CAT 2025 Previous Year Question Paper

Passage 1

Efficiency is usually praised without qualification. A factory that holds little inventory, a hospital that runs its wards at full occupancy, a supply chain with no idle lorries: each looks like a model of good management, and each frees money that would otherwise sit unused. The logic is hard to fault on an ordinary day. Spare capacity costs something and, on an ordinary day, does nothing.

The trouble is that systems are not tested on ordinary days. They are tested on the rare days when demand spikes, a supplier fails or two minor problems happen to coincide. On those days the slack that looked wasteful becomes the only thing standing between disruption and collapse. A hospital running at ninety per cent occupancy can absorb a sudden influx of patients; one running at full capacity must turn them away or treat them in corridors. A manufacturer with a few weeks of stock can wait out a delayed shipment; one relying on deliveries timed to the hour stops the line.

What makes the trade-off hard to manage is not that it is unknown but that its two sides are seen so differently. The cost of slack is visible every month, in budgets and balance sheets. The benefit is invisible for long stretches and then arrives all at once, in the form of a disaster that did not happen. Managers rewarded on quarterly figures will tend, quite rationally, to trim the reserve, and in most quarters they will be proved right. The bill comes due only occasionally, and often after the people who ran down the reserve have moved on.

Some analysts respond by recommending that organisations simply hold more of everything. That is too blunt. Slack is not uniformly valuable: an extra warehouse full of goods that never run short is pure waste, while a modest reserve at a single critical bottleneck may protect an entire operation. The useful question is where a system is tightly coupled, so that a failure in one part spreads quickly to others, and where it is loosely coupled enough to absorb shocks locally. Reserves belong at the points of tight coupling.

There is also a cultural dimension. In organisations that prize efficiency, unused capacity can look like evidence of poor management, and those responsible for it may feel obliged to justify its very existence. Treating resilience as a goal in its own right, measured and reported alongside efficiency, changes that conversation. It turns the reserve from a sign of slackness into what it actually is: insurance, whose value is real even in the years when no claim is made.

1. Which of the following best expresses the central idea of the passage?

   1. Organisations should eliminate all spare capacity to remain competitive.
   2. Hospitals are managed less efficiently than factories.
   3. Managers who trim reserves are acting irrationally.
   4. The pursuit of efficiency can erode resilience, so reserves should be valued like insurance and placed where failures would spread.
   Answer and explanation

   Answer: D (The pursuit of efficiency can erode resilience, so reserves should be valued like insurance and placed where failures would spread.)

   The passage argues that slack looks wasteful but protects systems on rare bad days, that it belongs at points of tight coupling, and that it should be treated as insurance. A is the view it questions; C contradicts 'quite rationally'; B is not discussed.

2. When the author says the two sides of the trade-off are 'seen so differently', the point is that

   1. the cost of slack is visible all the time, while its benefit shows up only rarely, as a disaster that did not happen.
   2. managers and analysts disagree about what slack costs.
   3. slack is valued more by hospitals than by manufacturers.
   4. the benefits of slack can be measured precisely every quarter.
   Answer and explanation

   Answer: A (the cost of slack is visible all the time, while its benefit shows up only rarely, as a disaster that did not happen.)

   The third paragraph contrasts a cost 'visible every month' with a benefit 'invisible for long stretches' that 'arrives all at once'. D contradicts this.

3. The author rejects the recommendation to 'hold more of everything' because

   1. the value of slack varies: it matters at critical, tightly coupled points and is wasteful elsewhere.
   2. spare capacity never provides any benefit.
   3. it would make managers' quarterly figures look better.
   4. loosely coupled systems cannot absorb shocks.
   Answer and explanation

   Answer: A (the value of slack varies: it matters at critical, tightly coupled points and is wasteful elsewhere.)

   Paragraph four: an extra warehouse of goods that never run short is 'pure waste', while a reserve at a critical bottleneck 'may protect an entire operation'. D reverses the passage's description of loose coupling.

4. Which of the following practices best fits the author's recommendation?

   1. A water utility installs spare pumps only at the single pumping station through which the whole city's supply passes.
   2. A retailer doubles its stock of every product it sells.
   3. A hospital closes its reserve beds to improve its occupancy figures.
   4. A company stops measuring efficiency altogether.
   Answer and explanation

   Answer: A (A water utility installs spare pumps only at the single pumping station through which the whole city's supply passes.)

