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CAT Mock Test- 6 - CAT MCQ


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66 Questions MCQ Test CAT Mock Test Series 2024 - CAT Mock Test- 6

CAT Mock Test- 6 for CAT 2024 is part of CAT Mock Test Series 2024 preparation. The CAT Mock Test- 6 questions and answers have been prepared according to the CAT exam syllabus.The CAT Mock Test- 6 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Mock Test- 6 below.
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CAT Mock Test- 6 - Question 1

The central idea of the passage is that

Detailed Solution for CAT Mock Test- 6 - Question 1

In the passage, the author comments on a human fallacy. They are more excited about the 'oomph' factor associated with comprehending an idea and are less concerned about analysing the idea's quality, as it's laborious and often unrewarding. This often results in people misinterpreting the true value/usefulness of the idea.
Option A is a distortion as the passage does not state that people are primarily motivated by an idea's ability to disrupt the prevalent worldview.
Option B talks about gratification, which is tangential to the discussion. 
Option C conveys the above inference. People are drawn to ideas, but they are often reluctant to carry out a qualitative analysis, leading to false impressions about the true worth of these ideas. Option C is the answer.
Option D has not been implied in the passage.

CAT Mock Test- 6 - Question 2

Which of the following statements is the author LEAST likely to agree with?
I. Bad ideas are more likely to raise human interest and enthusiasm than good ideas.
II. People are cognizant of bad ideas but still rely on them to make sense of the world.
III. New ideas can lead to fresh perspectives on the functioning of the world.
IV. Most ideas have very little bearing on the functioning of the world.

Detailed Solution for CAT Mock Test- 6 - Question 2

"We allow ideas' psychological effects on us rather their logical qualities to determine how we receive them. Unfortunately, given the way human minds work, bad ideas are more likely to have these attractive psychological effects than good ones." Statement I can be inferred from these lines. Hence, the author is likely to agree with it.
Statement II has not been implied in the passage. In the penultimate paragraph, the author comments that the feeling of gaining new knowledge and perspective clouds our ability to judge the quality of the ideas, including the bad ones. Furthermore, the statement is in sharp contrast to what the author discusses. To conclude that an idea is bad or good, people must assess its quality.  But according to the author, people almost always avoid this exercise. Hence, Statement II is wrong.
The author states the following about new ideas- {Indeed they do allow us to see the world differently. But while that shift in perspective generates a feeling of insight, that is not in itself evidence that we are now seeing things as they truly are.} So, the author does believe in an idea's ability to generate a fresh perspective but wants people to carry out a qualitative evaluation before confirming it. Hence, the author will agree with Statement III.
Statement IV is a distortion. The author states, "Unfortunately, most ideas are bad - wrong, misleading, dangerous, or of very limited use or relevance. " But he is also worried about the dreadful consequences of bad ideas, like conspiracy theories. So, though of little value, these ideas can have a big impact on the functioning of the world. Statement IV does not align with the author's view.
Statement II and IV are not likely to receive the author's approval. Hence, Option B is the answer. 

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CAT Mock Test- 6 - Question 3

Which of the following is NOT one of the effects associated with believing in conspiracy theories?

Detailed Solution for CAT Mock Test- 6 - Question 3

"Consider the perennial attraction of conspiracy theories (and most religions), which offer an alternative simplified way of making sense of the strange and unwelcome things happening in the world by turning them into a meaningful story with ourselves at the centre. This has the benefit of reducing the cognitive burdens of understanding the world." Option B can be inferred from these lines.
"In addition, the structure of these theories is distinctly flattering to believers: since the conspiracists are trying so hard to fool us, we must be important after all; since we can see through their ploys, we must be more powerful than we seemed." Option C can be inferred as well.
"This, in turn, gives you the feeling of gaining genuinely new and important knowledge, of enlightenment: of seeing further and truer than you did before and than all those other people still stuck in their dark cave." Option D can be inferred from these lines.
Option A has not been implied. The author does not assert that believing in conspiracy theories causes people to look down on or belittle others. Therefore, Option A is the correct answer.

CAT Mock Test- 6 - Question 4

According to the author, good ideas and bad ideas 

Detailed Solution for CAT Mock Test- 6 - Question 4

"....getting an idea is just a matter of understanding it (or thinking that you do) and this is just as easy in the case of bad ideas as it is for good ones..." Thus, the author opines that both good ideas and bad ideas require a similar intellectual effort to understand them. However, since they are classified in the passage as good and bad by the author, they differ in quality by default.
Option A is a distortion. It is not possible to conclude that these ideas are understood equally by all. There could always be a subjective element involved.
Option B is wrong. They are distinguishable and are not of equal quality.
Option C conveys the author's position correctly and is the answer.
Option D has not been implied in the passage. It can be eliminated.

CAT Mock Test- 6 - Question 5

Which of the following is not true as per the passage?

Detailed Solution for CAT Mock Test- 6 - Question 5

Let us pay heed to the following excerpt: {"...it might force the victim to reconcile with the perpetrator in an effort to end the behaviour, even if the victim doesn’t know why they’re apologizing..."} The author claims that the victims of ostracism might apologise to reconcile with the perpetrator despite being unaware of their mistake (unable to pinpoint them). However, the author doesn't establish a corollary to the same, which suggests that the perpetrators are at fault and are not justified in their treatment of the victims, hence undeserving of an apology. Hence, Option A is not true as per the passage. 
"...Some people may not even consciously choose it at all..." - this line from the passage makes Option B true.
"...The silent treatment might be employed by passive personality types to avoid conflict and confrontation..." - this line from the passage makes option D true as well.
"One study found that social rejection provoked a response in its victims similar to that of victims of physical abuse; the anterior cingulate cortex area of the brain—the area thought to interpret emotion and pain—was active in both instances." The silent treatment is a form of social rejection. Hence, option C is true.
Hence, Option A is the correct choice. 

CAT Mock Test- 6 - Question 6

Which of the following can be inferred from the passage?

Detailed Solution for CAT Mock Test- 6 - Question 6

"The silent treatment is a particularly insidious form of abuse because it might force the victim to reconcile with the perpetrator in an effort to end the behavior, even if the victim doesn’t know why they’re apologizing. “It’s especially controlling because it deprives both sides from weighing in,” Williams said." From these lines, it is clear that both the victim and the perpetrator may not be entirely approving of the manner of reconciliation. But nevertheless, the author does not assert that the perpetrators reject these reconciliatory efforts in most cases. Further evidence is required to validate this claim. Hence, option A cannot be inferred. 
It is mentioned in the passage that giving the silent treatment may become addictive for the perpetrator, but it is not enough for us to infer whether the extent of addiction is the same as that associated with the consumption of hard drugs. Option C cannot be inferred.
In the passage, it has been mentioned that not only does the victim get harmed, but also the perpetrator himself. But, from this, we cannot infer the relative degree of harm caused. Option D cannot be inferred.
From the fifth paragraph, we can infer that the perpetrator can either consciously or unintentionally give someone a silent treatment. If the choice was made consciously, then the reasons would vary with different personality types. But it does not matter to the victim. What matters to him is that he feels abandoned. So, option B can be inferred.

CAT Mock Test- 6 - Question 7

According to the passage, the perpetrators of silent treatment are compelled to justify their behavior because

Detailed Solution for CAT Mock Test- 6 - Question 7

In the last paragraph, the author makes the following observation - "Humans are predisposed to reciprocate social cues, so ignoring someone goes against our nature, Williams said. The perpetrator is therefore forced to justify the behaviour in order to keep doing it; they keep in mind all the reasons they’re choosing to ignore someone."
So, the perpetrators are forced to justify their behaviour because it goes against inherent human nature. Comparing the options, option B captures this idea correctly and is the answer.
Options A and C have not been implied in the passage and can be safely eliminated.
Though the silent treatment can be addictive, the author does not discuss the link between justification and prolonging the addiction in the passage. Option D can be eliminated as well.

CAT Mock Test- 6 - Question 8

Why does Williams tag ostracism as " psychological quicksand"?

Detailed Solution for CAT Mock Test- 6 - Question 8

The reason behind this labelling can be found in the following excerpt: { Worse, the silent treatment can become addictive. The father who couldn’t force himself to speak to his son again suffered the way many addicts suffer—through repeating an activity despite knowing its harm. “Most people who start giving the silent treatment never intend for it to go on for as long as it does, but it can be very difficult to stop,” Williams told me. “It’s psychological quicksand.” } The author highlights the detriment that silent treatment causes to the perpetrators - it becomes difficult to escape such behaviour. A quicksand often appears to be deceptively solid to tread; however, the moment you step on it, it entraps you and makes it nearly impossible to escape. Thus, from the above lines, it is evident that the 'psychological quicksand' is a metaphor for the addictive and non-abating nature of ostracism. On comparing the given options, we notice that Option C is closest to this interpretation.
The other options are tangential to the discussion and do not convey the point discussed above:
Option A: The focus is on the perpetrators and not on the victims. Thus, Option A can be eliminated.
Option B: The statement here partially captures the idea but fails to fails to hit the nail on the head. "What kind of behavioural transformation occurs?" - This question needs to be answered. The option, in this case, does not tell us about the manner of this psychological change and hence, can be discarded. 
Option D: This contains a distortion of the vicious cycle and thus can be eliminated.
Hence, Option C is the correct answer.

CAT Mock Test- 6 - Question 9

"A myopic minority is more powerful than a distracted majority." Which of the following statements best captures the essence of this statement?

Detailed Solution for CAT Mock Test- 6 - Question 9

The author explains the relevance of the statement using the American example, which has tried, albeit without success, to regulate the usage of guns. This is because, even though nearly two-thirds of the population favours gun regulation, they are not entirely devoted to this one cause. On the contrary, the minority, which voices the gun's role in protecting personal freedom, is almost exclusively devoted to this cause. Comparing the options, option D conveys this inference correctly.
All other options are either distorted or do not convey the inference elucidated above. Option A talks about short-term and long-term objectives, which is a distortion. 
Option B adds the distortion of homogenous and heterogeneous groups. The passage does not say that the group for guns is homogenous or the one opposed is heterogeneous. 
Option C is a stretch. It cannot be concluded based on the passage that strength due to number is irrelevant. Further, focus on one cause cannot be equated to depth.

