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
(1) n^3 - n is a multiple of 3
(2) n^3 + 2n^2+ n is a multiple of 3
(1) n^3 - n = n(n² - 1) = n(n - 1)(n + 1), which are consecutive integers.alltimeacheiver 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
So, n(n - 1)(n + 1) is a multiple of 3.
For any 3 consecutive integers, one of the 3 will always be a multiple of 3. But we cannot confirm if n - 1 is a multiple of 3.
So, (1) is NOT SUFFICIENT.
(2) n^3 + 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. And if n or n + 1 is a multiple of 3, then (n - 1) cannot be a multiple of 3, which is SUFFICIENT to answer the questions asked.
The correct answer is B.
