CAT 2021 Previous Year Question Paper

Passage 1

Governments have discovered that they can change behaviour without commanding anything. By altering the order in which options are presented, setting defaults or sending a well-timed reminder, they can raise savings rates, increase organ donation and reduce missed appointments, all while leaving every choice formally open. The approach, often called nudging, is attractive precisely because it seems to dissolve an old dilemma between respecting freedom and promoting welfare. People remain free to choose; they are merely helped to choose well.

Critics have objected that the dissolution is too neat. A nudge often works by exploiting predictable lapses in attention or reasoning: we stick with defaults because changing them takes effort, and we pick the first item on a list because we tire of reading. To steer someone through such tendencies is to bypass their deliberation rather than engage it. The person who ends up in a pension scheme because enrolment was automatic did not, in any robust sense, decide to save. Defenders reply that there is no neutral alternative. Every form must have some default and every menu some order; if choice architecture is unavoidable, it had better be designed with people's interests in mind than left to chance or to sellers with interests of their own.

The reply is strong, but it proves less than its proponents sometimes suggest. That some architecture is unavoidable does not settle which architecture is legitimate, nor who should decide. A default chosen by a public authority to serve the citizen differs from one chosen by a firm to maximise sales, yet both rely on the same psychological mechanism. The legitimacy of a nudge therefore cannot rest on the mechanism alone; it must depend on the aims it serves and on whether those aims could be defended openly.

This suggests a useful test. A nudge that would go on working even if the people subject to it were told exactly how it worked respects their agency in a way that a nudge relying on concealment does not. Automatic enrolment in a pension scheme usually passes: people who are told that they have been enrolled by default, and shown how to leave, mostly stay. A design that hides the cancellation button in a maze of menus fails, because its effectiveness depends on users not understanding what is being done to them.

The test does not resolve every case, and it places considerable weight on what counts as being told. But it moves the debate away from a false choice between manipulation and neutrality. The real question is not whether choices will be shaped, since they always are, but whether the shaping could survive being seen.

1. The author's assessment of the defenders' reply that 'there is no neutral alternative' is that it

   1. is mistaken, because neutral choice architecture is easy to design.
   2. correctly shows that some choice architecture is unavoidable but does not establish which architecture is legitimate.
   3. settles the debate in favour of nudging by public authorities.
   4. is irrelevant, since nudges do not in fact change behaviour.
   Answer and explanation

   Answer: B (correctly shows that some choice architecture is unavoidable but does not establish which architecture is legitimate.)

   Paragraph three: 'The reply is strong, but it proves less than its proponents sometimes suggest. That some architecture is unavoidable does not settle which architecture is legitimate, nor who should decide.'

2. Which of the following would pass the test proposed by the author?

   1. A subscription service that buries its cancellation option several menus deep.
   2. A canteen that places fruit at eye level, displays a notice explaining that it does so to encourage healthy eating, and continues to sell as much fruit.
   3. A sign-up form that pre-ticks consent to marketing in small grey text, hoping users will not notice.
   4. A website that shows a countdown timer falsely claiming that an offer is about to expire.
   Answer and explanation

   Answer: B (A canteen that places fruit at eye level, displays a notice explaining that it does so to encourage healthy eating, and continues to sell as much fruit.)

   The test asks whether a nudge would still work if people were told exactly how it works. The canteen discloses its method and the effect persists. A, C and D depend on users not noticing or on deception.

3. The author mentions that the person automatically enrolled in a pension scheme 'did not, in any robust sense, decide to save' in order to

   1. illustrate the critics' claim that nudges bypass rather than engage deliberation.
   2. state the author's own final verdict on automatic enrolment.
   3. show that automatic enrolment fails the publicity test.
   4. argue that people should not be encouraged to save.
   Answer and explanation

   Answer: A (illustrate the critics' claim that nudges bypass rather than engage deliberation.)

   The sentence sits within the critics' objection in paragraph two. The author later says automatic enrolment 'usually passes' the test, so B and C misread it.

4. Which of the following, if true, would most weaken the author's claim that automatic pension enrolment passes the test?

