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National and Regional Contests
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MAA AMC
AMC 12/AHSME
2001 AMC 12/AHSME
21
21
Part of
2001 AMC 12/AHSME
Problems
(1)
Integers with Product 8!
Source: 2001 AMC-12 #21
12/4/2005
Four positive integers
a
,
b
,
c
,
a,b,c,
a
,
b
,
c
,
and
d
d
d
have a product of 8! and satisfy\begin{align*}ab \plus{} a \plus{} b &\equal{} 524\\ bc \plus{} b \plus{} c &\equal{} 146\\ cd \plus{} c \plus{} d &\equal{} 104.\end{align*} What is a \minus{} d?
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<span class='latex-bold'>(A)</span> \ 4 \qquad <span class='latex-bold'>(B)</span> \ 6 \qquad <span class='latex-bold'>(C)</span> \ 8 \qquad <span class='latex-bold'>(D)</span> \ 10 \qquad <span class='latex-bold'>(E)</span> \ 12
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12
AMC