CAT 2015 Previous Year Question Paper

Passage 1

For most of human history, noon was a local event. A town's clock was set by the sun crossing the meridian above its own church tower, and a traveller who rode fifty miles east would find the hour slightly advanced, a discrepancy no one had reason to notice. The pace of travel matched the slowness of the discrepancy: by the time a horse covered the distance, a difference of a few minutes had dissolved into the general uncertainty of the journey.

The railway ended this comfortable vagueness. A timetable is a promise made across space, and it cannot be kept if each station measures the hour differently. Early railway companies responded not by abolishing local time but by adding a layer above it: each company ran its trains on the time of its headquarters, so that a single platform might display two or three clocks, each correct by its own lights. Passengers missed connections not because trains were late but because they had read the wrong clock. The problem, in other words, was not one of accuracy but of agreement.

It is tempting to tell the story of standard time as the triumph of science over parochialism. Astronomers had long known how to compute the time at any longitude, and the telegraph made it possible to send a time signal faster than any train could travel. But the technical solution existed decades before it was adopted. What delayed it was that time had become a matter of identity. Town councils objected that the sun, not a distant company, should tell their citizens when to eat; preachers denounced railway time as a falsehood imposed on daylight; some public clocks were fitted with two minute hands, one for local time and one for the line.

What eventually settled the matter was less argument than habit. As more of daily life (the post, newspapers, factory shifts, school bells) came to be coordinated with the trains, local time became the inconvenient exception rather than the natural rule. Legislation, when it came, largely ratified a change that commerce had already made. The law did not create standard time; it recognised that most people were already living by it.

There is a lesson here for anyone who believes that a superior technology wins simply by being superior. Standards are social agreements, and agreements hold only when enough people find the cost of disagreeing higher than the cost of conforming. A standard that arrives too early is resisted as an imposition; one that arrives late is accepted as common sense. The railways did not persuade the public that a uniform hour was correct. They made a non-uniform hour expensive.

1. Which of the following best captures the central argument of the passage?

   1. Standard time was adopted mainly because astronomers proved that local time was inaccurate.
   2. Railway companies abolished local time as soon as they began publishing timetables.
   3. Religious objections were the chief reason why standard time was delayed by several decades.
   4. Standard time spread less because the technology was available than because disagreeing about the hour became costly in everyday life.
   Answer and explanation

   Answer: D (Standard time spread less because the technology was available than because disagreeing about the hour became costly in everyday life.)

   The passage stresses that the technical means existed decades earlier (ruling out A) and that habit and coordination, not argument, settled the matter: railways 'made a non-uniform hour expensive'. B contradicts the second paragraph (companies added a layer above local time). C overstates one of several examples of resistance.

2. The author mentions public clocks fitted with two minute hands in order to illustrate

   1. how difficult it was to transmit an accurate time signal by telegraph.
   2. that local clocks were more accurate than railway clocks.
   3. a compromise that kept local time alive alongside the practical demands of the railway.
   4. the role legislation played in enforcing a single national time.
   Answer and explanation

   Answer: C (a compromise that kept local time alive alongside the practical demands of the railway.)

   The example appears in the list of ways time 'had become a matter of identity': towns kept their own hour while acknowledging the line's. Nothing is said about accuracy (B), telegraph difficulty (A) or law (D) in that context.

3. Which of the following, if true, would most weaken the author's claim that legislation 'largely ratified a change that commerce had already made'?

   1. Newspapers of the period regularly printed railway timetables.
   2. Leading astronomers publicly supported the new law.
   3. A few preachers continued to object to railway time after the law was passed.
   4. When the law was passed, most town clocks, shops and schools in the country still kept local time.
   Answer and explanation

   Answer: D (When the law was passed, most town clocks, shops and schools in the country still kept local time.)

   The claim is that people were already living by standard time before the law. Evidence that most of daily life still ran on local time when the law came would directly undercut it. A mildly supports the claim; B and C are irrelevant to whether practice preceded law.

