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What is the value of x given that |x - y| = |x - z|

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What is the value of x given that |x - y| = |x - z| [#permalink] New post 16 Jul 2003, 13:27
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42% (02:46) correct 58% (01:42) wrong based on 62 sessions
What is the value of x given that |x - y| = |x - z|

(1) y is not equal to z
(2) The sum of y and z is 10.
[Reveal] Spoiler: OA

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AkamaiBrah
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Vice President, Midtown NYC Investment Bank, Structured Finance IT
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MBA, Anderson School of Management, UCLA, Class of 1993


Last edited by Bunuel on 29 Jun 2015, 03:02, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: What is the value of x given that |x - y| = |x - z| [#permalink] New post 16 Jul 2003, 15:42
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Took me a while by trial and error...not sure if there is quick way to do this, but I got x = 5. [/quote]
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Re: What is the value of x given that |x - y| = |x - z| [#permalink] New post 16 Jul 2003, 15:42
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Took me a while by trial and error...not sure if there is quick way to do this, but I got x = 5. [/quote]
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Re: What is the value of x given that |x - y| = |x - z| [#permalink] New post 16 Jul 2003, 20:42
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must be C, cause if y may be equal z, then in B we have indifinite number of solutions.
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Re: What is the value of x given that |x - y| = |x - z| [#permalink] New post 16 Jul 2003, 21:27
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(1) restated says that X must be the average of Y and Z, but we don't know anything about Y and Z so it is not sufficient

(2) restated says that the average of Y and Z is 5, but since we don't know if Y is equal to Z or not, we don't know whether X = 5 is the solution, or whether there are an infinite number of solutions.

(1) and (2) combined says (from 1) that X = (Y + Z)/2 and (from 2) say that Y + Z = 10, hence we can solve for X and C is the answer.
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Re: What is the value of x given that |x - y| = |x - z| [#permalink] New post 16 Jul 2003, 21:44
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My solution:

Opening up up moduls, we get 4 combinations, of which 2 pairs are identical: Y=Z or 2X=Y+Z

(1) Y is not Z means that we have to deal with the second 2X=Y+Z, but we cannot find X

(2) Y+Z=10 fits for the second option but is of no use for the first, since there is no X.

Combine: the initial equation boils down to 2X=Y+Z that can be solved via the second set of data. X=5. Thus, it is C.
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Re: What is the value of x given that |x - y| = |x - z| [#permalink] New post 17 Jul 2003, 07:00
stolyar wrote:
My solution:

Opening up up moduls, we get 4 combinations, of which 2 pairs are identical: Y=Z or 2X=Y+Z

(1) Y is not Z means that we have to deal with the second 2X=Y+Z, but we cannot find X

(2) Y+Z=10 fits for the second option but is of no use for the first, since there is no X.

Combine: the initial equation boils down to 2X=Y+Z that can be solved via the second set of data. X=5. Thus, it is C.



working with your formula which I did to:
Where
2x=y+z
2x=10
x=5

Hence B clearly gives you the answer. correct me if I am wrong. Why do we need the first statement at all.
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Re: What is the value of x given that |x - y| = |x - z| [#permalink] New post 17 Jul 2003, 10:15
satgates wrote:
stolyar wrote:
My solution:

Opening up up moduls, we get 4 combinations, of which 2 pairs are identical: Y=Z or 2X=Y+Z

(1) Y is not Z means that we have to deal with the second 2X=Y+Z, but we cannot find X

(2) Y+Z=10 fits for the second option but is of no use for the first, since there is no X.

Combine: the initial equation boils down to 2X=Y+Z that can be solved via the second set of data. X=5. Thus, it is C.



working with your formula which I did to:
Where
2x=y+z
2x=10
x=5

Hence B clearly gives you the answer. correct me if I am wrong. Why do we need the first statement at all.


If y = z, then |x| = |x| and x can be ANYTHING. Hence, you need (1) to pin down x = 5.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Re: What is the value of x given that |x - y| = |x - z| [#permalink] New post 29 Jun 2015, 02:17
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Re: What is the value of x given that |x - y| = |x - z|   [#permalink] 29 Jun 2015, 02:17
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