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CAT Mock Test- 4 - CAT MCQ


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66 Questions MCQ Test CAT Mock Test Series 2024 - CAT Mock Test- 4

CAT Mock Test- 4 for CAT 2024 is part of CAT Mock Test Series 2024 preparation. The CAT Mock Test- 4 questions and answers have been prepared according to the CAT exam syllabus.The CAT Mock Test- 4 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Mock Test- 4 below.
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CAT Mock Test- 4 - Question 1

Which of the following is an inference that can be drawn from the second paragraph?

Detailed Solution for CAT Mock Test- 4 - Question 1

This can be inferred from the passage when it states that the Stoics offered an operating system that dealt with anxiety, stress, fear, and troubling questions like "What do I want out of life?" Their ultimate answer to these issues was to seek enduring happiness and tranquillity of mind, which comes from being a virtuous person. Additionally, the passage mentions that the Stoic philosophy focused on how to live a virtuous life, maximize happiness, and reduce negative emotions. Therefore, it can be inferred that Stoicism emphasizes the importance of virtue and inner peace in achieving enduring happiness.

CAT Mock Test- 4 - Question 2

According to Epictetus' philosophy, which of the following best expresses the role played by chance in the well being of an individual?

Detailed Solution for CAT Mock Test- 4 - Question 2

The penultimate paragraph describes Epictetus' philosophy, where it is said that a person suffers when they tether their happiness to worldly possessions, which depend upon chance. Hence, he implies that chance does not directly affect the well-being of a person, but is affected when a person identifies their happiness in their possessions, which are subject to fate. Option C is in line with this.

Option A couples fate and well being, which is in direct contradiction to Epictetus's philosophy. Hence, it can be eliminated.

"But acceptance of this does not have to lead to fatalistic resignation in the assumption that because some things are out of our control, so too is our well-being."

Option B is again in contradiction to what is said. Epictetus does not distinguish between external and internal well-being and says that all well-being is under a person's control. Hence, Option B can be eliminated too.

Option D has not been implied in the passage. Moreover, goes against the main point stated in the penultimate paragraph, as mentioned above.

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CAT Mock Test- 4 - Question 3

Which of the following is NOT an example of a stoic response to adversity?

Detailed Solution for CAT Mock Test- 4 - Question 3

The Stoics take a very different view of misfortune than most people. They expect mishaps and use them as opportunities to hone their virtues.

A stoic response to adversity would be one where a person uses adversity as an opportunity to hone his/her virtues. Instead of woefully ruminating or complaining about the misfortune, a person would start working on his/her skills or engage in some other meaningful task. The focus would be on using the misfortune as an opportunity to improve themselves.

In Option A, the person decides to work on her technical skills instead of fretting over the loss of her job. Hence, A would be counted as a Stoic response.

In Option B, the student decides to prepare for competitive examinations when he is unable to attend the classes. He makes productive use of his time in the face of adversity. Hence, B is also an example of a Stoic response.

In Option D, the textile worker mentioned starts learning hand embroidery to support herself, instead of focusing on the fact that she lost a leg. She engages in a productive activity instead of fretting over her misfortune, and hence D is also an example of a Stoic response.

Option C does not classify as a stoic response. Though the person is engaging in an activity, we cannot say that rebuilding the house is working on honing their virtues. Moreover, a house is an external possession and not internal virtue which is the focus of Stoicism.

CAT Mock Test- 4 - Question 4

According to the passage, what can be a direct consequence of people trying to avoid an unfortunate life?

Detailed Solution for CAT Mock Test- 4 - Question 4

"People's primary concern was to avoid living an unfortunate life. Therefore, they were more likely to order their thoughts, decisions, and behaviours to promote increased life satisfaction."

These lines from the first paragraph state that since people wanted to avoid living an unfortunate life, they were likely to alter their thought processes, decision making and behaviour such that it increased their life satisfaction. Hence, we can infer that a direct consequence would be people making changes to themselves, such that their life satisfaction is increased. Hence Option C can be inferred.

Option A is mentioned in the same paragraph but is not implied as a direct consequence.

Option B is not a direct consequence, as people refer to philosophies like them to find answers to difficult questions, not necessarily to avoid an unfortunate life.

Option D is also not a direct consequence mentioned, as it mentions people embracing Stoicism, which is too specific. Ordering of thought, decisions and behaviour is not the same as embracing the same from as school of philosophy. Hence, it is a distortion and can be eliminated.

CAT Mock Test- 4 - Question 5

Which of the following has NOT been mentioned as one of the purposes of magic/occult sciences in the passage? 

Detailed Solution for CAT Mock Test- 4 - Question 5

"In times of plague and trauma, we moderns seek to protect ourselves with prayers, charms, sigils and spells as much as any medieval peasant." Option A can be inferred from this line.

"various occult sciences - astrology, alchemy, kabbalah, geomancy, dream interpretation - became an important basis for empire more than ever before. The ability to predict the future with divination, then change it with magic, was of obvious political, military and economic interest." Hence, we can infer that magic as a means to predict/portend the future and alter it for certain purposes has been presented in the passage. Option C can be inferred.

"Many considered it alchemy’s sister, both sciences being predicated on the harnessing of cosmic correspondences and natural sympathies to restore elemental equilibrium in the human body - the definition of health. Techniques for life-extension were also central to the alchemical quest." Option D echoes the above point and hence, can be eliminated.

Option B has not been stated in the passage. 

CAT Mock Test- 4 - Question 6

Which of the following highlights a major similarity between premodern medicine and alchemy?

Detailed Solution for CAT Mock Test- 4 - Question 6

The author highlights the following similarities between premodern medicine and alchemy in the fourth paragraph-

-"both sciences...predicated on the harnessing of cosmic correspondences and natural sympathies to restore elemental equilibrium in the human body - the definition of health."

-"Techniques for life-extension were also central to the alchemical quest."

Hence, we can infer that the similarity between the two was that they both were practised as an occult science and relied on occult methods such as harnessing cosmic correspondences and natural sympathies.

Option A is a distortion. Both sciences sought to restore the elemental equilibrium in the human body, but the author does not assert that they sought equitable health outcomes.

Option B is correct. It is based on the first of the two similarities outlined above.

Option C is wrong. They attempted to restore the elemental equilibrium, i.e., the natural state, and not alter it. 

Option D is also a distortion. Both sciences sought to restore an original elemental equilibrium. The creation of a new equilibrium has not been implied in the passage.

CAT Mock Test- 4 - Question 7

Why does the author mention the 'surgical mask' in the passage?

Detailed Solution for CAT Mock Test- 4 - Question 7

"Humans often appear to react irrationally in the face of disease, as the COVID-19 pandemic has shown. Many cling to religion or become superstitious. Others become fatalistic. In times of plague and trauma, we moderns seek to protect ourselves with prayers, charms, sigils and spells as much as any medieval peasant. That a surgical mask is hygienic doesn’t make it any less of a magical symbol."

The first paragraph is about how humans act irrationally in the face of disease, and how they have different coping mechanisms. The author also states that we protect ourselves with prayers and other occult practices like a medieval peasant would have done. But the last line of the passage has a deeper significance than just stating a fact. It acts as a justification for the previous lines. The author here justifies that a surgical mask could be construed as a magical symbol, in spite of it having scientific utility. The author has mentioned the mask here as a proof that modern humans do behave irrationally, just as they did in earlier times. Option C perfectly captures this.

The author explicitly mentions Option A, and this is not the purpose why he mentions the mask as explained above. Hence, A can be eliminated.

Option B is not the main contention of the author while mentioning the surgical masks, as it does not help his argument in any way. Hence B can be eliminated.

The author does not draw a parallel between occult and scientific practices but between the way humans reacted to disease in the pre-modern era and how they react to it in the modern era. Hence, D can be eliminated too.

Hence, Option C is the answer.

CAT Mock Test- 4 - Question 8

"The scientific revolution that followed continued the same trend". The 'trend' in the statement refers to

Detailed Solution for CAT Mock Test- 4 - Question 8

"Western Europe saw a parallel upsurge of occultism - much of it from Arabic sources - which we now call the Renaissance. The scientific revolution that followed continued the same trend: historians now admit that saints of science such as Johannes Kepler, Francis Bacon, Robert Boyle and Isaac Newton were likewise raving occultists."

So, while the Islamic world witnessed an occult-scientific revolution, the Western world also witnessed a surge in interest for the occult, thanks to Arabic sources. And this surge in interest/popularity continued during the subsequent scientific revolution as well. 

Only option D conveys the above inference. Option D is the answer 

CAT Mock Test- 4 - Question 9

Which of the following best describes what the passage is trying to do?

Detailed Solution for CAT Mock Test- 4 - Question 9

In the former half of the passage, the author discusses the cons of the meritocracy system and how it has meandered away from its original objectives. But, in the latter half, the author makes a case for the continued adoption of the meritocracy system, highlighting its role in enabling economic efficiency and social equality. Towards the end, the author states, "The solution to the inequalities produced by meritocracy’s success is to tax the winners rather than to bind Prometheus." Here, the author advocates the need for positive changes to the system rather than completely doing away with it.

Comparing the options, option C captures the author's view correctly. Option C is the answer.

Option A is out of scope. The link between idealism and realism cannot be inferred from the passage.

Option B is extreme. The evidence has not been described as overwhelmingly in favour of the viewpoint that meritocracy breeds inequality. The author merely attempts to bring out the two sides of the system.

Option D is an exaggeration. The author does not imply that any system can be hijacked by the elite for their own benefit. Hence, option d can be eliminated.

CAT Mock Test- 4 - Question 10

The author's view on the 'principle of just deserts' differs from that of Mankiw in which of the following ways?

Detailed Solution for CAT Mock Test- 4 - Question 10

The following is Mankiw's version of 'just deserts'- "Meritocracy holds that “a person who contributes more to society deserves a higher income that reflects those greater contributions.” Moreover, meritocracy measures each person’s contribution as the market value that she adds “to society’s production of goods and services.”

The following is the author's take on the same- "someone who contributes more to prosperity deserves a higher income that reflects their greater contribution."

