal refers to one's worth and significance. Option C conveys this

CAT Mock Test- 3 - Question 11

Which of the following statements is the author LEAST likely to agree with?

Detailed Solution for CAT Mock Test- 3 - Question 11

Option A: In the second paragraph, the author states that "...as an ethical ideal...authenticity means more than self-consistency or a lack of pretentiousness." So, though it is not limited to self-consistency, it is still an essential feature. And a self-consistent person would react similarly in familiar situations. Hence option A can be inferred. The author is bound to stand by his claim, and hence, we can eliminate this choice.

Option B: "...Authenticity in this ethical sense also had a critical edge, standing against and challenging the utilitarian practices and conformist tendencies of the conventional social and economic order. Society erects barriers that the authentic person must break through..." Thus, Option B echoes the author's opinion and can be eliminated as the potential answer. 

Option C: The author highlights the difference between performative and inner authenticity in the following manner: "...The inner ideal aims at a way of being that is unfeigned and without illusions. It resists the cultivation of an affirming audience, because being a ‘whole’ person, with a noninstrumental relation to self and others, is often at odds with the demands of society. In the performative mode, by contrast, this tension between self and society disappears. Self-elaboration still requires self-examination, but not necessarily of any inner or even aesthetic kind..." The author does not present a cause-effect relationship concerning performative authenticity not requiring external validation and the "disappearance of tension between the self and the society". He mentions that inner authenticity disregards or does not demand the "cultivation of an affirming audience" and the opposite applies to performative authenticity. Thus, performative authenticity does require an audience. Hence, the author is unlikely to agree with the statement in C since it conflicts with his assertions.  

Option D: "...In the performative mode, by contrast, this tension between self and society disappears. Self-elaboration still requires self-examination, but not necessarily of any inner or even aesthetic kind..." Option D can be inferred from these lines. Even in the performative mode, self-examination is necessary.

Hence, Option C is the correct answer.

CAT Mock Test- 3 - Question 12

The inner and performative modes of authenticity differ in all of the following ways, EXCEPT:

Detailed Solution for CAT Mock Test- 3 - Question 12

In the second paragraph, the author makes the following observation about inner mode - {Authenticity in this ethical sense also had a critical edge, standing against and challenging the utilitarian practices and conformist tendencies of the conventional social and economic order.} Furthermore, in the fourth paragraph, the author states that "Performative authenticity is tied to economic success and social prestige" Hence, option B can be inferred.

{Performative authenticity is tied to economic success and social prestige, which means... that your specialness and self-realisation have to be performed...The inner ideal aims at a way of being that is unfeigned and without illusions.} Option C can be inferred from these lines.

In the penultimate paragraph, the author remarks the following about performative mode-{Self-elaboration still requires self-examination, but not necessarily of any inner or even aesthetic kind.} Option D can be inferred as well.

This leaves us with option A. The former part of option A is true- {...they must ...positively affect others with their self-representations, personal characteristics and quality of life.}

However, the latter part has not been implied in the passage. The inner mode resists the cultivation of an affirming audience, true, but this cannot be equated to a lack of desire to affect others positively.

Option A is the answer.

CAT Mock Test- 3 - Question 13

Which of the following statements is definitely TRUE according to the passage?

Detailed Solution for CAT Mock Test- 3 - Question 13

In the first paragraph, the author states that the meteorite strike wiped out non-avian dinosaurs. However, the author does not discuss the fate of avian dinosaurs in the passage. Option A cannot be inferred.

The author states the following: "But researchers have had no idea how the event changed the tropical rain forests of Africa or, until now, those of South America." In the penultimate paragraph, the author notes that "Within moments of the Chicxulub meteorite’s impact, however, this ecosystem was irrevocably altered." This description, however, is only limited to South America's forest ecosystems. The author then extends on how these ecosystems changed drastically. However, no information is provided concerning forests in Africa; the author focuses solely on the alterations in the tropical rainforests of South America. Hence, Option B can be eliminated.

"Yet Western European and North American palaeontologists have paid little attention to tropical forests". This statement, however, does not imply that Asian and African palaeontologists majorly carried out the research. Option C can be eliminated as well.

{" Prior to the meteorite, the authors determined, South America’s forests featured many conifers and a brightly lit open canopy...As flowering species competed for light, they formed dense canopies of leaves and created the layered Amazon rain forest we know today.}

So, before the meteorite strike, the forests had open canopies, while currently, they have dense canopies. Option D can be inferred.

Hence, Option D is the correct choice.

CAT Mock Test- 3 - Question 14

According to the passage, academic and amateur fossil hunters paid little attention to tropical forests because:

Detailed Solution for CAT Mock Test- 3 - Question 14

{Many academic and amateur fossil hunters have also tended to write off warm, wet locales as a lost cause for finds because they have assumed that conditions there would prevent organic materials from being preserved long enough to fossilize.} From this line, it can be inferred that they believed the tropical climate did not favour the fossilization of organic materials. Comparing the options, option C conveys this inference.

All other options are either distorted or do not convey the above point, central to the discussion.

CAT Mock Test- 3 - Question 15

Which of the following statements CAN be inferred from the passage?

I. The tropical rain forest ecosystem would not have developed had the dinosaurs not gone extinct. 

II. Location of the impact crater is crucial to understanding the effects of the meteoritic collision.

III. The effects of the collision on African tropical rain forests were not known until recently.

IV. Fires caused by the meteoritic collision led to the depletion of soil nutrients.

Detailed Solution for CAT Mock Test- 3 - Question 15

In the penultimate paragraph, the author states that dinosaurs played a crucial role in maintaining the pre-meteoritic ecosystem. However, it has not been implied that their extinction was necessary for the new ecosystem to develop. It was merely a chain of events. Statment I cannot be inferred.

{Scientists already knew that the effects of the meteorite collision and its aftermath—at least in temperate zones—varied with local conditions and distance from the Chicxulub impact crater in Mexico’s Yucatán Peninsula.} Hence, the effects varied with distance from the crater. So the location of the crater is important. Statement II can be inferred.

{But researchers have had no idea how the event changed the tropical rain forests of Africa or, until now, those of South America.} The study is centred on the effects of the collision on South American forests. The effects on African tropical forests remain a mystery. Statement III is wrong.

Though the soil was deficient in nutrients for a long-time after the collision, the exact cause for this depletion has not been discussed in the passage. Statement iv cannot be inferred.

CAT Mock Test- 3 - Question 16

According to the passage, all of the following aided in the emergence of the Amazon rainforest ecosystem, EXCEPT:

Detailed Solution for CAT Mock Test- 3 - Question 16

The passage does not discuss the impact of rainfall anywhere. Hence, option C is the answer.

All the other options can be inferred from the information presented in the last paragraph. {This influx of nitrogen, along with phosphorus from the meteorite’s ash, enabled other flowering plants to thrive alongside the legumes and to displace conifers. As flowering species competed for light, they formed dense canopies of leaves and created the layered Amazon rain forest we know today.}

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 17

DIRECTIONS for the question: The four sentences (labelled 1, 2, 3, 4) 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. Competition is the driving force behind the real benefits such systems achieve, but the logic of competition also imprisons its players to stay within their roles.
  2. Liberal democracy is like capitalism, a game designed to make its players compete against each other for points and prizes.
  3. As a result, democracies are surprisingly vulnerable to take over, as we have seen from the recent examples of Turkey, Hungary, and India.
  4. It is no one's job to defend the system of rules governing that competition.

Detailed Solution for CAT Mock Test- 3 - Question 17

After reading the given collection of statements, we identify that the core of the discussion appears to be liberal democracies and the inherent limitations associated with them. Statement 2 (independent sentence) first introduces us to this subject and sets the context, comparing liberal democracy to capitalism and subsequently to a competition/game. Sentence 1 follows 2 because the phrase 'such systems' (in 1) refers to liberal democracy and capitalism, discussed in the opening sentence. The author also describes the limitation originating from such competition: "imprisons its players to stay within their roles". Sentence 4 follows 1- 'that competition' (in 4) refers to the competition described in 1. Additionally, it adds to the preceding point that discusses the limitations. Finally, 3 ends the paragraph as it discusses a consequence of the drawback mentioned in 4. Hence, 2143 is the answer.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 18

DIRECTIONS for the question: The four sentences (labelled 1, 2, 3, 4) 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. By definition, parasites live in or on a host and take something from that host.
  2. Scientists warn of dire consequences if we disregard the rest.
  3. This has made them the pariahs of the animal world.
  4. But not all parasites cause noticeable harm to their hosts, and only a small percentage affect humans.

Detailed Solution for CAT Mock Test- 3 - Question 18

Sentence 1 is the opening line, as it introduces the subject of discussion-parasites. 3 follows 1. Because of the behaviour mentioned in 1, parasites are seen as pariahs or outcasts. 42 form a bloc. 4 discusses the other side associated with parasites and why they may not be all bad. And 2 builds on 4, urging us to consider this other side.  Hence, the correct order is 1342

CAT Mock Test- 3 - Question 19

The passage given below is followed by four summaries. Choose the option that best captures the author’s position.

