1) n not divisible by 2=> n is odd=> (n-1) and (n+1) must be consective even numbers.

if n=1, 0*2/24 leaves remainder 0
if n=3, 2*4/24 leaves remainder 8
not sufficient


2) n not divisible by 3=> n can be even or 1, 5, 7, 11, 13....

if n=5, 4*6/24 leaves remainder 0
if n=2, 1*3/24 leaves remainder 3
not sufficient

together,
n must be odd and not divisible by 3=> n can be 1, 5, 7, 11, 13...
if n=7, 6*8/24 leaves remainder 0
if n=11, 10*12/24 leaves remainder 0

hence C.

Scooby good solution. Additionally, based on both statements n could equal 1 which would result in a remainder of 0.

Scooby,

No problem with the math and logic until the very last. How do you know that for every prime number, n, (n-1)*(n+1) is evenly divisible by 24?

Thanks

@ pjasak: thanks for pointing out. sorry, did a bad generalization. will edit the post.

@ rossmj: thanks, true. missed that out.