2007 AMC 8 Problems/Problem 10

Problem

For any positive integer $n$ , define $\boxed{n}$ to be the sum of the positive factors of $n$ . For example, $\boxed{6} = 1 + 2 + 3 + 6 = 12$ . Find $\boxed{\boxed{11}}$ .

$\textbf{(A)}\ 13 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 24 \qquad \textbf{(D)}\ 28 \qquad \textbf{(E)}\ 30$

Solution

We have $\begin{align*} \boxed{\boxed{11}}&=\boxed{1+11} \\ &=\boxed{12} \\ &=1+2+3+4+6+12 \\ &=28, \end{align*}$ from which the answer is $\boxed{\textbf{(D)}\ 28}.$

~Aplus95 (Fundamental Logic)

~MRENTHUSIASM (Reconstruction)

Video Solution by WhyMath

https://youtu.be/Ih8lEBwPqEY

~savannahsolver

Video Solution by SpreadTheMathLove

https://www.youtube.com/watch?v=omFpSGMWhFc

2007 AMC 8 (Problems • Answer Key • Resources)
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2007 AMC 8 Problems/Problem 10

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Problem

Solution

Video Solution by WhyMath

Video Solution by SpreadTheMathLove

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