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1991 AHSME Problems/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 $|A\cap B\cap C|$?

(A) 96 (B) 97 (C) 98 (D) 99 (E) 100 The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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