Look f(k+32)=8 is the remainder..so k+32-8 =k+24/k is divisible...
or can say that
(k/k)+ (k/24) is divisible by k
or can say that 24 is divisible by k......................(1)

if remainder is 8 also k must be more than 8

Now 8<K ........................(2)

from (1) k can be 1, 2, 3, 4, 6, 8, 12, 24.
from (2) k can be 9.....................24
by combining we get k= 12 &/or 24.
in each case K is bigger than 10.

sufficient..

2. with same argument..36 should be divisible by k and k>6...value satisfying these,k=9,12,18,36..hence k>10 i not true always..

Insufficient