ISI2015-MMA-6

Question

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

• A. exactly two values both between $4$ and $8$
• B. exactly one value and this lies between $4$ and $8$
• C. exactly two values both between $8$ and $16$
• D. exactly one value and this lies between $8$ and $16$

Answer 1

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.

Comments

wow if u have this kind of thinking level nobody can stop u !!!!!!!

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Hey Jeet could you please tell where I can learn such methods and practice more questions like this? Some book I can study? Please it'd be really kind of you. Thank you.

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MathGirl MathGirl Study at least one book thoroughly. You can start with the kenneth rosen. Once you get to know the feel of every needed topic in DM, thereafter you can make your own hybrid concepts such as this.

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Hey Jeet, thank you for the book's name.