A Question is given followed by two Statements I and II. Consider the Question and the Statements.
There are three distinct prime numbers whose sum is a prime number.
- Question: What are those three numbers?
- Statement–I: Their sum is less than 23.
- Statement–II: One of the numbers is 5.
Which one of the following is correct in respect of the above Question and the Statements?
Answer & explanation
Answer: (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
Three distinct primes with a prime sum must all be odd, because including 2 makes the sum even. With the sum below 23, the only possibility is 3 + 5 + 11 = 19, so Statement I alone suffices. Statement II allows 3, 5, 11 and 5, 7, 11 and more.
- If 2 is one of them, the sum is 2 + odd + odd = even (and more than 2), so not prime. All three must be odd primes.
- Statement I: odd-prime triples with sum below 23 are 3 + 5 + 7 = 15, 3 + 5 + 11 = 19, 3 + 5 + 13 = 21 and 3 + 7 + 11 = 21; only 19 is prime. So the numbers are 3, 5 and 11: sufficient.
- Statement II: triples containing 5 with a prime sum include {3, 5, 11} (19), {5, 7, 11} (23) and {3, 5, 23} (31), so it is not sufficient.
- So the question can be answered by one statement (I) alone but not by the other.
Remember · A prime sum of three distinct primes cannot include 2 (the sum turns even). Start listing from the smallest odd primes.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·