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# Is positive integer n 1 a multiple of 3? (1) n^3 n is a

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Manager
Joined: 23 May 2007
Posts: 108
Is positive integer n 1 a multiple of 3? (1) n^3 n is a [#permalink]

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09 Jul 2007, 20:33
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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
Manager
Joined: 07 Feb 2007
Posts: 212

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10 Jul 2007, 05:42
Himalayan wrote:
dreamgmat1 wrote:
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

B.

Sorry, I made a mistake. B is right.
(2) n^3+2n^2+n=n*(n+1)^2
--> n=3a or n=3a-1, where a is a positive integer
--> n-1= 3a-1 or n-1=3a-2, none of which is a multiple of 3.
--> Sufficient.

The exaplanation relates to the link below:
http://www.gmatclub.com/phpbb/viewtopic.php?t=48376.

Last edited by wudy on 10 Jul 2007, 09:18, edited 1 time in total.
Manager
Joined: 12 Apr 2007
Posts: 168

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10 Jul 2007, 07:02
i'll go with B here too

S2: n(n+1)^2

this means either n or n+1 is a mult of 3. if this is the case, there is no way n-1 can be a mult of 3.
Director
Joined: 16 May 2007
Posts: 548

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10 Jul 2007, 08:51
I will go with E. Picking up numbers will help. Pick up n =3 and you will see both statements are insuff.
Manager
Joined: 12 Apr 2007
Posts: 168

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10 Jul 2007, 09:22
trahul4 wrote:
I will go with E. Picking up numbers will help. Pick up n =3 and you will see both statements are insuff.

What is an example for S2 where the answer is yes?
Manager
Joined: 07 Feb 2007
Posts: 212

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10 Jul 2007, 09:24
trahul4 wrote:
I will go with E. Picking up numbers will help. Pick up n =3 and you will see both statements are insuff.

Please check the above link. E is not the answer, although at first I got E too.
Manager
Joined: 23 May 2007
Posts: 108

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10 Jul 2007, 21:24
OA is B

Any three consecutive positive integers include exactly one multiple of 3
10 Jul 2007, 21:24
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