Interview Q&A / Aptitude

1. A 40-litre can is full of milk. 4 litres are taken out and replaced with water, and this is done three times in total. How much milk is left?

   29.16 litres. Each operation keeps (40 - 4)/40 = 0.9 of the milk, so after three rounds milk = 40 x 0.9^3 = 40 x 0.729 = 29.16 litres.

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2. A boat's speed in still water is 15 km/h. It goes 30 km upstream and returns in 4 hours 30 minutes. What is the speed of the stream?

   5 km/h. Solve 30/(15 - s) + 30/(15 + s) = 4.5. This gives 900/(225 - s^2) = 4.5, so 225 - s^2 = 200 and s = 5. Check: 30/10 + 30/20 = 3 + 1.5 = 4.5 hours.

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3. How do you find the HCF and LCM of fractions such as 2/3, 8/9 and 16/81?

   HCF of fractions = HCF of numerators / LCM of denominators; LCM of fractions = LCM of numerators / HCF of denominators. For 2/3, 8/9, 16/81 the HCF is 2/81 and the LCM is 16/3.

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4. In how many ways can 5 boys and 3 girls stand in a row so that no two girls are next to each other?

   14,400. Arrange the boys first: 5! = 120. They create 6 gaps (including the two ends). Choose and fill 3 of those gaps with the girls in order: 6 x 5 x 4 = 120. Total 120 x 120 = 14,400.

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5. In how many ways can a committee of 5 be formed from 6 men and 4 women so that it has at least 2 women?

   186. Total committees C(10,5) = 252. Subtract those with no woman, C(6,5) = 6, and with exactly one woman, 4 x C(6,4) = 60. 252 - 66 = 186.

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6. Ravi spends 75% of his income. His income rises by 20% and his spending by 10%. By what percentage do his savings increase?

   By 50%. Take income 100, spending 75, savings 25. New income 120, new spending 82.5, new savings 37.5. Increase = 12.5 on 25 = 50%.

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7. Statements: All roses are flowers. Some flowers are red. Conclusions: I. Some roses are red. II. No rose is red. Which follows?

   Either I or II follows. Neither is certain on its own, but they are a complementary pair about the same two terms: one of 'some roses are red' and 'no rose is red' must be true. So the answer is 'either I or II'.

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8. The minute hand of a clock overtakes the hour hand every 64 minutes of correct time. How much does the clock gain or lose in a day?

   It gains 32 8/11 minutes a day. In a correct clock the hands meet every 65 5/11 minutes. Here they meet after only 64 real minutes, so the clock runs fast: it shows 65 5/11 minutes in 64 real minutes, gaining 16/11 minutes every 64 minutes, which is 360/11 = 32 8/11 minutes in 1,440 minutes.

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9. What day of the week was 15 August 1947?

   Friday. Count odd days (days beyond complete weeks): 1,900 years give 1 odd day, 1901 to 1946 give 46 + 11 leap days = 57, which is 1, and 1 January to 15 August 1947 gives 227 days, which is 3. Total 5 odd days, and 5 corresponds to Friday.

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10. What is the probability that 4 randomly chosen people were all born on different days of the week?

    840/2401, about 0.35. The first person can be born on any day (7/7), the second on one of 6 other days, the third on 5, the fourth on 4: (7 x 6 x 5 x 4) / 7^4 = 840/2401.

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