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MathNet 2016-part-05 — 184 problems (EN–VI) Question 86

Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)

Question 86

In the equality of the three fractions $\frac{2}{6} = \frac{3}{9} = \frac{58}{174}$ each digit from $1$ to $9$ occurs exactly once and the value of all three fractions is $\frac{1}{3}$. Here is another example of such equality, $\frac{*}{*} = \frac{*}{*} = \frac{7*}{15*}$, where some of the digits have been replaced by an asterisk. What is the value of all three fractions in this case?
(A) $\frac{1}{2}$ (B) $\frac{1}{3}$ (C) $\frac{2}{3}$ (D) $\frac{3}{4}$ (E) $\frac{3}{5}$