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CAT 2020 Slot 2: Past Year Question Paper - CAT MCQ


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76 Questions MCQ Test CAT Mock Test Series 2024 - CAT 2020 Slot 2: Past Year Question Paper

CAT 2020 Slot 2: Past Year Question Paper for CAT 2024 is part of CAT Mock Test Series 2024 preparation. The CAT 2020 Slot 2: Past Year Question Paper questions and answers have been prepared according to the CAT exam syllabus.The CAT 2020 Slot 2: Past Year Question Paper MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT 2020 Slot 2: Past Year Question Paper below.
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CAT 2020 Slot 2: Past Year Question Paper - Question 1

The author identifies three essential factors according to which theories of aggression are most commonly categorised. Which of the following options is closest to the factors identified by the author?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 1

This is the easiest question of the passage. The clue to the right answer is given in the last part of the first paragraph. Reading that part is enough to spot the right choice. It says there are three variables present in an aggressive act. They are: the aggressor, the circumstances, and the victim.

CAT 2020 Slot 2: Past Year Question Paper - Question 2

The author discusses all of the following arguments in the passage EXCEPT that:

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 2

We must remember that this is an except question. We must pick the choice that is not presented as the author’s argument. Choice 1 goes out because the author discusses it towards the end of the passage. Men have higher levels of testosterone, resulting in higher aggression. The second sentence of the last paragraph provides clue for choice 2. Thus 2 is also eliminated. The first paragraph elaborately describes the varying nature of aggression. Thus 3 also is eliminated. The moderation of death instinct is nowhere discussed in the passage, although the presence of death instinct is discussed. Thus 4 is the right choice.

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CAT 2020 Slot 2: Past Year Question Paper - Question 3

All of the following statements can be seen as logically implied by the arguments of the passage EXCEPT:

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 3

Though this is an except question, this question can be easily answered if we look for the phrase “neural regulation” in the passage. The neural inhibition has been discussed with regards to aggressive impulses, not the hormone testosterone. Thus 2 is definitely not implied by the author. Once we have found the right answer there is no need to verify the others. The rest of the options, however, do find indirect reference in the passage.

CAT 2020 Slot 2: Past Year Question Paper - Question 4

“An enemy combatant may be subjected to torture in order to extract useful intelligence, though those inflicting the torture may have no real feelings of anger or animosity toward their subject.” Which one of the following best explicates the larger point being made by the author here?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 4

The point made by the author in the quoted remark is that you may be aggressive without any real feelings of anger or animosity. Why? Because inflicting pain is not the objective, but serves some other end. Thus 3 directly becomes the right choice. 

CAT 2020 Slot 2: Past Year Question Paper - Question 5

“Why toil away as a starving peasant in the 16th century when a successful pirate made up to £4,000 on each raid?” In this sentence, the author’s tone can best be described as being:

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 5

This is a passage easy to read and understand. The very first question is author’s tone in the given sentence. Indignant means angry, but there is no anger as the author is relating to something that used to happen 400 years ago. The author is not trying to be analytical, rather he is trying to be ironical. Irony is used to highlight a situation by using contrast in an amusing way. His intention is not to discuss the contrast between peasant life and pirate life way back in the 16th century. 3 is the best choice.

CAT 2020 Slot 2: Past Year Question Paper - Question 6

“A more eclectic history might have included the conquistadors, Vasco da Gama and the East India Company. But Lehr sticks to the disorganised small fry . . .” From this statement we can infer that the author believes that:

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 6

The author by giving the example of Vasco da Gama and the east India company to suggest that they both were not very different from piracy. Options 2 brings out that suggestion appropriately. 1 goes out because the author does consider them as pirates. 3 might look like a good choice but the phrase “laid the ground for modern piracy” brings something that is not implied or stated in the passage. 4 could have been another close choice, but the author’s intention is not to compare the disorganized piracy of today with the organized piracy of the past. His intention is to compare the disorganized small piracy of the past with the renegades of today. It is small Vs small, and not small Vs big. 2 is the right answer.

CAT 2020 Slot 2: Past Year Question Paper - Question 7

We can deduce that the author believes that piracy can best be controlled in the long run:

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 7

At the end of the fourth paragraph the author says that “root causes of piracy today are the same as they were a couple of hundred years ago”. What were the causes a couple of hundred years ago? According to the author it is poverty. Thus he believes that eliminating poverty will solve the problem. Thus 3 is the right choice. All the other choices are mentioned only to show that they haven’t brought the desired results.

CAT 2020 Slot 2: Past Year Question Paper - Question 8

The author ascribes the rise in piracy today to all of the following factors EXCEPT:

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 8

We have to pick the choice that is not the cause behind the rise in piracy. 1 goes out because it is the cause. The first sentence of the fourth paragraph offers the clue. The third paragraph says that “the main motive for piracy has always been a combination of need and greed...”. Thus 3 also is correct, as a cause of piracy. The fourth paragraph has clue to option 4 as well. Thus 2 is the right choice. The author believes that surveillance can never be an effect solution because it is not addressing the root cause.

CAT 2020 Slot 2: Past Year Question Paper - Question 9

“No amount of social analysis can account fully for the existence of Michelangelo or Leonardo.” In light of the passage, which one of the following interpretations of this sentence is the most accurate?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 9

This is so simple a question that one will not feel like marking the right choice just because it is too straightforward. The author in the third paragraph says that the study of visual culture is very important to understand the agents, practices and institutions that put images to work. Then he further goes to say that “no amount of social analysis (visual culture) can account fully for the existence of Michelangelo or Leonardo. They were unique creators. Choice 4 is very close to this statement. It is so easy that one is highly likely to miss out on this. Choice 2 is close but a little absurd. It says that because they are genius they cannot be subjected to social analysis. The author says that we may have social analysis of these artists but no matter how much we analyse; the analysis may not be enough.

