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MathNet 2021 — Part 09 Question 69

Math Olympiad Vault · MathNet 2021 — Part 09

Question 69

The knights in a certain kingdom come in two colors: $\frac{2}{7}$ of them are red, and the rest are blue. Furthermore, $\frac{1}{6}$ of the knights are magical, and the fraction of red knights who are magical is 2 times the fraction of blue knights who are magical. What fraction of red knights are magical?
  1. $\frac29$
  2. $\frac3{13}$
  3. $\frac7{27}$
  4. $\frac27$
  5. $\frac13$