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2015 AMC 10A Problem 15

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2015 AMC 10A Problem 15AMC 10 Step by Step
Name:                             Date: September 13, 2026
Diophantine Equations · difficulty 3 of 5 · about 5 min · position P11-15

Consider the set of all fractions xy,\tfrac{x}{y}, where xx and yy are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by 11 , the value of the fraction is increased by 10%10\% ?

  1. A)

    00

  2. B)

    11

  3. C)

    22

  4. D)

    33

  5. E)

    infinitely many\text{infinitely many}

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