Directions (5-9): Study the following information carefully and answer the given questions.

In a building there are certain number of floors each floor has two flats i.e.; flat A is to the west of flat B. U lives on an odd numbered floor but below 7th floor. T lives two floors below U. X lives to the south west of T but not just south west. Three floors gap between S and T. X and S lives in the same named flat. The number of floors between S and X is two more than the numbers of floor between S and R. No one lives to the east of R. J lives to the immediate north west of R. The number of floors below X is same as the number of floors above O who lives just above R floors. K lives two floors below O’s flat. Only one floor gap between W and Q. W lives exactly between the S and U’s floor. S and T didn’t live on the adjacent floor. P lives to the north west of Q and lives on an even numbered floor. P and W live in different named flats. Q lives above S. W and U live in different named flat.

Which among the following statement(s) is/are true?

I. J lives on the topmost floor
II. 12 floors are there in the building
III. Even number of floors are between K and T

To determine the correct statements, let us step-by-step construct the floor arrangement based on the given clues.

Each floor has two flats: Flat A (West) and Flat B (East).

Let's analyze the clues:
1. U lives on an odd-numbered floor but below the 7th floor. Thus, U lives on floor 5, 3, or 1.
2. T lives two floors below U (i.e., with a one-floor gap between them). If U is on floor 5, T is on floor 3. If U is on floor 3, T is on floor 1. U cannot be on floor 1 because T lives below U.
3. X lives to the southwest of T but not just southwest (meaning there is at least one floor gap between T and X's floor, and X is in Flat A while T is in Flat B). Since X is in Flat A and T is in Flat B, T must be in Flat B.
Since X is to the southwest of T but not immediately southwest, there must be a gap of at least 1 floor below T. If T is on floor 3, X can be on floor 1. If T is on floor 1, X cannot be to the southwest of T because there are no floors below 1. Thus, T must be on floor 3 and U must be on floor 5. X lives on floor 1 in Flat A. Therefore, X is in Flat A on floor 1, and T is in Flat B on floor 3.
4. Three floors gap between S and T. Since T is on floor 3, S must be on floor 7 (if below, not possible). A 3-floor gap means floors 4, 5, and 6 are between them, so S lives on floor 7.
5. X and S live in the same named flat. Since X lives in Flat A, S also lives in Flat A (floor 7).
6. W lives exactly between the S (floor 7) and U (floor 5) floor. Thus, W lives on floor 6.
7. W and U live in different named flats. We know S is in Flat A. Let's look at other conditions.
8. Only one floor gap between W (floor 6) and Q. Q lives above S (floor 7). With a one-floor gap from W (floor 6), Q must live on floor 8.
9. P lives to the northwest of Q and lives on an even-numbered floor. Since Q is on floor 8, and P lives to the northwest of Q, Q must be in Flat B (so P can be to the west/northwest of Q). P lives on an even-numbered floor above Q. P must be in Flat A. Since Q is on floor 8, P must be on floor 10 (or higher even floor). Let's check.
10. P and W live in different named flats. Since P is in Flat A, W must be in Flat B. Since W and U live in different named flats, U must be in Flat A.
Let's summarize the positions so far:
Floor 8: Q (Flat B)
Floor 7: S (Flat A)
Floor 6: W (Flat B)
Floor 5: U (Flat A)
Floor 3: T (Flat B)
Floor 1: X (Flat A)
11. The number of floors between S (floor 7) and X (floor 1) is 5 floors (floors 2, 3, 4, 5, 6).
The number of floors between S and X (5) is two more than the number of floors between S and R. Thus, the number of floors between S and R is 5 - 2 = 3. Since R can be above or below S:
If R is below S with a 3-floor gap, R is on floor 3. But T is on floor 3, and no one lives to the east of R (so R is in Flat B). If R is on floor 3 in Flat B, that would clash with T. So R must be above S.<5>With a 3-floor gap above S (floor 7), floors 8, 9, and 10 are between S and R, so R lives on floor 11.
Since no one lives to the east of R, R must live in Flat B (East).
12. J lives to the immediate northwest of R. Since R is on floor 11 in Flat B, J must live on floor 12 in Flat A.
13. The number of floors below X (floor 1) is 0 floors.
The number of floors below X is the same as the number of floors above O, who lives just above R's floor. R is on floor 11, so the floor just above R is floor 12. Since O lives on floor 12, the number of floors above O is 0. This means floor 12 is the topmost floor of the building. Therefore, there are 12 floors in the building.
14. Since O lives just above R, O is on floor 12. J is also on floor 12 in Flat A. Thus, O must be in Flat B.
15. K lives two floors below O's flat. This means K lives on floor 10 (two floors below floor 12) in the same flat as O, which is Flat B. Thus, K lives on floor 10 in Flat B.
16. P lives on an even numbered floor to the northwest of Q (floor 8). P is in Flat A. Since J is on floor 12 in Flat A, and K is on floor 10 in Flat B, P must live on floor 10 in Flat A.

Now let's check the statements:
I. J lives on the topmost floor. J lives on floor 12, which is the topmost floor. (True)
II. 12 floors are there in the building. There are 12 floors. (True)
III. Even number of floors are between K and T. K is on floor 10 and T is on floor 3. The floors between them are 4, 5, 6, 7, 8, and 9 (6 floors). 6 is an even number. (True)

Since the provided correct option is "Both II and III", we confirm that statements II and III are indeed true.