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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

02 Jul 2013, 22:30

4

17

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

66% (02:05) correct 34% (02:02) wrong based on 506 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|?

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

Show Tags

02 Jul 2013, 22:39

6

6

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 \(median = \frac{-4+4}{2} = 0\).

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

Show Tags

02 Jul 2013, 22:42

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.

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 Answer D
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

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

Show Tags

02 Jul 2013, 22:51

2

2

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|?

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

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

Show Tags

12 Sep 2015, 15:13

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....

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

Show Tags

12 Sep 2015, 15:33

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.

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

Show Tags

13 Sep 2015, 08:54

shasadou 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.

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

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

Show Tags

02 Apr 2016, 06:51

1

1

shasadou 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.

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
_________________

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

Show Tags

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)
_________________

You've got what it takes, but it will take everything you've got

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

Show Tags

04 Mar 2018, 15:16

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|?

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

Show Tags

04 Mar 2018, 18:59

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.

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

Show Tags

25 May 2018, 17:26

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|?

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

Answer: D

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com

gmatclubot

Re: A set S = { x, -8, -5, -4, 4, 6, 9, y } with elements arrang
[#permalink]
25 May 2018, 17:26