The least value of $x$ which makes $\frac{24}{x-4}$ an integer is
(A) -44
(B) -28
(C) -20
(D) -8
(E) 0
The least value of $x$ which makes $\frac{24}{x-4}$ an integer is
(A) -44
(B) -28
(C) -20
(D) -8
(E) 0

## Solution

If we determine the value of the expression for each of the given values of $x$ we would have,
(A) $\frac{24}{-44-4}$
(B) $\frac{24}{-28-4}$
(C) $\frac{24}{-20-4}$
(D) $\frac{24}{-8-4}$
(E) $\frac{24}{0-4}$

$$
\begin{array}{llll}
=\frac{24}{-48} & =\frac{24}{-32} & =\frac{24}{-24} & =\frac{24}{-12} \\
=\frac{-1}{2} & =\frac{-3}{4} & =-1 & =-2
\end{array}
$$

The smallest value of $x$ is thus -20 . Note that the answers for (A) and (B) are non-integers.

ANSWER: (C)