2000 AMC 12 Problems/Problem 12

Revision as of 20:58, 6 January 2015 by Mathyguy1123 (talk | contribs) (Solution)

Problem

Let $A, M,$ and $C$ be nonnegative integers such that $A + M + C=12$. What is the maximum value of $A \cdot M \cdot C + A \cdot M + M \cdot C + A \cdot C$?

$\mathrm{(A) \ 62 } \qquad \mathrm{(B) \ 72 } \qquad \mathrm{(C) \ 92 } \qquad \mathrm{(D) \ 102 } \qquad \mathrm{(E) \ 112 }$

Solution

When $A=M=C=4$ then $AMC+AM+AC+MC = 112$, and that is the greatest answer choice, so the answer is $\boxed{E}$.

See also

2000 AMC 12 (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
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All AMC 12 Problems and Solutions

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