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multiples of 3

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Source: — Data Sufficiency |
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by GmatKiss » Wed Aug 10, 2011 8:42 am
IMO: D
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by Frankenstein » Wed Aug 10, 2011 8:46 am
finance wrote:Is positive integer n - 1 a multiple of 3?

(1) n3 - n is a multiple of 3

(2) n3 + 2n2+ n is a multiple of 3
Hi,
From(1):
n^3-n = n(n^2-1) = n(n-1)(n+1).
Product of three consecutive numbers is always a multiple of 3(in fact multiple of 6).
So, irrespective of the value of n, n3 - n is always a multiple of 3.
Not sufficient
From(2):
n(n+1)^2 is multiple of 3.
So, either n is multiple of 3 or (n+1) is multiple of 3.
So, (n-1) cannot be multiple of 3
Sufficient

Hence, B
Cheers!

Things are not what they appear to be... nor are they otherwise
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by GmatKiss » Wed Aug 10, 2011 8:49 am
I thought the question had,

1) (n.3 - n) is a multiple of 3
2) (n.3 + 2.n.2)+ n is a multiple of 3

:( :(
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