In a building with three floors, each floor has two flats: Flat A (west) and Flat B (east). Each flat has an area of 576 sq ft but a different number of rooms. The area of each room in one of the flats on an even-numbered floor is 64 sq ft. The total number of rooms on the third floor is 7. The flat with rooms of area 72 sq ft is on an odd-numbered floor. The flat directly below the flat with 9 rooms has a total room area of 288 sq ft. There is exactly one floor between the flat with room area 192 sq ft and the flat with room area 72 sq ft. Also, there is no flat to the west of the flat having 6 rooms.

What is the **area of a room** in Flat A on the second floor?

Question

In a building with three floors, each floor has two flats: Flat A (west) and Flat B (east). Each flat has an area of 576 sq ft but a different number of rooms. The area of each room in one of the flats on an even-numbered floor is 64 sq ft. The total number of rooms on the third floor is 7. The flat with rooms of area 72 sq ft is on an odd-numbered floor. The flat directly below the flat with 9 rooms has a total room area of 288 sq ft. There is exactly one floor between the flat with room area 192 sq ft and the flat with room area 72 sq ft. Also, there is no flat to the west of the flat having 6 rooms.

What is the **area of a room** in Flat A on the second floor?

Accepted Answer

**Solution:**

1. Each flat has an area of 576 sq ft.

2. One flat on an even-numbered floor has rooms each of 64 sq ft.
   - Since floor 2 is even, one flat on floor 2 has room area 64 sq ft.

3. Total rooms on floor 3 = 7.

4. The flat with room area 72 sq ft is on an odd-numbered floor (floor 1 or 3).

5. The flat directly below the flat with 9 rooms has total room area 288 sq ft.
   - Since the flat with 9 rooms must be on floor 2 or 3 (because below floor 1 is ground), and the flat below it has total room area 288 sq ft.

6. There is exactly one floor between the flat with room area 192 sq ft and the flat with room area 72 sq ft.
   - So these flats are on floors 1 and 3.

7. No flat is to the west of the flat having 6 rooms, so the flat with 6 rooms must be Flat A (west) on some floor.

Let's analyze:

- Since total rooms on floor 3 = 7, and the flat with room area 72 sq ft is on an odd floor, it can be on floor 3 or floor 1.

- The flat with 9 rooms is on floor 2 or 3, and the flat below it has total room area 288 sq ft.

- The flat with room area 64 sq ft is on floor 2.

- The flat with room area 192 sq ft and the flat with room area 72 sq ft are separated by one floor.

From these clues, the flat on floor 2, Flat A, has rooms of area 96 sq ft.

**Answer:** 96

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