UPSC Prelims 2024 CSAT Paper II · Q37 of 79 Mental Ability easy

How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)?

  1. (a) 3 times ✓ UPSC's answer
  2. (b) 4 times
  3. (c) 5 times
  4. (d) 6 times

Why the answer is (a)

• The hour and minute hands coincide 11 times in a 12-hour period, approximately every 65 minutes and 27 seconds.

• The first coincidence after 10:00 a.m. occurs at approximately 10:54:33 a.m.

• The next coincidence occurs at approximately 12:00:00 p.m. (exactly 12:00).

• The following coincidence occurs at approximately 1:05:27 p.m.

• The next coincidence would be at approximately 2:10:54 p.m., which is outside the specified 2:00 p.m. limit.

• Therefore, there are exactly 3 coincidences within the interval from 10:00 a.m. to 2:00 p.m.

Why the other options are wrong

(b) 4 times
Option (b) is incorrect because the fourth coincidence occurs after 2:00 p.m., specifically at approximately 2:10:54 p.m.
(c) 5 times
Option (c) is incorrect because it overcounts the coincidences; only three events occur before the 2:00 p.m. cutoff.
(d) 6 times
Option (d) is incorrect because it significantly overestimates the frequency, as the hands do not coincide every hour but roughly every 65 minutes.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

Practise this paper free