Instructions

Study the given information carefully to answer the given questions.
Seven athletes — M, N, O, P, Q R and S live on seven . different floors of a building but not necessarily in the same order. The lower most floor of the building is numbered 1, the one above that is numbered 2 and so on till the topmost floor is numbered 7. Each one of them runs for a different distance in a marathon750 m, 1200 m, 2200m, 2900 m, 3600 m, 4300 m and 5000 m, but not necessarily in the same order. The one who runs for 4300 m lives on floor numbered 4. Only one person lives between M and the one who runs for 4300 m. Only two people live between M and S. The one who runs for 1200m lives on one of the even numbered floors above R. Only two people live between the one who runs for 1200 m and the one who runs for 2900 m. N lives on one of the floors above M. N runs for 2100 m more than the one who lives on floor numbered 3. The number of people living between the one who runs for 5000 m and S is same as the number of people living between M and R. Only one person lives between R and Q. The one who runs for the shortest distance lives immediately below Q. Only one person lives between P and the one who runs for 3600 m.

Question 168

How many people live between S and 0 ?

Solution

The one running 4300 m lives on the 4th floor.

Since only one person lives between the one running 4300m and M and also only 2 people live between M and S, the following 2 cases are possible :-

Case 2 :-
Now since only 2 people are there in between the one running 1200 m and the one running 2900 m and the one running 1200 m lives in an even numbered floor, the only possibilities are :-
The one running 1200 m lives on floor 2 and the one running 2900 m lives on floor 5. This possibility is rejected as N lives above M, i.e. on the 7th floor and has to run 2100 m more than the one living on floor 3. This would not be possible as the only pairs with difference of 2100 m among them are 2200 and 4300 m and 2900 and 5000 m.

The one running 1200 m lives on floor 6 and the one running 2900 m lives on floor 3. This makes N live on floor 7 and run 5000 m.
In this case, since the number of people living between the one running 5000 m and S is the same as the number of people living between M and R, R lives on floor 2.
Since only one person lives between R and Q, Q lives on floor 4.

Since the one running the shortest distance lives immediately below Q, this case is rejected.

Case 1 :-
Again in this case, the one who runs 1200 m can't live on floor 2, else the one running 2900 m would stay on floor 5. Now since N runs 2100 m more than the one who stays on floor 3, the one who stays on floor 3 has to run 2200 m and N has to live on floor 4. Also R would need to stay on floor 1 and since only 1 person stays between R and Q, Q would need to live in floor 3. Now the one living immediately below Q has to run the shortest distance, which contradicts with the fact that the one running 1200 m stays on floor 2. Hence this possibility is rejected.

This the one running 1200 m stays on floor 6 and the one running 2900 m stays on floor 3. This means that N runs 5000 m and lives on floor 7 (as he lives above M). R lives on floor as the number of people staying between the one running 5000 m and S is the same as the number of people between M and R. Consequently Q lives on floor 6 and S runs 750 m.