Bunuel wrote:

For positive integer n, is the product (n)(n+1)(n+2) divisible by 24?

(1) n is even

(2) n + 2 = 6

24 = 2^3 * 3, so for a number to be divisible by 24, it must be divisible by 8(three times 2) as well as by 3.

(1) If n is even, (n+2) is also even, and since n and n+2 have a difference of 2, one of them will be divisible by 4 also. So basically the product of n(n+2) will give us three 2's, hence divisible by 8. And since n(n+1)(n+2) is product of three consecutive integers, one of them will definitely be divisible by 3. Hence the product will be divisible by 8 as well as by 3, so by 24 also. Sufficient.

(2) n=2 = 6. So the given product is 4*5*6, which is divisible by 24. Sufficient.

Hence

D answer