jainrahul1985 wrote:If zy < xy < 0, is |x - z | + |x | = |z | ?
(1) z < x
(2) y > 0
OA D
This is a strange question.
The question stem itself gives sufficient information.
|x-z| = the positive distance between x and z.
From the question stem: zy < xy < 0.
If y<0:
Then x>0, z>0, and z>x, so that zy < xy < 0.
For example, if we plug y=-1, x=1 and z=2 into zy < xy < 0, we get:
-2 < -1 < 0.
Viewed on the number line:
The drawing above shows that |x-z| + |x| = |z|.
If y>0:
Then x<0, z<0 and z<x, so that zy < xy < 0.
For example, if we plug y=1, x=-1 and z=-2 into zy < xy < 0, we get:
-2 < -1 < 0.
Viewed on the number line:
The drawing above shows that |x-z| + |x| = |z|.
The information in the question stem itself proves that |x-z| + |x| = |z|.
The statements are irrelevant.
Thus, statement 1 is "sufficient", because -- no matter what information it offers -- |x-z| + |x| = |z|.
Thus, statement 2 is "sufficient", because -- no matter what information it offers -- |x-z| + |x| = |z|.
The correct answer is
D.
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