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

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Senior Manager
Joined: 21 Jun 2006
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Is positive integer n 1 a multiple of 3? (1) n^3 n is a [#permalink]

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27 Jun 2007, 21:12
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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

Kudos [?]: 144 [0], given: 0

Director
Joined: 26 Feb 2006
Posts: 900

Kudos [?]: 162 [0], given: 0

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27 Jun 2007, 21:22
ArvGMAT 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.

1: n^3 – n = (n -1) (n) (n+1) which is a consequtive integer. here among (n -1) or n or (n+1), any one could be a multiple of 3.

2: n^3 + 2n^2+ n = n (n + 1) (n + 1). here either n or (n+1) is a multiple of 3. so (n-1) cannot be a multiple of 3.

Kudos [?]: 162 [0], given: 0

VP
Joined: 10 Jun 2007
Posts: 1434

Kudos [?]: 371 [0], given: 0

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27 Jun 2007, 21:34
ArvGMAT 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

(1) n * (n+1) * (n -1) = integer * 3
either n, n+1, or n-1 one can be divisible by 3.
INSUFFICIENT.

(2) n * (n^2 + 2n + 1) = n * (n+1) * (n+1) = integer * 3
either n or n+1 is divisible by 3.
if n is divisible by 3, n+1 and n-1 must not be a multiple of 3
if n+1 is divisible by 3, n and n-1 must not be a multiple of 3
Either case, n-1 is not a multiple of 3.
SUFFICIENT.

B

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Re: DS: consecutive multiples   [#permalink] 27 Jun 2007, 21:34
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