What is the value of x given that |x - y| = |x - z| : GMAT Data Sufficiency (DS)
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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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16 Jul 2003, 13:27
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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.
[Reveal] Spoiler: OA

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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
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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]

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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]

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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]

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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]

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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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AkamaiBrah
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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, 21:44
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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]

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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]

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

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

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07 Jul 2016, 03:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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, 02:40
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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, 21:56
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, 17:13
| 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, 06:16
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, 20:20
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] 12 Sep 2016, 20:20
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