Directions: The question is followed by two statements. Mark your answer using the codes below. Question: X receives three coins of different denominations from 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5? Statement I: m is not a prime number. Statement II: The sum of the digits of m is greater than 5. (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 61 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 61

Question

Directions: The question is followed by two statements. Mark your answer using the codes below. Question: X receives three coins of different denominations from 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5? Statement I: m is not a prime number. Statement II: The sum of the digits of m is greater than 5.

(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: (a)The question can be answered using one of these statements alone, but cannot be answered using the other statement

Solution

Listing the ten three-coin sums, every sum with a digit-sum > 5 contains a 5, so Statement II alone answers "yes". But "m not prime" (I) is satisfied by 32 = 2 + 10 + 20 (no 5) as well as sums with a 5, so I alone is insufficient. Answerable by one statement but not the other.

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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