Directions: The question is followed by two statements. Mark your answer using the codes below. Question: If x and y are integers, then is x even? Statement I: x²y² is even. Statement II: 1 + x² + y² is odd. (a) The question can be answered using one of these statements alone, but cannot be answered using the other statement (b) The question can be answered using either statement alone (c) The question can be answered using both statements together, but cannot be answered using either statement alone (d) The question cannot be answered even using both statements together

UPSC Prelims 2026 · CSAT Paper 2 · Set DMathematicsQ 63 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 63

Question

Directions: The question is followed by two statements. Mark your answer using the codes below. Question: If x and y are integers, then is x even? Statement I: x²y² is even. Statement II: 1 + x² + y² is odd.

(a)The question can be answered using one of these statements alone, but cannot be answered using the other statement
(b)The question can be answered using either statement alone
(c)The question can be answered using both statements together, but cannot be answered using either statement alone
(d)The question cannot be answered even using both statements together

UnlockIAS answer: (c)The question can be answered using both statements together, but cannot be answered using either statement alone

Solution

I alone says x or y is even (x need not be). II alone says x and y have the same parity. Together they force x and y both even, so x is even — answerable using both, but neither alone.

UnlockIAS expert key, prepared 24 May 2026 and cross-verified by re-deriving the answer — this is our key, not the official UPSC provisional key (awaited).

Section

Mathematics

Topic Reference

Mathematics — Data Sufficiency

Official UPSC key still awaited

UPSC has announced (PIB Release 2262441, 18 May 2026) that the provisional answer key for CSE Prelims 2026 will be released “soon after Exam”. Until then, use the CSAT score calculator for your qualifying-status estimate, and join the per-question discussion below.

CSAT Score Calculator

Check your 33% qualifying status

Official Notification

PIB Release 2262441

Back to all 80 CSAT questions