The magnitude of plastic packaging that is used and casually discarded — air pillows, Bubble Wrap, shrink wrap, envelopes, bags — portends gloomy consequences. These single-use items are primarily made from polyethylene, though vinyl is also used. In marine environments, this plastic waste can cause disease and death for coral, fish, seabirds and marine mammals. Plastic debris is often mistaken for food, and microplastics release chemical toxins as they degrade. Data suggests that plastics have infiltrated human food webs and placentas. These plastics have the potential to disrupt the endocrine system, which releases hormones into the bloodstream that help control growth and development during childhood, among many other important processes.

Detailed Solution for CAT Mock Test- 3 - Question 19

The passage predicts the dreary consequences of mounting plastic waste; it infiltrates both marine and human food webs. It causes disease and death in marine organisms, whereas by infiltrating human food webs, it inhibits growth and development during childhood.

Option A focuses on plastic usage, whereas the author is more concerned about plastic waste. Option A can be eliminated.

Option B talks about the effect on the quality of life, which has not been implied in the passage.

Option C covers all the key points discussed above. Option C is the answer.

Option D is close but is too narrow as it mentions only unprocessed plastic. The author does not make an explicit distinction. 

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 20

Five jumbled-up sentences, related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd one out and key in the number of the sentence as your answer.

1. Over the past fortnight, one of its finest and most celebrated champions managed to match Winbeldon's grandeur again.

2. Wimbledon’s grandeur and enigma evoke a sense of timelessness and mystique.

3. At 35 years and 342 days, Roger Federer was crowned the Wimbledon champion for the 8th time thereby becoming the oldest man to win the Wimbledon singles title in the open era.

4. Once he had won the first three rounds, the semi-finals and finals witnessed the true magic of a rested Federer

5. Given that his game isn’t reliant on explosive athleticism or muscular power ball striking, both of which are vulnerable to decay with age, there is a high chance that the reign of King Federer will continue further into the future


Detailed Solution for CAT Mock Test- 3 - Question 20
  • The whole passage revolves around the t imelessness of Wimbledon and Roger Federrer.
  • Statement 1, 2 and 3 are connected as they define the timelessness of Wimbledon and Roger Federrer.
  • Statement 4 and 5 are close. But statement 4 talks about only a particular event
  • Statement 5 via the phrase 'in to the future' connects with the central theme of timelessness

Hence Statement 4 is the odd one out.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 21

Five jumbled-up sentences, related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd one out and key in the number of the sentence as your answer.

1. Quantum computing harnesses the peculiar dynamics of quantum physics to process information in novel ways.

2. Classical computing, the traditional form, operates with binary bits using 0s and 1s in a linear sequence.

3. The advent of quantum algorithms promises resolutions to complex problems unreachable by current machines.

4. These systems are revolutionizing climate study simulations with their advanced modeling.

5. In stark contrast, quantum bits, or qubits, can hold a vast amount of information, expanding computational boundaries exponentially.


Detailed Solution for CAT Mock Test- 3 - Question 21
  • Statements 1, 2, 3, and 5 form a cohesive explanation of quantum computing, contrasting it with classical computing and emphasizing the revolutionary capacity of quantum systems.
  • Statement 4, which specifically relates quantum computing to climate studies, diverges from the general theme of defining quantum computing and its fundamental differences from classical computing.
*Answer can only contain numeric values
CAT Mock Test- 3 - Question 22

Direction: Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.

1. This is only partially true because while most of the fighting did take place on the continent, one of the largest and most sophisticated undertakings of the war was conducted mainly at sea.

2. While the land war certainly contributed to the Entente's (Britain, France, Italy, U.S.) victory in 1918, it was the blockade that truly broke Germany's back.

3. This operation was the British blockade from 1914-1919 which sought to obstruct Germany's ability to import goods, and thus in the most literal sense starve the German people and military into submission.

4. The First World War is largely thought of as a conflict where the majority of the significant operations took place almost exclusively on mainland Europe with the exception of a handful of naval clashes fought throughout the world's oceans.


Detailed Solution for CAT Mock Test- 3 - Question 22

While arranging the parts of the paragraph, we should find some grammatical or contextual connections between them -

  • 4 is the first sentenceas it is an independent sentence which is introducing the subject 'The First World War'. It means that the First World War is widely regarded as a war in which the majority of significant operations took place on mainland Europe, and only a few naval battles were fought across the world's oceans. 
  • 1 is the second sentence as it says that ' this is only partially true '. From the phrase 'thought of as' in sentence 4, we can understand that it was just a perception or an opinion and it may or may not be true. 
  • 3 is the third sentence as the phrase 'this operation' is referring to the major operation that was conducted at sea. It means that the operation at sea was the British blockade that sought to obstruct Germany's ability to import goods. 
  • 2 is the last sentence as it says that the war that took place on land contributed to the victory of the allies (Britain, France, Italy, and the United States) in 1918, and it resulted in Germany's destruction.

Thus, the correct order is 4132:

  • 4: The First World War is largely thought of as a conflict where the majority of the significant operations took place almost exclusively on mainland Europe with the exception of a handful of naval clashes fought throughout the world's oceans. 
  • 1: This is only partially true because while most of the fighting did take place on the continent, one of the largest and most sophisticated undertakings of the war was conducted mainly at sea. 
  • 3: This operation was the British blockade from 1914-1919 which sought to obstruct Germany's ability to import goods, and thus in the most literal sense starve the German people and military into submission.
  • 2: While the land war certainly contributed to the Entente's (Britain, France, Italy, U.S.) victory in 1918, it was the blockade that truly broke Germany's back.
CAT Mock Test- 3 - Question 23

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

The debate over artificial intelligence's threats and promises is multifaceted. Critics argue that AI could eventually surpass human intelligence, making decisions incompatible with human survival. However, proponents believe AI, guided by regulations, has the potential to eradicate poverty and disease. The crux of the matter lies not in AI's capabilities but in human management.

Detailed Solution for CAT Mock Test- 3 - Question 23

The passage pivots on the idea that the essence of the AI debate is human management, not the potential of AI itself. Option C captures this without introducing new concepts or misrepresenting the passage's content.

CAT Mock Test- 3 - Question 24

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

Globalization promised an interconnected world, but it also led to significant parts of entire populations feeling left behind, stirring discontent and sociopolitical backlash. This unintended consequence has seen the rise of protectionism and nationalism, as those adversely affected seek to reclaim control over their economic prospects.

Detailed Solution for CAT Mock Test- 3 - Question 24

Option A succinctly summarizes the passage, highlighting the key theme: the unintended rise of protectionism and nationalism as a reaction to the negative repercussions of globalization.

CAT Mock Test- 3 - Question 25

Who picked a Purple ball in round 3?

Detailed Solution for CAT Mock Test- 3 - Question 25

The total number of times balls were picked is 4*4 = 16, i.e. all the balls Red, Blue, Yellow, Green and Purple were together picked a total of 16 times. Total points earned because of Yellow ball was 18 and available points are 1, 3, 5, 7 and 11 from these points. There is only possibility of making 18, which is when 3 points ball was picked 6 times. Therefore, Yellow ball was picked 6 times and carries 3 points. All balls were picked a total of 16 times out of which Yellow ball was picked 6 times and hence rest of the 4 balls were picked a total of 10 times. If each ball was picked at least once, then the only one way in which balls could have been picked is 1, 2, 3 and 4 times in any order. Red ball was picked in each round; therefore, Red ball was picked 4 times. Purple ball was picked more times than Green ball but less times than Blue ball; therefore, Purple ball was picked 2 times whereas Green and Blue balls were picked 1 and 3 times, respectively. The following table shows the points and the number of times a ball was picked:

Since Yellow ball was picked 6 times, this is the ball which was picked more than once in the last round. If in every other round, no 2 persons had picked the same ball. Then, there are two cases: 1. Yellow ball was picked by everyone in the last round and 2 other times in 2 other rounds 2. Yellow ball was picked by 3 friends in the last round and 3 other times in 3 other rounds. But Red ball was picked in every round; hence, case 1 is not possible. Therefore, Yellow ball was picked by 3 friends in the last round and 3 other times in 3 other rounds. P picked a Yellow ball in round 2; hence, P cannot pick a Yellow ball in round 4 because P, R and S picked different balls in each round. Therefore, Q, R and S picked a Yellow ball in the last round; and since Red ball was picked in every round, P picked a Red ball in the last round. P picked a Yellow ball in round 2. R and S picked different balls in each round; therefore, they could not have picked a Yellow ball in any other round but still Yellow ball is to be picked 2 times. Therefore, Yellow ball was picked 2 more times by Q and since Q picked Red ball in round 2, he would have picked a Yellow ball in round 1 and round 3. This information is given in the table shown below:

R picked the ball which was picked only in round 2, i.e. R picked a Green ball in round 2. Blue ball was picked 3 times; hence, it was picked in round 1, 2 and 3. In round 2, only S is the one whose ball colour is not known, so it should be Blue. P and R picked a Blue ball in round 1 and round 3 in any order. R and S picked a Red ball in round 1 and round 3 in any order. Purple ball was picked by P and S in round 1 and round 3 in any order. The final table is as given below:

Therefore, it cannot be determined who picked a Purple ball in round 3.
Hence, option 4 is the correct answer.

