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A clock is set at 6 a.m. Let the time when the minute and hour hand are together for the first time and the second time be x and y respectively. What is y - x?
- a)1 hour 11 minutes 28 seconds
- b)1 hour 32 minutes 43 seconds
- c)1 hour 9 minutes 28 seconds
- d)1 hour 3 minutes 8 seconds
- e)1 hour 5 minutes 28 seconds
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
A clock is set at 6 a.m. Let the time when the minute and hour hand ar...
When the hour hand and minute hand are together, the angle between the two hands is 0°.
The hands meet again between 7 a.m. and 8 a.m.
Here, h = 7 and θ = 0.
Here, h = 7 and θ = 0.
Most Upvoted Answer
A clock is set at 6 a.m. Let the time when the minute and hour hand ar...
To solve this problem, let's first understand how the hour and minute hands move on a clock.
- The hour hand moves 12 times slower than the minute hand. In other words, it takes 12 hours for the hour hand to make a full rotation while the minute hand takes 1 hour.
- The minute hand moves continuously, going through 360 degrees in 60 minutes, or 6 degrees per minute.
- The hour hand moves in discrete jumps, moving 30 degrees in 1 hour or 0.5 degrees per minute.
Now let's calculate the time when the minute and hour hands are together for the first time.
- At 6 a.m., the minute hand is at 0 degrees while the hour hand is at 180 degrees.
- To find the time when they are together, we need to find the time it takes for the minute hand to catch up to the hour hand.
- Since the minute hand moves 5.5 degrees per minute faster than the hour hand (6 - 0.5), it will take 180 degrees / 5.5 degrees per minute = 32.73 minutes for the minute hand to catch up to the hour hand.
- Therefore, the first time the minute and hour hands are together is approximately 6:32 a.m.
Now let's calculate the time when they are together for the second time.
- After the first time they are together, the minute hand continues to move while the hour hand remains stationary.
- The minute hand moves 6 degrees per minute, so it will take 360 degrees / 6 degrees per minute = 60 minutes for the minute hand to make a full rotation.
- Since the minute hand moves 30 degrees per hour faster than the hour hand (6 - 0.5 * 12), it will take 360 degrees / 30 degrees per hour = 12 hours for the minute hand to catch up to the hour hand again.
- Therefore, the second time the minute and hour hands are together is approximately 6:32 a.m. + 12 hours = 6:32 p.m.
Finally, let's calculate the difference between the second time and the first time.
- The difference is 6:32 p.m. - 6:32 a.m. = 12 hours.
- Converting 12 hours to minutes, we get 12 hours * 60 minutes per hour = 720 minutes.
- Therefore, y - x = 720 minutes.
- Converting 720 minutes to hours and minutes, we get 720 minutes / 60 minutes per hour = 12 hours and 720 minutes % 60 minutes per hour = 0 minutes.
- Therefore, y - x = 12 hours 0 minutes = 1 hour 0 minutes.
However, the correct answer is given as 1 hour 5 minutes 28 seconds. This could be due to rounding errors in the calculations or a mistake in the options provided.
- The hour hand moves 12 times slower than the minute hand. In other words, it takes 12 hours for the hour hand to make a full rotation while the minute hand takes 1 hour.
- The minute hand moves continuously, going through 360 degrees in 60 minutes, or 6 degrees per minute.
- The hour hand moves in discrete jumps, moving 30 degrees in 1 hour or 0.5 degrees per minute.
Now let's calculate the time when the minute and hour hands are together for the first time.
- At 6 a.m., the minute hand is at 0 degrees while the hour hand is at 180 degrees.
- To find the time when they are together, we need to find the time it takes for the minute hand to catch up to the hour hand.
- Since the minute hand moves 5.5 degrees per minute faster than the hour hand (6 - 0.5), it will take 180 degrees / 5.5 degrees per minute = 32.73 minutes for the minute hand to catch up to the hour hand.
- Therefore, the first time the minute and hour hands are together is approximately 6:32 a.m.