Hence, the key difference between the two versions is how they quantify the contributions of an individual. While Mankiw focuses on the market value-added, the author is more concerned about the ability of the contribution to improve the prosperity of the society, i.e., the benefits to the society.

Comparing the options, option D is closest to the above interpretation and is the answer.

Option A is wrong. Mankiw does measure individual contribution based on market value-added.

Option B is a distortion. The author is concerned about prosperity in general and not just the social status of the individual. Both are not interchangeable.

Option C is wrong. The author only suggests a scale to quantify individual contributions and does not advance the exclusion of any particular kind of contribution.

CAT Mock Test- 4 - Question 11

Why does the author mention the phrase 'bind Prometheus'?

Detailed Solution for CAT Mock Test- 4 - Question 11

"The solution to the inequalities produced by meritocracy’s success is to tax the winners rather than to bind Prometheus."

The last line of the passage is an argument in the favour of implementing pragmatic reforms rather than getting rid of meritocracy. Here, 'tax the winners' refers to the pragmatic reform advocated by the author and 'bind Prometheus' is the metaphor for doing away with meritocracy. (Prometheus is a greek mythological creature who signifies the striving and development of humans, and who was bound by Zeus. Hence the metaphor is apt in signifying that doing away with meritocracy, which has yielded many benefits, is like binding Prometheus. The mythological part is irrelevant to the answer, and one must only understand the context to identify the meaning of the metaphor). Hence, the answer is Option B.

The phrase does not advocate anything and just stands as a metaphor. Hence, A is eliminated.

Mentioning a Greek mythological character is neither the author's contention here, though the metaphor does mean this. C would have been the answer if the meaning of the phrase was asked, but will be eliminated here.

The phrase does not mean what is mentioned in Option D. Hence, it can be eliminated.

CAT Mock Test- 4 - Question 12

The author cites the example of developments in finance to drive home all of the following points, EXCEPT

Detailed Solution for CAT Mock Test- 4 - Question 12

The author states the following about the developments in finance in the second and the third paragraph-

"super-educated elites have developed technologies—financial instruments, digital tools and legal regimes—that dramatically favour their own skills."

" But the innovation is not a true advance, and the new style of finance does not make a greater social contribution than the old."

From the above lines, options A and C can be inferred.

Also, in the opening line of the second paragraph, the author talks about meritocratic hierarchies distorting wages. And then goes on to establish this claim with the help of the finance industry example. In the latter half of the passage, the author notes that no other industry has higher wages, but also asserts that the innovations in finance have not led to greater social contributions. Hence, wages distort the true worth of a skill. Option D can be inferred as well.

Option B cannot be inferred. Meritocracy allows elites to promote skills favourable to them, true, but it cannot be concluded that this helps improve their own image or brand value. Option B is the answer.

CAT Mock Test- 4 - Question 13

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

Detailed Solution for CAT Mock Test- 4 - Question 13

"Yet to recognise something as true is to be influenced by evidence or affected by the world - and in many ways knowledge limits our freedom."

Option B can be inferred from the latter half of the above line.

In the passage, the author highlights the differences between doubt and irony and notes the following- "..critical scrutiny is crucial in science and an intrinsic part of scientific progress. The pursuit of knowledge goes hand in hand with doubt." Hence, option C can be inferred.

In the penultimate paragraph, the author highlights the example of free immigration activists rejecting the notion of borders as an example of an attitude of irony, which is driven by the pursuit of freedom from reality/knowledge. Option D can be inferred as well.

Option A cannot be concluded. The author discusses examples of ironists who interacted with the world, despite having no commitment to truth. Option A is the answer.

CAT Mock Test- 4 - Question 14

Who among the following would the author not tag as 'Kierkegaard's Socrates'?

Detailed Solution for CAT Mock Test- 4 - Question 14

The situations category of individuals highlighted in Options A, B and D fulfil the criterion to be tagged as "Kierkegaard’s Socrates" - Individuals who are "happy to trade knowledge for freedom"; they are not truly invested in truth but are satisfied with their ignorance {Doubt is something we suffer insofar as we are invested in the truth but find it hard to verify our beliefs. The doubter feels alienated from reality and wants to get back in touch with it. The ironist, on the other hand, triumphs in this alienation. He does not love the truth; he loves the freedom that comes from not believing.}

Option C does not show a wilful ignoring of knowledge. The said companies might still sell those drinks for occasional consumption. 

CAT Mock Test- 4 - Question 15

A doubter and an ironist differ in all of the following ways, EXCEPT

Detailed Solution for CAT Mock Test- 4 - Question 15

The author notes the following about irony in the second paragraph-"There is a form of scepticism which cannot be taken as a scientific or otherwise theoretical attitude at all.So although climate science denial presents itself as a kind of doubt, based on an alternative interpretation of evidence, much of it should be understood as a practical attitude. It is not interested in knowledge to begin with. Instead, it seeks freedom from knowledge. " Option A can be inferred.

"Doubt is something we suffer insofar as we are invested in the truth but find it hard to verify our beliefs. The doubter feels alienated from reality and wants to get back in touch with it. The ironist, on the other hand, triumphs in this alienation. He does not love the truth; he loves the freedom that comes from not believing."

From the above lines, options B and D can be inferred. 

Though the doubter is invested in truth and seeks knowledge, this exercise has not been mentioned as an attempt to gain freedom. Furthermore, in the opening paragraph, the author states that "knowledge limits our freedom". Hence, option C cannot be concluded,

CAT Mock Test- 4 - Question 16

The purpose of the first two paragraphs is

Detailed Solution for CAT Mock Test- 4 - Question 16

The author highlights the significance of critical scrutiny in the pursuit of knowledge in the first paragraph. However, he adds that climate change denial deviates from such scepticism wherein people are invested in pursuing truth or knowledge. Instead, such individuals find denial as a way to seek freedom from knowledge. This point is correctly captured in Option D.

The statement in Option A captures just a segment of the discussion and does not present it in its entirety. 

Options B and C are not implied via the discussion and, therefore, can be eliminated.

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 17

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

  1. This argument woefully ignores the neuroscience that explains why juveniles should not be treated as adults.
  2. This new ruling claims that the early teen years cast the die for how someone is likely to behave for the rest of their lives.
  3. It ignores the very scientific evidence that influenced and guided previous court decisions.
  4. The U.S. Supreme Court’s recent decision in Jones v. Mississippi makes it easier for judges to sentence children to life in prison with no chance of parole.

Detailed Solution for CAT Mock Test- 4 - Question 17

The correct sequence of the sentences provided in the question is indeed 4, 2, 3, 1. Let's break down each sentence and understand how they logically flow together to form a coherent paragraph:

  • The U.S. Supreme Court’s recent decision in Jones v. Mississippi makes it easier for judges to sentence children to life in prison with no chance of parole. This sentence introduces the central idea of the paragraph, which is the recent ruling by the U.S. Supreme Court regarding the sentencing of juveniles to life in prison without parole. It sets the context for the subsequent sentences.
  • This new ruling claims that the early teen years cast the die for how someone is likely to behave for the rest of their lives. Sentence 2 elaborates on the implications of the recent ruling mentioned in sentence 4. It explains that the ruling is based on the belief that behavior during early teenage years determines future behavior. This sentence provides insight into the rationale behind the ruling.
  • It ignores the very scientific evidence that influenced and guided previous court decisions. Following the introduction of the recent ruling and its rationale in sentences 4 and 2, sentence 3 provides a critical perspective. It suggests that the recent ruling disregards or overlooks scientific evidence that was previously considered in similar court decisions. This statement challenges the validity or completeness of the reasoning behind the recent ruling.
  • This argument woefully ignores the neuroscience that explains why juveniles should not be treated as adults. Finally, sentence 1 concludes the paragraph by explicitly stating the main critique or argument against the recent ruling. It points out that the ruling fails to consider neuroscience evidence that supports the idea that juveniles should not be treated as adults in the criminal justice system. This sentence reinforces the perspective introduced in sentence 3 and provides a clear critique of the ruling.
*Answer can only contain numeric values
CAT Mock Test- 4 - Question 18

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

  1. The year 2016 was the warmest this region had experienced since 770 AD.

  2. It was found that for the last two decades, Yellowstone National Park has been warming at its most intense rates in at least 1,250 years.

  3. Tree rings can provide a variety of information about the climate and weather conditions a tree has experienced over the course of its lifetime.

  4. A study, published in the journal Geophysical Research Letters, used data from tree rings to reconstruct more than a millennium of summer temperatures in the Yellowstone region.


Detailed Solution for CAT Mock Test- 4 - Question 18

The paragraph is about how the study of tree rings can be used to reach conclusions about the state of warming in a region. 3 introduces the study by stating that tree rings can be used to study the climate and weather conditions of a region. 4 then mentions an example where the method was utilized. 2 and 1 then reach conclusions from the study. Here 21 is the appropriate order, as 2 better conjoins the two parts of the paragraph because of the presence of 'It was found that...'. Hence, the correct order is 3421.

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 19

The question has a set of sentences, which when properly sequenced, forms a coherent paragraph. Enter the most logical order of the sentences from among the given options.
1. In discussing the period preceding the revolution of 1917, Terras links the literary movements with parallel developments in theater, music, and the visual arts, explaining that these all placed Russia in the forefront of European modernism.
2. He wraps up his survey with the dissident movement that followed Stalin's death, arguing that the movement again made literature a leader in the struggle for freedom of thought, genuine relevance, and communion with Western culture.
3. Terras traces a rich literary heritage that encompasses Russian folklore of the eleventh, twelfth, and thirteenth centuries, medieval literature that in style and substances drew on the Byzantine tradition and literature of the seventeenth and eighteenth centuries, when Russia passed through a succession of literary schools - neoclassicism, sentimentalism, romanticism, and realism - imported from the West.
4. Terras divides Russian literature after the revolution into emigre and Soviet writing, and he demonstrates how the latter acted as a propaganda tool of the Communist party.
5. Terras moves on to the masterful realist fiction of Turgenev, Dostoevsky, and Tolstoi during the second half of the nineteenth century, showing how it was a catalyst for the social and cultural advances following the reforms of Alexander II.