4. In the second paragraph, the phrase 'each correct by its own lights' most nearly suggests that the clocks

   1. were illuminated so that passengers could read them at night.
   2. were all wrong, since none showed the true local time.
   3. were accurate relative to the reference time each followed, even though they disagreed with one another.
   4. showed the correct time only at the company's headquarters.
   Answer and explanation

   Answer: C (were accurate relative to the reference time each followed, even though they disagreed with one another.)

   Each clock faithfully showed its company's headquarters time, so each was right by its own standard; the trouble was that the standards differed ('not one of accuracy but of agreement').

Verbal ability

5. The five sentences below, labelled 1 to 5, form a coherent paragraph when properly ordered. Type in the correct order as a sequence of five numbers (for example, 12345). 1. Its duration, meanwhile, encodes distance: the longer the waggle, the farther away the flowers. 2. A forager bee that has found a rich patch of flowers returns to the hive carrying more than nectar; it carries information. 3. Watching hive-mates decode these runs, researchers concluded that the dance is less a signal than a map. 4. The angle of the straight 'waggle' run relative to the vertical encodes the direction of the food relative to the sun. 5. It passes this on through the waggle dance, a figure-of-eight run performed on the vertical face of the comb. (type in your answer)

   Answer and explanation

   Answer: 25413

   2 introduces the forager and the 'information'. 5 ('It passes this on') names the dance. 4 explains one feature of the waggle run (angle gives direction), and 1 ('Its duration, meanwhile') adds the second feature (distance). 3 draws the conclusion from both. Order: 2-5-4-1-3.

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. In much of the ancient world, salt was valuable enough to shape the routes along which goods and people moved. 2. Caravans crossing the Sahara traded slabs of salt for gold, sometimes, in the folklore of the trade, weight for weight. 3. Modern nutritionists warn that most people consume far more sodium than their bodies need. 4. Towns grew up at the points where salt could be taxed, stored or exchanged. 5. The word 'salary' is often, though perhaps fancifully, traced to payments connected with salt. (type in your answer)

   Answer and explanation

   Answer: 3

   Sentences 1, 2, 4 and 5 are about salt's historical economic importance (trade routes, caravans, towns, the word 'salary'). Sentence 3 is about present-day health advice and does not belong.

7. The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage. Many organisations measure what is easy to count rather than what matters. Call centres track the length of calls because the software records it automatically, yet a short call that fails to solve a customer's problem simply produces a second call. Once a metric becomes a target, employees learn to improve the number rather than the outcome it was supposed to represent, and the organisation ends up with excellent figures and unhappy customers.

   1. Call centres should stop recording call length because their software is unreliable.
   2. Employees routinely deceive their organisations by falsifying performance figures.
   3. Metrics chosen because they are convenient can, once turned into targets, pull behaviour away from the outcomes they were meant to track.
   4. Customer satisfaction is impossible to measure and should not be attempted.
   Answer and explanation

   Answer: C (Metrics chosen because they are convenient can, once turned into targets, pull behaviour away from the outcomes they were meant to track.)

   The passage argues that easily counted metrics, when made targets, are optimised at the expense of real outcomes. A misreads the software point, B goes beyond 'learn to improve the number' (no falsification is alleged), and D is never claimed.

Set 1

Five football teams, A, B, C, D and E, played a single round-robin tournament: every team played every other team exactly once, for 10 matches in all. A win earned 3 points, a draw 1 point to each side, and a loss 0 points. The final points table is given below. It is also known that D's only win in the tournament was against E, and that the match between B and E did not end in a draw.

8. Against which team did A draw its match?

   1. B
   2. C
   3. D
   4. E
   Answer and explanation

   Answer: D (E)

   Total points = 28. Ten matches give 30 points if none is drawn, and each draw lowers the total by 1, so exactly 2 matches were drawn. A has 10 = 3+3+3+1, so A won three and drew one. E has 1 point, so E drew once and lost three times. D has 4 = 3+1 (its only win was over E), so D drew once and lost twice. A team with exactly one draw has its other points in multiples of 3, so C (6 points) cannot have exactly one draw; with only two draws in all, C has none. E's draw is therefore not with C, not with B (given) and not with D (D beat E), so E drew with A.

