Question

What are the ages of the three brothers? I. The product of their ages is 21.
I II. The sum of their ages is not divisible by 3.

• A. If the question can be answered with the help of statement I alone
• B. If the question can be answered with the help of statement II alone
• C. If both, statement I and statement II are needed to answer the question
• D. If the question cannot be answered even with the help of both the statements

Hint:

Check all factor combinations when given product-based clues.

Answer 1

The Correct Option is D

From Statement I: the product of the three ages is 21.
Possible triplets: \( (1,3,7), (1,1,21), (3,3,3), (7,1,3) \), etc. But age order is not fixed.
Statement II: The sum is not divisible by 3.
Let’s examine possible sums:
- \(1 + 3 + 7 = 11\) → not divisible by 3
- \(3 + 3 + 3 = 9\) → divisible by 3
- \(1 + 1 + 21 = 23\) → not divisible by 3
Even combining both statements, multiple valid combinations still exist.
Hence, we cannot uniquely determine the three brothers' ages.