Deepthi Subbu wrote: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
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