|x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2
[spoiler]OA: D[/spoiler]
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tough one
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|x+2|=|y+2| implies TWO CASES:buoyant wrote:|x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2
[spoiler]OA: D[/spoiler]
Case 1: No signs changed
x+2 = y+2
x=y.
Case 2: Signs changed on ONE SIDE
x+2 = -(y+2)
x+2 = -y-2
x+y = -4.
Thus, |x+2|=|y+2| implies that x=y and/or that x+y=-4.
Statement 1: xy<0
Implication:
It is not possible that x=y.
Thus, x+y = -4.
SUFFICIENT.
Statement 2: x>2, y<2
Implication:
It is not possible that x=y.
Thus, x+y = -4.
SUFFICIENT.
The correct answer is D.
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The prompt indicates that |x+2| = |y+2|.buoyant wrote:Mitch,
in each statement even though case 1 doesn't hold good, how do we know that case 2 will apply. the information may be insufficient right?
This equation REQUIRES that Case 1 be true (x=y) or that Case 2 be true (x+y = -4).
Thus, if x≠y, then Case 2 must be true, implying that x+y = -4.
Since each statement indicates that x≠y, we know in each statement that x+y = -4.
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