Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
For 1, for following values of n, n^3 - n becomes multiple of 3 : 2,3,4,5,6,7,8....
However, by plugging these values in n-1, we have different results. thus, not sufficient
For 2, following values of n gets the equation as a multiple of 3 : 2,3,5,6,7,8.... Its again not sufficient.
Combining 1 & 2, we again can't be conclusive. Thus,answer should be E.
Please write where am I wrong?
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.