GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 Jan 2020, 09:13

### 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

# A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang

Author Message
TAGS:

### Hide Tags

Intern
Joined: 05 Jun 2013
Posts: 5
GPA: 3.7
A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

02 Jul 2013, 23:30
5
24
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:08) correct 36% (02:00) wrong based on 454 sessions

### HideShow timer Statistics

A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?

(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.
Math Expert
Joined: 02 Sep 2009
Posts: 60646
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

02 Jul 2013, 23:39
6
9
A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?

(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined

The median of a set with even (8) terms is the average of two middle terms, thus $$median = \frac{-4+4}{2} = 0$$.

$$mean = \frac{x - 8 - 5 - 4 + 4 + 6 + 9 + y}{8} = 0 = median$$ --> $$2 + x + y = 0$$ --> $$x + y = -2$$.

Now, since the elements in the set are arranged in increasing order, then $$x<0$$ and $$y>0$$, so $$|x|-|y|=-x-y=-(x+y)=-(-2)=2$$.

_________________
##### General Discussion
Senior Manager
Joined: 24 Aug 2009
Posts: 438
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

02 Jul 2013, 23:42
1
2
A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.

Median of the set = (-4+4)/2 = 0
As per statement, Mean of the set = 0

Mean of the set
|y|- |x| +19-17 = 0 (where x is negative n y is positive)
|y|- |x| = -2

So the absolute difference between two numbers is 2
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10011
Location: Pune, India
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

02 Jul 2013, 23:51
2
4
vtran wrote:
A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?

(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.

Alternatively, you can use the concept of deviation from mean to solve it.

Median is average of middle two terms = (-4 + 4)/2 = 0
So mean = 0 too.
Now notice the terms on either side of mean.
-4 is 4 less than 0 but 4 is 4 more so they balance out.
-5 is 5 less but 6 is 6 more so there is an extra positive 1.
-8 and 9 have an extra positive 1 too.
To get a mean of 0, x should have negative 2 more than y i.e. x = -12, y = 10 or x = -13, y = 11 etc.
In any case, |x|-|y| = 2

Check this post for more on this method: http://www.veritasprep.com/blog/2012/05 ... eviations/
_________________
Karishma
Veritas Prep GMAT Instructor

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15975
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

12 Sep 2015, 16:13
1
Hi,

This question is built around a number of statistics concepts and you have to pay careful attention to how you organize your work.

The prompt gives us a number of Facts to work with:
1) We're given the following set of values: {X, -8, -5, -4, 4, 6, 9, Y}
2) We're told that they are in INCREASING order
3) We're told the Median and the Mean are the SAME

We're asked for the value of |X| - |Y|

Since there are 8 terms, the Median will equal the average of the 'middle two' terms. Those 'middle two' terms are -4 and 4, so the Median is 0 (and since the Median = the Mean, the overall average is 0). Since the overall average is 0, the sum of the 8 terms MUST be 0...

Adding up the terms, we have...
X + Y + 2

So, since X+Y+2 = 0....

X+Y = -2

At this point, since X and Y have an established relationship, we can use any pair of values that fits all of the facts...We can TEST VALUES to prove the answer....

IF....
X = -12
Y = 10

|-12| - |10| = +2

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 13 Jun 2012
Posts: 197
Location: United States
WE: Supply Chain Management (Computer Hardware)
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arranged in incr  [#permalink]

### Show Tags

12 Sep 2015, 16:33
1
This is what I did, we know Median which is 0 ( -4+ 4/2),. since Mean is same, it has to be 0. ( x, -8, -5, -4, 4, 6, 9, y ) so how will it be 0. if x, -8, -5, -4 = 4, 6, 9, y .

hence the number is x -12 and and y 10. D is the answer.
Senior Manager
Joined: 20 Aug 2015
Posts: 382
Location: India
GMAT 1: 760 Q50 V44
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

13 Sep 2015, 09:54
A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?

A. -1
B. 0
C. 1
D. 2
E. Cannot be determined.

S = { x, -8, -5, -4, 4, 6, 9, y } with elements arranged in increasing order
This means x < 0 and y > 0.

