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

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

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02 Jul 2013, 22:30
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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.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43363
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang [#permalink]

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02 Jul 2013, 22:39
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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 $$|x|-|y|=-x-y=-(x+y)=-(-2)=2$$.

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Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang [#permalink]

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02 Jul 2013, 22:42
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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
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Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang [#permalink]

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02 Jul 2013, 22:51
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Expert's post
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/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 10734 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang [#permalink] ### Show Tags 12 Sep 2015, 15:13 1 This post received KUDOS Expert's post 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 Final Answer: [Reveal] Spoiler: D GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Joined: 13 Jun 2012
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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]

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12 Sep 2015, 15:33
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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.
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Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang [#permalink]

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13 Sep 2015, 08:54
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: 5537
Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arranged in incr [#permalink]

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02 Apr 2016, 06:51
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KUDOS
Expert's post
1
This post was
BOOKMARKED
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
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arranged [#permalink]

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13 Oct 2016, 23:13
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)
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Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang [#permalink]

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19 Dec 2017, 16:38
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Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang   [#permalink] 19 Dec 2017, 16:38
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