CAT Mock Test- 3 - Question 26

Winner is the person scoring the highest points at the end of all the rounds. Who is the winner?

Detailed Solution for CAT Mock Test- 3 - Question 26

The total number of times balls were picked is 4 × 4 = 16, i.e. all the balls Red, Blue, Yellow, Green and Purple were together picked a total of 16 times. Total points earned because of Yellow ball was 18 and available points are 1, 3, 5, 7 and 11 from these points. There is only possibility of making 18, which is when 3 points ball was picked 6 times. Therefore, Yellow ball was picked 6 times and carries 3 points. All balls were picked a total of 16 times out of which Yellow ball was picked 6 times and hence rest of the 4 balls were picked a total of 10 times. If each ball was picked at least once, then the only one way in which balls could have been picked is 1, 2, 3 and 4 times in any order. Red ball was picked in each round; therefore, Red ball was picked 4 times. Purple ball was picked more times than Green ball but less times than Blue ball; therefore, Purple ball was picked 2 times whereas Green and Blue balls were picked 1 and 3 times, respectively. The following table shows the points and the number of times a ball was picked:

Since Yellow ball was picked 6 times, this is the ball which was picked more than once in the last round. If in every other round, no 2 persons had picked the same ball. Then, there are two cases: 1. Yellow ball was picked by everyone in the last round and 2 other times in 2 other rounds 2. Yellow ball was picked by 3 friends in the last round and 3 other times in 3 other rounds. But Red ball was picked in every round; hence, case 1 is not possible. Therefore, Yellow ball was picked by 3 friends in the last round and 3 other times in 3 other rounds. P picked a Yellow ball in round 2; hence, P cannot pick a Yellow ball in round 4 because P, R and S picked different balls in each round. Therefore, Q, R and S picked a Yellow ball in the last round; and since Red ball was picked in every round, P picked a Red ball in the last round. P picked a Yellow ball in round 2. R and S picked different balls in each round; therefore, they could not have picked a Yellow ball in any other round but still Yellow ball is to be picked 2 times. Therefore, Yellow ball was picked 2 more times by Q and since Q picked Red ball in round 2, he would have picked a Yellow ball in round 1 and round 3. This information is given in the table shown below:

R picked the ball which was picked only in round 2, i.e. R picked a Green ball in round 2. Blue ball was picked 3 times; hence, it was picked in round 1, 2 and 3. In round 2, only S is the one whose ball colour is not known, so it should be Blue. P and R picked a Blue ball in round 1 and round 3 in any order. R and S picked a Red ball in round 1 and round 3 in any order. Purple ball was picked by P and S in round 1 and round 3 in any order. The final table is as given below:

Points scored by P = 1 + 5 + 3 + 7 = 16
Points scored by Q = 3 × 3 + 7 = 16
Points scored by R = 5 + 9 + 7 + 3 = 24
Points scored by S = 7 + 5 + 1 + 3 = 16
Therefore, R is the winner.
Hence, option C is the correct answer.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 27

How many more minimum conditions are required to find who picked what in all the rounds?


Detailed Solution for CAT Mock Test- 3 - Question 27

The total number of times balls were picked is 4 × 4 = 16, i.e. all the balls Red, Blue, Yellow, Green and Purple were together picked a total of 16 times. Total points earned because of Yellow ball was 18 and available points are 1, 3, 5, 7 and 11 from these points. There is only possibility of making 18, which is when 3 points ball was picked 6 times. Therefore, Yellow ball was picked 6 times and carries 3 points. All balls were picked a total of 16 times out of which Yellow ball was picked 6 times and hence rest of the 4 balls were picked a total of 10 times. If each ball was picked at least once, then the only one way in which balls could have been picked is 1, 2, 3 and 4 times in any order. Red ball was picked in each round; therefore, Red ball was picked 4 times. Purple ball was picked more times than Green ball but less times than Blue ball; therefore, Purple ball was picked 2 times whereas Green and Blue balls were picked 1 and 3 times, respectively. The following table shows the points and the number of times a ball was picked:

Since Yellow ball was picked 6 times, this is the ball which was picked more than once in the last round. If in every other round, no 2 persons had picked the same ball. Then, there are two cases: 1. Yellow ball was picked by everyone in the last round and 2 other times in 2 other rounds 2. Yellow ball was picked by 3 friends in the last round and 3 other times in 3 other rounds. But Red ball was picked in every round; hence, case 1 is not possible. Therefore, Yellow ball was picked by 3 friends in the last round and 3 other times in 3 other rounds. P picked a Yellow ball in round 2; hence, P cannot pick a Yellow ball in round 4 because P, R and S picked different balls in each round. Therefore, Q, R and S picked a Yellow ball in the last round; and since Red ball was picked in every round, P picked a Red ball in the last round. P picked a Yellow ball in round 2. R and S picked different balls in each round; therefore, they could not have picked a Yellow ball in any other round but still Yellow ball is to be picked 2 times. Therefore, Yellow ball was picked 2 more times by Q and since Q picked Red ball in round 2, he would have picked a Yellow ball in round 1 and round 3. This information is given in the table shown below:

R picked the ball which was picked only in round 2, i.e. R picked a Green ball in round 2. Blue ball was picked 3 times; hence, it was picked in round 1, 2 and 3. In round 2, only S is the one whose ball colour is not known, so it should be Blue. P and R picked a Blue ball in round 1 and round 3 in any order. R and S picked a Red ball in round 1 and round 3 in any order. Purple ball was picked by P and S in round 1 and round 3 in any order. The final table is as given below:

It is clear that even if we know which coloured ball P, R or S picked in round 1 or 3, we'll know who picked what in each round.
Therefore, 1 more condition is required.

CAT Mock Test- 3 - Question 28

If points scored by R in round 3 were 5, what was the colour of the ball picked by S in round 1?

Detailed Solution for CAT Mock Test- 3 - Question 28

The total number of times balls were picked is 4 × 4 = 16, i.e. all the balls Red, Blue, Yellow, Green and Purple were together picked a total of 16 times. Total points earned because of Yellow ball was 18 and available points are 1, 3, 5, 7 and 11 from these points. There is only possibility of making 18, which is when 3 points ball was picked 6 times. Therefore, Yellow ball was picked 6 times and carries 3 points. All balls were picked a total of 16 times out of which Yellow ball was picked 6 times and hence rest of the 4 balls were picked a total of 10 times. If each ball was picked at least once, then the only one way in which balls could have been picked is 1, 2, 3 and 4 times in any order. Red ball was picked in each round; therefore, Red ball was picked 4 times. Purple ball was picked more times than Green ball but less times than Blue ball; therefore, Purple ball was picked 2 times whereas Green and Blue balls were picked 1 and 3 times, respectively. The following table shows the points and the number of times a ball was picked:

Since Yellow ball was picked 6 times, this is the ball which was picked more than once in the last round. If in every other round, no 2 persons had picked the same ball. Then, there are two cases: 1. Yellow ball was picked by everyone in the last round and 2 other times in 2 other rounds 2. Yellow ball was picked by 3 friends in the last round and 3 other times in 3 other rounds. But Red ball was picked in every round; hence, case 1 is not possible. Therefore, Yellow ball was picked by 3 friends in the last round and 3 other times in 3 other rounds. P picked a Yellow ball in round 2; hence, P cannot pick a Yellow ball in round 4 because P, R and S picked different balls in each round. Therefore, Q, R and S picked a Yellow ball in the last round; and since Red ball was picked in every round, P picked a Red ball in the last round. P picked a Yellow ball in round 2. R and S picked different balls in each round; therefore, they could not have picked a Yellow ball in any other round but still Yellow ball is to be picked 2 times. Therefore, Yellow ball was picked 2 more times by Q and since Q picked Red ball in round 2, he would have picked a Yellow ball in round 1 and round 3. This information is given in the table shown below:

R picked the ball which was picked only in round 2, i.e. R picked a Green ball in round 2. Blue ball was picked 3 times; hence, it was picked in round 1, 2 and 3. In round 2, only S is the one whose ball colour is not known, so it should be Blue. P and R picked a Blue ball in round 1 and round 3 in any order. R and S picked a Red ball in round 1 and round 3 in any order. Purple ball was picked by P and S in round 1 and round 3 in any order. The final table is as given below:

If R scored 5 points in round 3, then he must have picked Blue in round 3.
Therefore, S must have picked a Purple coloured ball in round 1.
Hence, option 1 is the correct answer.

CAT Mock Test- 3 - Question 29

Whose total ticket cost is minimum?

