एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।
तीन भिन्न अभाज्य संख्याएँ हैं, जिनका योगफल एक अभाज्य संख्या है।
- प्रश्न: वे तीन संख्याएँ कौन-सी हैं?
- कथन–I: उनका योगफल 23 से कम है।
- कथन–II: उनमें से एक संख्या 5 है।
उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?
Read this question in English
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?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together
उत्तर और व्याख्या · explanation in English
Answer: (a) प्रश्न का उत्तर, दोनों में से अकेले एक कथन का प्रयोग कर दिया जा सकता है, किन्तु अकेले अन्य कथन का प्रयोग कर नहीं दिया जा सकता है
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). ·