Three persons A, B and C are standing in a queue not necessarily in the same order. There are 4 persons between A and B, and 7 persons between B and C. If there are 11 persons ahead of C and 13 behind A, what could be the minimum number of persons in the queue?
- (a) 22 ✓ UPSC's answer
- (b) 28
- (c) 32
- (d) 38
Why the answer is (a)
• Number positions from the front. '11 persons ahead of C' puts C at position 12.
• 7 persons between B and C means B is 8 places from C: position 4 or 20.
• 4 persons between A and B means A is 5 places from B: if B = 4, A = 9 (A cannot be at −1); if B = 20, A = 15 or 25.
• '13 persons behind A' means the total is A's position + 13: that gives 22, 28 or 38.
• The minimum is 22 (A at 9, B at 4, C at 12), option (a).
Why the other options are wrong
- (b) 28
- 28 is possible (A at 15, B at 20, C at 12), but it is not the minimum.
- (c) 32
- 32 does not arise from any arrangement; the possible totals are 22, 28 and 38.
- (d) 38
- 38 is possible (A at 25, B at 20, C at 12), but it is the largest, not the minimum.
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.