9. What was the result of the match between B and D?

   1. B won
   2. D won
   3. The match was drawn
   4. Cannot be determined
   Answer and explanation

   Answer: C (The match was drawn)

   The two draws are A–E and one involving D. D's draw cannot be with A (A's only draw is with E), with E (D beat E) or with C (C has no draws). So D drew with B, which fits B's 7 = 3 + 3 + 1 + 0.

10. How many matches did C win? (type in your answer)

    Answer and explanation

    Answer: 2

    C has 6 points with no draws, so C won exactly 2 matches (against D and E) and lost to A and B.

11. How many matches did B lose?

    1. 0
    2. 1
    3. 2
    4. 3
    Answer and explanation

    Answer: B (1)

    B lost to A, beat C, drew with D and beat E: 3 + 1 + 3 = 7 points, with exactly one loss.

12. A shopkeeper marks an article 40% above its cost price and then allows two successive discounts of 10% and 15%. What is his profit percentage?

    1. 5.6%
    2. 7.1%
    3. 8.4%
    4. 15%
    Answer and explanation

    Answer: B (7.1%)

    Selling price = 1.40 × 0.90 × 0.85 = 1.071 times the cost price, so the profit is 7.1%.

13. Two trains, 180 m and 120 m long, run on parallel tracks in opposite directions at 54 km/h and 36 km/h. How many seconds do they take to cross each other completely? (type in your answer)

    Answer and explanation

    Answer: 12

    Relative speed = 54 + 36 = 90 km/h = 25 m/s. Distance to cover = 180 + 120 = 300 m. Time = 300 ÷ 25 = 12 seconds.

14. If x + 1/x = 5, what is the value of x³ + 1/x³?

    1. 115
    2. 110
    3. 120
    4. 125
    Answer and explanation

    Answer: B (110)

    x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 125 − 15 = 110.

15. How many positive divisors does 720 have? (type in your answer)

    Answer and explanation

    Answer: 30

    720 = 2⁴ × 3² × 5, so the number of divisors is (4+1)(2+1)(1+1) = 30.

16. A right-angled triangle has legs of length 9 cm and 12 cm. What is the radius, in cm, of its incircle?

    1. 2
    2. 2.5
    3. 3.5
    4. 3
    Answer and explanation

    Answer: D (3)

    Hypotenuse = √(81 + 144) = 15. For a right triangle the inradius is (a + b − c)/2 = (9 + 12 − 15)/2 = 3 cm.

17. A committee of 4 is to be chosen from 6 men and 5 women. In how many ways can this be done if the committee must include at least 2 women? (type in your answer)

    Answer and explanation

    Answer: 215

    2 women, 2 men: C(5,2) × C(6,2) = 10 × 15 = 150. 3 women, 1 man: C(5,3) × 6 = 60. 4 women: C(5,4) = 5. Total = 150 + 60 + 5 = 215.

18. If log₂x + log₄x = 6, then x equals

    1. 8
    2. 32
    3. 64
    4. 16
    Answer and explanation

    Answer: D (16)

    log₄x = (log₂x)/2, so (3/2)·log₂x = 6, giving log₂x = 4 and x = 16.

19. A can finish a piece of work in 12 days and B in 18 days. They work together for 4 days, after which A leaves. How many more days does B need to finish the work? (type in your answer)

    Answer and explanation

    Answer: 8

    Together they do 1/12 + 1/18 = 5/36 per day; in 4 days they finish 20/36 = 5/9. The remaining 4/9 takes B (4/9) × 18 = 8 days.

20. A 60-litre mixture contains milk and water in the ratio 7 : 3. How many litres of water must be added to make the ratio 3 : 2?

    1. 6
    2. 8
    3. 12
    4. 10
    Answer and explanation

    Answer: D (10)

    Milk = 42 L and water = 18 L. We need 42/(18 + w) = 3/2, so 18 + w = 28 and w = 10 litres.