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1. f(k+32)=8 is the remainder..so k+32-8 =k+24 is divisible...implies k+24 is divisible by k or say,24 is divisible by k...also k must be more than theremaionder 8...so for k>8 and k dividing 24...the possible value of k could be 12 and 24....hence k>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..