Problem 20 · 2011 Math Kangaroo
Stretch
Number Theory
divisibilityfactorization
10 children are at a judo club. Their teacher has 80 sweets. If he gives each girl the same amount of sweets, there are three sweets left over. How many boys are at the club?
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Answer: C — 3
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Hint 1 of 2
Take away the 3 leftover sweets; the rest split evenly among the girls.
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Hint 2 of 2
The number of girls must divide that leftover-free amount exactly, and be fewer than 10.
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Approach: share the leftover-free sweets evenly among the girls
- After 3 are left over, 80 − 3 = 77 sweets are shared equally among the girls.
- 77 splits evenly only into 7 groups of 11 (or 11 groups of 7), and only 7 girls fits a club of 10, so there are 7 girls.
- Then boys = 10 − 7 = 3.
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