Author 
Message 
TAGS:

Hide Tags

Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 196
Location: Bangladesh
Concentration: Accounting
GMAT Date: 04062013
GPA: 3.65

Set S consists of 5 values, not necessarily in ascending [#permalink]
Show Tags
12 Dec 2012, 13:36
10
This post was BOOKMARKED
Question Stats:
36% (01:12) correct 64% (00:55) wrong based on 264 sessions
HideShow timer Statistics
Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S? (A) Zero (B) One (C) Two (D) Three (E) More than three
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 13 Dec 2012, 01:14, edited 1 time in total.
Renamed the topic and edited the question.



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 634
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: Set S consists of 5 values, not necessarily [#permalink]
Show Tags
12 Dec 2012, 23:15
2
This post received KUDOS
4
This post was BOOKMARKED
mun23 wrote: Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S? (A)0 (B)1 (C)2 (D)3 (E)More than 3
Need details explanation............. There could be 3 medians of this set. 8 , when x <8 x , when 8<=x<=12 and 12, when x>12 There could be 1 mean = (40+x)/5 Now, we can solve (40+x)/5 = 8 , x, 12 to find out values.. and if valid values are found that solution counts. We get x= 0 ,10, 20. Hence 3 solutions. Ans D it is.
_________________
Lets Kudos!!! Black Friday Debrief



Math Expert
Joined: 02 Sep 2009
Posts: 43831

Re: Set S consists of 5 values, not necessarily in ascending [#permalink]
Show Tags
13 Dec 2012, 01:21
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1372
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: Set S consists of 5 values, not necessarily in ascending [#permalink]
Show Tags
14 Dec 2012, 01:12
@vips and @bunuel: Since mean and median are the same for evenly spaced sets, so to make the entire set an evenly spaced set x can be made either 0 or 20. Can this concept be used to find x=10 as the mean and median?
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 634
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: Set S consists of 5 values, not necessarily in ascending [#permalink]
Show Tags
14 Dec 2012, 01:22
3
This post received KUDOS
1
This post was BOOKMARKED
Marcab wrote: @vips and @bunuel: Since mean and median are the same for evenly spaced sets, so to make the entire set an evenly spaced set x can be made either 0 or 20. Can this concept be used to find x=10 as the mean and median? Actually that (such numbers) could be a trap in this question. You might remember  If set is evenly spaced then for sure mean=median But, if mean=median, it doesnt mean that set is evenly spaced. It may or may not be. So, if we make x=0 and x=20, and find mean and median =10. We are pratically limiting our scope only to evenly spaced sets. And thus we get a few solutionsbut not all. We still need to look for solution for the other case where set is not evenly spaced. (Also x=10 doesnt give u an evenly spaced set.. so concept cant be applied directly, it would be more evident if the number of elements in set is even). One easy concept that u can use though is, if median =mean then numbers in the set will be symmetrical around median. Why it helps is that finding median is usually very simple,without calculation.
_________________
Lets Kudos!!! Black Friday Debrief



Senior Manager
Joined: 07 Sep 2014
Posts: 482
Concentration: Finance, Marketing

Re: Set S consists of 5 values, not necessarily in ascending [#permalink]
Show Tags
23 Aug 2016, 03:13
Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?
(A) Zero (B) One (C) Two (D) Three (E) More than three
Mean = 8+x/5
x<=4 median =8
x >8 & x<12 median = X
8+x/5 =X x=10
x>12 8+x/5 =12 x=20
So 3



Intern
Joined: 15 Oct 2017
Posts: 30
Location: Ireland
Concentration: Healthcare, Finance

Set S consists of 5 values, not necessarily in ascending [#permalink]
Show Tags
24 Nov 2017, 10:26
mun23 wrote: Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?
(A) Zero (B) One (C) Two (D) Three (E) More than three The mean is always equal to median when numbers in a set have equal deviation. For instance, in our case if deviation is 4, the x should 0 or 20. Another case when a set is ascending from the mean out both sides. x should be 10. Please, look the atachments. Hope, it helps. The answer is D
Attachments
sets.jpg [ 74.27 KiB  Viewed 746 times ]



Director
Joined: 07 Dec 2014
Posts: 906

Re: Set S consists of 5 values, not necessarily in ascending [#permalink]
Show Tags
24 Nov 2017, 19:19
1
This post received KUDOS
mun23 wrote: Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?
(A) Zero (B) One (C) Two (D) Three (E) More than three if mean=(x+40)/5, then x must be an even multiple of 5 let x=0: mean=8; median=8 yes let x=10: mean=10; median=10 yes let x=20; mean=12; median=12 yes let x=30; mean=14; median=12 no 3 values of x work D



Senior Manager
Joined: 02 Apr 2014
Posts: 396

Set S consists of 5 values, not necessarily in ascending [#permalink]
Show Tags
29 Dec 2017, 05:12
First rearrange the given set in ascending order = {4,8, 12,16} {x} average = (40 + x) / 5
now depending on value of x, the median will change, also median can be one of 8, 12, x
(1) suppose median = x, then average = median (40 + x)/5 = x => 4x = 40 => x = 10
(2) suppose median = 12, then average = 12 (40 + x)/5 = 12 => x = 20
(3) suppose median = 8, then average = 8 (40 + x)/5 = 8 => x = 0
so there are three possible values of x {0, 10, 20} for which median = mean => (D)




Set S consists of 5 values, not necessarily in ascending
[#permalink]
29 Dec 2017, 05:12