CAT 2020 Slot 2: Past Year Question Paper - Question 10

“Seeing . . . operates on the foundation of covenants with images that establish the conditions for meaningful visual experience.” In light of the passage, which one of the following statements best conveys the meaning of this sentence?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 10

This question asks us to interpret a phrase given in the passage. For meaningful visual experience, we need the conditions, which operate on the foundation of covenants. 3 precisely captures that meaning. In fact, the question asks us to pick the option that is similar in content to the one given in the question. 1 could have been close but it distorts the idea by saying “when there is foundational condition established in images”. It suggests that the foundation is established in images. Only 3 correctly rephrases the whole idea given in the question

CAT 2020 Slot 2: Past Year Question Paper - Question 11

Which set of keywords below most closely captures the arguments of the passage?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 11

This was an easy question. Two keywords are very important, one is visual images or imagery, and the other is visual culture or practices. Both these are important as per the first paragraph of the passage and only in choice 3 can we find these two keywords. Thus 3 is the best choice. 4 misses on imagery or visual images. 2 misses on the visual culture. 1 misses both visual culture and images.

CAT 2020 Slot 2: Past Year Question Paper - Question 12

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

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 12

We have to mark the choice that is not a valid inference. 2 can be inferred from last paragraph. 4 can be inferred from the first paragraph, and also the paragraph that discusses Michelangelo and Leonardo. In the third last paragraph the author says “how artifacts contribute to the construction of a world...”. Thus 3 also can be inferred. 1 cannot be inferred because structures of perception have been discussed as a physiological process, not as an institutional structure. Thus 1 is farfetched and the right choice as it cannot be inferred.

CAT 2020 Slot 2: Past Year Question Paper - Question 13

Which one of the following best describes the word “epiphenomena” in the last sentence of the passage?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 13

To mark the correct answer, we must understand the meaning of epiphenomenon, which means a secondary effect or a by-product. 3 is the right choice because supplemental means “provided in addition to”. Thus by-product=supplemental.

CAT 2020 Slot 2: Past Year Question Paper - Question 14

Based on the passage, we can infer that the author would be most supportive of which one of the following practices?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 14

The question asks us to pick a choice that the author would be most supportive of. 1 goes out because the author in the last paragraph says that localised renewable energy systems is unlikely to generate high returns for investors. 2 can be definitely inferred because the author clearly says at the end of second last para that disposal of toxic waste has perpetuated social injustice. Thus 2 is the right choice. For many 3 might be a tempting choice, but it is beside the point. The author is not concerned with more environment friendly carbon based fuels. He is talking about renewable energy sources, and the social and financial costs behind it. The whole discussion in the passage is based on the premise that we have already taken the path low carbon based renewable energy path. So the suggestion in 3 is pointless. 4 goes out because the author is not favouring any study. He wants resolution to the problem, so he wants action.

CAT 2020 Slot 2: Past Year Question Paper - Question 15

All of the following statements, if true, could be seen as supporting the arguments in the passage, EXCEPT:

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 15

This is a slightly difficult question. But 1 definitely supports the author. It must go out. We can find the evidence in the second paragraph. The second sentence of the last paragraph provides evidence for the 2nd choice. The third choice has already been inferred while solving the earlier question. It can be found in the last sentence of the second last para. 4 is the right answer because there is no reference for it in the passage. We have to mark the answer based on the evidence that we see in the passage.

CAT 2020 Slot 2: Past Year Question Paper - Question 16

Which one of the following statements, if false, could be seen as best supporting the arguments in the passage?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 16

This is the easiest question of the passage. We have to first falsify the choice and then see whether it is supporting the arguments in the passage. Choice 4, when falsified, says that renewable energy systems have an environmental impact. If that is the case, the author’s arguments find support in the passage. Thus 4 is the right choice. 1 goes out because the author says in the passage that renewable energy systems are not as profitable as nonrenewable energy systems. The Last sentence of the first paragraph provides evidence for this. The profitability aspect has been discussed in the last paragraph of the passage. Thus it takes care of both 2 and 3, because if the profitability is low, it means that the expense is high, and therefore economically unsustainable. Thus all 1,2 and 3 support the author without being negated, whereas 4 supports the author only when it is negated

CAT 2020 Slot 2: Past Year Question Paper - Question 17

Which one of the following statements, if true, could be an accurate inference from the first paragraph of the passage?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 17

This question is an easy question because to find the answer we have to read only the first paragraph. The author says “...but renewables need to be further scrutinized...”. This suggests that the author has some reservations or doubts pertaining to renewable energy. Thus 3 is the right choice. A very easy question indeed. 1 goes out because it talks of nonrenewable energy systems. 2 goes out because the author is equally concerned about environmental and social impact of renewable energy systems. 4 finds no mention in the passage and the first paragraph.

CAT 2020 Slot 2: Past Year Question Paper - Question 18

Which one of the following statements best captures the main argument of the last paragraph of the passage?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 18

This is a pretty interesting question. The author says “renewable energy can be produced at the household or neighbourhood level...but such small scale localised production is unlikely to generate high returns for investors.” This is a double edged sword. 2 goes out because efficiency has not at all been discussed in the last paragraph. Corporate control is indeed discussed but not in reference to democratic distribution of energy. Thus 3 goes out. 1 goes out because renewable energy has been discussed as a single idea, without any forms and types. Thus 1 also is a distortion

CAT 2020 Slot 2: Past Year Question Paper - Question 19

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

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 19

The official answer for this question seems to be a little weird. Though 4 is the official answer, we believe that sentence 5 should have been the right choice. 2 will open the paragraph. 1 and 4 focus on the victim’s past. 1 says “victim’s trauma after the assault rarely gets the attention...” and 4 says “even the most charitable question seems to focus on the victim’s past...”. 3 finally concludes by saying “the result is that we don’t have much of a vocabulary for what happens in a victim’s life after the painful past...”. 5 should have been the right answer, but the official answer is 4.

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 20

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. While you might think that you see or are aware of all the changes that happen in your immediate environment, there is simply too much information for your brain to fully process everything.
2. Psychologists use the term ‘change blindness’ to describe this tendency of people to be blind to changes though they are in the immediate environment.
3. It cannot be aware of every single thing that happens in the world around you.
4. Sometimes big shifts happen in front of your eyes and you are not at all aware of these changes.


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 20

This question is a difficult one, where two possible sequences might be correct. There is no doubt that 42 is one pair and 13 is the other. The point is which will come first 13 or 42. The official answer says 1342, though we believe that 4213 is just equally logical a sequence.

CAT 2020 Slot 2: Past Year Question Paper - Question 21

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

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 21

This is a question of moderate difficulty. 1 points at some truth. We must try to find the sentence that connects with 1. How can we monopolize and protect data? By having intellectual property rights. Thus 31 form a pair. 4 adds another idea to the story; it says “alongside the world of monopolised information (already discussed in 31), we have information as a social good, incapable of being owned. 5 concludes by saying that “information good are freely replicable....it can be copied and pasted infinitely”. In the light of intellectual property rights, and free information goods, 2 seems to be the odd one out.

