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Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
2000 AMC 12/AHSME
12
12
Part of
2000 AMC 12/AHSME
Problems
(1)
Maximizing Diophantus
Source:
3/21/2008
Let
A
A
A
,
M
M
M
, and
C
C
C
be nonnegative integers such that A \plus{} M \plus{} C \equal{} 12. What is the maximum value of A \cdot M \cdot C \plus{} A\cdot M \plus{} M \cdot C \plus{} C\cdot A?
<
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(
A
)
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62
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(
B
)
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72
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(
C
)
<
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92
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(
D
)
<
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102
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(
E
)
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112
<span class='latex-bold'>(A)</span>\ 62 \qquad <span class='latex-bold'>(B)</span>\ 72 \qquad <span class='latex-bold'>(C)</span>\ 92 \qquad <span class='latex-bold'>(D)</span>\ 102 \qquad <span class='latex-bold'>(E)</span>\ 112
<
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(
A
)
<
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62
<
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(
B
)
<
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>
72
<
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−
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>
(
C
)
<
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>
92
<
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x
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>
(
D
)
<
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>
102
<
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−
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>
(
E
)
<
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>
112
inequalities