Data Sufficiency

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.

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

OA is B

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.

Stmt 1: (not sufficient)
12u=8y+12
y = 3/2(u-1)
can't conclude anything from this.
If u is odd and not 1, we have a number greater than 1
If u is even, as (u-1) is odd, Y will be a fraction. so GCD should be 1 (experts, please correct me here)...

Stmt 2: (sufficient)
x = 12 (8z+1)
y = 12 z

for the above as 8z+1 and z have GCD of 1 (for all positive integer values for z), x and y will have GCD of 12.

So answer is [spoiler]B[/spoiler]