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From statement 1 we have n= k^3+ 3k^2 + 3k +1. and we have to fine n/k. that is (k^3+ 3k^2 + 3k +1)/k that is equal to k^2 +3k +3 + 1/k . Also in the question stem it is given that k is >1 so the remainder of n/k is 1. So sufficient
Statement 2 says that k=5. But no information of n is given and hence this statement alone is insuficient.