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At a school, 69% of Math Club members are also in the Physics Club, and 79%...

At a school, 69% of Math Club members are also in the Physics Club, and 79% of Math Club members are also on the Quiz Team. Consider the percentage, P, of Math Club members who are both in the Physics Club and also on the Quiz Team. Based on the given data alone, we can find a percentage M and a percentage N that will guarantee that M ≤ P ≤ N. What is the sum of the largest possible value for M and the smallest possible value for N?

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Answer #1

The total is 100% of Math Club members. P is the percentage of Math Club members who are both in Physics Club and the Quiz team.

So . This is because we know where A is the set of Physics Club members and B is the set of Quiz team members.

So we get Also P cannot exceed the physics club members so  .

This implies and is the best bound. M=48,N=69 their sum is   

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