Hi vinni.k,
We're told that A, B, X and Y are positive INTEGERS and that (A)(Y) = (B)(X). We're asked if 7 a factor of X. This is a YES/NO questions. While this prompt might look 'scary', it's built around a Prime Factorization 'shortcut' that you can use to avoid doing lots of math.
1) 35 is a factor of A.
Fact 1 tells us that A must be a multiple of 35. Thus (A)(Y) will have at least one 5 and at least one 7 among its prime factors. By extension (B)(X) must ALSO have at least one 5 and at least one 7 among its prime factors.
IF.... there's just one 7 and it's "in" the B, then the answer to the question is NO.
there's just one 7 and it's "in" the X, then the answer to the question is YES.
Fact 1 is INSUFFICIENT
2) B when prime-factorized will be of the form (5)^S.
Fact 2 tells us that the ONLY prime factors that COULD be in B are 5s, but this tells us nothing about the value of X.
Fact 2 is INSUFFICIENT
Combined, we know...
35 is a factor of A.
The ONLY prime factors that COULD be in B are 5s
(A)(Y) will have at least one 5 and at least one 7 among its prime factors and (B)(X) must ALSO have at least one 5 and at least one 7 among its prime factors. We know that there can NOT be any 7s 'in' B though, so that one 7 MUST be "in" X. Thus, X will ALWAYS be a multiple of 7 and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
