Problem 281

If $x = 1$, then $x^2 = 1$ and $x^3 = 1$ and so $x^3 = x^2$. If $x > 1$, then $x^3$ equals $x$ times $x^2$; since $x > 1$, then $x$ times $x^2$ is greater than $x^2$ and so $x^3 > x^2$. Therefore, if $x$ is positive with $x^3 < x^2$, we must have $0 < x < 1$. Of the given choices, only $x = \frac{3}{4}$ satisfies $0 < x < 1$, and so the answer is (B).