At a country club, 75% of the members play golf and 60% of the members

With percentages, often it is good to start with
total number of members = 100

If there are 100 members:
75% play golf: 75 play golf
60% play tennis: 60 play tennis

Can there be two sets,
ONLY golf players and
ONLY tennis players?
75 + 65 = 135. No

135 - 100 members =
AT LEAST 35 must play both (see diagram)

But - all 60 tennis players might also play golf.
AT MOST, 60 can play both - see diagram

(Only 75 play golf. The other sport is tennis.
60 play tennis. The group of 60 could be
inside the group of 75. In that case,
60 of the 75 golf players are also tennis players.),

35 of 100: 35% MUST play both
60 of 100: 60% MIGHT (can) play both

There is no way to decide.
Highest percent possible play both?
Lowest percent possible play both?
Some percent in between?
We need more information.

Answer E

We can let the total number of members = 100 and create the equation:

Total = Golf + Tennis - both + neither

100 = 75 + 80 - both + neither

Since we don’t know “neither,” we see that there is no way to determine “both.”

Answer: E

Total-neither= A + B +(A intersection B)

Not all values given so ans is E

Posted from my mobile device

Never Forget the lazy people who don't want to do anything. No golf No Tennis.

Please don't forget the "none" category in case of 2D venn diagram.

Answer E

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.