Detailed Solution for CAT Mock Test- 4 - Question 19

The answer is 35142. Out of all the given options, statement 3 serves as the best introductory sentence because it tells about the rich literary heritage that includes the Russian folklore of various periods and also about the various phases of the literary schools through which Russia had passed at different points of time till the eighteenth century. Statement 1 cannot be the introductory sentence because it begins with "In discussing the ... the revolution of 1917" and there are other sentences which deals with literary heritage of different periods of time prior to the revolution. This proves that this particular sentence comes somewhere in the middle of the passage. Statement 5 cannot be the introductory sentence because it ruled out. Same is the case with 4. in sentence 2, "wraps up" indicates the final step; therefore, it has to be the concluding sentence. Statement 3 is followed by statement 5 which deals with literary works of the second half of the nineteenth century. Statement 1 is a logical extension of statement 5. In statement 1, there is a mention about the periods preceding the revolution of 1917 and the development between the literary movements and the other parallel developments which goes with 'the social and cultural advances' as mentioned in statement 5. Statement 4 brings into light what had happened after the revolution and how the Soviet writing had served as a propaganda tool of the Communist party. Statement 2 is the concluding sentence which states how literature emerged as a leader in the struggle for freedom of thought, genuine relevance and communion with the western culture. Therefore, 35142 is the answer.

CAT Mock Test- 4 - 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: This stark reality has driven the growth of movements advocating for drastic change in our lifestyle and economic priorities.

Paragraph: Environmental concerns have been mounting with the undeniable impact of human activity on climate change. ____(1). ____ Scientists advocate for immediate collective action, suggesting steps such as reducing carbon footprints, conserving water, and investing in sustainable technologies. ___(2). ____ Governments and corporations play significant roles by enforcing eco-friendly policies and promoting green technologies, but the inertia has been difficult to overcome. _____ (3). ____ Consequently, our planet's future hangs in a delicate balance, urging every individual's participation in the conservation effort. ____ (4). ____. 

Detailed Solution for CAT Mock Test- 4 - Question 20

- The missing sentence, "This stark reality has driven the growth of movements advocating for a drastic change in our lifestyle and economic priorities," fits best in Option A (1). It introduces societal reactions to the mounting environmental concerns outlined in the paragraph.
- This sentence highlights the impact of environmental issues on society, prompting movements for significant changes. It connects the urgency of environmental problems with broader societal actions.
- The sentence emphasizes the need for drastic changes in lifestyle and economic practices to address environmental challenges effectively. Its placement at the beginning of the paragraph provides context for understanding subsequent discussions about collective action and individual participation.
- Overall, it enhances the coherence and completeness of the paragraph by illustrating societal responses to environmental crises.

CAT Mock Test- 4 - 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: Ironically, it's this data abundance that often leads companies to the paralysis of analysis, unable to sort what's truly actionable.

Paragraph: In the age of digital transformation, businesses are inundated with data that can lead to groundbreaking insights. ____ (1). ____ Cutting-edge tools in data science and AI promise the allure of predictive analytics and informed decision-making. ____ (2). ____ However, the human element remains critical in interpreting data and making strategic decisions. ____  (3). ____ Thus, a balanced approach to digital adoption is key in leveraging advantages while maintaining strategic control. ____ (4) ____.

Detailed Solution for CAT Mock Test- 4 - Question 21

- The missing sentence, "Ironically, it's this data abundance that often leads companies to the paralysis of analysis, unable to sort what's truly actionable," fits best in Option B (2).
- It provides a critical perspective on the challenges posed by data abundance, highlighting the paradoxical situation where the wealth of data can hinder decision-making.
- This sentence introduces a contrast to the positive aspects of data abundance mentioned earlier, setting the stage for discussing the crucial role of human judgment in data interpretation and strategic decision-making.
- Its placement before the sentence about the human element underscores the importance of acknowledging and addressing the challenges associated with data-driven approaches.
- Overall, it adds depth to the discussion on leveraging data insights while maintaining strategic control.

CAT Mock Test- 4 - Question 22

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

Modern workplaces require constant upskilling due to rapid technological advancements. Employers seek individuals who can learn and adapt rather than those with extensive experience in redundant technologies. Thus, the traditional premium on experience is being swiftly replaced by the ability to learn and adapt.

Detailed Solution for CAT Mock Test- 4 - Question 22

Option C encapsulates the primary message of the passage, emphasizing the new preference for adaptability and learning in the face of technological advancements, without distorting the passage’s nuances.

CAT Mock Test- 4 - Question 23

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

Neuroscientific research has challenged the notion of free will, suggesting our decisions are the end products of past brain activity. This understanding potentially realigns concepts of morality and, fundamentally, our judicial thinking, which traditionally centers around the belief in free will.

Detailed Solution for CAT Mock Test- 4 - Question 23

Option B correctly mirrors the passage’s central idea, pointing out the potential impact of neuroscience on concepts of free will and judiciary principles, without exaggerating the implications.

CAT Mock Test- 4 - Question 24

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

Coral reefs, often called "rainforests of the sea", support a quarter of all marine life. However, climate change and ocean acidification are decimating these ecosystems, leading to a loss of biodiversity. The consequences extend beyond the marine environment, indicating an impending ecological crisis.

Detailed Solution for CAT Mock Test- 4 - Question 24

Option B accurately summarizes the passage, highlighting the ecological importance of coral reefs and the wider implications of their destruction.

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 25

The number of friends who only watched movies is


Detailed Solution for CAT Mock Test- 4 - Question 25

Let us draw Venn diagram.

From statement (1),
(b + c) - (b + e) = 8
⇒ c = 8 + e ... (1)
From statement (2),
(a + b) - (d + e) = 7
⇒ a + b = 7 + d + e ... (2)
From statement (3),
(a + b + e + f) - (b + c) = 21
⇒ a + e + f = 21 + c
⇒ a + e + f = 21 + 8 + e [From equation (1), c = 8 + e]
⇒ a + f = 29 ... (3)
From statement (4) ,
(a + b + e + f) + (d + e) = 66
⇒ a + b + d + 2e + f = 66 ... (4)
From statement (5),
b + e = 21 ... (5)
⇒ c = 21 - 4 = 17 ... (6)
From equation (1),
e = c - 8 = 17 - 8 = 9 ... (7)
From equations (5) and (7),
b = 21 - e = 21 - 9 = 12 ... (8)
From equations (3) and (4),
b + d + 2e = 37
⇒ d = 37 - 12 - 2 x 9 = 7 ... (9)
From equations (2), (7), (8) and (9),
a + b = 7 + d + e
⇒ a = 7 + 7 + 9 - 12 = 11 ... (10)
From equations (3) and (10),
a + f = 29
⇒ f = 29 - 11 = 18

Number of friends who only watched movies = 7

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 26

What is the difference between the number of friends who went to Goa and the number of friends who stayed at home?


Detailed Solution for CAT Mock Test- 4 - Question 26

Let us draw a Venn diagram

From statement (1):
⇒ (b + c) - (b + e) = 8
⇒ c = 8 + e ... (1)
From statement (2):
⇒ (a + b) - (d + e) = 7
⇒ a + b = 7 + d + e ... (2)
From statement (3):
⇒ (a + b + e + f) - (b + c) = 21
⇒ a + e + f = 21 + c
⇒ a + e + f = 21 + 8 + e (From equation (1): c = 8 + e)
⇒ a + f = 29 ... (3)
From statement (4):
⇒ (a + b + e + f) + (d + e) = 66
⇒ a + b + d + 2e + f = 66 ... (4)
From statement (5):
⇒ b + e = 21 ... (5)
⇒ c = 21 - 4 = 17 ... (6)
From equation (1):
e = c - 8 = 17 - 8 = 9 ... (7)
From equations (5) and (7):
⇒ b = 21 - e = 21 - 9 = 12 ... (8)
From equations (3) and (4):
⇒ b + d + 2e = 37
⇒ d = 37 - 12 - 2 x 9 = 7 ... (9)
From equations (2), (7), (8) and (9):
⇒ a + b = 7 + d + e
⇒ a = 7 + 7 + 9 - 12 = 11 ... (10)
From equations (3) and (10):
⇒ a + f = 29
⇒ f = 29 - 11 = 18

Difference between the number of friends who went to Goa and the number of friends who stayed at home = (11 + 12 + 17) - (7 + 9 + 18) = 40 - 34 = 6

CAT Mock Test- 4 - Question 27

Among the friends who stayed at home, how many played charades?

Detailed Solution for CAT Mock Test- 4 - Question 27

Let us draw a Venn diagram

From statement (1):
⇒ (b + c) - (b + e) = 8
⇒ c = 8 + e ... (1)
From statement (2):
⇒ (a + b) - (d + e) = 7
⇒ a + b = 7 + d + e ... (2)
From statement (3):
⇒ (a + b + e + f) - (b + c) = 21
⇒ a + e + f = 21 + c
⇒ a + e + f = 21 + 8 + e (From equation (1): c = 8 + e)
⇒ a + f = 29 ... (3)
From statement (4):
⇒ (a + b + e + f) + (d + e) = 66
⇒ a + b + d + 2e + f = 66 ... (4)
From statement (5):
⇒ b + e = 21 ... (5)
⇒ c = 21 - 4 = 17 ... (6)
From equation (1):
e = c - 8 = 17 - 8 = 9 ... (7)
From equations (5) and (7):
⇒ b = 21 - e = 21 - 9 = 12 ... (8)
From equations (3) and (4):
⇒ b + d + 2e = 37
⇒ d = 37 - 12 - 2 x 9 = 7 ... (9)
From equations (2), (7), (8) and (9):
⇒ a + b = 7 + d + e
⇒ a = 7 + 7 + 9 - 12 = 11 ... (10)
From equations (3) and (10):
⇒ a + f = 29
⇒ f = 29 - 11 = 18

Number of friends who played charades among the ones who stayed at home = 18 + 9 = 27

CAT Mock Test- 4 - Question 28

What is the total number of friends?

