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.

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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.