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

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: 4

Kudos [? ]:
179
[1 ] , given: 6

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

This post received KUDOS

The answer is A . 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 = 3xm(m^2 + 2) = (3x)((3x)^2 + 2) = 3(x)(9x^2 + 2) DIVISIBLE BY 3 b) Let m = 3x + 1m(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 + 2m(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. The answer is A.

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:

The answer is A . 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 = 3xm(m^2 + 2) = (3x)((3x)^2 + 2) = 3(x)(9x^2 + 2) DIVISIBLE BY 3 b) Let m = 3x + 1m(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 + 2m(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. The answer is A.

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 [? ]:
14
[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: 177

Followers: 3

Kudos [? ]:
24
[0 ] , given: 13

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

swat wrote:

AKProdigy87 wrote:

The answer is A . 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 = 3xm(m^2 + 2) = (3x)((3x)^2 + 2) = 3(x)(9x^2 + 2) DIVISIBLE BY 3 b) Let m = 3x + 1m(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 + 2m(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. The answer is A.

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: 186

Followers: 1

Kudos [? ]:
79
[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
Author
Replies
Last post
Similar Topics:

1
If n is a positive integer, is n3 n divisible by 4? 1. n =
sondenso
6
24 Feb 2008, 17:59

If n is a positive integer, is n^3 - n divisible by 4? (1) n
mexicanhoney
2
07 Oct 2007, 12:20

If n is a positive integer, is n^3 - n divisible by 4? 1) n
asaf
7
27 Jul 2007, 20:55

If n is a positive integer, is n^3-n divisible by 4? 1) n =
Matador
7
15 Apr 2006, 20:07

If n is a positive integer, is n^3 - n divisible by 4? (1) n
TeHCM
15
24 Oct 2005, 21:12