If $x=\frac{1}{4}$, which of the following has the largest value?
(A) $x$
(B) $x^{2}$
(C) $\frac{1}{2} x$
(D) $\frac{1}{x}$
(E) $\sqrt{x}$
If $x=\frac{1}{4}$, which of the following has the largest value?
(A) $x$
(B) $x^{2}$
(C) $\frac{1}{2} x$
(D) $\frac{1}{x}$
(E) $\sqrt{x}$

Solution

If we calculate the value of the given expressions, we get
(A) $\frac{1}{4}$
(B) $\left(\frac{1}{4}\right)^{2}$
(C) $\frac{1}{2}\left(\frac{1}{4}\right)$
$=\frac{1}{16}$
$=\frac{1}{8}$
(D) $\frac{1}{\frac{1}{4}}$
(E) $\sqrt{\frac{1}{4}}$
$=1 \times 4 \quad=\frac{1}{2}$
$=4$

ANSWER: (D)