Problem 5 · 2020 Math Kangaroo
Medium
Fractions, Decimals & Percents
sum-constraintpercent-multiplier
The pie chart shows the number of inhabitants in the five zones of a city. The central zone has the same population as the north, west and east zones combined, and the south zone has half as many inhabitants as the west zone. What is the difference, in percentage points, between the inhabitants of the north and east zones?
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Answer: D — 13%
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Hint 1 of 2
The central slice (47%) equals north+west+east together.
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Hint 2 of 2
Use 'south is half of west' to pin down which slices are which.
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Approach: match the percentage slices to the zones using the constraints
- The non-central slices are 11, 6, 24, 12 (summing to 53), and central 47 = north+west+east, so south = 53 − 47 = 6.
- South is half of west, so west = 12.
- North + east = 47 − 12 = 35, which forces the pair to be 11 and 24.
- Their difference is 24 − 11 = 13%.
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