2019 AMC 10A Problems/Problem 9

Problem

What is the greatest three-digit positive integer $n$ for which the sum of the first $n$ positive integers is $\underline{not}$ a divisor of the product of the first $n$ positive integers?

$\textbf{(A) } 995 \qquad\textbf{(B) } 996 \qquad\textbf{(C) } 997 \qquad\textbf{(D) } 998 \qquad\textbf{(E) } 999$

Solution

Because the sum of $n$ positive integers is $(n)(n+1)/2$ , and we want this to not be a divisor of the $n!$ , $n+1$ must be prime. The greatest three-digit integer that is prime is $997$ . Subtract $1$ to get $996 => B$ -Lcz

2019 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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2019 AMC 10A Problems/Problem 9

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