Is |x-y| |x|-|y|? A. x y B. xy

Question

Is |x-y| > |x|-|y|?

A. x > y
B. xy < 0

GMATBLACKBELT · Answer

Test values

1: x=2 y=1 No these are equal. x=-1 y=-2. we have a Yes
Insuff.

2: one of these is negative. x=-1 y=-2 we have a Yes. x=-2 y=-1 we have No
Insuff.

Together. Suff.

C

maratikus · Answer

1) insufficient 
(3,-1) |3-(-1)| = 4 > |3| - |-1| = 2
(3,1) |3-1| = 2 = |3| - |1| = 2

2) sufficient
since xy < 0 -> |x-y| = |x| + |y| > |x| - |y| iff |y| > 0 which is true, because xy != 0

B is the answer

kanyshkae · Answer

I am a bit puzzled with the above answers.The way I reasoned is as follows:

(1) Given x > y. Thus, |x|>|y| and |x|-|y|> 0. (*)
As well, x-y>0. so |x-y|>0 (**). However, it is difficult to clearly ascribe a relative magnitude to * and **. So, unclear.

(2) Given xy<0. This leads to two cases.
***x<0 and y>0. While x-y < 0, |x-y|>0.
****x>0 and y<0. In this case, x-y >0 and |x-y|>0.
However, again it is unclear, the relative magnitude between |x-y| and |x|-|y|. So, this is unclear as well.

So, the answer is E.

pmenon · Answer

i just picked numbers for B, and considered all 4 cases .... in each case, the LS was > RS ... so suff.

neelesh · Answer

x = -2 , y = -5... while x > y but |x| < |y| ...

rishi2377 · Answer

Thx mates. 
OA is B ...guess what, this is a 720+ question on Prep. :p

Is |x-y| > |x|-|y|? A. x > y B. xy < 0

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