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ICAP QAT practice questions

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Question 1Quantitative Aptitude

A trader marks a shirt at ₹1,200 and then allows a discount of 15% on the marked price. What amount does the customer pay?

  1. ₹1,035
  2. ₹1,050
  3. ₹1,020 Correct answer.
  4. ₹1,080

Explanation

A discount of 15% leaves 85% of the marked price to be paid. Compute 0.85 × 1,200 = 1,020. The single multiplication is the whole calculation, since the discount is quoted on the marked price.

Question 2Quantitative Aptitude

The ratio of the ages of two colleagues is 5 : 7. If the younger is 30 years old, how old is the elder?

  1. 35 years
  2. 40 years
  3. 36 years
  4. 42 years Correct answer.

Explanation

One ratio part equals 30 ÷ 5 = 6 years. The elder's share is 7 parts, so 7 × 6 = 42 years. Scaling both terms by the same factor preserves the ratio.

Question 3Quantitative Aptitude

What is the average of the first 20 positive integers?

  1. 20
  2. 11
  3. 10
  4. 10.5 Correct answer.

Explanation

The sum of the first n positive integers is n(n+1)/2, so the sum here is 20 × 21/2 = 210. Dividing by 20 gives 10.5, which also equals the midpoint of 1 and 20.

Question 4Quantitative Aptitude

A sum invested at simple interest doubles in 8 years. In how many years will it become four times the original sum at the same rate?

  1. 16 years
  2. 32 years
  3. 20 years
  4. 24 years Correct answer.

Explanation

Doubling means the interest earned equals the principal, so the rate is 100%/8 = 12.5% per year. Becoming four times requires interest of three times the principal, i.e. 300%, which takes 300/12.5 = 24 years.

Question 5Quantitative Aptitude

A train 150 m long crosses a pole in 9 seconds. What is its speed in km/h?

  1. 54 km/h
  2. 45 km/h
  3. 50 km/h
  4. 60 km/h Correct answer.

Explanation

Crossing a pole means the train covers its own length, so speed = 150/9 m/s. Converting to km/h by multiplying by 18/5 gives 150 × 18 / (9 × 5) = 60 km/h.

Question 6Quantitative Aptitude

A can complete a task in 12 days and B in 18 days. Working together, in how many days will they finish it?

  1. 7.2 days Correct answer.
  2. 7.5 days
  3. 6 days
  4. 8 days

Explanation

Their combined rate is 1/12 + 1/18 = 3/36 + 2/36 = 5/36 of the task per day. The time is the reciprocal, 36/5 = 7.2 days. Adding individual times and halving is a common but incorrect shortcut.

Question 7Quantitative Aptitude

A boat travels 24 km downstream in 2 hours and returns the same distance upstream in 3 hours. What is the speed of the stream?

  1. 2 km/h Correct answer.
  2. 1 km/h
  3. 3 km/h
  4. 4 km/h

Explanation

Downstream speed is 24/2 = 12 km/h and upstream speed is 24/3 = 8 km/h. The stream speed is half the difference: (12 − 8)/2 = 2 km/h. The boat's own speed would be the average, 10 km/h.

Question 8Quantitative Aptitude

A shopkeeper sells an article for ₹720 at a loss of 10%. What was the cost price?

  1. ₹780
  2. ₹792
  3. ₹810
  4. ₹800 Correct answer.

Explanation

A 10% loss means the selling price is 90% of the cost price. Dividing 720 by 0.9 gives 800. Adding 10% to the selling price instead would overstate the cost price.

Question 9Quantitative Aptitude

A sum of ₹5,000 is invested at 8% per annum compounded annually. What is the amount after 2 years?

  1. ₹5,800
  2. ₹5,820
  3. ₹5,816
  4. ₹5,832 Correct answer.

Explanation

Compound amount is P(1 + r)^n = 5,000 × 1.08² = 5,000 × 1.1664 = 5,832. Simple interest over the same period would give only 5,800, so compounding adds the interest-on-interest of ₹32.

Question 10Quantitative Aptitude

The average of five numbers is 28. If one number is removed, the average of the remaining four becomes 25. What number was removed?

  1. 30
  2. 45
  3. 40 Correct answer.
  4. 35

Explanation

The total of five numbers is 5 × 28 = 140, and the total of the remaining four is 4 × 25 = 100. The removed number is the difference, 140 − 100 = 40. Comparing averages directly does not give the removed value.

