Data Sufficiency

hey_thr67 wrote:If x- 1 is a positive integer, is x- 1 divisible by 3?

(1) (x2 + x)(x + 1) is divisible by 3.

(2) x(x2-x) is divisible by 3.

x - 1 is an integer implies that x is an integer.

(1) (x² + x)(x + 1) is divisible by 3 implies x(x + 1)² is divisible by 3, which means either x or x + 1 is divisible by 3.
Out of three consecutive integers x - 1, x, and x + 1, only one of them is divisible by 3 and since we know that it's either x or x + 1 then x - 1 is definitely not divisible by 3; SUFFICIENT.

(2) x(x² - x) is divisible by 3 implies x²(x - 1) is divisible by 3, which means either x or x - 1 is divisible by 3.
No definite answer; NOT sufficient.

The correct answer is A.