   The author recommends reserves at points of tight coupling, where one failure would spread. A single pumping station on which the whole supply depends is such a point. B is the blunt 'more of everything' approach; C runs down the reserve; D goes beyond reporting resilience 'alongside efficiency'.

Verbal ability

5. In which of the following sentences is the word 'sanguine' used correctly?

   1. The surgeon was sanguine about the patient's chances and expected a full recovery.
   2. The sanguine walls of the nursery had been painted pale blue.
   3. He gave a sanguine refusal and slammed the door behind him.
   4. The soup was far too sanguine for her taste, so she added water.
   Answer and explanation

   Answer: A (The surgeon was sanguine about the patient's chances and expected a full recovery.)

   'Sanguine' means confidently optimistic, especially about a difficult situation. Only A uses it in that sense; B, C and D treat it as a colour, a manner of anger or a flavour.

6. 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. The bricks were easy to stack, survived long journeys and could be broken into smaller pieces for small purchases. 2. In Tibet and Mongolia, tea was once so valuable that it was pressed into bricks and used as money. 3. A trader could even scrape a little off a brick to brew a cup on the road, spending and drinking from the same purse. 4. Such money had a curious property: its value fell a little every time it was used to make tea. (type in your answer)

   Answer and explanation

   Answer: 2134

   2 introduces tea bricks as money. 1 ('The bricks') explains their practical advantages. 3 ('even') adds the striking detail of brewing from the same brick. 4 ('Such money') draws the wry conclusion from 3. Order: 2-1-3-4.

7. The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage. Loyalty cards are presented as a reward for faithful customers, offering small discounts in exchange for repeat visits. Their main value to the retailer, however, lies in the data they generate: a detailed record of what each customer buys, when, and in what combinations. The discount is less a gift than a payment for information the shopper may not realise they are selling.

   1. Loyalty cards give customers large discounts at the retailer's expense.
   2. The discounts on loyalty cards are effectively payment for shoppers' purchase data, which is the cards' real value to retailers.
   3. Retailers do not use the data collected through loyalty cards.
   4. Shoppers should refuse to use loyalty cards.
   Answer and explanation

   Answer: B (The discounts on loyalty cards are effectively payment for shoppers' purchase data, which is the cards' real value to retailers.)

   The passage reframes the discount as payment for data. A misdescribes the discounts as large; C contradicts the passage; D is a recommendation the passage does not make.

Set 1

The table shows the electricity consumption, in units, of five households, H1 to H5, in three months. Each month's bill is calculated separately using the following slab tariff: the first 100 units in a month cost ₹4 per unit, the next 100 units (101 to 200) cost ₹6 per unit, and every unit above 200 costs ₹9 per unit. There are no fixed charges.

8. What was H1's total electricity bill, in rupees, for the three months? (type in your answer)

   Answer and explanation

   Answer: 2150

   January (90 units): 90 × 4 = 360. February (150): 400 + 50 × 6 = 700. March (210): 400 + 600 + 10 × 9 = 1,090. Total = 360 + 700 + 1,090 = ₹2,150.

9. Which household paid the second-lowest total bill for the three months?

   1. H1
   2. H2
   3. H3
   4. H5
   Answer and explanation

   Answer: C (H3)

   Totals: H1 = 2,150; H2 = 520 + 880 + 1,450 = 2,850; H3 = 1,000 + 380 + 760 = 2,140; H4 = 1,540 + 1,270 + 640 = 3,450; H5 = 300 + 460 + 1,045 = 1,805. Lowest is H5 and second-lowest is H3, just ₹10 below H1.

10. In how many of the fifteen household-months did consumption exceed 200 units? (type in your answer)

    Answer and explanation

    Answer: 5

    H1 March (210), H2 March (250), H4 January (260), H4 February (230) and H5 March (205). H3 January is exactly 200, which does not exceed 200. Total 5.

11. Suppose H4 had used 30 fewer units in January and 30 more units in March, with February unchanged. How would its three-month bill have changed?

