Hi ahmedshafea,

We're told that Y is INTEGER and that Y = |X| + X. We're asked if Y = 0. This is a YES/NO question. Before we deal with the two Facts, we can certainly 'rewrite' the given question. Y would equal 0 under two circumstances:
-If X is ANY NEGATIVE value.
-If X is 0.

Y would NOT equal 0 if X was a positive (in this situation, Y would equal 2X). Thus, the question is ultimately asking... "Is X less than OR equal to 0?"

1) X < 0

Fact 1 clearly defines X as negative, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) Y < 1

The prompt tells us that Y is an INTEGER - and since Y cannot be negative, the only integer that's possible here is 0. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich