Question

Is the number completely divisible by 99?
I. The number is divisible by 9 and 11 simultaneously.
II. If the digits of the number are reversed, the number is divisible by 9 and 11.

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

For coprime divisors, divisibility by both implies divisibility by their product.

Answer 1

The Correct Option is A

From I: Divisible by 9 and 11 $\Rightarrow$ divisible by LCM(9,11) = 99. This alone answers the question.
From II: The reversal being divisible does not guarantee the original number is divisible by 99. So statement II alone is insufficient.