Passage

Directions for the following 5 (five) items : 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. (a) Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement (b) Select this option if the question can be answered using either statement alone (c) Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone (d) Select this option if the question cannot be answered even using any of the statements

Question : X receives three coins of different denominations : 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) Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement ✓ UPSC's answer
(b) Select this option if the question can be answered using either statement alone
(c) Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
(d) Select this option if the question cannot be answered even using any of the statements

Why the answer is (a)

• Three different coins from {1, 2, 5, 10, 20} give ten possible totals: 8 (1+2+5), 13 (1+2+10), 23 (1+2+20), 16 (1+5+10), 26 (1+5+20), 31 (1+10+20), 17 (2+5+10), 27 (2+5+20), 32 (2+10+20), 35 (5+10+20).

• Statement I (m not prime) leaves 8, 16, 26, 27, 32, 35. All contain a 5-coin except 32 = 2+10+20, so the answer can be yes or no: not sufficient.

• Statement II (digit sum of m greater than 5) leaves 8, 16, 17, 26, 27, 35. Every one of these contains a 5-coin, so the answer is a definite yes: sufficient.

• One statement alone (II) answers the question and the other (I) does not, so the answer is (a).

Why the other options are wrong

(b) Select this option if the question can be answered using either statement alone: Statement I alone fails: 32 = 2+10+20 is not prime but has no 5-coin.
(c) Select this option if the question can be answered using both the statements together…: Both statements are not needed; Statement II alone settles the question.
(d) Select this option if the question cannot be answered even using any of the statements: Statement II alone gives a definite yes, so the question can be answered.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.