CAT 2020 Slot 2: Past Year Question Paper - Question 22

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

With the Treaty of Westphalia, the papacy had been confined to ecclesiastical functions, and the doctrine of sovereign equality reigned. What political theory could then explain the origin and justify the functions of secular political order? In his Leviathan, published in 1651, three years after the Peace of Westphalia, Thomas Hobbes provided such a theory. He imagined a “state of nature” in the past when the absence of authority produced a “war of all against all.” To escape such intolerable insecurity, he theorized, people delivered their rights to a sovereign power in return for the sovereign’s provision of security for all within the state’s border. The sovereign state’s monopoly on power was established as the only way to overcome the perpetual fear of violent death and war.

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 22

The passage has three important keywords: sovereign equality, sense of insecurity, and what was done to overcome that insecurity. The passage tells us that people delivered their rights to a sovereign power in return for the sovereign’s provision of security. This was the only way to overcome the fear of insecurity. After all there is a give and take happening, and therefore there is a transaction. Thus 1 is the best choice. 2 misses on the people’s sense of insecurity. 3 goes out because limiting the power of papacy is not the essence of the discussion. Choice 4 misses the idea of give and take, people give their rights to the sovereign in return for his protection. It misses the crucial word “transactional relationship”.

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 23

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. It also has four movable auxiliary telescopes 1.8 m in diameter.
2. Completed in 2006, the Very Large Telescope (VLT) has four reflecting telescopes,8.2 m in diameter that can observe objects 4 billion times weaker than can normally be seen with the naked eye.
3. This configuration enables one to distinguish an astronaut on the Moon.
4. When these are combined with the large telescopes, they produce what is called interferometry: a simulation of the power of a mirror 16 m in diameter and the resolution of a telescope of 200 m.


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 23

This is one of the easiest questions. 2 introduces the idea of VLT and mentions what it has. 1 comes as an addition and mentions the additional things that VLT has. 4 talks about what happens when these are combined. 3 is the result of that combination. Thus 2143 is the right sequence. A very easy question indeed!

CAT 2020 Slot 2: Past Year Question Paper - Question 24

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

All humans make decisions based on one or a combination of two factors. This is either intuition or information. Decisions made through intuition are usually fast, people don’t even think about the problem. It is quite philosophical, meaning that someone who made a decision based on intuition will have difficulty explaining the reasoning behind it. The decision-maker would often utilize her senses in drawing conclusions, which again is based on some experience in the field of study. On the other side of the spectrum, we have decisions made based on information. These decisions are rational — it is based on facts and figures, which unfortunately also means that it can be quite slow. The decision-maker would frequently use reports, analyses, and indicators to form her conclusion. This methodology results in accurate, quantifiable decisions, meaning that a person can clearly explain the rationale behind it.

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 24

In the passage the author compares the two factors based on which humans make decisions. The first is intuition and the other is information. The author seems to be comparing the two without any preference. 1 goes out because it inaccurately says that “we choose intuition or information based on the time available”. Nothing of this sort has been given in the passage. Time in not the causative factor here. 2 says “it is better”. Since the author has not given any preference, it would be wrong to say which one is better. Thus 2 also goes out. 3 is the right summary, and captures the essence by stating that the difference is differential speed and ability to provide a rationale. 4 just focuses on intuition, and ignores the other factor entirely.

CAT 2020 Slot 2: Past Year Question Paper - Question 25

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

The rural-urban continuum and the heterogeneity of urban settings pose an obvious challenge to identifying urban areas and measuring urbanization rates in a consistent way within and across countries. An objective methodology for distinguishing between urban and rural areas that is based on one or two metrics with fixed thresholds may not adequately capture the wide diversity of places. A richer combination of criteria would better describe the multifaceted nature of a city’s function and its environment, but the joint interpretation of these criteria may require an element of human judgment.

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 25

There are three important keywords in this paragraph: the challenge posed by rural-urban continuum, the objective methodology with one or two metrics may not be enough to capture the wide diversity, it may require an element of human judgement. 2 captures all the keywords succinctly. 1 misses the element of human judgement, 3 also misses on the same. 4 goes out because it is not about the judgment of objective methodology, but human judgement coming as an additional factor to aid the methodology.

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 26

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. But the attention of the layman, not surprisingly, has been captured by the atom bomb, although there is at least a chance that it may never be used again.
2. Of all the changes introduced by man into the household of nature, [controlled]largescale nuclear fission is undoubtedly the most dangerous and most profound.
3. The danger to humanity created by the so-called peaceful uses of atomic energy may, however, be much greater.
4. The resultant ionizing radiation has become the most serious agent of pollution of the environment and the greatest threat to man’s survival on earth.


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 26

This might a little tricky question, but without doubt 2 will open the paragraph. The resultant ionising radiation in 4 is a consequence of large scale nuclear fission mentioned in 2. Thus 24 form a pair. 4 and 1 are contrasting ideas, something that justifies the presence of the conjunction “but” in 1. The resultant ionising radiation has become the most serious agent of pollution... but the attention of the layman has been captured by the atom bomb....3 comes as the appropriate conclusion. 3 can’t come after 4 because both 4 and 3 talk nuclear fission, which does not justify the presence of the word “however” in 3. We use however to contrast two ideas, but both 4 and 3 talk of peaceful uses of atomic energy. Nuclear fission is used for purposes other than atomic bomb. Thus 2413 is the right sequence.

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 27

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green.

While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.

Every unique, complete arrangement of twenty five beads is called a configuration.

The total number of possible configuration using beads of only two colours is:


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 27

As we need to use only two colours, in any row or column these two coloured beads will be
placed alternately like

So we cannot place Red coloured beads at position 1 or two as between any two Red beads there must at least two beads (at least one green and at least one Blue). Hence, we can use only Green and Blue coloured beads.

We can have two possible configurations:

Configuration 1: Green bead is placed at top left corner

Configuration 2: Blue bead is placed at top left corner

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 28

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green.

While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.

Every unique, complete arrangement of twenty five beads is called a configuration.

What is the maximum possible number of Red beads that can appear in any configuration ?


