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A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is

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by BTGmoderatorLU » Wed May 05, 2021 3:42 am

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Source: Official Guide

A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28?

A. 1/4
B. 56/27
C. 2
D. 3
E. 4

The OA is C
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Re: A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n,

by Scott@TargetTestPrep » Fri May 14, 2021 6:55 am
BTGmoderatorLU wrote: ↑
Wed May 05, 2021 3:42 am
 Source: Official Guide

A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28?

A. 1/4
B. 56/27
C. 2
D. 3
E. 4

The OA is C
Solution:

The factors of 28 are 1, 2, 4, 7, 14, and 28. Therefore, the sum of the reciprocals of these numbers is:

1 + ½ + ¼ + 1/7 + 1/14 + 1/28 = 28/28 +14/28 + 7/28 + 4/28 + 2/28 + 1/28 = 56/28 = 2

(Note: The sum of the reciprocals of all the factors of a perfect number is always 2.)

Answer: C

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