How many times from 4 pm to 10 pm will the hands of a clock be at right angles?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 11
The hands are at right angles twice in every hour, except that between 2 and 4 o’clock, and again between 8 and 10 o’clock, one right angle falls at 3:00 or 9:00 and is shared by two hours. So these two-hour spans have only 3 right angles, not 4.
4 pm to 8 pm: 4 hours × 2 \(=8\) right angles
8 pm to 10 pm: 3 right angles (about 8:27, at 9:00 and about 9:33)
Total \(=8+3=11\)
Tip: In 12 hours the hands are at right angles 22 times, not 24, because of the shared right angles at 3 and 9 o’clock; in a full day it is 44 times.