Problem 19 · 2021 Math Kangaroo
Medium
Logic & Word Problems
Ratios, Rates & Proportions
ratiocasework
A box of fruit contains twice as many apples as pears. Christy and Lily divided them up so that Christy had twice as many pieces of fruit as Lily. Which one of the following statements is always true?
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Answer: E — Christy took as many pears as Lily got apples.
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Hint 1 of 2
Let there be p pears and 2p apples, total 3p; Christy ends with 2p pieces and Lily with p.
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Hint 2 of 2
Test each statement against every possible split — only one holds in all cases.
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Approach: check each claim over all valid splits
- Pears = p, apples = 2p, total 3p; Christy has 2p pieces, Lily has p.
- If Christy takes a apples she takes 2p−a pears; Lily then gets the remaining 2p−a apples.
- So Christy's pears always equal Lily's apples; the other options can fail.
- So the answer is E.
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