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# Is positive integer n 1 a multiple of 3? (1) n3 n is a

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Manager
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Is positive integer n 1 a multiple of 3? (1) n3 n is a [#permalink]

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25 Nov 2007, 09:52
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Is positive integer n – 1 a multiple of 3?

(1) n3 – n is a multiple of 3

(2) n3 + 2(n^2)+ n is a multiple of 3
SVP
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25 Nov 2007, 10:21
JDMBA wrote:
Is positive integer n – 1 a multiple of 3?

(1) n3 – n is a multiple of 3

(2) n3 + 2(n^2)+ n is a multiple of 3

1. n^3 – n = n(n-1)(n+1) insuff.
2. n(n^2 + 2n + 1) = n(n+1)(n+1)

togather, either n or (n+1) is a multiple of 3. so (n-1) is not a multiple of 3.
so C.
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25 Nov 2007, 10:40
GMAT TIGER wrote:
JDMBA wrote:
Is positive integer n – 1 a multiple of 3?

(1) n3 – n is a multiple of 3

(2) n3 + 2(n^2)+ n is a multiple of 3

1. n^3 – n = n(n-1)(n+1) insuff.
2. n(n^2 + 2n + 1) = n(n+1)(n+1)

togather, either n or (n+1) is a multiple of 3. so (n-1) is not a multiple of 3.
so C.

Thanks, Tiger. Good and fast solution.
Manager
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25 Nov 2007, 10:46
Thats the answer I got but Manhattan GMAT says the answer is B. But if you plug 2 into B it is insufficient.
Senior Manager
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25 Nov 2007, 12:53
B is correct.

If (n)(n+1) yield a multiple of 3, it means that either n or n+1 is a mutliple of 3.

n-3, n-2 would also be a multiple of 3. They jump n-1. Therefore, n-1 not a multiple of 3.

If you plug in 2 into statement 2, the result is indeed a multiple of 3:
8 + 8 + 2 = 18, but 2-1 = 1 from the stem is not a mutliple of 3, so answer still is no.
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25 Nov 2007, 13:07
Is positive integer n – 1 a multiple of 3?

(1) n3 – n is a multiple of 3

(2) n3 + 2(n^2)+ n is a multiple of 3

Is N-1 = 3X
from 1

n(n-1)(n+1) , 3 consecutive intigers one of them is a multiple of 3 insuff

from 2

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

n(n+1)(n+1) = 3x if in a set of 3 consec intigers n,n+1,n-1

n,n+1 mutliplication is multiple of 3 then sure n-1 is and n+2 too.

B will do
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26 Nov 2007, 00:13
JDMBA wrote:
Is positive integer n – 1 a multiple of 3?

(1) n3 – n is a multiple of 3

(2) n3 + 2(n^2)+ n is a multiple of 3

1):
n^3-n --> n(n^2-1)--> (n-1)n(n+1) lets say n=3 n-1 is not a multiple of 3. lets say n=4 then n-1 is a multiple of 3. Insuff.

2): n(n+1)(n+1) n or n+1 is a multiple of 3. if n is a multiple of 3 then neither n-1 nor n+1 is a multiple of 3. if n+1 is a multiple of 3 then neither n nor n-1 is a mutiple of 3.

Go ahead pick some numbers I dare ya.

Anyway since n or n+1 is a multiple of 3. n-1 is NOT a multiple of 3 in either case.

B.

Given time constraints i doubt i wouldve gotten this.
Re: DS   [#permalink] 26 Nov 2007, 00:13
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