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The time is between 8 and 9 o’clock. The angle between th

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by Max@Math Revolution » Mon Jul 22, 2019 5:36 pm
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[GMAT math practice question]

The time is between 8 and 9 o’clock. The angle between the hour hand and the minute hand is 180. What time is it?

A. 8 hours 9 and (9/10) minutes
B. 8 hours 10 and (10/11) minutes
C. 8 hours 11 and (11/12) minutes
D. 8 hours 12 and (12/13) minutes
E. 8 hours 13 and (13/14) minutes
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by Max@Math Revolution » Tue Jul 23, 2019 11:56 pm
=>

The minute hand moves 6 ° and the hour hand moves 0.5° for every minute.
The angle between the hour hand and the minute hand at 8:00 is 120 °.
After x minutes, the angle between the hands is 120 ° + x * 6 ° - x * 0.5 ° = 120 ° + x * 5.5 ° = 180. So, x * 5.5 ° = 60 ° and x = 600 / 55 = 120 / 11 = 10 + (10/11).

Therefore, the answer is B.
Answer: B
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by swerve » Wed Jul 24, 2019 10:04 am
The relative speed of the two hands of the clock is to be calculated

Hour hand takes 1 hour to move 30 degree
Minute hand in 1 hour moves 360
Relative speed in 1 hour is 330 degrees

At 8 o'clock angle between the two hands is 120 degree. To form an angle of 180, 60 degrees more is covered with their relative speed.

To cover 330 degrees time required is 1 hour or 60 minutes
To cover 60 degrees time required is \((60\cdot 60)/330\) minutes (unitary method)
Simplifying further, the time required is 10 10/11 minutes ( in mixed fraction)

__B__ is the correct option.
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