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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A club with a total membership of 30 has formed 3 committees [#permalink]
14 Nov 2010, 22:42

1

This post received KUDOS

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

60% (02:14) correct
40% (01:26) wrong based on 181 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?

Helpful Geometry formula sheet:best-geometry-93676.html I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

Re: A club with a total membership of 30 [#permalink]
15 Nov 2010, 00:48

1

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

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.

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

Re: A club with a total membership of 30 [#permalink]
16 Nov 2010, 18:00

1

This post was BOOKMARKED

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.

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

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

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

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

Re: A club with a total membership of 30 has formed 3 committees [#permalink]
01 Mar 2015, 19:11

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. _________________

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?

Re: A club with a total membership of 30 has formed 3 committees [#permalink]
17 Apr 2015, 09:57

1

This post received KUDOS

Expert's post

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.

Re: A club with a total membership of 30 has formed 3 committees [#permalink]
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

gmatclubot

Re: A club with a total membership of 30 has formed 3 committees
[#permalink]
31 May 2015, 14:53

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

Today was the last day of our three-week Launch, that ended on a high note with a drinks and dance reception. The class decided to shift the party outside...

There is one comment that stands out; one conversation having made a great impression on me in these first two weeks. My Field professor told a story about a...