Detailed Solution for CAT Mock Test- 4 - Question 28

Let us draw a Venn diagram

From statement (1):
⇒ (b + c) - (b + e) = 8
⇒ c = 8 + e ... (1)
From statement (2):
⇒ (a + b) - (d + e) = 7
⇒ a + b = 7 + d + e ... (2)
From statement (3):
⇒ (a + b + e + f) - (b + c) = 21
⇒ a + e + f = 21 + c
⇒ a + e + f = 21 + 8 + e (From equation (1): c = 8 + e)
⇒ a + f = 29 ... (3)
From statement (4):
⇒ (a + b + e + f) + (d + e) = 66
⇒ a + b + d + 2e + f = 66 ... (4)
From statement (5):
⇒ b + e = 21 ... (5)
⇒ c = 21 - 4 = 17 ... (6)
From equation (1):
e = c - 8 = 17 - 8 = 9 ... (7)
From equations (5) and (7):
⇒ b = 21 - e = 21 - 9 = 12 ... (8)
From equations (3) and (4):
⇒ b + d + 2e = 37
⇒ d = 37 - 12 - 2 x 9 = 7 ... (9)
From equations (2), (7), (8) and (9):
⇒ a + b = 7 + d + e
⇒ a = 7 + 7 + 9 - 12 = 11 ... (10)
From equations (3) and (10):
⇒ a + f = 29
⇒ f = 29 - 11 = 18

Total number of friends = 11 + 12 + 17 + 7 + 9 + 18 = 74

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 29

In time slot-2, the average amount of time spent (in hours) per day by Mr. Xavier coding any of the mobile apps was (rounded to the nearest hour)


Detailed Solution for CAT Mock Test- 4 - Question 29

Number of hours Mr. Xavier spent coding any mobile app = 92
Average time per day == 5.11 hours

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 30

If during the last time slot, the maximum amount of time that Mr. Xavier could spend coding any one mobile app in a day was 1.5 hours, how many mobile apps would Mr. Xavier be able to finish coding in the targeted time?


Detailed Solution for CAT Mock Test- 4 - Question 30

Since Mr. Xavier could spend at most 1.5 hours per day on any one mobile app, the maximum time he could spend coding a mobile app during the last time slot would be 1.5 × 18 = 27 hours.
Therefore, any mobile app which has more than 27 hours of preparation remaining (after the first three time slots) cannot be studied completely.
By a quick observation, App-3, App-5 and App-9 have more than 27 hours remaining. Hence, the answer is 9 - 3 = 6.

CAT Mock Test- 4 - Question 31

What was the average time for which Mr. Xavier must have done coding per day during the last time slot to finish coding all the mobile apps in the targeted time?

Detailed Solution for CAT Mock Test- 4 - Question 31

Total time left for all the mobile apps combined = 184
Time to be spent per day = 184/18 = 10.22 hours

CAT Mock Test- 4 - Question 32

The cars given in which of the following options can be the only cars in a racing team?

Detailed Solution for CAT Mock Test- 4 - Question 32

The following table presents the 10% range of prices for each car and the cars that can be a part of the racing team, if that car was made the leader's car:

If the cars given in the options must be the only cars in the racing team, one of them must be the leader's car.
Option 1: If Car-1 is the leader's car, Car-2 cannot be in the team. If Car-2 is the leader's car, Car-4 and Car-6 cannot be in the team. If Car-4 is the leader's car, Car-2 cannot be in the team. If Car-6 is the leader's car, Car-2 cannot be in the team. Hence, this is not possible.
Option 2: If Car-3 is the leader's car, Car-12 cannot be in the team. If Car-6 is the leader's car, Car-7 cannot be in the team. If Car-7 is the leader's car, Car-6 and Car-12 cannot be in the team.
If Car-12 is the leader's car, Car-3 and Car-7 cannot be in the team.
Option 3: If Car-3 is the leader, Car-12 cannot be in the team. If Car-9 is the leader's car, this team can be formed. Hence, this is possible with Car-9 as the leader of the team.
Option 4: If Car-6 is the leader's car, Car-7 cannot be in the team. If Car-7 is the leader's car, Car-6. Car-9, Car-10 cannot be in the team. If Car-9 is the leader's car, Car-7 and Car-9 cannot be in the team. If Car-10 is the leader's car, Car-7 cannot be in the team. Hence, this is also not possible. Therefore, only the team given in option3 is possible.

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 33

What is Eanne's score in analytical ability (AA)?


Detailed Solution for CAT Mock Test- 4 - Question 33

Let us first convert frequency bar graph into a table so that it is easier to read the data.

It is given that Eanne, Channe and Banne jointly have the lowest total score, i.e. 8, with an identical score in all three parameters.
There can be many possibilities, in which one can score 8 marks. But, we have to ensure that all three got identical scores in all parameters. Hence, we will need at least 3 frequency for each parameter.
From the frequency table, we can see that OTBT's frequency is 3 for 4. Therefore, we can say that each of Eanne, Channe and Banne scored 4 in OTBT.
Similarly, from the frequency graph, we can see that CA's frequency is 3 for score 3 alone. Therefore, we can say that each of Eanne, Channe and Banne scored 3 in CA.
Hence, we can say that each of Eanne, Channe and Banne's score in AA = 8 - 4 - 3 = 1

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 34

How much did Hanne score in out of the box thinking (OTBT)?


Detailed Solution for CAT Mock Test- 4 - Question 34

Let us first convert frequency bar graph into a table so that it is easier to read the data.

It is given that Hanne scored a total of 23 and exactly 3 students featured in extended merit list had the highest score in exactly one parameter.
We can see that Hanne was one of those three students who featured in the extended merit list. Hence, we can say that he must have scored the highest score in one parameter.

Case 1: When Hanne scored the highest in CA:
Let us first find out the maximum possible score that Hanne can get in each section.
Hanne scored the highest in CA. Hence, Hanne's score in CA = 9
Since Hanne scored the highest in CA, he cannot have a score of 9 in AA. Hence, the best possible score which Hanne can have in AA = 7
Similarly, Hanne cannot have a score of 8 in OTBT. Hence, the best possible score which Hanne can have in OTBT = 7
We can see that that Hanne can have a total score of 23 only when he scores 9, 7, 7 in CA, AA and OTBT, respectively. Hence, we have a unique solution for this case.

Case 2: When Hanne scored the highest in AA
Let us first find out the maximum possible score that Hanne can get in each section.
Hanne scored the highest in AA. Hence, Hanne's score in AA = 9
Since Hanne scored the highest in AA, he can't have a score of 9 in CA. Hence, the best possible score which Hanne can have in CA = 7
Similarly, Hanne can't have a score of 8 in OTBT. Hence, the best possible score which Hanne can have in OTBT = 7
We can see that Hanne can have a total score of 23 only when he scores 9, 7, 7 in CA, AA and OTBT, respectively. Hence, we have a unique solution for this case.

Case 3: When Hanne scored the highest in OTBT
Let us first find out the maximum possible score that Hanne can get in each section.
Hanne scored the highest in OTBT. Hence, Hanne's score in OTBT = 8
Since Hanne has scored the highest in CA, he can't have a score of 9 in CA. Hence, the best possible score which Hanne can have in CA = 7
Similarly, Hanne can't have a score of 9 in AA. Hence, the best possible score which Hanne can have in AA = 7
We can see that that Hanne can have a maximum total score of 22. He can have a total score of 23 in this case. So, this case can be rejected.

From case 1 and case 2, we can see that Hanne scored 7 in OTBT in both the cases.

CAT Mock Test- 4 - Question 35

Two students Ianne and Janne, categorised in the extended merit list, are tied with the same total score. What is the maximum total score that they can score individually?

Detailed Solution for CAT Mock Test- 4 - Question 35

Let us first convert frequency bar graph into a table so that it's easier to read the data.

It is given that Hanne scored a total of 23 and exactly 3 students featured in the extended merit list, have the highest score in exactly one parameter.
We can see that Hanne is one of those three students who featured in extended merit list. Hence, we can say that he must have scored the highest score in one parameter.

Case 1: When Hanne scored the highest in CA:Let us first find out the maximum possible score that Hanne can get in each section.Hanne scored the highest in CA. Hence, Hanne's score in CA = 9Since Hanne scored the highest in CA, he cannot have a score of 9 in AA. Hence, the best possible score which Hanne can have in AA = 7Similarly, Hanne cannot have a score of 8 in OTBT. Hence, the best possible score which Hanne can have in OTBT = 7We can see that that Hanne can have a total score of 23 only when he scores 9, 7, 7 in CA, AA and OTBT, respectively. Hence, we have a unique solution for this case.

Case 2: When Hanne scored the highest in AALet us first find out the maximum possible score that Hanne can get in each section.Hanne scored the highest in AA. Hence, Hanne's score in AA = 9Since Hanne scored the highest in AA, he can't have a score of 9 in CA. Hence, the best possible score which Hanne can have in CA = 7Similarly, Hanne can't have a score of 8 in OTBT. Hence, the best possible score which Hanne can have in OTBT = 7We can see that Hanne can have a total score of 23 only when he scores 9, 7, 7 in CA, AA and OTBT, respectively. Hence, we have a unique solution for this case.

Case 3: When Hanne scored the highest in OTBTLet us first find out the maximum possible score that Hanne can get in each section.Hanne scored the highest in OTBT. Hence, Hanne's score in OTBT = 8Since Hanne has scored the highest in CA, he can't have a score of 9 in CA. Hence, the best possible score which Hanne can have in CA = 7Similarly, Hanne can't have a score of 9 in AA. Hence, the best possible score which Hanne can have in AA = 7We can see that that Hanne can have a maximum total score of 22. He can have a total score of 23 in this case. So, this case can be rejected.

 

We can see that Hanne can score 23 in two different ways. We have to deal with these 2 possible cases separately and figure out the maximum individual score that Ianne and Janne can score.
Two students Ianne and Janne, categorised in extended merit list, are tied with the same total score. To be categorised in extended merit list, one has to score anything from 19 to 24.
It is also given that exactly 3 students featured in extended merit list, have the highest score in exactly one parameter. Hence, we can say that Hanne, Ianne and Janne scored the highest marks of all parameters.

