Stmt I

2 is not a factor of n

n=5 then (5-1) (5+1) / 24 remainder 0

n=3 (3-1)(3+1) / 24 remainder 6

2 different values

INSUFF

Stmt II

3 is not a factor of n

n=5 then (5-1) (5+1) / 24 remainder 0

n=3 (2-1)(2+1) / 24 remainder 3

2 different values

INSUFF

Stmt I and II

The minimum possible value for n=5. Also if 2 is not a factor of n then n must be odd

(n-1) = odd-1(odd) = even (odd-odd=even)
n+1 = odd+1(odd) = even (odd+odd=even)

Lets take n=5

(5-1) (5+1) /24 remainder 0

Any n values after this would be divisble by 24 since it will provide atleast THREE 2's and ONE 3 which is nothing but 24

24 = 2^3 * 3

The remainder will always be 0

SUFF

Choose C)

Clue 1 and CLue 2 independenty cannot say what could be the values of n.

Based on clues 1 and 2, we know that n should be odd and should not be divisible by 3. So possible values of n are 1,5,7,11,13 etc.

Subustitute any of the values of possible n, and the remainder is always zero.

So ans is C.