Question

There are 20 students in the cast and crew of the school play. any group of 7 or more of these students must contain at least 1 boy. what’s more, any group of size 15 must contain at least 1 girl. how many boys are working on the play?

Answer 1

There will be 3 boys working on this play.

Answer 2

In the play, 14 boys are working.

Explanation:

First, we must evaluate the number of girls that can be at most in the group of 20.

Since if the group has 15 students there should be at least 1 girl, we can assume that in the group of 20 there should be 6 girls. In this way, we will not be able to put together any group of 15 without including a girl.

With the same reasoning, in a group of 7, there should be at least 1 boy, so we can deduce that in the group of 20 there are 14 boys. In this way, we will not be able to assemble a group of 7 without having at least one child.

14 boys + 6 girls = 20

In this way, we would be fulfilling both conditions, since we could form groups of 7 with at least 1 boy and groups of 15 with at least 1 girl.

Have a nice day!