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

It is currently 22 Oct 2019, 07:34

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If |x - y| = |x - z|, what is the value of x?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58431
If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 05 Jul 2018, 05:35
17
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

36% (02:21) correct 64% (02:29) wrong based on 295 sessions

HideShow timer Statistics

Most Helpful Expert Reply
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8006
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 05 Jul 2018, 09:33
4
1
If |x - y| = |x - z|, what is the value of x?

Now what does this mean...
This means that x is equidistant from y and z, but two options exist
[b][/b]
a) both y and z are on same side that is y=z
b) both are on either side of x then x will be the mean of y and z

(1) y < z
no numeric value ..
Only that \(y\neq{z}\) and hence x is MEAN of y and z
insuff


(2) The average (arithmetic mean) of y and z equal to the average (arithmetic mean) of y, z and 2.
\(\frac{y+z}{2}=\frac{y+z+2}{3}.........3y+3z=2y+2z+4......y+z=4\)
we can find mean of y and z as 4/2 = 2
so x=2 if \(y\neq{z}\)
But if y=z, value of x cannot be determined
insuff

combined
\(y\neq{z}\)
therefore x=2
suf
_________________
General Discussion
Director
Director
User avatar
G
Joined: 09 Aug 2017
Posts: 509
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 05 Jul 2018, 08:32
statement 1
y<z
this statement doesn't tell about X. not sufficient.

Statement 2
(X+Y)/2 = (X+Y+2)/3
X+Y= 4

x can be any number.
Not sufficient.

Statement 1 + statement 2
many values for x.

so E is answer.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58431
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 05 Jul 2018, 08:35
Senior Manager
Senior Manager
User avatar
G
Joined: 19 Nov 2017
Posts: 253
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Premium Member
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 05 Jul 2018, 08:43
1
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION:



If |x - y| = |x - z|, what is the value of x?

(1) y < z
(2) The average (arithmetic mean) of x and y equal to the average (arithmetic mean) of x, y and 2.


I am not quite sure about this, BUT imo answer should be B.

Consider only statement B.
|x - y| = |x - z|
either
\(x-y = x-z\) => \(y=z\) (1)
or
\(-x+y = x-z\) => \(2x = y+z\) (2)

Statement 2 says
\((x+y)/2 = (x+y+2)/3\)
\(3x+3y = 2x+2y+4\)
\(x+y=4\) (3)

Substituting (3) in (2),

\(2x = 4-x + z\)
and \(z=y\) from (1)

\(2x = 4-x+4-x\)
\(4x=4\)
\(x=1\)
_________________

Vaibhav



Sky is the limit. 800 is the limit.

~GMAC
Director
Director
User avatar
P
Joined: 14 Dec 2017
Posts: 516
Location: India
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 05 Jul 2018, 10:02
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION:



If |x - y| = |x - z|, what is the value of x?

(1) y < z
(2) The average (arithmetic mean) of y and z equal to the average (arithmetic mean) of y, z and 2.



Given, |x - y| = |x - z|, which means distance of x from y & distance of x from z are equal.

so we have

(a) if (x - y) > 0 & (x - z) > 0, then y = z, & x can take any value

(b) if (x - y) < 0 & (x - z) < 0, then y = z, & x can take any value

(c) if (x - y) > 0 & (x - z) < 0, then x = (y + z)/2, & x > y , x < z & y < x < z

(d) if (x - y) < 0 & (x - z) > 0, then x = (y + z)/2, & x < y, x > z & z < x < y



Statement 1: y < z , hence case (d) is possible, x lies between y & z, as y < x < z. However not sufficient to find value of x.

Statement 2: \(\frac{(y + z)}{2}\) = \(\frac{(y + z + 2)}{3}\)

Simplifying this we get, y + z = 4, however we cannot say anything about of position of x & hence cannot calculate x.

Since y = z = 2, hence x can take any value

or y = 1, z = 3, then x = 2

Hence statement 2 is not sufficient.

Combining both Statements, we have y < z & y + z = 4. hence we have case (c), y < x < z

Hence x = (y + z)/2 = 4/2 = 2.

Combining both statements is Sufficient.

Answer C.



Thanks,
GyM
_________________
Intern
Intern
avatar
B
Joined: 17 Sep 2016
Posts: 40
GMAT 1: 640 Q44 V35
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 11 Jul 2018, 08:06
chetan2u wrote:
If |x - y| = |x - z|, what is the value of x?

Now what does this mean...
This means that x is equidistant from y and z, but two options exist
[b][/b]
a) both y and z are on same side that is y=z
b) both are on either side of x then x will be the mean of y and z

(1) y < z
no numeric value ..
Only that \(y\neq{z}\) and hence x is MEAN of y and z
insuff


(2) The average (arithmetic mean) of y and z equal to the average (arithmetic mean) of y, z and 2.
\(\frac{y+z}{2}=\frac{y+z+2}{3}.........3y+3z=2y+2z+4......y+z=4\)
we can find mean of y and z as 4/2 = 2
so x=2 if \(y\neq{z}\)
But if y=z, value of x cannot be determined
insuff

combined
\(y\neq{z}\)
therefore x=2
suf


Hi chetan, will you please explain second part explanation, why y=z cant determine value of x ?
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8006
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 11 Jul 2018, 08:42
akhiparth wrote:
chetan2u wrote:
If |x - y| = |x - z|, what is the value of x?

