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]
02 Sep 2010, 20:52

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

62% (02:11) correct
38% (01:23) wrong based on 172 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 member 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 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 member 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

please answer with explanation

thank you so much

Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.

Hence only M is 8. Now we need to consider only S, (S n R) and R.

(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.

Now the max value of x could be 5 and the min value of x could be 0.

When x is 5 (max), Neither is 10. When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.

Answer 10 (D). _________________

Support GMAT Club by putting a GMAT Club badge on your blog

For a less mathematical approach (I still haven't gotten a good handle on permutations and combinations):

8 members of the club are on committee M. None of those 8 are on the other committees, so the 12 members of committee S are all different members (you can ignore R since there might be overlap with S and it's a smaller number than S). 12+8=20 members minimum of the club are on committees. 30-20=10 members maximum are not on any committees.

I don't know if this would work on more complex problems, though, so it's probably good to learn and understand the mathematical approach (which I need to do as well).

I solved it correct but made a silly mistake acc to me 12 + 8 =22 hence answer is 30 - 22 = 8 what a mess I am into anyways

Answer should be 10 that all the members of the R are also members of the S committee hence 12 +8 =20 30 -20 = 10 Answer D _________________

I will give a Fight till the End

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed." - Bernard Edmonds

A person who is afraid of Failure can never succeed -- Amneet Padda

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 member 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

please answer with explanation

thank you so much

Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.

Hence only M is 8. Now we need to consider only S, (S n R) and R.

(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.

Now the max value of x could be 5 and the min value of x could be 0.

When x is 5 (max), Neither is 10. When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.

Answer 10 (D).

first of all, thanks your great answer. However, I just have one more question

HOw can you draw the equation

(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.

help me explain it to me. I try to figure out but i can't

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 member 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

please answer with explanation

thank you so much

Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.

Hence only M is 8. Now we need to consider only S, (S n R) and R.

(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.

Now the max value of x could be 5 and the min value of x could be 0.

When x is 5 (max), Neither is 10. When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.

Answer 10 (D).

first of all, thanks your great answer. However, I just have one more question

HOw can you draw the equation

(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.

help me explain it to me. I try to figure out but i can't

I had setup the Venn diagram to solve this question. Also I have incorrectly setup the equation but when I substituted the values I did use the equation correctly because I referred from the Venn diagram.

(M U R U S) = M + R + S [highlight]-[/highlight] (M n R) [highlight]-[/highlight] (M n S) [highlight]-[/highlight] (R n S) [highlight]+[/highlight] (M n R n S) + Neither.

In fact, I can't figure out why (M U R U S) = 30. because ( M U R U S ) means that elements of M, R, and S. In fact, there are some elements doesn't belong to these sets. Therefore, I believe there should be less than 30.

In fact, I can't figure out why (M U R U S) = 30. because ( M U R U S ) means that elements of M, R, and S. In fact, there are some elements doesn't belong to these sets. Therefore, I believe there should be less than 30.

Could you help me clear this

This information is given in the question itself -- "A club with a total membership of 30 has formed 3 committees, M, S and R".

The club's total membership consists of members in the committees (M, S and R) and also members not in any of the committees. _________________

Support GMAT Club by putting a GMAT Club badge on your blog

any one can help me with full explanation with this question.

I have spent two days to try to understand it and understand the explanation of others. But I haven't figured out them yet.

I think this question is so important. everyone helps me????

thank you in advance

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 member 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.

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 member 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

please answer with explanation

thank you so much

Solved this one pretty quickly. 30 people/ 3 committees. M,S,R with 8,12,5 respectively.

--> If the 8 people in M can not be in any other committee, that leaves 22 people left to be in the two committees remaining, or not be in a committee at all. Out of these 22, 12 must be in group S. Of the 12 in group S, 5/12 could serve in both committee S and committee R. You would not need to draw any more people out of the remaining to form group R since this group is represented by individuals from group S that are serving double duty. Hence, the 8 from M, plus the 12 from S (including the 5 that serve on R as well) is 20 people out of the 30. 30-20=10, or the maximum number of people possible in the club that do jack shit!

This was just what quickly went through my head when I saw this problem. I'm not sure this is even a question to deal with probabilities. I thought it was gonna be a permu/combo question, but that wasn't necessary.

The easiest way to solve this question is to just think about what conditions need to be true in order to maximize the number of people who are not in any of the three groups. You know that M is completely self-contained with 8 people, so you don't even need to think about them. Just consider a group of 22 people split into R, S, both, or neither. You know how many people are in R (12) and how many are in S (5). You don't know how many people are in both. So what number of people do you need to have in both groups to maximize the number of people who are in neither?

Think about it like this: if NOBODY was in both R and S, you would have 17 people in the groups, leaving 5 people in neither group. What if EVERYONE in group S was also in group R? Then you would have 12 people in the groups, leaving 10 in neither group. So 10 is the answer.

I don't agree with (or can't find) the official answer. Without coming up with any equation, I find that the answer is 5. My line of reasoning: since there is no overlapping between any two other member groups, to maximize the non-group members, the number of members belonging to all the 3 groups must zero 30 = (12 + 8 + 5 ) + 5 Also with Equations: Group M :8 Group S : 12 Group R: 5 Non-Group: y Total : 30 Let's x = M&S&R, a = M&S, b = M&R and c = S&R. So 30 = (8-a-b-x) + (12-a-c-x) + (5-c-b-x) + x + y a, b and c are said to be 0 30 = 25 -2x + y ==> y = 5 + 2x. To minimize y x got to be 0, thus y = 5. What's wrong w/t my line of reasoning Please help out. Brother Karamazov

Re: A club with a total membership of 30 has formed 3 committees [#permalink]
17 Oct 2013, 12:17

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: A club with a total membership of 30 has formed 3 committees [#permalink]
06 Dec 2014, 22:53

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. _________________

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...

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...

Our Admissions Committee is busy reviewing Round 1 applications. We will begin sending out interview invitations in mid-October and continue until the week of November 9th, at which point...