नीचे दो कथन दिए गए हैं जिनके बाद दो निष्कर्ष दिए गए हैं :
- कथन.सभी संख्याएँ 2 से विभाज्य हैं। सभी संख्याएँ 3 से विभाज्य हैं।
- निष्कर्ष–I: सभी संख्याएँ 6 से विभाज्य हैं।
- निष्कर्ष–II: सभी संख्याएँ 4 से विभाज्य हैं।
ऊपर लिखे हुए निष्कर्षों में से कौन-सा/से दिए गए दो कथनों से तार्किक रूप से निकाला/निकाले जा सकता/सकते है/हैं?
Read this question in English
Two Statements are given followed by two Conclusions:
Statements. All numbers are divisible by 2. All numbers are divisible by 3.
Conclusion-I. All numbers are divisible by 6.
Conclusion-II. All numbers are divisible by 4.
Which of the above Conclusions logically follows/follow from the two given Statements?
(a) Only Conclusion-I · (b) Only Conclusion-II · (c) Neither Conclusion-I nor Conclusion-II · (d) Both Conclusion-I and Conclusion-II
उत्तर और व्याख्या · explanation in English
Answer: (a) केवल निष्कर्ष–I
A number divisible by both 2 and 3 is divisible by their LCM, 6, so Conclusion-I follows. Divisibility by 2 and 3 says nothing about a second factor of 2, so 4 need not divide the numbers — 6 itself is a counter-example.
- 2 and 3 have no common factor, so a number divisible by both is divisible by 2 × 3 = 6: Conclusion-I follows.
- Divisibility by 4 needs two factors of 2; the statements guarantee only one.
- Counter-example: 6 is divisible by 2 and 3 but not by 4, so Conclusion-II does not follow.
Remember · Divisible by a and b means divisible by LCM(a, b) — no more. Test any stronger claim with the LCM itself.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·