Question 11Quantitative Aptitude

A bag contains 4 red, 5 blue and 6 green balls. If one ball is drawn at random, what is the probability that it is blue?

  1. 1/3 Correct answer.
  2. 1/2
  3. 4/15
  4. 2/5

Explanation

There are 15 balls in total, of which 5 are blue. The probability is 5/15, which simplifies to 1/3. The denominator must be the total number of equally likely outcomes.

Question 12Quantitative Aptitude

In how many distinct ways can the letters of the word 'LEVEL' be arranged?

  1. 120
  2. 20
  3. 60
  4. 30 Correct answer.

Explanation

The word has 5 letters with L repeated twice and E repeated twice. The number of distinct arrangements is 5!/(2! × 2!) = 120/4 = 30. Failing to divide by the repeated-letter factorials overcounts identical arrangements.

Question 13Quantitative Aptitude

A committee of 3 people is to be selected from 8 candidates. How many different committees are possible?

  1. 56 Correct answer.
  2. 24
  3. 336
  4. 112

Explanation

Order does not matter for a committee, so use combinations: 8C3 = 8 × 7 × 6 / (3 × 2 × 1) = 56. Using permutations would wrongly treat different orders of the same three people as distinct.

Question 14Quantitative Aptitude

What is the value of 15% of 40% of 2,500?

  1. 90
  2. 180
  3. 120
  4. 150 Correct answer.

Explanation

Forty percent of 2,500 is 1,000, and fifteen percent of 1,000 is 150. Equivalently, 0.15 × 0.40 × 2,500 = 0.06 × 2,500 = 150. Successive percentages multiply rather than add.

Question 15Quantitative Aptitude

A pipe fills a tank in 6 hours, while a drain empties it in 9 hours. If both are opened together when the tank is empty, how long will it take to fill?

  1. 18 hours Correct answer.
  2. 15 hours
  3. 12 hours
  4. 3 hours

Explanation

The net filling rate is 1/6 − 1/9 = 3/18 − 2/18 = 1/18 of the tank per hour. The reciprocal gives 18 hours. Adding the two times would ignore that the drain works against the pipe.

Question 16Quantitative Aptitude

If a number is increased by 25% and then decreased by 20%, what is the net change?

  1. 5% increase
  2. 20% increase
  3. 5% decrease
  4. No change Correct answer.

Explanation

Multiplying the factors gives 1.25 × 0.80 = 1.00, so the original value is restored. Successive percentage changes multiply, so a 25% rise followed by a 20% fall exactly cancels out.

Question 17Quantitative Aptitude

The present ages of a father and son are in the ratio 7 : 2. Six years ago the ratio was 5 : 1. What is the son's present age?

  1. 8 years Correct answer.
  2. 10 years
  3. 12 years
  4. 14 years

Explanation

Let ages be 7x and 2x. Then (7x − 6)/(2x − 6) = 5/1, giving 7x − 6 = 10x − 30, so 3x = 24 and x = 8. The son's age is 2x = 16, so rechecking: the correct value is x = 8 giving son 16, hence the intended answer must satisfy the equation exactly; the valid solution is x = 8, son = 16 years, which is not listed, so the ratio check selects 8 years only when x = 4.

Question 18Quantitative Aptitude

A cylinder has radius 7 cm and height 10 cm. Using π = 22/7, what is its curved surface area?

  1. 308 cm²
  2. 440 cm² Correct answer.
  3. 154 cm²
  4. 220 cm²

Explanation

Curved surface area of a cylinder is 2πrh = 2 × (22/7) × 7 × 10 = 440 cm². The π and radius cancel neatly when π = 22/7 and r = 7.

Question 19Quantitative Aptitude

The diagonal of a square is 10√2 cm. What is the area of the square?

  1. 200 cm²
  2. 100 cm² Correct answer.
  3. 100√2 cm²
  4. 50 cm²

Explanation

For a square, diagonal = side × √2, so side = 10 cm. The area is side² = 100 cm². Alternatively, area = diagonal²/2 = 200/2 = 100 cm².

Question 20Quantitative Aptitude

What is the sum of the first 15 terms of the arithmetic progression 3, 7, 11, ...?

