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CAT Mock Test- 5 - CAT MCQ


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66 Questions MCQ Test CAT Mock Test Series 2024 - CAT Mock Test- 5

CAT Mock Test- 5 for CAT 2024 is part of CAT Mock Test Series 2024 preparation. The CAT Mock Test- 5 questions and answers have been prepared according to the CAT exam syllabus.The CAT Mock Test- 5 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Mock Test- 5 below.
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CAT Mock Test- 5 - Question 1

Why does the author give the examples of the Santa Susana Lab and Chernobyl?

Detailed Solution for CAT Mock Test- 5 - Question 1

Through the passage, the author argues against nuclear power generation as an alternative to fossil fuels especially in the context of climate change. The author then gives these two examples to highlight how much damage they did to people and the planet and continue to do so. These two examples are extreme examples of how nuclear power generation can go terribly wrong. Thus, the primary reason to introduce these examples is to highlight the impact of nuclear disasters on the planet and people. Hence, option D.

Though the author does say that with climate change, the nuclear fallout of these disasters is likely to get worse, these examples are not introduced for that purpose. By highlighting the negative impact of these disasters, the author is trying to make the larger point against nuclear power. Hence, we can eliminate option B.

Though option A is the purpose behind the whole passage, it is not the reason why these two examples are introduced. Hence, we can eliminate option A. For the same reason we can eliminate option C.

CAT Mock Test- 5 - Question 2

What is the author's opinion on nuclear energy?

Detailed Solution for CAT Mock Test- 5 - Question 2

Through the passage, the author argues against nuclear power. Hence, options B and C which are not negative can be eliminated. Both options A and D are close. But option A misses the primary motivation behind the author's recommendation. The author feels that with climate change, the number of nuclear disasters is likely to increase and thus nuclear power should be avoided. Hence, option D.

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CAT Mock Test- 5 - Question 3

What is the main point of the last paragraph?

Detailed Solution for CAT Mock Test- 5 - Question 3

Through the last paragraph, the author is trying to counter the argument in favour of nuclear energy. The author says that though they have the advantage of reliability and capability, as the plants age they become inefficient and risky. Hence, option A is the right answer. 
Options B, C and D miss out the point of how aging of plants makes them a worse bet. Hence, option A.

CAT Mock Test- 5 - Question 4

What was the conclusion based on the research by the MIT ?

Detailed Solution for CAT Mock Test- 5 - Question 4

The MIT research showed conclusively that the frequent forest fires, surface runoffs and flooding spread radiation. The research concluded that we are still paying for the nuclear by-products that were made in the 20th century. Only option C captures this point and hence is the right answer.
Option D, though true, is not the main conclusion of the study.
Option A contains a distortion. The study does not mention that only areas with radiation will experience acid rain. Hence, we can eliminate option A.
Option B is an exaggeration and hence can be eliminated.
Thus option C is the correct answer. 

CAT Mock Test- 5 - Question 5

Which of the following adds the least depth to the author’s argument?

Detailed Solution for CAT Mock Test- 5 - Question 5

The author begins the passage by explaining how country music has been termed “hill-billy”. He then goes on to explain what it means. The second paragraph speaks of the negative perceptions that country music has and the author states that this image is not true. The author explains how country music has been more progressive right from the beginning. The remaining paragraphs cite examples of issues that country music has dealt with. It is clear from the passage that the main argument of the author is to show that country music is progressive and not conservative. 
Option A is incorrect since it contributes to the author’s argument that country music is progressive.
Option B is a possible answer. Cultural ambassadors have not been discussed in the passage, although them exhibiting a varied history of America would still be beneficial for country music.
Option C is correct. Furthering "Christian" music would bolster Country Music's conservative credentials and not its progressive ones. 
Option D is incorrect since it tackles social issues which have been discussed in the passage.

CAT Mock Test- 5 - Question 6

The passage makes all the following claims EXCEPT:

  1. “Hill-billy” was considered a derogatory word.
  2. Country music was more progressive than it was perceived to be.
  3. The audience of country music was diverse.
Detailed Solution for CAT Mock Test- 5 - Question 6

The claim in statement 1 is made in the first paragraph. “Hill billy” has been stereotypically linked to a supposedly degenerate and backwards culture. We can further infer this from Abel Green’s description.
The claim in statement 2 is the main argument of the passage. We can infer it from the second paragraph.
Statement 3 can be inferred from the lines “These kinds of negative projections of the people who have made country music, and have listened to it, linger even unto today. The stereotype is that they all harbour conservative political and social beliefs, setting them as sexist, racist, jingoistic and fundamentalist Christian by nature. But this image is a lie. For, right from the start, country music spoke up with a progressive voice.”
So, Option D is correct.

CAT Mock Test- 5 - Question 7

What is the author is trying to do by citing the example of Loretta Lynn?

Detailed Solution for CAT Mock Test- 5 - Question 7

Through the passage, the author argues that country music has always had a progressive voice. To support this assertion, the author first gives the example of Blind Alfred Reed who spoke of racial equality and equitable society. Then he gives the example of Loretta Lynn's progressive stand on women's reproductive rights. Thus, through this paragraph, the author is trying to highlight the progressive voices in country music's history to show that country music always had a progressive voice. Thus, option A is closest to the answer.

Option B is incorrect because the author has not claimed that country music facilitated the human rights movement.

Option C is incorrect. Although the author does say that “The Pill” stands out that is not the main point. We must see why the author believes it stands out. Read the lines “In the country-music market, this song stands out as an unabashed and rather radical call for sexual liberation and biological control, challenging the man’s past sexual prerogative and presenting a situation where the woman may also enjoy a variety of sexual liaisons without the social/economic restrictions that come with pregnancy, childbirth and childcare.” Through this example, the author is trying to make a larger point.

Option D is true but only captures a part of what Loretta Lynn’s song indicates. Option A is more accurate.

CAT Mock Test- 5 - Question 8

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

Detailed Solution for CAT Mock Test- 5 - Question 8

The author says that “These kinds of negative projections of the people who have made country music, and have listened to it, linger even unto today. The stereotype is that they all harbour conservative political and social beliefs, setting them as sexist, racist, jingoistic and fundamentalist Christian by nature. But this image is a lie. For, right from the start, country music spoke up with a progressive voice.” However, from these lines we cannot infer that the entire audience was literate and liberal. Hence, option A is incorrect.

Similarly “every song” need not have been progressive. Option B is gross generalization of country music.

Option C is incorrect because it is a generalization as well. 

Option D is correct, we can infer this from the lines “These kinds of negative projections of the people who have made country music, and have listened to it, linger even unto today. The stereotype is that they all harbour conservative political and social beliefs, setting them as sexist, racist, jingoistic and fundamentalist Christian by nature.”

CAT Mock Test- 5 - Question 9

What is the primary purpose of the passage?

Detailed Solution for CAT Mock Test- 5 - Question 9

The author begins by asking the question why dancing is universal to humans? Then she goes on to give the current theories that try to explain this. She dismisses the first theory on the basis that it does not explain the ubiquity of dancing and dismisses the second on the basis that it does not explain the tenacity of the practice. Then she goes on to propose a hypothesis that dancing is an evolutionary strategy that allows for our social and psychological development. She goes on to add that research seems to back up this hypothesis and how this explains both the ubiquity and tenacity of dancing.
Hence, the passage is written with the purpose of introducing the author's hypothesis. Hence, option A is the most apt answer.
Option B is incorrect because the theories and their pros and cons are discussed only as a part of the passage. This also omits the hypothesis presented by the author.
Option C is incorrect because although the passage does discuss human development in relation to dancing, why humans dance is the focal point of the passage.
Option D and Option A are close. However, the author does not conclude with on one reason as to why humans dance. Thus, option A is more accurate.

CAT Mock Test- 5 - Question 10

What is the author most likely to discuss after the final paragraph?

Detailed Solution for CAT Mock Test- 5 - Question 10

The author cites an alternative theory that she believes after giving the shortcomings of two other theories. The alternative theory is that dancing helped enable our distinctively large and interconnected brain, empathic heart and ecological adaptability. In the final paragraph, she gives evidence to support this. It would make sense for the author to continue by discussing what part of the brain dance traditions and techniques exercise. Option B is the most accurate.
Option A is incorrect because it does not help further the author’s point and dancing in cultures has already been discussed in the introductory paragraph.
Option C is incorrect because the differences in dance forms have not been discussed yet. The effect the author speaks of is for all dances.
Option D would be reverting back to the points the author has already made. So, although possible, it is a weak option.

CAT Mock Test- 5 - Question 11

Which of the following is the author most likely to support?

Detailed Solution for CAT Mock Test- 5 - Question 11

Through the passage, the author presents the hypothesis that dancing is an evolutionary strategy that plays a role in our social and psychological development. Hence, she is likely to support the inclusion of dance in schooling. Thus, the author is likely to agree with option A.
The author does not distinguish between different dance forms. Hence, B is unlikely to be the answer.
Though dancing helps human beings, we cannot infer that the author would agree with making it mandatory at social functions, especially when the function is not geared towards social or psychological development. Hence, option C can be ruled out.
The impact of dance on culture has not been discussed in the passage. Hence, the author's views on option D cannot be inferred.

CAT Mock Test- 5 - Question 12

What is the main idea behind the second paragraph?

Detailed Solution for CAT Mock Test- 5 - Question 12

The second paragraph begins by citing the two approaches used currently to explain why humans dance. Then it states the shortcomings of these theories. Option D summarizes this, so it is correct.
Though the second paragraph hints at options A and C, the main idea behind the paragraph is neither A nor B. Hence option (a) and option (b) are incorrect.
Option C is incorrect because it is not mentioned that the two theories complete each other. Hence option C is incorrect as well.

