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

This topic has expert replies
Moderator
Posts: 2205
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7222
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage