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At Daifu university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all Daifu students are members of the swim team?

At Daifu university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all Daifu students are members of the swim team?

A. 20% B. 30% C. 40% D. 50% E. 60%

Assume there are total of 100 students. 40 students are members of both clubs. We are told that: "20% of members of the swim team are not members of the chess club", thus if S is a # of members of the swim team then 0.2S is # of members of ONLY the swim team:

\(40+0.2S=S\), so \(S=50\).

Or another way: since "20% of members of the swim team are not members of the chess club" then the rest 80% of members of the swim team (S) ARE members of the chess club, so members of both clubs: \(0.8*S=40\), so \(S=50\).

I think the answer should be E. The question does not say that ALL swim team members are included in the 40%, but rather that 40% of all students are members of both. If we assume that there are 100 total students, there could be 40 members of the swim team, or 100 members of the swim team. All we know is that 40% of these students are members of both.

I set up a table:

Chess Yes No Total Swim Yes .40x .20x .60x No n/a n/a .40x Total 1.0x

Sorry if the above table is garbled, but I hope it presents properly. If you add all the members of the swim team (40% who are both Swim and Chess and 20% who are not on the Chess team) then you get 60%.

I think the answer should be E. The question does not say that ALL swim team members are included in the 40%, but rather that 40% of all students are members of both. If we assume that there are 100 total students, there could be 40 members of the swim team, or 100 members of the swim team. All we know is that 40% of these students are members of both.

I set up a table:

Chess Yes No Total Swim Yes .40x .20x .60x No n/a n/a .40x Total 1.0x

Sorry if the above table is garbled, but I hope it presents properly. If you add all the members of the swim team (40% who are both Swim and Chess and 20% who are not on the Chess team) then you get 60%.

No, the answer is D, not E. Here is the correct table:

Attachment:

Untitled.png

40 + 0.2S = S --> S = 50.

Hope it helps.

>> !!!

You do not have the required permissions to view the files attached to this post.

Please, can you help me here? Should not the tic tac toe board works here? I dont know what Im doing wrong...

Regards

Bunuel wrote:

brinckma wrote:

I think the answer should be E. The question does not say that ALL swim team members are included in the 40%, but rather that 40% of all students are members of both. If we assume that there are 100 total students, there could be 40 members of the swim team, or 100 members of the swim team. All we know is that 40% of these students are members of both.

I set up a table:

Chess Yes No Total Swim Yes .40x .20x .60x No n/a n/a .40x Total 1.0x

Sorry if the above table is garbled, but I hope it presents properly. If you add all the members of the swim team (40% who are both Swim and Chess and 20% who are not on the Chess team) then you get 60%.

No, the answer is D, not E. Here is the correct table:

Yes, the tic-tac-toe board will work on this question - you just have to be careful about how you're filling in the grid. Bunuel's solution (directly above your post) shows how to do it.

I think this is a poor-quality question and I agree with explanation. The question should have been 'what percentage of all Daifu students are members of the swim team and not members of chess club?' The answer would then be 50. For the question as given, the answer would be 50+40 = 90%

No, the answer is D, not E. Here is the correct table:

Attachment:

Untitled.png

40 + 0.2S = S --> S = 50.

Hope it helps.

Perfect table. I was trying to make this table when I was trying to do the problem but couldn't think of it. Venn diagram was not helping. Once the table is made the answer is easy to find