Consider the following statements : 1. Either A and B are of the same age or A is older than B 2. Either C and D are of the same age or D is older than C 3. B is older than C Which of the following conclusions can be drawn from the above statements ?

(a) A is older than B
(b) B and D are of the same age
(c) D is older than C
(d) A is older than C ✓ UPSC's answer

Why the answer is (d)

• Statement 1 says A is either the same age as B or older than B, so A is at least as old as B.

• Statement 2 says D is either the same age as C or older than C, so D is at least as old as C, but it does not force D to be older than C.

• Statement 3 says B is older than C, so B > C.

• Combining A >= B and B > C gives A > C, because if A equals B, A is still older than C, and if A is older than B, A is even more older than C.

• Therefore, the only conclusion that must follow is that A is older than C, which is option (d).

Why the other options are wrong

(a) A is older than B: A may be the same age as B, so A being older than B is not certain.
(b) B and D are of the same age: B and D need not be the same age because only B > C and D >= C are given.
(c) D is older than C: D may be the same age as C, so D being older than C is not certain.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.