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Difficult Math Problem #93 - Sets

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Difficult Math Problem #93 - Sets

by 800guy » Fri Feb 02, 2007 9:27 am
answer coming after some people answer:

There are 30 people and 3 clubs M, S, and Z in a company. 10 people joined M, 12 people joined S and 5 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not join any club?

A: 4
B: 5
C: 6
D: 7
E: 8
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by telugupilla » Fri Feb 02, 2007 1:15 pm
Assuming all the 5 pl in club Z also joined club S. It would 30-10+7+5 = 8
Am I right?
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by 800guy » Mon Feb 05, 2007 2:52 pm
oa:

total no of people = 30
no joining M = 10
no joining S = 12
no joining Z = 5
question asked - AT MOST how many people did not join any group?


solution: now since none of the members of M joined any other group, the no of people left = 30-10(for M)=20
since the question says at most how many did not join any group, lets assume the all people who join Z also join S. so no of people joining group S and Z are 12 (note that there will be 5 people in group S who have also joined Z)

therefore no of people not joining any group = 20-12=8
Hence e
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by navdeepbajwa » Wed Oct 21, 2009 12:42 pm
I think if you make a diagram it will be explained much better.If you make a diagram and since M=10 does not share with any all the intersections containing 10 will be zero and assume intersection of S and Z be X and so Z only will be Z-X or 5-X and other will be S-X or 12-X
Since Z only cant be negative so max value X can take is 5 So X will be 5 and Sum will be 10+7+5=22 therefore no of people not joining any group = 30-22=8
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by briantime » Wed Oct 21, 2009 1:27 pm
I made a Venn diagram to solve this:

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by navdeepbajwa » Wed Oct 21, 2009 1:55 pm
Thanks buddy
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by briantime » Wed Oct 21, 2009 1:59 pm
The most important information is that the members of club M did not join any other club. This gives you the information that 0 members join M & S, M & Z and M & S & Z.
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by Scott@TargetTestPrep » Mon Mar 19, 2018 5:43 am
800guy wrote:answer coming after some people answer:

There are 30 people and 3 clubs M, S, and Z in a company. 10 people joined M, 12 people joined S and 5 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not join any club?

A: 4
B: 5
C: 6
D: 7
E: 8
To find the maximum number of people of the company who did not join any club, we can assume that all 5 people who joined club Z also joined club S. Since 10 people joined club M (and no other clubs) and 12 people joined club S or club Z or both, we have 10 + 12 = 22 people who joined at least one club. Thus, at most, 30 - 22 = 8 people did not join any club.

Answer: E

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