Data Sufficiency

Deepthi Subbu wrote:If |x| = |2y| , what is the value of x - 2y?
(1) x + 2y = 6
(2) xy>0

Dear Deepthi Subbu,
I'm happy to help with this.

From the prompt information, we have no idea whether both x & y are positive, both negative, or one positive and one negative.

Statement #1: x + 2y = 6
If x & y are both positive, then x = 2y, so x + 2y = x + x = 6 ----> x = 2y = 3, and x - 2y = 0
If one is positive and one is negative, then x = - 2y, and then x + 2y would have to have a sum of zero, and it would not be possible to equal 6.
If both are negative, the sum x + 2y would be negative, and it would not be possible to equal 6.
Thus, this statement requires that x & y are both positive, and therefore we can calculate the numerical value of x - 2y. This statement, alone and by itself is sufficient.

Statement #2: (xy) > 0
This tells us, x & y are either both positive or both negative. We know x = 2y, which means x - 2y = 0. Voila! This statement, alone and by itself is sufficient

Answer = D

Does this make sense?
Mike