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

It is currently 10 Jul 2014, 05:07

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

A club with a total membership of 30 has formed 3 committees

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
User avatar
Joined: 06 Feb 2010
Posts: 175
Concentration: Marketing, Leadership
Schools: University of Dhaka - Class of 2010
GMAT 1: Q0 V0
GPA: 3.63
WE: Business Development (Consumer Products)
Followers: 37

Kudos [?]: 511 [1] , given: 182

GMAT Tests User
A club with a total membership of 30 has formed 3 committees [#permalink] New post 14 Nov 2010, 22:42
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

74% (01:00) correct 25% (01:23) wrong based on 51 sessions
A club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?

(A) 5
(B) 7
(C) 8
(D) 10
(E) 12
[Reveal] Spoiler: OA

_________________

Practice Makes a Man Perfect. Practice. Practice. Practice......Perfectly

Critical Reasoning: best-critical-reasoning-shortcuts-notes-tips-91280.html

Collections of MGMAT CAT: collections-of-mgmat-cat-math-152750.html

MGMAT SC SUMMARY: mgmat-sc-summary-of-fourth-edition-152753.html

Sentence Correction: sentence-correction-strategies-and-notes-91218.html

Arithmatic & Algebra: arithmatic-algebra-93678.html

Helpful Geometry formula sheet: best-geometry-93676.html


I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18480
Followers: 3185

Kudos [?]: 21162 [0], given: 2534

Re: A club with a total membership of 30 [#permalink] New post 15 Nov 2010, 00:48
Expert's post
monirjewel wrote:
A club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 12


As "no member of committee M is on either of the other 2 committees" then 30-M=30-8=22 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.


So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 22-12=10 is the greatest possible number of members in the club who are on none of the committees.

Answer: D.

Hope it's clear.
_________________

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: 05 Oct 2009
Posts: 33
Followers: 0

Kudos [?]: 1 [0], given: 3

GMAT ToolKit User GMAT Tests User
Re: A club with a total membership of 30 [#permalink] New post 15 Nov 2010, 00:54
monirjewel wrote:
A club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 12


IMO D: 10

Total members to be considered for committees S and R = 30 - 8 = 22

Greatest possible members on none of the committees would be a situation when all the members in R are from S, leading to answer as 22 - 12 = 10 members on none of the committees.
Manager
Manager
User avatar
Joined: 13 Jul 2010
Posts: 170
Followers: 1

Kudos [?]: 14 [0], given: 7

Re: A club with a total membership of 30 [#permalink] New post 16 Nov 2010, 18:00
I used a venn diagram to solve this, usually find these problems easier to solve that way.

So we have a total of 8+12+5=25 members in the 3 groups M,S,R. But we have 30 members in total. This tells you that 5 members could be those that participate in none of the groups. Further since the members in M are not part of any of the other committees, only a total of 17 members are possible that remain. Out of these 5 of group R are also part of S since you need to minimize the number of committee participants hence 7 are only in committee R. This leave 17-7=10 that can potentially be the maximum number not participating in any of the committees.
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4516
Location: Pune, India
Followers: 1011

Kudos [?]: 4297 [0], given: 161

Re: A club with a total membership of 30 [#permalink] New post 16 Nov 2010, 18:44
Expert's post
gettinit wrote:
I used a venn diagram to solve this, usually find these problems easier to solve that way.

So we have a total of 8+12+5=25 members in the 3 groups M,S,R. But we have 30 members in total. This tells you that 5 members could be those that participate in none of the groups. Further since the members in M are not part of any of the other committees, only a total of 17 members are possible that remain. Out of these 5 of group R are also part of S since you need to minimize the number of committee participants hence 7 are only in committee R. This leave 17-7=10 that can potentially be the maximum number not participating in any of the committees.


You are right gettinit. Generally venn diagrams work the best for these kind of questions. One good thing to note here is that M is disjoint from the other two since no member of M can be a member of either of the other two sets. Therefore, out of 30 members, 8 are already out. Out of the other 22, we have to give 12 to S and 5 to R. Once we give 12 to S, just put the circle of R inside S (5 of the members of S become members of R too) so that you have 10 left outside who needn't be in any committee.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Retired Moderator
avatar
Joined: 03 Aug 2010
Posts: 248
Followers: 2

Kudos [?]: 29 [0], given: 41

GMAT Tests User
Re: A club with a total membership of 30 [#permalink] New post 30 Nov 2010, 10:56
VeritasPrepKarishma wrote:
gettinit wrote:
I used a venn diagram to solve this, usually find these problems easier to solve that way.

