2000 AMC 10 Problems/Problem 11

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Problem

Solution

Two prime numbers between $4$ and $18$ are both odd.

odd*odd=odd.

odd-odd-odd=odd.

Thus, we can discard the even choices.

$ab-a-b=(a-1)(b-1)-1$.

$(a-1)(b-1)-1=21,119,231$.

Both of these factors are even, so the number +1 must be a multiple of $4$.

$120$ is the only possiblity.

$11,13$ satisfy this, $11*13-11-13=143-24=119$.

C

See Also

2000 AMC 10 (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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All AMC 10 Problems and Solutions
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