Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 Jul 2015, 12:08

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# n and m are positive integers, can n divisible by 3? 1/ n

Author Message
TAGS:
Intern
Joined: 24 Sep 2009
Posts: 16
Followers: 0

Kudos [?]: 4 [0], given: 0

n and m are positive integers, can n divisible by 3? 1/ n [#permalink]  24 Sep 2009, 12:58
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

100% (04:33) correct 0% (00:00) wrong based on 2 sessions
n and m are positive integers, can n divisible by 3?
1/ n divisible by m(m^2+2)
2/ n divisible by m^2(m+2)

I guess it's C ???
Manager
Joined: 11 Sep 2009
Posts: 129
Followers: 5

Kudos [?]: 229 [1] , given: 6

Re: Divisible question [#permalink]  24 Sep 2009, 17:18
1
KUDOS

Any integer can be represented in terms of divisibility by 3 by placing them in the following 3 groups:

a) (3x) - Divisible by 3 (ex. 3, 6, 9, etc.)
b) (3x + 1) - Remainder of 1 (ex. 4, 7, 10, etc.)
c) (3x + 2) - Remainder of 2 (ex. 5, 8, 11, etc.)

where x is an integer.

Statement 1: n divisible by m(m^2+2):

a) Let m = 3x
$$m(m^2 + 2) = (3x)((3x)^2 + 2) = 3(x)(9x^2 + 2)$$ DIVISIBLE BY 3

b) Let m = 3x + 1
$$m(m^2 + 2) = (3x+1)((3x+1)^2 + 2) = (3x + 1)(9x^2 + 6x + 1 + 2)$$
$$= (3x + 1)(9x^2 + 6x + 3) = 3(3x^2 + 2x + 1)(3x + 1)$$ DIVISIBLE BY 3

c) Let m = 3x + 2
$$m(m^2 + 2) = (3x+2)((3x+2)^2 + 2) = (3x + 1)(9x^2 + 12x + 4 + 2)$$
$$= (3x + 1)(9x^2 + 12x + 6) = 3(3x^2 + 4x + 2)(3x + 1)$$ DIVISIBLE BY 3

Therefore Statement 1 is sufficient. If n is divisible by m(m^2 + 2), then it is divisible by 3.

Statement 2: n divisible by m^2(m+2):
...
c) Let m = 3x + 2
[m]m^2(m + 2) = (3x+2)(3x+2)(3x+2+2) = (3x+2)(3x+2)(3x+4) NOT DIVISIBLE BY 3

Therefore Statement 2 is not sufficient.

Intern
Joined: 24 Sep 2009
Posts: 16
Followers: 0

Kudos [?]: 4 [0], given: 0

Re: Divisible question [#permalink]  24 Sep 2009, 19:29
AKProdigy87 wrote:

Any integer can be represented in terms of divisibility by 3 by placing them in the following 3 groups:

a) (3x) - Divisible by 3 (ex. 3, 6, 9, etc.)
b) (3x + 1) - Remainder of 1 (ex. 4, 7, 10, etc.)
c) (3x + 2) - Remainder of 2 (ex. 5, 8, 11, etc.)

where x is an integer.

Statement 1: n divisible by m(m^2+2):

a) Let m = 3x
$$m(m^2 + 2) = (3x)((3x)^2 + 2) = 3(x)(9x^2 + 2)$$ DIVISIBLE BY 3

b) Let m = 3x + 1
$$m(m^2 + 2) = (3x+1)((3x+1)^2 + 2) = (3x + 1)(9x^2 + 6x + 1 + 2)$$
$$= (3x + 1)(9x^2 + 6x + 3) = 3(3x^2 + 2x + 1)(3x + 1)$$ DIVISIBLE BY 3

c) Let m = 3x + 2
$$m(m^2 + 2) = (3x+2)((3x+2)^2 + 2) = (3x + 1)(9x^2 + 12x + 4 + 2)$$
$$= (3x + 1)(9x^2 + 12x + 6) = 3(3x^2 + 4x + 2)(3x + 1)$$ DIVISIBLE BY 3

Therefore Statement 1 is sufficient. If n is divisible by m(m^2 + 2), then it is divisible by 3.

Statement 2: n divisible by m^2(m+2):
...
c) Let m = 3x + 2
[m]m^2(m + 2) = (3x+2)(3x+2)(3x+2+2) = (3x+2)(3x+2)(3x+4) NOT DIVISIBLE BY 3

Therefore Statement 2 is not sufficient.

