What is the remainder when (n-1)*(n+1) is divided by 24?

(1) When n is divided by 3, the remainder is 1.
So n-1 is divisible by 3. Thus, (n-1)(n+1) is divisible by 3. But we do not know anything about the divisibility by 8.
If n is odd, n-1 and n+1 will be consecutive even integers, meaning one of n-1 and n+1 will surely be divisible by 4, and thus (n-1)(n+10 will be divisible by 2*4 or 8 also.
But if n is even, n-1 and n+1 will be consecutive odd integers and not divisible by 8.

(2) n is odd.
Nothing about divisibility by 24.
Say n=1, remainder will be 1, and when n=7, the remainder will be 7.

Combined.
(n-1)*(n+1) is divisible by 3 and 2*4, so divisible by 2*4*3=24
Suff

C