Consider the following statements : 1. Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide. 2. Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide. Which of the above statements is/are correct?

(a) 1 only
(b) 2 only
(c) Both 1 and 2 ✓ UPSC's answer
(d) Neither 1 nor 2

Why the answer is (c)

• The hour and minute hands coincide 11 times in 12 hours, specifically at intervals of 65 5/11 minutes starting from 12:00.

• The 3rd coincidence occurs at 3:16 4/11 p.m., which falls within the interval between 3:16 p.m. and 3:17 p.m., making Statement 1 correct.

• The minute and second hands coincide 11 times in 12 hours, at intervals of 65 5/11 seconds starting from 00:00:00.

• The 59th coincidence occurs at 4:58 58/11 seconds (approx. 4:58:5.27), which falls within the interval between 4:58 p.m. and 4:59 p.m., making Statement 2 correct.

• Since both statements are factually accurate based on clock geometry, the correct option is (c).

Why the other options are wrong

(a) 1 only: This option is incorrect because Statement 2 is also correct, as the minute and second hands do coincide between 4:58 p.m. and 4:59 p.m.
(b) 2 only: This option is incorrect because Statement 1 is also correct, as the hour and minute hands do coincide between 3:16 p.m. and 3:17 p.m.
(d) Neither 1 nor 2: This option is incorrect because both Statement 1 and Statement 2 are correct, not neither.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.