Now let's calculate the time when they are together for the second time.
- After the first time they are together, the minute hand continues to move while the hour hand remains stationary.
- The minute hand moves 6 degrees per minute, so it will take 360 degrees / 6 degrees per minute = 60 minutes for the minute hand to make a full rotation.
- Since the minute hand moves 30 degrees per hour faster than the hour hand (6 - 0.5 * 12), it will take 360 degrees / 30 degrees per hour = 12 hours for the minute hand to catch up to the hour hand again.
- Therefore, the second time the minute and hour hands are together is approximately 6:32 a.m. + 12 hours = 6:32 p.m.
Finally, let's calculate the difference between the second time and the first time.
- The difference is 6:32 p.m. - 6:32 a.m. = 12 hours.
- Converting 12 hours to minutes, we get 12 hours * 60 minutes per hour = 720 minutes.
- Therefore, y - x = 720 minutes.
- Converting 720 minutes to hours and minutes, we get 720 minutes / 60 minutes per hour = 12 hours and 720 minutes % 60 minutes per hour = 0 minutes.
- Therefore, y - x = 12 hours 0 minutes = 1 hour 0 minutes.
However, the correct answer is given as 1 hour 5 minutes 28 seconds. This could be due to rounding errors in the calculations or a mistake in the options provided.
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A clock is set at 6 a.m. Let the time when the minute and hour hand are together for the first time and the second time be x and y respectively. What is y - x?a)1 hour 11 minutes 28 secondsb)1 hour 32 minutes 43 secondsc)1 hour 9 minutes 28 secondsd)1 hour 3 minutes 8 secondse)1 hour 5 minutes 28 secondsCorrect answer is option 'E'. Can you explain this answer?
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A clock is set at 6 a.m. Let the time when the minute and hour hand are together for the first time and the second time be x and y respectively. What is y - x?a)1 hour 11 minutes 28 secondsb)1 hour 32 minutes 43 secondsc)1 hour 9 minutes 28 secondsd)1 hour 3 minutes 8 secondse)1 hour 5 minutes 28 secondsCorrect answer is option 'E'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A clock is set at 6 a.m. Let the time when the minute and hour hand are together for the first time and the second time be x and y respectively. What is y - x?a)1 hour 11 minutes 28 secondsb)1 hour 32 minutes 43 secondsc)1 hour 9 minutes 28 secondsd)1 hour 3 minutes 8 secondse)1 hour 5 minutes 28 secondsCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A clock is set at 6 a.m. Let the time when the minute and hour hand are together for the first time and the second time be x and y respectively. What is y - x?a)1 hour 11 minutes 28 secondsb)1 hour 32 minutes 43 secondsc)1 hour 9 minutes 28 secondsd)1 hour 3 minutes 8 secondse)1 hour 5 minutes 28 secondsCorrect answer is option 'E'. Can you explain this answer?.
A clock is set at 6 a.m. Let the time when the minute and hour hand are together for the first time and the second time be x and y respectively. What is y - x?a)1 hour 11 minutes 28 secondsb)1 hour 32 minutes 43 secondsc)1 hour 9 minutes 28 secondsd)1 hour 3 minutes 8 secondse)1 hour 5 minutes 28 secondsCorrect answer is option 'E'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A clock is set at 6 a.m. Let the time when the minute and hour hand are together for the first time and the second time be x and y respectively. What is y - x?a)1 hour 11 minutes 28 secondsb)1 hour 32 minutes 43 secondsc)1 hour 9 minutes 28 secondsd)1 hour 3 minutes 8 secondse)1 hour 5 minutes 28 secondsCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A clock is set at 6 a.m. Let the time when the minute and hour hand are together for the first time and the second time be x and y respectively. What is y - x?a)1 hour 11 minutes 28 secondsb)1 hour 32 minutes 43 secondsc)1 hour 9 minutes 28 secondsd)1 hour 3 minutes 8 secondse)1 hour 5 minutes 28 secondsCorrect answer is option 'E'. Can you explain this answer?.
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