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?
- (a) 147
- (b) 150
- (c) 294 ✓ UPSC's answer
- (d) 300
Why the answer is (c)
• A = 2B = 3C = 4D = 5E = 6F, so A must be a multiple of 2, 3, 4, 5 and 6, i.e. of their LCM 60.
• With A = 60: B = 30, C = 20, D = 15, E = 12, F = 10 — but D = 15 is odd.
• The next choice, A = 120, gives B = 60, C = 40, D = 30, E = 24, F = 20, all even.
• Total = 120 + 60 + 40 + 30 + 24 + 20 = 294 pens, option (c).
Why the other options are wrong
- (a) 147
- 147 is the total for A = 60, but then D gets 15 pens, which is odd.
- (b) 150
- 150 cannot be split in the required ratio: totals must be multiples of 147.
- (d) 300
- 300 is not a multiple of 147, so it cannot be split in the required ratio.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.