AAPL wrote:If a and b are integers, is ab divisible by 24?

(1) a = 12x, where x is an integer.
(2) b = 8x, where x is an integer.

The OA is C.

I don't have clear this DS question. Please, can any expert help me with it? Thanks.

Statement 1: We're told that a is a multiple of 12. If a = 12 and b = 1, then ab = 12, and NO, ab is not divisible by 24
If a = 24 and b =1, then ab = 24, and YES ab is divisible by 24
Not Sufficient

Statement 2: We're told that b is a multiple of 8. If a = 1 and b = 8, ab = 8, and NO ab is not divisible by 24
If a =1 and b = 24, ab = 24 and YES ab is divisible by 24

Together. If a = 12x and b = 8x, then ab = 12x*8x = 96* x^2. Because 96 is itself divisible by 24, and x is an integer, 96* x^2 will always be divisible by 24, and the statements together are sufficient. (You can also think of it this way: (96 * x^2)/24 = 4 * x^2, which will have to be an integer if x must be an integer.) The answer is C.