Hi M7MBA,
We're told that X, Y and Z are positive integers, X < Y < Z and that Z is an ODD. We're asked if X is a factor of Z. This is a YES/NO question and is based on a couple of Number Property rules.
1) X and Y are prime numbers and the sum is a factor of 57.
The factors of 57 are 1, 3, 19 and 57 (which are all odd numbers). Since X and Y are PRIMES - and Fact 1 tells us that the sum of those numbers must be an ODD - there must be one EVEN and one ODD number. This means that X MUST be 2 and Y MUST be an odd prime. Since Z is an ODD number, then X (which is EVEN) will NEVER be a factor of Z. Thus, the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT
2) Z is a factor of 57
From Fact 1, we know that the factors of 57 are 1, 3, 19 and 57. Since the 3 variables are all positive integers, then Z must be 3, 9 or 57.
IF....
X=1, then the answer to the question is YES (regardless of the value of Z).
X=2, then the answer to the question is NO (regardless of the value of Z).
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
