एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।
- प्रश्न: x और y के अद्वितीय मान क्या हैं जहाँ x, y भिन्न धनपूर्ण संख्याएँ हैं?
- कथन–I: x / y विषम है।
- कथन–II: xy = 12
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.
Question. What are the unique values of x and y, where x, y are distinct natural numbers?
Statement–I. x / y is odd.
Statement–II. xy = 12
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: (c) प्रश्न का उत्तर, दोनों कथनों का एक-साथ प्रयोग कर दिया जा सकता है, किन्तु अकेले किसी भी एक कथन का प्रयोग कर नहीं दिया जा सकता है
‘x/y is odd’ alone allows endless pairs, and xy = 12 alone allows six ordered pairs. Together, of the pairs with product 12, only x = 6, y = 2 gives an odd quotient (3).
- Statement I alone: x = 3y, 5y, 7y, …, for example (3, 1), (5, 1), (6, 2); not unique.
- Statement II alone: (1, 12), (2, 6), (3, 4), (4, 3), (6, 2), (12, 1); not unique.
- Together, test x/y for each pair: 12/1 = 12 (even), 6/2 = 3 (odd); 4/3, 3/4, 2/6 and 1/12 are not whole numbers.
- Only x = 6, y = 2 works, so both statements together answer the question.
Remember · When one statement gives a short list, test each item on it against the other statement.
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). ·