Mo2men wrote:Is |x−z−y| > x−z+y?
(1) 0<x<z<y
(2) (x-z-y) is negative
Statement 1: 0<x<z<y
Since x<z, x-z < 0.
Inequalities in which the <> faces the SAME DIRECTION can be ADDED TOGETHER.
Adding together x-z < 0 and 0 < y, we get:
(x-z) + 0 < 0 + y
x-z-y < 0.
Since x-z-y < 0, |x-z-y| = -(x-z-y).
Substituting |x-z-y| = -(x-z-y) into the question stem, we get:
Is -(x-z-y) > x-z+y?
Simplifying the question stem, we get:
-(x-z-y) > x-z+y ?
-x+z+y > x-z+y ?
2z > 2x ?
z > x ?
Since Statement 1 indicates that z>x, the answer to the question stem is YES.
SUFFICIENT.
Statement 2: (x-z-y) is negative
As shown in the blue portion above, x-z-y < 0 enables us to rephrase the question stem as follows:
z > x ?
x-z-y < 0 implies that z > x-y.
No way to determine whether z>x.
INSUFFICIENT.
The correct answer is
A.
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