Six persons N, O, P, Q, R and S live in a six storey

Solution

P lives two floors above R. Q lives just below S. S lives on a prime numbered floor. We will have three cases, first, when S lives on second floor, second, when S lives on third floor and third when S lives on fifth floor. O lives below P but above N. N doesn't live below Q. Case 3 gets eliminated. In case 1, P lives on 6 th floor, O lives on 5 th floor. In case 2, O lives on 5 th floor and N lives on 1 st floor but this case will get discarded as N doesn't live below Q. The final arrangement is as follows.