CAT Mock Test- 5 - Question 13

Which of the following can be inferred about Asa Gray?
I: He studied at Cambridge University
II: He was a writer
III: He was an editor
IV: He was a confidant of the editors of the journal from which the article is taken

Detailed Solution for CAT Mock Test- 5 - Question 13

Only II and IV are mentioned in the passage. The passage refers to Asa as ‘Cambridge botanist’, but that doesn’t mean that he studied at Cambridge University. In the 3rd passage, it is mentioned that Asa wrote for both student and professional naturalist. In the first passage, the author states ‘They lose a wise and sympathetic adviser of great experience and mature judgment to whom they could always have turned with entire freedom and in perfect confidence’, from which we can infer that IV is true. Thus, the answer is C.

CAT Mock Test- 5 - Question 14

Which of the following is not an aspect of Asa Gray’s written work?

Detailed Solution for CAT Mock Test- 5 - Question 14

In the second para, the author states that 'this power of comprehensive generalization he showed in his paper', from which we can conclude that generalization was one of the aspects of his work. Further in the third para, the author states that 'His long list of educational works have no equals in accuracy and in beauty and compactness of expression'. Thus, B and C are also true. Nowhere in the passage has the author regarded Asa's work as systematically organized. Thus, the answer is D.

CAT Mock Test- 5 - Question 15

According to the passage, what were Gray’s views on Darwin?

Detailed Solution for CAT Mock Test- 5 - Question 15

Refer to this line from the 4th para, ‘almost alone and single-handed he bore in America the brunt of the disbelief in the Darwinian Theory’. The only takeaway from this sentence is that Gray did believe the Darwinian theory to be true. However, the question asks about Gray’s views on Darwin, which cannot be inferred from the passage. The answer is D.

CAT Mock Test- 5 - Question 16

Which of the following best explains the reason behind the author stating Asa Gray as less fortunate than George Bentham?

Detailed Solution for CAT Mock Test- 5 - Question 16

In the 5th para of the passage, the author states that 'Less fortunate than his greatest botanical contemporary, George Bentham, who turned from the last page of corrected proof of his work upon the genera of plants to the bed from which he was never to rise again, Asa Gray’s great work is left unfinished.' From this we can infer that the author calls Asa as less fortunate because unlike George Bentham, his work was left unfinished. None of the options suggest this. Thus, the answer is D.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 17

Four sentences are given below. These sentences, when rearranged in proper order, form a logical and meaningful paragraph. Rearrange the sentences and enter the correct order as the answer.

  1. Wherever the rhythm was most delicate, wherever the emotion was most ecstatic, her art was the most beautiful, and yet, although she sometimes spoke to a little tune, it was never singing, as we sing to-day, never anything but speech.
  2. I have always known that there was something I disliked about singing, and I naturally dislike print and paper, but now at last I understand why, for I have found something better.
  3. A friend, who was here a few minutes ago, has sat with a beautiful stringed instrument upon her knee, her fingers passing over the strings, and has spoken to me some verses from Shelley’s Skylark and Sir Ector’s lamentation over the dead Launcelot out of the Morte d’Arthur and some of my own poems.
  4. I have just heard a poem spoken with so delicate a sense of its rhythm, with so perfect a respect for its meaning, that if I were a wise man and could persuade a few people to learn the art I would never open a book of verses again.

Detailed Solution for CAT Mock Test- 5 - Question 17

After reading all the sentences, we know that the paragraph is about the author's dislike for singing and his new found love for spoken poetry. Statement 2 is the opening sentence as it mentions the author's dislike for singing. The author also mentions how discovering spoken poetry changed his understanding of why he disliked singing. Statements 4,3 and 1 together describe the author's experience of the poem recited with the help of a stringed instrument.
Hence, the order is 2-4-3-1.
Hence, 2431 is the correct answer.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 18

Five sentences are given below. Four of which when arranged in a proper order, form a logical and meaningful paragraph. Identify the sentence that does not belong to the paragraph and enter its number as your answer.

  1. With the modern tendency toward specialization, the natural outgrowth of necessity, there is no inherent reason why the bones of a building should not be devised by one man and its fleshly clothing by another, so long as they understand one another, and are in ideal agreement, but there is in general all too little understanding, and a confusion of ideas and aims.
  2. Preoccupied as he is with the building's strength, safety, economy; solving new and staggeringly difficult problems with address and daring, he has scant sympathy with such inconsequent matters as the stylistic purity of a façade, or the profile of a moulding.
  3. To the designer, on the other hand, the engineer appears in the light of a subordinate to be used for the promotion of his own ends, or an evil to be endured as an interference with those ends.
  4. In the field of domestic architecture these dramatic contrasts are less evident, less sharply marked.
  5. To the average structural engineer the architectural designer is a mere milliner in stone, informed in those prevailing architectural fashions of which he himself knows little and cares less.

Detailed Solution for CAT Mock Test- 5 - Question 18

The correct order is 1523. 4 is the odd one out. The passage begins by saying that a building could possibly be built and styled by two different people as long as they worked in harmony. Sentence 5 goes on to explain why this is not so since the average engineer does not value the average designer. Sentence 2 explains what the priorities of the engineer are, while sentence 5 states what a designer feels. Option 4 is the odd one out since it speaks of contrasts in domestic architecture which is unrelated to the remaining lines.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 19

Five sentences are given below labelled as 1, 2, 3, 4 and 5. Of these, four sentences, when arranged properly, make a meaningful and coherent paragraph. Identify the odd one out.

  1. Even where the advancer of the art was also a psychologist, the pedagogics and the psychology ran side by side, and the former was not derived in any sense from the latter.
  2. To know psychology, therefore, is absolutely no guarantee that we shall be good teachers.
  3. The art of teaching grew up in the schoolroom, out of inventiveness and sympathetic concrete observation.
  4. That ingenuity in meeting and pursuing the pupil, that tact for the concrete situation, though they are the alpha and omega of the teacher's art, are things to which psychology cannot help us in the least.
  5. The two were congruent, but neither was subordinate.

Detailed Solution for CAT Mock Test- 5 - Question 19

All the five sentences talk about the relation between psychology and teaching. But the structure of sentence 4 indicates that the topic of "ingenuity" and "tact" has already been discussed in the preceding lines. Since, there is no mention of "ingenuity" and "tact" in any other sentences, sentence 4 cannot be a continuation of any of the sentences given. The other 4 sentences can be arranged in the sequence 3-1-5-2.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 20

The four sentences (labelled 1, 2, 3, and 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. Yet, its implications in disrupting traditional power structures are often grossly underestimated.

2. The digital revolution, much like previous revolutions, has been a source of profound economic and social transformation.

3. Historically, revolutions have redefined space for innovation and freedom, creating unforeseen opportunities for decentralization.

4. Conversely, it opens a Pandora's Box of heightened surveillance, control, and societal imbalance, overshadowing its emancipatory potential.


Detailed Solution for CAT Mock Test- 5 - Question 20

The paragraph logically progresses from a general statement about revolutions, particularly the digital one (2), relating it historically and conceptually with how revolutions bring change (3), the underestimation of this current revolution (1), and finally the drawbacks it entails (4). The sequence interlinks historical context, the nature of the digital revolution, and its contradictory consequences.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 21

The four sentences (labelled 1, 2, 3, and 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 shift necessitates an interrogation of traditional economic models, demanding innovative perspectives on wealth and productivity.

2. As automation and artificial intelligence take center stage, the global workforce faces unprecedented transformation.

3. Thus, nations grapple with the intricacies of integrating rapidly evolving technology into an already fragile global economy.

4. Interestingly, these advancements could herald a new era where human potential is optimized, redefining conventional work boundaries.


Detailed Solution for CAT Mock Test- 5 - Question 21

The paragraph begins by introducing the impact of automation and AI on the workforce (2), prompting a reconsideration of economic norms (1), , and concluding with a speculative, positive outlook on the future of work (4), followed by the challenges faced by nations due to these advancements (3)

CAT Mock Test- 5 - Question 22

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

In the last two decades, the phenomenon of 'digital nomads' has emerged, signifying a deeper change in conceptions of work and life. These individuals leverage technology to work remotely, often traveling globally. While this lifestyle offers unprecedented freedom and flexibility, it also entails significant downsides. Digital nomads frequently face issues related to psychological isolation, unpredictable finances, and the absence of a stable community. This lifestyle, embodying a post-modernist rebellion against traditional 9-5 jobs, questions the very fabric of societal norms but also underscores the human yearning for connection, stability, and security.

Detailed Solution for CAT Mock Test- 5 - Question 22

The passage presents a balanced view of the 'digital nomad' lifestyle, acknowledging the freedom it offers while highlighting inherent challenges. Option B accurately captures this duality and the deeper societal implications discussed. The other options either oversimplify the lifestyle, ignore its complexities, or focus narrowly on one aspect, missing the broader thematic content.

CAT Mock Test- 5 - Question 23

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

Artificial intelligence (AI) in healthcare is a revolutionary force, with the potential to significantly cut costs and improve patient outcomes. By analyzing vast datasets beyond human capability, AI can identify patterns and predictions invaluable for diagnosis and treatment strategies. However, this innovation comes with caveats. Concerns about data privacy, algorithm biases, and a potential decrease in face-to-face patient care necessitate careful integration of AI, with an emphasis on ethics and quality of human interaction to complement technological prowess.

