MathDB
AHSME Sets

Source: AHSME 1991 problem 30

November 2, 2011
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Problem Statement

For any set SS, let S|S| denote the number of elements in SS, and let n(S)n(S) be the number of subsets of SS, including the empty set and the set SS itself. If AA, BB and CC are sets for which n(A) + n(B) + n(C) = n(A \cup B \cup C) \text{and}  |A| = |B| = 100, then what is the minimum possible value of ABC|A \cap B \cap C|?
<spanclass=latexbold>(A)</span> 96<spanclass=latexbold>(B)</span> 97<spanclass=latexbold>(C)</span> 98<spanclass=latexbold>(D)</span> 99<spanclass=latexbold>(E)</span> 100 <span class='latex-bold'>(A)</span>\ 96\qquad<span class='latex-bold'>(B)</span>\ 97\qquad<span class='latex-bold'>(C)</span>\ 98\qquad<span class='latex-bold'>(D)</span>\ 99\qquad<span class='latex-bold'>(E)</span>\ 100