Problem 11 · 2018 Math Kangaroo
Medium
Fractions, Decimals & Percents
percent-multiplierproportion
Two cubes with volumes V and W intersect each other as shown. 90% of the volume of the cube with volume V does not belong to both cubes, and 85% of the volume of the cube with volume W does not belong to both cubes. What is the relationship between the volumes of the two cubes?
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Answer: B — \(V = \tfrac{3}{2}\,W\)
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Hint 1 of 2
The shared (overlap) part is what each percentage leaves out.
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Hint 2 of 2
Set the two expressions for the common volume equal.
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Approach: equate the two descriptions of the overlap volume
- 90% of V is outside the overlap, so the overlap is 0.1V.
- 85% of W is outside the overlap, so the overlap is 0.15W.
- Equating: 0.1V = 0.15W gives V = 1.5W = (3/2)W.
- Answer: V = (3/2)W.
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