Thread: Venn Diagrams

200 people were asked which of these grand slam tournaments that they have attended. The tournaments inquired about were: US Open, Wimbledon, or Australian Open.

• 30 people have not attended any of these tournaments.
• 10 people have been to all thee tournaments.
• 25 people have been to Wimbledon and the Australian Open.
• 20 people have been to the US Open and the Australian Open but not to Wimbledon.
• 65 people have been to exactly two of the tournaments.
• 165 people have been to the US Open or to Wimbledon.
• 120 people have been to Wimbledon or to the Australian Open.

I do not understand how 50 is in the US open only, 40 Wimbledon only, and 5 Australian open only. Please explain. Thank you.
I know that:
W+U=90 and W+A=45. How can they say these numbers. To have a system I would need to have the same the same letters.

I think that I have it. Thanks U+A+W=95 U+W=90 so 90+A=95

If you look at the image then you see the sets of the US Open, Wimbledon and Australian Open have some parts in common (the intersection of the sets).

If you have to determine the only persons (I guess the numbers are persons) who are @Wimbledon for example, then you see there are 40 of them, because 15 of them are @Wimbledon and @Australian Open, ...