Difference between revisions of "2007 iTest Problems/Problem 3"

(category)
(Solution)
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<math>28\Rightarrow 1+2+4+7+14=28\not>28</math>
 
<math>28\Rightarrow 1+2+4+7+14=28\not>28</math>
  
<math>56\Rightarrow 1+2+7+8+14+28=60>56</math>
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<math>56\Rightarrow 1+2+4+7+8+14+28=60>56</math>
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Thus, <math>56\Rightarrow \boxed{\mathrm{C}}</math> is the answer.
  
Thus, <math>56\Rightarrow \boxed{\mathrm{B}}</math> is the answer.
 
 
==See Also==
 
==See Also==
 
{{iTest box|year=2007|num-b=2|num-a=4}}
 
{{iTest box|year=2007|num-b=2|num-a=4}}
  
 
[[Category:Introductory Number Theory Problems]]
 
[[Category:Introductory Number Theory Problems]]

Revision as of 20:58, 23 May 2008

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.

See Also

2007 iTest (Problems, Answer Key)
Preceded by:
Problem 2
Followed by:
Problem 4
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