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 28

Between Any two Red beads there must be at least two Beads. So any Row or column there can be maximum two red beads. If we place two red beads in each row then two columns will have three red bead which cannot be accepted.

The above configuration is not correct.

So in the third row we will place only one Red bead at the middle of the third row. Also we will adjust other rows so that between any two Red beads there are at least two beads in any column.

So maximum 9 Red beads are possible in any configuration. At remaining places Green and Blue coloured beads can be placed in such way that all the conditions given are satisfied. There are multiple configurations are possible. One of the configurations is given as below.

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 29

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green.

While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.

Every unique, complete arrangement of twenty five beads is called a configuration.

What is the minimum number of Blue beads in any configuration ?


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 29

To minimise number of Blue beads we need to maximise number of Red and Green beads. From the previous question solution, Maximum no. Red beads can be 9. The row in which has two red beads, we will place two green and one Blue bead additionally.

The row with only one red bead we will place two green and two blue beads additionally. So overall there will be minimum 6 Blue beads.

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 30

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green.

While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.

Every unique, complete arrangement of twenty five beads is called a configuration.

Two Red beads have been placed in ‘second row, third column’ and ‘third row, second column’. How many more Red beads can be placed so as to maximise the number of Red beads used in the configuration?


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 30

We can place maximum 6 more beads as shown below.

CAT 2020 Slot 2: Past Year Question Paper - Question 31

In HomeDecor departments of which cities were the sales amounts the highest in 2018 and 2019, respectively?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 31

From (6)
HomeDecor
Delhi (2018) = 100-20 = 80
Bengaluru (2018) = 80-20 = 60
From (3)
HomeDecor
Let Mumbai (2018) = Kolkata (2018) = a
So, Data for HomeDecor will be as follows

From (5)
(80 + a + 60 + a) + 70 = (100 + 72 + 80 + 54)
2a + 210 = 306
2a = 96
a = 48
We have found all the values for HomeDecor. Now we will find values for Apparels
From (1)
Apparels
Let Delhi (2018) = Kolkata (2018) = b
From (2)
Apparels
Let Mumbai (2018) = Bengaluru (2018) = Delhi (2019) = c


From (7)
Apparels
Bengaluru (2019) = c + (c-b) = 2c -b
Also, Mumbai (2019) = c + (54-b) = c-b + 54

Now there are two variables. We need two equations to get their values.
From (8)
Apparels 2019
Delhi - Kolkata = Kolkata - Bengaluru
Delhi + Bengaluru = 2 (Kolkata)
c + 2c - b = 2(54)
3c -b = 108 ..............(I)
From (4) From 2018 to 2019
Total Increase in apparels Sales = Total Increase in Electronics Sales
[c + (c - b + 54) + (2c - b) + 54] - [b + c + c + b] = [98 + 102 + 70 + 100 ] - [78 + 82 + 90 + 80]
[4c - 2b + 108 ] - [2b + 2c ] = 370 - 330
2c - 4b + 108 = 40
2c - 4b = - 68
c - 2b = - 34 .......... ( II )
Solving ( I ) and ( II ) we get
b = 42 and c = 50
Substituting we get

HomeDecor 2018 Highest sales in Delhi
HomeDecor 2019 Highest Sales in Delhi

CAT 2020 Slot 2: Past Year Question Paper - Question 32

What was the increase in sales amount, in Crore Rupees, in the Apparel department of Mumbai from 2018 to 2019?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 32

From (6)
HomeDecor
Delhi (2018) = 100-20 = 80
Bengaluru (2018) = 80-20 = 60
From (3)
HomeDecor
Let Mumbai (2018) = Kolkata (2018) = a
So, Data for HomeDecor will be as follows

From (5)
(80 + a + 60 + a) + 70 = (100 + 72 + 80 + 54)
2a + 210 = 306
2a = 96
a = 48
We have found all the values for HomeDecor. Now we will find values for Apparels
From (1)
Apparels
Let Delhi (2018) = Kolkata (2018) = b
From (2)
Apparels
Let Mumbai (2018) = Bengaluru (2018) = Delhi (2019) = c


From (7)
Apparels
Bengaluru (2019) = c + (c-b) = 2c -b
Also, Mumbai (2019) = c + (54-b) = c-b + 54

Now there are two variables. We need two equations to get their values.
From (8)
Apparels 2019
Delhi - Kolkata = Kolkata - Bengaluru
Delhi + Bengaluru = 2 (Kolkata)
c + 2c - b = 2(54)
3c -b = 108 ..............(I)
From (4) From 2018 to 2019
Total Increase in apparels Sales = Total Increase in Electronics Sales
[c + (c - b + 54) + (2c - b) + 54] - [b + c + c + b] = [98 + 102 + 70 + 100 ] - [78 + 82 + 90 + 80]
[4c - 2b + 108 ] - [2b + 2c ] = 370 - 330
2c - 4b + 108 = 40
2c - 4b = - 68
c - 2b = - 34 .......... ( II )
Solving ( I ) and ( II ) we get
b = 42 and c = 50
Substituting we get

62 - 50 = 12

CAT 2020 Slot 2: Past Year Question Paper - Question 33

Among all the 12 departments (i.e., the 3 departments in each of the 4 cities), what was the maximum percentage increase in sales amount from 2018 to 2019?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 33

From (6)
HomeDecor
Delhi (2018) = 100-20 = 80
Bengaluru (2018) = 80-20 = 60
From (3)
HomeDecor
Let Mumbai (2018) = Kolkata (2018) = a
So, Data for HomeDecor will be as follows

From (5)
(80 + a + 60 + a) + 70 = (100 + 72 + 80 + 54)
2a + 210 = 306
2a = 96
a = 48
We have found all the values for HomeDecor. Now we will find values for Apparels
From (1)
Apparels
Let Delhi (2018) = Kolkata (2018) = b
From (2)
Apparels
Let Mumbai (2018) = Bengaluru (2018) = Delhi (2019) = c


From (7)
Apparels
Bengaluru (2019) = c + (c-b) = 2c -b
Also, Mumbai (2019) = c + (54-b) = c-b + 54

