1991 AHSME Problems/Problem 30

Problem

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

Solution

$\fbox{}$

1991 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 29	Followed by Problem 30
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1991 AHSME Problems/Problem 30

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