   1. Most employees, once told they had been enrolled by default and how to leave, promptly opted out.
   2. Many people rarely think about their pensions.
   3. Private firms also use default options to influence customers.
   4. Savings rates rose after automatic enrolment was introduced.
   Answer and explanation

   Answer: A (Most employees, once told they had been enrolled by default and how to leave, promptly opted out.)

   The claim rests on people staying enrolled after being told how the default works. If most left once informed, the nudge would depend on their ignorance and so fail the test. D concerns effectiveness, not disclosure.

Verbal ability

5. The four sentences below, labelled 1 to 4, form a coherent paragraph when properly ordered. Type in the correct order as a sequence of four numbers. 1. In effect, the animal's decisions are shared between a central brain and eight partly self-governing limbs. 2. This raises a puzzle for researchers: what it might be like to be a creature whose thinking is so spread out. 3. Each arm can therefore taste, touch and respond to its surroundings with a surprising degree of independence. 4. Most of an octopus's neurons lie not in its central brain but in its arms. (type in your answer)

   Answer and explanation

   Answer: 4312

   4 states the fact. 3 ('therefore') draws the consequence for each arm. 1 ('In effect') generalises to the whole animal. 2 ('This raises a puzzle') closes. Order: 4-3-1-2.

6. Five sentences related to a topic are given below. Four of them can be put together to form a coherent paragraph. Identify the sentence that does not fit and type in its number. 1. A city's tree canopy cools the streets beneath it by providing shade and releasing water vapour. 2. Neighbourhoods with few trees can be several degrees hotter on summer afternoons than leafy ones nearby. 3. These differences often follow lines of income, since wealthier districts were planted earlier and maintained better. 4. Planting programmes that target the hottest neighbourhoods can therefore narrow both temperature and health gaps. 5. Some trees shed their leaves in autumn to reduce water loss through the winter. (type in your answer)

   Answer and explanation

   Answer: 5

   Sentences 1–4 form an argument about urban tree cover, heat and inequality. Sentence 5 is a general fact about tree biology unconnected to that argument.

7. The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage. Museums once displayed objects with little more than a label giving name, date and place. Today many surround each object with stories, interactive screens and reconstructions, on the assumption that visitors need help to find objects meaningful. The change has broadened audiences, but it risks teaching visitors to look at the screen rather than the thing, so that the object becomes an illustration for the story instead of the reason for the visit.

   1. Museums should remove interpretive material and return to simple labels.
   2. Richer interpretation has widened museums' appeal but may draw attention away from the objects themselves.
   3. Interactive screens have reduced the number of museum visitors.
   4. Simple labels giving name, date and place are enough for every visitor.
   Answer and explanation

   Answer: B (Richer interpretation has widened museums' appeal but may draw attention away from the objects themselves.)

   The passage balances a gain (broader audiences) against a risk (the object becomes secondary). A and D prescribe what the passage does not; C contradicts 'broadened audiences'.

Set 1

Seven trainees, A, B, C, D, E, F and G, are split into three project teams: team X has three members, and teams Y and Z have two members each. The following is known:

1. A and B are in the same team. 2. C is not in A's team. 3. D is in team Z. 4. E and F are in different teams. 5. F is not in team X. 6. G is not in C's team.

8. How many different allocations of the seven trainees to the three teams are possible? (type in your answer)

   Answer and explanation

   Answer: 4

   A and B cannot be in Z (D is there and Z has only two places), so they are in X or Y. If they formed team Y, team X would be three of C, E, F, G without F (condition 5), i.e. C, E, G, which breaks condition 6. So A and B are in X with one more member from E or G (not C, not F, not D). If E: Y and Z (with D) share C, F, G with C and G apart: Y = CF, Z = DG or Y = FG, Z = CD (Y = CG is not allowed). If G: Y and Z share C, E, F with E and F apart: Y = CE, Z = DF or Y = CF, Z = DE. That gives 4 allocations.

9. If F and G are in the same team, who is in team Z?

   1. D and C
   2. D and E
   3. D and F
   4. D and G
   Answer and explanation

   Answer: A (D and C)

   F and G together happens only in the allocation X = ABE, Y = FG, Z = CD. So team Z is D and C.

