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Re: Abs equation from GMATPrep [#permalink]
05 Oct 2009, 04:31
12
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Expert's post
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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) 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 _________________
PhD in Applied Mathematics Love GMAT Quant questions and running.
Re: Inequality Problem [#permalink]
01 Aug 2010, 13:15
1
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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).
Re: Abs equation from GMATPrep [#permalink]
25 Nov 2012, 17:17
1
This post received KUDOS
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|)
Re: Abs equation from GMATPrep [#permalink]
01 Oct 2013, 09:41
1
This post received KUDOS
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.
Bunuel, I was wondering if we can square the sides and then evaluate:
Re: Abs equation from GMATPrep [#permalink]
05 Oct 2012, 04:44
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, 05:12
Expert's post
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.
Re: Abs equation from GMATPrep [#permalink]
02 Oct 2013, 01:28
Expert's post
emailmkarthik 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.
Bunuel, I was wondering if we can square the sides and then evaluate:
Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
29 Apr 2015, 12:21
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Re: Is |x| = y - z ? (1) x + y = z (2) x < 0 [#permalink]
13 Dec 2015, 10:39
DenisSh wrote:
Is |x| = y - z ?
(1) x + y = z (2) x < 0
Question: x=y-z (when x is +ve) or x=z-y (when x is -ve) (1) x=z-y, we don't know the sign of x (2) clearly not sufficient (1) + (2) from (2) we know that x<0 --> in this case |x| = y - z is equal to x=z-y and (1) gives us this expression Answer C _________________
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