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|x – y|>|x-z|?

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Source: — Data Sufficiency |
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by thephoenix » Fri Feb 19, 2010 9:09 pm
gmatnmein2010 wrote:Is |x - y|>|x-z|?

1)|y|>|z|
2) z<0

rephrasing modulus always helps
|x - y|>|x-z|=
(x-y)^2>(x-z)^2=
(x-y)^2-(x-z)^2>0=
(x-y-x+z). (2x-y-z) >0

to get an ans we must have relationship b/n x,yand z in a no. line

1) provides relationship b/n Y and z and also we dnt knw how these are related to 0
hence insuff

2) insuff..

1+2) insuff no information abt x
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by girish3131 » Tue Mar 09, 2010 3:45 am
IMO E

plz put OA

ta
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by firdaus117 » Tue Mar 09, 2010 4:41 am
Rephrasing the question,we can say that the question asks if the given statements are sufficient to prove that "the distance between x and y is greater than that between x and z or not".
Statement I
The absolute value of y is greater than that of z.No information about x.Hence insufficient.
e.g.For y=-5, z=-1, x=-2, |x - y|=3 , |x-z|=1 gives |x - y|>|x-z|
But for y=-5,z=-1,x=-4 , |x - y|=1 , |x-z|=3 gives |x - y|<|x-z|
Statement II
z<0.Again nothing about x.Insufficient.In above examples, z<0
Combining both we again can't say anything.Above two examples satisfying both conditions yet inconclusive.
Hence,Option E
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