Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Aug 2014, 08:50

Flash Sale:

The Economist GMAT Tutor - 15% Off All Courses


Close

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
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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the mean of set S does not exceed mean of any subset of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 20 Aug 2010
Posts: 6
Schools: Duke,Darden,Chicago University
Followers: 0

Kudos [?]: 0 [0], given: 1

GMAT Tests User
If the mean of set S does not exceed mean of any subset of [#permalink] New post 15 Jan 2012, 07:28
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

39% (01:50) correct 61% (00:59) wrong based on 153 sessions
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

[Reveal] Spoiler:
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??
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24373 [0], given: 2677

Re: GMat Club Tests: M16 Q23 [#permalink] New post 15 Jan 2012, 07:40
Expert's post
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: ps-challenge-93565.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24373 [0], given: 2677

Re: If the mean of set S does not exceed mean of any subset of [#permalink] New post 03 Jun 2013, 02:08
Expert's post
Director
Director
avatar
Joined: 03 Aug 2012
Posts: 887
Concentration: General Management, General Management
Schools: ISB '16
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
Followers: 12

Kudos [?]: 181 [0], given: 304

Premium Member CAT Tests
Re: If the mean of set S does not exceed mean of any subset of [#permalink] New post 30 Sep 2013, 10:17
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!
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24373 [0], given: 2677

Re: If the mean of set S does not exceed mean of any subset of [#permalink] New post 01 Oct 2013, 00:59
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 21 Sep 2013
Posts: 18
Location: United States
Concentration: Finance, General Management
GMAT Date: 10-25-2013
GPA: 3
WE: Operations (Mutual Funds and Brokerage)
Followers: 0

Kudos [?]: 5 [0], given: 62

Re: GMat Club Tests: M16 Q23 [#permalink] New post 17 Oct 2013, 00:53
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: ps-challenge-93565.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)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24373 [0], given: 2677

Re: GMat Club Tests: M16 Q23 [#permalink] New post 17 Oct 2013, 02:05
Expert's post
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: ps-challenge-93565.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?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 21 Sep 2013
Posts: 18
Location: United States
Concentration: Finance, General Management
GMAT Date: 10-25-2013
GPA: 3
WE: Operations (Mutual Funds and Brokerage)
Followers: 0

Kudos [?]: 5 [0], given: 62

Re: GMat Club Tests: M16 Q23 [#permalink] New post 17 Oct 2013, 02:22
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: ps-challenge-93565.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.
Re: GMat Club Tests: M16 Q23   [#permalink] 17 Oct 2013, 02:22
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic If the mean of set S does not exceed mean of any subset of angel2009 32 01 May 2010, 23:12
The mean of set S does not exceed mean of any subset of set arjtryarjtry 1 28 Aug 2008, 19:30
1 Experts publish their posts in the topic The mean of set S does not exceed mean of any subset of set sondenso 5 23 May 2008, 01:27
The mean of set S does not exceed mean of any subset of set marcodonzelli 1 02 Mar 2008, 03:23
Experts publish their posts in the topic The mean of set S does not exceed mean of any subset of set beckee529 9 31 Oct 2007, 15:22
Display posts from previous: Sort by

If the mean of set S does not exceed mean of any subset of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.