Hi All,
This question has some interesting 'pattern-matching shortcuts' built into it that you can take advantage of IF you take enough notes.
We're told that X and Y are NON-0 INTEGERS and |X| + |Y| = 32. We're asked for the value of (X)(Y).
Before dealing with the two Facts, it's worth noting that the prompt provides a significant limitation on the possible values of X and Y. Since the absolute values will turn negative results into positive ones, and the variables CANNOT be 0, there really are NOT that many possible values for X and Y.
+-1 and +-31
+-2 and +-30
+-3 and +-29
Etc.
We can use this to our advantage when dealing with the two Facts....
Fact 1: -4X - 12Y = 0
Here, we can do some algebra to simplify the equation...
-4X = 12Y
-X = 3Y
This tells us that one variable MUST be POSITIVE and one MUST be NEGATIVE. When we include the absolute value equation given in the prompt, we know that one absolute value must be 3 times the value of the other....
That leaves us with two options for X and Y....
X = +24 and Y = -8
or
X = -24 and Y = +8
Either way, we get the SAME PRODUCT: -192
Fact 1 is SUFFICIENT
Fact 2: |X| – |Y| = 16
Here, we can use the work we did in Fact 1 to save us some time (and help us create some new possibilities)...
IF...
X = +24, Y = -8, the answer to the question is -192
IF...
X = +24, Y = +8, the answer to the question is +192
Fact 2 is INSUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich