Hi Mo2men,
There are some subtle Number Property rules in this question (which you'll have to do a little bit of work to define), but you can ultimately use a bit of 'brute force' math to get to the correct answer.
We're told that:
X + |X| + Y = 7
X + |Y| - Y = 6
Notice the role that the absolute value plays in each equation:
-In the first equation, IF X is negative or 0, then Y = 7.... but plugging Y=7 into the second equation gives us X = 6 (and THAT does not match X being negative or 0). Thus, X CANNOT be negative or 0.
-In the second equation, IF Y is positive or 0, then X = 6.... but plugging X = 6 into the first equations gives us Y = -5 (and THAT does not match Y being positive or 0). Thus Y CANNOT be positive or 0.
Now we know that X MUST be positive and Y MUST be negative. Since the answer choices are all simple integers, let's see what happens when we check simple integer values for X and Y (starting with the first equation)....
X=1, Y=5 --> doesn't fit the restriction that Y is negative.
X=2, Y=3 --> doesn't fit the restriction that Y is negative.
X=3, Y=1 --> doesn't fit the restriction that Y is negative.
X=4, Y=-1 --> fits BOTH equations, thus X+Y = 3
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
