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# Which of the following is/are perfect numbers if "Perfect Number" is d

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CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
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Which of the following is/are perfect numbers if "Perfect Number" is d  [#permalink]

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08 Oct 2018, 00:20
00:00

Difficulty:

55% (hard)

Question Stats:

51% (01:57) correct 49% (01:54) wrong based on 48 sessions

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Which of the following is/are perfect numbers if "Perfect Number" is defined as number for which sum of all it's factors is twice the number.
I) 6
II) 28
III) 36

A) I only
B) II only
C) III only
D) I and II only
D) I, II and III

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Which of the following is/are perfect numbers if "Perfect Number" is d  [#permalink]

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08 Oct 2018, 03:37
GMATinsight wrote:
Which of the following is/are perfect numbers if "Perfect Number" is defined as number for which sum of all it's factors is twice the number.
I) 6
II) 28
III) 36

A) I only
B) II only
C) III only
D) I and II only
D) I, II and III

http://www.GMATinsight.com

If someone knows about perfect number, one would choose I and II because these are the two smallest perfect number and next is in 400s and then in 8000s.

Let us see..
6= 1*2*3*6, so sum =1+2+3+6=12...yes
28=1*2*4*7*14*28 so sum =1+2+4+7+14+28=56..yes
36=1*2*3*4*6*9*12*18*36, sum is clearly>72..no
Only I and II

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: Which of the following is/are perfect numbers if "Perfect Number" is d  [#permalink]

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08 Oct 2018, 03:48
In case someone is curious,
General formula of perfect number is P=(2^(n-1))(2^n-1) when n=prime number
.
Putting n =2, we get smallest perfect no= 2*3 = 6
Next perfect no, put n = 3, we get, P = (2^2)*(2^3 -1)= 28
Next , put n = 5, P = (2^4)(2^5 -1) = 16*31= 496
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Re: Which of the following is/are perfect numbers if "Perfect Number" is d   [#permalink] 08 Oct 2018, 03:48
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