Detailed Solution for CAT Mock Test- 3 - Question 29

From (2), (7) and (8):

From (4), ticket cost of `D` is the highest, that means he did not get Rs. 50 ticket; and from (3), the ticket cost is different for all the five friends. So, one has to get all Rs. 50 tickets.
So, he is `C`, because all A, B, D, E, went to M2 for 4th show, which is not Rs. 50, because `D` did not get Rs. 50 ticket.
But `D` watched all the four movies. So, he should watch M4 in 2nd show (because M3 costs Rs. 50) and M3 in 1st show.
From (1), B went to M1 in 1st show.
So, the table becomes as follows:

From (5), C and E watch 1st show together, because, `C` doesn`t go for M1 and M2 in 3rd and 4th shows.
From (2), B`s cost is more than `E`.
So, B got only one Rs. 50 ticket and E got two Rs. 50 tickets. (From (5)).
So, A got three Rs. 50 tickets.
So, the Rs. 50 tickets are for M4, M3, M2 and M1, respectively for 1st, 2nd, 3rd and 4th shows.
So, the complete table is as follows:

CAT Mock Test- 3 - Question 30

How many among these 5 watched all the four movies?

Detailed Solution for CAT Mock Test- 3 - Question 30

From (2), (7) and (8):

From (4), ticket cost of `D` is the highest, that means he did not get Rs. 50 ticket; and from (3), the ticket cost is different for all the five friends. So, one has to get all Rs. 50 tickets.
So, he is `C`, because all A, B, D, E, went to M2 for 4th show, which is not Rs. 50, because `D` did not get Rs. 50 ticket.
But `D` watched all the four movies. So, he should watch M4 in 2nd show (because M3 costs Rs. 50) and M3 in 1st show.
From (1), B went to M1 in 1st show.
So, the table becomes as follows:

From (5), C and E watch 1st show together, because, `C` doesn`t go for M1 and M2 in 3rd and 4th shows.
From (2), B`s cost is more than `E`.
So, B got only one Rs. 50 ticket and E got two Rs. 50 tickets. (From (5)).
So, A got three Rs. 50 tickets.
So, the Rs. 50 tickets are for M4, M3, M2 and M1, respectively for 1st, 2nd, 3rd and 4th shows.
So, the complete table is as follows:

From above table it is clear that C,D and E watched all 4 movies.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 31

How many persons have more red cards than Joana?


Detailed Solution for CAT Mock Test- 3 - Question 31

Given that the sum of the number of cards with any person is an odd number, then, for each person, the number of one of the two colored cards with him must be an odd one and the other an even one.

From (4), Finch has 3 red cards. Since he has odd number of red cards, then he must be having even number of blue cards. Hence, his blue cards can be 2/4/6. However, he has less blue cards than at least 3 persons. Hence, he must have 2 blue cards.
From (6), Nick has 4 blue cards. Hence, his red cards can be 1/3/5. Since Finch has 3 red cards, Nick can have 1/5 red cards. From (6), he has more red cards than Harper. Hence, he cannot have 1 red card. Hence, Nick must have 5 red cards.
From (2), Cody cannot have 1 or 2 blue cards (since Finch has 2 blue cards).
From (3), if Bill has 1 blue card, Harper must have 3 red cards. This is not possible as Finch has 3 red cards. Hence, Bill cannot have 1 blue card.
From (5), Harper can have 4/5/6 blue cards. Since Nick has 4 blue cards, Harper can have 5/6 blue cards.
Joana is the only person who can have 1 blue card.
From (5), Harper cannot have 1 red card and from (6), Harper cannot have 6 red cards. He also cannot have 3 or 5 red cards because Finch and Nick have 3 and 5 red cards, respectively. Hence, Harper can have 2/4 red cards. He must have odd number of blue cards (since he has even number of red cards). Therefore, Harper must have 5 blue cards.
If Harper has 2 red cards, Bill must have 4 blue cards, which is not possible as Nick has 4 blue cards. If Harper has 4 red cards, Bill must be having 6 blue cards (as Bill cannot have 4). This is the only possibility. Hence, Harper has 4 red cards and Bill has 6 blue cards.
Since Joana has 1 blue card, she must be having 2/4/6 red cards. From (5), Joana must have 2 red cards (since Harper has more red cards than Joana).
Since Bill has 6 blue cards, he must have 1 red card.
Cody has 3 blue cards and must have 6 red cards.

The following table provides the cards of each person.

Four persons (Finch, Harper, Nick and Cody) have more red cards than Joana.

CAT Mock Test- 3 - Question 32

How many Blue cards Cody Have?

Detailed Solution for CAT Mock Test- 3 - Question 32

Given that the sum of the number of cards with any person is an odd number, then, for each person, the number of one of the two colored cards with him must be an odd one and the other an even one.

From (4), Finch has 3 red cards. Since he has odd number of red cards, then he must be having even number of blue cards. Hence, his blue cards can be 2/4/6. However, he has less blue cards than at least 3 persons. Hence, he must have 2 blue cards.
From (6), Nick has 4 blue cards. Hence, his red cards can be 1/3/5. Since Finch has 3 red cards, Nick can have 1/5 red cards. From (6), he has more red cards than Harper. Hence, he cannot have 1 red card. Hence, Nick must have 5 red cards.
From (2), Cody cannot have 1 or 2 blue cards (since Finch has 2 blue cards).
From (3), if Bill has 1 blue card, Harper must have 3 red cards. This is not possible as Finch has 3 red cards. Hence, Bill cannot have 1 blue card.
From (5), Harper can have 4/5/6 blue cards. Since Nick has 4 blue cards, Harper can have 5/6 blue cards.
Joana is the only person who can have 1 blue card.
From (5), Harper cannot have 1 red card and from (6), Harper cannot have 6 red cards. He also cannot have 3 or 5 red cards because Finch and Nick have 3 and 5 red cards, respectively. Hence, Harper can have 2/4 red cards. He must have odd number of blue cards (since he has even number of red cards). Therefore, Harper must have 5 blue cards.
If Harper has 2 red cards, Bill must have 4 blue cards, which is not possible as Nick has 4 blue cards. If Harper has 4 red cards, Bill must be having 6 blue cards (as Bill cannot have 4). This is the only possibility. Hence, Harper has 4 red cards and Bill has 6 blue cards.
Since Joana has 1 blue card, she must be having 2/4/6 red cards. From (5), Joana must have 2 red cards (since Harper has more red cards than Joana).
Since Bill has 6 blue cards, he must have 1 red card.
Cody has 3 blue cards and must have 6 red cards.

The following table provides the cards of each person.

Cody has 3 blue cards.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 33

How many people have less cards than Harper in both blue and red colours?


Detailed Solution for CAT Mock Test- 3 - Question 33

Given that the sum of the number of cards with any person is an odd number, then, for each person, the number of one of the two colored cards with him must be an odd one and the other an even one.

From (4), Finch has 3 red cards. Since he has odd number of red cards, then he must be having even number of blue cards. Hence, his blue cards can be 2/4/6. However, he has less blue cards than at least 3 persons. Hence, he must have 2 blue cards.
From (6), Nick has 4 blue cards. Hence, his red cards can be 1/3/5. Since Finch has 3 red cards, Nick can have 1/5 red cards. From (6), he has more red cards than Harper. Hence, he cannot have 1 red card. Hence, Nick must have 5 red cards.
From (2), Cody cannot have 1 or 2 blue cards (since Finch has 2 blue cards).
From (3), if Bill has 1 blue card, Harper must have 3 red cards. This is not possible as Finch has 3 red cards. Hence, Bill cannot have 1 blue card.
From (5), Harper can have 4/5/6 blue cards. Since Nick has 4 blue cards, Harper can have 5/6 blue cards.
Joana is the only person who can have 1 blue card.
From (5), Harper cannot have 1 red card and from (6), Harper cannot have 6 red cards. He also cannot have 3 or 5 red cards because Finch and Nick have 3 and 5 red cards, respectively. Hence, Harper can have 2/4 red cards. He must have odd number of blue cards (since he has even number of red cards). Therefore, Harper must have 5 blue cards.
If Harper has 2 red cards, Bill must have 4 blue cards, which is not possible as Nick has 4 blue cards. If Harper has 4 red cards, Bill must be having 6 blue cards (as Bill cannot have 4). This is the only possibility. Hence, Harper has 4 red cards and Bill has 6 blue cards.
Since Joana has 1 blue card, she must be having 2/4/6 red cards. From (5), Joana must have 2 red cards (since Harper has more red cards than Joana).
Since Bill has 6 blue cards, he must have 1 red card.
Cody has 3 blue cards and must have 6 red cards.

The following table provides the cards of each person.

Only two persons have less cards than Harper in both blue and red colours.

CAT Mock Test- 3 - Question 34

Who has the same number of blue cards as the number of red cards with Bill?

Detailed Solution for CAT Mock Test- 3 - Question 34

Given that the sum of the number of cards with any person is an odd number, then, for each person, the number of one of the two colored cards with him must be an odd one and the other an even one.

