an elite society plays

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Feb 21, 2012 4:36 am

Each member in an elite society plays at least one of the three games, tennis, billiards, and soccer. No member in the society plays either all of the three games together or tennis and soccer together. If there is a total of 100 members in the society, how many members play exactly two of the three games?
I. 55 members in the society play billiards and 20 members in the society play only billiards.
II. 65 members in the society play exactly one of the three games.

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Source: Beat The GMAT — Data Sufficiency | Tue Feb 21, 2012 4:36 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Feb 21, 2012 5:24 am

sanju09 wrote:Each member in an elite society plays at least one of the three games, tennis, billiards, and soccer. No member in the society plays either all of the three games together or tennis and soccer together. If there is a total of 100 members in the society, how many members play exactly two of the three games?
I. 55 members in the society play billiards and 20 members in the society play only billiards.
II. 65 members in the society play exactly one of the three games.

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]

No member in the society plays either all of the three games together or tennis and soccer together implies members can play tennis and billiards or soccer and billiards.

(1) 55 members in the society play billiards and 20 members in the society play only billiards implies that 55 - 20 = 35 is sum of the members who play tennis and soccer, means we know the members who play exactly two of the three games; SUFFICIENT.

(2) 65 members in the society play exactly one of the three games implies tennis only + soccer only + billiards only = 65 and it is given that each member in the society plays at least one of the three games.
Since there are 100 members in all, so the members who play exactly 2 games = 100 - 65 = 35; SUFFICIENT.

The correct answer is D.

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