CAT Mock Test- 6 - Question 10

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

Detailed Solution for CAT Mock Test- 6 - Question 10

"In fact, there are nearly as many motor-vehicle deaths each year in this country as there are firearm deaths, but far more people have access to cars on a daily basis than to guns." Even though the frequency of access to firearms is much lesser than the access to cars, the number of deaths is almost equal. So, option A is wrong.
"..fight for the right to life, as it is called, which, has, through small-bore actions, effectively curtailed abortion rights throughout the South, particularly for low-income women and women of colour. This is a repellent parallel for progressives..."  From these lines, it can be inferred that progressives are against the curtailment of abortion rights, but it cannot be concluded that women of colour and low-income women back progressive measures. Option B can be eliminated.
".. big change happens through incremental measures." The author backs this statement with the help of the abortion rights and motor-vehicle regulation examples, where incremental actions have led to significant developments. Hence, option C can be inferred.
"..And, as reformers well know, it does not always matter where the reform starts.." The phrase is not categorical. It seldom matters but could matter in some cases, nevertheless. Hence, it cannot be concluded that the origin is inconsequential or irrelevant in all cases
Option C is the answer.

CAT Mock Test- 6 - Question 11

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

Detailed Solution for CAT Mock Test- 6 - Question 11

"And, as reformers well know, it does not always matter where the reform starts—if it starts at all, it magnetizes other reforms toward it." So, once one reform movement starts, it could expand to include under its umbrella other reform movements as well. Option A can be inferred.
In the antepenultimate paragraph, the author discusses how state and local level regulations have resulted in a decrease in motor-vehicle incidents. Also, in the third paragraph, the author points out that states with strong gun laws have significantly fewer gun deaths. Hence, the author would agree with option B.
"The truth of reform is that it can begin anywhere, on any scale, and, once begun, it tends to be self-renewing." Reform, once it has begun, can be self-renewing. Hence, option c can be inferred.
Option D runs contrary to the author's efforts in the passage. The author mentions Yglesias' counsel and says that this is a policy of despair. In fact, he argues in the subsequent paragraphs that we need not resign ourselves to this policy. Hence, the author is not likely to argue for heeding the counsel.
Therefore, Option D is the correct answer. 

CAT Mock Test- 6 - Question 12

Why does the author draw an analogy between guns and cars?

Detailed Solution for CAT Mock Test- 6 - Question 12

The author makes the analogy in the fourth paragraph. He is prompted to do so to counter the analogy between guns and alcohol. Yglesias argued that banning guns would be as ineffective as banning alcohol. The author disagrees and instead puts forward the analogy between guns and cars - similar to guns, cars when used irresponsibly can kill people. The author then uses the example of cars to drive home two points - given their potential for deadly harm, access to cars is heavily regulated with licenses and training. Similarly, local and state-level regulations, that have been effective in the case of cars, can also be effective for gun control. Thus, the overall purpose of making the analogy is to argue that gun control is not futile as argued by Yglesias. Car regulations show that gun control reforms are possible. Option B which captures this is the right answer.
Option A is an exaggeration. The author does not extend his argument for all instruments of action with potential deadly use. Moreover, the focus is not on the fact that both are instruments of action but on making the case for gun control reforms.
Option C is beyond the scope of the passage. The author does not discuss which level of regulation is more effective.
Option D is a distortion of what is given in the passage. The author never says that limiting access to guns is less important. The author says that even though cars are more accessible than guns, the number of deaths caused by cars is lesser due to regulation. Thus, the author does not say that one form of gun control is more important than another.

CAT Mock Test- 6 - Question 13

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

Detailed Solution for CAT Mock Test- 6 - Question 13

Option A cannot be inferred from the passage. In the third paragraph, the author states that there existed a tension between speed and accuracy and that intellectuals paid hefty sums for timely and accurate information. Hence, quick and prompt reporting need not necessarily compromise accuracy.
Option B is a distortion. Promulgation of falsehoods and rumours have always followed the same basic steps - discovery and amplification.  But, from the printing press to social media, different channels have been employed.
Option C cannot be inferred from the passage. The author does not say that the newspapers took any such action with the intention of protecting trust.
{"Early journalists were far from perfect, and many of the first newspapers competed for attention by aggressively peddling false, outrageous, or nakedly partisan stories, gruesome crime coverage in particular."}  Option D can be inferred from this line.
Hence, Option D is the correct answer.

CAT Mock Test- 6 - Question 14

The author discusses the examples of the Leicestershire woman and the Black Plague to drive home the point that

Detailed Solution for CAT Mock Test- 6 - Question 14

In the first paragraph, the author makes the following observation- 
{Many of these stories were consequence-free, such as the widely believed report in 1569 of a Leicestershire woman who was “confirmed” to have given birth to a cat. Others led to tragedy and horror, such as viral rumours that the Black Plague was caused by Jews poisoning wells, which led to executions and violent pogroms throughout Europe} Thus, the consequences of rumours were not always serious but, on occasions, have attracted tragedy and horror. Comparing the options, Option A conveys this inference correctly.
Option B: deceives the author's tone in the passage. The author is wary of the consequences of peddling fake news. Option B is more of a reassuring statement, which is not the author's intention. Additionally, the author doesn't talk about the repercussions with a time span in his mind; instead, his focus is on the severity of the outcome. Option B can be eliminated.
Option C: Although the examples discussed led to consequences that fall on either end of the spectrum, this cannot be generalised. This is not the author's main intention.
Option D: comes close but contains 2 distortions. The author does not say that the pogroms against the Jews were unexpected. Also, the degree has been altered from 'many' to 'most' when it comes to the number of cases that are harmless.
Hence, Option A is the correct answer.

CAT Mock Test- 6 - Question 15

Which of the following courses of action is the author LEAST likely to endorse?

Detailed Solution for CAT Mock Test- 6 - Question 15

In the passage, the author advocates the need for verifying the content that's circulated online and is wary of the pace and scale at which misinformation is promulgated in the absence of a friction mechanism.
Option A is in line with the author's concern. It would slow down the pace of information exchange and sharing. It would also nudge people to evaluate the content before sharing. Similarly, Options C and D do not contradict the author's viewpoint. They serve to render requisite friction (the option to verify content) and thereby reduce the spread of misinformation.
In the last paragraph, the author mentions that "Reduced friction has enabled important new voices to be heard". The author is more concerned about the veracity of the information and not the source of it. The measure described in Option B may stifle genuine information from sources that wish to be anonymous, and hence, the author might be reluctant to agree with such a proposition.
Hence, Option B is the correct choice. 

CAT Mock Test- 6 - Question 16

Which of the following statements CANNOT be inferred from the passage?
I. Ubiquitous access to the internet and social networking websites has led to the repudiation of established facts. 
II. Fear of losing their reputation and sponsors was one of the reasons that forced the earliest newsmen to filter out erroneous information scrupulously.
III. People trust journalists not because they report accurate information but because they debunk rumours.
IV. Misinformation campaigns could potentially amend the core values that define a democratic society.

Detailed Solution for CAT Mock Test- 6 - Question 16

Statement I has not been implied in the passage (no mention of established facts being refuted) and hence, cannot be inferred.
"Newsmen added “friction” to the process of sharing knowledge, painstakingly validating stories through second-and third-hand sources before they published—lest they lose their reputation and sponsors." Statement II can be inferred from this line.
In the fourth paragraph, the author states, "We learned to trust journalists, largely because they fact-check rumours." But this has not been laid out as the sole reason. The author does not negate the role the publishing of authentic information plays in generating trust. Hence, statement III cannot be inferred.
Statement IV is a distortion. In the second paragraph, the author states, "Widespread belief in certain types of viral rumours poses a threat to institutions that we rely on, including democracy itself." But this observation cannot be equated to the "amendment of the core values." Misinformation campaigns undermine the institution itself. Statement IV cannot be inferred.
Hence, statements I, III and IV can not be inferred from the passage - Option C is the correct answer.

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 17

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. The dialogue was paralleled by the signing of the Japan-Australia Joint Declaration on Security Cooperation in March 2007, and joint military exercises between the United States, India, Japan, and Australia, titled Exercise Malabar.
2. The Quadrilateral Security Dialogue was initiated in August 2007 by then Prime Minister Shinzo Abe of Japan on "seas of freedom and prosperity", with the support of Prime Minister Manmohan Singh of India, Vice President Dick Cheney of the US and Prime Minister John Howard of Australia.
3. The Chinese government responded to the Quad by issuing formal diplomatic protests to its members.
4. The diplomatic and military arrangement was widely viewed as a response to increased Chinese economic and military power.


Detailed Solution for CAT Mock Test- 6 - Question 17

The passage talks about the Quadrilateral Security Dialogue coupled with the joint military exercises between the United States, India, Japan, and Australia. The author mentions that this was initiated as a response to China's growing economic and militaristic strength. Statement 2  cites the origin of this initiative, thereby being the introductory comment. Statement 1 follows 2 as 'the dialogue' in 1 refers to the Quadrilateral Security Dialogue introduced earlier. The additional element to this joint drill is further stated (military exercises). Statement 4 presents the rationale behind the aforementioned enterprise (Quad Security dialogue + military exercises) - the intention was to counteract or respond to China's growing economic and military strength. Statement 3 concludes the discussion by depicting China's response (in the form of diplomatic protests) to this alliance. Hence, 2-1-4-3 forms a coherent paragraph. 

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 18

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. Last month, astronauts collected samples from across the interior of the ISS to build an unprecedented three-dimensional map of its microbiome.
2. We do not even know the full spectrum of spacefaring species living onboard the International Space Station (ISS), but new studies are designed to change that.
3. Yet we are still mostly in the dark about how these communities of microscopic hitchhikers react to microgravity.
4. Each astronaut voyaging off-world is accompanied by up to 100 trillion bacteria, viruses and other microorganisms, any number of which could jeopardize human health.


Detailed Solution for CAT Mock Test- 6 - Question 18

The passage discusses the lack of knowledge concerning the microbiome at the ISS and how this aspect is being dealt with. Sentence 4 is the starting sentence because it sets the context. It mentions the presence of about 100 trillion microorganisms (carried mainly by astronauts to space), many of which can jeopardise human health. Sentence 3 will follow 4 as it states that despite the fact stated in 4, we are still in the dark about how these microorganisms react to microgravity. Sentence 2 resonates with the idea in 3 and highlights the intention to change the status quo (by undertaking new studies). Sentence 1 elaborates on one such 'new study'. Therefore, we notice that 4-3-2-1 forms a coherent paragraph.

