If $x$ is a number between 0 and 1 , which of the following represents the smallest value?
(A) $x$
(B) $x^{2}$
(C) $2 x$
(D) $\sqrt{x}$
(E) $\frac{1}{x}$
Since $x$ can be any value in between 0 and 1 , we choose a specific value for $x$ in this range.

For example, we allow $x$ to be $\frac{1}{4}$ and then evaluate each of the five expressions.

We get, $x=\frac{1}{4} ; x^{2}=\left(\frac{1}{4}\right)^{2}=\frac{1}{16} ; 2 x=2\left(\frac{1}{4}\right)=\frac{2}{4}=\frac{1}{2} ; \sqrt{x}=\sqrt{\frac{1}{4}}=\frac{1}{2} ; \frac{1}{x}=\frac{1}{\frac{1}{4}}=4$.

Since $\frac{1}{16}$ is the smallest value, then for any value of $x$ between 0 and $1, x^{2}$ will produce the smallest value of the five given expressions.

In fact, no matter what $x$ between 0 and 1 is chosen, $x^{2}$ is always smallest.

ANSWER: (B)