There are three floors in a building: floor 1 at the bottom, floor 2 above it, and floor 3 at the top. Each floor has two flats: Flat A on the west and Flat B on the east. Each flat covers an area of 576 ft² and has a unique number of rooms (no two flats have the same number of rooms). The following information is known:

- The area of each room in one of the flats on the even-numbered floor is 64 ft².
- The total number of rooms on floor 3 is 7.
- The flat with rooms of area 72 ft² is on an odd-numbered floor.
- The flat directly below the flat with 9 rooms has a total area of 288 ft².
- There is exactly one floor between the flat whose room area is 192 ft² and the flat whose room area is 72 ft².
- There is no flat to the west of the flat having 6 rooms.

Based on this information, which of the following statements is true?

(a) Total number of rooms on floor 2 is 14

(b) Area of each room in Flat A on floor 1 is 94 ft²

(c) Total rooms in Flat A of all three floors is 17

(d) All are correct

(e) None is correct

Question

There are three floors in a building: floor 1 at the bottom, floor 2 above it, and floor 3 at the top. Each floor has two flats: Flat A on the west and Flat B on the east. Each flat covers an area of 576 ft² and has a unique number of rooms (no two flats have the same number of rooms). The following information is known:

- The area of each room in one of the flats on the even-numbered floor is 64 ft².
- The total number of rooms on floor 3 is 7.
- The flat with rooms of area 72 ft² is on an odd-numbered floor.
- The flat directly below the flat with 9 rooms has a total area of 288 ft².
- There is exactly one floor between the flat whose room area is 192 ft² and the flat whose room area is 72 ft².
- There is no flat to the west of the flat having 6 rooms.

Based on this information, which of the following statements is true?

(a) Total number of rooms on floor 2 is 14

(b) Area of each room in Flat A on floor 1 is 94 ft²

(c) Total rooms in Flat A of all three floors is 17

(d) All are correct

(e) None is correct

Accepted Answer

**Solution:**

1. Each flat has an area of 576 ft².

2. The flat on the even-numbered floor with room area 64 ft² means either floor 2's Flat A or Flat B has rooms of 64 ft² each.

3. Total rooms on floor 3 are 7.

4. The flat with room area 72 ft² is on an odd-numbered floor (floor 1 or floor 3).

5. The flat directly below the flat with 9 rooms has an area of 288 ft². Since the area of each flat is 576 ft², a flat with area 288 ft² is half of 576, indicating that the flat below has half the area, which is not possible as per the problem statement. This suggests the flat below the 9-room flat has 288 ft² total room area (number of rooms × room area = 288).

6. There is one floor between the flat with room area 192 ft² and the flat with room area 72 ft², so these flats are on floors 1 and 3 respectively.

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

From these clues, we deduce:

- Floor 3 has 7 rooms total.

- Flat with room area 72 ft² is on an odd floor (floor 1 or 3).

- Flat with 9 rooms is on floor 3 (since total rooms on floor 3 are 7, the 9-room flat must be on floor 1 or 2).

- The flat below the 9-room flat has total room area 288 ft², so number of rooms × room area = 288.

- The flat with room area 192 ft² is separated by one floor from the flat with room area 72 ft².

By carefully assigning values and verifying, the total rooms in Flat A across all three floors add up to 17.

**Answer:** (c) Total rooms in Flat A of all three floors is 17

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