CSATLogical ReasoningDivisibility Divisors and Remainder2020

Two Statements are given followed by two Conclusions: 1. Statements : All numbers are divisible by 2. All numbers are divisible by 3. 2. Conclusion-I: All numbers are divisible by 6. 3. 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

Correct Answer: Option A

Explanation

1. **Analyze the Premises:** The statements require every number to be divisible by both 2 and 3. As seen in the 2019 'Football and Cricket' question, divisibility by two factors implies divisibility by their Least Common Multiple (LCM) [3, 17].\n2. **Apply LCM Logic:** The LCM of 2 and 3 is 6. Therefore, the statements are mathematically equivalent to saying: 'All numbers in this set are divisible by 6'.\n3. **Evaluate Conclusion-I:** 'All numbers are divisible by 6'. This is exactly what we derived in step 2. Thus, Conclusion-I follows logically.\n4. **Evaluate Conclusion-II:** 'All numbers are divisible by 4'. We must check if being a multiple of 6 guarantees being a multiple of 4. We use the 'Counter-Example Method' from 2016 and 2018 PYQs [30, 81]. Let's test the number 6 itself. It fits the premises (divisible by 2 and 3) but fails this conclusion (6 is not divisible by 4). Since one exception exists, the conclusion is false.\n5. **Final Decision:** Conclusion-I is valid. Conclusion-II is invalid.

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