Problem Solving

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

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

No. of persons playing tennis are 33; golf 42;squash 43;

as no. of persons playing all the three games are 5; therefore no. of people playing at least tennis and squash alone would be 11; similarly no. of people playing golf and squash alone atleast would be 13; and no. of people playing tennis and golf alone would be 3;

now no. of persons playing tennis alone would be 14;
no. of persons playing golf alone would be 21 and no. of persons playing squash alone would be 14
adding all these we have 14+14+21+11+5+3+13 = 81

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.

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.

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.

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.

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.

yep...!!! bingo..!!!

yes great well explained

the question is misleading! I doubt you will encounter such a question on the GMAT. It should have said at least golf and tennis or shouldn't have mentioned "at least" in the previous couples.

take care