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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]

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Updated on: 29 Jun 2015, 04:02
2
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Difficulty:

85% (hard)

Question Stats:

47% (01:59) correct 53% (02:04) wrong based on 435 sessions

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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.

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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

Originally posted by AkamaiBrah on 16 Jul 2003, 14:27.
Last edited by Bunuel on 29 Jun 2015, 04:02, 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]

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16 Jul 2003, 16:42
1
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]

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16 Jul 2003, 16:42
1
1
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]

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16 Jul 2003, 21:42
1
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]

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16 Jul 2003, 22:27
2
(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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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]

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16 Jul 2003, 22:44
1
1
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]

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17 Jul 2003, 08:00
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]

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17 Jul 2003, 11:15
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]

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08 Jul 2016, 03:40
1
I've always found it easier to deal with mods by squaring

Since |x - y| = |x - z|

(x - y)^2 = (x -z)^2

So ( x - y + x -z )*(x - y - x + z ) = 0

(z - y) ( 2x - (y + z) = 0

1)
Z != y

so 2x = y + z.

No clue about y and z. A and D out

2) y + z = 10.
But if y = z
it holds true for all values of x.

So we need 1

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Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

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08 Jul 2016, 22:56
1
since the question says |x - y| = |x - z|. There are four possibilities :

(a) x>y and x<z ----> x-y = z-x ---> 2x = y+x
(b) x<y and x<z-----> y-x = z-x ---> y=z
(c) x>y and x>z -----> x-y = x-z ----> y=z
(d) x<y and x>z------> y-x = x-z ----> 2x= y+x

Now looking at options :

(1)y!=z

Eliminates (b) and (c).. But still don't know the value of y+z to evaluate x. INSUFFICIENT.

(2)y+z = 10

We can't eliminate any of (a) to (d) based on this. INSUFFICIENT.

Now (1) and (2)

We can find the value of x.

ANS: C

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Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

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05 Sep 2016, 18:13
| x - y | = | x - z |

can be written as

x - y = x - z OR x - y = z - x (Considering the two cases when we open the mod symbl)

Solving each of the above, we get two equation

1. y = z
or
2. 2x = y + z

Going to the statements, Statement 1 says y is not equal to z. So, we consider equation 2 as the valid case. However, no information about the values of y and z. hence, insufficient.

Statement 2 alone, does not clarify whether y=z. Hence, insufficient

Combining the two, we get our value of x.

Hence, C
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Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

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08 Sep 2016, 07:16
AkamaiBrah wrote:
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.

This is how interpret the question:

Given that |x - y| = |x - z|
This can be restated as x is equidistant from y and x is equidistant from z, on a number line

Statement 1 states y not equal to z
this means y=0, x=5, z=10 or y=-5 ,x=0, z=5 (and all such combinations) i.e. more than one value of x

Statement 2 states sum of y & z = 10
this means y=5, x=0, z=5 or y=-2, x=5, z=12 (and all such combinations) i.e, more than one value of x

st 1 & st 2 combine will always result in one value of x which is x=5
Hence C

Is this interpretation correct?
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Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

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12 Sep 2016, 21:20
can someone explain why B is not the answer ?

2x = y+z

stat ii) y+z =10

2x = 10 => so x = 5

am i missing anything ?
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Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

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26 Nov 2018, 13:48
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Re: What is the value of x given that |x - y| = |x - z|   [#permalink] 26 Nov 2018, 13:48
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