Interview Q&A / Aptitude

61. 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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62. 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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63. 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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64. 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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65. 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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66. 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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67. 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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68. 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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69. 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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70. 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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71. 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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72. 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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