Now what does this mean...
This means that x is equidistant from y and z, but two options exist
[b][/b]
a) both y and z are on same side that is y=z
b) both are on either side of x then x will be the mean of y and z

(1) y < z
no numeric value ..
Only that \(y\neq{z}\) and hence x is MEAN of y and z
insuff


(2) The average (arithmetic mean) of y and z equal to the average (arithmetic mean) of y, z and 2.
\(\frac{y+z}{2}=\frac{y+z+2}{3}.........3y+3z=2y+2z+4......y+z=4\)
we can find mean of y and z as 4/2 = 2
so x=2 if \(y\neq{z}\)
But if y=z, value of x cannot be determined
insuff

combined
\(y\neq{z}\)
therefore x=2
suf


Hi chetan, will you please explain second part explanation, why y=z cant determine value of x ?



Now we know y+z=4 and that x is equidistant from y and z..
So if the layout is y.....x....z x is in middle of y and z or mean of y and z that is (y+z)/2=4/2=2......
So if y=0, z=4...............0.......x=2......4
Or if y =1 , z=3.............1....x=2.....3
BUT if y=z.... y+z=4, so y=z=2
But the problem lies here..
Every point will be equidistant from y and z now..
X=1....y and z=2.......1.....2&2
Or x=10, y and z=2.......... 2&2........10
So x can be any value
_________________
Manager
Manager
avatar
G
Joined: 20 Feb 2017
Posts: 162
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 11 Jul 2018, 09:25
|x - y| = |x - z|
Squaring both the side
x^2+y^2-2xy= X^2+z^2-2xz
y^2-z^2= 2x(y-z)
(y-z)(y+z)-2x(y-z)=0
(y-z)(y+z-2x)=0
From statement 1
y<z
hence y+z-2x=0
or y+z=2x
we don't know the value of y+z and hence insufficient
Statement 2
(y+z)/2 = (y+z+)2/3
3(y+z)=2(y+z+2)
y+z=4
our equation is (y-z)(y+z-2x)=0
so we don't know if y-z=0 or y+z-2x=0
hence we cannot put y+z = 4 here. Therefore Not sufficient
From both the statements,
we know y<z , hence y+z=2x or x=(y+z)/2 or x= 2 (sufficient)
Hence the answer is C
The explanation looks big but on real time this can be solved under a minute
_________________
If you feel the post helped you then do send me the kudos (damn theya re more valuable than $)
Intern
Intern
avatar
B
Joined: 08 May 2016
Posts: 1
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 07 Aug 2018, 01:04
Hi ,

Its not mentioned that these values are integers. This makes the whole situation different as x and take any value between
1 and 3
Please clarify
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58431
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 24 Dec 2018, 01:35
Manager
Manager
avatar
S
Joined: 24 Nov 2018
Posts: 107
Location: India
GPA: 3.27
WE: General Management (Retail Banking)
Premium Member
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 25 Dec 2018, 23:18
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION:



If |x - y| = |x - z|, what is the value of x?

(1) y < z
(2) The average (arithmetic mean) of y and z equal to the average (arithmetic mean) of y, z and 2.


If y=z, x can take any value, there are infinite possibilities for x.

Statement 1) y<z. No information about x. Insufficient.

Statement 2) (y+z)/2=(y+z+2)/3 or y+z=4. Simplifying Expression|x-y|=|x-z| to x=(y+z)/2 assuming x, y and z are distinct numbers. So, as mentioned above, if y=z, x can be anything to satisfy the expression. Insufficient.

(1)+(2),
Our assumption needed to find x is statement 1. i.e. y is not equal to z. So, Sufficient.

The correct answer is C.
_________________
Kudos encourage discussions. Share it to amplify collective education!
Director
Director
avatar
P
Joined: 31 Jul 2017
Posts: 512
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If |x - y| = |x - z|, what is the value of x?  [#permalink]

Show Tags

New post 25 Dec 2018, 23:55
1
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION:



If |x - y| = |x - z|, what is the value of x?

(1) y < z
(2) The average (arithmetic mean) of y and z equal to the average (arithmetic mean) of y, z and 2.


By Squaring on both sides, from the question, we have -

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

So either, y =z or y+z = 2x --------Eqn 1

Statement I:

z > y.. Insufficeint.

Statement II:

y + z = 4. This is tempting but from the given statement in the Question we don't know whether y = z or y+z = 2x

Combining I & II:

From I we have , z > y so z cannot be equal to y. Hence. y + z = 2x.

x = 2.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
GMAT Club Bot
Re: If |x - y| = |x - z|, what is the value of x?   [#permalink] 25 Dec 2018, 23:55
Display posts from previous: Sort by

If |x - y| = |x - z|, what is the value of x?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne