BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

a perfect number?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

a perfect number?

by sanju09 » Sat Oct 08, 2011 4:20 am
A perfect number is defined as one that is equal to the sum of its distinct positive integer divisors that are less than the number itself. Which of the following is a perfect number?
(A) 24
(B) 25
(C) 28
(D) 30
(E) 35
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 496
Joined: Tue Jun 07, 2011 5:34 am
Thanked: 38 times
Followed by:1 members

by sl750 » Sat Oct 08, 2011 4:25 am
Factors of 28

1,2,4,7,14 , Sum of the distinct factors = 28
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sat Oct 08, 2011 4:28 am
sanju09 wrote:A perfect number is defined as one that is equal to the sum of its distinct positive integer divisors that are less than the number itself. Which of the following is a perfect number?
(A) 24
(B) 25
(C) 28
(D) 30
(E) 35
(A) 1 + 2 + 3 + 4 + 6 + 8 + 12 is not 24, FALSE
(B) 1 + 5 is not 25, FALSE
(C)1 + 2 + 4 + 7 + 14 = 28, TRUE

The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 359
Joined: Wed Mar 11, 2009 4:37 am
Location: Kolkata, India
Thanked: 50 times
Followed by:2 members

by Abhishek009 » Sat Oct 08, 2011 4:50 am
sanju09 wrote:A perfect number is defined as one that is equal to the sum of its distinct positive integer divisors that are less than the number itself. Which of the following is a perfect number?
(A) 24
(B) 25
(C) 28
(D) 30
(E) 35
All the known Perfect numbers can be found out using the simple formula -

All of the perfect numbers that have been found so far fit the formula

{2^(n-1) * ( 2^n ) - 1 }


Try plugging in the values of n , we can get the answer in seconds...

2^1 * ( 2^2 - 1 ) = 2 * 3 = 6

2^2 * ( 2^3 - 1 ) = 4 * 7 = 28



I didn't invent the formula here is the original formula -

https://mathforum.org/dr.math/faq/faq.pe ... l#allknown
Abhishek
Top
Post new topic Post Reply
• Page 1 of 1