Logical Reasoning
hardQ. No. 19700
What is the smaller angle between the hour and minute hands at 1:38?
Last Updated:
A180°
B178°
C181°
D179°
Correct Answer: 179°Your Answer: D
Explanation
Correct answer: Option D — 179°. Hour-hand position = 30×1 + 0.5×38 = 49.0°. Minute-hand position = 6×38 = 228°. Their absolute difference is 179.0°; the smaller angle is 179°. Option A (180°) is rejected because it does not equal the computed result; it represents a counting, direction, leap-year, interval, or hand-motion error. Option B (178°) is rejected because it does not equal the computed result; it represents a counting, direction, leap-year, interval, or hand-motion error. Option C (181°) 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.