Interview Q&A / Aptitude

61. The sum of the ages of 5 children born at intervals of 3 years each is 50 years. What is the age of the youngest child?

    4 years. If the youngest is x, the others are x + 3, x + 6, x + 9 and x + 12. So 5x + 30 = 50 and x = 4. The ages are 4, 7, 10, 13 and 16.

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62. Two numbers are in the ratio 3 : 5. If 9 is added to each, the ratio becomes 3 : 4. Find the numbers.

    9 and 15. Let them be 3x and 5x. Then (3x + 9)/(5x + 9) = 3/4, so 12x + 36 = 15x + 27, giving x = 3. The numbers are 9 and 15, and 18 : 24 is indeed 3 : 4.

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63. Two vessels contain milk and water in the ratios 3 : 1 and 5 : 3. If equal quantities from both are mixed, what is the ratio of milk to water?

    11 : 5. Milk fractions are 3/4 and 5/8. Taking one litre from each gives milk 3/4 + 5/8 = 11/8 litres out of 2, so milk is 11/16 and water 5/16 of the mixture.

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64. Walking at 3/4 of his usual speed, a student reaches college 20 minutes late. What is his usual time for the journey?

    60 minutes. For a fixed distance, time is inversely proportional to speed. At 3/4 speed the time becomes 4/3 of usual, so the extra 1/3 of the usual time equals 20 minutes and the usual time is 60 minutes.

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65. What are the fourth proportional, third proportional and mean proportional, with an example of each?

    For a : b = c : d, d is the fourth proportional, d = bc/a (4, 9, 12 gives 27). For a : b = b : c, c is the third proportional, c = b^2/a (4, 6 gives 9). The mean proportional between a and b is the square root of ab (9 and 16 give 12).

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66. What digit x makes the number 4x6723 divisible by 11?

    x = 2. For divisibility by 11, the difference between the sum of digits in odd places and in even places (counted from the right) must be 0 or a multiple of 11. Here that difference is x - 2, so x = 2, giving 426723 = 11 x 38793.

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67. What is the angle between the hour and minute hands of a clock at 3:40?

    130 degrees. The minute hand is at 40 x 6 = 240 degrees. The hour hand is at 3 x 30 + 40 x 0.5 = 110 degrees. The difference is 130 degrees (the reflex angle on the other side is 230).

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68. What is the compound interest on ₹10,000 for 1 year at 10% per annum, compounded half-yearly?

    ₹1,025. Half-yearly compounding means 5% per half-year for 2 periods: 10,000 x 1.05 x 1.05 = ₹11,025, so CI = ₹1,025, which is ₹25 more than yearly compounding.

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69. What is the difference between compound interest and simple interest on ₹5,000 for 2 years at 8% per annum?

    ₹32. For 2 years the difference is P x (R/100)^2 = 5,000 x 0.08 x 0.08 = ₹32. It is the interest earned in year 2 on year 1's interest.

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70. What is the least number which, when divided by 12, 15, 20 and 54, leaves a remainder of 8 in each case?

    548. The number minus 8 must be a multiple of all four divisors. LCM(12, 15, 20, 54) = 540, so the least such number is 540 + 8 = 548.

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71. What is the next letter in the series A, C, F, J, O, ...?

    U. Using positions A = 1, C = 3, F = 6, J = 10, O = 15, the gaps are 2, 3, 4, 5, so the next gap is 6 and the next position is 21, which is U.

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72. What is the next number in the series 2, 3, 5, 9, 17, ...?

    33. The differences are 1, 2, 4, 8, which double each time, so the next difference is 16 and 17 + 16 = 33. Each term is also 2^n + 1, or double the previous term minus 1.

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73. What is the next term in the series 4, 9, 25, 49, 121, ...?

    169. The terms are squares of consecutive prime numbers: 2^2, 3^2, 5^2, 7^2, 11^2, so the next is 13^2 = 169.

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74. What is the probability that a randomly chosen leap year has 53 Sundays?

    2/7. A leap year has 366 days = 52 weeks + 2 extra days. Those 2 consecutive days can be any of 7 pairs (Mon-Tue, ..., Sun-Mon), and 2 of them include a Sunday.

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75. What is the unit digit of 7^95?

    The answer is 3. Unit digits of powers of 7 repeat in a cycle of four (7, 9, 3, 1). 95 leaves remainder 3 when divided by 4, so 7^95 ends like 7^3, which ends in 3.

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76. ₹10,000 is lent partly at 8% and partly at 12% simple interest. The total interest for one year is ₹960. How much was lent at each rate?

    ₹6,000 at 8% and ₹4,000 at 12%. The overall rate is 960/10,000 = 9.6%. Alligation gives (12 - 9.6) : (9.6 - 8) = 2.4 : 1.6 = 3 : 2.