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 19

The five sentences (labelled 1, 2, 3, 4, 5) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper order for the sentences and key in this sequence of five numbers as your answer.

1. Camelids are unusual in that their modern distribution is almost the reverse of their origin. 
2. The original camelids of North America remained common until the quite recent geological past, but then disappeared, possibly as a result of hunting or habitat alterations by the earliest human settlers, and possibly as a result of changing environmental conditions after the last ice age, or a combination of these factors. 
3. Camelids first appeared around 45 million years ago during the middle Eocene, in present-day North America. 
4. Three species groups survived: the dromedary of northern Africa and southwest Asia; the Bactrian camel of central Asia; and the South American group, which has now diverged into a range of forms that are closely related, but usually classified as four species: llamas, alpacas, guanacos and vicuñas. 
5. The family remained confined to the North American continent until only about two or three million years ago, when representatives arrived in Asia, and (as part of the Great American Interchange that followed the formation of the Isthmus of Panam1] South America. 


Detailed Solution for CAT Mock Test- 6 - Question 19

At first glance, either 1 or 3 would make a suitable opening sentence; but on looking through all the sentences, it becomes clear that sentence 1 encapsulates the main topic of the paragraph (the distribution of camelids) better, and so makes for a better first sentence. Sentences 3 and 5 then follow from 1, as they talk about the origin and spread of camelids, respectively, in chronological order. Sentence 2 states that the original camelids of North America disappeared; and sentence 4 lists the species groups of camelids that survived on other continents. Thus, 2 and 4 illustrate the point stated in the first sentence – that the current distribution of camelids is the reverse of their origin – and therefore, together, they conclude the paragraph. Hence, 13524.

CAT Mock Test- 6 - Question 20

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence: Such conditions often manifest subtly, with societal norms discouraging individuals from seeking timely help.

Paragraph: Mental health remains a taboo topic in many societies, even though it's crucial to overall well-being. ____ (1) ____ . The stress of modern life, relentless digital connectivity, and social isolation have led to a rise in conditions like depression and anxiety. ____ (2) ____ . To tackle this, awareness campaigns and access to professional help are being amplified. ____ (3) ____ . Yet, overcoming deeply ingrained prejudices about mental health issues proves to be a monumental challenge. ____ (4) ____ .

Detailed Solution for CAT Mock Test- 6 - Question 20

To determine the correct placement of the sentence, we need to consider the overall flow and coherence of the paragraph. Let's analyze each option:

- Option 1: Placing the sentence as the first sentence of the paragraph would provide a clear introduction to the topic of mental health being a taboo. It sets the context for the following sentences that discuss the causes and challenges related to mental health. This option is correct.

- Option 2: Placing the sentence as the second sentence of the paragraph disrupts the flow. It would jump straight into discussing the causes of mental health issues without introducing the topic of mental health being a taboo. This option is incorrect.

- Option 3: Placing the sentence as the third sentence of the paragraph would disrupt the flow. It would discuss awareness campaigns and access to professional help without establishing the context of mental health being a taboo. This option is incorrect.

- Option 4: Placing the sentence as the last sentence of the paragraph would disrupt the flow. It would conclude the paragraph without addressing the challenges related to mental health and the need to overcome prejudices. This option is incorrect.

Therefore, the correct answer is option A: 1.

CAT Mock Test- 6 - Question 21

There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1, 2, 3, or 4) the following sentence would best fit.

Sentence: In this pursuit, the idea of establishing a human settlement on Mars has captivated scientists, policymakers, and entrepreneurs alike.

Paragraph: The final frontier, space, has always been a source of human fascination. Astronomers and space agencies have long directed their resources toward the exploration of this vast unknown. ___ (1) ___ . The advancements in technology have enabled ambitious projects, such as probes sent to the farthest reaches of our solar system and telescopes peering into the depths of space and time. ___ (2) ___ . Despite these technological leaps, space travel presents significant challenges, including the physiological effects on astronauts and the sustainability of life in hostile environments. ___ (3) ___ . The prospect of interplanetary travel extends beyond scientific exploration, hinting at a potential future for humanity that could span multiple celestial bodies. ___ (4) ___ .

Detailed Solution for CAT Mock Test- 6 - Question 21

The sentence introducing the concept of Mars colonization fits perfectly after the initial mention of space exploration's general goals, setting a specific context before discussing technological advancements in broader terms.

CAT Mock Test- 6 - Question 22

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

The influence of social media on public opinion is undeniable, serving as a double-edged sword. On one hand, it democratizes information, breaking monopolies that traditional media outlets had on public opinion. Conversely, it allows for the rampant spread of misinformation. During crises, this aspect becomes particularly dangerous, as seen in various health emergencies and political conflicts. The speed at which information (or misinformation) spreads can create unwarranted panic or prompt public responses based on falsehoods, showcasing the need for improved digital literacy and regulation.

Detailed Solution for CAT Mock Test- 6 - Question 22

The passage discusses social media’s dual nature, emphasizing its dangerous potential during crises due to misinformation. Option B correctly identifies this challenge, suggesting solutions like increased digital literacy and regulation, reflecting the passage’s nuanced stance. Other options are either overly positive, negate the problem discussed, or completely miss the passage’s main point.

CAT Mock Test- 6 - Question 23

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

"Smart cities" integrate technology into urban planning, aiming to optimize efficiency for urban systems and improve residents' quality of life. However, the transformation into a smart city isn't without drawbacks. Critics argue that excessive reliance on technology can create more problems, like surveillance concerns, data security risks, and a widening digital divide, potentially leading to new forms of inequality. As cities continue to evolve, the challenge lies in leveraging technology for genuine societal benefits without infringing on individual rights or exacerbating social divides.

Detailed Solution for CAT Mock Test- 6 - Question 23

This passage highlights the promising aspects of "smart cities" but devotes significant attention to the potential downsides and criticisms. Option B is correct because it captures this balance and the essence of the critique without either glorifying or outright dismissing the concept. Other options misinterpret the passage, leaning too heavily towards the benefits or the negatives, or inaccurately describing modern urban planning.

CAT Mock Test- 6 - Question 24

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

The recent trend towards space tourism represents a significant milestone in human space exploration. However, it also brings forth ethical dilemmas. The exorbitant costs associated with these ventures highlight stark economic disparities, as only the wealthy can afford such experiences. Moreover, the environmental impact of increased space travel remains largely unaddressed, with potential consequences for Earth’s upper atmosphere and beyond. As space tourism continues to develop, a regulatory framework is needed to mitigate environmental damage and consider the broader implications of commercializing space.

Detailed Solution for CAT Mock Test- 6 - Question 24

The passage emphasizes the ethical concerns and environmental impacts surrounding space tourism, advocating for regulations. Option B captures this essence, discussing both the need for mitigating environmental harm and addressing the economic aspects. The other options either disregard key points or present inaccurate affirmations.

CAT Mock Test- 6 - Question 25

Read the following passage and answer the questions that follow:

The rain flashed across the midnight window with a myriad feet. There was a groan in outer darkness, the voice of all nameless dreads. The nervous candle-flame shuddered by my bedside. The groaning rose to a shriek, and the little flame jumped in a panic, and nearly left its white column. Out of the corners of the room swarmed the released shadows. Black specters danced in ecstasy over my bed.............................................

They talk of the candle-power of an electric bulb. What do they mean? It cannot have the faintest glimmer of the real power of my candle. It would be as right to express, in the same inverted and foolish comparison, the worth of "those delicate sisters, the Pleiades." That pinch of star dust, the Pleiades, exquisitely remote in deepest night, in the profound where light all but fails, has not the power of a sulphur match; yet, still apprehensive to the mind though tremulous on the limit of vision, and sometimes even vanishing, it brings into distinction those distant and difficult hints—hidden far behind all our verified thoughts—which we rarely properly view. I should like to know of any great arc-lamp which could do that. So the star-like candle for me. No other light follows so intimately an author's most ghostly suggestion. We sit, the candle and I, in the midst of the shades we are conquering, and sometimes look up from the lucent page to contemplate the dark hosts of the enemy with a smile before they overwhelm us; as they will, of course. Like me, the candle is mortal; it will burn out.

As the bed-book itself should be a sort of night-light, to assist its illumination, coarse lamps are useless. They would douse the book. The light for such a book must accord with it. It must be, like the book, a limited, personal, mellow, and companionable glow; the solitary taper beside the only worshiper in a sanctuary. That is why nothing can compare with the intimacy of candle-light for a bed-book. It is a living heart, bright and warm in central night, burning for us alone, holding the gaunt and towering shadows at bay. There the monstrous specters stand in our midnight room, the advance guard of the darkness of the world, held off by our valiant little glim, but ready to flood instantly and founder us in original gloom.

The wind moans without; ancient evils are at large and wandering in torment. The rain shrieks across the window. For a moment, for just a moment, the sentinel candle is shaken, and burns blue with terror. The shadows leap out instantly. The little flame recovers, and merely looks at its foe the darkness, and back to its own place goes the old enemy of light and man. The candle for me, tiny, mortal, warm, and brave, a golden lily on a silver stem!

Q. Why is the author disappointed with the term 'the candle power of electirc bulb'?

Detailed Solution for CAT Mock Test- 6 - Question 25

Throughout the passage, the author explains that the candle provides a personal touch that lamps are not capable of providing. By stating that a lamp can never compete with the power of the candle, the author does not imply that lamps are not as powerful as candles. Rather, he emphasizes that lamps can never provide the touch that the candles are capable of providing. 

We can eliminate option A since the author is not worried about the anachronistic comparison. Nowhere has the author mentioned that the comparison is between the light sources of different eras. Options B and C can be eliminated since the author has not compared the power of the lamp or the nature of the light it produces to that of the candle. The author believes that the comparison undermines the intimacy that the candle provides to the reader and hence, option D is the right answer.