    1. Decreased by ₹90
    2. Decreased by ₹270
    3. Increased by ₹90
    4. No change
    Answer and explanation

    Answer: A (Decreased by ₹90)

    January: 260 units cost 400 + 600 + 540 = 1,540; 230 units cost 400 + 600 + 270 = 1,270, a fall of 270 (the 30 units were all in the ₹9 slab). March: 140 units cost 640; 170 units cost 400 + 420 = 820, a rise of 180 (₹6 slab). Net change = −270 + 180 = −₹90.

12. In an election between two candidates, 10% of registered voters did not vote and 300 of the votes cast were invalid. The winner received 54% of the valid votes and won by 1,200 votes. How many registered voters were there?

    1. 15,300
    2. 16,000
    3. 18,000
    4. 17,000
    Answer and explanation

    Answer: D (17,000)

    The margin is 54% − 46% = 8% of valid votes, so valid votes = 1,200 ÷ 0.08 = 15,000. Votes cast = 15,300, which is 90% of registered voters: 15,300 ÷ 0.9 = 17,000.

13. A boat travels at 15 km/h in still water. It goes 36 km upstream and returns in a total of 5 hours. What is the speed of the stream in km/h? (type in your answer)

    Answer and explanation

    Answer: 3

    36/(15 − s) + 36/(15 + s) = 5 gives 36 × 30 / (225 − s²) = 5, so 225 − s² = 216 and s = 3 km/h. Check: 36/12 + 36/18 = 3 + 2 = 5 hours.

14. For how many integer values of n is (n² + 7n + 12)/(n + 2) an integer?

    1. 2
    2. 4
    3. 3
    4. 6
    Answer and explanation

    Answer: B (4)

    n² + 7n + 12 = (n + 2)(n + 5) + 2, so the expression equals n + 5 + 2/(n + 2). It is an integer when n + 2 divides 2: n + 2 = ±1 or ±2, giving n = −1, −3, 0, −4. That is 4 values.

15. What is the remainder when 7²⁰²⁵ is divided by 100? (type in your answer)

    Answer and explanation

    Answer: 7

    7⁴ = 2401 leaves remainder 1 on division by 100. 2025 = 4 × 506 + 1, so 7²⁰²⁵ = (7⁴)⁵⁰⁶ × 7 leaves remainder 7.

16. In triangle ABC, AB = 9 cm, AC = 6 cm and BC = 10 cm. The bisector of angle A meets BC at D. What is BD?

    1. 4 cm
    2. 5 cm
    3. 7.5 cm
    4. 6 cm
    Answer and explanation

    Answer: D (6 cm)

    By the angle bisector theorem, BD : DC = AB : AC = 9 : 6 = 3 : 2. So BD = 10 × 3/5 = 6 cm.

17. An isosceles trapezium has parallel sides of 10 cm and 22 cm, and each non-parallel side is 10 cm long. What is its area in cm²? (type in your answer)

    Answer and explanation

    Answer: 128

    Each overhang is (22 − 10)/2 = 6 cm, so the height is √(10² − 6²) = 8 cm. Area = ½ × (10 + 22) × 8 = 128 cm².

18. How many four-digit numbers divisible by 5 can be formed using the digits 0, 1, 2, 3, 4, 5 and 6, if no digit is repeated?

    1. 220
    2. 200
    3. 240
    4. 260
    Answer and explanation

    Answer: A (220)

    Last digit 0: the other three positions can be filled in 6 × 5 × 4 = 120 ways. Last digit 5: the first digit cannot be 0 or 5 (5 choices), then 5 and 4 choices: 100 ways. Total = 220.

19. If log₃x + log₉x + log₂₇x = 11/2, what is x?

    1. 9
    2. 81
    3. 27
    4. 243
    Answer and explanation

    Answer: C (27)

    log₉x = (log₃x)/2 and log₂₇x = (log₃x)/3. So log₃x × (1 + 1/2 + 1/3) = (11/6) log₃x = 11/2, giving log₃x = 3 and x = 27.

20. A, B and C can complete a job in 10, 12 and 15 days respectively. All three start together; A leaves after 2 days and B leaves 3 days before the job is finished. How many days does the job take in all?

    1. 6
    2. 7
    3. 8
    4. 9
    Answer and explanation

    Answer: B (7)

    Let the job take T days. A works 2 days, B works T − 3 days and C works T days: 2/10 + (T − 3)/12 + T/15 = 1. Multiplying by 60: 12 + 5(T − 3) + 4T = 60, so 9T = 63 and T = 7.