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?
Answer & explanation
Answer: (a) Only Conclusion-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). ·