Logical Reasoning
hardQ. No. 19730
Using relative angular motion, answer this: how many times are the hour and minute hands exactly opposite in 24 hours?
Last Updated:
A23times
B22times
C21times
D24times
Correct Answer: 22timesYour Answer: B
Explanation
Correct answer: Option B — 22times. The relative speed of the minute hand over the hour hand is 5.5° per minute. Applying the required separation over a 12-hour cycle gives the verified result 22times. Option A (23times) is rejected because it does not equal the computed result; it represents a counting, direction, leap-year, interval, or hand-motion error. Option C (21times) is rejected because it does not equal the computed result; it represents a counting, direction, leap-year, interval, or hand-motion error. Option D (24times) is rejected because it does not equal the computed result; it represents a counting, direction, leap-year, interval, or hand-motion error.
Important Notes
- Read the complete condition before calculating and write the required reference point, date, or clock time separately. This prevents a correct calculation from answering the reverse question.
- Keep units consistent. Reduce day differences modulo 7; treat 12 on a clock as zero for angle work; and convert gained or lost minutes into the same time unit as the stated interval.
- Check boundary cases explicitly: February, century years, noon, midnight, and an angle greater than 180 degrees often change the apparent answer. A century is a leap year only when divisible by 400.