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Source: — Data Sufficiency |
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by ajith » Sat Feb 20, 2010 3:11 am
gmatnmein2010 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
1)n^3 - n is a multiple of 3

(n-1) n+1) n is a multiple of 3... not sufficient

2) n(n+1)^2 is a multiple of 3 .. Either n or n+1 is a multiple of 3

In either case n-1 is not a multiple of 3 .. Sufficient

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by thephoenix » Sat Feb 20, 2010 3:20 am
gmatnmein2010 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
1) INSUFFICIENT: (n - 1)(n)(n + 1) is a multiple of 3. Any three consecutive positive integers include exactly one multiple of 3 . Of the three terms n - 1, n, and n + 1, oneis a multiple of 3 but wedont know which one.

(2) SUFFICIENT: n(n + 1)(n + 1) is a multiple of 3. This tells us that either n or n + 1 is a multiple of 3. now n - 1, n, and n + 1 represent three consecutive integers and any three consecutive integers include exactly one multiple of 3. If the multiple of 3 is either the n or the n + 1 term, then the n - 1 term cannot be a multiple of 3.

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by shashank.ism » Sat Feb 20, 2010 1:28 pm
gmatnmein2010 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

St.1: n3 - n = n(n2 -1)=n(n+1)(n-1) so either n or n+1 or n-1 is multiple of 3 it doesn't clarifies whether n-1 is a multiple of 3 or not =========== insufficient.
St.2: n3 + 2n2+ n = n (n2+2n+1) = n(n+1)^2 is a multiple of 3 so either n or n+1 is a multiple of 3=========== insufficient.

combined : since either n or n+1 is a multiple of 3 so n-1 is surely not ----suff.
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by onedayi'll » Sat Feb 20, 2010 4:09 pm
What's the OA?

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