Both the numerator and the denominator of 3/17 are increased by a positive integer z, and those of 5/19 are decreased by...

Question

Both the numerator and the denominator of 3/17 are increased by a positive integer z, and those of 5/19 are decreased by the same integer z. This operation results in the same value for both the fractions. What is the value of z?

A. 1  B. 2  C. 3  D. 4

Accepted Answer

The value of z is 3. Adding z to both parts of 3/17 gives (3+z)/(17+z), and subtracting z from both parts of 5/19 gives (5-z)/(19-z). Setting these equal and cross-multiplying produces a linear equation in z. Solving it gives z = 3, which is option C.