Set problem again

garuhape wrote:At alpha athletics club the members are required to play at least one sport besides their normal fitness training. In fact 33 members play tennis, 43 members play squash, and 42 members play golf. 16 members play at least tennis and squash, 18 members play at least squash and golf and 8 members play golf and tennis. If 5 members play all three sports, how many members are in the club?

What's wrong with my solution?

T = G1 + G2 + G3 - (those in 2 of the groups) - 2*(those in all 3 groups)

T = 33 + 43 + 42 - (8 + 11 + 13) - 2*(5) = 76

However, the OA is 81.

In the solution they say that #(tennis and golf) = 3 and not 8 but I do not understand why since in the question they say that "8 members play golf and tennis"

Thx

manpsingh87 wrote:and no. of people playing tennis and golf alone would be 3;

garuhape wrote:

manpsingh87 wrote:and no. of people playing tennis and golf alone would be 3;

Why? In the text it says that 8 members play golf and tennis and not that at least 8 members play golf and tennis.

manpsingh87 wrote: 8 member plays golf and tennis of these 8 member 5 were those which play all the three sports so we have to subtract these 5 persons from 8 to find those member which only play tennis and golf. make a venn diagram, and you'll realize your mistake.

garuhape wrote:

manpsingh87 wrote: 8 member plays golf and tennis of these 8 member 5 were those which play all the three sports so we have to subtract these 5 persons from 8 to find those member which only play tennis and golf. make a venn diagram, and you'll realize your mistake.

I understand it now. It's because the 5 people are only included in the two groups and therefore we only have to subtract them once and not twice.