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.

How many flats are there in the building?

The correct answer is 24.

Let us determine the total number of floors in the building by analyzing the clues step-by-step:

Step 1: Determine the positions of U, T, and X
- Each floor has two flats: Flat A (West) and Flat B (East).
- U lives on an odd-numbered floor below the 7th floor (so U could be on floor 5, 3, or 1).
- T lives two floors below U, which means:
${\mathrm{Floor}}_T={\mathrm{Floor}}_U-2$
- X lives to the south-west of T but not "just" south-west. This means X is in Flat A on a floor that is at least two floors below T.
- For X to be at least two floors below T, T must be on floor 3 or higher. Thus, U must be on floor 5, T must be on floor 3, and X must be on floor 1 in Flat A. Since X is to the south-west of T, T must be in Flat B on floor 3.

Step 2: Find the position of S
- There is a three-floor gap between S and T. Since T is on floor 3, S must be above T on floor:
$3+3+1=7$
- X and S live in the same named flat. Since X is in Flat A, S is also in Flat A (floor 7).

Step 3: Find the position of R and J
- The number of floors between S (floor 7) and X (floor 1) is 5 floors (floors 2, 3, 4, 5, and 6).
- This number (5) is two more than the number of floors between S and R. Thus, the number of floors between S and R is:
$5-2=3\text{floors}$
- This means R lives either 4 floors below S (floor 3) or 4 floors above S (floor 11).
- Since T already lives on floor 3, R must live on floor 11.
- No one lives to the east of R, which means R lives in Flat B (floor 11). J lives to the immediate north-west of R, placing J in Flat A on floor 12.

Step 4: Determine the total number of floors
- O lives just above R, which means O is on floor 12.
- The number of floors below X (floor 1) is 0.
- The number of floors above O is the same as the number of floors below X, which is 0.
- Therefore, floor 12 is the top-most floor of the building, meaning there are 12 floors in total.

Step 5: Calculate the total number of flats
- Since there are 12 floors and each floor has 2 flats (Flat A and Flat B), the total number of flats is:
$12\times 2=24$