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)

• Statement-1 states X is a brother of Y and Y is a brother of Z, which confirms X and Z are male siblings but does not explicitly state Z is a brother of X in a way that excludes other interpretations without assuming symmetry, though typically 'brother' implies male sibling; however, the core issue is whether Z is specifically the brother of X.

• Statement-2 states X, Y, and Z are siblings, which confirms they share parents but does not specify the gender of Z or X, so Z could be a sister.

• Since Statement-2 does not confirm Z is male, it cannot answer if Z is a brother.

• Statement-1 confirms X is male and Z is male (as Y is a brother of Z, implying Z is a sibling of a male, but wait, 'Y is a brother of Z' means Y is male; it does not define Z's gender directly in all logical frameworks, but usually 'brother of' implies the subject is male. Let's re-evaluate: 'Y is a brother of Z' means Y is male. It does not state Z is male. Z could be a sister. Therefore, we do not know if Z is a brother.

• Consequently, neither statement alone nor together provides sufficient information to definitively conclude that Z is a brother of X, as Z's gender is not confirmed in either statement.

Why the other options are wrong

(a) Statement-1 alone is sufficient to answer the Question: Statement-1 does not specify the gender of Z, as 'Y is a brother of Z' only confirms Y is male, leaving Z's gender ambiguous.
(b) Statement-2 alone is sufficient to answer the Question: Statement-2 only establishes that X, Y, and Z are siblings without specifying the gender of Z, so Z could be a sister.
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question: Even combined, the statements do not confirm that Z is male, which is required to answer 'Yes' to the question of whether 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.