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On a 12-hour analog clock, the hour hand moves at a constant rate of
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Updated on: 29 Feb 2024, 20:40
Updated on: 29 Feb 2024, 20:40
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On a 12-hour analog clock, the hour hand moves at a constant rate of 1 revolution every 12 hours, and the minute hand moves at a constant rate of 1 revolution every hour. The hands are perpendicular at 3:00 in the morning. To the nearest second, the next time they are superimposed (i.e., both pointing at the same point on the outer rim of the clock face) is M minutes and S seconds after 3:00 in the morning.Select for M and for S values that are consistent with the information provided. Make only two selections, one in each column.
All Data Insight question: TPA [ Official Guide DI Review 2023-24]
On a 12-hour analog clock, the hour hand moves at a constant rate of 1 revolution every 12 hours, and the minute hand moves at a constant rate of 1 revolution every hour. The hands are perpendicular at 3:00 in the morning. To the nearest second, the next time they are superimposed (i.e., both pointing at the same point on the outer rim of the clock face) is M minutes and S seconds after 3:00 in the morning.Select for M and for S values that are consistent with the information provided. Make only two selections, one in each column.
| M | S | |
| 15 | ||
| 16 | ||
| 17 | ||
| 20 | ||
| 22 | ||
| 34 |
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Official Answer
M: 16
S: 22
On a 12-hour analog clock, the hour hand moves at a constant rate of
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15 Mar 2024, 05:30
15 Mar 2024, 05:30
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Wow! What a question this is. On the surface, it appears to be simple – why? Since it is based on an equipment that we see on a daily basis – a clock. In fact, it looks simple enough more so because the author has explained how a clock works – something that is general information. But the real complexity of this question lies in what it asks and the kind of processing that it requires.
Watch the video solution and realize these complexities in the question and how each of these are places where a test taker can falter.
Beautiful question – one that is packed with learnings!
Watch the video solution and realize these complexities in the question and how each of these are places where a test taker can falter.
- Visualizing what it means when the author says that the two hands superimpose – And draw inference to set the stage for this question.
- Hour hand would have traveled 90 degrees more than the minute hand.
- If one is unable to draw this inference, then they might as well randomly mark some answer and move to the next question, in the test environment. This is how critical this step is.
- Translating the inference into mathematical terms is the next critical step. This is where you need to apply your understanding of Geometry concepts pertaining to angles in a circle. See how practical application of Geometry is tested so beautifully here. This is where you set the approach to solve this question.
- Once you have the approach established, the execution is also extensive. And there are places where you could falter – not doing the unitary conversion correctly and hence arriving at incorrect equation.
- Lastly, not doing the correct conversion to find minutes and seconds.
Beautiful question – one that is packed with learnings!
Re: On a 12-hour analog clock, the hour hand moves at a constant rate of
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14 Mar 2024, 21:53
14 Mar 2024, 21:53
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Engineer1 wrote:
On a 12-hour analog clock, the hour hand moves at a constant rate of 1 revolution every 12 hours, and the minute hand moves at a constant rate of 1 revolution every hour. The hands are perpendicular at 3:00 in the morning. To the nearest second, the next time they are superimposed (i.e., both pointing at the same point on the outer rim of the clock face) is M minutes and S seconds after 3:00 in the morning.Select for M and for S values that are consistent with the information provided. Make only two selections, one in each column.
All Data Insight question: TPA [ Official Guide DI Review 2023-24]
On a 12-hour analog clock, the hour hand moves at a constant rate of 1 revolution every 12 hours, and the minute hand moves at a constant rate of 1 revolution every hour. The hands are perpendicular at 3:00 in the morning. To the nearest second, the next time they are superimposed (i.e., both pointing at the same point on the outer rim of the clock face) is M minutes and S seconds after 3:00 in the morning.Select for M and for S values that are consistent with the information provided. Make only two selections, one in each column.
The clock questions are easily done using relative speed.
Consider this: an hour hand covers 30 degrees in 1 hr
A minute hand covers 360 degrees (full circle) in 1 hr
Relative speed of minute hand = 330 degree per hour.
When the two hands are perpendicular at 3:00, they have angle of 90 degrees between them. To overlap, they need to cover this relative distance of 90 degrees
\(Time Taken = \frac{Distance}{Speed} =\frac{90}{330}*60 mins = 16\frac{4}{11} min\)
\(\frac{4}{11} mins = \frac{4}{11} * 60 secs = 21.8 secs\)
ANSWER 16 mins, 22 secs
Check this video for a discussion on relative speed in clocks: https://youtu.be/dGqC_6DIKkY