CAT Mock Test- 6 - Question 26

Read the following passage and answer the questions that follow:

The rain flashed across the midnight window with a myriad feet. There was a groan in outer darkness, the voice of all nameless dreads. The nervous candle-flame shuddered by my bedside. The groaning rose to a shriek, and the little flame jumped in a panic, and nearly left its white column. Out of the corners of the room swarmed the released shadows. Black specters danced in ecstasy over my bed.............................................

They talk of the candle-power of an electric bulb. What do they mean? It cannot have the faintest glimmer of the real power of my candle. It would be as right to express, in the same inverted and foolish comparison, the worth of "those delicate sisters, the Pleiades." That pinch of star dust, the Pleiades, exquisitely remote in deepest night, in the profound where light all but fails, has not the power of a sulphur match; yet, still apprehensive to the mind though tremulous on the limit of vision, and sometimes even vanishing, it brings into distinction those distant and difficult hints—hidden far behind all our verified thoughts—which we rarely properly view. I should like to know of any great arc-lamp which could do that. So the star-like candle for me. No other light follows so intimately an author's most ghostly suggestion. We sit, the candle and I, in the midst of the shades we are conquering, and sometimes look up from the lucent page to contemplate the dark hosts of the enemy with a smile before they overwhelm us; as they will, of course. Like me, the candle is mortal; it will burn out.

As the bed-book itself should be a sort of night-light, to assist its illumination, coarse lamps are useless. They would douse the book. The light for such a book must accord with it. It must be, like the book, a limited, personal, mellow, and companionable glow; the solitary taper beside the only worshiper in a sanctuary. That is why nothing can compare with the intimacy of candle-light for a bed-book. It is a living heart, bright and warm in central night, burning for us alone, holding the gaunt and towering shadows at bay. There the monstrous specters stand in our midnight room, the advance guard of the darkness of the world, held off by our valiant little glim, but ready to flood instantly and founder us in original gloom.

The wind moans without; ancient evils are at large and wandering in torment. The rain shrieks across the window. For a moment, for just a moment, the sentinel candle is shaken, and burns blue with terror. The shadows leap out instantly. The little flame recovers, and merely looks at its foe the darkness, and back to its own place goes the old enemy of light and man. The candle for me, tiny, mortal, warm, and brave, a golden lily on a silver stem!

Q. From the information provided in the passage, we can infer that the Pleiades

Detailed Solution for CAT Mock Test- 6 - Question 26

The author mentions that the Pleiades have a profound impact. They are not profound in the night-sky. The author mentions that they sometimes vanish from the vision and are barely visible at other times. 

Option A can be eliminated since the author explains the philosophical aspects of the light from the Pleiades. The author does not reduce the significance of the Pleiades to their utility. Therefore, we can eliminate option A.

Option B can be eliminated since it mentions that the stars are invisible. They are barely visible and vanish from the vision sometimes.

We can eliminate option D since it mentions that the Pleiades are profound in the night-sky.
Only option C is correct (the Pleiades are at times not visible to the human eye) and hence, it is the right answer.

CAT Mock Test- 6 - Question 27

Read the following passage and answer the questions that follow:

The rain flashed across the midnight window with a myriad feet. There was a groan in outer darkness, the voice of all nameless dreads. The nervous candle-flame shuddered by my bedside. The groaning rose to a shriek, and the little flame jumped in a panic, and nearly left its white column. Out of the corners of the room swarmed the released shadows. Black specters danced in ecstasy over my bed.............................................

They talk of the candle-power of an electric bulb. What do they mean? It cannot have the faintest glimmer of the real power of my candle. It would be as right to express, in the same inverted and foolish comparison, the worth of "those delicate sisters, the Pleiades." That pinch of star dust, the Pleiades, exquisitely remote in deepest night, in the profound where light all but fails, has not the power of a sulphur match; yet, still apprehensive to the mind though tremulous on the limit of vision, and sometimes even vanishing, it brings into distinction those distant and difficult hints—hidden far behind all our verified thoughts—which we rarely properly view. I should like to know of any great arc-lamp which could do that. So the star-like candle for me. No other light follows so intimately an author's most ghostly suggestion. We sit, the candle and I, in the midst of the shades we are conquering, and sometimes look up from the lucent page to contemplate the dark hosts of the enemy with a smile before they overwhelm us; as they will, of course. Like me, the candle is mortal; it will burn out.

As the bed-book itself should be a sort of night-light, to assist its illumination, coarse lamps are useless. They would douse the book. The light for such a book must accord with it. It must be, like the book, a limited, personal, mellow, and companionable glow; the solitary taper beside the only worshiper in a sanctuary. That is why nothing can compare with the intimacy of candle-light for a bed-book. It is a living heart, bright and warm in central night, burning for us alone, holding the gaunt and towering shadows at bay. There the monstrous specters stand in our midnight room, the advance guard of the darkness of the world, held off by our valiant little glim, but ready to flood instantly and founder us in original gloom.

The wind moans without; ancient evils are at large and wandering in torment. The rain shrieks across the window. For a moment, for just a moment, the sentinel candle is shaken, and burns blue with terror. The shadows leap out instantly. The little flame recovers, and merely looks at its foe the darkness, and back to its own place goes the old enemy of light and man. The candle for me, tiny, mortal, warm, and brave, a golden lily on a silver stem!

Q. Why does the author not consider coarse lamp to be a companion for a bed-book?

Detailed Solution for CAT Mock Test- 6 - Question 27

The author mentions that the light for a bed-book should accord with it. He states that the coarse lamp cannot compete with the intimacy that the candle light provides. 

Let us evaluate the options.

Option A mentions that a coarse lamp cannot keep the evil at bay. The author refers to the shadows and darkness as the monstrous specters. Therefore, he does not refer to a ghost or spirit using the term and hence, we can eliminate option A. 

Option B states that the self-illuminating stories do away with the need for an external light source. The author just mentions that the glow should accompany the story of the book. Also, the author recommends having a candle and hence, we can eliminate option B.

Option D can be eliminated since the author uses the term 'douse' to indicate that coarse lamps do not have a character and undermine the story. He does not use the term literally and hence, we can eliminate option D as well. 

Option C captures the fact that the coarse lamp lacks the personal touch of a candle flame and this is the reason why the author is against coarse lamps. Therefore, option C is the right answer.

CAT Mock Test- 6 - Question 28

Read the following passage and answer the questions that follow:

The rain flashed across the midnight window with a myriad feet. There was a groan in outer darkness, the voice of all nameless dreads. The nervous candle-flame shuddered by my bedside. The groaning rose to a shriek, and the little flame jumped in a panic, and nearly left its white column. Out of the corners of the room swarmed the released shadows. Black specters danced in ecstasy over my bed.............................................

They talk of the candle-power of an electric bulb. What do they mean? It cannot have the faintest glimmer of the real power of my candle. It would be as right to express, in the same inverted and foolish comparison, the worth of "those delicate sisters, the Pleiades." That pinch of star dust, the Pleiades, exquisitely remote in deepest night, in the profound where light all but fails, has not the power of a sulphur match; yet, still apprehensive to the mind though tremulous on the limit of vision, and sometimes even vanishing, it brings into distinction those distant and difficult hints—hidden far behind all our verified thoughts—which we rarely properly view. I should like to know of any great arc-lamp which could do that. So the star-like candle for me. No other light follows so intimately an author's most ghostly suggestion. We sit, the candle and I, in the midst of the shades we are conquering, and sometimes look up from the lucent page to contemplate the dark hosts of the enemy with a smile before they overwhelm us; as they will, of course. Like me, the candle is mortal; it will burn out.

As the bed-book itself should be a sort of night-light, to assist its illumination, coarse lamps are useless. They would douse the book. The light for such a book must accord with it. It must be, like the book, a limited, personal, mellow, and companionable glow; the solitary taper beside the only worshiper in a sanctuary. That is why nothing can compare with the intimacy of candle-light for a bed-book. It is a living heart, bright and warm in central night, burning for us alone, holding the gaunt and towering shadows at bay. There the monstrous specters stand in our midnight room, the advance guard of the darkness of the world, held off by our valiant little glim, but ready to flood instantly and founder us in original gloom.

The wind moans without; ancient evils are at large and wandering in torment. The rain shrieks across the window. For a moment, for just a moment, the sentinel candle is shaken, and burns blue with terror. The shadows leap out instantly. The little flame recovers, and merely looks at its foe the darkness, and back to its own place goes the old enemy of light and man. The candle for me, tiny, mortal, warm, and brave, a golden lily on a silver stem!

Q. Which of the following can be said to be true about the shriek described in the first paragraph of the passage?

Detailed Solution for CAT Mock Test- 6 - Question 28

Nowhere has it been mentioned that the author was frightened on hearing the shriek. We can eliminate option D.

It has been given in the first passage that the candle flame jumps on the shriek. Also, the groaning noise slowly rises to a shriek. It is unlikely for a candle flame to shudder due to noise. The shriek should have been caused due to the flow of the wind and the candle should have shuddered due to the wind (not due to the noise). Therefore, option B is the right answer. 

CAT Mock Test- 6 - Question 29

Read the following passage and answer the questions that follow:

The rain flashed across the midnight window with a myriad feet. There was a groan in outer darkness, the voice of all nameless dreads. The nervous candle-flame shuddered by my bedside. The groaning rose to a shriek, and the little flame jumped in a panic, and nearly left its white column. Out of the corners of the room swarmed the released shadows. Black specters danced in ecstasy over my bed.............................................

They talk of the candle-power of an electric bulb. What do they mean? It cannot have the faintest glimmer of the real power of my candle. It would be as right to express, in the same inverted and foolish comparison, the worth of "those delicate sisters, the Pleiades." That pinch of star dust, the Pleiades, exquisitely remote in deepest night, in the profound where light all but fails, has not the power of a sulphur match; yet, still apprehensive to the mind though tremulous on the limit of vision, and sometimes even vanishing, it brings into distinction those distant and difficult hints—hidden far behind all our verified thoughts—which we rarely properly view. I should like to know of any great arc-lamp which could do that. So the star-like candle for me. No other light follows so intimately an author's most ghostly suggestion. We sit, the candle and I, in the midst of the shades we are conquering, and sometimes look up from the lucent page to contemplate the dark hosts of the enemy with a smile before they overwhelm us; as they will, of course. Like me, the candle is mortal; it will burn out.