Detailed Solution for CAT Mock Test- 5 - Question 23

The passage does not singularly praise AI’s contributions to healthcare or simplify its implications; instead, it delves into the nuanced challenges and ethical considerations. Option B reflects this complexity, recognizing AI's advantages and acknowledging the essential balance with ethics, privacy, and human interaction. Other options misrepresent the passage's content, ignoring either the benefits or the necessary caution.

CAT Mock Test- 5 - Question 24

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

Climate change-induced migration is becoming a stark reality. As habitats become inhospitable, mass movements of populations are causing geopolitical tensions. Wealthier nations are building barriers, both legal and physical, against migrants whom they perceive as threats to economic stability and social identity. This approach is short-sighted, ignoring the shared responsibility of humankind in climate change and the universal rights of those displaced. A more humane and sustainable approach would be global cooperation towards climate solutions, acknowledging the interconnectedness of our environmental actions.

Detailed Solution for CAT Mock Test- 5 - Question 24

The passage critically discusses the refusal of wealthier nations to accept climate migrants, emphasizing a lack of acknowledgment of shared global responsibility. Option C encapsulates the passage's main arguments, reflecting the complexity and global scope of the issue. Other options either contradict specific passage elements or fail to encompass the broader ethical and global considerations presented.

CAT Mock Test- 5 - Question 25

Suppose the total number of people following any sports club was as low as possible, what is the difference between the number of people who follow exactly 2 clubs and those who follow exactly 4 clubs?

Detailed Solution for CAT Mock Test- 5 - Question 25

If the number of people in the club is minimum, we can distribute them in the following way:
395 people who support CSK can support all other clubs as well. The remaining who follow KKR can follow all other clubs except CSK. The remaining who follow RCB can follow SRH as well, and the remaining people can follow only the club SRH. Hence, we get the Venn DIagram as follows:

Required number = 395 - 101 = 294.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 26

If it is known that the total number of people in the sports club were 2300 and out of them, only 395 followed none of the clubs, what can be the maximum number of people who follow exactly 3 clubs?


Detailed Solution for CAT Mock Test- 5 - Question 26

I + II + III + IV = 2300 - 395 = 1905
I + 2 II + 3 III + 4 IV = 597 + 667 + 496 + 395 = 2155
II + 2 III + 3 IV = 2155 - 1905 = 250
To maximise III, we can distribute 250 to III
250 / 2 = 125.
Hence, a maximum number of 125 people follow 3 clubs.

CAT Mock Test- 5 - Question 27

If the following data is additionally given, which of the following can be a possible number of people who followed all but CSK?

  1. Every person follows at least one club.
  2. No person follows exactly 2 clubs.
  3. The number of persons who follow all but RCB is 49.
  4. The number of persons who follow all but SRH is 53.
  5. The number of persons who follow all but KKR is 37.
  6. The total number of people in the sports club is 1307.
Detailed Solution for CAT Mock Test- 5 - Question 27

Let the number of people who followed all but CSK be x.
Now, 
I + II + III + IV = 1307.
I + 2 II + 3 III + 4 IV = 2155
Hence,
II + 2 III + 3 IV = 2155 - 1307 = 848
Now it is given that II = 0
Also, III = 49 + 53 + 37 + x = 139 + x
Hence, 2(139 + x) + 3 IV = 848
278 + 2x + 3 IV = 848
2x + 3 IV = 570
Now, IV = (570 - 2x)/3
IV = 190 - 2x/3
Since, IV must be an integer, x must be a multiple of 3 for sure. 
Hence, 63 is a possibility and none other option is possible. 

CAT Mock Test- 5 - Question 28

If the total number of people in the sports club is 1306, and everyone follows a minimum of one of the four clubs and the number of people who support all 4 clubs is the maximum, what is the ratio of the number of people who follow only RCB to those who follow only SRH?

Detailed Solution for CAT Mock Test- 5 - Question 28

I + II + II + IV = 1306
I + 2 II + 3 III + 4 IV = 2155
II + 2 III + 3 IV = 849
To maximise 4, we must distribute these 849 counts to IV.
So, IV = 849 / 3 = 283.
Hence, II = III = 0.
So, people who follow only RCB = 597 - 283 = 314
And, people who follow only SRH = 667 - 283 = 384
Required ratio = 314/384 = 157/192

CAT Mock Test- 5 - Question 29

Who among the following is definitely a neighbour of A in session 1?

Detailed Solution for CAT Mock Test- 5 - Question 29

First, we would try to determine the relative positions of A to H for the first session. We know in hint 5 that all the people are facing the table.
Using hint 6,

Using hint 4 and hint 3 together, we get the following 2 arrangements.


Using hint 2, we can add F to the arrangements as follows:

Using hint 1, we can add G to the arrangements as follows:

We are yet to figure out the positions of D and H. So let us consider all possible alternatives for their positions:

Now let us use the hints given to determine the positions in the second session. We know that they are facing the table. 
Using hints 5 and 4 in all the four configurations, we get their arrangements in the second sessions as follows:

In the second session, A moves 3 places to his left, but in arrangements 1 and 2, that place is already occupied.
So, those are invalidated. We can process the remaining information on arrangements 3 and 4. Also, we can add this information (new position of A) in 3 and 4.

Using hint (2) and the fact that all people but H are in different seats, we get the following:

G is not adjacent to H.


Therefore the 2 different possible seating arrangements in the first and second sessions are as follows:

H is definitely a neighbour of A, because H sits beside A in both possible cases.

CAT Mock Test- 5 - Question 30

Who is sitting opposite E in Session 2?

Detailed Solution for CAT Mock Test- 5 - Question 30

First, we would try to determine the relative positions of A to H for the first session. We know in hint 5 that all the people are facing the table.
Using hint 6,

​Using hint 4 and hint 3 together, we get the following 2 arrangements.


Using hint 2, we can add F to the arrangements as follows:

Using hint 1, we can add G to the arrangements as follows:

We are yet to figure out the positions of D and H. So let us consider all possible alternatives for their positions:

Now let us use the hints given to determine the positions in the second session. We know that they are facing the table. 
Using hints 5 and 4 in all the four configurations, we get their arrangements in the second sessions as follows:

In the second session, A moves 3 places to his left, but in arrangements 1 and 2, that place is already occupied.
So, those are invalidated. We can process the remaining information on arrangements 3 and 4. Also, we can add this information (new position of A) in 3 and 4.

Using hint (2) and the fact that all people but H are in different seats, we get the following:


G is not adjacent to H.


Therefore the 2 different possible seating arrangements in the first and second sessions are as follows:

E is sitting opposite C in session 2 in either arrangement.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 31

How many people are definitely moving to one of their adjacent positions in Session 2 as compared to Session 1?


Detailed Solution for CAT Mock Test- 5 - Question 31

First, we would try to determine the relative positions of A to H for the first session. We know in hint 5 that all the people are facing the table.
Using hint 6,

​Using hint 4 and hint 3 together, we get the following 2 arrangements.
 


Using hint 2, we can add F to the arrangements as follows:


Using hint 1, we can add G to the arrangements as follows:


We are yet to figure out the positions of D and H. So let us consider all possible alternatives for their positions:


Now let us use the hints given to determine the positions in the second session. We know that they are facing the table. 
Using hints 5 and 4 in all the four configurations, we get their arrangements in the second sessions as follows:


In the second session, A moves 3 places to his left, but in arrangements 1 and 2, that place is already occupied.
So, those are invalidated. We can process the remaining information on arrangements 3 and 4. Also, we can add this information (new position of A) in 3 and 4.


Using hint (2) and the fact that all people but H are in different seats, we get the following:


G is not adjacent to H.


Therefore the 2 different possible seating arrangements in the first and second sessions are as follows:

Hence, in either arrangement, no person moves to his adjacent position in Session 2.

CAT Mock Test- 5 - Question 32

If E is sitting to the immediate left of G in the second session, who was sitting one seat to the left of A in the first session?

Detailed Solution for CAT Mock Test- 5 - Question 32

First, we would try to determine the relative positions of A to H for the first session. We know in hint 5 that all the people are facing the table.
Using hint 6,


​Using hint 4 and hint 3 together, we get the following 2 arrangements.
 


Using hint 2, we can add F to the arrangements as follows:


Using hint 1, we can add G to the arrangements as follows:


We are yet to figure out the positions of D and H. So let us consider all possible alternatives for their positions:

Now let us use the hints given to determine the positions in the second session. We know that they are facing the table. 
Using hints 5 and 4 in all the four configurations, we get their arrangements in the second sessions as follows:

In the second session, A moves 3 places to his left, but in arrangements 1 and 2, that place is already occupied.
So, those are invalidated. We can process the remaining information on arrangements 3 and 4. Also, we can add this information (new position of A) in 3 and 4.

Using hint (2) and the fact that all people but H are in different seats, we get the following:


G is not adjacent to H.


Therefore the 2 different possible seating arrangements in the first and second sessions are as follows:

E is sitting to the immediate left of G in the second session, so it is the arrangement numbered 4. In the same arrangement, H was sitting one place to the left of A.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 33

What is the square root of TS? (Enter the closest integer if in decimal)


Detailed Solution for CAT Mock Test- 5 - Question 33

In such questions, we can draw a table as shown below. But the digit as shown in the third row is not necessarily the sum of the digits in the first two columns, as we know that in addition, we have carry-forward. This means that if the sum of two digits yields a two-digit sum, the tens digit is carried forward to the forward column and only the ones digit is written.

The alphabets in the units place are S S and O. So we have units digit of S + S = O or S + O = S 

Case 1: S + O = S
⇒ O = zero and S,T,P are non zero. Hence SCORPIO will be a 7 digit number and TAURUS and PISCES will be 6 digit numbers. We can't get a 6 digit number by adding a 7 digit number and a 6 digit number. Hence this case case is not possible.

