UPSC Prelims 2024 · CSAT
Question 37: Logical Reasoning and Mental Ability
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)?
AnswerUPSC’s answer is (a).
The hands coincide once every 12/11 hours, i.e. 11 times in 12 hours, at about 12:00, 1:05, 2:11, 3:16, 4:22, 5:27, 6:33, 7:38, 8:44, 9:49 and 10:55. Between 10:00 a.m. and 2:00 p.m. the coincidences fall at about 10:55 a.m., 12:00 noon and 1:05 p.m. The next one, at about 2:11 p.m., is after 2:00 p.m. So the hands coincide 3 times.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Right. About 10:55, 12:00 and 1:05.
- (b) Wrong. The fourth coincidence is about 2:11 p.m., after the window ends.
- (c) Wrong. Coincidences are about 65.5 minutes apart, so a four-hour window cannot hold five.
- (d) Wrong. Six would need over five hours at 65.5 minutes apart.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.