Difference between revisions of "2007 AMC 8 Problems/Problem 10"

Latest revision as of 14:54, 2 July 2024

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)
Preceded by Problem 9	Followed by Problem 11
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
All AJHSME/AMC 8 Problems and Solutions

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

@@ Line 24: / Line 24: @@
 ~savannahsolver
+==Video Solution by SpreadTheMathLove==
+https://www.youtube.com/watch?v=omFpSGMWhFc
 ==See Also==
 {{AMC8 box|year=2007|num-b=9|num-a=11}}
 {{MAA Notice}}

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