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# m04 #31

Author Message
Senior Manager
Status: Happy to join ROSS!
Joined: 29 Sep 2010
Posts: 279
Concentration: General Management, Strategy
Schools: Ross '14 (M)
Followers: 19

Kudos [?]: 120 [0], given: 48

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21 Nov 2010, 07:25
A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and . Which of the following is also a perfect number?

12
20
28
48
60
===
OA is just 28 w/o any explanation.
Is there any shortcut for solving such questions?
Kaplan GMAT Instructor
Joined: 21 Jun 2010
Posts: 148
Location: Toronto
Followers: 44

Kudos [?]: 173 [0], given: 0

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21 Nov 2010, 08:07
Vorskl wrote:
A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and . Which of the following is also a perfect number?

12
20
28
48
60
===
OA is just 28 w/o any explanation.
Is there any shortcut for solving such questions?

No shortcut - you just have to work through the choices as quickly as you can.

When we see "which of the following" on problem solving questions, the answer is D or E a disproportionate (i.e. more than 40%) amount of the time, so we should start at the bottom:

60: 1, 60, 2, 30, 3, 10, 4, 15... even adding up 1, 2, 3, 4, 10, 15 and 30 it's already more than 60... move on!

48: 1, 48, 2, 24, 3, 16, 4, 12... even adding up 1, 2, 3, 4, 12, 16 and 24 it's already more than 48... move on!

28: 1, 28, 2, 14, 4, 7... that's it - 1 + 2 + 4 + 7 + 14 = 28... done!

You could have narrowed the field a bit by thinking "well, if the number has too many factors, they'll likely add up to too much; so, I should check the answers with fewer factors first", but it really doesn't take long to check the choices if you're quick with factoring.
Re: m04 #31   [#permalink] 21 Nov 2010, 08:07
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# m04 #31

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