Case 2: S + S = O
The sum will look like as below:


In the last column, we can see that S+S=O. Hence S can't be zero as O will also be zero then. 
We know that the maximum sum of any two distinct digits can be 17, and the minimum can be 3. Since S cannot be zero S can only attain a value of 1, which is carried forward. Since there is a carry forward, neither of T and P can be zero.
In the last column, we can see that S+S=O. Hence the value of O is 2.
Also, UR and US are consecutive numbers. As S=1, R can be either 0 or 2. Since O has the value 2 already, R will be 0. The sum looks like this:

 

Here we can see that in the third last column, 0 is added to C to get P. Now since each letter represents a unique number, 1 must have been carried forward from the sum of U and E. So we have the following equations:
U+E=10+I
C+1=P or C+1=10+P
Now C+1 cannot be 10+P as only 1 is being added to C here. So to give a two digit number, C will be 9 and P will be 0, which is not possible as 0 is already assigned to R. Hence C+1=P.
Hence no carry-forward is there from the third last column. This means that U+1=0, and U=9. The distribution of digits to letters looks as follows:

Now, we need to do hit and trial to ascertain the values of other letters. Since it has been given that there is a unique combination, we need to do trials only till we find a solution.
As P=C+1, we will place them in consecutive positions on the above distribution. We will try with 3 and 4:

Now, since the sum in the 4th column is 10, so 1 will get carried forward to column 3. Hence the equation for column 3:
A+I+1=10+2, as sum of A and I cannot be 2, as 0 and 1 are already taken. So the sum is a two-digit number.
We have A+I=11.
In the distribution, we have only 5 and 6 left which can give a sum of 11.

Since the sum in column 3 is 11, 1 will get carried forward to column 2, and we get:
T+P+1=13, since C=3.
Hence T+P=12. Now P=4, so T=8 and E=7.
Since U+E=10+I, I= 9+7-10= 6 and A=5.
The final distribution:

So TS = 81 and its square root= 9.

CAT Mock Test- 5 - Question 34

Which letter among the following has the highest value of digit associated with it?

Detailed Solution for CAT Mock Test- 5 - Question 34

In such questions, we can draw a table as shown below. But the digit as shown in the third row is not necessarily the sum of the digits in the first two columns, as we know that in addition, we have carry-forward. This means that if the sum of two digits yields a two-digit sum, the tens digit is carried forward to the forward column and only the ones digit is written.

The alphabets in the units place are S S and O. So we have units digit of S + S = O or S + O = S 

Case 1: S + O = S
⇒ O = zero and S,T,P are non zero. Hence SCORPIO will be a 7 digit number and TAURUS and PISCES will be 6 digit numbers. We can't get a 6 digit number by adding a 7 digit number and a 6 digit number. Hence this case case is not possible.

Case 2: S + S = O
The sum will look like as below:


In the last column, we can see that S+S=O. Hence S can't be zero as O will also be zero then. 
We know that the maximum sum of any two distinct digits can be 17, and the minimum can be 3. Since S cannot be zero S can only attain a value of 1, which is carried forward. Since there is a carry forward, neither of T and P can be zero.
In the last column, we can see that S+S=O. Hence the value of O is 2.
Also, UR and US are consecutive numbers. As S=1, R can be either 0 or 2. Since O has the value 2 already, R will be 0. The sum looks like this:

Here we can see that in the third last column, 0 is added to C to get P. Now since each letter represents a unique number, 1 must have been carried forward from the sum of U and E. So we have the following equations:
U+E=10+I
C+1=P or C+1=10+P
Now C+1 cannot be 10+P as only 1 is being added to C here. So to give a two digit number, C will be 9 and P will be 0, which is not possible as 0 is already assigned to R. Hence C+1=P.
Hence no carry-forward is there from the third last column. This means that U+1=0, and U=9. The distribution of digits to letters looks as follows:

Now, we need to do hit and trial to ascertain the values of other letters. Since it has been given that there is a unique combination, we need to do trials only till we find a solution.
As P=C+1, we will place them in consecutive positions on the above distribution. We will try with 3 and 4:

Now, since the sum in the 4th column is 10, so 1 will get carried forward to column 3. Hence the equation for column 3:
A+I+1=10+2, as sum of A and I cannot be 2, as 0 and 1 are already taken. So the sum is a two-digit number.
We have A+I=11.
In the distribution, we have only 5 and 6 left which can give a sum of 11.

Since the sum in column 3 is 11, 1 will get carried forward to column 2, and we get:
T+P+1=13, since C=3.
Hence T+P=12. Now P=4, so T=8 and E=7.
Since U+E=10+I, I= 9+7-10= 6 and A=5.
The final distribution:

We can see that E has the highest value among the four equal to 7.

CAT Mock Test- 5 - Question 35

The values of which of the following letters if exchanged with S will lead to the maximum change in the value of Scorpio? (Consider this independently and after the values have been assigned to the letters.)

Detailed Solution for CAT Mock Test- 5 - Question 35

In such questions, we can draw a table as shown below. But the digit as shown in the third row is not necessarily the sum of the digits in the first two columns, as we know that in addition, we have carry-forward. This means that if the sum of two digits yields a two-digit sum, the tens digit is carried forward to the forward column and only the ones digit is written.

The alphabets in the units place are S S and O. So we have units digit of S + S = O or S + O = S 

Case 1: S + O = S
⇒ O = zero and S,T,P are non zero. Hence SCORPIO will be a 7 digit number and TAURUS and PISCES will be 6 digit numbers. We can't get a 6 digit number by adding a 7 digit number and a 6 digit number. Hence this case case is not possible.

Case 2: S + S = O
The sum will look like as below:


In the last column, we can see that S+S=O. Hence S can't be zero as O will also be zero then. 
We know that the maximum sum of any two distinct digits can be 17, and the minimum can be 3. Since S cannot be zero S can only attain a value of 1, which is carried forward. Since there is a carry forward, neither of T and P can be zero.
In the last column, we can see that S+S=O. Hence the value of O is 2.
Also, UR and US are consecutive numbers. As S=1, R can be either 0 or 2. Since O has the value 2 already, R will be 0. The sum looks like this:

Here we can see that in the third last column, 0 is added to C to get P. Now since each letter represents a unique number, 1 must have been carried forward from the sum of U and E. So we have the following equations:
U+E=10+I
C+1=P or C+1=10+P
Now C+1 cannot be 10+P as only 1 is being added to C here. So to give a two digit number, C will be 9 and P will be 0, which is not possible as 0 is already assigned to R. Hence C+1=P.
Hence no carry-forward is there from the third last column. This means that U+1=0, and U=9. The distribution of digits to letters looks as follows:

Now, we need to do hit and trial to ascertain the values of other letters. Since it has been given that there is a unique combination, we need to do trials only till we find a solution.
As P=C+1, we will place them in consecutive positions on the above distribution. We will try with 3 and 4:

Now, since the sum in the 4th column is 10, so 1 will get carried forward to column 3. Hence the equation for column 3:
A+I+1=10+2, as sum of A and I cannot be 2, as 0 and 1 are already taken. So the sum is a two-digit number.
We have A+I=11.
In the distribution, we have only 5 and 6 left which can give a sum of 11.

Since the sum in column 3 is 11, 1 will get carried forward to column 2, and we get:
T+P+1=13, since C=3.
Hence T+P=12. Now P=4, so T=8 and E=7.
Since U+E=10+I, I= 9+7-10= 6 and A=5.
The final distribution:

Since S is the leftmost digit, only the change in its value matter. This means that we have to either replace S with the highest digit possible or the lowest digit possible. In any case, if S is replace by the value of U, that is 9, the difference would be the largest: |1320462-9320462|=8000000. Hence the answer is A.

CAT Mock Test- 5 - Question 36

How many factors does the number CO have?

Detailed Solution for CAT Mock Test- 5 - Question 36

In such questions, we can draw a table as shown below. But the digit as shown in the third row is not necessarily the sum of the digits in the first two columns, as we know that in addition, we have carry-forward. This means that if the sum of two digits yields a two-digit sum, the tens digit is carried forward to the forward column and only the ones digit is written.

The alphabets in the units place are S S and O. So we have units digit of S + S = O or S + O = S 

Case 1: S + O = S
⇒ O = zero and S,T,P are non zero. Hence SCORPIO will be a 7 digit number and TAURUS and PISCES will be 6 digit numbers. We can't get a 6 digit number by adding a 7 digit number and a 6 digit number. Hence this case case is not possible.

Case 2: S + S = O
The sum will look like as below:


In the last column, we can see that S+S=O. Hence S can't be zero as O will also be zero then. 
We know that the maximum sum of any two distinct digits can be 17, and the minimum can be 3. Since S cannot be zero S can only attain a value of 1, which is carried forward. Since there is a carry forward, neither of T and P can be zero.
In the last column, we can see that S+S=O. Hence the value of O is 2.
Also, UR and US are consecutive numbers. As S=1, R can be either 0 or 2. Since O has the value 2 already, R will be 0. The sum looks like this:

Here we can see that in the third last column, 0 is added to C to get P. Now since each letter represents a unique number, 1 must have been carried forward from the sum of U and E. So we have the following equations:
U+E=10+I
C+1=P or C+1=10+P
Now C+1 cannot be 10+P as only 1 is being added to C here. So to give a two digit number, C will be 9 and P will be 0, which is not possible as 0 is already assigned to R. Hence C+1=P.
Hence no carry-forward is there from the third last column. This means that U+1=0, and U=9. The distribution of digits to letters looks as follows:

Now, we need to do hit and trial to ascertain the values of other letters. Since it has been given that there is a unique combination, we need to do trials only till we find a solution.
As P=C+1, we will place them in consecutive positions on the above distribution. We will try with 3 and 4:

Now, since the sum in the 4th column is 10, so 1 will get carried forward to column 3. Hence the equation for column 3:
A+I+1=10+2, as sum of A and I cannot be 2, as 0 and 1 are already taken. So the sum is a two-digit number.
We have A+I=11.
In the distribution, we have only 5 and 6 left which can give a sum of 11.

