2014-09-15 09:00:18

If |x - 2| + 6 = 9, and |y + 3| + 4 = 11, then xy could be:

(A) -10
(B) -5
(C) -4
(D) 4
(E) 50

The correct answer is E
Explanation: Start by simplifying each expression:

|x - 2| + 6 = 9 simplifies to |x - 2| = 3.
|y + 3| + 4 = 11 simplifies to |y + 3| = 7.

Both expressions involve absolute values, which means that both equations will provide 2 solutions: a positive one and a negative one (that is, |x - 2| = 3 means that either x -2 is 3 or x - 2 is -3). Thus, solve both equations for both the positive and negative solutions.

If x - 2 = 3, then x is 5.
If x - 2 = -3, then x is -1.

If y + 3 = 7, then y is 4.
If y + 3 = -7, then y is -10.

Finally, multiply the different x and y solutions together to find possible values of xy:

5 times 4 is 20
5 times 10 is 50
-1 times 4 is -4
-1 times -10 is 10

Of these, only 50 is an answer choice, making E correct.