[email protected] wrote:If n is a positive integer and r is remainder, when (n-1)(n+1) is divided by 24 what is value of r?

(1) n is not divisible by 2
(2) n is not divisible by 3

Answer -C

Given:
n > 0 and is a +ive integer (n = 1, 2, 3 ...)
(n-1)(n+1) --> (n^2-1) when divided by 24 yields a remainder r, thus n^2-1 may or may not be divisible by 24.

r = ?

St1: n is not divisible by 2 (in other words n is not even). Test some numbers:
n = 1, n^2 -1 / 24 --> remainder = 0
n = 3, n^2 -1 / 24 --> remainder = 8
As we can't answer the target question definitely , INSUFFICIENT

St2: n is not divisible by 3. Test some numbers:
n = 1, n^2 -1 / 24 --> remainder = 0
n = 2, n^2 -1 / 24 --> remainder = 3
As we can't answer the target question definitely , INSUFFICIENT

St1+St2: We now know : n is not even, not divisible by 3 --> thus not divisible by 6.
Again test some numbers:
n = 1, n^2 -1 / 24 --> remainder = 0
n = 5, n^2 -1 / 24 --> remainder = 0
n = 7, n^2 -1 / 24 --> remainder = 0

Since in all the cases we get the remainder as 0, [spoiler]Answer = C[/spoiler]

Regards,
Vivek