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Re: Four different boards consist of 7, 10, 11, and 15 members. [#permalink]
I didnt understand this :(
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Re: Four different boards consist of 7, 10, 11, and 15 members. [#permalink]
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Farina wrote:
I didnt understand this :(


Let's say that the four boards are: Board A, Board B, Board C, and Board D

That's also say that:
There are 7 people on board A
There are 10 people on board B
There are 11 people on board C
There are 15 people on board D

Since board D consists of 15 members, we'll need at least 15 people.
So, let's show 15 people and the fact that they are on board D:

Person #1: D
Person #2: D
Person #3: D
Person #4: D
Person #5: D
Person #6: D
Person #7: D
Person #8: D
Person #9: D
Person #10: D
Person #11: D
Person #12: D
Person #13: D
Person #14: D
Person #15: D

We've now dealt with the information about board D, let's deal with the fact that there are 7 people on board A
Since a person can be on more than one boards, it's possible that 7 of the people on board D are also on board A.
We get:
Person #1: D, A
Person #2: D, A
Person #3: D, A
Person #4: D, A
Person #5: D, A
Person #6: D, A
Person #7: D, A
Person #8: D
Person #9: D
Person #10: D
Person #11: D
Person #12: D
Person #13: D
Person #14: D
Person #15: D

There are 10 people on board B.
So let's say that 10 of the people on board D are also on board B.
We get:
Person #1: D, A, B
Person #2: D, A, B
Person #3: D, A, B
Person #4: D, A, B
Person #5: D, A, B
Person #6: D, A, B
Person #7: D, A, B
Person #8: D, B
Person #9: D, B
Person #10: D, B
Person #11: D
Person #12: D
Person #13: D
Person #14: D
Person #15: D

There are 11 people on board C.
So let's say that 11 of the people on board D are also on board C.
We get:
Person #1: D, A, B, C
Person #2: D, A, B, C
Person #3: D, A, B, C
Person #4: D, A, B, C
Person #5: D, A, B, C
Person #6: D, A, B, C
Person #7: D, A, B, C
Person #8: D, B, C
Person #9: D, B, C
Person #10: D, B, C
Person #11: D, C
Person #12: D
Person #13: D
Person #14: D
Person #15: D

So 15 is the smallest number of people that can satisfy the given information

Answer: 15

Cheers,
Brent
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Re: Four different boards consist of 7, 10, 11, and 15 members. [#permalink]
Why not 4?
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Re: Four different boards consist of 7, 10, 11, and 15 members. [#permalink]
Expert Reply
Please sir, refer to the explanations above. It was explained extensively

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Re: Four different boards consist of 7, 10, 11, and 15 members. [#permalink]
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