As the bed-book itself should be a sort of night-light, to assist its illumination, coarse lamps are useless. They would douse the book. The light for such a book must accord with it. It must be, like the book, a limited, personal, mellow, and companionable glow; the solitary taper beside the only worshiper in a sanctuary. That is why nothing can compare with the intimacy of candle-light for a bed-book. It is a living heart, bright and warm in central night, burning for us alone, holding the gaunt and towering shadows at bay. There the monstrous specters stand in our midnight room, the advance guard of the darkness of the world, held off by our valiant little glim, but ready to flood instantly and founder us in original gloom.

The wind moans without; ancient evils are at large and wandering in torment. The rain shrieks across the window. For a moment, for just a moment, the sentinel candle is shaken, and burns blue with terror. The shadows leap out instantly. The little flame recovers, and merely looks at its foe the darkness, and back to its own place goes the old enemy of light and man. The candle for me, tiny, mortal, warm, and brave, a golden lily on a silver stem!

Q. Which of the following can be inferred from the passage?

Detailed Solution for CAT Mock Test- 6 - Question 29

None of the options can be inferred from the passage. The passage is about the author's preference for candlelight while reading a book in bed, and does not provide any information about academic administrators, professors, or motivators of productivity in an academic setup.

CAT Mock Test- 6 - Question 30

Directions: Answer the question on the basis of the information given below.

Akash, a mechanic, used to make and sell four types of custom-made bikes. He used four different brands of each of the four major components of bikes which were tires, engine, speedometer and brakes.
The different brands of tires were Kapollo, Zeat, Chelin and NRF. The different brands of engine were Kamaha, Zonda, Tajaj and Genfield. The different brands of speedometer were Lanta, Etre, Kamp and Dale. The different brands of brakes were Rakas, Cando, Abco and Losa. Out of the four models which Akash sold, one was the cheapest, in which he used the cheapest brand of all the four components, and the other was the costliest, in which he used the costliest brand of all the four components.

Further, the following information is known:
a) The Etre speedometer is the costliest among the four brands of speedometer.
b) Losa brakes can be fitted only with Kapollo tires.
c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.
e) The costliest brakes are neither of Cando nor of Losa brand.
f) Abco brakes and Lanta speedometer are used on the same bike.
g) Tajaj engines are the cheapest among the four engine brands.
h) Dale speedometer cannot be used with Chelin and Kapollo tires.

Q. Which brand's engine is the costliest?

Detailed Solution for CAT Mock Test- 6 - Question 30

(a) The Etre speedometer is the costliest among the four brands of speedometer.
(g) Tajaj engines are the cheapest among the four engine brands.
(c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
(e) The costliest brakes are neither of Cando nor of Losa brand.
(f) Abco brakes and Lanta speedometer are used on the same bike.

(b) Losa brakes can be fitted only with Kapollo tires.
(h) Dale speedometer cannot be used with Chelin and Kapollo tires.
(d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.

Possibility 1

Possibility 2

CAT Mock Test- 6 - Question 31

Directions: Answer the question on the basis of the information given below.

Akash, a mechanic, used to make and sell four types of custom-made bikes. He used four different brands of each of the four major components of bikes which were tires, engine, speedometer and brakes.
The different brands of tires were Kapollo, Zeat, Chelin and NRF. The different brands of engine were Kamaha, Zonda, Tajaj and Genfield. The different brands of speedometer were Lanta, Etre, Kamp and Dale. The different brands of brakes were Rakas, Cando, Abco and Losa. Out of the four models which Akash sold, one was the cheapest, in which he used the cheapest brand of all the four components, and the other was the costliest, in which he used the costliest brand of all the four components.

Further, the following information is known:
a) The Etre speedometer is the costliest among the four brands of speedometer.
b) Losa brakes can be fitted only with Kapollo tires.
c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.
e) The costliest brakes are neither of Cando nor of Losa brand.
f) Abco brakes and Lanta speedometer are used on the same bike.
g) Tajaj engines are the cheapest among the four engine brands.
h) Dale speedometer cannot be used with Chelin and Kapollo tires.

Q. Which speedometer is used along with Losa brakes?

Detailed Solution for CAT Mock Test- 6 - Question 31

(a) The Etre speedometer is the costliest among the four brands of speedometer.
(g) Tajaj engines are the cheapest among the four engine brands.
(c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
(e) The costliest brakes are neither of Cando nor of Losa brand.
(f) Abco brakes and Lanta speedometer are used on the same bike.

(b) Losa brakes can be fitted only with Kapollo tires.
(h) Dale speedometer cannot be used with Chelin and Kapollo tires.
(d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.

Possibility 1

Possibility 2

Hence, option 3 is the right choice.

CAT Mock Test- 6 - Question 32

Directions: Answer the question on the basis of the information given below.

Akash, a mechanic, used to make and sell four types of custom-made bikes. He used four different brands of each of the four major components of bikes which were tires, engine, speedometer and brakes.
The different brands of tires were Kapollo, Zeat, Chelin and NRF. The different brands of engine were Kamaha, Zonda, Tajaj and Genfield. The different brands of speedometer were Lanta, Etre, Kamp and Dale. The different brands of brakes were Rakas, Cando, Abco and Losa. Out of the four models which Akash sold, one was the cheapest, in which he used the cheapest brand of all the four components, and the other was the costliest, in which he used the costliest brand of all the four components.

Further, the following information is known:
a) The Etre speedometer is the costliest among the four brands of speedometer.
b) Losa brakes can be fitted only with Kapollo tires.
c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.
e) The costliest brakes are neither of Cando nor of Losa brand.
f) Abco brakes and Lanta speedometer are used on the same bike.
g) Tajaj engines are the cheapest among the four engine brands.
h) Dale speedometer cannot be used with Chelin and Kapollo tires.

Q. Which brand's brakes are the costliest?

Detailed Solution for CAT Mock Test- 6 - Question 32

(a) The Etre speedometer is the costliest among the four brands of speedometer.
(g) Tajaj engines are the cheapest among the four engine brands.
(c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
(e) The costliest brakes are neither of Cando nor of Losa brand.
(f) Abco brakes and Lanta speedometer are used on the same bike.

(b) Losa brakes can be fitted only with Kapollo tires.
(h) Dale speedometer cannot be used with Chelin and Kapollo tires.
(d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.

Possibility 1

Possibility 2

option 2 is the right choice.

CAT Mock Test- 6 - Question 33

Directions: Answer the question on the basis of the information given below.

Akash, a mechanic, used to make and sell four types of custom-made bikes. He used four different brands of each of the four major components of bikes which were tires, engine, speedometer and brakes.
The different brands of tires were Kapollo, Zeat, Chelin and NRF. The different brands of engine were Kamaha, Zonda, Tajaj and Genfield. The different brands of speedometer were Lanta, Etre, Kamp and Dale. The different brands of brakes were Rakas, Cando, Abco and Losa. Out of the four models which Akash sold, one was the cheapest, in which he used the cheapest brand of all the four components, and the other was the costliest, in which he used the costliest brand of all the four components.

Further, the following information is known:
a) The Etre speedometer is the costliest among the four brands of speedometer.
b) Losa brakes can be fitted only with Kapollo tires.
c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.
e) The costliest brakes are neither of Cando nor of Losa brand.
f) Abco brakes and Lanta speedometer are used on the same bike.
g) Tajaj engines are the cheapest among the four engine brands.
h) Dale speedometer cannot be used with Chelin and Kapollo tires.

Q. Which of the following combinations for a custom bike can be correct?

Detailed Solution for CAT Mock Test- 6 - Question 33

(a) The Etre speedometer is the costliest among the four brands of speedometer.
(g) Tajaj engines are the cheapest among the four engine brands.
(c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
(e) The costliest brakes are neither of Cando nor of Losa brand.
(f) Abco brakes and Lanta speedometer are used on the same bike.

(b) Losa brakes can be fitted only with Kapollo tires.
(h) Dale speedometer cannot be used with Chelin and Kapollo tires.
(d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.

Possibility 1

Possibility 2

Therefore, option (3) is the right choice.

CAT Mock Test- 6 - Question 34

Directions: Answer the question on the basis of the information given below.

Akash, a mechanic, used to make and sell four types of custom-made bikes. He used four different brands of each of the four major components of bikes which were tires, engine, speedometer and brakes.
The different brands of tires were Kapollo, Zeat, Chelin and NRF. The different brands of engine were Kamaha, Zonda, Tajaj and Genfield. The different brands of speedometer were Lanta, Etre, Kamp and Dale. The different brands of brakes were Rakas, Cando, Abco and Losa. Out of the four models which Akash sold, one was the cheapest, in which he used the cheapest brand of all the four components, and the other was the costliest, in which he used the costliest brand of all the four components.

Further, the following information is known:
a) The Etre speedometer is the costliest among the four brands of speedometer.
b) Losa brakes can be fitted only with Kapollo tires.
c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.
e) The costliest brakes are neither of Cando nor of Losa brand.
f) Abco brakes and Lanta speedometer are used on the same bike.
g) Tajaj engines are the cheapest among the four engine brands.
h) Dale speedometer cannot be used with Chelin and Kapollo tires.

Q. Which engine is used with dale?

Detailed Solution for CAT Mock Test- 6 - Question 34

(a) The Etre speedometer is the costliest among the four brands of speedometer.
(g) Tajaj engines are the cheapest among the four engine brands.
(c) Chelin tires can be fitted only with Abco brakes and Tajaj engine.
(e) The costliest brakes are neither of Cando nor of Losa brand.
(f) Abco brakes and Lanta speedometer are used on the same bike.

(b) Losa brakes can be fitted only with Kapollo tires.
(h) Dale speedometer cannot be used with Chelin and Kapollo tires.
(d) NRF tires cannot be fitted with Genfield engine, and Zeat tires can be fitted only with Kamaha engine.

Possibility 1

Possibility 2

CAT Mock Test- 6 - Question 35

Directions: Answer the question on the basis of the information given below.

