UPSC Prelims 2014 · CSAT
Question 12: Logical Reasoning and Mental Ability
Assume that
- 1.the hour and minute hands of a clock move without jerking.
- 2.the clock shows a time between 8 o'clock and 9 o'clock.
- 3.the two hands of the clock are one above the other.
After how many minutes (nearest integer) will the two hands be again lying one above the other ?
AnswerUPSC’s answer is (c).
The minute hand gains 5.5 degrees per minute on the hour hand, and it must gain a full 360 degrees for the hands to lie one above the other again. Time needed = 360 / 5.5 = 720/11 = 65 5/11 minutes, nearest integer 65. The hour (between 8 and 9) only places the first overlap, near 8:43; the gap to the next overlap is the same at any hour.
- 1. Given: the hands move smoothly, so the gain per minute is steady.
- 2. Given: the first overlap falls between 8 and 9.
- 3. Given: the hands lie one above the other at that first moment.
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) 60 minutes is one lap of the minute hand; the hour hand has moved on meanwhile.
- (b) 62 is short of the 65 5/11 minutes needed.
- (c) Right. 360 / 5.5 = 65 5/11, nearest integer 65.
- (d) 67 overshoots the 65 5/11 minutes.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2014, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.