The median of a series with even numbers is the average of the middle two numbers
Hence the median here is (-4 + 4)/2 = 0

Mean = sum of all the terms/ no. of terms
(x - 8 -5 -5 +4 +6 +9 + y)/8 = 0 (Given that median = mean)

Hence, x + y = 2
We need to find |x| - |y|
and we know that x < 0 and y > 0

Opening the modulus with appropriate signs:
Modulus of any number is the absolute value of the number, or simply the positive value
Always remember that the modulus of a negative number opens with a negative sign and of a positive number opens with a positive sign

We have ,
|x| - |y| = -x - y = -(x + y) = -(-2) = 2
Hence Option D
Math Expert
Joined: 02 Aug 2009
Posts: 8336
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arranged in incr  [#permalink]

### Show Tags

02 Apr 2016, 07:51
1
1
A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?

A. -1
B. 0
C. 1
D. 2
E. Cannot be determined.

Hi,
the set is
{ x, -8, -5, -4, 4, 6, 9, y }
median is the center of middle 2 numbers as number of elements in set is EVEN..
median= (-4+4)/2=0..
it is given MEAN = MEDIAN..
so MEDIAN= MEAN = { x +(-8)+( -5)+( -4)+ 4+ 6+ 9+ y }/8 = 0
$$\frac{(x+y+2)}{8}=0$$..
or x+y+2=0..
x= -(y+2)
|x|=(y+2)..
so
|x|-|y|= |y+2|-|y|= y+2-y=2
D
_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3286
Location: India
GPA: 3.12
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arranged  [#permalink]

### Show Tags

14 Oct 2016, 00:13
We know that the median in this set is 0
If the mean of this set must be equal to 0,
the sum of elements in the set must always be zero

Adding the terms, we get x-17+19+y = 0
This is only possible when -x = 2+y eg, if y = 10, x=-12
Since x will always bme greater than y & we will have a difference of 2.

mod(x) - mod(y) = 2 always(Option B)
_________________
You've got what it takes, but it will take everything you've got
Intern
Joined: 17 Nov 2016
Posts: 24
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

04 Mar 2018, 16:16
Quote:
Now, since the elements in the set are arranged in increasing order, then x<0x<0 and y>0y>0, so |x|−|y|=−x−y=−(x+y)=−(−2)=2|x|−|y|=−x−y=−(x+y)=−(−2)=2.

Can you please elaborate more on how you came up with -x-y from |x|−|y|?
Intern
Joined: 15 Oct 2016
Posts: 28
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

04 Mar 2018, 19:59
Zoser wrote:
Quote:
Now, since the elements in the set are arranged in increasing order, then x<0x<0 and y>0y>0, so |x|−|y|=−x−y=−(x+y)=−(−2)=2|x|−|y|=−x−y=−(x+y)=−(−2)=2.

Can you please elaborate more on how you came up with -x-y from |x|−|y|?

For x<0, |x|= -x because anything thatches out of || has to be a non negative number (and we know that x is negative).
Since, y is positive,, |y| = y

However, a more intuitive way to look at this problem is that it is asking you for the difference of magnitudes of x and y.

We know that, the remaining elements (except x and y) add upto 2 and to nullify the same you need the magnitude of X greater than that of Y by 2 units.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4228
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

25 May 2018, 18:26
Top Contributor
vtran wrote:
A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?

(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.

First off, the question tells us that the numbers are arranged in ascending order.
So, we know that x ≤ -8, and y ≥ 9

There are 8 elements in the set. So, the median = the average of the two middlemost values.
Here, the two middlemost values are -4 and 4
So, the median = (-4 + 4)/2 = 0/2 = 0

Since the median and the mean of the set are EQUAL, we know that the mean is also 0

That is, [x + (-8) + (-5) + (-4) + 4 + 6 + 9 + y]/8 = 0
Multiply both sides by 8 to get: x + (-8) + (-5) + (-4) + 4 + 6 + 9 + y = 0
Simplify: x + y + 2 = 0
This means x + y = -2

So, here's what we know:
x + y = -2
x ≤ -8
y ≥ 9

Let's find some values of x and y and see where this leads us....

x = -12 and y = 10
In this case, |x|-|y|= |-12|-|10| = 12 - 10 = 2

x = -13 and y = 11
In this case, |x|-|y|= |-13|-|11| = 13 - 11 = 2

x = -12.5 and y = 10.5
In this case, |x|-|y|= |-12.5|-|10.5| = 12.5 - 10.5 = 2

x = -100 and y = 98
In this case, |x|-|y|= |-100|-|98| = 100 - 98 = 2

As we can see, the answer will always be 2

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Manager
Joined: 17 Oct 2015
Posts: 146
Location: India
Concentration: Finance
Schools: ISB '21
GMAT 1: 690 Q47 V37
GMAT 2: 700 Q44 V41
WE: Corporate Finance (Commercial Banking)
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang  [#permalink]

### Show Tags

06 Nov 2019, 08:29
vtran wrote:
A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?

(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.

Thus, Mean is also = 0
Solving we get.....--> x+y+2=0,

==> x+y=-2

x= -2-y

as x<0, mod x = 2+y
as y>0, mod y = y

Therefeore, mod x - mod y= 2+y-y ==> 2
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang   [#permalink] 06 Nov 2019, 08:29
Display posts from previous: Sort by