In an inter-school quiz contest, teams A, B and C reached the finals. In the final, each team was asked 4 questions, followed by the next team. When all the teams had finished one such round, the process was repeated. If a team answered a question correctly, then the team was awarded 20 points, and if a team answered incorrectly, the other teams were awarded 10 points each. The first team to score 500 points won the competition. In the contest, the final scores were: A = 500, B = 340, and C = 240. If out of a total of 54 questions asked, 37 were answered correctly, then answer the following question:

Q. The first round was started by team

Detailed Solution for CAT Mock Test- 6 - Question 35

There were three teams A, B and C taking part in the quiz. Each team was asked 4 questions before the next team got his chance. Thus, a round was completed after 12 questions. A total of 54 questions were asked, out of which 37 were answered correctly and 17 incorrectly. This means that the first team was asked (4 × 4 + 4) 20 questions and the next team got (4 × 4 + 2) 18 questions and the third got 16 questions.
Scores of teams were as follows: A = 500, B = 340, C = 240
Suppose team A got X questions (X can be 20,18 or 16), out of which team A gave 'a' answers correctly and X - a
incorrectly. Total incorrect answers were 17.
a × 20 + ( 17 - (X - a)) × 10 = 500
a = (33 + X)/3
As a is an integer, so X should be divisible by 3, i.e X should be 18. This means Team A faced a total of 18 questions.
a = (33 + 18) /3 = 17
Similarly, for teams B and C, we get

Since team C faced the maximum number of questions, i.e. 20, the round of questions began with it.

CAT Mock Test- 6 - Question 36

Directions: Answer the question on the basis of the information given below.

In an inter-school quiz contest, teams A, B and C reached the finals. In the final, each team was asked 4 questions, followed by the next team. When all the teams had finished one such round, the process was repeated. If a team answered a question correctly, then the team was awarded 20 points, and if a team answered incorrectly, the other teams were awarded 10 points each. The first team to score 500 points won the competition. In the contest, the final scores were: A = 500, B = 340, and C = 240. If out of a total of 54 questions asked, 37 were answered correctly, then answer the following question:

Q. Which team was asked the second highest number of questions?

Detailed Solution for CAT Mock Test- 6 - Question 36

There were three teams A, B and C taking part in the quiz. Each team was asked 4 questions before the next team got his chance. Thus, a round was completed after 12 questions. A total of 54 questions were asked, out of which 37 were answered correctly and 17 incorrectly. This means that the first team was asked (4 × 4 + 4) 20 questions and the next team got (4 × 4 + 2) 18 questions and the third got 16 questions.
Scores of teams were as follows: A = 500, B = 340, C = 240
Suppose team A got X questions (X can be 20,18 or 16), out of which team A gave 'a' answers correctly and X - a
incorrectly. Total incorrect answers were 17.
a × 20 + ( 17 - (X - a)) × 10 = 500
a = (33 + X)/3
As a is an integer, so X should be divisible by 3, i.e X should be 18.
a = (33 + 18)/3 = 17
Similarly, for teams B and C, we get

Thus, Team A was asked the 2nd highest number of questions (18 in no.)

CAT Mock Test- 6 - Question 37

Directions: Answer the question on the basis of the information given below.

In an inter-school quiz contest, teams A, B and C reached the finals. In the final, each team was asked 4 questions, followed by the next team. When all the teams had finished one such round, the process was repeated. If a team answered a question correctly, then the team was awarded 20 points, and if a team answered incorrectly, the other teams were awarded 10 points each. The first team to score 500 points won the competition. In the contest, the final scores were: A = 500, B = 340, and C = 240. If out of a total of 54 questions asked, 37 were answered correctly, then answer the following question:

Q. How many questions did team A answer correctly?

Detailed Solution for CAT Mock Test- 6 - Question 37

There were three teams A, B and C taking part in the quiz. Each team was asked 4 questions before the next team got his chance. Thus, a round was completed after 12 questions. A total of 54 questions were asked, out of which 37 were answered correctly and 17 incorrectly. This means that the first team was asked (4 × 4 + 4) 20 questions and the next team got (4 × 4 + 2) 18 questions and the third got 16 questions.
Scores of teams were as follows: A = 500, B = 340, C = 240
Suppose team A got X questions (X can be 20,18 or 16), out of which team A gave 'a' answers correctly and X - a
incorrectly. Total incorrect answers were 17.
a × 20 + ( 17 - (X - a)) × 10 = 500
a = (33 + X)/3
As a is an integer, so X should be divisible by 3, i.e X should be 18.
a = (33 + 18)/3 = 17
Similarly, for teams B and C, we get

Team A answered 17 questions correctly.

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 38

Directions: Answer the question on the basis of the information given below.

In an inter-school quiz contest, teams A, B and C reached the finals. In the final, each team was asked 4 questions, followed by the next team. When all the teams had finished one such round, the process was repeated. If a team answered a question correctly, then the team was awarded 20 points, and if a team answered incorrectly, the other teams were awarded 10 points each. The first team to score 500 points won the competition. In the contest, the final scores were: A = 500, B = 340, and C = 240. If out of a total of 54 questions asked, 37 were answered correctly, then answer the following question:

Q. What is the percentage accuracy of Team C? Key in the percent value.


Detailed Solution for CAT Mock Test- 6 - Question 38

There were three teams A, B and C taking part in the quiz. Each team was asked 4 questions before the next team got his chance. Thus, a round was completed after 12 questions. A total of 54 questions were asked, out of which 37 were answered correctly and 17 incorrectly. This means that the first team was asked (4 × 4 + 4) 20 questions and the next team got (4 × 4 + 2) 18 questions and the third got 16 questions.
Scores of teams were as follows: A = 500, B = 340, C = 240
Suppose team A got X questions (X can be 20,18 or 16), out of which team A gave 'a' answers correctly and X - a
incorrectly. Total incorrect answers were 17.
a × 20 + ( 17 - (X - a)) × 10 = 500
a = (33 + X)/3
As a is an integer, so X should be divisible by 3, i.e X should be 18.
a = (33 + 18)/3 = 17
Similarly, for teams B and C, we get

Team C answered 9 of 20 questions correctly, so its percentage accuracy is 45%

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 39

Directions: Answer the question on the basis of the information given below.

In an inter-school quiz contest, teams A, B and C reached the finals. In the final, each team was asked 4 questions, followed by the next team. When all the teams had finished one such round, the process was repeated. If a team answered a question correctly, then the team was awarded 20 points, and if a team answered incorrectly, the other teams were awarded 10 points each. The first team to score 500 points won the competition. In the contest, the final scores were: A = 500, B = 340, and C = 240. If out of a total of 54 questions asked, 37 were answered correctly, then answer the following question:

Q. The least number of incorrect questions answered by any team is _____.


Detailed Solution for CAT Mock Test- 6 - Question 39

There were three teams A, B and C that took part in the quiz. Each team was asked 4 questions before the next team got its chance. Thus, a round was completed after 12 questions. A total of 54 questions were asked, out of which 37 were answered correctly and 17 incorrectly. This means that the first team was asked (4 × 4 + 4) 20 questions, the next team got (4 × 4 + 2) 18 questions and the third got 16 questions.
Scores of teams were as follows: A = 500, B = 340, C = 240
Suppose team A got X questions (X can be 20, 18 or 16), out of which team A gave 'a' answers correctly and X - a incorrectly. Total incorrect answers were 17.
a × 20 + (17 - (X - a)) × 10 = 500
a = (33 + X)/3
As a is an integer, X should be divisible by 3, i.e. X should be 18.
a = (33 + 18)/3 = 17
Similarly, for teams B and C, we get

Only 1 question was answered incorrectly by Team A.

CAT Mock Test- 6 - Question 40

Directions: Study the information given below and answer the question that follows.

On a particular day, six monster trucks Truck-1 to Truck 6 participated in a racing event consisting of 5 laps - lap-1 to lap-5. Each truck had different mileage. It is known that the quantity of fuel with any truck immediately before it crossed Lap 4 was the same.

The following graph provides the quantity of fuel (in gallons) that each truck used during each Lap:


Q. Which truck had the least fuel in it before it crossed Lap 1?

Detailed Solution for CAT Mock Test- 6 - Question 40


After each truck crossed from Lap 3, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 used a total of 50, 75, 100, 50, 70 and 35 respectively.
Since they all had the same quantity after using this quantity of fuel, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 would have started with x + 50, x + 75, x + 100, x + 50, x + 70 and x + 35 respectively.

The following table provides the quantity of fuel in them after they crossed from each Lap:

Truck-6 had the least quantity of fuel with it before it crossed Lap 1.

CAT Mock Test- 6 - Question 41

Directions: Study the information given below and answer the question that follows.

On a particular day, six monster trucks Truck-1 to Truck 6 participated in a racing event consisting of 5 laps - lap-1 to lap-5. Each truck had different mileage. It is known that the quantity of fuel with any truck immediately before it crossed Lap 4 was the same.

The following graph provides the quantity of fuel (in gallons) that each truck used during each Lap:


Q. Which truck had the highest quantity of fuel in it after it crossed Lap 5?

Detailed Solution for CAT Mock Test- 6 - Question 41


After each truck crossed from Lap 3, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 used a total of 50, 75, 100, 50, 70 and 35 respectively.
Since they all had the same quantity after using this quantity of fuel, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 would have started with x + 50, x + 75, x + 100, x + 50, x + 70 and x + 35 respectively.

The following table provides the quantity of fuel in them after they crossed from each Lap:

Truck-3 had the highest quantity of fuel after it crossed Lap 5.

CAT Mock Test- 6 - Question 42

Directions: Study the information given below and answer the question that follows.

On a particular day, six monster trucks Truck-1 to Truck 6 participated in a racing event consisting of 5 laps - lap-1 to lap-5. Each truck had different mileage. It is known that the quantity of fuel with any truck immediately before it crossed Lap 4 was the same.

The following graph provides the quantity of fuel (in gallons) that each truck used during each Lap:


Q. After the six trucks crossed each Lap, their drivers compared the fuel left and declared the trucks with the maximum quantity as the Most Efficient. Which of the following trucks would have been declared the Most efficient at least twice?

Detailed Solution for CAT Mock Test- 6 - Question 42


After each truck crossed from Lap 3, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 used a total of 50, 75, 100, 50, 70 and 35 respectively.
Since they all had the same quantity after using this quantity of fuel, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 would have started with x + 50, x + 75, x + 100, x + 50, x + 70 and x + 35 respectively.

