Logical Reasoning
mediumQ. No. 19703
What is the smaller angle between the hour and minute hands at 1:52?
Last Updated:
A105°
B103°
C104°
D106°
Correct Answer: 104°Your Answer: C
Explanation
Correct answer: Option C — 104°. Hour-hand position = 30×1 + 0.5×52 = 56.0°. Minute-hand position = 6×52 = 312°. Their absolute difference is 256.0°; the smaller angle is 104°. Option A (105°) is rejected because it does not equal the computed result; it represents a counting, direction, leap-year, interval, or hand-motion error. Option B (103°) is rejected because it does not equal the computed result; it represents a counting, direction, leap-year, interval, or hand-motion error. Option D (106°) 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.