At all the times given, the minute hand is pointing to $$12$$. When the minute hand is pointing to $$12$$ and the angle between the hands is $$150^{}\circ$$, the hour hand has turned $$\frac{150}{360}= \frac{5}{12}$$ of a complete turn. Therefore the hour hand will point at $$5$$ and the time will be $$5\text{pm}$$. (There are other times when the angle between the hands is $$150^{}\circ$$ but, of these, only at $$7\text{pm}$$ does the minute hand point to $$12$$ and $$7\text{pm}$$ is not one of the times given.) 
At which of~ these times is the angle between the minute hand and the hour hand of a clock equal to $$150^{}\circ$$? 
[A] $$9\text{pm}$$ 
[B] $$8\text{pm}$$ 
[C] $$6\text{pm}$$ 
[D] $$5\text{pm}$$ 
[E] $$4\text{pm}$$ 