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 ✓ UPSC's answer
- (b) Only Conclusion-II
- (c) Neither Conclusion-I nor Conclusion-II
- (d) Both Conclusion-I and Conclusion-II
Why the answer is (a)
• The first statement establishes that every number in the set is divisible by 2.
• The second statement establishes that every number in the set is also divisible by 3.
• Since 2 and 3 are co-prime integers, any number divisible by both must be divisible by their least common multiple, which is 6.
• Therefore, Conclusion-I logically follows from the combination of the two statements.
• Conclusion-II claims divisibility by 4, but being divisible by 2 does not guarantee divisibility by 4 (e.g., 2 is divisible by 2 but not 4).
• Thus, only Conclusion-I is valid, making option (a) the correct answer.
Why the other options are wrong
- (b) Only Conclusion-II
- Conclusion-II does not follow because divisibility by 2 does not imply divisibility by 4.
- (c) Neither Conclusion-I nor Conclusion-II
- Conclusion-I does logically follow because any number divisible by both 2 and 3 is divisible by 6.
- (d) Both Conclusion-I and Conclusion-II
- Conclusion-II does not follow, so it is incorrect to say both conclusions follow.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.