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.

Who among the following persons live to the south east of P?

To find the person(s) living to the south-east of P, let us analyze the step-by-step arrangement of floors and flats based on the given clues:

1. Understand the Grid: Each floor has two flats: Flat A (West) and Flat B (East). Thus, Flat A is to the left of Flat B.
2. Analyze U and T:
- U lives on an odd-numbered floor below the 7th floor. This means U can live on floor 5, 3, or 1.
- T lives two floors below U (i.e., U's floor minus 2). Since T lives below U, U cannot be on floor 1. Therefore, U is on floor 5 or 3, placing T on floor 3 or 1 respectively.
3. Analyze X and T:
- X lives to the south-west of T but not just south-west. Since X is to the south-west of T, T must be in Flat B and X must be in Flat A.
- "Not just south-west" means X is not on the floor immediately below T; there must be at least one floor gap between T's floor and X's floor.
- Since T is on floor 3 or 1, and X is at least two floors below T, T must be on floor 3 (which means U is on floor 5) and X must be on floor 1. Thus, T is on floor 3, Flat B, and X is on floor 1, Flat A.
4. Analyze S and T:
- There is a three-floor gap between S and T. Since T is on floor 3, S must be on floor 7 (with floors 4, 5, and 6 in between).
- S and T do not live on adjacent floors (which holds true since floor 7 and 3 are not adjacent).
- X and S live in the same named flat. Since X is in Flat A, S is in Flat A (Floor 7, Flat A).
5. Analyze R, S, and X:
- The number of floors between S (floor 7) and X (floor 1) is 5.
- According to the clue, the number of floors between S and X (which is 5) is 2 more than the number of floors between S and R.
- Therefore, the number of floors between S and R is $5-2=3$ floors.
- Since S is on floor 7, R must be on floor 3 (gap of floors 4, 5, 6).
- No one lives to the east of R. This means R lives in Flat B (Floor 3, Flat B). But wait, T is already in Floor 3, Flat B. Let's re-verify the floor gap logic:
If the total number of floors is higher, S could be above or below. Since S is on floor 7 and R is on floor 3, this would create a conflict. Let's trace the total number of floors.
If S is on floor 7, and R is on floor 3, let's look at the relation: "The number of floors between S and X is two more than the number of floors between S and R."
Let X be on floor 1, S on floor 7. The floors between them are 2, 3, 4, 5, 6 (5 floors).
If the gap between S and R is 3, R must be on floor 3. But T is on floor 3. Since there are two flats per floor, and T is in Flat B, R (who has no one to the east of him, meaning he is in Flat B) would conflict.
Let's re-evaluate: "The number of floors below X is same as the number of floors above O who lives just above R."
Let's check if the building has more floors. If X is on floor 2, then U is on floor 5, T is on floor 3. X is south-west of T (T is on floor 3 Flat B, X is on floor 1 Flat A - this is "just south-west", which is forbidden).
If X is on floor 1 Flat A, and U is on floor 5, T is on floor 3 Flat B. X (floor 1 Flat A) is south-west of T (floor 3 Flat B) with 1 floor gap (floor 2), which satisfies "not just south-west".
If the number of floors below X (floor 1) is 0, then the number of floors above O is 0. O must live on the top floor.
O lives just above R's floor. So if O is on the top floor, R is on the floor below O.
Let the total number of floors be 9.
If total floors = 9:
- O is on floor 9.
- R is on floor 8.
- S is on floor 7, Flat A.
- Number of floors between S (7) and R (8) is 0.
- Number of floors between S (7) and X (1) is 5.
But 5 is not $0+2$.
Let the total number of floors be 10:
- O is on floor 10.
- R is on floor 9.
- Number of floors between S (7) and R (9) is 1.
- Floors between S (7) and X (1) is 5. But $5\ne 1+2$.
Let's test if S is below R:
If total floors is 12:
- O is on floor 12.
- R is on floor 11.
- Floors between S (7) and R (11) is 3 (floors 8, 9, 10).
- Floors between S (7) and X (1) is 5 (floors 2, 3, 4, 5, 6).
- Here, 5 is indeed 2 more than 3! This fits perfectly.
So, O is on floor 12, R is on floor 11.
No one lives to the east of R, so R is in Flat B (Floor 11, Flat B).
J lives to the immediate north-west of R, so J is in Floor 12, Flat A.
O lives just above R's floor, so O is on floor 12 (Flat B).
K lives two floors below O's flat, so K is on floor 10 (Flat B).
W lives exactly between S (floor 7) and U (floor 5) floor, so W is on floor 6.
W and U live in different named flats. Since U is on floor 5, and W is on floor 6.
Only one floor gap between W (floor 6) and Q. Q lives above S (floor 7), so Q is on floor 8.
P lives to the north-west of Q, so Q is in Flat B and P is in Flat A.
P lives on an even-numbered floor. Since Q is on floor 8, P can be on an even floor above Q, i.e., floor 10. Thus, P is on Floor 10, Flat A, and Q is on Floor 8, Flat B.
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 flats, U must be in Flat A.

6. Determine positions relative to P (Floor 10, Flat A):
- T lives on Floor 3, Flat B.
- W lives on Floor 6, Flat B.
- Since both T and W are on lower floors than P and are in Flat B (which is to the east of Flat A), both of them live to the south-east of P.

Therefore, both T and W live to the south-east of P.