2007 iTest Problems/Problem 3

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Problem

An abundant number is a natural number that's proper divisors' sum is greater than the number. Which one of the following natural numbers is an abundant number?

$\mathrm{(A)}\, 14\quad\mathrm{(B)}\, 28\quad\mathrm{(C)}\, 56$

Solution

$14\Rightarrow 1+2+7=10\not>14$

$28\Rightarrow 1+2+4+7+14=28\not>28$

$56\Rightarrow 1+2+4+7+8+14+28=60>56$

Thus, $56\Rightarrow \boxed{\mathrm{C}}$ is the answer.

2007 iTest (Problems)
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2007 iTest Problems/Problem 3

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