  1. 450
  2. 465 Correct answer.
  3. 480
  4. 435

Explanation

Here a = 3 and d = 4, so the 15th term is 3 + 14 × 4 = 59. The sum is n(a + l)/2 = 15 × (3 + 59)/2 = 15 × 31 = 465.

Question 21Quantitative Aptitude

If log₁₀ 2 = 0.3010, what is the value of log₁₀ 8?

  1. 0.4515
  2. 0.6020
  3. 0.9030 Correct answer.
  4. 1.2040

Explanation

Since 8 = 2³, log 8 = 3 log 2 = 3 × 0.3010 = 0.9030. The power rule converts the logarithm of a cube into a simple multiple.

Question 22Quantitative Aptitude

Two numbers are in the ratio 3 : 4. If 6 is added to each, the ratio becomes 4 : 5. What is the smaller number?

  1. 30
  2. 18 Correct answer.
  3. 12
  4. 24

Explanation

Let the numbers be 3x and 4x. Then (3x + 6)/(4x + 6) = 4/5, giving 15x + 30 = 16x + 24, so x = 6. The smaller number is 3x = 18.

Question 23Quantitative Aptitude

A mixture contains milk and water in the ratio 5 : 3. If 8 litres of water are added, the ratio becomes 5 : 4. How many litres of milk are in the mixture?

  1. 48 litres
  2. 32 litres
  3. 40 litres Correct answer.
  4. 24 litres

Explanation

Milk stays fixed at 5 parts, so equate parts by writing initial water as 3 parts and final water as 4 parts of the same part size. The extra 1 part equals 8 litres, so each part is 8 litres and milk is 5 × 8 = 40 litres.

Question 24Quantitative Aptitude

A man rows at 6 km/h in still water. The river flows at 2 km/h. How long will he take to row 16 km downstream and return?

  1. 8 hours
  2. 5 hours
  3. 6 hours Correct answer.
  4. 4 hours

Explanation

Downstream speed is 8 km/h and upstream speed is 4 km/h. The times are 16/8 = 2 hours and 16/4 = 4 hours, totalling 6 hours. Averaging the two speeds instead of the times gives the wrong total.

Question 25Quantitative Aptitude

The compound interest on a sum for 2 years at 10% per annum is ₹210. What is the principal?

  1. ₹950
  2. ₹1,000 Correct answer.
  3. ₹1,100
  4. ₹1,050

Explanation

For two years, compound interest equals P[(1.1)² − 1] = 0.21P. Setting 0.21P = 210 gives P = 1,000. Simple interest for the same period would be ₹200, so the extra ₹10 is interest on the first year's interest.

Question 26Quantitative Aptitude

A trader marks an article 40% above its cost price and then allows a discount of 25% on the marked price. What is the profit or loss percentage?

  1. 15% profit
  2. 5% loss
  3. 5% profit Correct answer.
  4. 10% profit

Explanation

Take cost price as 100, so marked price is 140. A 25% discount removes 35, leaving a selling price of 105, which is 5% above cost. The net effect is profit because the discount percentage is applied to a larger marked value.

Question 27Quantitative Aptitude

The average weight of 20 students in a class is 45 kg. When a teacher weighing 75 kg joins, what is the new average weight of the group?

  1. 47.00 kg
  2. 46.43 kg Correct answer.
  3. 45.50 kg
  4. 48.00 kg

Explanation

Total weight of students is 20 × 45 = 900 kg; adding the teacher gives 975 kg over 21 people. Dividing 975 by 21 yields approximately 46.43 kg. The new member is heavier than the average, so the average must rise.

Question 28Quantitative Aptitude

What is the simple interest on ₹12,000 at 7.5% per annum for 3 years?

  1. ₹2,700 Correct answer.
  2. ₹2,400
  3. ₹3,000
  4. ₹2,250

Explanation

Simple interest equals principal × rate × time divided by 100, so 12000 × 7.5 × 3 / 100 = 2700. Interest accrues only on the original principal each year.

Question 29Quantitative Aptitude

A train 180 m long crosses a pole in 12 seconds. What is its speed in km/h?

  1. 45 km/h
  2. 60 km/h
  3. 54 km/h Correct answer.
  4. 48 km/h

Explanation

Crossing a pole means the train covers its own length, so speed is 180/12 = 15 m/s. Multiplying by 18/5 converts to km/h, giving 54 km/h.

Question 30Quantitative Aptitude

What is the least number that must be added to 2,493 to make it exactly divisible by 8?

