Problem 24 · 2015 Math Kangaroo
Stretch
Logic & Word Problems
divisibilitywork-backward
Anna, Berta, Charlie, David and Elisa baked biscuits at the weekend. Anna baked 24, Berta 25, Charlie 26, David 27 and Elisa 28 biscuits. By the end of the weekend one of the children had twice as many, one 3 times, one 4 times, one 5 times and one 6 times as many biscuits as on Saturday. Who baked the most biscuits on Saturday?
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Answer: C — Charlie
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Hint 1 of 2
Each child's weekend total is their Saturday pile shared into 2, 3, 4, 5 or 6 equal groups (each size used once).
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Hint 2 of 2
Find which totals can be shared evenly by 5 and by 3 first, since only one each can.
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Approach: see how each total splits evenly, then share it out to find Saturday
- Each total (24, 25, 26, 27, 28) is a Saturday pile copied 2, 3, 4, 5 or 6 times, with each copy-number used once.
- Only 25 shares evenly into 5 groups (25 ÷ 5 = 5) and only 27 shares evenly into 3 groups (27 ÷ 3 = 9).
- That leaves 26 as 2 copies (26 ÷ 2 = 13), 28 as 4 copies (28 ÷ 4 = 7), and 24 as 6 copies (24 ÷ 6 = 4).
- Saturday piles: Anna 4, Berta 5, Charlie 13, David 9, Elisa 7 — Charlie's 13 is the biggest, so the answer is Charlie.
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