नीचे दिए गए प्रश्न और दो कथनों पर विचार कीजिए :
- प्रश्न: क्या x पूर्णांक है?
- कथन–1: x / 3 पूर्णांक नहीं है।
- कथन–2: 3x पूर्णांक है।
उपर्युक्त प्रश्न और कथनों के बारे में निम्नलिखित में से कौन-सा एक सही है?
Read this question in English
Consider the Question and two Statements given below:
Question. Is x an integer?
Statement–1. x/3 is not an integer.
Statement–2. 3x is an integer.
Which one of the following is correct in respect of the Question and the Statements?
(a) Statement–1 alone is sufficient to answer the Question · (b) Statement–2 alone is sufficient to answer the Question · (c) Both Statement–1 and Statement–2 are sufficient to answer the Question · (d) Both Statement–1 and Statement–2 are not sufficient to answer the Question
उत्तर और व्याख्या · explanation in English
Answer: (d) कथन–1 और कथन–2, दोनों, प्रश्न का उत्तर देने के लिए पर्याप्त नहीं हैं
x = 1 and x = 1/3 both satisfy both statements, but one is an integer and the other is not. So the statements cannot settle the question even when used together.
- Statement–1 alone: x = 1 gives x/3 = 1/3 (not an integer) and x is an integer; x = 1/2 gives x/3 = 1/6 and x is not an integer. Not sufficient.
- Statement–2 alone: x = 1 gives 3x = 3 and x = 1/3 gives 3x = 1; both are integers, yet only one x is an integer. Not sufficient.
- Together: x = 1 fits both (1/3 is not an integer, 3 is) and so does x = 1/3 (1/9 is not an integer, 1 is). One is an integer, the other is not.
- So even both statements together are not sufficient.
Remember · Data sufficiency: find two values that satisfy every statement yet give different answers — one such pair proves insufficiency.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·