MGMAT

f2001290 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

I will go with D. Any explanations???

How did you get D ?

1 - n(n^2-1) = 3k
n*(n+1)*(n-1) = 3k
So, n, n+1 or a n-1 is a multiple of 3. Insufficient.

As an example take n = 3 and n = 4. n^3-n is a multiple of 3 for
both values of n but only n=4 will yield n-1 as a multiple of 3.

2 - n*(n+1)^2 = 3*m
n or n+1 is a multiple of 3. So, n-1 cannot be a multiple of 3.
Sufficient.

My vote for B.

Thanks Jay- Typing mistake. B is the right option