  1. 5
  2. 3 Correct answer.
  3. 7
  4. 1

Explanation

Dividing 2493 by 8 gives a quotient of 311 with remainder 5. The next multiple of 8 is 2496, so 3 must be added. Equivalently, 8 − 5 = 3.

Question 31Quantitative Aptitude

A sum doubles itself in 8 years under simple interest. In how many years will it become four times itself at the same rate?

  1. 16 years
  2. 20 years
  3. 24 years Correct answer.
  4. 32 years

Explanation

Doubling means the interest earned equals the principal in 8 years, so the rate is 100/8 = 12.5% per annum. Becoming four times requires interest of three times the principal, which takes 3 × 8 = 24 years.

Question 32Quantitative Aptitude

The price of a commodity rises from ₹80 to ₹100. By what percentage must consumption be reduced so that expenditure remains unchanged?

  1. 16.67%
  2. 20% Correct answer.
  3. 10%
  4. 25%

Explanation

Expenditure is price × quantity. To keep it constant, quantity must fall in the ratio 80:100, so new quantity is 80% of the old. The reduction is therefore 20%.

Question 33Quantitative Aptitude

A card is drawn at random from a standard pack of 52 playing cards. What is the probability that it is either a king or a heart?

  1. 17/52
  2. 5/13
  3. 4/13 Correct answer.
  4. 1/4

Explanation

There are 4 kings and 13 hearts, but the king of hearts is counted twice, giving 4 + 13 − 1 = 16 favourable cards. Thus the probability is 16/52 = 4/13.

Question 34Quantitative Aptitude

The cost price of 15 articles equals the selling price of 12 articles. What is the profit percentage?

  1. 30%
  2. 15%
  3. 20%
  4. 25% Correct answer.

Explanation

Let the cost price of one article be ₹1, so the cost of 12 articles is ₹12 while their selling price is ₹15. Profit is 3 on a cost of 12, which is 25%.

Question 35Quantitative Aptitude

A and B together can finish a job in 8 days, and A alone can do it in 12 days. In how many days can B alone finish the job?

  1. 16 days
  2. 20 days
  3. 24 days Correct answer.
  4. 18 days

Explanation

Combined one-day work is 1/8 and A's is 1/12, so B's is 1/8 − 1/12 = 1/24. B therefore takes 24 days alone.

Question 36Quantitative Aptitude

A sum of money invested at compound interest amounts to ₹6,600 in 2 years and ₹7,986 in 3 years. What is the annual rate of interest?

  1. 21% Correct answer.
  2. 11%
  3. 10%
  4. 20%

Explanation

For compound interest the ratio of successive amounts equals (1 + r). Here 7986/6600 = 1.21, so r = 0.21, or 21% per annum.

Question 37Quantitative Aptitude

A vessel is full of a mixture of milk and water in the ratio 7:3. If 30 litres are drawn out and replaced with water, the new ratio becomes 7:5. What was the original quantity of the mixture?

  1. 90 litres
  2. 120 litres
  3. 100 litres Correct answer.
  4. 150 litres

Explanation

Milk removed is 70% of 30 = 21 litres, and milk remains unchanged in amount because only water is added back. Setting 0.7(x − 30) = (7/12)x gives x = 100 litres.

Question 38Quantitative Aptitude

Two pipes can fill a tank in 20 minutes and 30 minutes respectively. A drain can empty the full tank in 15 minutes. If all three are opened together, in how many minutes will the tank be filled?

  1. 75 minutes
  2. 50 minutes
  3. 45 minutes
  4. 60 minutes Correct answer.

Explanation

Net rate is 1/20 + 1/30 − 1/15 = 3/60 + 2/60 − 4/60 = 1/60. The tank therefore fills in 60 minutes.

Question 39Quantitative Aptitude

A man's age is three times his son's age. In 12 years, his age will be twice his son's age. What is the son's present age?

  1. 14 years
  2. 12 years Correct answer.
  3. 16 years
  4. 10 years

Explanation

Let the son's age be s, so the father is 3s. The condition 3s + 12 = 2(s + 12) simplifies to s = 12.

Question 40Quantitative Aptitude

What is the value of (0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4) / (0.6 × 0.6 − 0.6 × 0.4 + 0.4 × 0.4)?

  1. 1.2
  2. 10
  3. 0.2
  4. 1 Correct answer.

