A group of 630 children is seated in rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible ?
- (a) 3
- (b) 4
- (c) 5
- (d) 6 ✓ UPSC's answer
Why the answer is (d)
• Let the front row have x children; for n rows the row sizes are x, x-3, x-6, ..., x-3(n-1).
• Their total is n/2 [2x - 3(n-1)] = 630, so x = (1260/n + 3(n-1))/2 must be a whole number.
• For n = 3, 4, and 5, x equals 213, 162, and 132 respectively, giving valid integer row sizes.
• For n = 6, x = (210 + 15)/2 = 112.5, which is not an integer, so 6 rows is impossible; hence option (d).
Why the other options are wrong
- (a) 3
- 3 rows are possible with 213, 210, and 207 children, which sum to 630.
- (b) 4
- 4 rows are possible with 162, 159, 156, and 153 children, which sum to 630.
- (c) 5
- 5 rows are possible with 132, 129, 126, 123, and 120 children, which sum to 630.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.