From (4), Finch has 3 red cards. Since he has odd number of red cards, then he must be having even number of blue cards. Hence, his blue cards can be 2/4/6. However, he has less blue cards than at least 3 persons. Hence, he must have 2 blue cards.
From (6), Nick has 4 blue cards. Hence, his red cards can be 1/3/5. Since Finch has 3 red cards, Nick can have 1/5 red cards. From (6), he has more red cards than Harper. Hence, he cannot have 1 red card. Hence, Nick must have 5 red cards.
From (2), Cody cannot have 1 or 2 blue cards (since Finch has 2 blue cards).
From (3), if Bill has 1 blue card, Harper must have 3 red cards. This is not possible as Finch has 3 red cards. Hence, Bill cannot have 1 blue card.
From (5), Harper can have 4/5/6 blue cards. Since Nick has 4 blue cards, Harper can have 5/6 blue cards.
Joana is the only person who can have 1 blue card.
From (5), Harper cannot have 1 red card and from (6), Harper cannot have 6 red cards. He also cannot have 3 or 5 red cards because Finch and Nick have 3 and 5 red cards, respectively. Hence, Harper can have 2/4 red cards. He must have odd number of blue cards (since he has even number of red cards). Therefore, Harper must have 5 blue cards.
If Harper has 2 red cards, Bill must have 4 blue cards, which is not possible as Nick has 4 blue cards. If Harper has 4 red cards, Bill must be having 6 blue cards (as Bill cannot have 4). This is the only possibility. Hence, Harper has 4 red cards and Bill has 6 blue cards.
Since Joana has 1 blue card, she must be having 2/4/6 red cards. From (5), Joana must have 2 red cards (since Harper has more red cards than Joana).
Since Bill has 6 blue cards, he must have 1 red card.
Cody has 3 blue cards and must have 6 red cards.

The following table provides the cards of each person and the cards they have.

Joana has the same number of blue cards as number of red cards with Bill.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 35

How many red cards more/less does Harper have than Bill? Key in the number.


Detailed Solution for CAT Mock Test- 3 - Question 35

Given that the sum of the number of cards with any person is an odd number, then, for each person, the number of one of the two colored cards with him must be an odd one and the other an even one.

From (4), Finch has 3 red cards. Since he has odd number of red cards, then he must be having even number of blue cards. Hence, his blue cards can be 2/4/6. However, he has less blue cards than at least 3 persons. Hence, he must have 2 blue cards.
From (6), Nick has 4 blue cards. Hence, his red cards can be 1/3/5. Since Finch has 3 red cards, Nick can have 1/5 red cards. From (6), he has more red cards than Harper. Hence, he cannot have 1 red card. Hence, Nick must have 5 red cards.
From (2), Cody cannot have 1 or 2 blue cards (since Finch has 2 blue cards).
From (3), if Bill has 1 blue card, Harper must have 3 red cards. This is not possible as Finch has 3 red cards. Hence, Bill cannot have 1 blue card.
From (5), Harper can have 4/5/6 blue cards. Since Nick has 4 blue cards, Harper can have 5/6 blue cards.
Joana is the only person who can have 1 blue card.
From (5), Harper cannot have 1 red card and from (6), Harper cannot have 6 red cards. He also cannot have 3 or 5 red cards because Finch and Nick have 3 and 5 red cards, respectively. Hence, Harper can have 2/4 red cards. He must have odd number of blue cards (since he has even number of red cards). Therefore, Harper must have 5 blue cards.
If Harper has 2 red cards, Bill must have 4 blue cards, which is not possible as Nick has 4 blue cards. If Harper has 4 red cards, Bill must be having 6 blue cards (as Bill cannot have 4). This is the only possibility. Hence, Harper has 4 red cards and Bill has 6 blue cards.
Since Joana has 1 blue card, she must be having 2/4/6 red cards. From (5), Joana must have 2 red cards (since Harper has more red cards than Joana).
Since Bill has 6 blue cards, he must have 1 red card.
Cody has 3 blue cards and must have 6 red cards.

The following table provides the cards of each person and the cards they have.

Harper has 3 more red cards than Bill.

CAT Mock Test- 3 - Question 36

Which of the following is correct?

Detailed Solution for CAT Mock Test- 3 - Question 36

Given that the sum of the number of cards with any person is an odd number, then, for each person, the number of one of the two colored cards with him must be an odd one and the other an even one.

From (4), Finch has 3 red cards. Since he has odd number of red cards, then he must be having even number of blue cards. Hence, his blue cards can be 2/4/6. However, he has less blue cards than at least 3 persons. Hence, he must have 2 blue cards.
From (6), Nick has 4 blue cards. Hence, his red cards can be 1/3/5. Since Finch has 3 red cards, Nick can have 1/5 red cards. From (6), he has more red cards than Harper. Hence, he cannot have 1 red card. Hence, Nick must have 5 red cards.
From (2), Cody cannot have 1 or 2 blue cards (since Finch has 2 blue cards).
From (3), if Bill has 1 blue card, Harper must have 3 red cards. This is not possible as Finch has 3 red cards. Hence, Bill cannot have 1 blue card.
From (5), Harper can have 4/5/6 blue cards. Since Nick has 4 blue cards, Harper can have 5/6 blue cards.
Joana is the only person who can have 1 blue card.
From (5), Harper cannot have 1 red card and from (6), Harper cannot have 6 red cards. He also cannot have 3 or 5 red cards because Finch and Nick have 3 and 5 red cards, respectively. Hence, Harper can have 2/4 red cards. He must have odd number of blue cards (since he has even number of red cards). Therefore, Harper must have 5 blue cards.
If Harper has 2 red cards, Bill must have 4 blue cards, which is not possible as Nick has 4 blue cards. If Harper has 4 red cards, Bill must be having 6 blue cards (as Bill cannot have 4). This is the only possibility. Hence, Harper has 4 red cards and Bill has 6 blue cards.
Since Joana has 1 blue card, she must be having 2/4/6 red cards. From (5), Joana must have 2 red cards (since Harper has more red cards than Joana).
Since Bill has 6 blue cards, he must have 1 red card.
Cody has 3 blue cards and must have 6 red cards.

The following table provides the cards of each person and the cards they have.

The difference between the number of blue cards that Joana has and the number of red cards that Cody has is 5.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 37

Find the least possible number of Wagons in all the showrooms put together.


Detailed Solution for CAT Mock Test- 3 - Question 37

A = {Sedan, Coupe}
B = {SUV, Hatchback, Wagon}
Mr. Gray identifies cars of set A correctly and Mr. White identifies cars of set B correctly.
Now, if we look at the given information:
Mr. Gray identifies Sedans and Coupes correctly, i.e. if he looks at a Sedan, he identifies it as a Sedan and if he looks at a Coupe, he will identify that as a Coupe, and he cannot identify the other types of cars properly, i.e. if he looks at a Hatchback, he may name it as a Sedan/Coupe/SUV/Hatchback/Wagon.
If Mr. Gray says there are five Sedans in Showroom-A, there are not more than five Sedans in Showroom-A and similarly there are not more than 3 Coupes. But from Chart I, we cannot say anything definite about the other three varieties of cars.
Similarly, from the second chart, in Showroom-A, Mr. White is saying there are 14 cars of set B, the number of this set B cars is at most 14 and thus that of set A cars is at least 6.
Now by combining the information from Mr. Gray and Mr. White:
In Showroom-A, there are at least six and at most eight cars of set A and at least twelve and at most fourteen cars of set B.

Range of number of Cars:

We have to make the number of Wagons as least as possible. For that, the number of total cars of set B must be as least as possible and the other varieties of cars of set B must be maximum as possible. In Showroom-A, there must be only 12 cars of set B, there can be at most 2 Hatchbacks and 1 SUV.
There must be at least 9 Wagons. Similarly, in showrooms II, III, IV and V there must be at least 8, 8, 5 and 1 Wagons, respectively. There are at least 31 Wagons in total.

CAT Mock Test- 3 - Question 38

Find the least possible number of Wagons in all the showrooms put together.

Detailed Solution for CAT Mock Test- 3 - Question 38

A = {Sedan, Coupe}
B = {SUV, Hatchback, Wagon}
Mr. Gray identifies cars of set A correctly and Mr. White identifies cars of set B correctly.
Now, if we look at the given information:
Mr. Gray identifies Sedans and Coupes correctly, i.e. if he looks at a Sedan, he identifies it as a Sedan and if he looks at a Coupe, he will identify that as a Coupe, and he cannot identify the other types of cars properly, i.e. if he looks at a Hatchback, he may name it as a Sedan/Coupe/SUV/Hatchback/Wagon.
If Mr. Gray says there are five Sedans in Showroom-A, there are not more than five Sedans in Showroom-A and similarly there are not more than 3 Coupes. But from Chart I, we cannot say anything definite about the other three varieties of cars.
Similarly, from the second chart, in Showroom-A, Mr. White is saying there are 14 cars of set B, the number of this set B cars is at most 14 and thus that of set A cars is at least 6.
Now by combining the information from Mr. Gray and Mr. White:
In Showroom-A, there are at least six and at most eight cars of set A and at least twelve and at most fourteen cars of set B.

