Number system

vipulgoyal wrote:N is an integer, r is the remainder when (N-1)(N+1) is divided by 24. r=?

1) N is not a multiple of 2
2) N is not a multiple of 3

Statement 1: This means N is odd.
So, both (N - 1) and (N + 1) are two consecutive even integers.
--> exactly one of (N - 1) and (N + 1) is a multiple of 4
--> (N - 1)(N + 1) is divisible by 8

This doesn't help us to identify r as r can have different values depending upon whether (N - 1)(N + 1) is divisible by 3 or not.

Not sufficient

Statement 2: Exactly one among three consecutive integers is divisible by 3.
As N is not divisible by 3, either (N - 1) or (N + 1) is divisible by 3.
So, (N - 1)(N + 1) is divisible by 3.

This doesn't help us to identify r as r can have different values depending upon whether (N - 1)(N + 1) is divisible by 8 or not.

Not sufficient

1 & 2 Together: Now we know that (N - 1)(N + 1) is divisible by both 3 and 8.
Hence, r = 0

Sufficient

The correct answer is C.

vipulgoyal wrote:what if N = 1

0x1x2 / 24

Zero is divisible by any integer you can think of except zero.
Hence, zero leaves a remainder of zero when divided by any integer other than zero.