Since the sum in column 3 is 11, 1 will get carried forward to column 2, and we get:
T+P+1=13, since C=3.
Hence T+P=12. Now P=4, so T=8 and E=7.
Since U+E=10+I, I= 9+7-10= 6 and A=5.
The final distribution:

CO = 32 = 25. So it has 5 + 1 = 6 factors.

CAT Mock Test- 5 - Question 37

What can be the cumulative score of G?

Detailed Solution for CAT Mock Test- 5 - Question 37

Let the multiplier of Healthcare, Population, and Infrastructure be a, b and c respectively.
Let us start by finding out which parameter has a multiplying factor of 1 and which parameter has a multiplying factor of 2.
Case I: If all of the parameters have a multiplying factor of 2, then the cumulative score would always be even. But we see that the cumulative score of H is odd, hence it is not possible.
Case II: If every country has a multiplying factor of 1 then the maximum possible cumulative score can be 8+8+8 =24. But H has a cumulative score of 27, thus this is also not the case.
Thus there is at least 1 parameter that has a multiplying factor of 1 and at least 1 parameter which has a multiplying factor of 2.
Let us look at the country E. 
Since rank 8 has a cumulative score of 15, E should have a cumulative score ≥ 17 to have a rank of 6.
Thus 3a + 5b + 3c ≥ 17. It is only possible when atleast 2 of a,ba,b and cc has value of 2.
Thus 1 parameter has a multiplier of 1 and 2 parameters have a multiplier of 2
Country B has value for a score for Population parameter = 6. If we assume the score for other parameters to be xx and yy respectively and b=1, then a = c = 2. Thus 2x + 6 + 2y = 15 or 2x + 2y = 9 which is not possible. Hence b = 2.
For country F we see that the cumulative score = 25 which is odd. And score for healthcare is 5. It is only possible when a = 1 and b = c = 2. Else the sum will be even.
Thus a = 1,b = 2 and c = 2. The table can be updated as follows:

The score of B for Healthcare and Infrastructure has to be 1 so that cumulative becomes 15. Thus score of A for Population is also 1.
Cumulative of E = 19
The score of F for the population has to be 2 for cumulative to be 25
Score of 19 has a rank of 6 and score of 25 has a rank of 4. Thus C has a rank of 5

The score of A for Population is 1. The maximum score for Healthcare can be 8 and for infrastructure can be 7. The maximum cumulative score of A can be 24. But we know that at 25 the rank is 4 and at rank 5 the score is 22. Thus rank of A has to be worse than 5. Therefore only possibility is rank 7.
Then the rank of D can be either 2 or 3. Thus the score of D has to be greater than 25
The score for D for Health can be 2 or 4 or 6 or 8. The score of D can be thus 20 or 22 or 24 or 26 respectively. Thus score of D for Healthcare should be 8 with a cumulative score of 26. Thus D has rank 3 and H will have rank 2

Exactly 3 countries have the same Healthcare and Infrastructure score. B and E two of these countries. The third country can be A or C or G or H.
For A, the common score can be  4 only. In the case of which cumulative becomes. 14 But the score of A has to be 16 or more as it has rank 7. Thus rejected.
For C, since the score of Infrastructure is 6, the score of Healthcare needs to be 6. For cumulative to be 22 the score of Population has to be 2 but, F has that score so it is also not possible.
For G, the common number can be 4. In the case of which if G gets 8 score in population, still the cumulative will be 26. Which is a contradiction as G should have score 28 or above
If the score of H for Infrastructure = 7 then the Population score has to be 3. This is the only possible case

The score of Population for C can be 4 or 8. If the score is  8 then the cumulative will exceed 22. Thus THE score of C for the population is 4. Its score for Healthcare has to be 2. G has a population score = 8

Since the score of Healthcare for A can be 4 or 6. The cumulative score will be even. Thus a cumulative score of A can be 16 or 18.
Case I: 
If A has a Healthcare score of 4 then A needs either an Infrastructure score to be 5 or 6. The only possibility is 5. Thus is cumulative will be 16. It will imply that score for G has to be 6,8,4. The cumulative score, in this case, will be 30.

Case II: A has a healthcare score of 6. Thus Infrastructure score has to be 4 or 5. If it is 4 then the cumulative score of A will be 16. The score of G, in that case, will be 4,8,5 which has a total cumulative of 30.
If the infrastructure score of A is 5, then its cumulative will be 18. The score of G, in that case, will be 4,8,4 with a cumulative of 26. Which is not possible as it has to be above 28. This is rejected

The above mentioned are the only possible 2 cases. Both the cases the score of G is 30

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 38

What is rank of country C?
Enter -1 if the answer can't be determined.


Detailed Solution for CAT Mock Test- 5 - Question 38

Let the multiplier of Healthcare, Population, and Infrastructure be a, b and c respectively.
Let us start by finding out which parameter has a multiplying factor of 1 and which parameter has a multiplying factor of 2.
Case I: If all of the parameters have a multiplying factor of 2, then the cumulative score would always be even. But we see that the cumulative score of H is odd, hence it is not possible.
Case II: If every country has a multiplying factor of 1 then the maximum possible cumulative score can be 8+8+8 =24. But H has a cumulative score of 27, thus this is also not the case.
Thus there is at least 1 parameter that has a multiplying factor of 1 and at least 1 parameter which has a multiplying factor of 2.
Let us look at the country E. 
Since rank 8 has a cumulative score of 15, E should have a cumulative score ≥ 17 to have a rank of 6.
Thus 3a + 5b + 3c ≥ 17. It is only possible when atleast 2 of a,ba,b and cc has value of 2.
Thus 1 parameter has a multiplier of 1 and 2 parameters have a multiplier of 2
Country B has value for a score for Population parameter = 6. If we assume the score for other parameters to be xx and yy respectively and b=1, then a = c = 2. Thus 2x + 6 + 2y = 15 or 2x + 2y = 9 which is not possible. Hence b = 2.
For country F we see that the cumulative score = 25 which is odd. And score for healthcare is 5. It is only possible when a = 1 and b = c = 2. Else the sum will be even.
Thus a = 1,b = 2 and c = 2. The table can be updated as follows:

The score of B for Healthcare and Infrastructure has to be 1 so that cumulative becomes 15. Thus score of A for Population is also 1.
Cumulative of E = 19
The score of F for the population has to be 2 for cumulative to be 25
Score of 19 has a rank of 6 and score of 25 has a rank of 4. Thus C has a rank of 5

The score of A for Population is 1. The maximum score for Healthcare can be 8 and for infrastructure can be 7. The maximum cumulative score of A can be 24. But we know that at 25 the rank is 4 and at rank 5 the score is 22. Thus rank of A has to be worse than 5. Therefore only possibility is rank 7.
Then the rank of D can be either 2 or 3. Thus the score of D has to be greater than 25
The score for D for Health can be 2 or 4 or 6 or 8. The score of D can be thus 20 or 22 or 24 or 26 respectively. Thus score of D for Healthcare should be 8 with a cumulative score of 26. Thus D has rank 3 and H will have rank 2

Exactly 3 countries have the same Healthcare and Infrastructure score. B and E two of these countries. The third country can be A or C or G or H.
For A, the common score can be  4 only. In the case of which cumulative becomes. 14 But the score of A has to be 16 or more as it has rank 7. Thus rejected.
For C, since the score of Infrastructure is 6, the score of Healthcare needs to be 6. For cumulative to be 22 the score of Population has to be 2 but, F has that score so it is also not possible.
For G, the common number can be 4. In the case of which if G gets 8 score in population, still the cumulative will be 26. Which is a contradiction as G should have score 28 or above
If the score of H for Infrastructure = 7 then the Population score has to be 3. This is the only possible case

The score of Population for C can be 4 or 8. If the score is  8 then the cumulative will exceed 22. Thus THE score of C for the population is 4. Its score for Healthcare has to be 2. G has a population score = 8

Since the score of Healthcare for A can be 4 or 6. The cumulative score will be even. Thus a cumulative score of A can be 16 or 18.
Case I: 
If A has a Healthcare score of 4 then A needs either an Infrastructure score to be 5 or 6. The only possibility is 5. Thus is cumulative will be 16. It will imply that score for G has to be 6,8,4. The cumulative score, in this case, will be 30.

Case II: A has a healthcare score of 6. Thus Infrastructure score has to be 4 or 5. If it is 4 then the cumulative score of A will be 16. The score of G, in that case, will be 4,8,5 which has a total cumulative of 30.
If the infrastructure score of A is 5, then its cumulative will be 18. The score of G, in that case, will be 4,8,4 with a cumulative of 26. Which is not possible as it has to be above 28. This is rejected

The above mentioned are the only possible 2 cases. Both the cases the score of G is 30

CAT Mock Test- 5 - Question 39

What is cumulative score of E?

