Problem 21 · 2021 Math Kangaroo
Stretch
Number Theory
divisibilitycasework
A box has fewer than 50 cookies in it. The cookies can be divided evenly between 2, 3, or 4 children. However, they cannot be divided evenly between 7 children, because 6 more cookies would be needed. How many cookies are there in the box?
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Answer: D — 36
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Hint 1 of 2
Sharing evenly between 2, 3 and 4 children means the number is in the 2, 3 and 4 times tables — so it is in the 12 times table.
Still stuck? Show hint 2 →
Hint 2 of 2
List the multiples of 12 under 50, then check which one becomes a multiple of 7 after you add the 6 missing cookies.
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Approach: list multiples of 12 under 50, then test the sharing-by-7 clue
- To share evenly between 2, 3 and 4 children the number must be in all three times tables, which means the 12 times table: 12, 24, 36, 48.
- Needing 6 more cookies to share between 7 means that number plus 6 lands in the 7 times table.
- Check each: 12+6=18, 24+6=30, 36+6=42, 48+6=54 — only 42 is in the 7 times table (6 x 7), so the number is 36.
- So there are 36 cookies (D).
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