Hi Uva@90,

This question can be solved by TESTing VALUES.

We're told that X and Y are INTEGERS and that Y = |X+3| + |4 - X|. We're asked if Y equals 7. This is a YES/NO question.

Fact 1: X < 4

IF...
X = 3
Y = |3+3| + |4-3| = 7 and the answer to the question is YES

IF...
X = -10
Y = |-10+3| + |4-(-10)| = 21 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: X > -3

IF...
X = 3
Y = |3+3| + |4-3| = 7 and the answer to the question is YES

IF...
X = 10
Y = |10+3| + |4-10| = 19 and the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know...
-3 < X < 4

Since X is an INTEGER, there are a limited possible number of values for X: -2, -1, 0, 1, 2, and 3. If you TEST each of these values, you'll find that the resulting sum is ALWAYS 7. It'll take a bit of work, but the work is easy.
Combined, SUFFICIENT

Final Answer: C

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