Detailed Solution for CAT Mock Test- 5 - Question 39

Let the multiplier of Healthcare, Population, and Infrastructure be a, b and c respectively.
Let us start by finding out which parameter has a multiplying factor of 1 and which parameter has a multiplying factor of 2.
Case I: If all of the parameters have a multiplying factor of 2, then the cumulative score would always be even. But we see that the cumulative score of H is odd, hence it is not possible.
Case II: If every country has a multiplying factor of 1 then the maximum possible cumulative score can be 8+8+8 =24. But H has a cumulative score of 27, thus this is also not the case.
Thus there is at least 1 parameter that has a multiplying factor of 1 and at least 1 parameter which has a multiplying factor of 2.
Let us look at the country E. 
Since rank 8 has a cumulative score of 15, E should have a cumulative score ≥ 17 to have a rank of 6.
Thus 3a + 5b + 3c ≥ 17. It is only possible when atleast 2 of a,ba,b and cc has value of 2.
Thus 1 parameter has a multiplier of 1 and 2 parameters have a multiplier of 2
Country B has value for a score for Population parameter = 6. If we assume the score for other parameters to be xx and yy respectively and b=1, then a = c = 2. Thus 2x + 6 + 2y = 15 or 2x + 2y = 9 which is not possible. Hence b = 2.
For country F we see that the cumulative score = 25 which is odd. And score for healthcare is 5. It is only possible when a = 1 and b = c = 2. Else the sum will be even.
Thus a = 1,b = 2 and c = 2. The table can be updated as follows:

The score of B for Healthcare and Infrastructure has to be 1 so that cumulative becomes 15. Thus score of A for Population is also 1.
Cumulative of E = 19
The score of F for the population has to be 2 for cumulative to be 25
Score of 19 has a rank of 6 and score of 25 has a rank of 4. Thus C has a rank of 5

The score of A for Population is 1. The maximum score for Healthcare can be 8 and for infrastructure can be 7. The maximum cumulative score of A can be 24. But we know that at 25 the rank is 4 and at rank 5 the score is 22. Thus rank of A has to be worse than 5. Therefore only possibility is rank 7.
Then the rank of D can be either 2 or 3. Thus the score of D has to be greater than 25
The score for D for Health can be 2 or 4 or 6 or 8. The score of D can be thus 20 or 22 or 24 or 26 respectively. Thus score of D for Healthcare should be 8 with a cumulative score of 26. Thus D has rank 3 and H will have rank 2

Exactly 3 countries have the same Healthcare and Infrastructure score. B and E two of these countries. The third country can be A or C or G or H.
For A, the common score can be  4 only. In the case of which cumulative becomes. 14 But the score of A has to be 16 or more as it has rank 7. Thus rejected.
For C, since the score of Infrastructure is 6, the score of Healthcare needs to be 6. For cumulative to be 22 the score of Population has to be 2 but, F has that score so it is also not possible.
For G, the common number can be 4. In the case of which if G gets 8 score in population, still the cumulative will be 26. Which is a contradiction as G should have score 28 or above
If the score of H for Infrastructure = 7 then the Population score has to be 3. This is the only possible case

The score of Population for C can be 4 or 8. If the score is  8 then the cumulative will exceed 22. Thus THE score of C for the population is 4. Its score for Healthcare has to be 2. G has a population score = 8

Since the score of Healthcare for A can be 4 or 6. The cumulative score will be even. Thus a cumulative score of A can be 16 or 18.
Case I: 
If A has a Healthcare score of 4 then A needs either an Infrastructure score to be 5 or 6. The only possibility is 5. Thus is cumulative will be 16. It will imply that score for G has to be 6,8,4. The cumulative score, in this case, will be 30.

Case II: A has a healthcare score of 6. Thus Infrastructure score has to be 4 or 5. If it is 4 then the cumulative score of A will be 16. The score of G, in that case, will be 4,8,5 which has a total cumulative of 30.
If the infrastructure score of A is 5, then its cumulative will be 18. The score of G, in that case, will be 4,8,4 with a cumulative of 26. Which is not possible as it has to be above 28. This is rejected

The above mentioned are the only possible 2 cases. In both the cases the score of E is 19

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 40

How many possible tables can be made from above given information?


Detailed Solution for CAT Mock Test- 5 - Question 40

Let the multiplier of Healthcare, Population, and Infrastructure be a, b and c respectively.
Let us start by finding out which parameter has a multiplying factor of 1 and which parameter has a multiplying factor of 2.
Case I: If all of the parameters have a multiplying factor of 2, then the cumulative score would always be even. But we see that the cumulative score of H is odd, hence it is not possible.
Case II: If every country has a multiplying factor of 1 then the maximum possible cumulative score can be 8+8+8 =24. But H has a cumulative score of 27, thus this is also not the case.
Thus there is at least 1 parameter that has a multiplying factor of 1 and at least 1 parameter which has a multiplying factor of 2.
Let us look at the country E. 
Since rank 8 has a cumulative score of 15, E should have a cumulative score ≥ 17 to have a rank of 6.
Thus 3a + 5b + 3c ≥ 17. It is only possible when atleast 2 of a,ba,b and cc has value of 2.
Thus 1 parameter has a multiplier of 1 and 2 parameters have a multiplier of 2
Country B has value for a score for Population parameter = 6. If we assume the score for other parameters to be xx and yy respectively and b=1, then a = c = 2. Thus 2x + 6 + 2y = 15 or 2x + 2y = 9 which is not possible. Hence b = 2.
For country F we see that the cumulative score = 25 which is odd. And score for healthcare is 5. It is only possible when a = 1 and b = c = 2. Else the sum will be even.
Thus a = 1,b = 2 and c = 2. The table can be updated as follows:

The score of B for Healthcare and Infrastructure has to be 1 so that cumulative becomes 15. Thus score of A for Population is also 1.
Cumulative of E = 19
The score of F for the population has to be 2 for cumulative to be 25
Score of 19 has a rank of 6 and score of 25 has a rank of 4. Thus C has a rank of 5

The score of A for Population is 1. The maximum score for Healthcare can be 8 and for infrastructure can be 7. The maximum cumulative score of A can be 24. But we know that at 25 the rank is 4 and at rank 5 the score is 22. Thus rank of A has to be worse than 5. Therefore only possibility is rank 7.
Then the rank of D can be either 2 or 3. Thus the score of D has to be greater than 25
The score for D for Health can be 2 or 4 or 6 or 8. The score of D can be thus 20 or 22 or 24 or 26 respectively. Thus score of D for Healthcare should be 8 with a cumulative score of 26. Thus D has rank 3 and H will have rank 2

Exactly 3 countries have the same Healthcare and Infrastructure score. B and E two of these countries. The third country can be A or C or G or H.
For A, the common score can be  4 only. In the case of which cumulative becomes. 14 But the score of A has to be 16 or more as it has rank 7. Thus rejected.
For C, since the score of Infrastructure is 6, the score of Healthcare needs to be 6. For cumulative to be 22 the score of Population has to be 2 but, F has that score so it is also not possible.
For G, the common number can be 4. In the case of which if G gets 8 score in population, still the cumulative will be 26. Which is a contradiction as G should have score 28 or above
If the score of H for Infrastructure = 7 then the Population score has to be 3. This is the only possible case

The score of Population for C can be 4 or 8. If the score is  8 then the cumulative will exceed 22. Thus THE score of C for the population is 4. Its score for Healthcare has to be 2. G has a population score = 8

Since the score of Healthcare for A can be 4 or 6. The cumulative score will be even. Thus a cumulative score of A can be 16 or 18.
Case I: 
If A has a Healthcare score of 4 then A needs either an Infrastructure score to be 5 or 6. The only possibility is 5. Thus is cumulative will be 16. It will imply that score for G has to be 6,8,4. The cumulative score, in this case, will be 30.

Case II: A has a healthcare score of 6. Thus Infrastructure score has to be 4 or 5. If it is 4 then the cumulative score of A will be 16. The score of G, in that case, will be 4,8,5 which has a total cumulative of 30.
If the infrastructure score of A is 5, then its cumulative will be 18. The score of G, in that case, will be 4,8,4 with a cumulative of 26. Which is not possible as it has to be above 28. This is rejected

The above mentioned are the only possible 2 cases.

CAT Mock Test- 5 - Question 41

If the cost in Q1 is $ 15 Million. The profit in the 4 quarters Q1, Q2, Q3, Q4 are in the ratio of 1 : 2 : 3 : 2. Then find the total cost in Q2 & Q4

Detailed Solution for CAT Mock Test- 5 - Question 41

Q1 cost is $15 Million.
So, Q1 profit is ($20 - $15) Million = $5 Million.
Thus, the profits are $5 Million, $10 Million, $15 Million and $10 Million respectively in Q1, Q2, Q3 & Q4 as per the ratio (1 : 2 : 3 : 2).
The cost in Q2 = ($18 - $ 10) Million = $8 Million
The cost in Q3 = ($22 - $ 15) Million = $7 Million
The cost in Q4 = ($24 - $ 10) Million = $14 Million
Thus, total cost in Q2 & Q4 is $22 Million

CAT Mock Test- 5 - Question 42

If the cost in Q1 is $ 15 Million. The profit in the 4 quarters Q1, Q2, Q3, Q4 are in the ratio of 1 : 2 : 3 : 2., then find the % increase in cost from Q2 to Q4?

