IanStewart
If 2/3rds of the members of the Golf Club are also members of the Tennis Club, and 1/2 of the members of the Tennis Club are also members of the Golf Club, what percentage of all people who belong to one or both Clubs belong only to the Golf Club?
There are quite a few good ways to do this type of problem. I'd normally draw a Venn diagram, and fill it in as follows:
-if 2/3 of the people in the Golf Club are in the Tennis Club, then the Golf Club membership can be divided in a 2 to 1 ratio; for every 3 people in the Golf Club, 2 people are in both clubs, and 1 person is in the Golf Club only. So, we have:
x people in Golf only
2x people in Golf+Tennis
-since half the people in the Tennis Club are also in the Golf Club, the number in Tennis only is equal to the number in Tennis+Golf. So we have:
x people in Golf only
2x people in Golf+Tennis
2x people in Tennis only
From here it's straightforward to answer any question. So, what % of all members are in only Golf? x/(x + 2x + 2x) = x/5x = 1/5 = 20%.