Question

How many times do the hands of a clock make an angle of 90${}^o$ in 36 hours?

• A. 11
• B. 22
• C. 44
• D. 72
• E. 66

Answer 1

The correct option is E 66

If you switch to a rotating coordinate system in which the hour hand stands still, then the minute hand makes only 11 revolutions, and so it is at right angles with the hour hand 22 times. In 36 hours, you get 322=66.