If ZY<XY<0 , is |X-Z|+|X|=|Z| 1. Z is less than X 2. Y : DS Archive
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# If ZY<XY<0 , is |X-Z|+|X|=|Z| 1. Z is less than X 2. Y

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Director
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If ZY<XY<0 , is |X-Z|+|X|=|Z| 1. Z is less than X 2. Y [#permalink]

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09 Aug 2007, 18:39
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If ZY<XY<0 , is |X-Z|+|X|=|Z|

1. Z is less than X
2. Y is greater than 0

Last edited by trahul4 on 09 Aug 2007, 19:12, edited 3 times in total.
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Re: DS : Absolute Values [#permalink]

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09 Aug 2007, 20:02
trahul4 wrote:
If ZY<XY<0 , is |X-Z|+|X|=|Z|

1. Z is less than X
2. Y is greater than 0

Got B, but not really sure.
OA?

Is |X-Z| + |X| = |Z| ?

(1) Z<X
Knowing this, we know that X-Z > 0
We have
X-Z + |X| = |Z|
From this, we have no idea if X or Z is positive or negative.
Say if X and Z are both negative
X-Z - X = -Z => X-Z = X-Z Yes!
Say if X and Z are both positive
X-Z + X = Z => X-Z = Z-X No!
INSUFFICIENT.

(2) Knowing Y is greater than 0, both X and Z must be negative.
Using this, find two cases of |X-Z|
First case, X-Z > 0; thus, X>Z, we have
X-Z - X = -Z => X-X = -Z + Z Yes!
Second case, X-Z < 0; thus, X<Z, we have
-X+Z - X = -Z => -2X = -2Z => X=Z. This cannot be true due to the condition.
SUFFICIENT.
Director
Joined: 09 Aug 2006
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Re: DS : Absolute Values [#permalink]

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10 Aug 2007, 00:28
trahul4 wrote:
If ZY<XY<0 , is |X-Z|+|X|=|Z|

1. Z is less than X
2. Y is greater than 0

Getting B.

Stat1: Z<X
If Z=4 X=5 then no
If Z=-5 X=-4 then yes
insuff.

Stat2:
Both X and Z have to be -ve and Z<X.
Plug in any value satisfying the above and the answer is always yes.
Suff.
Director
Joined: 16 May 2007
Posts: 549
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Kudos [?]: 59 [0], given: 0

Re: DS : Absolute Values [#permalink]

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11 Aug 2007, 04:06
bkk145 wrote:
trahul4 wrote:
If ZY<XY<0 , is |X-Z|+|X|=|Z|

1. Z is less than X
2. Y is greater than 0

Got B, but not really sure.
OA?

Is |X-Z| + |X| = |Z| ?

(1) Z<X> 0
We have
X-Z + |X| = |Z|
From this, we have no idea if X or Z is positive or negative.
Say if X and Z are both negative
X-Z - X = -Z => X-Z = X-Z Yes!
Say if X and Z are both positive
X-Z + X = Z => X-Z = Z-X No!
INSUFFICIENT.

(2) Knowing Y is greater than 0, both X and Z must be negative.
Using this, find two cases of |X-Z|
First case, X-Z > 0; thus, X>Z, we have
X-Z - X = -Z => X-X = -Z + Z Yes!
Second case, X-Z < 0; thus, X<Z> -2X = -2Z => X=Z. This cannot be true due to the condition.
SUFFICIENT.

Well done. OA is B. Was it easy ? I just gave it up and guessed it in my GMATPrep
Re: DS : Absolute Values   [#permalink] 11 Aug 2007, 04:06
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