So we have a total of 8+12+5=25 members in the 3 groups M,S,R. But we have 30 members in total. This tells you that 5 members could be those that participate in none of the groups. Further since the members in M are not part of any of the other committees, only a total of 17 members are possible that remain. Out of these 5 of group R are also part of S since you need to minimize the number of committee participants hence 7 are only in committee R. This leave 17-7=10 that can potentially be the maximum number not participating in any of the committees.


You are right gettinit. Generally venn diagrams work the best for these kind of questions. One good thing to note here is that M is disjoint from the other two since no member of M can be a member of either of the other two sets. Therefore, out of 30 members, 8 are already out. Out of the other 22, we have to give 12 to S and 5 to R. Once we give 12 to S, just put the circle of R inside S (5 of the members of S become members of R too) so that you have 10 left outside who needn't be in any committee.



Can someone show how to solve this with the image of ven diagram.. i know its cumbersome to draw and all.. but that will be a great help

thanks
_________________

http://www.gmatpill.com/gmat-practice-test/

Amazing Platform

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4516
Location: Pune, India
Followers: 1011

Kudos [?]: 4297 [1] , given: 161

Re: A club with a total membership of 30 [#permalink] New post 30 Nov 2010, 11:45
1
This post received
KUDOS
Expert's post
hirendhanak wrote:

Can someone show how to solve this with the image of ven diagram.. i know its cumbersome to draw and all.. but that will be a great help

thanks


It is but only when you have to draw on a laptop! On paper, it is the easiest tool to get the answer.
There you go:
Attachment:
Ques1.jpg
Ques1.jpg [ 11.53 KiB | Viewed 1851 times ]

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 29 Jul 2010
Posts: 34
Location: San Francisco, CA
Followers: 1

Kudos [?]: 2 [0], given: 0

Re: A club with a total membership of 30 [#permalink] New post 01 Dec 2010, 00:11
Thanks for posting the venn. diagram. A little more helpful to see with overlapping sets.
Manager
Manager
avatar
Status: Last few days....Have pressed the throttle
Joined: 20 Jun 2010
Posts: 73
WE 1: 6 years - Consulting
Followers: 3

Kudos [?]: 21 [0], given: 27

Re: A club with a total membership of 30 [#permalink] New post 17 Mar 2011, 19:10
Bunuel wrote:
monirjewel wrote:
A club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 12


As "no member of committee M is on either of the other 2 committees" then 30-M=30-8=22 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.


So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 22-12=10 is the greatest possible number of members in the club who are on none of the committees.

Answer: D.

Hope it's clear.


Bunuel, This is definitely perfect. But I have a question. Can this be solved with the "Exactly two" set formula. Bcos I tried and it also gives me the right answer, here it is:

Formula:
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

30=8+12+5-(5)-2*0+N - ( here intersection of all three=0; and to maximize the
result, I took 2 group overlap as 5 -between 12 and 5)
=> N = 30-20=10

Please confirm if this is the right approach as well.
_________________

Consider giving Kudos if my post helps in some way

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1692
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 30

Kudos [?]: 272 [0], given: 36

GMAT Tests User Premium Member Reviews Badge
Re: A club with a total membership of 30 [#permalink] New post 19 Mar 2011, 00:38
Because 8 members from committee M are not common, so to minimize non-members we havt to "commonize" S and R, who can have 5 common (and total # of members = 12 including B and C). So total number of members = 12+8 = 20

=> Non-members = 30-20 = 10
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: A club with a total membership of 30   [#permalink] 19 Mar 2011, 00:38
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic A club with a total membership of 30 has formed 3 committees ajit257 10 11 Dec 2010, 07:32
3 Experts publish their posts in the topic A club with a total membership of 30 has formed 3 committees bupbebeo 18 02 Sep 2010, 20:52
A club with a total membership of 30 has formed 3 arjtryarjtry 2 25 Jul 2008, 02:34
A club with a total membership of 30 has formed 3 committees puma 2 10 May 2008, 22:19
A club with a total membership of 30 has formed 3 alohagirl 3 30 Oct 2007, 06:16
Display posts from previous: Sort by

A club with a total membership of 30 has formed 3 committees

  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®.