Bunuel wrote:

ShreeCS 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

Is positive integer n – 1 a multiple of 3?(1) n^3 – n is a multiple of 3 -->

n^3-n=n(n^2-1)=(n-1)n(n+1)=3q. Now,

n-1,

n, and

n+1 are 3 consecutive integers and one of them must be multiple of 3, so no wonder that their product is a multiple of 3. However we don't know which one is a multiple of 3. Not sufficient.

(2) n^3 + 2n^2+ n is a multiple of 3 -->

n^3 + 2n^2+ n=n(n^2+2n+1)=n(n+1)^2=3p --> so either

n or

n+1 is a multiple of 3, as out of 3 consecutive integers

n-1,

n, and

n+1 only one is a multiple of 3 then knowing that it's either

n or

n+1 tells us that

n-1 IS NOT multiple of 3. Sufficient.

Answer: B.

Hi Bunuel,

I got a question. "Is positive integer n-1 a multiple of 3" doesn't require a specific answer?

Through the Statement 2 we figure out that n-1 is a multiple of 3 only if n+1 would be as well, and the answer is yes, conversely if n would be a multiple of 3, in this case the answer is no.

Could me please explain better this doubt

Thank you