There are three types of rectangular tiles: 3' × 3', 3' × 7' and 3' × 11'. An area of rectangular shape of dimensions 3' × 100' i…

Question

There are three types of rectangular tiles: 3' × 3', 3' × 7' and 3' × 11'. An area of rectangular shape of dimensions 3' × 100' is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x − y is

1. A. 20 (Correct answer)
2. B. 12
3. C. 10
4. D. 7

Correct Answer

Option A — 20

Detailed Solution & Explanation

The correct answer is Option A (20).

Key Points

• The length 100 (width fixed at 3) must be tiled with pieces of length 3, 7 and 11.
• Maximum tiles: use as many 3s as possible — 100 = 3 × 31 + 7 × 1 → 32 tiles.
• Minimum tiles: use larger pieces — 100 = 11 × 8 + 3 × 4 → 12 tiles.

Additional Information

• x − y = 32 − 12 = 20, so Option A.