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2015 Math Kangaroo

Problem 1

Problem 1 · 2015 Math Kangaroo Easy
Spatial & Visual Reasoning area-fractionsymmetry
Figure for Math Kangaroo 2015 Problem 1
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Answer: B
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Hint 1 of 2
For each shape, ask whether the grey part and the white part are the same size.
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Hint 2 of 2
An altitude of a triangle splits it into two pieces of equal area; check which figure is cut into two matching halves.
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Approach: compare grey area to whole in each picture
  1. In the triangle the line goes straight down from the top vertex, cutting it into two pieces of equal area, and exactly one of them is grey.
  2. The circle is in thirds (grey = one third), the four-square figure has three of four shaded, and the square-with-X and the pentagon-star are not split into two equal grey/white halves.
  3. Only the triangle has exactly one half coloured grey, so the answer is B.
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