GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 11 Dec 2018, 07:59

Starting NOW!

YouTube Live with Cornell Johnson - Join HERE  |  HBS Chat - Decisions at Noon ET  |  HaaS Chat  HaaS calling admits |  Darden Chat 


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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
Joined: 06 Feb 2010
Posts: 149
Concentration: Marketing, Leadership
Schools: University of Dhaka - Class of 2010
GPA: 3.63
WE: Business Development (Consumer Products)
A club with a total membership of 30 has formed 3 committees  [#permalink]

Show Tags

New post 14 Nov 2010, 22:42
2
6
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:44) correct 33% (01:42) wrong based on 274 sessions

HideShow timer Statistics

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

_________________

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

Critical Reasoning: http://gmatclub.com/forum/best-critical-reasoning-shortcuts-notes-tips-91280.html

Collections of MGMAT CAT: http://gmatclub.com/forum/collections-of-mgmat-cat-math-152750.html

MGMAT SC SUMMARY: http://gmatclub.com/forum/mgmat-sc-summary-of-fourth-edition-152753.html

Sentence Correction: http://gmatclub.com/forum/sentence-correction-strategies-and-notes-91218.html

Arithmatic & Algebra: http://gmatclub.com/forum/arithmatic-algebra-93678.html

Helpful Geometry formula sheet: http://gmatclub.com/forum/best-geometry-93676.html


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

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51099
Re: A club with a total membership of 30  [#permalink]

Show Tags

New post 15 Nov 2010, 00:48
5
4
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
avatar
Joined: 05 Oct 2009
Posts: 26
GMAT ToolKit User
Re: A club with a total membership of 30  [#permalink]

Show Tags

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: 136
Re: A club with a total membership of 30  [#permalink]

Show Tags

New post 16 Nov 2010, 18:00
1
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.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8659
Location: Pune, India
Re: A club with a total membership of 30  [#permalink]

Show Tags

New post 16 Nov 2010, 18:44
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.
_________________

[b]Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Retired Moderator
avatar
Joined: 03 Aug 2010
Posts: 203
Re: A club with a total membership of 30  [#permalink]

Show Tags

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

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8659
Location: Pune, India
Re: A club with a total membership of 30  [#permalink]

Show Tags

New post 30 Nov 2010, 11:45
1
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 4956 times ]

_________________

[b]Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern
Intern
avatar
Joined: 29 Jul 2010
Posts: 28
Location: San Francisco, CA
Re: A club with a total membership of 30  [#permalink]

Show Tags

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: 57
WE 1: 6 years - Consulting
Re: A club with a total membership of 30  [#permalink]

Show Tags

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

Retired Moderator
avatar
B
Joined: 16 Nov 2010
Posts: 1425
Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: A club with a total membership of 30  [#permalink]

Show Tags

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)

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 06 Oct 2014
Posts: 10
Re: A club with a total membership of 30 has formed 3 committees  [#permalink]

Show Tags

New post 17 Apr 2015, 01:09
Bunuel

Would one be wrong to assume that since you have the total groups that sum to 25, 5 ppl are unaccounted for, and in order to maximize members you essentially have an additional 5 spaces to bring you to 30 members... 5+5=10....thus answer D? Or did I just get lucky?

Thanks!
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13058
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A club with a total membership of 30 has formed 3 committees  [#permalink]

Show Tags

New post 17 Apr 2015, 09:57
1
Hi FTS185,

The method you've described is not perfectly clear, so it's tough to say if it's logical or lucky.

In this question, to MAXIMIZE the number of people who are NOT on a committee, we have to "overlap" as many people as possible (put as many of them onto MORE than one committee as possible). We're told that the 8 members of committee M are NOT on any other committee, so we can't do anything with them. However, the members of the other 2 committees COULD overlap (the 5 members of committee R COULD be on committee S). This means that we COULD be dealing with just 12 members accounting for everyone on those 2 committees. With the other 8 members from committee M, we have 12 + 8 = 20 members. THAT leaves 10 members that are on NO committee.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Intern
Intern
avatar
Joined: 27 Oct 2014
Posts: 4
Re: A club with a total membership of 30 has formed 3 committees  [#permalink]

Show Tags

New post 31 May 2015, 14:53
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


{total} = {M} + {S} + {R} - {Both} + {Neither}

We want to maximize Neither, so Both has to be as large as possible. The max of {Both} is 5 because {R} = 5.

30 = 8 + 12 + 5 - 5 + Neither

Neither = 10
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9116
Premium Member
Re: A club with a total membership of 30 has formed 3 committees  [#permalink]

Show Tags

New post 24 Aug 2018, 11:58
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: A club with a total membership of 30 has formed 3 committees &nbs [#permalink] 24 Aug 2018, 11:58
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.