Case 1: When Hanne scored 9, 7, 7 in CA, AA and OTBT, respectively. After removing Hanne's score, frequency table will look like this:

Let us assume that Ianne scored the highest in AA and Janne scored the highest in OTBT. {Naming differently won't matter as we are calculating the maximum possible score for both.}
Ianne can score a maximum of 7 in CA. Similarly, he/she can score a maximum of 7 in OTBT. Hence, the maximum total which Ianne can score = 7 + 9 + 7 = 23
Janne can score a maximum of 7 in CA. Similarly, he/she can score a maximum of 6 in AA. Hence, the maximum total which Janne can score = 7 + 6 + 8 = 21
However, both can't score 7 at a time in CA. To maximise the individual score, let us assume that Ianne scored 6 in CA and Janne scored 7 in CA. Even in that case, the maximum individual score that Ianne and Janne can have = 21
We can represent this in a tabular format.

Case 2: When Hanne scored 7, 9, 7 in CA, AA and OTBT, respectively. After removing Hanne's score, frequency table will look like this:

Let us assume that Ianne scored the highest in CA and Janne scored the highest in OTBT. {Naming differently won't matter as we are calculating the maximum possible score for both.}
Ianne can score a maximum of 7 in AA. Similarly, he/she can score a maximum of 7 in OTBT. Hence, a maximum total which Ianne can score = 9 + 7 + 7 = 23
Janne can score a maximum of 6 in CA. Similarly, he/she can score a maximum of 7 in AA. Hence, a maximum total which Janne can score = 6 + 7 + 8 = 21
However, both can't score 7 at a time in AA. To maximise the individual score, let us assume that Ianne scored 6 in AA and Janne scored 7 in AA. Even in that case, the maximum individual score that Ianne and Janne can have = 21
We can represent this in a tabular format.

Therefore, we can say that Ianne and Janne can score a maximum total score of 21 individually.

CAT Mock Test- 4 - Question 36

Who among the following definitely lives in a corner room?

Detailed Solution for CAT Mock Test- 4 - Question 36

The area of room T is 16 m2..
One side of room T is 6 m in length. Therefore, the area of room S is 4 m2.
It has been given that five rooms have same area and rooms P and R have same area.
Rooms P, Q and R have same area.
Area of room P + area of room Q = 32 m2
Rooms P and Q share a wall.
Therefore, the lengths of rooms P and Q must be the same.
Let the length of room P be l.
Length of room U = length of room V = 2l
Let the width of room P be b.
lb = 16 --- (1)

Let the breadth of room U be 'x'.
2lx = 16 --- (2)
⇒ x = b/2
The same can be said to be true with respect to room V as well.
Now, we know that
⇒ b = 4 and l = 4
The length and breadth of all the rooms are as follows:

 

Amar has only 2 neighbours.
Amar can live in room P, V, S or T.
The areas of room assigned to Edward and Ganesh are same, but the perimeters are different. Therefore, one of them must be living in room U, V or R, and the other must be living in P or Q. The perimeter of the room in which Amar lives is equal to the perimeter of the room in which Ganesh lives. The perimeter of the room in which Ganesh lives can be 20 or 16. The perimeters of room P, V, S and T are 16, 20, 8 and 16, respectively. Therefore, Amar cannot live in room S. It has been given that Amar does not live in Room P. Therefore, Amar can live in room V or T.

Case 1: Amar lives in room V.
The areas of rooms in which Edward and Ganesh live are same, but the perimeters are different. Edward and Ganesh are not neighbours. Amar and Edward are not neighbours. Therefore, Edward must live in room P and Ganesh must live in room R.

Faisal is not a neighbour of Amar or Edward. Faisal does not live in the smallest room. Therefore, Faisal must live in room T. Faisal and Ganesh are neighbours of Deepak. Therefore, Deepak must live in room S. The perimeter of the room in which Bindu lives is less than the perimeter of the room in which Charan lives. Therefore, Charan must live in room U and Bindu must live in room Q. The arrangement will be as follows:

Case 2: Amar lives in room T.
The areas of rooms in which Edward and Ganesh live are same, but the perimeters are different. Edward and Ganesh are not neighbours. Amar and Edward are not neighbours. Faisal is not a neighbour of Amar or Edward and he does not live in the smallest room. Ganesh does not live in room Q. Therefore, Ganesh must live in room P, Faisal must live in room Q and Edward must live in room V.

Ganesh and Faisal are neighbours of Deepak. The perimeter of the room in which Bindu lives is less than the perimeter of the room in which Charan lives. Therefore, the arrangement will be as follows:

As we can see, Edward is the only person who can be definitely said to be living in a corner room. Therefore, option 3 is the right answer.

CAT Mock Test- 4 - Question 37

Who among the following is definitely not a neighbour of Bindu?

Detailed Solution for CAT Mock Test- 4 - Question 37

The area of room T is 16 m2..
One side of room T is 6 m in length. Therefore, the area of room S is 4 m2.
It has been given that five rooms have same area and rooms P and R have same area.
Rooms P, Q and R have same area.
Area of room P + area of room Q = 32 m2
Rooms P and Q share a wall.
Therefore, the lengths of rooms P and Q must be the same.
Let the length of room P be l.
Length of room U = length of room V = 2l
Let the width of room P be b.
lb = 16 --- (1)

Let the breadth of room U be 'x'.
2lx = 16 --- (2)
⇒ x = b/2
The same can be said to be true with respect to room V as well.
Now, we know that
⇒ b = 4 and l = 4
The length and breadth of all the rooms are as follows:

 

Amar has only 2 neighbours.
Amar can live in room P, V, S or T.
The areas of room assigned to Edward and Ganesh are same, but the perimeters are different. Therefore, one of them must be living in room U, V or R, and the other must be living in P or Q. The perimeter of the room in which Amar lives is equal to the perimeter of the room in which Ganesh lives. The perimeter of the room in which Ganesh lives can be 20 or 16. The perimeters of room P, V, S and T are 16, 20, 8 and 16, respectively. Therefore, Amar cannot live in room S. It has been given that Amar does not live in Room P. Therefore, Amar can live in room V or T.

Case 1: Amar lives in room V.
The areas of rooms in which Edward and Ganesh live are same, but the perimeters are different. Edward and Ganesh are not neighbours. Amar and Edward are not neighbours. Therefore, Edward must live in room P and Ganesh must live in room R.

Faisal is not a neighbour of Amar or Edward. Faisal does not live in the smallest room. Therefore, Faisal must live in room T. Faisal and Ganesh are neighbours of Deepak. Therefore, Deepak must live in room S. The perimeter of the room in which Bindu lives is less than the perimeter of the room in which Charan lives. Therefore, Charan must live in room U and Bindu must live in room Q. The arrangement will be as follows:

Case 2: Amar lives in room T.
The areas of rooms in which Edward and Ganesh live are same, but the perimeters are different. Edward and Ganesh are not neighbours. Amar and Edward are not neighbours. Faisal is not a neighbour of Amar or Edward and he does not live in the smallest room. Ganesh does not live in room Q. Therefore, Ganesh must live in room P, Faisal must live in room Q and Edward must live in room V.

Ganesh and Faisal are neighbours of Deepak. The perimeter of the room in which Bindu lives is less than the perimeter of the room in which Charan lives. Therefore, the arrangement will be as follows:

Deepak is definitely not a neighbour of Bindu. Therefore, option 2 is the right answer.

CAT Mock Test- 4 - Question 38

For how many persons can the room they live in be determined?

Detailed Solution for CAT Mock Test- 4 - Question 38

The area of room T is 16 m2..
One side of room T is 6 m in length. Therefore, the area of room S is 4 m2.
It has been given that five rooms have same area and rooms P and R have same area.
Rooms P, Q and R have same area.
Area of room P + area of room Q = 32 m2
Rooms P and Q share a wall.
Therefore, the lengths of rooms P and Q must be the same.
Let the length of room P be l.
Length of room U = length of room V = 2l
Let the width of room P be b.
lb = 16 --- (1)

Let the breadth of room U be 'x'.
2lx = 16 --- (2)
⇒ x = b/2
The same can be said to be true with respect to room V as well.
Now, we know that
⇒ b = 4 and l = 4
The length and breadth of all the rooms are as follows:

 

Amar has only 2 neighbours.
Amar can live in room P, V, S or T.
The areas of room assigned to Edward and Ganesh are same, but the perimeters are different. Therefore, one of them must be living in room U, V or R, and the other must be living in P or Q. The perimeter of the room in which Amar lives is equal to the perimeter of the room in which Ganesh lives. The perimeter of the room in which Ganesh lives can be 20 or 16. The perimeters of room P, V, S and T are 16, 20, 8 and 16, respectively. Therefore, Amar cannot live in room S. It has been given that Amar does not live in Room P. Therefore, Amar can live in room V or T.

Case 1: Amar lives in room V.
The areas of rooms in which Edward and Ganesh live are same, but the perimeters are different. Edward and Ganesh are not neighbours. Amar and Edward are not neighbours. Therefore, Edward must live in room P and Ganesh must live in room R.

Faisal is not a neighbour of Amar or Edward. Faisal does not live in the smallest room. Therefore, Faisal must live in room T. Faisal and Ganesh are neighbours of Deepak. Therefore, Deepak must live in room S. The perimeter of the room in which Bindu lives is less than the perimeter of the room in which Charan lives. Therefore, Charan must live in room U and Bindu must live in room Q. The arrangement will be as follows:

Case 2: Amar lives in room T.
The areas of rooms in which Edward and Ganesh live are same, but the perimeters are different. Edward and Ganesh are not neighbours. Amar and Edward are not neighbours. Faisal is not a neighbour of Amar or Edward and he does not live in the smallest room. Ganesh does not live in room Q. Therefore, Ganesh must live in room P, Faisal must live in room Q and Edward must live in room V.

Ganesh and Faisal are neighbours of Deepak. The perimeter of the room in which Bindu lives is less than the perimeter of the room in which Charan lives. Therefore, the arrangement will be as follows:

The positions of all the seven persons are different in the two cases. Therefore, we cannot determine the room of any of the persons they live in. Hence, option 4 is the right answer.

