rakeshd347 wrote:Is |x-y|>|x|-|y| ?
(1) y < x
(2) xy < 0
OA to follow soon.
|x-y| = the DISTANCE between x and y.
Statement 1: y<x
Case 1: Try to MAXIMIZE the distance between x and y by giving them DIFFERENT SIGNS.
If y=-1 and x=2, then |x-y| = 3 and |x|-|y| = 1.
In this case, |x-y| > |x|-|y|.
Case 2: Try to MINIMIZE the distance between x and y by giving them the SAME SIGN.
If y=1 and x=2, then |x-y| = 1 and |x|-|y| = 1.
In this case, |x-y| = |x|-|y|.
Since in the first case |x-y| > |x|-|y|, and in the second case |x-y| = |x|-|y|, INSUFFICIENT.
Statement 2: xy<0
Case 1 also satisfies statement 2.
In this case, y<x.
Check what happens when xy<0 and x<y.
Case 3: xy<0 and x<y
If x=-1 and y=2, then |x-y| = 3 and |x|-|y| = -1.
As in Case 1, |x-y| > |x|-|y|.
Implication:
If xy<0, then |x-y| > |x|-|y|.
SUFFICIENT.
The correct answer is
B.
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