Now there are two variables. We need two equations to get their values.
From (8)
Apparels 2019
Delhi - Kolkata = Kolkata - Bengaluru
Delhi + Bengaluru = 2 (Kolkata)
c + 2c - b = 2(54)
3c -b = 108 ..............(I)
From (4) From 2018 to 2019
Total Increase in apparels Sales = Total Increase in Electronics Sales
[c + (c - b + 54) + (2c - b) + 54] - [b + c + c + b] = [98 + 102 + 70 + 100 ] - [78 + 82 + 90 + 80]
[4c - 2b + 108 ] - [2b + 2c ] = 370 - 330
2c - 4b + 108 = 40
2c - 4b = - 68
c - 2b = - 34 .......... ( II )
Solving ( I ) and ( II ) we get
b = 42 and c = 50
Substituting we get

Maximum percentage increase is form Mumbai HomeDecor from 2018 to 2019 Percentage increase

CAT 2020 Slot 2: Past Year Question Paper - Question 34

What was the total sales amount, in Crore Rupees, in 2019 for the chain of departmental stores?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 34

From (6)
HomeDecor
Delhi (2018) = 100-20 = 80
Bengaluru (2018) = 80-20 = 60
From (3)
HomeDecor
Let Mumbai (2018) = Kolkata (2018) = a
So, Data for HomeDecor will be as follows

From (5)
(80 + a + 60 + a) + 70 = (100 + 72 + 80 + 54)
2a + 210 = 306
2a = 96
a = 48
We have found all the values for HomeDecor. Now we will find values for Apparels
From (1)
Apparels
Let Delhi (2018) = Kolkata (2018) = b
From (2)
Apparels
Let Mumbai (2018) = Bengaluru (2018) = Delhi (2019) = c


From (7)
Apparels
Bengaluru (2019) = c + (c-b) = 2c -b
Also, Mumbai (2019) = c + (54-b) = c-b + 54

Now there are two variables. We need two equations to get their values.
From (8)
Apparels 2019
Delhi - Kolkata = Kolkata - Bengaluru
Delhi + Bengaluru = 2 (Kolkata)
c + 2c - b = 2(54)
3c -b = 108 ..............(I)
From (4) From 2018 to 2019
Total Increase in apparels Sales = Total Increase in Electronics Sales
[c + (c - b + 54) + (2c - b) + 54] - [b + c + c + b] = [98 + 102 + 70 + 100 ] - [78 + 82 + 90 + 80]
[4c - 2b + 108 ] - [2b + 2c ] = 370 - 330
2c - 4b + 108 = 40
2c - 4b = - 68
c - 2b = - 34 .......... ( II )
Solving ( I ) and ( II ) we get
b = 42 and c = 50
Substituting we get

CAT 2020 Slot 2: Past Year Question Paper - Question 35

Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car) arrive. At this moment, which among the following numbered car is parked next to car 3?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 35

The parking slots will be numbered as follows.

The cars that are parked next to car 3 are car 2 and car 7.

CAT 2020 Slot 2: Past Year Question Paper - Question 36

Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a compact and car 7 is an SUV. Which of the following is a POSSIBLE current configuration of the parking lot?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 36

When cars 5 and 6 are present, car 7 cannot take a place between them. So , 5,7,6 is not
possible.
8,2,3, V, 5,6,7 is possible in the following sequence of arrival of cars.
I. Cars 1,2,3,4,5,6 and 7 arrive one after the other.
II. Car 1 leaves
III. Car 8 arrives and is parked in the slot vacated by car 1
IV. Car 4 leaves.
V. 2,3,7,5,6,8 is not possible as car 7 (SUV) cannot be parked in place of car 4 (compact)
while cars 3 and 5 are still parked. 8, 2, 3, V, 6,5,7 is not possible as car 6 cannot be between a vacant slot and to the left of car 5 for the following reasons.
If no slot is vacant when car 6 is arrived, it would have been parked to the right of car 5.
If car 4 (compact) left by the time car 6 arrives it would either be parked in the slot vacated by car 4 or to the right of car 5.

CAT 2020 Slot 2: Past Year Question Paper - Question 37

Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is NOT necessarily true?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 37

From the given arrangement it can be understood that cars 1, 2 and 3 arrived first and then cars 1 and 2 left before cars 4, 5 and 6 arrived. Now, there are four slots to the left of car 3. Hence, cars 1 and 2 are SUVs. Since three out of four slots are occupied by cars 4, 5 and 6, all these are compact cars. Whether car 3 is a compact car or an SUV, the given
arrangement is possible.

CAT 2020 Slot 2: Past Year Question Paper - Question 38

Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements MUST be false?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 38

As cars 3 and 5 are still in their positions and that car 4 is not the first car to leave, at least one of cars 1 and 2 left before car 4. Let us consider the following cases. Both cars 1 and 2 left before car 4: In this case car 6, whether it is a compact car or an SUV, would have been parked in the parking lots vacated by cars 1 and 2. Hence, this case is not possible.

Only car 1 left before car 4: As car 6 is parked in the lot vacated by car 4, car 7 would have been parked in place of car 1. But the s lot vacated by car 1 is still vacant. Hence, this case is not possible.

Only 2 left before car 4: If the car 2 is an SUV, car 6 would have been parked in that lot. Hence, cars 2 and 7 are compact cars. Car 1 left after car 7 arrived.

CAT 2020 Slot 2: Past Year Question Paper - Question 39

Which one of the following statements is true?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 39

Given,
Students: A, B, C, D, E, F, G, H
Guides: P (2 students), Q (1 student), R (2 students), S (1 student), T (2 students)
Economics (4 students), Sociology (3 students), Anthropology (1 student)
Slots: 9:00, 9:30, 10:00, 10:30
From (1), one economics seminar is held in each of the four slots.
From (1) and (2), A is students of economics and is guided by R. Hence, R is from economics department (given, each student is guided by a guide belonging to their department).
The information from (1), (2), (3) and (4) can be tabulate as follows.

From (5), two sociology seminars and one economics seminar are held in the same slot. It cannot be 10:00 slot or 10:30 slot as at most three seminars can be conducted in one slot.
From (5) and (7), seminars of B, G and T are held in 9:30 slot.
From (6) and the given point that students who are guided by the same guide must be scheduled in consecutive slots, C is a sociology student and his/her seminar is held in 9:00 slot.

From the above we also know the following combination of guides, their subject and their students

We know that G is a sociology student and F is an anthropology student. Hence, the rest D, E and H are economics students. Thus, one among D, E and H (economics students) is guided by R and the remaining two are guided by T. Now, G and F are guided by Q and S in any order. We get the following combinations.

