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2019 Math Kangaroo

Problem 12

Problem 12 · 2019 Math Kangaroo Hard
Fractions, Decimals & Percents percent-multiplierdivisibility

This school year the number of boys in my class increased by 20% compared with last year, and the number of girls decreased by 20%. There is now one more person in the class than before. Which of the following could be the current number of students in my class?

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Answer: B — 26
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Hint 1 of 2
A change of 20% gives a whole number only if the count is a multiple of 5, so last year's boys and girls were each multiples of 5.
Still stuck? Show hint 2 →
Hint 2 of 2
Write boys = 5b and girls = 5g; the net headcount change of +1 pins down b − g.
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Approach: boys and girls were each multiples of 5 last year
  1. Let last year's boys = 5b and girls = 5g, so the 20% changes give whole numbers.
  2. New count = 6b + 4g, old count = 5b + 5g; the increase is b − g = 1, so b = g + 1.
  3. New total = 6(g+1) + 4g = 10g + 6, which for g = 2 gives 26.
  4. Answer (B) 26.
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