It is claimed that 75 percent of teenagers can ride a bike and 65 percent can swim. What can be said about the percentage who do both?

Let 's name the set of bikers B and the set of swimmers S. Also name the set of all teenagers T. So all of T is 100 percent. Name the set of teenagers who both bike and swim P.

Now, we will bound the size of P. From above: every teenager in P has to swim, so P is equal to or smaller than S, i.e. 65 percent. From below: This depends on the amount of overlap between B and S. Suppose the overlap is minimal. T\B=25 percents, so we suppose P = S\(T\B), and we get 65-25=40 percent minimal size.

Thus, the percentage of teenagers who can do both is between 40 and 65 percents.