tonebeeze wrote:How many divisors does positive integer N have?

1. The difference between the largest and the smallest divisor of N is 21

2. N+1 has 2 divisors

Statement 1: The difference between the largest and the smallest divisor of N is 21
Largest divisor of any positive integer is the integer itself and smallest divisor of any positive integer is 1. Thus, (Integer - 1) = 21 => The integer is 22. We can easily determine the number of divisors of 22.

Sufficient.

Statement 2: N+1 has 2 divisors
This implies (N + 1) is a prime. But there is infinite number of positive integers N such that (N + 1) is prime.

Not Sufficient.

The correct answer is A.