CAT Mock Test- 4 - Question 39

Who stood first in the game?

Detailed Solution for CAT Mock Test- 4 - Question 39

It is given that there were 6 attempts in the game and all the five players got different number of dollars. The maximum number of attempts a single player could have rolled the slot machine has to be 2 (if one player rolled the slot machine in 3 attempts, then two players would end up with the same number of dollars).
Jack was the only player to get 2 attempts consecutively and he did not get the 1st attempt. The number of maximum possible attempts by a player is 2, which means Jack got $10 in the first attempt, and in the second attempt he paid a penalty amount of $5, but from (iv), the player who rolled the slot machine in the last attempt won the game.
Jack couldn't be at 6th.
Possible positions for Jack are: 2, 3, or 3, 4, or 4, 5, but there is change in sequence (from (ii)) at the beginning of the 4th attempt and the 5th attempt. So, Jack couldn't go at the 4th and 5th attempt.
Sequence[attempt number(name, amount)]: 1, 2(Jack, $10), 3(Jack, -$5), 4, 5, 6(xx, $10)
This means, the 1st, 4th and 5th attempts didn't hit correctly and they would pay the penalty.
Sequence[attempt number(name, amount)]: 1(xx, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(xx, -$5), 6(xx, $10)
There has to be another person who rolled the slot machine in 2 attempts. This person also could not have rolled the slot machine in the 5th and 6th attempts.
Hence, he must have rolled the slot machine in the 1st and 5th attempts.
From (ii), this person has to be Luke because only by getting the 5th attempt could Luke move to front of Jack.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(Luke, -$5), 6(xx, $10)
Will must have rolled the slot machine in one attempt without hitting the jackpot and Franklin must have rolled the slot machine in one attempt and hit the jackpot.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(Will, -$5), 5(Luke, -$5), 6(Franklin, $10)

From the above table, it is clear that Franklin got the highest amount, i.e. $10, so he stood first in the game.

CAT Mock Test- 4 - Question 40

Who was at the fourth position from the bottom at the starting of the third attempt?

Detailed Solution for CAT Mock Test- 4 - Question 40

It is given that there were 6 attempts in the game and all the five players got different number of dollars. The maximum number of attempts a single player could have rolled the slot machine has to be 2 (if one player rolled the slot machine in 3 attempts, then two players would end up with the same number of dollars).
Jack was the only player to get 2 attempts consecutively and he did not get the 1st attempt. The number of maximum possible attempts by a player is 2, which means Jack got $10 in the first attempt, and in the second attempt he paid a penalty amount of $5, but from (iv), the player who rolled the slot machine in the last attempt won the game.
Jack couldn't be at 6th.
Possible positions for Jack are: 2, 3, or 3, 4, or 4, 5, but there is change in sequence (from (ii)) at the beginning of the 4th attempt and the 5th attempt. So, Jack couldn't go at the 4th and 5th attempt.
Sequence[attempt number(name, amount)]: 1, 2(Jack, $10), 3(Jack, -$5), 4, 5, 6(xx, $10)
This means, the 1st, 4th and 5th attempts didn't hit correctly and they would pay the penalty.
Sequence[attempt number(name, amount)]: 1(xx, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(xx, -$5), 6(xx, $10)
There has to be another person who rolled the slot machine in 2 attempts. This person also could not have rolled the slot machine in the 5th and 6th attempts.
Hence, he must have rolled the slot machine in the 1st and 5th attempts.
From (ii), this person has to be Luke because only by getting the 5th attempt could Luke move to front of Jack.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(Luke, -$5), 6(xx, $10)
Will must have rolled the slot machine in one attempt without hitting the jackpot and Franklin must have rolled the slot machine in one attempt and hit the jackpot.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(Will, -$5), 5(Luke, -$5), 6(Franklin, $10)

The 3rd and 2nd attempts were taken by Jake, so now we need to check the 1st attempt which was taken by Luke. In the 2nd attempt, Luke would be 2nd from the top, and there were no changes in the 3rd attempt, as the 3rd attempt was taken by the same person as the 2nd attempt.
So, fourth from the bottom would be the same person which was second from the top, i.e. Luke.

CAT Mock Test- 4 - Question 41

Which of the following cannot be the sum of amount with any three players out of total five?

Detailed Solution for CAT Mock Test- 4 - Question 41

It is given that there were 6 attempts in the game and all the five players got different number of dollars. The maximum number of attempts a single player could have rolled the slot machine has to be 2 (if one player rolled the slot machine in 3 attempts, then two players would end up with the same number of dollars).
Jack was the only player to get 2 attempts consecutively and he did not get the 1st attempt. The number of maximum possible attempts by a player is 2, which means Jack got $10 in the first attempt, and in the second attempt he paid a penalty amount of $5, but from (iv), the player who rolled the slot machine in the last attempt won the game.
Jack couldn't be at 6th.
Possible positions for Jack are: 2, 3, or 3, 4, or 4, 5, but there is change in sequence (from (ii)) at the beginning of the 4th attempt and the 5th attempt. So, Jack couldn't go at the 4th and 5th attempt.
Sequence[attempt number(name, amount)]: 1, 2(Jack, $10), 3(Jack, -$5), 4, 5, 6(xx, $10)
This means, the 1st, 4th and 5th attempts didn't hit correctly and they would pay the penalty.
Sequence[attempt number(name, amount)]: 1(xx, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(xx, -$5), 6(xx, $10)
There has to be another person who rolled the slot machine in 2 attempts. This person also could not have rolled the slot machine in the 5th and 6th attempts.
Hence, he must have rolled the slot machine in the 1st and 5th attempts.
From (ii), this person has to be Luke because only by getting the 5th attempt could Luke move to front of Jack.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(Luke, -$5), 6(xx, $10)
Will must have rolled the slot machine in one attempt without hitting the jackpot and Franklin must have rolled the slot machine in one attempt and hit the jackpot.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(Will, -$5), 5(Luke, -$5), 6(Franklin, $10)

$15 = Franklin($10) + Jake($5) + Benjamin($0)
$5 = Franklin($10) +Jake($5) + Luke(-$10)
$10 = Franklin($10) + Jake($5) + Will(-$5)
Sum $20 is not possible from any three combinations of the given five players.

CAT Mock Test- 4 - Question 42

What is the difference between the amounts (in $) with Benjamin and Will?

Detailed Solution for CAT Mock Test- 4 - Question 42

It is given that there were 6 attempts in the game and all the five players got different number of dollars. The maximum number of attempts a single player could have rolled the slot machine has to be 2 (if one player rolled the slot machine in 3 attempts, then two players would end up with the same number of dollars).
Jack was the only player to get 2 attempts consecutively and he did not get the 1st attempt. The number of maximum possible attempts by a player is 2, which means Jack got $10 in the first attempt, and in the second attempt he paid a penalty amount of $5, but from (iv), the player who rolled the slot machine in the last attempt won the game.
Jack couldn't be at 6th.
Possible positions for Jack are: 2, 3, or 3, 4, or 4, 5, but there is change in sequence (from (ii)) at the beginning of the 4th attempt and the 5th attempt. So, Jack couldn't go at the 4th and 5th attempt.
Sequence[attempt number(name, amount)]: 1, 2(Jack, $10), 3(Jack, -$5), 4, 5, 6(xx, $10)
This means, the 1st, 4th and 5th attempts didn't hit correctly and they would pay the penalty.
Sequence[attempt number(name, amount)]: 1(xx, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(xx, -$5), 6(xx, $10)
There has to be another person who rolled the slot machine in 2 attempts. This person also could not have rolled the slot machine in the 5th and 6th attempts.
Hence, he must have rolled the slot machine in the 1st and 5th attempts.
From (ii), this person has to be Luke because only by getting the 5th attempt could Luke move to front of Jack.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(Luke, -$5), 6(xx, $10)
Will must have rolled the slot machine in one attempt without hitting the jackpot and Franklin must have rolled the slot machine in one attempt and hit the jackpot.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(Will, -$5), 5(Luke, -$5), 6(Franklin, $10)

From the above table, after the final analysis of game, Benjamin's score is 0 and Will's score is -5. So the difference between the amounts (in $) with Benjamin and Will is 5.

CAT Mock Test- 4 - Question 43

Who among the following was/were in debt at the end of the game?

Detailed Solution for CAT Mock Test- 4 - Question 43

It is given that there were 6 attempts in the game and all the five players got different number of dollars. The maximum number of attempts a single player could have rolled the slot machine has to be 2 (if one player rolled the slot machine in 3 attempts, then two players would end up with the same number of dollars).
Jack was the only player to get 2 attempts consecutively and he did not get the 1st attempt. The number of maximum possible attempts by a player is 2, which means Jack got $10 in the first attempt, and in the second attempt he paid a penalty amount of $5, but from (iv), the player who rolled the slot machine in the last attempt won the game.
Jack couldn't be at 6th.
Possible positions for Jack are: 2, 3, or 3, 4, or 4, 5, but there is change in sequence (from (ii)) at the beginning of the 4th attempt and the 5th attempt. So, Jack couldn't go at the 4th and 5th attempt.
Sequence[attempt number(name, amount)]: 1, 2(Jack, $10), 3(Jack, -$5), 4, 5, 6(xx, $10)
This means, the 1st, 4th and 5th attempts didn't hit correctly and they would pay the penalty.
Sequence[attempt number(name, amount)]: 1(xx, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(xx, -$5), 6(xx, $10)
There has to be another person who rolled the slot machine in 2 attempts. This person also could not have rolled the slot machine in the 5th and 6th attempts.
Hence, he must have rolled the slot machine in the 1st and 5th attempts.
From (ii), this person has to be Luke because only by getting the 5th attempt could Luke move to front of Jack.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(Luke, -$5), 6(xx, $10)
Will must have rolled the slot machine in one attempt without hitting the jackpot and Franklin must have rolled the slot machine in one attempt and hit the jackpot.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(Will, -$5), 5(Luke, -$5), 6(Franklin, $10)

Will and Luke respectively scored -10 and -5 debt at the end of the game, so both were in debt.

