n-1 a multiple of 3?

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 76
Joined: Tue Dec 26, 2006 11:26 am
Followed by:3 members

n-1 a multiple of 3?

by maxim730 » Wed Feb 07, 2007 5:06 am
Source: Manhattan GMAT



Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3


OA in a few, please explain. THanks:)
Last edited by maxim730 on Fri Feb 09, 2007 8:46 am, edited 1 time in total.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2228
Joined: Wed Dec 27, 2006 3:28 pm
Location: Montreal, Canada
Thanked: 639 times
Followed by:694 members
GMAT Score:780

by Stacey Koprince » Wed Feb 07, 2007 10:54 pm
Hey, maxim - can you check your formatting please? Please indicate any exponents with a carat (eg x^3). Thanks!
Please note: I do not use the Private Messaging system! I will not see any PMs that you send to me!!

Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT

Contributor to Beat The GMAT!

Learn more about me

Senior | Next Rank: 100 Posts
Posts: 38
Joined: Sat Dec 30, 2006 7:46 pm
Thanked: 1 times

IS n-1 amultiple of 3 ?

by banona » Fri Feb 09, 2007 7:57 am
Hi maxim 730,
let's try to guess if positive integer n – 1 a multiple of 3?

REGRADING THE QUESTIONS FIRST ASSUMPTION :

(1) n3 – n is a multiple of 3 : this means that n(n-1)(n+1) IS MULTIPLE OF 3 : this means that each one could suffisantly be a multiple of three. So the assumption 1 is insuffisant ( so answer is either B, D or E).
To make sure of this first answer, you can pick n = 2. or n=3; both possibilities give you a number of ( n^3 - n) that is multiple of 3;

REGARDING THE ASSUMPTION 2: (2) says that n3 + 2n2+ n is a multiple of 3
this leads to n(n+1)^2 is multiple of 3 , we, here, have two possibilities, either n is multiple of 3 or (n+1)^2 is multiple of 3

let's take look at each of these conclusions :

* if n is multiple of 3, then n-1 is not multiple of 3 ( to rephrase, we would say that the remainder of the division of n-1 by 3 is 2)

* If (n+1)^2 is multiple of 3, ( to rephrase, 3 is prime factor of (n+1)2) , then necessarely, n+1 is multilpe 3, because if it wasn't not a prime factor of (n+1), it would'nt be a factor of (n+1)^2, ALL THAT means that (n+1) is multiple of 3, and consequently ( n-1) is not a multiple of 3.

So I would go for B;

I appplogize for my wordy and awkward sentences, you would understand that english my third langage.

PLEASE CAN ANYBODY COMMENT MY REASONING,

good luck for us.

Senior | Next Rank: 100 Posts
Posts: 76
Joined: Tue Dec 26, 2006 11:26 am
Followed by:3 members

by maxim730 » Fri Feb 09, 2007 8:47 am
Modified the original topic to include ^. I totally did not see that it was missing.

User avatar
Legendary Member
Posts: 540
Joined: Sat Dec 20, 2008 7:24 pm
Thanked: 37 times
Followed by:6 members

by navami » Mon Mar 14, 2011 6:41 am
looks E to me
This time no looking back!!!
Navami

Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Tue Jun 19, 2007 8:38 am

by santosh_surathkal » Mon Mar 14, 2011 8:01 am
(1) n^3 - n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3

Option 1...
n^3 -n = n(n^2 - 1) = n (N^2 - 1^2) = n (n + 1) ( n - 1)



Option 2 ...

n^3 + 2n^2+ n = n(n^2 + 2n + 1) = n (n+1) ( n + 1)

now from option (2) . either n or (n+1) is multiple of 3.

in any case n - 1 would not be a multiple of 3.

Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Tue Jun 19, 2007 8:38 am

by santosh_surathkal » Mon Mar 14, 2011 8:05 am
Option B alone