Passage

Directions for the following 2 (two) items : Read the following passage and answer the 2 (two) items that follow : A, B, C, D, E and F are cousins. No two cousins are of the same age, but all have birthdays on the same day of the same month. The youngest is 17 years old and the oldest E is 22 years old. F is somewhere between B and D in age. A is older than B. C is older than D. A is one year older than C.

Which one of the following is possible ?

(a) D is 20 years old
(b) F is 18 years old ✓ UPSC's answer
(c) F is 19 years old
(d) F is 20 years old

Why the answer is (b)

• The ages are six different whole numbers from 17 to 22, and E is 22.

• A = C + 1 and C > D, so A and C are near the top; with E at 22, A can be at most 21. Trying A = 21, C = 20 leaves 17, 18 and 19 for B, D and F.

• F must lie between B and D, so F takes the middle value 18, with B and D taking 17 and 19 in either order. (Lower values of A and C leave no room for F between B and D while keeping A > B.)

• So F must be 18 years old — option (b).

• Hence option (b).

Why the other options are wrong

(a) D is 20 years old: D is either 17 or 19, never 20 (C is 20).
(c) F is 19 years old: F must be 18; 19 belongs to B or D.
(d) F is 20 years old: 20 is C's age, so F cannot be 20.

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.