UPSC PYQPrelims 2026

Civil Services Examination · Question 1

Each item contains a question followed by two statements. Answer using these instructions: (a) if the question can be answered using one of the statements alone, but cannot be answered using the other statement (b) if the question can be answered using either statement alone (c) if the question can be answered using both the statements together, but cannot be answered using either statement alone (d) 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.

  1. Answerable using one statement alone, but not the other
  2. Answerable using either statement alone
  3. Answerable using both statements together, but not either alone
  4. Cannot be answered even using both statements
Show answer & explanation

Answer: (A) Answerable using one statement alone, but not the other

Explanation

Possible sums of three different coins: 8, 13, 23, 16, 26, 31, 17, 27, 32, 35. Statement I (m not prime) leaves 8, 16, 26, 27, 32, 35; 32 = 2+10+20 has no 5-coin, so I is insufficient. Statement II (digit sum > 5) leaves 8, 16, 26, 17, 27, 35, and every one of these includes the 5-coin, so II alone answers it.