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A club with $x$ members is organized into four committees such that

1. each member is in exactly two committees,
2. any two committees have exactly one member in common.

Then $x$ has

1. exactly two values both between $4$ and $8$
2. exactly one value and this lies between $4$ and $8$
3. exactly two values both between $8$ and $16$
4. exactly one value and this lies between $8$ and $16$

recategorized | 20 views

+1 vote

Answer: $\mathbf B$

Explanation:

This problem can be converted into the graphical form where each nodes represent a committee and the edges represent the member.

So, this problem reduces to nothing but a complete graph. in which each edge can have exactly two nodes(members) or two nodes(members) have exactly one edge(committee).

Hence, $\mathbf B$ is the correct option.

by Boss (12.9k points)
edited by

+1 vote