Range of number of Cars:

In Showroom-D, the least possible number of SUVs = least possible number of Cars of set B — (maximum possible number of (Hatchbacks + Wagons))
= 16 — (6 + 7) = 3.
Hence, (1) is false, whereas the other three statements can be true.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 39

If the number of Hatchbacks in Showroom-D is 6, then find the number of Coupes in Showroom-D.


Detailed Solution for CAT Mock Test- 3 - Question 39

A = {Sedan, Coupe}
B = {SUV, Hatchback, Wagon}
Mr. Gray identifies cars of set A correctly and Mr. White identifies cars of set B correctly.
Now, if we look at the given information:
Mr. Gray identifies Sedans and Coupes correctly, i.e. if he looks at a Sedan, he identifies it as a Sedan and if he looks at a Coupe, he will identify that as a Coupe, and he cannot identify the other types of cars properly, i.e. if he looks at a Hatchback, he may name it as a Sedan/Coupe/SUV/Hatchback/Wagon.
If Mr. Gray says there are five Sedans in Showroom-A, there are not more than five Sedans in Showroom-A and similarly there are not more than 3 Coupes. But from Chart I, we cannot say anything definite about the other three varieties of cars.
Similarly, from the second chart, in Showroom-A, Mr. White is saying there are 14 cars of set B, the number of this set B cars is at most 14 and thus that of set A cars is at least 6.
Now by combining the information from Mr. Gray and Mr. White:
In Showroom-A, there are at least six and at most eight cars of set A and at least twelve and at most fourteen cars of set B.

Range of number of Cars:

Number of Hatchbacks in Showroom-D = 6
One extra car which is identified as Hatchback by Mr. White must be from set A.
Total number of cars of set A must be at least 1 + 2 + 1, i.e. 4.
From the above table, the number of cars in set A must be exactly 4. Since Mr. Gray identified only 4 cars (2 Sedans and 2 Coupes) of set A, there are only 2 Coupes and 2 Sedans in Showroom-D.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 40

With the given information, in how many of the five showrooms can the number of SUVs be determined correctly?


Detailed Solution for CAT Mock Test- 3 - Question 40

A = {Sedan, Coupe}
B = {SUV, Hatchback, Wagon}
Mr. Gray identified cars of set A correctly and Mr. White identified cars of set B correctly.
Now, if we look at the given information.
Mr. Gray identified Sedans and Coupes correctly, i.e. if he looked at a Sedan, he identified it as a Sedan and if he looked at a Coupe, he would identify that as a Coupe, and he could not identify the other types of cars properly, i.e. if he looked at a Hatchback, he might name it as a Sedan / a Coupe / an SUV / a Hatchback / a Wagon.
If Mr. Gray said that there were five Sedans in Showroom-A, there were not more than five Sedans in Showroom-A; similarly in Showroom-A, there were not more than 3 Coupes, but from the first Chart, we cannot say anything definite about the other three types of cars.
Similarly, from the second chart, in Showroom-A, Mr. White said that there were 14 cars of set B, the number of this set B cars was at most 14 and thus that of set A cars was at least 6.
Now, by combining the pieces of information from Mr. Gray and Mr. White:
In Showroom-A, there were at least six and at most eight cars of set A and at least twelve and at most fourteen cars of set B.
Range of the Number of Cars:

As Mr. White (who identified SUVs as SUVs) identified only one SUV in Showroom-A, and there was at least one car of each type in each showroom, there was only one SUV in Showroom-A.
From the above table, we can say that in Showroom-C, the total number of cars in set A was 4 and that of in set B was 16.
As Mr. White identified 2 SUVs, 6 Hatchbacks and 8 Wagons in Showroom-C, which add up to 16, there would be exactly 2 SUVs in Showroom-C.
The number of SUVs in the other showrooms cannot be found uniquely.
Range of Individual Cars:

CAT Mock Test- 3 - Question 41

If the second ranker voted for IIM-B, then the fifth ranker definitely did not vote for

Detailed Solution for CAT Mock Test- 3 - Question 41

We represent IIM-A, IIM-B, IIM-C and IIM-I as A, B, C and I, respectively.
Now, from the given data, the following diagram can be formed:

If the second ranker voted for B, the fifth ranker voted for any among A, B and I.
So, he definitely did not vote for C.

CAT Mock Test- 3 - Question 42

If the third ranker voted for IIM-I, then the fifth ranker should have voted for

Detailed Solution for CAT Mock Test- 3 - Question 42

We represent IIM-A, IIM-B, IIM-C and IIM-I as A, B, C and I, respectively.
Now, from the given data, the following diagram can be formed:

If the third ranker voted for IIM-I, then the fifth ranker should have voted for either IIM-B or IIM-C.

CAT Mock Test- 3 - Question 43

If the fifth ranker voted for IIM-B, then the second ranker definitely did not vote for

Detailed Solution for CAT Mock Test- 3 - Question 43

We represent IIM-A, IIM-B, IIM-C and IIM-I as A, B, C and I, respectively.
Now, from the given data, the following diagram can be formed:

If the fifth ranker voted for IIM-B, then the second ranker definitely did not vote for IIM-I.

CAT Mock Test- 3 - Question 44

If the fifth ranker voted for IIM-B, then the third ranker definitely did not vote for

Detailed Solution for CAT Mock Test- 3 - Question 44

We represent IIM-A, IIM-B, IIM-C and IIM-I as A, B, C and I, respectively.
Now, from the given data, the following diagram can be formed:

If the fifth ranker voted for IIM-B, then the third ranker definitely did not vote for IIM-B.

CAT Mock Test- 3 - Question 45

A dishonest milkman sells milk to three customers- A, B and C. He replaces 20% of pure milk with water before selling to A. After this, he replaces 25% of the mixture with water before selling to B and furthermore 30% of the mixture is replaced before selling to C. What is the percentage of pure milk in the mixture sold by the milkman to C?

Detailed Solution for CAT Mock Test- 3 - Question 45

Since, the milk is getting replaced by water, we will use the formula M' = where M, r1, r2 and r3 are the milk's proportion in the beginning, % of milk replaced before selling to A, % of milk replaced before selling to B and % of milk sold before selling to C, respectively. 

Milk % before selling to C = M' = 

CAT Mock Test- 3 - Question 46

f(x) is a polynomial function of degree 4 such that f(0) = 1, f(1)=3 , f(2) = 9 and f(3) = 19.

What will be f(-1) if the coefficient of x4 is 2 in f(x)

Detailed Solution for CAT Mock Test- 3 - Question 46

f(0) = 1 = 2 × 02 + 1

f(1) = 3 = 2 × 12 + 1

f(2) = 9 = 2 × 22 + 1

f(3) = 19 = 2 × 32 + 1

Since f(x) is a 4 degree polynomial,

f(x) - (2x2 + 1) has 4 roots 0,1,2 and 3

thus f(x) = a(x) (x−1) (x−2) (x−3) + 2x+ 1

Coef of x4 is 2 in f(x) thus a = 2

f(x) = 2(x)(x−1)(x−2)(x−3) + 2x2 + 1

f(-1) = 2(−1)(−2)(−3)(−4)+ 2(−12)+1

f(-1) = 48+2+1 = 51

CAT Mock Test- 3 - Question 47

A cricket camp invited 500 cricket players who were batsmen, bowlers, and all-rounders(who can both bat and bowl). 60% of the players were batsman and 70% of them were bowlers. 50% of the pure batsmen (who can only bat), 60% of the pure bowlers (who can only bowl) and 20% of the all-rounders were left-handed. How many right-handed players were part of the cricket camp?

Detailed Solution for CAT Mock Test- 3 - Question 47

Given, there are 60% batsmen and 70% bowlers


So, (60-x) + x + (70-x) = 100

=> 130 - x = 100

.'. x = 30%

So, the team has 30% of pure batsman, 30% of all rounders and 40% of pure bowlers.

Left handed players = (50% of 30% of the team)+(60% of the 40% of team) + (20% of 30% of the team)

  = 75 + 120+30 = 225

The total number of right-handed players = 500 - 225 = 275. 

CAT Mock Test- 3 - Question 48

If x3 + 2x2−Ax has only one of its three real and unequal roots between [-1,3). Then the value of A can lie between?

Detailed Solution for CAT Mock Test- 3 - Question 48

The given equation can be written as (x2 + 2x − A) = 0

=> x = 0 is one such root which lie between 3 and -1.

=> x2 + 2x − A = 0 must not have a single root between 3 and -1 => f(3)*f(-1) > 0

=> (15-A) (-1-A) > 0

=> (A-15)(A+1) > 0

=> A ∈ (−∞ ,−1) U (15, ∞ )

But the given equation x(x+ 2x−A) = 0 has unequal roots => x2 + 2x−A = 0 must have real and unequal roots => 4 + 4A > 0 => A > -1.  

