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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
A perfect number is one which is equal to the sum of all its
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01 Jan 2020, 04:18
01 Jan 2020, 04:18
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A perfect number is one which is equal to the sum of all its positive factors that are less than the number itself. Which of the following is a perfect number?
(A) 1
(B) 4
(C) 6
(D) 8
(E) 10
(A) 1
(B) 4
(C) 6
(D) 8
(E) 10
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: A perfect number is one which is equal to the sum of all its
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02 Jan 2020, 08:50
02 Jan 2020, 08:50
Let's take each option choice and try to find the factors which are less than the number and the sum of these factors
A. 1
No factor less than 1 so sum = 0 ≠ 1 => Not perfect square
B. 4
Factors less than 4 = 1,2 => Sum = 1 + 2 = 3 ≠ 4 => Not perfect square
C. 6
Factors less than 6 = 1,2,3 => Sum = 1 + 2 + 3 = 6 => perfect square
We don't need to solve further but solving just for reference
D. 8
Factors less than 8 = 1,2,4 => Sum = 1 + 2 + 4= 7 ≠ 8 => Not perfect square
E. 10
Factors less than 10 = 1,2,5 => Sum = 1 + 2 + 5= 8 ≠ 10 => Not perfect square
So, Answer will be C
Hope it helps!
A. 1
No factor less than 1 so sum = 0 ≠ 1 => Not perfect square
B. 4
Factors less than 4 = 1,2 => Sum = 1 + 2 = 3 ≠ 4 => Not perfect square
C. 6
Factors less than 6 = 1,2,3 => Sum = 1 + 2 + 3 = 6 => perfect square
We don't need to solve further but solving just for reference
D. 8
Factors less than 8 = 1,2,4 => Sum = 1 + 2 + 4= 7 ≠ 8 => Not perfect square
E. 10
Factors less than 10 = 1,2,5 => Sum = 1 + 2 + 5= 8 ≠ 10 => Not perfect square
So, Answer will be C
Hope it helps!
gmatclubot
Re: A perfect number is one which is equal to the sum of all its [#permalink]
02 Jan 2020, 08:50
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