Hi Maysaa,
This DS question is loaded with Number Property rules. If you understand (and can spot) those rules, then you'll be able to take advantage of many of the built-in patterns that will appear on Test Day (and save some time and effort).
Here, we're told that X is an INTEGER. The question asks if (X^2 + 1)(X+5) is even. This is a YES/NO question.
Even before we get to the two Facts, there's a pair of Number Properties built into the question.
IF X = ODD, then (X^2+1) = even and (X+5) = even, so the product will be (even)(even) = even.
IF X = EVEN then (X^2+1) = odd and (X+5) = odd, so the product will be (odd)(odd) = odd.
So, as complex as this question might look, it's really just asking "is X consistently even or consistently odd?"
In Fact 2, we're told that each prime factor of X^2 is greater than X. This means that X is NOT divisible by 2, 3, 5 or 7. Since we know that X is an integer, since it's NOT divisible by 2, it CANNOT be even. Thus, X MUST be odd. By extension, the answer to the question will ALWAYS be YES and Fact 2 is SUFFICIENT.
GMAT assassins aren't born, they're made,
Rich
