1. At which of these times is the angle between the minute hand and the hour hand of a clock equal to $150^{\circ}$ ?
A $9 \mathrm{pm}$
B $8 \mathrm{pm}$
C $6 \mathrm{pm}$
D $5 \mathrm{pm}$
E $4 \mathrm{pm}$
1. D 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 $5 \mathrm{pm}$. (There are other times when the angle between the hands is $150^{\circ}$ but, of these, only at $7 \mathrm{pm}$ does the minute hand point to 12 and $7 \mathrm{pm}$ is not one of the times given.)