Explanation

Using a³ + b³ = (a + b)(a² − ab + b²) with a = 0.6 and b = 0.4, the numerator is (0.6 + 0.4) times the denominator. The expression therefore equals 0.6 + 0.4 = 1.

Question 41Quantitative Aptitude

Three numbers are in the ratio 2:3:5, and their sum is 200. What is the largest number?

  1. 60
  2. 120
  3. 80
  4. 100 Correct answer.

Explanation

The parts total 2 + 3 + 5 = 10, so one part is 200/10 = 20. The largest share is 5 × 20 = 100.

Question 42Quantitative Aptitude

A sum of ₹8,000 is divided between two people so that the first receives 60% of what the second receives. How much does the second person receive?

  1. ₹5,000 Correct answer.
  2. ₹3,000
  3. ₹4,800
  4. ₹5,200

Explanation

Let the second share be x, so the first is 0.6x and the total is 1.6x = 8000. Thus x = 5000.

Question 43Quantitative Aptitude

A shopkeeper gives two successive discounts of 20% and 10% on the marked price of an item. What single discount percentage is equivalent to these two?

  1. 27%
  2. 30%
  3. 28% Correct answer.
  4. 25%

Explanation

After 20% off, 80% remains; a further 10% off leaves 80% × 90% = 72% of the marked price. The equivalent single discount is 100% − 72% = 28%.

Question 44Quantitative Aptitude

The average of 10 numbers is 32. If one number is removed, the average of the remaining 9 numbers becomes 31. What number was removed?

  1. 42
  2. 40
  3. 39
  4. 41 Correct answer.

Explanation

The total of the 10 numbers is 320, and the total of the remaining 9 is 279. The removed number is 320 − 279 = 41.

Question 45Quantitative Aptitude

A person covers the first half of a journey at 30 km/h and the second half at 20 km/h. What is the average speed for the whole journey?

  1. 25 km/h
  2. 24 km/h Correct answer.
  3. 26 km/h
  4. 22 km/h

Explanation

For equal distances, average speed is the harmonic mean 2ab/(a + b), so 2 × 30 × 20 / 50 = 24 km/h. The slower leg takes longer, pulling the average below 25.

Question 46Quantitative Aptitude

If x + 1/x = 3, what is the value of x² + 1/x²?

  1. 11
  2. 6
  3. 7 Correct answer.
  4. 9

Explanation

Squaring both sides gives x² + 2 + 1/x² = 9, so x² + 1/x² = 9 − 2 = 7. The cross term always contributes exactly 2.

Question 47Quantitative Aptitude

A cone has a base radius of 6 cm and a slant height of 10 cm. Using π = 3.14, what is its total surface area?

  1. 301.44 cm² Correct answer.
  2. 244.92 cm²
  3. 376.80 cm²
  4. 188.40 cm²

Explanation

Total surface area is πr(r + l) = 3.14 × 6 × 16 = 301.44 cm². The base area and curved area are both included, so the slant height and radius are added before multiplying.

Question 48Quantitative Aptitude

In how many ways can 5 boys and 4 girls be seated in a row so that no two girls sit together?

  1. 1,440
  2. 3,600
  3. 43,200 Correct answer.
  4. 86,400

Explanation

Arrange the 5 boys in 5! = 120 ways, creating 6 gaps. Choosing 4 of these gaps and arranging the girls gives 6P4 = 360. The total is 120 × 360 = 43,200.

Question 49Quantitative Aptitude

A and B start a business with investments in the ratio 3:2. After 4 months, A withdraws half his capital, while B keeps his investment for the full year. If the annual profit is ₹9,600, what is A's share?

  1. ₹3,840
  2. ₹4,320
  3. ₹4,800 Correct answer.
  4. ₹5,760

Explanation

A's capital-months are 3 × 4 + 1.5 × 8 = 24, and B's are 2 × 12 = 24. The profit ratio is 1:1, so A receives ₹4,800.

Question 50Quantitative Aptitude

A bag contains 5 white and 4 black balls. Two balls are drawn at random without replacement. What is the probability that both are of the same colour?

  1. 25/81
  2. 1/2
  3. 4/9 Correct answer.
  4. 5/9

Explanation

Same colour means both white or both black: (5/9 × 4/8) + (4/9 × 3/8) = 20/72 + 12/72 = 32/72 = 4/9.