UPSC Prelims 2026 · CSAT

Question 3: Data Interpretation

If x and y are integers, then is x even?

Statement Ix^2 y^2 is even.
Statement II1 + x^2 + y^2 is odd.

Each item in this section contains a question followed by two statements. Answer each item using the following instructions and mark your response on the Answer Sheet accordingly.

aSelect this option if the question can be answered using one of these statements alone, but cannot be answered using other statement

bSelect this option if the question can be answered using either statement alone

cSelect this option if the question can be answered using both the statements together, but cannot be answered using either statement alone

dSelect this option if the question cannot be answered even using any of the statements

AnswerUPSC’s answer is (c).

Statement I says xy is even, so x or y is even; x could still be odd. Statement II says x² + y² is even, so x and y have the same parity; both could be odd or both even. Together: if both were odd, xy would be odd, which contradicts I. So both are even, and x is even. Neither statement is enough alone, but the two together settle it.

Why each option is right or wrong

(a) Wrong: neither statement alone works (I allows x odd with y even; II allows both odd).
(b) Wrong: neither statement alone is sufficient.
(c) Right: same parity from II plus an even product from I forces both even.
(d) Wrong: the two statements together do give a definite answer.

Only the provisional key (27 May 2026) was found; the final key replaces it when found.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.