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Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
 04 Oct 2009, 23:26
Question Stats:
55% (01:49) correct
44% (00:37) wrong based on 5 sessions
Is |x| = y - z ? (1) x + y = z (2) x < 0
Last edited by Bunuel on 11 Feb 2012, 13:04, edited 2 times in total.
Edited the question and added the OA
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Re: Abs equation from GMATPrep [#permalink]
05 Oct 2009, 05:31
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sayak636 wrote: Is |X|= Y- Z?
1. X+Y= Z
2. X< 0 (1) Can be rewritten as X = -Y + Z, so |X| = |-Y + Z|, which would be equal to Y - Z, if and only if -Y+Z\leq0. Obviously, we don't know that, so (1) insufficient. (2) Cannot be sufficient, it doesn't say anything about Y and Z. (1) and (2) together: X = -Y + Z < 0, therefore |X| = Y - Z, sufficient. Answer: C
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Re: Abs equation from GMATPrep [#permalink]
05 Oct 2009, 02:49
From 1, we get x= z-y => -x= y-z
Thus, |x| = y-z
Statement 2 does not give us anything more.
So, A.
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Re: Abs equation from GMATPrep [#permalink]
05 Oct 2009, 05:58
Bunuel wrote: y-z=|x|? --> y-z must be >=0... Brilliant, thank you! :^)
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Re: Abs equation from GMATPrep [#permalink]
17 Oct 2009, 15:04
pm4553 wrote: eresh wrote: From 1, we get x= z-y => -x= y-z
Thus, |x| = y-z
Statement 2 does not give us anything more.
So, A. For Abs Q's, you'll always have 2 solutions; A is insuff. Oh...My bad...got that now :D
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Re: Inequality Problem [#permalink]
01 Aug 2010, 14:15
is |x|=y-z?
given:
(1) x+y=z
(2) x<0
solving (1) first:
y=z-x
|x|=(z-x)-z
|x|=-x
take x=1, z=2, y=1
1=1-2 (no)
take x=-1, z=2, y=3
|x|=y-z?
|-1|=3-2=1 YES
so what solving for |x|=-x meant was that x MUST be negative for the equation to be true, if it is positive then it is not true (since in that case, |x| would not equal -x).
hence the answer is C.
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
24 Apr 2012, 00:01
Hey Bunuel I am not very sure of what the question is asking ... Can you please explain the question....
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
24 Apr 2012, 12:11
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Is |X|= Y- Z?
1. X+Y= Z
2. X< 0
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Re: Abs equation from GMATPrep [#permalink]
05 Oct 2012, 05:44
Bunuel wrote: Is |x|=y-z?
Note that y-z must be \geq{0}, because absolute value (in our case |x|) can not be negative.
Generally question asks whether y-z\geq{0} and whether the difference between them equals to |x|.
(1) -x=y-z
if x>0 --> y-z is negative --> no good for us;
if x\leq{0} --> y-z is positive --> good.
Two possible answers not sufficient;
(2) x<0
Not sufficient (we need to know value of y-z is equal or not to |x|)
(1)+(2) Sufficient.
Answer: C. Hi bunuel, I am not able to understand the solution for this problem. Can you kindly explain the highlighted areas. Note that y-z must be \geq{0}, because absolute value (in our case |x|) can not be negative. Generally question asks whether y-z\geq{0} and whether the difference between them equals to |x|. (1) -x=y-z if x>0 --> y-z is negative --> no good for us; if x\leq{0} --> y-z is positive --> good. Waiting for reply.
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Re: Abs equation from GMATPrep [#permalink]
05 Oct 2012, 06:12
fameatop wrote: Bunuel wrote: Is |x|=y-z?
Note that y-z must be \geq{0}, because absolute value (in our case |x|) can not be negative.
Generally question asks whether y-z\geq{0} and whether the difference between them equals to |x|.
(1) -x=y-z
if x>0 --> y-z is negative --> no good for us;
if x\leq{0} --> y-z is positive --> good.
Two possible answers not sufficient;
(2) x<0
Not sufficient (we need to know value of y-z is equal or not to |x|)
(1)+(2) Sufficient.
Answer: C. Hi bunuel, I am not able to understand the solution for this problem. Can you kindly explain the highlighted areas. Note that y-z must be \geq{0}, because absolute value (in our case |x|) can not be negative. Generally question asks whether y-z\geq{0} and whether the difference between them equals to |x|. (1) -x=y-z if x>0 --> y-z is negative --> no good for us; if x\leq{0} --> y-z is positive --> good. Waiting for reply. Look at |x|=y-z: the left hand side is absolute value (|x|), which cannot be negative, hence the right hand side (y-z) also cannot be negative. Therefore must be true that y-z\geq{0}. Next, for (1) given that -x=y-z. Now, if x>0, or if x is positive, then we'll have that -positive =y-z --> negative=y-z. But as we concluded above y-z cannot be negative, hence this scenario is not good. Hope it's clear.
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Re: Abs equation from GMATPrep [#permalink]
25 Nov 2012, 18:17
The question poses as x being the centerpiece variable but Bunuel turns it on its face and makes y-z the main subject. Which makes all the difference with data pt 1 when u look at it as y-z=-x. You immediately see that the right side has to be -ve for the LEft side to be +ve. Brilliant approach. Bunuel wrote: Is |x|=y-z?
Note that y-z must be \geq{0}, because absolute value (in our case |x|) can not be negative.
Generally question asks whether y-z\geq{0} and whether the difference between them equals to |x|.
(1) -x=y-z
if x>0 --> y-z is negative --> no good for us;
if x\leq{0} --> y-z is positive --> good.
Two possible answers not sufficient;
(2) x<0
Not sufficient (we need to know value of y-z is equal or not to |x|)
(1)+(2) Sufficient.
Answer: C.
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Re: Abs equation from GMATPrep
[#permalink]
25 Nov 2012, 18:17
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