What is the number of times the hour hand and the minute hand of a clock form a right angle

Q: What is the number of times the hour hand and the minute hand of a clock form a right angle with each other between 0600 and 1200 on the same day?
A. 11
B. 12
C. 23
D. 24

Answer: A

The times the hour hand and the minute hand of a clock form a right angle with each other between 0600 and 1200 are approximately at 0617, 0649, 0722, 0754, 0828, 0900, 0933, 1005, 1038, 1111, 1149.

Note that this happens twice every hour, except between 0800 and 1000 when it happens only three times and not four times as expected. This is because at 0900 exactly the hands form a right angle. Thus between 0600 and 1200 it happens (6 × 2) − 1= 11 times.