Problem 2 · 2021 Math Kangaroo
Easy
Fractions, Decimals & Percents
Spatial & Visual Reasoning
symmetryarea-fractionpercent-multiplier
The figure shows three concentric circles with four lines passing through their common centre. What percentage of the figure is shaded?
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Answer: E — 50%
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Hint 1 of 2
Four lines through the centre cut the picture into equal pie-slice sectors — count how many.
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Hint 2 of 2
Notice the shading repeats every other slice, so the same fraction is shaded in every ring.
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Approach: exploit the equal sectors and alternating shading
- The four lines through the common centre split the figure into 8 equal sectors.
- Going around, the sectors alternate shaded / unshaded, so exactly half of every ring is shaded.
- Half of the whole figure is shaded, which is 50%.
- So the answer is E.
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