2003 AMC 10B Problems/Problem 18

Problem 18

What is the largest integer that is a divisor of $(n+1)(n+3)(n+5)(n+7)(n+9)$ for all positive even integers $n$ ?

$\textbf{(A) } 3 \qquad\textbf{(B) } 5 \qquad\textbf{(C) } 11 \qquad\textbf{(D) } 15 \qquad\textbf{(E) } 165$

Solution

Since the numbers being multiplied are all odd, $2$ is not a factor of the product, but $3$ and $5$ are since they are 5 consecutive odd numbers. This gives $\boxed{\textbf{(D) } 15}$ as the answer.

2003 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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2003 AMC 10B Problems/Problem 18

Problem 18

Solution

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