Data Sufficiency

55 people live in an apartment complex with three fitness clubs (A, B, and C). Of the 55 residents, 40 residents are members of exactly one of the three fitness clubs in the complex. Are any of the 55 residents members of both fitness clubs A and C but not members of fitness club B?

(1) 2 of the 55 residents are members of all three of the fitness clubs in the apartment complex.
(2) 8 of the 55 residents are members of fitness club B and exactly one other fitness club in the apartment complex.

To start we can subtract 40 from 55 to get the 15 members that are members of either 2 or 3 fitness clubs.


Statement 1: If two people are members of all 3, this leave 13 to be members of just 2 clubs. However, we do not know to what clubs they belong. INSUFFICIENT


Statement 2: If 8 people are members of B and another club, then 7 people are members of either 3 or A and C. We do not know specifics. INSUFFICIENT


Putting them together we know 7 = All 3 + (A and C) and All 3 = 2. Thus, A and C = 5.


THE ANSWER IS C.