2011 AMC 8 Problem 3
Attempt Problem 3 of the 2011 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
3.
Extend the square pattern of shaded and unshaded square tiles by attaching a border of shaded tiles around the square. What is the ratio of shaded tiles to unshaded tiles in the extended pattern?
Answer: D
Small hint:
A border around a by square adds the outside ring of tiles.
Big hint:
The original unshaded tiles stay the same.
Solution:
The original pattern is a square. Extending it by one tile on every side makes a square, so the new shaded border contains tiles. Together with the original shaded tiles, there are shaded tiles. The original unshaded tiles do not change, so the ratio of shaded tiles to unshaded tiles is
Thus, D is the correct answer.
Problem 3 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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