Detailed Solution for CAT Mock Test- 5 - Question 42

Q1 cost is $15 Million.
So, Q1 profit is ($20 - $15) Million = $5 Million.
Thus, the profits are $5 Million, $10 Million, $15 Million and $10 Million respectively in Q1, Q2, Q3 & Q4.
The cost in Q2 = ($18 - $ 10) Million = $8 Million
The cost in Q3 = ($22 - $ 15) Million = $7 Million
The cost in Q4 = ($24 - $ 10) Million = $14 Million
Thus, the answer is= 75%

CAT Mock Test- 5 - Question 43

Because of Global Financial turmoil, ABC company is projecting total revenue for 2023 to be down by 14.29% with respect to 2022 and the ratio of the projected revenues in Q1, Q2, Q3 & Q4 is 2 : 3 : 3 :4. Then find out the projected revenue from Q4 in 2023.

Detailed Solution for CAT Mock Test- 5 - Question 43

Total revenue in 2022 is $(20 + 18 + 22 + 24) Million = $ 84 Million.
The projected revenue for 2023 is $84 MillionMillion
The ratio of the projected revenues in Q1, Q2, Q3 & Q4 is 2 : 3 : 3 : 4
So, the revenue in Q1Million.
The revenue in Q2 = revenue in Q3 = $ 18 Million.
The revenue in Q4 = $72 - $12 - $18 - $18 = $24 Million.
Thus, the answer is $24 Million.

CAT Mock Test- 5 - Question 44

Because of Global Financial turmoil, ABC company is projecting total revenue for 2023 to be down by 14.29% with respect to 2022 and the ratio of the projected revenues in Q1, Q2, Q3 & Q4 is 2 : 3 : 3 :4, if the quarterly costs in Q1, Q2, Q3 & Q4 are in the ratio of 1 : 2 : 1 : 2 respectively and the savings are in the ratio of 1 : 1 between Q3 and Q4 then find the total projected savings of Q1 & Q4 combined in 2023 (in $ Million)

Detailed Solution for CAT Mock Test- 5 - Question 44

Total revenue in 2022 is $(20 + 18 + 22 + 24) Million = $ 84 Million.
The projected revenue for 2023 is $84 MillionMillion.
The ratio of the projected revenues in Q1, Q2, Q3 & Q4 is 2 : 3 : 3 : 4
So, the revenue in Q1 
= $ 12 Million.
The revenue in Q2 = revenue in Q3 = $ 18 Million.
The revenue in Q4 = $72 - $12 - $18 - $18 = $24 Million.
Let’s assume that the cost for quarter 1 is $x Million, then we can say that
⇒ (18 – x) = (24 – 2x)
⇒ x = 6
So, the savings in Q1 = $12 Million - $ 6 Million
= $ 6 Million.
The savings in Q2 = $18 Million - $ 12 Million
= $ 6 Million
The savings in Q3 = $18 Million - $ 6 Million
= $ 12 Million
The savings in Q4 = $24 Million - $ 12 Million
= $ 12 Million
Total savings from Q1 & Q4 = $(6 + 12) Million
= $18 Million.

CAT Mock Test- 5 - Question 45

A milkman has 2 varieties of milk-water solution, solution A has 65% pure milk and solution B has 78% pure milk. He is mixing x mL of solution A with y mL of solution B such that the resultant solution has no less than 70% pure milk and no more than 72% pure milk. If y can take any value between 625mL and 630mL, both inclusive, what is the difference between the minimum and maximum value x can take? It is given that x and y are both integers.

Detailed Solution for CAT Mock Test- 5 - Question 45

According to the information,

This breaks down to


We have been given the range of values y can take, putting the extremes, we get,
When y = 625,

Hence, the minimum value x can take is 536 and the maximum it can take is 1008.
Hence difference = 472.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 46

A survey was conducted in a society to get an estimate of how many people read the following newspapers, The Telegraph, The Economic Times and The Times of India. It was found out that 20% of people of the society read The Telegraph, 30% of people of the society read The Economic Times and 40% of the people of the society read The Times of India. If the society had a total of 600 people, what can be the maximum number of people in the society who read none of the newspapers?


Detailed Solution for CAT Mock Test- 5 - Question 46

Let the newspapers be abbreviated as follows:
The Telegraph - TT
The Economic Times - ET
The Times of India - TOI
Let the number of people in the society be 100 (only for calculation, later we will substitute the correct value)
Therefore, n(TT) = 20
n(ET) = 30
n(TOI) = 40
To maximise the number of people reading no newspaper, we will have to maximise the number of people who read 3 and 2 newspapers as follows.
 

Hence, maximum number of people who read no newspapers = 60 = 60%.
Total number of people in the society = 600
Hence, the maximum number of people in the society who read none of the newspapers = 0.6 x 600 = 360

CAT Mock Test- 5 - Question 47

In a certain country, all the people are fans of exactly one of the following clubs, Real Madrid, Barcelona and Juventus. The percentage of people who follow Real Madrid is 60%. Out of these, 80% are followers of Cristiano. In the transfer season, Cristiano moved to Juventus. As a result, 50% of the Real Madrid followers who followed Cristiano stopped following Real Madrid and started following Juventus. Also, 25% of the Real Madrid followers who did not follow Cristiano stopped following Real Madrid and started following Barcelona. If the absolute difference between the final number of Juventus and Barcelona fans is equal to the final number of Real Madrid fans, what percentage of the population of the country initially followed Barcelona?

Detailed Solution for CAT Mock Test- 5 - Question 47

Let the number of people in the country be 100.
Hence, the number of people following Real Madrid = 60
Let the number of people who follow Barcelona be x.
Hence, the number of people who follow Juventus = 40 - x.
The number of people following Cristiano among the Real Madrid followers = 0.8 x 60 = 48
The number of people not following Cristiano among the Real Madrid followers = 60 - 48 = 12.
The number of people who stopped following Real Madrid and started following Juventus = 0.5 x 48 = 24.
The number of people who stopped following Real Madrid and started following Barcelona = 0.25 x 12 = 3.
Number of people who still follow Real Madrid = (48 - 24) + (12 - 3) = 24 + 9 = 33.
Number of people who now follow Barcelona = x + 3
Number of people who now follow Juventus = 40 - x + 24 = 64 - x
Hence,
Case 1: x + 3 - 64 + x = 33
2x = 94
x = 47. (Not possible because 40 - x would become -7)
Case 2: 64 - x - x - 3 = 33
2x = 28
x = 14

CAT Mock Test- 5 - Question 48

If a function f(x) is defined as h(x+1), where h(x) is a real function. g(x) is defined as f(x+1). If g(x+1) = x+ 6x + 10
Find the value of h(5).

Detailed Solution for CAT Mock Test- 5 - Question 48

g(x+1) = x+ 6x + 10
g(x+1) = x+ 6x +9 +1 = (x + 3)2 + 1
g(x+1) = (x + 1 + 2)2 + 1
g(x) = (x + 2)2 + 1
f(x+1) = g(x) = (x + 2)2 +1
f(x+1) = (x + 1 + 1)2 +1
f(x) = (x + 1)+ 1
h(x+1) = f(x) = (x + 1)2 + 1
h(x) = x2 +1
Hence, h(5) = 26

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 49

If ax = b, by = c and cz = a, find the value of xyz.


Detailed Solution for CAT Mock Test- 5 - Question 49

ax = b, by = c, cz = a

Taking log of both sides, we get:

x log a = log b, 

y log b = log c,

z log c = log a,

xyz = 1

CAT Mock Test- 5 - Question 50

A square, ABCD has a side of length 12 cm each. An equilateral triangle, MAB exists such that M is outside the square ABCD. If a circle is drawn in such a way that it passes through the points M, C and D, then what will be the radius of that circle?

Detailed Solution for CAT Mock Test- 5 - Question 50

The problem figure in the question can be drawn as:

If we construct an equilateral triangle with base CD, we will get:

 

AM and DK are parallel to each other (makes 60 degrees with the base) and AD and MK are parallel to each other. 
∴AMKD is a parallelogram and hence AM= DK and AD= MK.
But since AM=AB=AD.
So, AMKD is a rhombus. 
Also, since MK= KD and M and D are the points on the circle, K must be centre of the circle and so, the radius = KD = CD = 12 cm.

CAT Mock Test- 5 - Question 51

A man is standing facing the north. He moves 45 metres east and then turns to his left and moves 50 metres in that direction. He then turns 45 degrees towards his right and moves a distance of 45√2 metres in that direction. He then turns 135 degrees to his right and walked a distance of 20 metres in that direction. Finally, he turns 45 degrees to the left and walks a distance of 50√2 metres. He stops at this point. What is the shortest distance(in metres) that he needs to travel from this point to reach his starting point?

Detailed Solution for CAT Mock Test- 5 - Question 51

We can depict all the directions in the given information as follows:



AJ = 45 + 45 + 50 = 140
FJ = 50 + 45 - 20 - 50 = 25

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 52

A solid hemisphere of radius 0.3 metres is molten and recast into small hollow cylinders, with an outer diameter of 14 cm, an inner diameter of 6 cm and a height of 2.5 cm. What is the maximum number of hollow cylinders that can be formed?


Detailed Solution for CAT Mock Test- 5 - Question 52

Let's convert everything to cm.
Volume of the hemisphere

Volume of each hollow cylinder = π R2h − π r2h = π (R2 − r2)h = π (49 − 9)2.5 = 100π 
Hence, number of hollow cylinders that can be formed

CAT Mock Test- 5 - Question 53

A circle is inscribed in a right triangle ABC, where the right angle is at point C as shown. The circle is tangent to the segment AB at D and the lengths of the segments DB and AD are 7 cm and 13 cm, respectively. Find the area of the triangle (in sq. cm).