=> A ∈ [15,∞ )

CAT Mock Test- 3 - Question 49

A company was purchasing 30 barrels of oil every month during lockdown from March 2020 till August 2020. The price per barrel paid by the company increased every month by a constant amount of $10. They purchased the barrels at $25 in March 2020. In September 2020, the company then sold half of the barrels at $45 each, half of the remaining at $50 each and all the remaining barrels at $70 each. What is the company's profit in percentage?

Detailed Solution for CAT Mock Test- 3 - Question 49

The company purchased 30 barrels of oil for 6 months. So, it has 180 barrels of oil in total. 

Cost of 1 barrel of oil in March = $25 and the cost per barrel increases by $10 every month.

So, it follows an A.P. with first term, 'a' = $25 and common difference, 'd' = $10 and 'n', number of terms = 6 (March to August).

If someone purchased 1 barrel a month, his total cost = Sum of A.P.= n/2 ​[2a+(n−1)d] = 6/2​[50 + (5×10)] = 3 × 100 = 300   

.'. Cost of 30 oil barrels every month = $300 × 30 = $9000

Now, half of the oil barrels, i.e. 90 barrels were sold at $45 each making a sale of $90 × 45 = $4050.

Remaining barrels = 90.

Half of it were, i.e. 45 barrels were sold at $50 each making a sales of $50 × 45 = $2250

All the remaining barrels, 45 barrels were sold at $70 each making further sales of $70 × 45 = $3150

Total Selling Price= $(4050+2250+3150)= $9450.

Profit= $9450-$9000= $450

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 50

Prasoon purchased a new bike M15, which soon met with an accident. He went to the service centre and the service centre charged him for repairs. The labour cost, tyre replacement cost, accessory replacement cost and the servicing costs were 5%, 15%, 25% and 35% of the total servicing cost respectively. The remaining charges were for oil replacement (brake oil, engine oil, etc.). Luckily Prasoon was the lucky customer that day and got discounts of 10% each for labour, servicing and oil replacement costs and discounts of 20% on the accessory replacement. The insurance company paid him 80% of the cost paid by him in the service centre by giving him Rs. 56,960. What was the original bill amount (before discount) for accessory replacements in Rupees?


Detailed Solution for CAT Mock Test- 3 - Question 50

Let the total cost be Rs. x

Labour cost= 0.05x

Tyre replacement cost= 0.15x

Accessory replacement cost= 0.25x

Servicing cost= 0.35x

Oil replacement cost= x-(0.05x+0.15x+0.25x+0.35x)= 0.2x

After discount, labour cost= 0.9\times×0.05x= 0.045x

Servicing cost= 0.9\times×0.35x= 0.315x

Oil replacement cost= 0.9\times×0.2x= 0.18x

Accessory replacement cost= 0.8\times×0.25x= 0.2x

'.' No discount is given on replacing tyres, its cost remains the same at 0.15x

Total amount payable by Prasoon= 0.045x+0.315x+0.18x+0.2x+0.15x= 0.89x

Total amount reimbursed by the service center= 0.8\times×0.89x=0.712x

Given, 0.712x=56960

.'.x= Rs. 80000

Original accessory replacement cost=0.25x= 0.25\times×80000= Rs. 20000

CAT Mock Test- 3 - Question 51

A compound 'M' is to be created, one unit of which consists of 3 units of 'X', 4 units of 'Y' and 6 units of 'Z'.  1 unit of X is made by A and B in the ratio 5:7 respectively, 1 unit of Y is made by B and C in the ratio 2:3 respectively, and 1 unit of Z is made by A and D in the ratio 1:4 respectively. What is the approximate percentage contribution of A in 1 unit of M?

Detailed Solution for CAT Mock Test- 3 - Question 51

The ratio of A, B, C and D in X, Y and Z is given to be

Since 1 unit of M has 3X, 4Y and 6Z, we can show the contribution of A, B, C and D in 1 unit of M or 3 units of X, 4 units of Y and 6 units of Z.

Therefore 1 unit of M has 147/60​ units of A, 201​/60 units of B, 12/5​ units of C and 24/5​ units of D.

Also, the total quantity of 1 unit of M= (3+4+6) units= 13 units.

.'. Percentage contribution of A in 1 unit of M = 

CAT Mock Test- 3 - Question 52

A pizza store sold pizzas in 3 sizes- Small, medium and large with diameters of pizza equal to 8 inches, 11 inches and 14 inches. If the cost of the pizza depends on the volume of the pizza and the prices of the pizza are in the ratio 2:3:4, then the ratio of thickness of the small, medium and large pizza is in the ratio-

Detailed Solution for CAT Mock Test- 3 - Question 52

Let the thickness of the small, medium and large pizzas be t1​, t2​, t3​ respectively.

The diameter of small, medium and large pizzas = 8, 11 and 14 inches.

Volume of any pizza = Area × thickness = π r2 × t 

Volume of small pizza = π(8​)2 × t1​ = 16πt1​  

Volume of the medium pizza =

Volume of the large pizza = 

P1​:P2​:P3​ = V1​:V2​:V3​ 

=> 2:3:4 = 16πt​: 121​πt2​ : 49πt3 ​= 2:3:4   

64t1 = 2x
121t2 = 3x
196t3 = 4x
t1 : t2 : t3 = 1/32​ : 3/121 ​: 1​/49

CAT Mock Test- 3 - Question 53

Shruti was wrapping gifts for her brothers and found that the amount of gift paper used to wrap 6 similar spherical gift boxes of radius 7 cm each is exactly same as the amount of gift papers used to wrap 14 similar cube gift boxes. What was the length of the body diagonal of the cube gift boxes?

Assume that π = 22/7

Detailed Solution for CAT Mock Test- 3 - Question 53

Amount of paper used to wrap spherical gift boxes= Total surface area of 6 spheres with radius = 7cm = 6 x 4πr2 = 24 × 22/7 ​× 7 × 7  ....(1)

The gift paper used to wrap 14 cube boxes is also same. Let the length of each side of the cube be 'l'

Then, total surface area of 14 cubes = 14 × 6l2 = 84l2    .....(2)

Equating (1) and (2), we get:

24 × 22 × 7 = 84l2

.'. l= 44 or l = 2√11

We know that in a cube, body diagonal = l√3 = 2√33 cm.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 54

There is a dumbbell which consists of a solid long cylinder of radius r and height 10r with a solid hemisphere of radius 3r attached at either end as follows:


If this is molten and restructured into a maximum of N solid spheres of radius r/10, what is the value of N?


Detailed Solution for CAT Mock Test- 3 - Question 54

Total volume of the dumbbell = 2 x Volume of hemispheres + Volume of cylinder

Volume of one small sphere =  

Hence, the number of spheres = 

CAT Mock Test- 3 - Question 55

The values for which |(x-2)-|x+2||-5\ge\≥ 0 holds are:

Detailed Solution for CAT Mock Test- 3 - Question 55

First, we will deal with the inner modulus. The critical point of the inner modulus is -2.

Case 1: x ≥ -2

|(x-2)-|x+2||-5 becomes |(x-2)-x-2|-5=|-4|-5=-1 which is always <0

Therefore for x ≥ -2, the inequality does not holds.

Case 2: x<-2

|(x-2)-|x+2||-5 becomes |(x-2)+x+2|-5=|2x|-5.

So, |2x ≥ 5 is satisfied under 2 conditions:

(i) 2x ≤-5 => x ≤ −5/2​. We have already asumed that x<-2 and upon solving, we get x ≤ −5/2​. 

.'. x ≤ −5/2​ holds true.

(ii) 2x>5 => x>5/2​. We have already assumed that x<-2 and upon solving, we get x>5/2​ which contradicts our main assumption. So, we reject this.

So, the range of x is (−∞ , −5/2​]

CAT Mock Test- 3 - Question 56

A laptop had 40 medium-sized keys of size 1 cm\times×1 cm, 20 small keys and 10 large keys, such that the area covered by one small key and one large key are 60% and 150% of that covered by one medium key respectively. If the touchpad covers the same area as 8 large keys, what is the approximate percentage of area in the keyboard panel that is not in use? Consider the keyboard panel to have an area of 300 square cm and that nothing else other than the keys and touch pad to be present in the panel.

