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?

The correct answer is Only Conclusion - I.

Step-by-step Explanation:

1. Analyze the Given Statements:

• Statement 1: All numbers are divisible by 2.

• Statement 2: All numbers are divisible by 3.

2. Evaluate Conclusion-I: "All numbers are divisible by 6."

• By number theory rules, a number is divisible by 6 if and only if it is divisible by both 2 and 3 simultaneously.

• Since the statements tell us that every number is divisible by 2 AND every number is divisible by 3, every number must be divisible by their least common multiple, which is:

$\text{LCM}(2,3)=6$

• Therefore, Conclusion-I logically follows from the given statements.

3. Evaluate Conclusion-II: "All numbers are divisible by 4."

• A number being divisible by 2 and 3 does not necessarily make it divisible by 4. For example, 6 is divisible by 2 and 3, but 6 is not divisible by 4.

• Thus, Conclusion-II does not logically follow.

Conclusion:

Only Conclusion - I logically follows from the given statements.