10. Which of the following must be true?

    1. A and B are in team X.
    2. C is in team Y.
    3. F is in team Y.
    4. G is in team X.
    Answer and explanation

    Answer: A (A and B are in team X.)

    In all four allocations (ABE/CF/DG, ABE/FG/CD, ABG/CE/DF, ABG/CF/DE) A and B are in team X. C is in Z in one case, F in Z in one case and G outside X in two cases.

11. If C is in team Y and E is in team Z, who is the third member of team X?

    1. E
    2. F
    3. G
    4. D
    Answer and explanation

    Answer: C (G)

    E in Z with D means X = AB plus G (E is taken, F is barred, C is in Y). Then Y = CF. Allocation: X = ABG, Y = CF, Z = DE.

12. A man spends 75% of his income. His income rises by 20% and his expenditure by 10%. By what percentage do his savings increase?

    1. 30%
    2. 40%
    3. 50%
    4. 60%
    Answer and explanation

    Answer: C (50%)

    Take income 100: spending 75, savings 25. New income 120, new spending 82.5, new savings 37.5. Increase = 12.5/25 = 50%.

13. A and B set out at the same time from towns X and Y towards each other. After they meet, A takes 9 hours to reach Y and B takes 4 hours to reach X. If A's speed is 30 km/h, what is B's speed in km/h? (type in your answer)

    Answer and explanation

    Answer: 45

    For travellers who meet and continue, speed of A ÷ speed of B = √(time B takes after meeting ÷ time A takes after meeting) = √(4/9) = 2/3. So B's speed = 30 × 3/2 = 45 km/h.

14. If a and b are the roots of x² − 6x + 4 = 0, what is a² + b²?

    1. 20
    2. 28
    3. 32
    4. 36
    Answer and explanation

    Answer: B (28)

    a + b = 6 and ab = 4, so a² + b² = (a + b)² − 2ab = 36 − 8 = 28.

15. How many integers x satisfy both (x − 2)(x − 9) < 0 and x² < 50? (type in your answer)

    Answer and explanation

    Answer: 5

    (x − 2)(x − 9) < 0 means 2 < x < 9, i.e. x = 3, …, 8. x² < 50 removes 8 (64). The values 3, 4, 5, 6, 7 remain: 5 integers.

16. A right circular cone and a hemisphere stand on equal circular bases and have equal volumes. What is the ratio of the cone's height to its base radius?

    1. 2 : 1
    2. 1 : 1
    3. 3 : 1
    4. 1 : 2
    Answer and explanation

    Answer: A (2 : 1)

    (1/3)πr²h = (2/3)πr³ gives h = 2r, so h : r = 2 : 1.

17. What is the sum of all positive divisors of 72? (type in your answer)

    Answer and explanation

    Answer: 195

    72 = 2³ × 3². Sum of divisors = (1 + 2 + 4 + 8)(1 + 3 + 9) = 15 × 13 = 195.

18. In how many ways can 5 boys and 3 girls sit in a row so that no two girls sit next to each other?

    1. 2880
    2. 4320
    3. 14400
    4. 7200
    Answer and explanation

    Answer: C (14400)

    Seat the boys in 5! = 120 ways, creating 6 gaps. Choose 3 gaps for the girls in C(6,3) = 20 ways and arrange them in 3! = 6 ways. Total = 120 × 20 × 6 = 14,400.

19. The average of 11 consecutive odd numbers is 37. What is the largest of them?

    1. 47
    2. 41
    3. 45
    4. 49
    Answer and explanation

    Answer: A (47)

    The average of an odd count of consecutive odd numbers is the middle (6th) number, 37. The largest is 5 steps of 2 above it: 37 + 10 = 47.

20. What is the area of the triangle with vertices (1, 2), (5, 5) and (−2, 6)?

    1. 12
    2. 12.5
    3. 13
    4. 25
    Answer and explanation

    Answer: B (12.5)

    Area = ½ |1(5 − 6) + 5(6 − 2) + (−2)(2 − 5)| = ½ |−1 + 20 + 6| = ½ × 25 = 12.5 square units.