Problem 10 · 2021 Math Kangaroo
Easy
Logic & Word Problems
substitution
Byron is 5 cm taller than Aaron, but 10 cm shorter than Caron. Darren is 10 cm taller than Caron, but 5 cm shorter than Erin. Which of the following statements is true?
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Answer: E — Aaron is 30 cm shorter than Erin
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Hint 1 of 2
Anchor everyone to Aaron's height and step through the comparisons one at a time.
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Hint 2 of 2
Chain Byron, Caron, Darren, Erin back to Aaron.
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Approach: express each height relative to Aaron
- Byron = Aaron + 5; Caron = Byron + 10 = Aaron + 15.
- Darren = Caron + 10 = Aaron + 25; Erin = Darren + 5 = Aaron + 30.
- So Erin is 30 cm taller than Aaron, i.e. Aaron is 30 cm shorter than Erin.
- So the answer is E.
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