    IntermediateQuick answer1 min read
77. A bag has ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8, worth ₹210 in total. How many coins of each kind are there?

    105 one-rupee, 126 fifty-paise and 168 twenty-five-paise coins. Take counts 5x, 6x, 8x. Their value is 5x + 3x + 2x = 10x rupees = 210, so x = 21.

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78. A boat takes twice as long to go upstream as to cover the same distance downstream. What is the ratio of the boat's speed in still water to the speed of the stream?

    3 : 1. Same distance and double the time means the downstream speed is twice the upstream speed: b + s = 2(b - s), so b = 3s.

    IntermediateQuick answer1 min read
79. A can do a job in 20 days. A works alone for 4 days, then B joins and together they finish the rest in 6 days. How long would B take alone?

    12 days. A works all 10 days and does 10/20 = half the job. B does the other half in 6 days, so B alone would need 12 days.

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80. A can finish a job in 6 days and B in 12 days. If they work on alternate days, starting with A, in how many days will the job be finished?

    8 days. With 12 units of work, A does 2 units a day and B 1. Every 2-day cycle does 3 units, so 4 cycles (8 days) finish exactly 12 units.

    IntermediateQuick answer1 min read
81. A milkman buys milk at ₹60 per litre. How much water should he add per litre so that by selling the mixture at ₹60 per litre he makes a 20% profit?

    200 ml per litre (milk : water = 5 : 1). For 20% profit at ₹60, the mixture's cost must be 60 / 1.2 = ₹50 per litre. Alligation of milk (₹60) and water (₹0) about ₹50 gives 50 : 10 = 5 : 1.

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82. A sells a bicycle to B at a 20% profit, and B sells it to C at a 25% profit. If C pays ₹1,500, what did A pay for it?

    ₹1,000. Each sale multiplies the price: CP of A x 1.2 x 1.25 = 1,500, so A's cost = 1,500 / 1.5 = ₹1,000.

    IntermediateQuick answer1 min read
83. A sum at compound interest amounts to ₹6,050 in 2 years and ₹6,655 in 3 years. Find the rate and the principal.

    Rate = 10% and principal = ₹5,000. The third year's interest is 6,655 - 6,050 = ₹605, which is 10% of ₹6,050. Then P = 6,050 / (1.1)^2 = 6,050 / 1.21 = ₹5,000.

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84. At what time between 4 and 5 o'clock are the hands of a clock together?

    At 21 9/11 minutes past 4 (about 4:21:49). At 4:00 the minute hand is 120 degrees behind, and it gains 5.5 degrees a minute, so it catches up in 120/5.5 = 240/11 = 21 9/11 minutes.

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85. Find the greatest number that divides 43, 91 and 183 leaving the same remainder in each case.

    The answer is 4. If a number leaves the same remainder for all three, it divides their differences exactly: 48, 92 and 140. HCF(48, 92, 140) = 4, and indeed each number leaves remainder 3 when divided by 4.

    IntermediateQuick answer1 min read
86. How do you quickly approximate a value like '3,487 is what percent of 15,012?' in a timed data interpretation section?

    Round both numbers to friendly values close to the originals: 3,500 / 15,000 = 7/30, about 23.3%. The exact value is 23.23%, so the estimate is enough to pick the right option when choices are reasonably far apart.

    IntermediateQuick answer1 min read
87. How many factors does 360 have, and what is the sum of those factors?

    Write 360 = 2^3 x 3^2 x 5. Number of factors = (3+1)(2+1)(1+1) = 24. Sum of factors = (1+2+4+8)(1+3+9)(1+5) = 15 x 13 x 6 = 1170.

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88. If a boy walks to school at 5 km/h he is 7 minutes late; at 6 km/h he is 5 minutes early. How far is the school?

    6 km. The two journey times differ by 7 + 5 = 12 minutes = 1/5 hour. So d/5 - d/6 = 1/5, which gives d/30 = 1/5 and d = 6 km.

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89. If DELHI is coded as 73541 and CALCUTTA as 82589662, how is CALICUT coded?

    8251896. Each letter has a fixed digit: D 7, E 3, L 5, H 4, I 1, C 8, A 2, U 9, T 6. So C-A-L-I-C-U-T becomes 8-2-5-1-8-9-6.

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90. If P + Q means P is the father of Q, P - Q means P is the wife of Q, and P x Q means P is the brother of Q, what does A - B + C x D mean about A and D?

    A is D's mother. A - B: A is B's wife. B + C: B is C's father. C x D: C is D's brother, so D is also B's child. Since A is B's wife, A is the mother of D.

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