The following table provides the quantity of fuel in them after they crossed from each Lap:

Every truck would have been declared Most Efficient after it crossed Lap 3. Among the given options, Truck-6 would have been declared Most efficient again after it crossed Lap 4.

CAT Mock Test- 6 - Question 43

Directions: Study the information given below and answer the question that follows.

On a particular day, six monster trucks Truck-1 to Truck 6 participated in a racing event consisting of 5 laps - lap-1 to lap-5. Each truck had different mileage. It is known that the quantity of fuel with any truck immediately before it crossed Lap 4 was the same.

The following graph provides the quantity of fuel (in gallons) that each truck used during each Lap:


Q. If each truck used at least 50% of the fuel that it had at the beginning of the race, what is the maximum quantity of fuel with any truck before any of them crossed Lap 1?

Detailed Solution for CAT Mock Test- 6 - Question 43


After each truck crossed from Lap 3, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 used a total of 50, 75, 100, 50, 70 and 35 respectively.
Since they all had the same quantity after using this quantity of fuel, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 would have started with x + 50, x + 75, x + 100, x + 50, x + 70 and x + 35 respectively.

The following table provides the quantity of fuel in them after they crossed from each Lap:

Since each truck used at least 50% of the quantity of fuel that it initially had, Truck-1 must have used 50% of x + 50. But Truck-1 used a total of 110.
Hence, 
Similarly, for Truck-2 we get x ≤ 145.
For Truck-3, we get x ≤ 150. For Truck-4, we get x ≤ 150.
For Truck-5 we get x ≤ 210.
For Truck-6 we get x ≤ 155.
For each truck to spend at least 50%. x can be at most 145.
Hence, the maximum quantity with any truck will be 245.

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 44

Directions: Study the information given below and answer the question that follows.

On a particular day, six monster trucks Truck-1 to Truck 6 participated in a racing event consisting of 5 laps - lap-1 to lap-5. Each truck had different mileage. It is known that the quantity of fuel with any truck immediately before it crossed Lap 4 was the same.

The following graph provides the quantity of fuel (in gallons) that each truck used during each Lap:


Q. What is the difference (in gallons) between the fuel left in Truck 2 and Truck 4 after crossing Lap 2?


Detailed Solution for CAT Mock Test- 6 - Question 44


After each truck crossed from Lap 3, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 used a total of 50, 75, 100, 50, 70 and 35 respectively.
Since they all had the same quantity after using this quantity of fuel, Truck-1, Truck-2, Truck-3, Truck-4, Truck-5 and Truck-6 would have started with x + 50, x + 75, x + 100, x + 50, x + 70 and x + 35 respectively.

The following table provides the quantity of fuel in them after they crossed from each Lap:

Truck-6 had the least quantity of fuel with it before it crossed Lap 1.
After crossing Lap 2, fuel in Truck 2 was x + 30.
After crossing Lap 2, fuel in Truck 4 was x + 5.
So, required difference = 25 gallons

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 45

A town had a population of 140000. 1/7th of the people were diagnosed with a disease. The municipality had arranged for 2 variants of medicines A and B to treat all of them. A succeeded in healing 1/14th of patients it was given to, and B succeeded in healing 40% of people it was given to. Finally, a total of 3400 people recovered, with the help of these medicines. Find how many people were given Medicine A.


Detailed Solution for CAT Mock Test- 6 - Question 45

Total number of people having the disease = (1/7) x 140000 = 20000
Let number of patients given A be x.
Therefore, the number of patients given B = 20000 - x 
Therefore, 

x = 14000

CAT Mock Test- 6 - Question 46

2 friends Joey and Chandler had ordered Pizza from the Pizza House. The pizza was supposed to be sliced into 8 equal pieces as follows:

But, somehow, it got sliced into pieces of different sizes. Each slice subtended an angle at the centre. The angles subtended by the pieces, in order from A to H were in an increasing AP. Joey decided he would have alternate pieces starting from A, and the remaining pieces would be eaten by Chandler. The absolute difference between the angle subtended by the largest piece of Chandler and the smallest piece of Joey is 84 degrees. If the total charge for the pizza was 100 USD, and they divide the amount in the ratio of the total area of pieces they had, what was the cost of Chandler's second-largest piece?

Detailed Solution for CAT Mock Test- 6 - Question 46

Let the angles subtended by pieces A to H be a to h respectively.
Let the common difference be d.
Hence, b = a + d, c = a + 2d, d = a + 3d, e = a + 4d, f = a + 5d, g = a + 6d, h = a + 7d
Angle subtended by Joey's smallest piece = a 
Angle subtended by Chandler's largest piece = h = a + 7d '
Difference = 7d = 840
d = 120
Also, a + b + c + d + e + f + g + h = 3600
Hence, 8a + 28d = 360
8a + 336 = 360
a = 24/8 =30
Let the total area be A.
Area of Chandler's second-largest piece = 

Cost of this piece = (7/40) x 100 = 7 x 2.5 = 17.5

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 47

A and B have notes of Rs.500 and Rs.2000 denomination with them. The ratio of Rs. 500 notes with A and B respectively is 2:3, the ratio of Rs. 2000 notes with A and B respectively is 4:5. If the total amount with A is 24000 and the total amount with B is 32000, find the absolute difference between the number of Rs. 500 notes with A and Rs. 2000 notes with B.


Detailed Solution for CAT Mock Test- 6 - Question 47

Let the number of Rs. 500 notes with A and B be 2x and 3x respectively.
Let the number of Rs. 2000 notes with A and B be 4y and 5y respectively.
Hence, total amount with A = 1000x + 8000y = 24000 or x + 8y = 24...(i)
Total amount with B = 1500x + 10000y = 32000 or 1.5x + 10y = 32...(ii)
Multiplying 1.5 with (i), and then subtracting (ii)
1.5x + 12y = 36
1.5x + 10y = 32
Hence, y = 2.
Solving for x, x = 8.
Hence, difference = 2x - 5y = 16 - 10 = 6

CAT Mock Test- 6 - Question 48

The following figure consists of a square, inside which there is a second square formed by joining the midpoints of the sides of the outer square. Inside the second square is inscribed a circle, and it continues in a similar manner. Find the ratio of the sum of areas of all the squares combined to the sum of the areas of the circles combined.

Detailed Solution for CAT Mock Test- 6 - Question 48

Let the length of each side of the outermost square be a.
Hence, the length of each side of the second square = 
The radius of circle = length of side of square / 2 = 
Let the side of the square inside the circle be b.

Hence, b =a/2
Similarly, the side of the square inner to this square = 
Similarly radius of the inner circle = 
And it continues.
Hence, the sum of areas of the squares =  ...

Hence, ratio = 

CAT Mock Test- 6 - Question 49

A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

Detailed Solution for CAT Mock Test- 6 - Question 49

Let number of rows be n.
Total number of students = 630
n/2 [2a + (n - 1)d] = 630
Where d = 3, a is the number of students in last row.
⇒ 2an + 3n2 - 3n = 1260
Now, checking by options.
For n = 6:
12a + 108 - 18 = 1260
⇒ a = 1170/12 = 97.5
This is not possible, as number of children should be a positive integer.

CAT Mock Test- 6 - Question 50

Radius AB of the outer circle is a tangent to the inner circle at P. The radii of the outer and the inner circles are 18 and 5 respectively. Find the ratio in which P divides segment AB.

Detailed Solution for CAT Mock Test- 6 - Question 50

As shown in the fig.

In right angled triangle D APC,

PC = 5 and AC = AT - TC = 18 - 5 = 13

Since AT = AB = 18 = Radius of outer circle

Now AP = 

= 12

Now PB = AB - AP = 18 - 12 = 6

\ Point P dividing the line AB in the ratio

= 2 : 1

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 51

How many ordered pairs (x,y) exist that satisfy the following inequality?

xy + 5x + 6y < 20

It has been given that x is a whole number and y is a natural number.


Detailed Solution for CAT Mock Test- 6 - Question 51

xy + 5x + 6y < 20

If we add 30 to both sides, we can easily factorize the left side.

xy + 5x + 6y + 30 < 50

x(y+5) + 6(y+5) < 50

(y+5)(x+6) < 50

(x+6)(y+5) < 50

It has been given that x is a whole number and y is a natural number.

Hence, let us assume the above inequality as AB < 50, where A = x+6 and B = y+5

Since, x ≥ 0 and y ≥ 1, the minimum value of A = 6 and the minimum value of B = 6

Hence, possible ordered pairs of A and B satisfying the inequality is,

6 x 6 < 50

6 x 7 < 50

6 x 8 < 50

7 x 6 < 50

7 x 7 < 50

8 x 6 < 50

Hence, (A,B) can be (6,6), (6,7), (6,8), (7,6), (7,7) or (8,6).

Hence, ordered pair (x,y) can be (0,1), (0,2), (0,3), (1,1), (1,2), (2,1).

Hence, count = 6

CAT Mock Test- 6 - Question 52

If logα​ 5 = k, logα​ 30 = l, logα 210 =  m, find the value of log35  ​42 in terms of k, l and m.

Detailed Solution for CAT Mock Test- 6 - Question 52

logα 5 = k,

logα 30 = l ⟶ logα​ 5× 6 = l ⟶ logα ​5   + logα​6 = l⟶ logα ​6 = l−k,

logα​ 210 = m ⟶ logα​ 30 × 7 = m ⟶ logα 30 + logα ​7 = m ⟶ logα​ 7 = m − l

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 53

In a test, there are 34 multiple-choice questions. A correct answer fetches +3, and a wrong answer fetches -1. There is no penalty for unattempted questions. In how many ways can a student achieve 67 marks in this test?


Detailed Solution for CAT Mock Test- 6 - Question 53

Let us assume that the student answers all the questions.

If he has answered all of the questions correctly, he gets a total of 34 x 3 = 102 marks.

Now, for every wrong answer, there is a subtraction of 4 marks, so for n incorrect answers, marks achieved = 102 - 4n

Now, we need to equate this to 67, which is the actual marks achieved. But this is not possible, because 67 is odd, and 102-4n is even

Similarly, we can assume he had attempted 33 questions, with n wrong answers,

33 x 3 - 4n = 67

99 - 4n = 67

4n = 32, n = 8. This is possible.

