What is the number of logically possible orders of all six cousins in terms of increasing age ?
- (a) 1
- (b) 2 ✓ UPSC's answer
- (c) 3
- (d) 4
Why the answer is (b)
• From the previous item, E = 22, A = 21, C = 20 and F = 18 are fixed, while B and D share 17 and 19 in either order.
• The two possible orders of increasing age are B, F, D, C, A, E (B = 17, D = 19) and D, F, B, C, A, E (D = 17, B = 19).
• Both satisfy every condition, so there are 2 logically possible orders — option (b).
• Hence option (b).
Why the other options are wrong
- (a) 1
- B and D can swap 17 and 19, so there are two orders, not one.
- (c) 3
- Only B and D can swap; there is no third arrangement.
- (d) 4
- Only two arrangements satisfy all the conditions, not four.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.