M01-15

Question

At Daifu University, 40% of all students are members of both a chess club and a swim team. If 20% of swim team members 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%

Show Answer

Official Answer

D

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

Bunuel · Accepted Answer

Official Solution:

At Daifu University, 40% of all students are members of both a chess club and a swim team. If 20% of swim team members 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%

Show Answer

Official Answer

D

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

Assume there are a 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 the number of members in the swim team, then 0.2S is the number of students who are members of the swim team only:
  
 40 + 0.2S = S , which implies  S = 50 .
  
Alternatively, since "20% of members of the swim team are not members of the chess club," the remaining 80% of swim team members are part of the chess club. Therefore, the number of students in both clubs is  0.8 * S = 40 , which also results in  S = 50 .

Answer: D

Bunuel · Answer

No, the answer is D, not E. Here is the correct table: Untitled.png 40 + 0.2S = S --> S = 50. Hope it helps.

brinckma · Answer

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%.

760Abhi · Answer

Hi  Bunuel

I have a doubt about your explanation. Requesting you to please help.

out of 100 total students, there can be the case that a student is neither a part of chess club nor a part of swim team. How you have managed this case in your explanation? Please explain.

Thank You.

Bunuel · Answer

There certainly can be students who are neither in a chess club nor in a swim team but to solve the question we don't need to know how many. In  this post  there is a matrix that might help.

760Abhi · Answer

Thank you so much,  Bunuel . Got it.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Emi4016 · Answer