Problem 21 · 2021 Math Kangaroo
Stretch
Logic & Word Problems
Counting & Probability
casework
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Answer: E — Yvonne's set.
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Hint 1 of 2
Translate each friend's statement into a condition on the counts of planets, moons and stars in their set.
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Hint 2 of 2
Yvonne's set must have more stars than planets; check which option keeps the other clues consistent.
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Approach: match each statement to the right collection
- Zach has exactly half planets: only set (C) (3 planets out of 6) fits, so Zach = (C).
- Paul has more moons than stars: among what's left only (D) (3 moons, 2 stars) works, so Paul = (D).
- Of the remaining sets (A), (B), (E): Xenia needs an even total, so Xenia = (A) (4 pins); Sue has no moons, so Sue = (B).
- Yvonne gets the last set (E), which has 2 stars and 1 planet — more stars than planets, as she said. So the answer is E.
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