2003 AMC 12B Problems/Problem 12

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 $n$ ?

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

Solution

Since for all consecutive odd integers, one of every five is a multiple of 5 and one of every three is a multiple of 3, the answer is $3 * 5 = 15$ , so $\framebox{D}$ . The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2003 AMC 12B Problems/Problem 12

Solution