Problem 6 · 2008 AMC 8
Easy
Geometry & Measurement
unit-area-count
In the figure, what is the ratio of the area of the gray squares to the area of the white squares?
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Answer: D — 3 : 5.
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Hint 1 of 2
Every little square is the same size, so "area" just means "how many squares" — you can count instead of measure.
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Hint 2 of 2
The question asks gray-to-white, not gray-to-total — watch which two amounts you're comparing.
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Approach: count squares, then compare the right two groups
- All 16 squares are congruent, so area becomes a counting problem. Gray: the central 2×2 block (4) plus 2 gray corners = 6. White: the other 16 − 6 = 10.
- The ratio asked is gray : white = 6 : 10 = 3 : 5. (If you wrongly used gray : total = 6 : 16 = 3 : 8 you'd pick the trap answer B.)
- Why this transfers: a ratio compares two specific quantities — always reread which is named before simplifying.
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