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| ==Problem 18==
| | #REDIRECT [[2003 AMC 12B Problems/Problem 12]] |
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| What is the largest integer that is a divisor of
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| <cmath> (n+1)(n+3)(n+5)(n+7)(n+9) </cmath>
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| for all positive even integers <math>n</math>?
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| <math>\textbf{(A) } 3 \qquad\textbf{(B) } 5 \qquad\textbf{(C) } 11 \qquad\textbf{(D) } 15 \qquad\textbf{(E) } 165</math>
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| ==Solution==
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| Since the numbers being multiplied are all odd, <math>2</math> is not a factor of the product, but <math>3</math> and <math>5</math> are since they are 5 consecutive odd numbers. This gives <math>\boxed{\textbf{(D) } 15}</math> as the answer.
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| ==See Also==
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| {{AMC10 box|year=2003|ab=B|num-b=17|num-a=19}}
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| {{MAA Notice}}
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