You can solve it using algebra, but i prefer to use some numbers as explained below:-

Statement 1) x = 12 u

So, for x to be a multiple of 12, we have (36,3) and (60,6) satisfy the eqn x = 8*y + 12. In these cases the HCF is 3 and 6 respectively. Not Sufficient!!!

Statement 2) y = 12 z

So, for y to be a multiple of 12, we have (12*9,12) and (12*17,24) and (12*25,36) and (12*33,48) satisfy the eqn x = 8*y + 12. In each case the HCF is 12. Sufficient!!!

Answer B.

varun289 wrote:If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?
(1) x = 12u, where u is an integer.
(2) y = 12z, where z is an integer.

For many test-takers, the most efficient approach on test day would be to plug in.

Statement 1: x=12u, where u is an integer and x=8y+12.
In other words, x is a multiple of 12.
For x to be a multiple of 12, 8y must be a multiple of 12.

If y=3, then x = 8*3 + 12 = 36.
The GCD of 3 and 36 is 3.

If y=6, then x = 8*6 + 12 = 60.
The GCD of 6 and 60 is 6.

Since the GCD can be different values, INSUFFICIENT.

Statement 2: y=12z, where z is an integer and x=8y+12.
In other words, y is a multiple of 12.
Since we're looking for the GCD, view x in terms of its FACTORS.

If y=12, then x = 8(12) + 12 = 12(8+1) = 12*9.
The GCD of 12 and 12*9 is 12.

If y=24, then x = 8(24) + 12 = 12(8*2 + 1) = 12*17.
The GCD of 24 and 12*17 is 12.

I'm almost convinced: the GCD is 12.
Maybe one more just to be sure:

If y=36, then x = 8(36) + 12 = 12(8*3 + 1) = 12*25.
The GCD of 36 and 12*25 is 12.
SUFFICIENT.

The correct answer is B.

GCD or Greatest Common Divisor = GCF or Greatest Common Factor

Whenever the word "divisor" is seen in a GMAT question, it can be replaced with "factor" - since factors and multiples are what most study when preparing for the GMAT.

Just wanted to clarify since this constantly confuses me!

Also want to point out for this question that a quick way of knowing B is sufficient is the rule that states that if two numbers are both multiplies of a certain number, adding or subtracting them will generate an answer that is a multiple of that same number.

For example: 35 (multiple of 7) - 21 (multiple of 7) = 14 (multiple of 7)

So, we can apply this rule to statement 2.

if y = 12z, then x = 96z + 12 -> in other words, y is a multiple of 12, so a multiple of 12 added together with a multiple of 12 must be a multiple of 12! So, x is a multiple of 12 as well. Knowing that x will always be greater than y, means that 12 will always be the greatest common factor of x and y.