Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 Aug 2010
Posts: 3
Schools: Duke,Darden,Chicago University

If the mean of set S does not exceed mean of any subset of
[#permalink]
Show Tags
15 Jan 2012, 08:28
Question Stats:
41% (01:17) correct 59% (01:39) wrong based on 382 sessions
HideShow timer Statistics
If the mean of set S does not exceed mean of any subset of set S, which of the following must be true about set S ? I. Set S contains only one element II. All elements in set S are equal III. The median of set S equals the mean of set S A. None of the three qualities is necessary B. II only C. III only D. II and III only E. I, II, and III I: Not True: If Set contains only One element, then Set S won't have any SS. II: True: When all the elements are equal, then mean of S=mean of any SS. III: Not True: Consider Consecutive No in Set S.Mean of S will always be greater than the smallest No. of the Consecutive series of Set S, and hence Mean of S becomes greater then Subset of S.
Why the answer is Not B??
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59147

Re: GMat Club Tests: M16 Q23
[#permalink]
Show Tags
15 Jan 2012, 08:40
If the mean of set S does not exceed mean of any subset of set S , which of the following must be true about set S?I. Set S contains only one element II. All elements in set S are equal III. The median of set S equals the mean of set S A. none of the three qualities is necessary B. II only C. III only D. II and III only E. I, II, and III "The mean of set S does not exceed mean of any subset of set S" > set S can be: A. \(S=\{x\}\)  S contains only one element (eg {7}); B. \(S=\{x, x, ...\}\)  S contains more than one element and all elements are equal (eg{7,7,7,7}). Why is that? Because if set S contains two (or more) different elements, then we can always consider the subset with smallest number and the mean of this subset (mean of subset=smallest number) will be less than mean of entire set (mean of full set>smallest number). Example: S={3, 5} > mean of S=4. Pick subset with smallest number s'={3} > mean of s'=3 > 3<4. Now let's consider the statements: I. Set S contains only one element  not always true, we can have scenario B too (\(S=\{x, x, ...\}\)); II. All elements in set S are equal  true for both A and B scenarios, hence always true; III. The median of set S equals the mean of set S   true for both A and B scenarios, hence always true. So statements II and III are always true. Answer: D. Also discussed here: pschallenge93565.html
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 59147

Re: If the mean of set S does not exceed mean of any subset of
[#permalink]
Show Tags
03 Jun 2013, 03:08
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Director
Joined: 03 Aug 2012
Posts: 656
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

Re: If the mean of set S does not exceed mean of any subset of
[#permalink]
Show Tags
30 Sep 2013, 11:17
Hi Bunuel,
I am still unable to get the solution.
When we can have an empty set {0} as a subset of each set, in that case we would have a average as 0 and thus consider the below example.
You have a set : {1,1,1}
One possible subset : {0}
Average of the set : 1
Average of subset:0
So still it exceeds the average of subset .
Can you advise on that?
Rgds, TGC!



Math Expert
Joined: 02 Sep 2009
Posts: 59147

Re: If the mean of set S does not exceed mean of any subset of
[#permalink]
Show Tags
01 Oct 2013, 01:59
TGC wrote: Hi Bunuel,
I am still unable to get the solution.
When we can have an empty set {0} as a subset of each set, in that case we would have a average as 0 and thus consider the below example.
You have a set : {1,1,1}
One possible subset : {0}
Average of the set : 1
Average of subset:0
So still it exceeds the average of subset .
Can you advise on that?
Rgds, TGC! An empty set has no mean or the median.
_________________



Intern
Joined: 21 Sep 2013
Posts: 26
Location: United States
Concentration: Finance, General Management
GMAT Date: 10252013
GPA: 3
WE: Operations (Mutual Funds and Brokerage)

Re: GMat Club Tests: M16 Q23
[#permalink]
Show Tags
17 Oct 2013, 01:53
Bunuel wrote: If the mean of set S does not exceed mean of any subset of set S , which of the following must be true about set S?I. Set S contains only one element II. All elements in set S are equal III. The median of set S equals the mean of set S A. none of the three qualities is necessary B. II only C. III only D. II and III only E. I, II, and III "The mean of set S does not exceed mean of any subset of set S" > set S can be: A. \(S=\{x\}\)  S contains only one element (eg {7}); B. \(S=\{x, x, ...\}\)  S contains more than one element and all elements are equal (eg{7,7,7,7}). Why is that? Because if set S contains two (or more) different elements, then we can always consider the subset with smallest number and the mean of this subset (mean of subset=smallest number) will be less than mean of entire set (mean of full set>smallest number). Example: S={3, 5} > mean of S=4. Pick subset with smallest number s'={3} > mean of s'=3 > 3<4. Now let's consider the statements: I. Set S contains only one element  not always true, we can have scenario B too (\(S=\{x, x, ...\}\)); II. All elements in set S are equal  true for both A and B scenarios, hence always true; III. The median of set S equals the mean of set S   true for both A and B scenarios, hence always true. So statements II and III are always true. Answer: D. Also discussed here: pschallenge93565.html hi bunuel , little confused here .. Please explain me where am i going wrong. I took the elements of set S={1,2,3,4) And the subset elemets as ={2,3,4) however this does not meet the second situation requirement. i.e. ( all elemets in set s are equal)



