Problem 24 · 2024 Math Kangaroo
Stretch
Logic & Word Problems
caseworkwork-backward
A tray of biscuits is in the kitchen (see picture). Three girls take biscuits from the tray, in some unknown order: Tina takes all the heart-shaped biscuits still on the tray, Emma takes all the white biscuits still on the tray, and Rosa takes all the large biscuits still on the tray. One girl ends up with 3 biscuits, one with 6, and one with 7. Which of the pictured groups of biscuits (A)–(E) is exactly what one of the girls took?
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Answer: E
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Hint 1 of 2
Whoever goes first takes a whole category from all 16 cookies; figure out an order giving takes of 3, 6, and 7.
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Hint 2 of 2
Rosa (large) going first takes 7, then Tina (hearts) takes 6, leaving Emma (white) just 3.
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Approach: find the order of takers that yields 7, 6, 3
- There are 16 cookies, and the takes are 3, 6, 7, so the first taker removes 7.
- If Rosa takes the 7 large cookies first, only small ones remain.
- Tina then takes the 6 small hearts, leaving three small white round cookies.
- Emma takes those three round white cookies — the set in option E.
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