It is currently 21 Oct 2017, 02:00

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 16 Apr 2010
Posts: 35

Kudos [?]: 22 [0], given: 1

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

### Show Tags

02 Sep 2010, 21:52
4
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:09) correct 35% (01:27) wrong based on 225 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 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
[Reveal] Spoiler: OA

Kudos [?]: 22 [0], given: 1

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 404

Kudos [?]: 249 [2], given: 50

Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB

### Show Tags

02 Sep 2010, 22:09
2
KUDOS
bupbebeo 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 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

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.

30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.

22 = (12-x) + (5-x) + x + 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.

_________________

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

Kudos [?]: 249 [2], given: 50

Manager
Joined: 25 Jun 2010
Posts: 86

Kudos [?]: 14 [1], given: 19

Location: Sacramento, CA
Schools: Cambridge (R2-Matriculating), Nyenrode (Accepted), Oxford (R2-Interview invite)
WE 1: Army officer (Corps of Engineers)
WE 2: Air Quality Control Engineer
WE 3: Water Resources Engineer

### Show Tags

02 Sep 2010, 23:01
1
KUDOS
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).

Kudos [?]: 14 [1], given: 19

Manager
Joined: 20 Apr 2010
Posts: 242

Kudos [?]: 45 [0], given: 52

WE 1: 4.6 years Exp IT prof

### Show Tags

03 Sep 2010, 00:40
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

Don't Forget to give the KUDOS

Kudos [?]: 45 [0], given: 52

Intern
Joined: 16 Apr 2010
Posts: 35

Kudos [?]: 22 [0], given: 1

### Show Tags

03 Sep 2010, 01:04
ezhilkumarank wrote:
bupbebeo 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 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

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.

30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.

22 = (12-x) + (5-x) + x + 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.

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

Kudos [?]: 22 [0], given: 1

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 404

Kudos [?]: 249 [0], given: 50

Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB

### Show Tags

03 Sep 2010, 15:34
bupbebeo wrote:
ezhilkumarank wrote:
bupbebeo 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 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

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.

30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.

22 = (12-x) + (5-x) + x + 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.

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.

30 = 8 + (12 - x) + (5 - x) [highlight]+[/highlight] 0 [highlight]+[/highlight] 0 [highlight]+[/highlight] x [highlight]+[/highlight] 0 + Neither.

Attachment:

Venn-Diagram.jpg [ 14.13 KiB | Viewed 3973 times ]

_________________

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

Kudos [?]: 249 [0], given: 50

Intern
Joined: 16 Apr 2010
Posts: 35

Kudos [?]: 22 [0], given: 1

### Show Tags

03 Sep 2010, 19:49
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

Kudos [?]: 22 [0], given: 1

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 404

Kudos [?]: 249 [0], given: 50

Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB

### Show Tags

03 Sep 2010, 19:56
bupbebeo wrote:
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

Kudos [?]: 249 [0], given: 50

Intern
Joined: 16 Apr 2010
Posts: 35

Kudos [?]: 22 [0], given: 1

### Show Tags

03 Sep 2010, 23:24
as you say: " The club's total membership consists of members in the committees (M, S and R) and also members not in any of the committees."

Therefore, I guess 30 = ( M U R U S ) + member not belong to any these sets.

(M U R U S) alone cannot be 30

do you think so

Kudos [?]: 22 [0], given: 1

Intern
Joined: 16 Apr 2010
Posts: 35

Kudos [?]: 22 [0], given: 1

### Show Tags

05 Sep 2010, 07:56
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????

Kudos [?]: 22 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129069 [1], given: 12194

### Show Tags

05 Sep 2010, 08:13
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
bupbebeo wrote:
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????

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.

Hope it's clear.
_________________

Kudos [?]: 129069 [1], given: 12194

Intern
Joined: 05 Sep 2010
Posts: 1

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

### Show Tags

05 Sep 2010, 09:07
bupbebeo 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 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

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.

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

Intern
Joined: 16 Apr 2010
Posts: 35

Kudos [?]: 22 [0], given: 1

### Show Tags

07 Sep 2010, 00:46
Can anyone help me, why we have this formula

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

I really appreciate who can help me clear this.

Kudos [?]: 22 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129069 [0], given: 12194

### Show Tags

07 Sep 2010, 05:36
Expert's post
1
This post was
BOOKMARKED
bupbebeo wrote:
Can anyone help me, why we have this formula

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

I really appreciate who can help me clear this.

I don't think that Venn diagram is the best way to solve this question. Moreover the formula you posted has typos in it. Anyway check below link for formulas of 3 overlapping sets:
formulae-for-3-overlapping-sets-69014.html?hilit=formula%20exactly

Hope it helps.
_________________

Kudos [?]: 129069 [0], given: 12194

Manager
Joined: 06 Aug 2010
Posts: 218

Kudos [?]: 225 [0], given: 5

Location: Boston

### Show Tags

07 Sep 2010, 07:34
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.

Kudos [?]: 225 [0], given: 5

Intern
Joined: 18 Jun 2017
Posts: 9

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

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

### Show Tags

04 Oct 2017, 21:01
bupbebeo wrote:
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????

See use the formula:

Total = A + B + C - (sum of 2 group overlaps) + (all three) + Neither
which would translate as

Total membership of club = Committee M + Committee S + Committe R - (sum of members belonging to atleast 2 committees) + (members belonging to all 3 committees) + Neither

Since we have been given that members of M do not belong to any committee so we have (members belonging to all 3 committees as '0')
Also the terms (sum of members belonging to atleast 2 committees) can only be found from Committee S and R since M does not belong to any other committee.
So out of 12 and 5 (committee S and R) the maximum common members on 2 committees can be 5 (i.e. from R)

so the formula becomes
30 = 8 + 12 + 5 - 5 + 0 + Neither
Neither = 30 - 20 = 10 members

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

Re: A club with a total membership of 30 has formed 3 committees   [#permalink] 04 Oct 2017, 21:01
Display posts from previous: Sort by

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

 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®.