I'm not very confident with the forthcoming, but here it goes...
X=8Y + 12
Right off of the bat we know that Y has to be a multiple of 8 and that we need to find the value of both variables in order to know what their greatest common divisor is.
Statement one is not sufficient because all it tells us is that X is a multiple of 12. So, for instance if X = 12, then the value of the equation becomes
12=8Y+12 and 8Y=0, so Y=0. However, if X = 24 then the value of the Y is not zero, it is 24=8Y+12 => 8Y=12 => y=3/2. Thus, statement one gives different values for X and Y, each of which yields a different greatest common divisor of X and Y.
Statement two is sufficient because it let's us know that in addition to Y being a multiple of 8, it is also a multiple of 12. Looking at the equation X=8Y+12, it's clear to see that if Y is a multiple of 12 then X has to be a multiple of 12. Thus, the greatest common divisor of both X and Y will be 12.
Like I said, I'm not very confident that I've absolutely "proved" that 12 will always be the GCD of both X and Y with the info. given in statement two. If anyone else can shed some more light on the subject, that'd be helpful.
Thanks!
