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What is the angle between the hour hand and the minute hand

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by Max@Math Revolution » Mon Oct 14, 2019 11:17 pm
[GMAT math practice question]

What is the angle between the hour hand and the minute hand at the time of 5 hours 44 minutes?

A. 89
B. 90
C. 91
D. 92
E. 93
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by deloitte247 » Thu Oct 17, 2019 6:19 am
$$There\ is\ 360^0\ in\ 12\ hours$$
$$In\ 1\ hour,\ there\ is\ \frac{360^0}{12^0}=30^0\ per\ hour$$
$$=>30^0\ in\ 60\ \min utes,\ this\ will\ be\ \frac{30^0}{60^0}=0.5^0\ in\ 1\ \min ute$$
$$The\ \min ute\ hand\ moves\ 360^0\ in\ 60\ \min utes\ and\ \frac{360^0}{60^0}=6^0\ per\ \min ute$$
At 5 hours 44 minutes, the hour hand has covered 5.7 hours and the minute hand has covered 44 minutes.
[5.7 hours is gotten by converting 5 hours 44 minutes to hours]
$$Therefore,\ hour\ hand\ has=>30^0\cdot5.7hours\ =\ 171^0$$
$$Minite\ hand\ has=>6^0\cdot44\ \min utes\ =\ 264^0$$
$$The\ angle\ at\ 5\ hour\ 44\ \min utes=\ 264^0-171^0=93^0$$
Answer = option E
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by Max@Math Revolution » Thu Oct 17, 2019 4:53 pm
=>

Image

The minute hand moves 6° every minute and < x = 44*6°=264°.
The hour hand moves 0.5° every minute and < y = 44*0.5°+150 = 172°.
Then the angle between the minute hand and the hour hand is 264°-172°=92°.

Therefore, D is the answer.
Answer: D
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