Directions: The question is followed by two statements. Mark your answer using the codes below. Question: X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of which are either from X or from Y. Is every number of T from Y? Statement I: The sum of any two numbers belonging to T is even. Statement II: If both p and q are picked from T, then (p − 1)q is even. (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 64 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 64

Question

Directions: The question is followed by two statements. Mark your answer using the codes below. Question: X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of which are either from X or from Y. Is every number of T from Y? Statement I: The sum of any two numbers belonging to T is even. Statement II: If both p and q are picked from T, then (p − 1)q is even.

(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: (d)The question cannot be answered even using both statements together

Solution

I says all of T has the same parity (could be all odd or all even). II is always true regardless of parity, so it adds nothing. Even together, T could be all odd, so we cannot conclude every number is from Y.

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.

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Official Notification

PIB Release 2262441

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