Directions: Study the following information carefully and answer the question…
2018
Directions: Study the following information carefully and answer the question given below.
There are three floors in a building such that floor 2 is above floor 1 and floor 3 is above floor 2. On each floor there are two flats such that Flat A is to the west of Flat B. Each flat has an area of 576 sq ft and a certain number of equal-sized rooms, and no two flats have the same number of rooms. The area of each room of one of the flats on the even-numbered floor is 64 sq ft. The total number of rooms on floor 3 is seven. The flat whose room area is 72 sq ft is on an odd-numbered floor. The room area of the flat exactly below the 9-room flat is 288 sq ft. There is exactly one floor between the flat whose room area is 192 sq ft and the flat whose room area is 72 sq ft. There is no flat to the west of the flat having 6 rooms.
Which of the following statements is true?
- A.
Total number of rooms on floor 2 is 14.
- B.
The area of each room of Flat A on floor 1 is 94 sq ft.
- C.
The total number of rooms in Flat A across all three floors is 17.
- D.
All are correct.
- E.
None is correct.
Show answer & explanation
Correct answer: C
Concept
In such floor-and-flat puzzles, every flat has the same total area, so for any flat the number of rooms and the area of each room are inversely related:
number of rooms = total flat area ÷ area of one room
Here every flat is 576 sq ft, so once you know either the room count or the room area you immediately get the other. The strategy is to convert each "room-area" clue into a fixed room count, anchor the flats to floors using the floor clues, then fix the east-west (Flat A / Flat B) positions last.
Step-by-step deduction
Convert each clue using 576 ÷ (room area): room area 64 → 9 rooms; 72 → 8 rooms; 288 → 2 rooms; 192 → 3 rooms; 96 → 6 rooms.
"One flat on the even floor has room area 64" → the 9-room flat is on floor 2.
"The room area of the flat exactly below the 9-room flat is 288" → the flat below floor 2 is floor 1, so a 2-room flat is on floor 1.
"Exactly one floor between the 192-area flat (3 rooms) and the 72-area flat (8 rooms)" → these two sit on floors 1 and 3 (which are two apart). Since floor 3 has only 7 rooms in total, it cannot hold the 8-room flat, so the 8-room flat is on floor 1 and the 3-room flat is on floor 3.
Floor 1 now holds the 8-room and 2-room flats. Floor 3 total is 7, and one floor-3 flat has 3 rooms, so the other floor-3 flat has 7 − 3 = 4 rooms (room area 144).
The remaining floor-2 flat must have 6 rooms (room area 96): the counts 2, 3, 4, 6, 8, 9 are then all distinct, satisfying the "no two flats alike" rule.
"No flat is to the west of the 6-room flat" → the 6-room flat is the westmost, i.e. Flat A on floor 2. "Exactly below the 9-room flat is 288 sq ft" then forces the 9-room flat to be Flat B on floor 2, and the 2-room flat to be Flat B on floor 1, leaving the 8-room flat as Flat A on floor 1.
The 72 sq ft flat (8 rooms) is fixed as Flat A on floor 1, i.e. the west column. Every room count and floor is now fixed except which of the two floor-3 flats (3 rooms/192 sq ft, or 4 rooms/144 sq ft) sits in the west (Flat A) position -- the given clues fix floor 3's total at 7 but do not themselves fix that column. This item is a previously administered exam question whose published solution places the 192 sq ft (3-room) flat at Flat A on floor 3, so Flat A's total across the three floors is 8 + 6 + 3 = 17.
Resulting arrangement
Floor | Flat A (west) — rooms | Flat B (east) — rooms |
|---|---|---|
3 | 3 rooms (192 sq ft each) | 4 rooms (144 sq ft each) |
2 | 6 rooms (96 sq ft each) | 9 rooms (64 sq ft each) |
1 | 8 rooms (72 sq ft each) | 2 rooms (288 sq ft each) |
Checking the statements
Floor 2 total rooms = 6 + 9 = 15, not 14.
Flat A on floor 1 has 8 rooms of 72 sq ft each, not 94 sq ft.
Flat A totals across floors = 8 (floor 1) + 6 (floor 2) + 3 (floor 3) = 17. This statement is true.
Cross-check
Verify areas: 8×72 = 576, 2×288 = 576, 6×96 = 576, 9×64 = 576, 3×192 = 576, 4×144 = 576 — every flat is 576 sq ft, and floor-3 rooms 3 + 4 = 7, as required. The only statement that survives is that Flat A holds 17 rooms in total.