A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p^{2} - 1) is

- always divisible by 6, and may or may not be divisible by 12
- always divisible by 24
- never divisible by 6
- always divisible by 12, and may or may not be divisible by 24

**Solution**

If p is a prime number greater than 3, then p^{2}-1 is always divisible by 24.

p^{2} - 1 = (p - 1) x (p + 1)

As p is a prime number, it must be odd. So, p - 1 and p + 1 must be even. Now, these 2 even numbers are consecutive. One of them must be a multiple of 4.

p - 1, p and p + 1 form three consecutive numbers. In any three consecutive numbers, one will be a multiple of 3. As p is not a multiple of 3 (p is prime), hence either p - 1 or p + 1 is a multiple. Therefore p^{2} - 1 has factors: 2, 4, & 3.

Hence, p^{2} - 1 = 24n

When p = 7, p^{2} - 1 = 48

When p = 11, p^{2} - 1 = 120

**The correct option is B.**