vittalgmat wrote:If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?
(1) a = 2b + 6
(2) a = 3b
[spoiler]OA is probably A (not sure)[/spoiler]
If you don't recall the relevant rule or are uncomfortable with proceeding algebraically (as many test-takers might be here), you can handle this question fairly quickly by picking numbers.
We know from the stem that both a and b are positive integers divisible by 6; in other words, 6 is a factor of both a and b. The question is asking: Is 6 their
greatest common factor?
(1) a = 2b + 6
So, let's say b is 6. Then, a = 2(6) + 6 = 18. Is 6 the greatest common factor of 6 and 18? Yes. But we need to convince ourselves that a and b will
always have 6 as their greatest common factor. So, now, let's say b is 12. Then, a = 30. Is 6 the greatest common factor of 12 and 30? Again, yes. (And, if b = 18, then a = 42. Is 6 the greatest common factor of 18 and 42? Yes: 6 is the biggest number that can divide both 18 and 42.) You can go for another trial if you want but, at this point, we have convinced ourselves that no matter what multiples of 6 we let a and b be, 6 will always be their greatest common factor.
Sufficient.
(2) a = 3b
If b = 6, then, a = 18. Is 6 the greatest common factor of 6 and 18? Yes. But if b = 12, then a = 36. Is 6 the greatest common factor of 12 and 36? No; 12 is. Because, from (2), we can get both a yes and a no answer to the yes/no question, this statement is insufficient.
The first statement is sufficient by itself while the second one is not; choice A.
