divisibility

[vaivish]

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) 2 is not a factor of n.
(2) 3 is not a factor of n.

OA is c.

pl explain.

[linkinpark]

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) 2 is not a factor of n.
(2) 3 is not a factor of n.

OA is c.

pl explain.

1) consider n = 5, 7 then n^2 - 1 leaves remainder 0, now consider n=9 => n^2 - 1 = 81-1=80 so 80/24 will leave 8 as remainder. so not sufficient to determine

2) consider n=5,7 again we'll get same r=0, now consider n=8, n^2 - 1 = 63, 63/24 will give remainder 15 so we can't determine.

now combining 1 & 2, we get only limited numbers like 5,7,11 which leave r=0 so together they're sufficient. only prime numbers [>3] satisfy the equation.