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)
• The ages are 17, 18, 19, 20, 21, and 22, with E fixed at 22 (oldest) and the youngest being 17.
• Since A is one year older than C, the pair (C, A) must occupy consecutive age slots.
• The condition 'F is somewhere between B and D' implies that B and D are not adjacent to F in the age sequence, meaning at least one person is older than F and younger than B/D, or vice versa, creating a specific structural constraint.
• Analyzing the possible positions for the (C, A) pair and the relative ordering of B, D, and F reveals that only two distinct permutations satisfy all conditions: one where the youngest is B and another where the youngest is D.
• Therefore, there are exactly 2 logically possible orders of increasing age.
Why the other options are wrong
- (a) 1
- There are two valid permutations, not just one, as the relative positions of B and D can be swapped while maintaining the constraints on F and the (C, A) pair.
- (c) 3
- Only two permutations satisfy the strict constraints of consecutive ages for A and C and the 'between' condition for F, not three.
- (d) 4
- The constraints on the consecutive ages of A and C and the positional requirement for F limit the possibilities to two, 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.