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# Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0

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Senior Manager
Joined: 28 Jun 2007
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Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 [#permalink]  27 Oct 2007, 12:53
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Is |x - y| > |x| - |y|?

(1) y < x

(2) xy < 0
Manager
Joined: 19 Aug 2007
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1) if x > y then if theyre both positive then
|x-y| is the same as |x| - |y| so in this case |x-y| is not greater

but if x is positive and ys i negative, letws say x=3 and y=-2
then |x-y| = 5 which is greater than |x| - |y| = 1
insufficient

2) xy<0 means one is negative and one is positive.
if x is positive and y is negative, then we know that |x-y| is greater.

if x is negative and y is positive, lets say x=-2 and y=3
then |x-y| =5 and |x| - |y| is -1 so again its greater
so this should be sufficient.
can anyone confirm?
VP
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this post was edited !

this problem (as all absolute value problems do) ask you about distances on the number line.

You can ask ---> is the distance from x to y is greater then the difference in the distance from x to 0 and from y to 0.

statement 1

the distance from x to zero and y to zero will be greater then the distance of x to y only when x and y don't have the same sign.

insufficient

statement 2

the distance from x to zero and y to zero will be greater then the distance of x to y only when x and y don't have the same sign.

from statemtn 2 we can tell that x,y don't have the same sign !

sufficient.

Last edited by KillerSquirrel on 28 Oct 2007, 00:12, edited 3 times in total.
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Re: DS: absolute values [#permalink]  27 Oct 2007, 14:53
gluon wrote:
Is |x - y| > |x| - |y|?

(1) y < x
(2) xy < 0

B. if xy < 0, one is -ve and the other is +ve. so in that case, |x - y| > |x| - |y| is always true.
VP
Joined: 08 Jun 2005
Posts: 1147
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Re: DS: absolute values [#permalink]  28 Oct 2007, 00:13
GMAT TIGER wrote:
gluon wrote:
Is |x - y| > |x| - |y|?

(1) y < x
(2) xy < 0

B. if xy <0> |x| - |y| is always true.

Perfect !

see my edited post

Re: DS: absolute values   [#permalink] 28 Oct 2007, 00:13
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