2007 AMC 8 Problem 10

Attempt Problem 10 of the 2007 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.

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10.

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 $\boxed{\boxed{11}}.$

$13$

$20$

$24$

$28$

$30$

Answer: D

Concepts:sum of factors custom operation

Difficulty rating: 1150

Solution:

First, we find that $\boxed{11} = 1 + 11 = 12$ since $11$ is prime. Then we need to find $\boxed{12}.$ The factors of $12$ are $1, 2, 3, 4, 6, 12.$ Adding these yields $\boxed{12} = 28.$

Thus, D is the correct answer.

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