It is also given that students who are guided by the same guide must be scheduled in consecutive slots. Hence, 9:00 economics seminar is of T and 10:30 seminar is that of R.

From the above table, it is clear that the statement that two seminars are scheduled in the first slot is true

CAT 2020 Slot 2: Past Year Question Paper - Question 40

Who all are NOT guiding any Economics students?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 40

Given,
Students: A, B, C, D, E, F, G, H
Guides: P (2 students), Q (1 student), R (2 students), S (1 student), T (2 students)
Economics (4 students), Sociology (3 students), Anthropology (1 student)
Slots: 9:00, 9:30, 10:00, 10:30
From (1), one economics seminar is held in each of the four slots.
From (1) and (2), A is students of economics and is guided by R. Hence, R is from economics department (given, each student is guided by a guide belonging to their department).
The information from (1), (2), (3) and (4) can be tabulate as follows.

From (5), two sociology seminars and one economics seminar are held in the same slot. It cannot be 10:00 slot or 10:30 slot as at most three seminars can be conducted in one slot.
From (5) and (7), seminars of B, G and T are held in 9:30 slot.
From (6) and the given point that students who are guided by the same guide must be scheduled in consecutive slots, C is a sociology student and his/her seminar is held in 9:00 slot.

From the above we also know the following combination of guides, their subject and their students

We know that G is a sociology student and F is an anthropology student. Hence, the rest D, E and H are economics students. Thus, one among D, E and H (economics students) is guided by R and the remaining two are guided by T. Now, G and F are guided by Q and S in any order. We get the following combinations.

It is also given that students who are guided by the same guide must be scheduled in consecutive slots. Hence, 9:00 economics seminar is of T and 10:30 seminar is that of R.

We know that R is guiding an economics student. Hence, choices with R can be are eliminated. None among P, Q and S is guiding an economics student.

CAT 2020 Slot 2: Past Year Question Paper - Question 41

Which of the following statements is necessarily true?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 41

Given,
Students: A, B, C, D, E, F, G, H
Guides: P (2 students), Q (1 student), R (2 students), S (1 student), T (2 students)
Economics (4 students), Sociology (3 students), Anthropology (1 student)
Slots: 9:00, 9:30, 10:00, 10:30
From (1), one economics seminar is held in each of the four slots.
From (1) and (2), A is students of economics and is guided by R. Hence, R is from economics department (given, each student is guided by a guide belonging to their department).
The information from (1), (2), (3) and (4) can be tabulate as follows.

From (5), two sociology seminars and one economics seminar are held in the same slot. It cannot be 10:00 slot or 10:30 slot as at most three seminars can be conducted in one slot.
From (5) and (7), seminars of B, G and T are held in 9:30 slot.
From (6) and the given point that students who are guided by the same guide must be scheduled in consecutive slots, C is a sociology student and his/her seminar is held in 9:00 slot.

From the above we also know the following combination of guides, their subject and their students

We know that G is a sociology student and F is an anthropology student. Hence, the rest D, E and H are economics students. Thus, one among D, E and H (economics students) is guided by R and the remaining two are guided by T. Now, G and F are guided by Q and S in any order. We get the following combinations.

It is also given that students who are guided by the same guide must be scheduled in consecutive slots. Hence, 9:00 economics seminar is of T and 10:30 seminar is that of R.

B is scheduled in the second slot. W e are not sure of who are guiding G and F. So, two other
choice s are not necessarily true.

CAT 2020 Slot 2: Past Year Question Paper - Question 42

If D is scheduled in a slot later than Q's, then which of the following two statement(s) is(are) true?
(i) E and H are guided by T.
(ii) G is guided by Q.

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 42

D‘s seminar is scheduled later than Q’s seminar, indicates that Q’s seminar cannot be in the last slot. It implies F is guided by S and G by Q. Hence, statement (ii) is true. Now that Q’s seminar is scheduled in the second slot, D’s seminar is scheduled in the lost slot. i.e D is guided by R. Hence, E and H are guided by T. Thus, statement (i ) is also true. Both (i) and (ii) are true.

CAT 2020 Slot 2: Past Year Question Paper - Question 43

If E and Q are both scheduled in the same slot, then which of the following statements BEST describes the relationship between D, H, and T?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 43

If E and Q are scheduled in the same slot, it is possible both in the second slot and the last slot. If it is in the second slot, then E is guided by T and one among D and E is also guided by T. If it is in the last slot, then E is guided by R and both D and E are guided by T. Thus, at least one of D and H is guided by T.

CAT 2020 Slot 2: Past Year Question Paper - Question 44

If D is scheduled in the slot immediately before Q’s, then which of the following is NOT necessarily true?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 44

If D is scheduled in the slot immediately before Q’s, it is only possible with D is in the first slot and Q is in the second slot. It implies that D is guided by T, G is guided by Q and F is guided by S. One among E and H is guided by T and the other one b y R, in any order. Hence
the statement that E is guided by R is NOT necessarily true.

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 45

What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 45

Total valid votes in A = 5,00,000 Minimum no of valid votes required to save the security
deposits 

As per 1st additional information ⇒ the gap between 1st and 2nd runners up is 10,000 So
the table for A⇒ total →5,00,000

Winner →2,75,000
1st runner up →55,000
2nd runner up →85,000
Total →4,55,000
The valid votes got by the other 7 candidates = 5,00,000 - 4,55,000
= 45,000
∴ the % of votes by the candidates who lost the security deposit is 

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 46

How many candidates who contested in constituency B lost their security deposit?


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 46

Total valid votes in A=3,25,000

Minimum no of valid votes required to save the security deposits

We can see the winner himself/herself has got 48,750 no of votes which is less than 1/6th of the total votes.
∴ all of the candidates got less than 1/6th of the valid votes.
∴ security deposits will be forfeited for all of the candidates as winner is exempted from
this condition. (total no of such candidates =12 -1 =11)

CAT 2020 Slot 2: Past Year Question Paper - Question 47

How many candidates who contested in constituency B lost their security deposit?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 47

As it is given in the question that the first runner-up polled 10,000 more votes than the second runner-up in constituency A. Now the first runner-up has got 95000 votes, hence the second runner-up will get 85000 votes. Therefore the remaining votes will be  500000 - 275000 - 95000 - 85000 = 45000

As per the second additional point given, None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000 ⇒ the person who got the 5th highest votes must have got greater than 600030/6 ⇒ 100006. As it is also given that the difference of votes is greater than 10000, the only possible case is winner, 1st runner up, 2nd runner up, 3rd runner up, 4th runner up must have got 140006,130006,120006,110006,100006 respectively which sums up to exactly 600030.

