1991 AHSME Problem 30

For any set S, let |S| denote the number of elements in S, and let n(S) be the number of subsets of S, including the empty set and the set S itself. If A, B, and C are sets for which n(A)+n(B)+n(C)=n(A\cup B\cup C) and |A|=|B|=100, then what is the minimum possible value of |A\cap B\cap C|?

\textbf{(A) } 96 \qquad \textbf{(B) } 97 \qquad \textbf{(C) } 98 \qquad \textbf{(D) } 99 \qquad \textbf{(E) } 100

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.