Data Sufficiency

kwah wrote:Attached is a question from GMAT Prep Test 2.

Please advise how to achieve the result.

Answer: A

Thanks,
K

A similar kind of question is posted here: https://www.beatthegmat.com/n-1-n-1-is-d ... 78998.html

For this question:


If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?

n² - 1 = (n - 1)(n + 1)

(1) n is odd implies both n - 1 and n + 1 are even.
Also n - 1 and n + 1 are consecutive even integers, so one of them will be divisible by 4.
Since one is divisible by 2 and another by 4, so (n - 1)(n + 1) is divisible by 2 * 4 = 8; SUFFICIENT.

(2) n is not divisible by 8.
If n = 1 then the answer is yes.
If n = 2 then the answer is no.
No definite answer; NOT sufficient.

The correct answer is A.