Let the number of votes polled in D be 100x.

From 3, The winning candidate in constituency D must have got 15x + 37500 The table now looks like this:

In constituency B, the mark for not losing the security deposit is 1/6(325000) or 54167 but the winner got less than 54167 ⇒ all the candidates lost their security deposits. 

∴ 11 is the correct answer.

CAT 2020 Slot 2: Past Year Question Paper - Question 48

What was the number of valid votes polled in constituency D?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 48

Let the no of valid votes → 100x
The table looks like the following:
Total votes →100x
Winner → 39,375
1st →37,500
2nd → 30,000
3rd → 10x
Total → 1,06,875
As the winner got 51 more than 1st runner up (as per 3 )
Total no of votes has to be more than

=1,10,208
∴ option (62,500) is ruled out.
To eliminate two more options, lets consider 1,50,000 to be the correct one [as one option is less than & the other one is the greater than this option]
∴100x = 1,50,000
Total →1,50,000
Winner →45,000
1st →37,500
2nd →30,000
3rd →15,000
Total →1,06,875
Minimum rates to save security deposits 

So we can see except 3 candidates all others have lost their security deposits.
Candidates who saved their security deposits = (100 -35)% = 65%[ as per 3rd additional
inform]
∴ 65% of 1,50,000 = 97,500
→ which is less than 1,12,500
∴ answer will be more than 1,50,000

CAT 2020 Slot 2: Past Year Question Paper - Question 49

The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up. Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 49

Margins
A → 2,75,000 - 95,000 = 1,80,000
B →
C  → 1,50,000 -1, 40,000 =10,000
D → 39,375 - 37,500 =1,875
Clearly the margin in C is more than that of D. So clearly the sequence B , C , D , A is not
possible.

CAT 2020 Slot 2: Past Year Question Paper - Question 50

For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 50

The no. of votes got by the candidates who has lost their security deposits is as follows
In A → 45,000
In B → 3,25,000 - 48,750 = 2,76,250
In C → 0
In D → 1,75,000 - 46,250 - 37,500 - 30,000 = 61250

CAT 2020 Slot 2: Past Year Question Paper - Question 51

The sum of the perimeters of an equilateral triangle and a rectangle is 90 cm. Thearea, T, of the triangle and the area, R, of the rectangle, both in sq cm, satisfy therelationship R = T2 . If the sides of the rectangle are in the ratio 1: 3, then the length, in cm,of the longer side of the rectangle, is

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 51

Let the breadth of the rectangle be b.
Length of the rectangle  3b
Let a be the side of the equilateral triangle.
Given,

Given,
2(4b) + 3a = 90
8(a2 / 4)+ 3a - 90 = 0 
⇒ 2a2 + 3a - 90 = 0
⇒ (a - 6)(2a +15) = 0
⇒ a = 6
⇒ b = 9
⇒ 3b = 27

CAT 2020 Slot 2: Past Year Question Paper - Question 52

In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent ₹ 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent ₹ 450 on rice in April, then how much did he spend on wheat in May?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 52

Amount spent on rice in May = 450 x1.2 = ?540.
If the amount spent on wheat in April is w, then in May it would be 1.12w.
Given, (1.12w+ 540) - (w+ 450) 150
⇒12w = 60
⇒ w = 500
∴ The amount spent on wheat in May =1.12w i.e., ? 560

CAT 2020 Slot 2: Past Year Question Paper - Question 53

In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beatscar C by 90 km. The distance (in km) over which the race has been conducted is

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 53

Let the length of the racetrack be D.
When A covers D km, B covers ( D -45) km and C covers (D-90) km
When B covers D km, C covers ( D -50) km
The ratio of the speeds of the racers is same as the ratio of the distance travelled in a given
time period.
Ratio of speed of B and C is

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 54

John takes twice as much time as Jack to finish a job. Jack and Jim together take onethirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 54

Let the individual times taken by John, Jack and Jim to complete the works be a, b and c respectively.
Given, a = 2b ... (1)

From (1) and (2), we've c = 2b

CAT 2020 Slot 2: Past Year Question Paper - Question 55

Let the m-th and n-th terms of a geometric progression be  3/4 and 12 , respectively, where m<n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 55

To get the minimum value for r + n -m, r should be minimum.
∴ r = - 4
n -m = 2
∴ Required answer =-2

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 56

If x and y are positive real numbers satisfying x+y=102, then the minimum possible value of
 is 


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 56


Given x + y = 102

The minimum value of

CAT 2020 Slot 2: Past Year Question Paper - Question 57

The value of  for 1< a ≤ b cannot be equal to

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 57



∴  The above value is ≤ 0 .
∴ 1 can't be the answer.

CAT 2020 Slot 2: Past Year Question Paper - Question 58

In how many ways can a pair of integers (x , a) be chosen such that x2 - 2 | x | + | a - 2 |= 0 ?

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 58

since x is integer 3- a ≥ 0
a ≤ 3
The possible values of a is = 3
Then x = ±1;

Since x is integer a -1≥ 0⇒a ≥1
∴ The possible values of a is 1


∴ The possible pairs =(-1,3), (1,3), (1,1), (-1,1), (2,2),(-2,2), (0,2) i.e., 7

CAT 2020 Slot 2: Past Year Question Paper - Question 59

Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 59

Let a, b, c represent number of students who opted for two subjects - Maths and Chemistry,
Maths and Physics and Physics and Chemistry respectively.
Given, a + b = 23-18 = 5
and b +c = 25-18 = 7
Since a, b and c cannot be negative the least value for any of the three is 5 .
We get a + c +18 = (23 + 25 -18) - 2b
Minimum value of number of students who chose chemistry = 23+ 25-18 -10 = 20

CAT 2020 Slot 2: Past Year Question Paper - Question 60

For real x, the maximum possible value of  

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 60

Hence the maximum value of 

CAT 2020 Slot 2: Past Year Question Paper - Question 61

Aron bought some pencils and sharpeners. Spending the same amount of money asAron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of onesharpener is ₹ 2 more than the cost of a pencil, then the minimum possible number ofpencils bought by Aron and Aditya together is

