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What is the angle between the minute and the hour hand of the clock wh

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What is the angle between the minute and the hour hand of the clock which shows 12:24?

A. 115
B. 120
C. 124
D. 130
E. 132

M12-26
[Reveal] Spoiler: OA
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Re: What is the angle between the minute and the hour hand of the clock wh [#permalink]

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ritula wrote:
What is the angle between the minute and the hour hand of the clock which shows 12:24?

115
120
124
130
132


At 12:24
-minute hand will be at 24*6 = 144 degrees from position of 12.
- Hour hand will move by 2*6 = 12 degree during the same time

So the difference between the two hands will be 144-12 = 132 degrees.
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New post 17 Nov 2008, 04:06
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hour hand moves 5 minutes when minute hand moves 60 minutes. Hence when minute hand moved 24 minutes, hour hand moved 24 *5 / 60 i.e. 2 minutes.
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New post 17 Nov 2008, 05:19
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ritula wrote:
can u pls explain this?
alpha_plus_gamma wrote:

At 12:24
-minute hand will be at 24*6 = 144 degrees from position of 12.
- Hour hand will move by 2*6 = 12 degree during the same time

So the difference between the two hands will be 144-12 = 132 degrees.


yeah, exactly in the way provided by gameCode

gameCode wrote:
hour hand moves 5 minutes when minute hand moves 60 minutes. Hence when minute hand moved 24 minutes, hour hand moved 24 *5 / 60 i.e. 2 minutes.
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New post 14 Dec 2009, 01:58
I read somewhere there is a direct formula to solve this question..2)
Angle between m and h hand is ( 11/2) *m – 30 * h
can this be apply here? if yes should i take the value of h =12 ..taking this I am not getting the answer..
Please suggest
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New post 14 Dec 2009, 15:19
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KocharRohit wrote:
I read somewhere there is a direct formula to solve this question..2)
Angle between m and h hand is ( 11/2) *m – 30 * h
can this be apply here? if yes should i take the value of h =12 ..taking this I am not getting the answer..
Please suggest


You just should substitute h=0 in it, not h=12.

General formula is:

\(|\frac{11}{2}m - 30h|\)

If the result is greater than 180 degrees, subtract it from 360 to get the included angle.

The above can be derived from the fact that:
In 1 minute:
Hour hand moves 0.5 degrees,
Minute hand moves 6 degrees.

AND

In an hour:
Hour hand moves 30 degrees,
Minute hand moves 360 degrees.

Hope it's clear.
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Re: What is the angle between the minute and the hour hand of the clock wh [#permalink]

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New post 30 Sep 2014, 07:01
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such questions are asked on GMAT? I have never encountered this type in OG, gmatprep or any other test prep material
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ritula wrote:
What is the angle between the minute and the hour hand of the clock which shows 12:24?

A. 115
B. 120
C. 124
D. 130
E. 132

M12-26


What is the angle between the minute and the hour hand of the clock which shows 12:24?

A. 115
B. 120
C. 124
D. 130
E. 132

From the position of hands on 12:00 (both hands are vertical) hour hand moves \(\frac{360}{12*60}=0.5\) degrees in 1 minute and minute hand moves \(\frac{360}{60}=6\) degrees in 1 minute.

Hence at 12:24, after 24 minutes from 12:00, when both hands are vertical, hour hand will move \(24*0.5=12\) degrees from the vertical position and minute hand will move \(24*6=144\) degrees from vertical position.

So the angle between them will be \(144-12=132\) degrees.


Answer: E
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Re: What is the angle between the minute and the hour hand of the clock wh [#permalink]

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New post 22 Oct 2016, 05:44
This Q reminds me of good old school days.

Formula for included angle between minute hand and a hour hand = 11/2m - 30h

Since the hour hand is at 12 , we have h =0

Putting the values in formula above

11/2 * 24 - 0 = 132 Option E
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Re: What is the angle between the minute and the hour hand of the clock wh [#permalink]

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New post 22 Oct 2016, 11:05
[quote="ritula"]What is the angle between the minute and the hour hand of the clock which shows 12:24?

A. 115
B. 120
C. 124
D. 130
E. 132

24-(0+24/12)=22
22*6°=132°
Re: What is the angle between the minute and the hour hand of the clock wh   [#permalink] 22 Oct 2016, 11:05
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