For 32 attempted questions also,

32 x 3 - 4n = 67 is not possible because left side is even and right side is odd.

For 31 attempted questions,

31 x 3 - 4n = 67

93 - 4n = 67

4n = 26, not possible

Similarly, 30 attempted questions is not possible.

For 29 attempted questions,

29 x 3 - 4n = 67

87 - 4n = 67

n = 5. This is possible.

Again for 28, 27, 26 attempted questions, it is not possible.

For 25 questions attempted,

25 x 3 - 4n = 67

75 - 4n = 67

n = 2

It is not possible for any other combination.

Hence, it is possible in 3 different ways.

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 54

It is given that 

f(a,b) = logb​ α

g(x) = x3 - 2x2 + 7x + 11

h(x) = 2x + 1

Find the sum of values of x for which the following equality holds

f(g(x),h(x)) = 2


Detailed Solution for CAT Mock Test- 6 - Question 54

f(g(x),h(x)) = 2

logh(x) g (x) = 2

log2x+1​ x3 − 2x2 + 7x + 11 = 2

(2x+1)2 = x3 − 2x2 + 7x + 11

4x2 + 4x + 1 = x− 2x2 + 7x + 11

x3 − 6x2 + 3x + 10 = 0

Also, x = -1 satisfies the above equation. Hence, (x+1) is a factor of the expression.

Using algebraic division and further factorization, we get

(x+1) (x-2) (x-5) = 0

Hence, the roots are -1, 2 and 5.

But if we consider -1, the base of the logarithm, 2x + 1 becomes -1, which is  not possible, hence the only possible values are 2 and 5.

Hence, sum = 7.

CAT Mock Test- 6 - Question 55

Find the remainder when 70627062 + 20972096 is divided by 100. 

Detailed Solution for CAT Mock Test- 6 - Question 55

First, we will solve for the first term 70627062

7062 = 2 x 3531

70627062 = 27062 × 35317062

= 27060.22 × 35317062

= 1024706.4 × 35317062

Now, we know that (..24)even =(..76) and (..24)odd = (..24)

Also, (..b1)n = (..(unit′s digit of b × n)1)

Hence, 

70627062

= 1024706.4× 35317062

= (..76) × 4 × (..61) = (..76) × (..44)

Now, we will solve for the second term 20972096 

20972096 = 20974 × 524 = (20974)524 =((..97)4)524

= (..81)524 = (..21)

Hence the total remainder = Remainder1 + Remaider2 = 44 + 21 = 65 

CAT Mock Test- 6 - Question 56

A telecom company has decided to come up with new sim cards. It got the permission that it could assign its customers ten-digit numbers with the constraint that the numbers should start with 7809 and the remaining 6 digits can be selected from all 10 digits, without repetition such that they appear in the sim card number in ascending order. Find the maximum number of sim card numbers the company can come up with.

Detailed Solution for CAT Mock Test- 6 - Question 56

Since the first 4 digits are fixed, all the arrangement and selection is to be done for the next 6 digits.

Now, we can select the 6 digits from all 10 digits, without repetition in 10c6 ways.

Once, we select any set of 6 numbers, there is only one arrangement in which they appear in ascending order. So, for each possible selection, the number of ways = 1.

Hence, the total number of ways of selecting 10-digit numbers = 10C6​ × 1 = 10C6​ = 10C4 ​= 

CAT Mock Test- 6 - Question 57

A shopkeeper marks up his goods by 100%. One day during the Dussehra Sale, he gave a discount of 40% to all customers who visited his shop in the morning slot and a discount of 20% to all the customers who visited his shop in the evening slot. All the goods in his shop were of the same type and had the same cost price. Let x be the number of goods sold during the morning slot and y be the number of goods sold during the evening slot, which of the following represents possible values of x and y, in order to have at least 50% profit?

Detailed Solution for CAT Mock Test- 6 - Question 57

Let p be the cost price CP of each item.

Hence, marked price MP = p + p = 2p

Selling price SP of items in the morning slot = 

Selling price SP of the items in the evening slot = 

Since the minimum profit should be 50% for all items,

Hence, y should be greater than or equal to 3 times x. Only option C satisfies the condition.

CAT Mock Test- 6 - Question 58

Ram bought oranges from the whole-seller. After buying the oranges from the shop to the whole seller to his shop, he found that 15% of his oranges have been damaged. By what percentage should he markup the cost to make a 10% profit

Detailed Solution for CAT Mock Test- 6 - Question 58

Let Shopkeeper buy 100 kgs of oranges at the cost Rs P/kg

The total cost incurred by the shopkeeper = 100P

Profit expected by him is 10%, therefore the amount he should get after selling his oranges = (1 + 10%)100P = 110P

However, 15% of the oranges were damaged. So he is left with 85% of 100 kg = 85 kgs of Oranges.

Let him markup the price by x

Then 85 (1+x%) P = 110P

(1 + x%) = 110​/85

(1 + x%) = 1.2941

x% = 29.41%

CAT Mock Test- 6 - Question 59

Given the quadratic equation x2 - (A - 3)x - (A - 7), for what value of A will the sum of the squares of the roots be zero?

Detailed Solution for CAT Mock Test- 6 - Question 59

Let the roots be p and q.
The given quadratic equation can be written as ax2 + bx + c, where a = 1, b = - (A - 3), c = - (A - 7).
The sum of the roots is (p + q) = (-b/a) = (A - 3), and the product of the roots is (pq) = (c/a) = (- A + 7).
The sum of the squares of the roots is [(p + q)2 - 2pq ] = (A - 3)2 - 2(-A + 7) = 0.
Solving this quadratic, we get A = 5 or A = -1.
Neither of these values is among the first three choices.

CAT Mock Test- 6 - Question 60

A retailer buys a certain amount of tea at the rate of Rs. 100 per 500gm from a wholesaler. He then distributes the tea into small packets, each containing 20gm of tea, with negligible overhead costs. He marks each packet at Rs. 6. Later, he finds out that 90 packets had packaging issues and he had to reject them. He sells the remaining packets at their marked price and gets a profit of 39.20% in the entire process. What is the amount of tea he had bought initially?

Detailed Solution for CAT Mock Test- 6 - Question 60

Let the amount of tea he bought be x kg.

Therefore, cost price = x × 2 × 100 = 200x

Number of packets = x × 1000/20 ​= 50x

Number of packets he could sell = 50x − 90

Total selling price = 6 × (50x−90) = 300x − 540

Hence, profit = 300x − 540 − 200x = 100x − 540

Profit percent = × 100 = 39.20

Hence, amount he had bought initially = 25 kg.

CAT Mock Test- 6 - Question 61

Find the sum of the following series:

Detailed Solution for CAT Mock Test- 6 - Question 61

If we look at the series, we can observe that there are 3 different infinite GP series.

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 62

Minku, Tinku, Pinku and Rinku contribute a total of Rs. 360 to buy a gift. Minku contributes one-fifth of what the others contribute. Tinku contributes one-fourth of what the others contribute. Pinku contributes one-third of what the others contribute. Find the amount contributed by Rinku. Key in the value in Rs.


Detailed Solution for CAT Mock Test- 6 - Question 62

Let the amounts contributed by Minku, Tinku, Pinku and Rinku be m, t, p and r, respectively.
According to the question,
m = (t + p + r)/5
Adding m to both sides,
6m = m + t + p + r = 360
or m = 60 ---(I)

According to the question,
t = (m + p + r)/4
4t = m + p + r
Adding t to both sides,
5t = m + t + p + r = 360
t = 72 ---(II)

According to the question,
p = (m + t + r)/3
3p = m + t + r
Adding p to both sides,
4p = m + t + p + r = 360
p = 90 ---(III)
Hence, r = 360 - (m + t + p) = 360 - (60 + 72 + 90) = 138

CAT Mock Test- 6 - Question 63

A quadratic equation f(x) = 0 has one positive and one negative root. If the graph of f(x) is shifted left along the x-axis to form f'(x) in such a way that the sum of roots of the quadratic equation f'(x) = 0 is zero, the distance between the minima of f(x) and f'(x) is 5 units. Which of the following is a possible sum of the roots of the equation f(x) = 0?

Detailed Solution for CAT Mock Test- 6 - Question 63

Let the roots of f'(x) = -a,a

The distance between the minima of f(x) and f'(x) = 5. This implies that f(x) has been shifted 5 units towards the left to get f'(x).

Hence, the roots of f(x) = -a+5 and a+5.

Hence, sum of roots of f(x) = -a+5+a+5 = 10 units.

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 64

If N is a 26 digit number, and M= log 10.
Let F(x) = logN/M, what will be the integral part of F(x)?


Detailed Solution for CAT Mock Test- 6 - Question 64

The integral part of the logarithm (base 10) of a natural number is always 1 less than the no. of digits in it. So the integral part of f(x) is 25.

*Answer can only contain numeric values
CAT Mock Test- 6 - Question 65

A cube is painted on five visible faces. Now it is cut in 64 identical smaller cubes by applying three equidistant cuts along each edge. Among 64 identical smaller cubes, how many cubes have no painted face?


Detailed Solution for CAT Mock Test- 6 - Question 65

After cutting, there 64 identical smaller cubes i.e cube’s dimensions are 4 X 4 X 4
One face is not painted. Therefore, there will be 4 cubes on this face which are not painted.
Similarly, there will be 8 more cubes.
Hence, total number of cubes = 12

CAT Mock Test- 6 - Question 66

A quadratic equation f(x) = 0 exists such that f(x) = 3x2 + 9x + 3. A second quadratic expression g(x) is formed by shifting f(x) towards the right along the x-axis by 5 units. What is the sum of the roots of equation g(x) = 0?

Detailed Solution for CAT Mock Test- 6 - Question 66

g(x) is formed by shifting f(x) towards the right along the x-axis by 5 units,

g(x) = 3(x−5)+ 9(x−5) + 3

g(x) = 3(x2−10x+25) + 9(x−5) + 3

g(x) = 3x− 30x + 75 + 9x − 45 + 3

g(x) = 3x− 21x + 33

Hence g(x) = 0

3x2 − 21x + 33 = 0

x2 − 7x + 11 = 0

Hence, sum of the roots = (−7)​/1 = 7

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