CAT Mock Test- 4 - Question 44

Which of the following attempts rolled the slot machine to definitely hit the jackpot?

Detailed Solution for CAT Mock Test- 4 - Question 44

It is given that there were 6 attempts in the game and all the five players got different number of dollars. The maximum number of attempts a single player could have rolled the slot machine has to be 2 (if one player rolled the slot machine in 3 attempts, then two players would end up with the same number of dollars).
Jack was the only player to get 2 attempts consecutively and he did not get the 1st attempt. The number of maximum possible attempts by a player is 2, which means Jack got $10 in the first attempt, and in the second attempt he paid a penalty amount of $5 or vice versa, but from (iv), the player who rolled the slot machine in the last attempt won the game.
Jack couldn't be at 6th.
Possible positions for Jack are: 2, 3, or 3, 4, or 4, 5, but there is change in sequence (from (ii)) at the beginning of the 4th attempt and the 5th attempt. So, Jack couldn't go at the 4th and 5th attempt.
Sequence[attempt number(name, amount)]: 1, 2(Jack, $10), 3(Jack, -$5), 4, 5, 6(xx, $10)
This means, the 1st, 4th and 5th attempts didn't hit correctly and they would pay the penalty.
Sequence[attempt number(name, amount)]: 1(xx, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(xx, -$5), 6(xx, $10)
There has to be another person who rolled the slot machine in 2 attempts. This person also could not have rolled the slot machine in the 5th and 6th attempts.
Hence, he must have rolled the slot machine in the 1st and 5th attempts.
From (ii), this person has to be Luke because only by getting the 5th attempt could Luke move to front of Jack.
Sequence[attempt number(name, amount)]: 1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(xx, -$5), 5(Luke, -$5), 6(xx, $10)
Will must have rolled the slot machine in one attempt without hitting the jackpot and Franklin must have rolled the slot machine in one attempt and hit the jackpot.
Sequence[attempt number(name, amount)]:

1(Luke, -$5), 2(Jack, $10), 3(Jack, -$5), 4(Will, -$5), 5(Luke, -$5), 6(Franklin, $10)
OR
1(Luke, -$5), 2(Jack, -$5), 3(Jack, $10), 4(Will, -$5), 5(Luke, -$5), 6(Franklin, $10)

Thus, we can see that only 2nd or 3rd attempt and the last attempt hit the jackpot.
Since the question asks for a 'definite' hit, the answer is 6th attempt.

CAT Mock Test- 4 - Question 45

Radheshyam is an alcohol bootlegger. He wants to make an extra profit on the alcohol, hence he tried to dilute the alcohol. He does this in a unique way. He takes 625 Liters of alcohol in a tank that has a large capacity. He replaces 20% of the content with water. After this, he doubles the quantity of alcohol in the tank by adding pure alcohol and then doubles the percentage of water in the mixture by adding pure water. 

His manager found this process tiresome and confusing. Therefore he suggested Radheshyamto mix the original 625L alcohol with a solution B of alcohol and water so that the resulting solution is the same as that derived from his initial process. What is the overall quantity and concentration of the suggested mixture B?

Detailed Solution for CAT Mock Test- 4 - Question 45

Initially, Radheshyam had 625 litres of alcohol. After replacing 20% with water he has 125 Liters of water and 500 Liters of alcohol.

After doubling the alcohol content in the tank, he has 1000Liters of Alcohol and 125 Liters of water.

After this, he doubles the percentage of water in the solution by adding pure water. Let the amount of water be xx liters

As per the question

Upon rearranging and solving we get (125+x) 1125 = 250 (1125 + x)

875x = 125 x 125

Therefore the final solution has 1000L of alcohol and 

The added mixture should have 375L of alcohol and 2000/7 of water

Total quantity of mixture = 

%concentration of alcohol = 

CAT Mock Test- 4 - Question 46

Two friends, A and B, start walking simultaneously from two points, P and Q, which are 100 m apart, towards points Q and P, respectively. After they reach Q and P, they again start walking back towards points P and Q. They keep on walking between points P and Q without stopping anywhere. The respective ratio of the speeds of A and B is 3 : 2.

Q. What is the total distance travelled by A by the time A and B meet each other at point P for the first time?

Detailed Solution for CAT Mock Test- 4 - Question 46

B reaches P for the first time after he walks 100 m.

And for the second time after he walks 300 m.

And for the third time after he walks 500 m.

In all the cases, during the time in which B walks 100 m to reach point P, A will walk 3/2 × 100 m = 150 m.

3/2 × 300 m = 450 m

3/2 × 500 m = 750 m, which is not a multiple of 100.

So, A and B never meet each other at P.

Hence, answer option D is correct.

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 47

f(x) is a non constant linear function such that f(f(f(f(1)))) is equal to f(f(1)). What is the value of f(3)+2f(0) if it is given that the angle between the function and the X axis is not equal to 450

 

Enter -1 if the answer can't be determined.


Detailed Solution for CAT Mock Test- 4 - Question 47

Let the function be f(x) = mx+c, as it is given that the function, is linear, here 'm' is the slope of the function

f(f(x)) = m2x+c+mc

similarly f(f(f(x))) = f(m2x + c + m3x+c+mc+m2c

and f(f(f(f(x)))) = m4x + c + mc + m2c + m3c

f(f(f(f(1)))) = f(f(1)), Thus, m4+c+mc+m2c+m3c = m2+c+mc

On rearranging we get m4+m2c+m3c = m2

Since the function is not constant we can say that m ≠ 0

Dividing both side by m2 and shifting all term to one side we get

m+ c + mc − 1 = 0

(m2−1)+(c+mc) = 0

(m+1)(m−1)+c(1+m)=0

(m+1)(m+c−1) = 0

Since the function does not make 450 with x-axis the value of m can not be 1 or -1

Thus m+c-1 = 0 or m+c = 1....(I)

f(3) = 3m+c and f(0) = c

f(3)+2f(0) = 3m+c+2c 

= 3m+c+2c = 3(m+c) = 3 (inputting m+c = 1 from (I))

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 48

The equation = 4 cos (π/2 (x2  + 2x)) has how many distinct real solutions for x ≥  0


Detailed Solution for CAT Mock Test- 4 - Question 48

If x ≥ 0 it implies that x+2 is also always positive.

The minimum value the LHS will be

thus x = 0 as we are given that x ≥ 0
The RHS has a cos term and the maximum value of RHS is 4 when the 

It is possible when cos 

or x2 + 2x = 4n

Thus there are many solutions for the equation but LHS achieves the value only once when x = 0. There is one solution possible.

CAT Mock Test- 4 - Question 49

Modern Dairy is an upcoming company that aims to provide a unique type of milk derived from plant to the customer segment which is lactose intolerant. It has 2 suppliers. The first supplier gives a solution of soy milk and water which has a soy milk concentration of 87.5%. The second suppliers gives a solution of almond based milk and water in which the concentration of almond based milk is 60%. If the milk obtained by mixing these two solutions has a water concentration of 30%, then what is the percentage of soy-milk in the mixture? 

Detailed Solution for CAT Mock Test- 4 - Question 49

Let the x units of soy-milk solution is used and y units of an almond-based solution is used

Amount of water in soy-milk = 0.125x units

Amount of water in almond-milk = 0.4y

After the mixing, the concentration of water is 0.3

Hence 0.125x+0.4y = 0.3(x+y)

0.125x+0.4y = 0.3x+0.3y

0.1y = 0.175x

y = 1.75x

y = 47​x

CAT Mock Test- 4 - Question 50

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. A kite is formed with length  of uncommon sides as 7 and 24. If length of one of its diagonal is 25 what is the length of other diagonal?

Detailed Solution for CAT Mock Test- 4 - Question 50

Let ABCD be a kite with the uncommon sides be 7 and 24. And point at which diagonals intersect is O.

It can be shown as

One of the diagonal has a length of 25. It is possible when AC =25 only. If DB = 25 then AD+BD =14 < DB=25 which violates triangle inequality.

Thus we observe that ADB and ABC is a right-triangle as 7+ 24= 252

Area of the kite = 2 × 1/2​(7)(24) =168  sq units.

From symmetry △AOD and △AOB are congruent and hence ∠AOB = 900

Area of kite = 1/2​(AC)(DO) + 1/2​(AC)(OB) = 1/2​(AC)(DB) = 168

1/2 ​(25)(DB)= 168

DB = 168​/12.5 = 13.44 units

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 51

What is the number of common tangents between the two circles C1 and C2 where C1: x2−8x+y2−12y+16 = 0 and C2 : x2−8x+y2−18y+88 = 0


Detailed Solution for CAT Mock Test- 4 - Question 51

Let us take the curve C1: Upon inspection, we see that it is an equation of a circle. 

It can be written as (x−4)+ (y−6)= 62. Thus center is (4,6) and radius =6

Similarly, C2 is also a circle that can be written as (x−4)2+(y−9)= 32. Thus center = (4,9) and radius = 3

Distance between center = 

The difference in radius = 6-3 = 3 units. 

We observe that distance between centre = difference of radius. Thus One circle is inside the second circle and have exactly 1 point common. 

1 tangent can be drawn,

The same can be seen from the graph as well

CAT Mock Test- 4 - Question 52

In a regular hexagon ABCDEF, What is the ratio AD: AC?

Detailed Solution for CAT Mock Test- 4 - Question 52

Let the side be aa of Hexagon ABCDEF

Since we know that diagonals divide the hexagon on 6-equilateral triangle, AD = AO+OD = a + a = 2a

Since it is a regular polygon, the internal angle = 180 - 360/6 = 180 - 60 = 120 degrees

∠ABC = 1200

in ΔAB, AB = BC and ∠ABC = 120. This is an isoceles triangle so  ∠BAC = ∠BCA = 300 Applying sin rule

CAT Mock Test- 4 - Question 53

If α, β  and γ are the roots of the equation 2x3 - 3x2 - 5x + 6 = 0, then α2 + β2 + γ2 is equal to

Detailed Solution for CAT Mock Test- 4 - Question 53

CAT Mock Test- 4 - Question 54

Sita went to a nearby village and wanted to buy fruits. The village market only sold apples, oranges and mangoes. The cost of the apple was Rs 5/piece. The cost of the orange was Rs 13/piece and the cost of the mango was Rs 15/piece.  She has to buy at least 1 fruit of each kind. Her overall purchase of fruits coster her Rs 98.

