, 2021

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 $0<x<1$. We note that if $0 < x < 1$, then both $x$, $x^2$ and $x^3$ are all positive, and $x^3 = x^2 \times x < x^2 \times 1 = x^2$.

Of the given choices, only $x = \frac{3}{4}$ satisfies $0 < x < 1$, and so the answer is (B).

We can verify by direct calculation that this is the only correct answer from the given choices.