Detailed Solution for CAT Mock Test- 5 - Question 53

CAT Mock Test- 5 - Question 54

What is the area (in sq units) bound between the following regions?
|y| ≥ |x|
y ≥ 0
x2 + y2 ≤ 49

Detailed Solution for CAT Mock Test- 5 - Question 54

If we plot the regions, we get

Hence the intersection of these regions is one-fourth the region inside the circle.
Hence, area enclosed 

Area of the circle


Therefore area of the enclosed region = 154/4 = 38.5

CAT Mock Test- 5 - Question 55

How many integers do not satisfy the following inequation?
|x|3 + 8x2 + 5|x| - 50 > 0

Detailed Solution for CAT Mock Test- 5 - Question 55

Let |x| = z.
|x|3 + 8x2 + 5|x| - 50 > 0
z3 + 8z2 + 5z - 50 > 0
Using hit and trial, we can see that z = 2 satisfies the equation
Hence, z-2 is a factor.
Using algebraic division, we can derive, 

z+ 8z+ 5z - 50 = (z − 2)(z2 + 10z + 25) = (z − 2)(z + 5)2  

For z > 2, the condition is satisfied. Hence for -5 < x < 2, the expression is less than zero. SInc the power of z + 5 is even, the expression < 0 for z < - 5 a well.
So, the condition is satisfied for z > 2 |x| > 2.
Hence, the condition is not satisfied for x = -2, -1, 0, 1, 2.

CAT Mock Test- 5 - Question 56

If the value of log25 is a, the value of log180 is b, and the value of log750 is ma + nb, where m and n are constants, find the value of m + n.

Detailed Solution for CAT Mock Test- 5 - Question 56

log 25 = a
∴ 2 log 5 = a
∴ log 5 = a/2
log 180 = b
∴ log 5 x 6 x 6 = b
∴  log 5 + 2 log 6 = b
∴ a/2 + 2 log 6 =b
∴ log 6 = b/2 - a/4
log 750 = log 5 x 5 x 5 x 6 = 3log 5 + log 6 = 3a/2 + b/2 - a/4 = b/2 + 5a/4
m = 5/4, n = 1/2
m + n = 5/4 + 1/2 =7/4

CAT Mock Test- 5 - Question 57

The cost of booking a football turf for 5 hours, a badminton court for 6 hours and a tennis court for 9 hours is Rs.7300. The cost of booking a football turf for 7 hours, a badminton court for 2 hours and a tennis court for 3 hours is Rs.3500. In a mega tournament, the organising committee needs to book the football turf for 50 hours, the badminton court for 28 hours and the tennis court for 42 hours. What is the total cost spent on booking?

Detailed Solution for CAT Mock Test- 5 - Question 57

5f + 6b + 9t = 7300 ....(i)
7f + 2b + 3t = 3500 ....(ii)
50f + 28b + 42t = ? ....(iii)
Multiplying (i) by a and (ii) by b and then adding, we should get eqn. (iii)
Hence, 5a + 7b = 50
6a + 2b = 28
Solving, we get, a = 3, b = 5.
It satisfies the coefficient of t as well. (9 x 3 + 3 x 5 = 42)
Now,  
5f + 6b + 9t = 7300 [x3]
7f + 2b + 3t = 3500 [x5]
15f + 18b + 27t = 21900
35f + 10b + 15t = 17500
Adding, we get
50f + 28b + 42t = 39400

CAT Mock Test- 5 - Question 58

If log7 log6 log5 a = 0 and log4 log3 logb a = 0 , find the sum of a and b.

Detailed Solution for CAT Mock Test- 5 - Question 58

log7 log6 log5 a = 0
log6 log5 a = 1
log5 a = 6
a = 56 
log4 log3 logb a = 0
log3 logb a = 1
logb a = 3
a = b3
b3 = 56
b = 25
a + b = 56 + 25 = 15625 + 25=15650

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 59

What is the number of ways in which 25364can be expressed as the product of 2 numbers which are not prime(order of numbers is not important)?


Detailed Solution for CAT Mock Test- 5 - Question 59

25364can be written as 21936
Hence it has 20 x 7 =140 factors. 
Hence, it can be written as a product of 2 numbers in 140/2 = 70 ways
Out of these 70 ways, in 2 of these ways, one of the numbers is prime, as follows

Hence, total number of ways = 70 - 2 = 68.

CAT Mock Test- 5 - Question 60

Harry got the order to make two xerox copies of a certain book. For the first copy, he took help from Mr. Z for the first half and for the second half, Harry took help from Mr. X and Mr. Y each of whom is twice efficient as compared to Mr. Z. He xeroxed the second copy by himself without any help. If Harry earned three quarter of profit, then what is the ratio of the efficiency of Harry to that of Mr. Z?

Detailed Solution for CAT Mock Test- 5 - Question 60

Let the total wages be Rs. 4.
As Harry got three quarter of the total profit, he got Rs. 3.
But he alone completed one of the books, hence completed half of the total work, and got Rs. 2.
He completed half of the work on the other book and earned Re. 1, which means Mr. Z, Mr. X and Mr. Y together had completed half of the work on that side.
Let the ratio of efficiencies of Harry and Mr. Z be x : a.
Therefore,

⇒ x2 + 4ax + x2 + ax = x2 + 5ax + 4a2
⇒ x2 = 4a2 ⇒ x : a = 2 : 1

CAT Mock Test- 5 - Question 61

If the dictionary ranking of a word 'RONALD_' among all the seven letter words formed by using the same letters is 4155, which of the following English alphabets can replace the _?

Detailed Solution for CAT Mock Test- 5 - Question 61

Arranging all the letters in alphabetical order, we get,
R O N A L D _  ->  A D L N O R _
We are not yet aware of what comes in the dash.
A comes before R, so all words starting with A will come before the given word. Hence 6!
Now, the best way to proceed is to first see how many 6! comes in the number 4155.
6! = 720.
720 x 5 = 3600 but 720 x 6  = 4320
Hence, there are exactly 5 letters in the word, which comes alphabetically before R.
These are A, D, L, N, O. Hence the letter replacing the dash should come alphabetically after R.
The only option is U.

CAT Mock Test- 5 - Question 62

In a set of consecutive odd numbers, the average of the first 'n' numbers is 'A', and the average of the first 'm' numbers (where 'm' is greater than 'n') is 'B'. If the sum of the first 'm' numbers is 'S', what is the average of the odd numbers from 'n + 1' to 'm' in terms of 'A', 'B', and 'S'?

Detailed Solution for CAT Mock Test- 5 - Question 62

Let the first odd number in the set = x
So, set of numbers will be: x, x + 2, x + 4, x + 6, x + 8, ...

Since the average of the first 'n' numbers is 'A',

i.e. 

Now, to find the sum of the odd numbers from 'n + 1' to 'm', we subtract the sum of the first 'n' odd numbers from the sum of the first 'm' odd numbers:
then by subtracting (3) and (1), we get
S(m - n) = Sm - Sn

Required average =   [from (2) and (4)]

CAT Mock Test- 5 - Question 63

Find the sum of the following series up to 50 terms:
3, 1, -2, -6, -11, -17,....

Detailed Solution for CAT Mock Test- 5 - Question 63

The differences between the terms of the series are in AP.
1 - 3 = -2
-2 - 1 = -3
-6 + 2 = -4 and so on.
We represent such a series as 
T(n) = an+ bn + c
Substituting n = 1,2,3, we get
a + b + c = 3 ....(i)
4a + 2b + c = 1 ....(ii)
9a + 3b + c = -2 ....(iii)
(ii) - (i), we get
3a + b = -2
(iii) - (i), we get
8a + 2b = -5
Solving these 2 equations, we get,
a = -0.5, b = -0.5
Putting these values in equation (i), we get c = 4.

CAT Mock Test- 5 - Question 64

2 shopkeepers A and B sell similar articles. Both the shopkeepers buy the articles at the rate of 60 articles for Rs.40. A sells the articles at 60 for Rs.50, whereas B marks up the price of each article by 50% and then offers a 20% discount. What is the ratio of the number of articles A has to sell and the number of articles B has to sell to obtain the same profit?

Detailed Solution for CAT Mock Test- 5 - Question 64

CP for both A and B = 40/60  = 2/3 per article.
For A,
SP = 50/60 = 5/6 per article.
Hence profit = 1/6 per article.
Hence profit on 'a' articles = a/6.
For B,
MP = 1.5 X 2/3 = 1 per article
SP = 0.8MP = 4/5 per article.

Hence, profit on 'b' articles = 2b/15
Hence, 

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 65

If the number of distinct real roots of the following equation is n, find the value of n.
x4 + x3 - 3x2 - x + 2 = 0


Detailed Solution for CAT Mock Test- 5 - Question 65

x4 + x3 - 3x2 - x + 2 = 0
Using Hit and Trial, we can see that both x = 1 and x = -1 satisfy the equation.
Hence, (x + 1) and (x - 1) are factors of the expression.
Dividing the expression by x- 1 we get
x4 + x3 - 3x2 - x + 2 = (x2 - 1) (x2 + x -2)
x2 + x - 2 = (x + 2) (x - 1)
Hence, 
x4 + x3 - 3x2 - x + 2 = (x + 1) (x - 1)2 (x + 2)
Hence, the equation has 3 distinct roots.

*Answer can only contain numeric values
CAT Mock Test- 5 - Question 66

How many 4 digit numbers, having all distinct digits exist, such that the digits are all in ascending order?


Detailed Solution for CAT Mock Test- 5 - Question 66

Basically, any 4 digits chosen from 1-9, can be arranged in exactly 1 way, such that all four digits are in ascending order. Hence total number of such numbers possible is 9C4 = 126.
For instance if the digits chosen are 7, 3, 4 and 8, we can arrange them in ascending order in exactly one way, as 3478.
Thus 126 such numbers are obtainable.

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