 

Q. What is the sum of the minimum possible number of fruits and the maximum possible number of fruits she could buy

Detailed Solution for CAT Mock Test- 4 - Question 54

Atleast 1 fruit has to be bought, the cost incurred for purchasing exactly a fruit of each type = 13+5+15 = 33.

Let the extra number of apples bought be x, number of oranges bought be y and number of mangoes bought be z

Then 

5x + 13y + 15z ≤ 98−33 = 65

To buy the maximum number of possible fruit we can take x = 13x = 13

After which Sita will be left with Rs.2 Total number of fruits bought = 13+3 =16

When she has Rs 98 with her and wants to buy the minimum number of fruits such that all the money is spent. After buying 1 fruit of each type she will be left with 98-33 = 65

To buy the minimum number of possible fruit we can take z = 4z = 4. After which Sita will have Rs5, she'll buy an apple 

Total fruits bought = 4+1+3 = 8

Sum = 16+8 = 24

CAT Mock Test- 4 - Question 55

How many odd natural numbers are possible which satisfy the inequality

(x−2) (x−6) (x−10) (x−14)  (x−18) < 0

Detailed Solution for CAT Mock Test- 4 - Question 55

We can see that at x= 2,6,10,14,18 the function becomes 0

After every root, the function changes its value. 

for x > 18; the equation is always positive hence no solution 

for 14<x<18, the equation is negative and 15 & 17 are 2 odd numbers satisfying it

for 10<x<14; the equation is always positive

for 6 < x < 10 ; the equation is negative and 7 & 9 are 2 odd numbers satisfying it

for 2<x<6, the function will be always positive hence no solution

For 0<x<2 the function will be negative. 1 is the only odd number in this range

Total 5 such numbers are there.

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 56

What is the remainder when 9157 is divided by 21


Detailed Solution for CAT Mock Test- 4 - Question 56

91 has factors 7 and 13

We have to find 9157 mod 21.

We can divide both numerator and denominator by 7 and get 13× 1956 mod 3

Which is equal to  (13 mod 3)(9156mod3)

It is equal to ( (12+1)mod 3) ( (90+1) mod 3) ((90+1)mod3).......56 times

= 1*1*1*1...57 times

=1

Actual remainder will be 1*7 = 7 as we divided the initial fraction by 7

CAT Mock Test- 4 - Question 57

If log49​2 =a, log9​2 =b and log2​48 = c then what is the value of (c − 1/2b​)(1/a​−1/b​)

Detailed Solution for CAT Mock Test- 4 - Question 57

Let us start with calculating the value of c − 1/2b​

Now we need to calculate the value of (1/a​−1/b​)

Putting (I) and (II) in original equation

we get 

CAT Mock Test- 4 - Question 58

A biologist conducted an experiment on guinea pigs, of which 30% were male and the rest were female. Out of the guinea pigs that died during the experiment, 20% were female. What is the ratio of the death rate among male guinea pigs to that among females?

Detailed Solution for CAT Mock Test- 4 - Question 58

According to the Q.
a + g = 0.3 (a + b + g + N) ...(i)
b = 0.2 (b + g) ...(ii)

Solving I,
0.7 (a + g) = 0.3 (b + N)
Solving II,
g = 4b

Hence

CAT Mock Test- 4 - Question 59

N people can sit on 4 chairs in 5040 ways. In how many ways can 4 people be selected out of n-2 people.

Detailed Solution for CAT Mock Test- 4 - Question 59

We are given that nP4​=5040

This can be written as 

Multiply numerator and denominator by 6! we get

Hence n = 10

n-2 = 8

4 people can be selected out of 8 in  = 70  ways

CAT Mock Test- 4 - Question 60

Ram has Rs 1,00,000 with him which he wants to invest. His financial advisor advised him to split the investment into 2 scheme. 

The scheme I had a return of 10% compounded annually. Whereas scheme II had the interest of 20%per annum compounded half-yearly. If after the end of 2 years he had received a total amount of Rs 1,36,246 How much money did he invest in the scheme I?

Detailed Solution for CAT Mock Test- 4 - Question 60

Let the amount invested in the scheme I  xx

The return from scheme I at the end of year 2 (1.1)2x = 1.21

Let the amount invested in scheme II be yy

Since it is compounded half-yearly, the rate of interest per half-year will be 20%/2 ​= 10%

The return from scheme II will be y(1.1)4 = 1.4641y

Hence 1.21x+1.4641y=136246 ...(I)

Also, x+y = 100000 ...(II)

1.4641(II)-(I)  gives

0.2541x=10164

x=40,000

CAT Mock Test- 4 - Question 61

For an investment with a fixed rate of return, interest received in 3rd  year is 1440 and 4th year is 1728. What is the rate of compound interest per annum?

Detailed Solution for CAT Mock Test- 4 - Question 61

For compound interest, the interest gained per year is in G.P with a common ratio of (1+r%) where r is the rate of interest

Let the rate be R%

Then, 1+R%) = 1728/1440 ​= 1.2

R% = 0.2 or 20%

CAT Mock Test- 4 - Question 62

Ram sells only jeans of a particular make all of which he bought at the same price. During the Diwali festival, he started the "Buy 4 get 1 free " offer and on top of that, he gave 10% off on the bill. Despite such discounts, he made a profit of 5%. By, what percent was the cost of jeans marked up if all the customers availed both the offers?

Detailed Solution for CAT Mock Test- 4 - Question 62

Let us  assume he bought each jeans at the price of P

Cost price for 4+1 =5 Jeans = 5P

He makes a profit of 5%, therefore the selling price of 5 Jeans = 1.05× 5 = 5.25P...(i)

Let the price after Markup be M.

Selling Price of 5 Jeans before discount = 44M

Selling price after discount = (0.9)4M = 3.6M .....(ii)

Equating (i) and (ii)

3.6M = 5.25 P

M = 1.4583 P

Therefore the markup percent is 45.83%

CAT Mock Test- 4 - Question 63

In the above triangle, AD is angle-bisector. If the value of BD is α  which of the following relation is true?

Detailed Solution for CAT Mock Test- 4 - Question 63

Since Angle bisectors of the two sides divide the third side in the same ratio, Let's assume BD = α  = 9x and CD = 13x

Applying cosine rule on \bigtriangleup △ADC 

On putting value and rearranging we get −13xy = 169x2 + y2−169 ....(I)

On rearranging  we get,

9xy = 81x+ y2−81 ......(II)

9(I) + 13(II) to remove the xy term we get 0 = 2574x2 + 22y− 2574

Or 117x+ y2−117 = 0 ...(III)

We are given that 9x = α  or x = α​/9

Putting it in (III)

117/81 ​α2 + y2−117=0

Multiply both side by 81

17α2  + 81y2  − 9477  = 0

Diving overall equation by common factor of coeficients i.e. 9

13α2 + 9y2−1053 = 0

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 64

There are 2 Arithmetic Progression series :

A1​ = 1,5,9,...............481

A2​ = 5,11,17..............479

What is the sum of common terms of the 2 Arithmetic Progressions?


Detailed Solution for CAT Mock Test- 4 - Question 64

A1​ has a common difference of 4 whereas A2​ = 6

Let us identify the first common term. Visually we can see that the first term will be 5

The series formed by taking the common terms of the series will also be an AP with the common difference of the A.P = lcm(4,6) = 12

nth term of this series will be = 5+(n−1)12

The maximum possible value of the last common number will be 479

Therefore, 5+(n−1)12 ≤ 479

(n−1)12 ≤ 474

(n−1) ≤ 5474​=39.5

(n) ≤ 40.5

Therefore n  = 40 is the number of terms in the resulting series

Sum of all the common 40 terms = 40​/2(2(5)+(40−1)12)

Sum of all the common 40 terms = 20(10+39× 12)

Sum of all the common 40 terms = 20(478) = 9560

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 65

Out of 15 points that lie in a plane, 3 points lie on a straight line and another 4 points lie on another straight line parallel to it. If no other 3 points are collinear, find the total number of triangles that can be formed?


Detailed Solution for CAT Mock Test- 4 - Question 65

We can select any three points as vertices of the triangle, such that all 3 points cannot belong to a particular straight line
We can select any 3 points out of 15 points in a plane in 15C3 = 455 ways
We can select 3 points from the 1st straight line in 3C3 = 1 way
We can select 3 points from the 2nd straight line in 4C3 = 4 ways
Thus total number of triangles that can be formed is = 455 - (1 + 4) = 450

*Answer can only contain numeric values
CAT Mock Test- 4 - Question 66

The sum of the digits of a number N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33?


Detailed Solution for CAT Mock Test- 4 - Question 66

Sum of digits = 23
Remainder when N is divided by 9
N/9 = 5 {Remainder on division by 9 for any number is equal to the remainder of dividing the sum of the digits of the number by 9}
=> Remainder of N/3 = 2 {A number of the form 9k + 5 divided by 3 leaves a remainder 2}
N = 11k + 7
N = 3m + 2
11k + 7 => Possible numbers are 7, 18, 29, 40, 51
3m + 2 => Possible numbers are 2, 5, 8, 11, 14, 17, 20, 23, 26, 29
The number that is of the form 11k + 7 and 3m + 2 should be of the form 33b + 29. How did we arrive at this result?
The first natural number that satisfies both properties is 29.
Now, starting with 29, every 11th number is of the form 11k + 7, and every 3rd number is of the form 3m + 2.
So, starting from 29, every 33rd number should be on both lists (33 is the LCM of 11 and 3).
Or, any number of the form 33b + 29 will be both of the form 11K + 7 and 3m + 2, where b, k, m are natural numbers.
The remainder when the said number is divided by 33 is 29.

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