Problem 18 · 2012 Math Kangaroo
Stretch
Number Theory
divisibility
Among the classmates of Thomas there are twice as many girls as boys. How many children could be in the class?
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Answer: D — 25
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Hint 1 of 2
If girls are twice the boys, the classmates split into equal-size thirds (boys : girls = 1 : 2).
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Hint 2 of 2
So the number of classmates is a multiple of 3; remember Thomas himself is also in the class.
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Approach: use divisibility by 3 plus Thomas
- Among Thomas's classmates the girls are twice the boys, so the classmates number a multiple of 3.
- The class is those classmates plus Thomas, so the class size is (a multiple of 3) + 1.
- Among the options only 25 fits: 24 classmates (8 boys, 16 girls) plus Thomas.
- So the class could have 25 children.
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