Divisible problem

gmat009 wrote:If n and k are positive integers, is n divisible by 6?
(1) n = k(k + 1)(k - 1)
(2) k – 1 is a multiple of 3.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

duongthang wrote:how do you know that product of 3 consecutives is divided by 3.2

pls, prove.

Brent@GMATPrepNow wrote:

gmat009 wrote:If n and k are positive integers, is n divisible by 6?
(1) n = k(k + 1)(k - 1)
(2) k-1 is a multiple of 3.

Target question: Is n divisible by 6?

Aside: For a number to be divisible by 6, it must be divisible by 2 AND by 3

Statement 1: n = k(k + 1)(k - 1)
First recognize that k-1, k and k+1 are 3 consecutive integers

There's a nice rule that says: If there are b consecutive integers, then exactly one of them is divisible by b

Since there are 3 consecutive integers, we know that one of them is divisible by 3.
We can also conclude that at least one of them is divisible by 2.
Given all of this, the product of the 3 integers (n) must be divisible by 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: k-1 is a multiple of 3
Since there's no information about n, there's no way to determine whether or not n is divisible by 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent