4. The positive integer $k$ is a solution of the equation $(k \div 12) \div(15 \div k)=20$. What is the sum of the digits of $k$ ?
A 15
B 12
C 9
D 6
E 3
SOLUTION
D
We have
$$
\begin{aligned}
(k \div 12) \div(15 \div k) & =\frac{k}{12} \div \frac{15}{k} \\
& =\frac{k}{12} \times \frac{k}{15} \\
& =\frac{k \times k}{12 \times 15} \\
& =\frac{k^{2}}{180} .
\end{aligned}
$$

It follows that
$$
\begin{aligned}
(k \div 12) \div(15 \div k)=20 & \Leftrightarrow \frac{k^{2}}{180}=20 \\
& \Leftrightarrow k^{2}=3600 \\
& \Leftrightarrow k=60, \text { as } k>0 .
\end{aligned}
$$

The sum of the digits of 60 is $6+0=6$.