Problem 10 · 2024 Math Kangaroo
Medium
Logic & Word Problems
caseworkwork-backward
A basket holds five fruits: apple, grapes, cherry, strawberry and banana. Ann likes only the cherry. Ben likes all five. Cam likes the cherry, strawberry and banana. Dan likes the cherry and banana. Eli likes the grapes and strawberry. Each child takes one fruit that they like (and no two take the same fruit). Which fruit does Ben take?
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Answer: A
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Hint 1 of 2
Start with the child who likes only one fruit — that fruit is fixed.
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Hint 2 of 2
Remove each taken fruit and see what choices the other children have left.
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Approach: assign forced choices first, then eliminate
- Ann likes only the cherry, so Ann takes the cherry.
- Dan likes cherry or banana; the cherry is gone, so Dan takes the banana.
- Cam likes cherry, strawberry, banana — only the strawberry is left for Cam; then Eli (grapes or strawberry) takes the grapes.
- Ben likes them all, and only the apple remains, so Ben takes the apple (A).
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