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

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New post 15 Oct 2019, 00:34
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Difficulty:

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Question Stats:

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[GMAT math practice question]

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

\(A. 89^o\)

\(B. 90^o\)

\(C. 91^o\)

\(D. 92^o\)

\(E. 93^o\)

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New post 15 Oct 2019, 01:15
MathRevolution wrote:
[GMAT math practice question]

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

\(A. 89^o\)

\(B. 90^o\)

\(C. 91^o\)

\(D. 92^o\)

\(E. 93^o\)


Whenever we deal with clock problems, these are some points that come in handy.

1. Every hour is \(\frac{360^o}{12} = 30^o\) in measure
2. Every minute will cause the minute hand to move \(\frac{360^o}{60} = 6^o\). As 12 minutes
pass in every hour, the hour hand will move \(\frac{30^o}{5} = 6^o\) towards the next hour.

Coming to the problem at hand, we have the hour hand standing between 5 and 6.

The hour hand has moved \(\frac{44}{60}*30 = 22^o\) away from 5(which is at \(150^o\)) and is at \(172^o\).
The minute hand is at \(44* 6^o = 264^o\). The angle between the hour and the minute hand
is the difference between the hour and minute hand.

Therefore, the angle between the minute and hour hand is \(264^o - 172^o = 92^o\)(Option D)
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Re: What is the angle between the hour hand and the minute hand at the tim  [#permalink]

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New post 15 Oct 2019, 02:00
we can use formula
angle = 11/2* min-30*hr
angle = 11/2* 44-30*5 ; 92
IMO D


MathRevolution wrote:
[GMAT math practice question]

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

\(A. 89^o\)

\(B. 90^o\)

\(C. 91^o\)

\(D. 92^o\)

\(E. 93^o\)
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: What is the angle between the hour hand and the minute hand at the tim  [#permalink]

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New post 17 Oct 2019, 18:20
=>

Attachment:
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10.15ps(a).png [ 29.35 KiB | Viewed 197 times ]


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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Re: What is the angle between the hour hand and the minute hand at the tim   [#permalink] 17 Oct 2019, 18:20
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