# Thread: VENN DIAGRAM Q thank you

1. ## VENN DIAGRAM Q thank you

There are 40 members in a sports club. 2 play all three sports. 23 play squash. 24 play tennis. 18 play golf. 14 play squash and tennis. 8 play tennis and golf. 1 member makes the refreshments and does not play any sport. How many play squash and golf?

2. Venn Diagram is not necessary but it is way much easier to figure the problem using it. This one consist of three circle.
-You know that 14 play both tennis and squash. Because 2 play all sports, 12 play ONLY tennis and squash.
-You know that 8 play both golf and tennis. Because 2 play all sports, 6 play ONLY golf and tennis.
-You know that 24 play tennis and that 12+2+6 play tennis and something else so 4 play only tennis.
Now you get this system of equations:
Let x be the number of people that play only golf, y the number of people that play squash and golf but not all three sports and z the number of people that play only squash.
18 = 6 + 2 + x + y
23 = 12 + 2 + y + z
39 = 24 + x + y + z
You have three equations and three unknown. You can solve for y.
Ans : y=4