GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Jun 2019, 00:19 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  What is the value of x given that |x - y| = |x - z|

Author Message
TAGS:

Hide Tags

GMAT Instructor Joined: 07 Jul 2003
Posts: 726
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

2
18 00:00

Difficulty:   85% (hard)

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

HideShow timer Statistics

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.

_________________
Best,

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.
Intern  Joined: 23 Jun 2003
Posts: 14
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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]
Intern  Joined: 23 Jun 2003
Posts: 14
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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]
Manager  Joined: 07 Jul 2003
Posts: 54
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

1
must be C, cause if y may be equal z, then in B we have indifinite number of solutions.
GMAT Instructor Joined: 07 Jul 2003
Posts: 726
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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.
_________________
Best,

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
SVP  Joined: 03 Feb 2003
Posts: 1530
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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.
Manager  Joined: 07 Jul 2003
Posts: 56
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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.
_________________
Attain Moksha
GMAT Instructor Joined: 07 Jul 2003
Posts: 726
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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.
_________________
Best,

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
Manager  Joined: 03 May 2015
Posts: 184
Location: South Africa
GPA: 3.49
WE: Web Development (Insurance)
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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

_________________
Kudos if I helped Intern  Joined: 15 Jun 2016
Posts: 46
Location: India
Concentration: Technology, Strategy
GMAT 1: 730 Q50 V39 Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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

------------------------
Give Kudos pls if you find it helpful.
Manager  B
Joined: 17 Jun 2015
Posts: 201
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37 Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

| 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
_________________
Fais de ta vie un rêve et d'un rêve une réalité
Intern  Joined: 20 Jul 2016
Posts: 22
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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?
Manager  Joined: 15 Apr 2016
Posts: 68
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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 ?
_________________
Cheers,
Shri
-------------------------------
GMAT is not an Exam... it is a war .. Let's Conquer !!!
Non-Human User Joined: 09 Sep 2013
Posts: 11396
Re: What is the value of x given that |x - y| = |x - z|  [#permalink]

Show Tags

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: What is the value of x given that |x - y| = |x - z|   [#permalink] 26 Nov 2018, 13:48
Display posts from previous: Sort by

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