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.

Question

Mathematics

Allisson Kelley

21 April, 07:51

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.

+5

Answers (1)

Know the Answer?

Huff · Answer 1

Answer: yes, it is

Step-by-step explanation:

A number is divisible by 6 if it is divisible by 2 and 3 simultaniously.

n = k (k+1) (k-1)

If k-1 is a multiple of 3, n is divisible by 3, so one of the requirements is ok.

Now, if k-1 is a multiple of 3, it can be even or odd.

if k-1 is even, then it is divisible by 2 and as it is divisible by 3 as well, n is divisible by 6

if k-1 is odd, then k and k+1 is even, hence, divisible by 2.

As n = k (k+1) (k-1), n is also divisible by 6.