Civil Services Prep

Prelims 2022 · CSAT / Quantitative Aptitude · Question 47

A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?

  1. 147
  2. 150
  3. 294
  4. 300

Answer

294

Let the numbers received be in the ratio (A:B:C:D:E:F = 60:30:20:15:12:10), obtained from (A=2B=3C=4D=5E=6F). Total pens in one such set = (60+30+20+15+12+10=147).

Now each child must get an even number. In the basic set, (D=15) is odd, so multiplying by 1 will not work. The smallest multiplier making all shares even is 2. Hence minimum total pens = (147 \times 2 = 294).

Option check:

  • (a) 147: Basic ratio total, but D gets 15 (odd). Incorrect.
  • (b) 150: Does not fit the required ratio total. Incorrect.
  • (c) 294: Ratio maintained and all shares become even. Correct.
  • (d) 300: Larger than minimum. Incorrect.
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