sunilrawat wrote:If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?
1. n is not divisible by 2
2. n is not divisible by 3
OA C
Please also specify what the value should be.
(1) n is odd.
Hence, (n - 1) and (n + 1) are even consecutive integers, i.e. one of them is divisible by 2 and the other one is by 4. Therefore we can only conclude that (n - 1)(n + 1) is divisible by 8; NOT sufficient.
(2) As (n - 1), n, and (n + 1) are three consecutive integers and n is not divisible by 3, either (n - 1) or (n + 1) is divisible by 3. Therefore we can only conclude that (n - 1)(n + 1) is divisible by 3; Not sufficient.
Combining (1) and (2), (n - 1)(n + 1) is divisible by 8 and 3 and hence by 24.
Therefore, the value r is 0; Sufficient.
The correct answer is
C.
