A4. Half of a fifth of twice the square of the negative number $m$ is 242. What is the number $m$?
(A) $-2 \sqrt{2}$
(B) 60
(C) $\sqrt{122}$
(D) $-11 \sqrt{10}$
(E) $\sqrt{1210}$
A4. We consider the problem statement and set up the equation $\frac{1}{2} \cdot \frac{1}{5} \cdot 2 m^{2}=242$. We simplify the equation and get $m^{2}=1210$. The solutions are $m_{1,2}= \pm \sqrt{1210}= \pm 11 \sqrt{10}$. Since we are looking for the negative number $m$, the appropriate solution is $-11 \sqrt{10}$.