Directions: Study the following information carefully and answer the question…
2018
Directions: Study the following information carefully and answer the question given below.
A building has three floors, numbered 1 to 3 from bottom to top (floor 2 is above floor 1 and floor 3 is above floor 2). Each floor has two flats: Flat A is to the west of Flat B. Each of the six flats has an area of 576 sq ft and is divided into a certain number of equal-sized rooms; no two flats have the same number of rooms.
The rooms of one flat on an even-numbered floor each have an area of 64 sq ft. The total number of rooms on floor 3 is seven. The flat whose rooms each have an area of 72 sq ft is on an odd-numbered floor. In the flat that is exactly below the flat with nine rooms, each room has an area of 288 sq ft. There is exactly one floor between the flat whose rooms each have an area of 192 sq ft and the flat whose rooms each have an area of 72 sq ft. There is no flat to the west of the flat that has 6 rooms.
How many rooms are there in the flat to the west of the flat whose rooms each have an area of 288 sq ft?
- A.
6
- B.
4
- C.
3
- D.
8
- E.
None of these
Show answer & explanation
Correct answer: D
Concept
In a fixed-area flat divided into equal rooms, the number of rooms equals the flat area divided by the area of one room. Here every flat is 576 sq ft, so room-area uniquely fixes the room count: 576 ÷ 64 = 9, 576 ÷ 72 = 8, 576 ÷ 96 = 6, 576 ÷ 144 = 4, 576 ÷ 192 = 3, and 576 ÷ 288 = 2. Solve such grid puzzles by converting every area clue into a room count, then placing the flats floor by floor and side by side (A = west, B = east).
Application
Translate the area clues into room counts: 64 sq ft → 9 rooms, 72 sq ft → 8 rooms, 192 sq ft → 3 rooms, 288 sq ft → 2 rooms, and the “6 rooms” flat corresponds to 96 sq ft.
The 9-room flat (64 sq ft) is on an even-numbered floor, so it sits on floor 2.
The flat exactly below the 9-room flat has rooms of 288 sq ft, i.e. 2 rooms; so the 2-room flat sits on floor 1, directly under the 9-room flat, on the same side as the 9-room flat (the side is fixed as east later, once the 6-room flat is placed).
The 8-room flat (72 sq ft) is on an odd floor, and there is exactly one floor between the 8-room flat and the 3-room flat (192 sq ft); a one-floor gap means floors 1 and 3. Since floor 3 must total 7 rooms and 9 is already used on floor 2, the 8-room flat fits on floor 1 and the 3-room flat on floor 3.
Floor 3 totals 7 rooms; with a 3-room flat there, the other floor-3 flat has 4 rooms.
“No flat to the west of the 6-room flat” means the 6-room flat occupies the west side (Flat A). The only remaining west slot is floor 2, so the 6-room flat (96 sq ft) is the west flat on floor 2, leaving the 9-room flat on the east of floor 2 — and therefore the 2-room flat on the east of floor 1.
The 2-room flat (288 sq ft) is the east flat on floor 1. The flat to its west on floor 1 is the 8-room flat. Hence 8 rooms lie to the west of the 288-sq-ft-room flat.
Final arrangement (cross-check)
Floor | West (Flat A) | East (Flat B) |
|---|---|---|
3 | 4 rooms | 3 rooms (192 sq ft) |
2 | 6 rooms (96 sq ft) | 9 rooms (64 sq ft) |
1 | 8 rooms (72 sq ft) | 2 rooms (288 sq ft) |
Every clue holds: 9 rooms on an even floor, 288-sq-ft flat directly below it, 8-room flat on an odd floor with one floor between it and the 3-room flat, floor 3 totalling 7 rooms, and nothing west of the 6-room flat. The flat west of the 288-sq-ft-room flat has 8 rooms.