Consider the Question and two Statements given below : Question : Is Z brother of X ? Statement-1 : X is a brother of Y and Y is a brother of Z. Statement-2 : X, Y and Z are siblings. Which one of the following is correct in respect of the Question and the Statements?

(a) Statement-1 alone is sufficient to answer the Question
(b) Statement-2 alone is sufficient to answer the Question
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question ✓ UPSC's answer

Why the answer is (d)

• To answer 'Is Z the brother of X?' we need to know that Z is male and that Z and X are siblings.

• Statement-1: 'X is a brother of Y and Y is a brother of Z' tells us X and Y are male and that X, Y and Z are siblings, but says nothing about Z's gender. Z could be a brother or a sister, so Statement-1 is not sufficient.

• Statement-2: 'X, Y and Z are siblings' again gives no information about Z's gender, so it is not sufficient.

• Together the statements still leave Z's gender unknown, so the Question cannot be answered.

• Hence option (d).

Why the other options are wrong

(a) Statement-1 alone is sufficient to answer the Question: Statement-1 shows Y is male, not Z; Z could be X's sister, so it is not sufficient.
(b) Statement-2 alone is sufficient to answer the Question: Statement-2 only says the three are siblings; Z could be a sister, so it is not sufficient.
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question: Even together the statements never state Z's gender, so they cannot confirm Z is a brother.

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.