Modulus

[Deepthi Subbu]

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

[Mike@Magoosh]

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

[GMATGuruNY]

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

Statement 1: x + 2y = 6
Thus, x = 6-2y.
Substituting x = 6-2y into |x| = |2y|, we get:
|6-2y| = |2y|.

Case 1: Signs unchanged
6-2y = 2y
6 = 4y
y = 3/2.
Thus, x = 6-2y = 6 - 2 * (3/2) = 3.
In this case, x-2y = 3 - 2 * (3/2) = 0.

Case 2: Signs of one side changed
-6+2y = 2y
-6=0.
Not possible.

Since only Case 1 is possible, x-2y=0.
SUFFICIENT.

Statement 2: xy>0
In other words, x and y have the SAME SIGN.
We must also satisfy the constraint that |x| = |2y|.

If y=1, then x=2.
In this case, x-2y = 2 - (2*1) = 0.

If y=-1, then x=-2.
In this case, x-2y = -2 - (2 * -1) = 0.
I'm almost convinced: x-2y = 0.

One more case to be safe:
If y=100, then x=200.
In this case, x-2y = 200 - (2*100) = 0.

Since x-2y = 0 in every case, SUFFICIENT.

The correct answer is D.