Math Expert
Joined: 02 Sep 2009
Posts: 59147

Re: GMat Club Tests: M16 Q23
[#permalink]
Show Tags
17 Oct 2013, 03:05
Yash12345 wrote: Bunuel wrote: If the mean of set S does not exceed mean of any subset of set S , which of the following must be true about set S?I. Set S contains only one element II. All elements in set S are equal III. The median of set S equals the mean of set S A. none of the three qualities is necessary B. II only C. III only D. II and III only E. I, II, and III "The mean of set S does not exceed mean of any subset of set S" > set S can be: A. \(S=\{x\}\)  S contains only one element (eg {7}); B. \(S=\{x, x, ...\}\)  S contains more than one element and all elements are equal (eg{7,7,7,7}). Why is that? Because if set S contains two (or more) different elements, then we can always consider the subset with smallest number and the mean of this subset (mean of subset=smallest number) will be less than mean of entire set (mean of full set>smallest number). Example: S={3, 5} > mean of S=4. Pick subset with smallest number s'={3} > mean of s'=3 > 3<4. Now let's consider the statements: I. Set S contains only one element  not always true, we can have scenario B too (\(S=\{x, x, ...\}\)); II. All elements in set S are equal  true for both A and B scenarios, hence always true; III. The median of set S equals the mean of set S   true for both A and B scenarios, hence always true. So statements II and III are always true. Answer: D. Also discussed here: pschallenge93565.html hi bunuel , little confused here .. Please explain me where am i going wrong. I took the elements of set S={1,2,3,4) And the subset elemets as ={2,3,4) however this does not meet the second situation requirement. i.e. ( all elemets in set s are equal) We are given that "the mean of set S does not exceed mean of ANY subset of set S". Now, notice that S cannot be {1, 2, 3, 4), because it has subsets with the mean smaller than the mean of {1, 2, 3, 4): Mean of S = 10/4 = 2.5. Mean of {1}, which is a subset of S, is 1 > 2.5 > 1. Does this make sense?
_________________



Intern
Joined: 21 Sep 2013
Posts: 26
Location: United States
Concentration: Finance, General Management
GMAT Date: 10252013
GPA: 3
WE: Operations (Mutual Funds and Brokerage)

Re: GMat Club Tests: M16 Q23
[#permalink]
Show Tags
17 Oct 2013, 03:22
Bunuel wrote: Yash12345 wrote: Bunuel wrote: If the mean of set S does not exceed mean of any subset of set S , which of the following must be true about set S?I. Set S contains only one element II. All elements in set S are equal III. The median of set S equals the mean of set S A. none of the three qualities is necessary B. II only C. III only D. II and III only E. I, II, and III "The mean of set S does not exceed mean of any subset of set S" > set S can be: A. \(S=\{x\}\)  S contains only one element (e B. \(S=\{x, x, ...\}\)  S contains more than one element and all elements are equal (eg{7,7,7,7}). Why is that? Because if set S contains two (or more) different elements, then we can always consider the subset with smallest number and the mean of this subset (mean of subset=smallest number) will be less than mean of entire set (mean of full set>smallest number). Example: S={3, 5} > mean of S=4. Pick subset with smallest number s'={3} > mean of s'=3 > 3<4. Now let's consider the statements: I. Set S contains only one element  not always true, we can have scenario B too (\(S=\{x, x, ...\}\)); II. All elements in set S are equal  true for both A and B scenarios, hence always true; III. The median of set S equals the mean of set S   true for both A and B scenarios, hence always true. So statements II and III are always true. Answer: D. Also discussed here: pschallenge93565.html hi bunuel , little confused here .. Please explain me where am i going wrong. I took the elements of set S={1,2,3,4) And the subset elemets as ={2,3,4) however this does not meet the second situation requirement. i.e. ( all elemets in set s are equal) We are given that "the mean of set S does not exceed mean of ANY subset of set S". Now, notice that S cannot be {1, 2, 3, 4), because it has subsets with the mean smaller than the mean of {1, 2, 3, 4): Mean of S = 10/4 = 2.5. Mean of {1}, which is a subset of S, is 1 > 2.5 > 1. Does this make sense? Yes bunuel my doubt is solved . Thus it is compulsory that all the elements of set s are equal. thank you.



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 402
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: If the mean of set S does not exceed mean of any subset of
[#permalink]
Show Tags
25 Dec 2014, 09:03
I did it in a more practical way, like this:
Lets say S is {5,6,7,8,9}  i used consecutive integerns to make my life a bit easier and s is {6,7,8} or {5,6,7}
Then, taking the options one by one: I: Obviously, we could have more than one elements and still have the same mean. NO II: We can see that for the first s this is wrong (same mean but different numbers). But for the second s this is true (different mean and different numbers). So, we can say that they should all be equal. III: This seems to be true too, as if we choose an s, the mean of which is 7 or less than 7, then for S, the mean equals the median.
Perhaps it makes absolutely no sense and could be random, but it led me to the correct answer in about half a minute...



Intern
Joined: 08 Jan 2018
Posts: 3

Re: If the mean of set S does not exceed mean of any subset of
[#permalink]
Show Tags
22 May 2018, 08:21
Hi,
I'm considering an extreme scenario.
What if S = {1,1,2,3,7} Mean = 7 subset of S = {1,1,2} or {1,2,3} or {3,7}. All have lesser mean than 7
If above is true, II would be wrong then???
Please advice. Thanks!



NonHuman User
Joined: 09 Sep 2013
Posts: 13611

Re: If the mean of set S does not exceed mean of any subset of
[#permalink]
Show Tags
23 May 2019, 09:10
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: If the mean of set S does not exceed mean of any subset of
[#permalink]
23 May 2019, 09:10






