If a and b are positive integers divisible by 6, is 6 the..?

by **ichai** Wed Aug 20, 2008 6:55 am

(1) a = 2b + 6

(2) a = 3b

(1) SUFFICIENT: We are already told in the question stem that 6 is a divisor of both a and b. This statement tells us that a is exactly 6 more than 2b. If one number is x units away from another number, and x is also a factor of both of those numbers, than x is also the GCF of those two numbers. This always holds true because x is the greatest number separating the two; in order to have a larger GCF, the two numbers would have to be further apart.

Does this explanation hold in this case? X (6) is not the greatest number separating a and b; b+6 is the number separating a and b. So can you assume 6 is still the GCF?

by **RonPurewal** Tue Sep 09, 2008 7:25 am

what's the rest of the question?

thx