Detailed Solution for CAT Mock Test- 3 - Question 56

The available area in the keyboard= 300 sq. cm

Area covered by 1 medium-sized key= 1 sq. cm

Area covered by 1 small sized key= 60% of medium sized key= 0.6 sq. cm

Area covered by 1 large key= 150% of the medium sized key= 1.5 sq. cm

Area covered by the touch pad= 8\times×1.5 sq. cm= 12 sq. cm

Total area occupied by the keys= 40 medium+ 20 small + 10 large + touchpad = (40×1) +(20×0.6) + (10×1.5) + 12 = 40 + 12 + 15 + 12 = 79sq. cm

% area covered by the keys and the touch pad= 79​/300 ×100 = 26.33%

.'. % area not in used in the keyboard panel= (100-26.33)% = 73.67%

CAT Mock Test- 3 - Question 57

What is the value of x for which 2(1+3+5+...x) = (0.0625)−25

Detailed Solution for CAT Mock Test- 3 - Question 57

Given, 2(1+3+5+...x) = (0.0625)−25

Taking log on both sides, we will get,

(1+3+5+...x)log2 = −25log0.0625 

=>(1+3+5+...x)log2 = −25log(1/16​) 

=> (1+3+5+...x)log2 = −25log(2−4

=>(1 + 3 + 5 +...x)log2 = 100log2 

=> Sum of odd numbers upto x= 100.

Let the total odd numbers be n, then sum of n odd numbers starting from 1= n2

So, n2 = 100 or n, Number of odd terms= 10.

.'. x is the 10th odd number from the beginning = 19.

CAT Mock Test- 3 - Question 58

If log125​ 40= a and log5​ 98 = b. Then how can log14​ 5 be represented in terms of a and b?

Detailed Solution for CAT Mock Test- 3 - Question 58

CAT Mock Test- 3 - Question 59

If the number of factors of N is 8 and that of 5N is 16, then the number of factors of 2*N can be

Detailed Solution for CAT Mock Test- 3 - Question 59

Let p1, p2, p3 be distinct prime numbers which are not equal to 5.

From the given information, we can conclude that N can be

Case 1: N = p1*p2*p3

Case 2: N = p13∗p2

Case 3: N = p17

Now, 2 can or cannot be one of p1,p2,p3

In case 1:

If 2 ≠ ​p1/p2/p3 then number of factors of 2*p1*p2*p3 = 16.

If 2 is equal to p1 or p2 or p3 then the number of factors of 2*N will be 12.

In case 2:

If 2 ≠  p1 or p2, then number of factors of 2*N=16.

If 2=p1, the number of factors of 2*N will be 10

If 2=p2, the number of factors of 2*N will be 12.

Case 3:

If 2 ≠  p, the number of factors of 2*N = 16.

If 2=p1, the number of factors of 2*N = 9

.'. The number of factors of 2N can be 9,10,12,16.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 60

In how many ways can we select a square of side length at most 4 units from a chess board if one square of the chess board is considered to have a side length of 1 unit?


Detailed Solution for CAT Mock Test- 3 - Question 60

Selecting squares of side 1 unit each:

We can do so by selecting 1 unit from the 8 squares along the length and 1 unit from 8 squares along the breadth. So, total ways of selecting a square of length 1 unit= 8C1​×8C1​= 8×8= 64  

Selecting squares of side 2 units each:

We can do so by selecting 2 continuous units from the 8 squares along the length and 2 continuous units from 8 squares along the breadth. So, total ways of selecting a square of length 1 unit= 7×7=49

Selecting squares of side 3 units each:

We can do so by selecting 3 continuous units from the 8 squares along the length and 3 continuous units from 8 squares along the breadth. So, total ways of selecting a square of length 1 unit= 6×6=36

Selecting squares of side 4 units each:

We can do so by selecting 4 continuous units from the 8 squares along the length and 4 continuous units from 8 squares along the breadth. So, total ways of selecting a square of length 1 unit= 5×5=25

.'. Total ways of selecting a square of side length at most 4 units from a chess board= 64+49+36+25= 174

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 61

The number of even factors of S, where S = 13 + 23 + 33 +... 10003 is


Detailed Solution for CAT Mock Test- 3 - Question 61

S = 13 + 23 + 33 +... 10003 is

We know that the sum of cubes of natural number starting from 1 upto n is given by: 

So, for even factors, we need at least one 2 among the four 2s available with S. We can select either one, two, three or four 2s. For the other prime factors, we also have the option to choose 0 out of the available number of 5s, 11s, 7s and 13s.

So, total even factors= 4×7×3×3×3 = 756.

CAT Mock Test- 3 - Question 62

What is the sum of the first 10 terms of an increasing A.P. where the first, second and fourth terms are in G.P. and the fifth term of the A.P. is 13?

Detailed Solution for CAT Mock Test- 3 - Question 62

Let the first term of the A.P. be 'a', and common difference be 'd'.

Then, the first, second and fourth terms of the A.P. are 'a', 'a+d' and 'a+3d' respectively.

Since, they are in G.P., (a+d)2 = a(a+3d)

=> a2+d2+2ad=a2+3ad

=> d2=ad

=> d2−ad = 0

=> d(d-a) = 0

.'. d=0 or d=a.

 Since, it is mentioned that the A.P is increasing, we will take the value of d= a.

Hence, a+4d= 13 reduces to 5a= 13 or a= 13/5=d.

Sum of first 10 terms of the A.P.= 10​/2 [2a+9d] = 5[11a] = 55a = 55 × 513​ = 143 

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 63

Raghav went to an orphanage of 5 kids with 22 similar notebooks to gift the children. Kids in the orphanage demanded at least 1, at least 2, at least 3, at least 4 and at least 5 notebooks with no two kids demanding the same minimum number of books. In how many ways can Raghav distribute the notebooks to them?


Detailed Solution for CAT Mock Test- 3 - Question 63

Let the five kids be given A, B, C, D and E notebooks.

As per the demands, A= 1+a; where a≥0

B = 2+b; where b≥0

C = 3+c; where c≥0

D = 4+d; where d≥0 and

E = 5+e; where e≥0

Now, A+B+C+D+E = 22

=> (1+a)+(2+b)+(3+c)+(4+d)+(5+e)= 22

=> 15+a+b+c+d+e= 22

=> a+b+c+d+e= 7

This is similar to distributing n similar objects to r different people. This can be done in (n+r−1)C(r−1)​

In our case, n= 7, r=5.

Total ways of distribution =  

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 64

If a quadratic equation x2−ax+b has roots in the ratio 1:4, then the minimum value of b-4a+3 can be written in the form −p/q​, where p and q are co-prime natural numbers. Then the value of p-q=?


Detailed Solution for CAT Mock Test- 3 - Question 64

Let the roots of the given equation be k and 4k.

Then sum of roots= 5k = - (-α−1)​ = α

And product of roots= 4k2 =  b/1​ or b.

So, a = 5k and b = 4k2.

So, b-4a+3= 4k2−4(5k)+3 = 4k2−20k+3.

So, the given expression reduces to the form of a quadratic expression, which opens upward (Co-efficient of k2 is 1, which is positive)

For any quadratic equation of the form αx2+bx+c, the minima occurs at -b/α​ and the minima= - D/4α​, where D is the discriminant of the quadratic equation.

In our case, 4k2−20k+3 has a= 4, b = -20 and c=3.

D= b2−4ac = (-20)2 −4×4 ×3 = 400−48 = 352

4a  = 16.

.'. Minima= - D/4α ​= − 352/16 = −22 or −22/1​.

So, p = 22, q = 1. .'. p-q= 22-1 = 21.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 65

If all the diagonals of a regular hexagon are drawn, the number of points intersection, not counting the corners of the hexagon is


Detailed Solution for CAT Mock Test- 3 - Question 65

let ABCDEF be the regular hexagon.
Diagonals AD, BE, CF will intersect in a regular hexagon
Number of diagonals = n(n-3)/2
Hence, there will be 9 diagonsl.

From the figure it is easily seen that the number of points of intersection is 13.

*Answer can only contain numeric values
CAT Mock Test- 3 - Question 66

On the market of Covent Garden, Mrs. Smith and Mrs. Jones sell apples. Mrs. Jones sells her apples for two per rupee. The apples of Mrs. Smith are a bit smaller; she sells hers for three per rupee. At a certain moment, when both ladies have the same number of apples left, Mrs. Smith is being called away. She asks her neighbor to take care of her goods. To make everything not too complicated, Mrs. Jones simply puts all apples to one big pile, and starts selling them for two rupee per five apples. When Mrs. Smith returns the next day, all apples have been sold out. But when they start dividing the money, there appears to be a shortage of seven rupees. Supposing they divide the amount equally, how much in Rupees does Mrs. Jones lose in this deal?


Detailed Solution for CAT Mock Test- 3 - Question 66

The big pile of apples contains the same amount of large apples of half a rupee each (from Mrs. Jones), as smaller apples of one-third rupee each (from Mrs. Smith). The average price is therefore (1/2 + 1/3)/2 = 5/12 rupee.
But the apples were sold for 2/5 rupees each (5 apples for 2 rupees). Or: 25/60 and 24/60 rupee respectively. This means that per sold apple, there is a shortage of 1/60 rupee. The total shortage is Rs.7. so the ladies together started out with 420 apples. These are worth 2/5x 420 = 168 rupees, or with equal division, 84 rupees for each. If Mrs. Jones would have sold her apples herself, she would have received 105 rupees. Conclusion: Mrs. Jones loses 21 rupees in this deal.

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