Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to $x^2$ and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?

Correct Answer: (B) 1/5

Given $y = k x^2$ and $x = c / z$. Using the initial conditions $x = 5$, $y = 50$, and $z = 7/25$: $50 = k(5^2)$$\implies$ k = 2, so $y = 2x^2$. Also, $5 = c / (7/25)$$\implies$ c = 5 $\times$ $\frac{7}{25}$ = $\frac{7}{5}$, so $x =$$\frac{7/5}{z}$. When $y = 98$, we have $98 = 2x^2$$\implies$ x^2 = 49 $\implies$ x = 7. Substituting $x = 7$ into the inverse relationship yields $7 =$$\frac{7/5}{z}$ $\implies$ z = $\frac{7/5}{7}$ = $\frac{1}{5}$.