Hi AKProdigy87,

I don't quite understand that. Say we have n=4 and m=2.
Then m(m^2+2)=2(2^2+2)=12
n=4 is devisible by 12 but doesn't mean 3 is divisible by n.
Manager
Joined: 14 Dec 2008
Posts: 171
Followers: 1

Kudos [?]: 16 [0], given: 39

Re: Divisible question [#permalink]  25 Sep 2009, 07:11
hi AKProdigy87 , good way of solving, but is this kind of substitution correct?
Manager
Joined: 08 Jul 2009
Posts: 176
Followers: 3

Kudos [?]: 34 [0], given: 13

Re: Divisible question [#permalink]  25 Sep 2009, 10:34
swat wrote:
AKProdigy87 wrote:

Any integer can be represented in terms of divisibility by 3 by placing them in the following 3 groups:

a) (3x) - Divisible by 3 (ex. 3, 6, 9, etc.)
b) (3x + 1) - Remainder of 1 (ex. 4, 7, 10, etc.)
c) (3x + 2) - Remainder of 2 (ex. 5, 8, 11, etc.)

where x is an integer.

Statement 1: n divisible by m(m^2+2):

a) Let m = 3x
$$m(m^2 + 2) = (3x)((3x)^2 + 2) = 3(x)(9x^2 + 2)$$ DIVISIBLE BY 3

b) Let m = 3x + 1
$$m(m^2 + 2) = (3x+1)((3x+1)^2 + 2) = (3x + 1)(9x^2 + 6x + 1 + 2)$$
$$= (3x + 1)(9x^2 + 6x + 3) = 3(3x^2 + 2x + 1)(3x + 1)$$ DIVISIBLE BY 3

c) Let m = 3x + 2
$$m(m^2 + 2) = (3x+2)((3x+2)^2 + 2) = (3x + 1)(9x^2 + 12x + 4 + 2)$$
$$= (3x + 1)(9x^2 + 12x + 6) = 3(3x^2 + 4x + 2)(3x + 1)$$ DIVISIBLE BY 3

Therefore Statement 1 is sufficient. If n is divisible by m(m^2 + 2), then it is divisible by 3.

Statement 2: n divisible by m^2(m+2):
...
c) Let m = 3x + 2
[m]m^2(m + 2) = (3x+2)(3x+2)(3x+2+2) = (3x+2)(3x+2)(3x+4) NOT DIVISIBLE BY 3

Therefore Statement 2 is not sufficient.

Hi AKProdigy87,

I don't quite understand that. Say we have n=4 and m=2.
Then m(m^2+2)=2(2^2+2)=12
n=4 is devisible by 12 but doesn't mean 3 is divisible by n.

The q is saying n is divisible by m(m^2+2) if m is 12 then the minimum value of n is 12 which is divisible by 3.
Manager
Joined: 27 Oct 2008
Posts: 185
Followers: 1

Kudos [?]: 106 [0], given: 3

Re: Divisible question [#permalink]  25 Sep 2009, 22:39
Yes. Statement 1 alone is sufficient
taking m(m^2+2) and since m is positive integer, you can take m = 1,2,3 and so on
for any such value of m, this equation m(m^2+2) will always be a multiple of 3.
Since its a multiple of 3 and is a factor of n, thus n will be a multiple of 3 or in other words n will be divisible b 3.

Statement 2 is not sufficient
taking m^2(m+2) and since m is positive integer, you can take m = 1,2,3 and so on
for any such value of m, this equation m^2(m+2), seems to be a multiple of 3 in some cases and not a multiple in some cases. So based on this alone we cannot guess if n is divisible by 3 or not.

Hence A.
Re: Divisible question   [#permalink] 25 Sep 2009, 22:39
Similar topics Replies Last post
Similar
Topics:
If n is positive integer, is (n^3 - n) divisible by 4? 1. n 5 08 Sep 2008, 13:34
2 If n is a positive integer, is n3 n divisible by 4? 1. n = 6 24 Feb 2008, 17:59
If n is a positive integer, is n^3 - n divisible by 4? (1) n 2 07 Oct 2007, 12:20
If n is a positive integer, is n^3 - n divisible by 4? 1) n 7 27 Jul 2007, 20:55
If n is a positive integer, is n^3-n divisible by 4? 1) n = 7 15 Apr 2006, 20:07
Display posts from previous: Sort by

# n and m are positive integers, can n divisible by 3? 1/ n

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.