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A positive integer n is a perfect number provided that the sum of all

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Re: A positive integer n is a perfect number provided that the sum of all  [#permalink]

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New post 02 Sep 2018, 18:41
Factors of 28 are 1,28,2,14,4 and 7
So sum of their reciprocals is
1+1/28+1/2+1/14+1/4+1/7
28/28+1/28+14/28+2/28+7/28+4/28
(28+1+14+2+7+4)/28
56/28
2

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Re: A positive integer n is a perfect number provided that the sum of all  [#permalink]

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New post 20 Dec 2018, 01:06
Bunuel wrote:
Ndkms wrote:
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

Can somebody explain what the question asks and gives ? Is quite convoluted I would say.


A perfect number is a positive integer if the sum of its factors equals twice that number. For example, 6 is a perfect number because the sum of the factors of 6 (which are 1, 2, 3, and 6) is 6*2 = 12: 1 + 2 +3 + 6 = 12.

We are given another perfect number 28 and asked to find the sum of the reciprocals of its factors, so to find 1 + 1/2 + 1/4 + 1/7 + 1/14 + 1/28.

Hope it's clear.


What is the purpose of giving the info about 2n here? Its not been used anywhere in calculation of question. (perhaps just to see if we have all the factors?)
GMAT Club Bot
Re: A positive integer n is a perfect number provided that the sum of all &nbs [#permalink] 20 Dec 2018, 01:06

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