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 61

Let the price of each pencil be Rs. x and price of each sharpens be Rs. y

Required value = 3a

Its possible only when y =22
∴ a =11
Required answer =33

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 62

A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3:2, while the ratio of the shares of Sunil and Mita is 4:5. If the difference between the largest and the smallest of these three shares is Rs 400, then Sunil’s share, in rupees, is


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 62

Given ratio of shares of Amal and Sunil is 3: 2
Also the ratio of shares of Sunil and Mita is 4: 5 .
Hence the ratio of shares of Anil, Sunil and Mita is 6: 4: 5

CAT 2020 Slot 2: Past Year Question Paper - Question 63

Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have bee

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 63

Let the cost price and marked price of each toy be c and m respectively.
Overall selling price

Given, 110% of 12c = 8.8m

Required profit percentage

CAT 2020 Slot 2: Past Year Question Paper - Question 64

Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A.Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2 atspeeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will makebefore he meets Rahim again for the first time is

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 64

Time taken by each of them to complete one round

Time taken for Ram to cover one round

Time taken for Rahim to cover one round

Time taken by Ram and Rahim meet each other for the first time = LCM of 48π and 28.8π =144π
∴ Number of rounds made by Ram before he meets Rahim for the first time 

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 65

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 65

Consider four blanks
- - - -
7 is in thousand place, then 3 can be placed in any of the 3 places in 3 ways. Remaining two
blanks can be filled with remaining eight digits in 8P2 ways. The number of numbers that
have 7 is in thousand place is 3 x 8P = 168
Thousand place cannot be 0,7 and 3, it can be filled with remaining 7 digits in 7 ways. In
remaining 3 blanks, 7 and 3 can be arranged in 3 ways. Fourth blank can be filled in 7 ways.
The number of numbers that are formed where 7 and 3 is not in thousand place is
7x3x7 =147 . Hence total required numbers =168+147 = 315 .

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 66

The number of pairs of integers (x , y) satisfying x ≥ y ≥ -20 and 2x +5y = 99 is


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 66

2x +5y = 99

When y = -19, x≥ 97; since x ≥ y ; the maximum value of y is 13 and corresponding value of x is 17 .
We know that the solutions of y are in arithmetic progression with common difference 2 .
Here a = - 19, d = 2, tn= 13

Hence number of pairs integers is 17

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 67

If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5, then the maximum possible value of 2x + y equals


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 67

Given x + 9 = z = y + 1 and x + y < z + 5
⇒ (z -9)+(z -1) < z +5
⇒ z < 15
Hence the maximum value of z = 14, max of x = 5 and max of y = 13
Required answer, 2 x + y = 2 ´ 5 + 13 = 23

CAT 2020 Slot 2: Past Year Question Paper - Question 68

A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 68

Required ratio of speeds = Square root of inverse ratio of times taken after crossing each other. = √4 : √1 i.e., 2: 1 

CAT 2020 Slot 2: Past Year Question Paper - Question 69

The distance from B to C is thrice that from A to B. Two trains travel from A to C via B.The speed of train 2 is double that of train 1 while traveling from A to B and their speeds areinterchanged while traveling from B to C. The ratio of the time taken by train 1 to that takenby train 2 in travelling from A to C is

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 69

Given,

Let the speed of train 1 from A to B be s. Then the speed of train 2 from A to B is 2s. 
Time taken by train 1 to cover A to 

And, time taken by train 2 to cover A to C 

CAT 2020 Slot 2: Past Year Question Paper - Question 70

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest to

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 70



OT = 2.4M
In ΔOTQ
OQ2 = OT2 + TQ2 ⇒ TQ2 = OQ2 - OT2
= (5)2 - (2.4)2
=19.24 

CAT 2020 Slot 2: Past Year Question Paper - Question 71

The number of integers that satisfy the equality  is

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 71


We know, for ab = 1,
if -a = -1 then b is even.
-a = 1 then b is any number
-a > 0 then b = 0
Case 1: x + 1 = 0
⇒ x = -1
Case 2: x2 -5x+7 =1
⇒ x2 -5x+6 = 0
⇒ x = 2 or 3
Case 3: x2 -5x + 7 = -1
⇒ x2 -5x + 8 = 0
but x is not an integer 
∴ The number of integers satisfies the equation is 3 

CAT 2020 Slot 2: Past Year Question Paper - Question 72

Let f ( x) = x2 + ax + b and g( x) = f ( x + 1) - f ( x - 1) . If f ( x)≥ 0 for all real x, and g (20) = 72 , then the smallest possible value of b is 

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 72

f ( x) = x2 + ax + b
g( x) = f ( x + 1) - f ( x - 1)
= {(x + 1)2 + a(x +1) + b} - {(x -1)2 + a(x -1) + b}
g( x) = 4x + 2a
g(20) = 72
80 + 2a = 72
⇒ a = - 4
∴ f (x) = x2 - 4x + b f (x) = (x - 2)2 + b - 4
when b ≥ 4 f ( x) ≥ 0 for all x
∴ The minimum value of b is 4 

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 73

Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 is 


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 73

Given, d + 2 = D ⇒ r + 1 = R
In the figure OT = r and OB = r + 1
OT ⊥ AB as AB is the tangent
OT bisects AB i.e., TB = 6/2 = 3
Now, in DOTB, OT2 + TB2 = OB
∴ r2 + 32 = (r + 1)2⇒ r = 4
∴ D = 2(R ) = 2(r + 1) = 10cm

CAT 2020 Slot 2: Past Year Question Paper - Question 74

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is s. Then the area of the triangle is 

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 74


PD + PE + PF = s
Area of 

*Answer can only contain numeric values
CAT 2020 Slot 2: Past Year Question Paper - Question 75

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is 


Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 75

Let the principal be P.

 

CAT 2020 Slot 2: Past Year Question Paper - Question 76

In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

Detailed Solution for CAT 2020 Slot 2: Past Year Question Paper - Question 76

Let x1 be the least number x10 be the largest number 



Sum of 10 observations 

Since the minimum value of x10 is 47, the minimum value of x1 is 2, minimum average

The maximum value of x1 is 42 ,

Required difference =4 

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