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At what time between 3:00 and 4:00 will the hour and minute hands of a clock overlap? (1) The hands overlap once between any two consecutive hours (2) The minute hand gains 55 minutes per hour on the hour hand

GMAT · 2022 · Quantitative

Question:
At what time between 3:00 and 4:00 will the hour and minute hands of a clock overlap? (1) The hands overlap once between any two consecutive hours (2) The minute hand gains 55 minutes per hour on the hour hand

Options

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

(D) EACH statement ALONE is sufficient

(E) Statements (1) and (2) TOGETHER are NOT sufficient

Answer: (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

Explanation:
Statement (1): True but does not give exact time. Insufficient. Statement (2): At 3:00, hour hand is at 15 minutes (3×5). Minute hand gains 55 min/hour = 11/12 min/min relative to hour hand. To overlap, minute hand must gain 15 minutes: time = 15/(11/12) = 180/11 = 16.36... minutes past 3. Sufficient.

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At what time between 3:00 and 4:00 will the hour and minute hands of a clock overlap? (1) The hands overlap once between any two consecutive hours (2) The minute hand gains 55 minutes per hour on the hour hand

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At what time between 3:00 and 4:00 will the hour and minute hands of a clock overlap? (1) The hands overlap once between any two consecutive hours (2) The minute hand gains 55 minutes per hour on the hour hand

Options

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