Hi npalani07,
This DS question has a quirky element to it which you really have to deal with first before you deal with the two Facts.
X^3 - 3X^2 + 2X can be factored into....
X(X^2 - 3X + 2) which can be further factored into....
X(X-1)(X-2)
So, the question ultimately asks: Is X(X-1)(X-2) evenly divisible by 4? This is a YES/NO question. We're told that X is an integer.
The "secret" to this question is that if X OR (X-1) OR (X-2) is divisible by 4, then the answer is YES. If NONE of them are divisible by 4, then the answer is NO.
Fact 1: X = 3Y; Y is an integer
This tells us that X is a multiple of 3 (0, 3, 6, 9, etc.)
If X = 0, then (0)(-1)(-2) = 0 and the answer is YES
If X = 3, then (3)(2)(1) = 6 and the answer is NO
Fact 1 is INSUFFICIENT
Fact 2: X = 7Z; Z is an integer
This tells us that X is a multiple of 7 (0, 7, 14, 21, etc.)
If X = 0, then (0)(-1)(-2) = 0 and the answer is YES
If X = 7, then (7)(6)(5) = 210 and the answer is NO
Fact 2 is INSUFFICIENT
Together, we know that X has to be a multiple of 3 AND 7 (0, 21, 42, etc.)
If X = 0, the the answer is YES
If X = 21, then (21)(20)(19) has 20 as a factor, so it IS divisible by 4 (YES answer)
If X = 63, then (63)(62)(61) has NO factor divisible by 4 (NO answer)
Together, INSUFFICIENT
Final Answer: E
These individual concepts can (and likely will) show up on the GMAT, but they're not necessarily going to show up "packaged" this way.
GMAT assassins aren't born, they're made,
Rich
