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

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VP
Joined: 18 May 2008
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What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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Updated on: 26 Feb 2019, 05:30
6
26
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Difficulty:

45% (medium)

Question Stats:

68% (01:58) correct 32% (02:01) wrong based on 393 sessions

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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

Originally posted by ritula on 16 Nov 2008, 23:15.
Last edited by Bunuel on 26 Feb 2019, 05:30, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 53771
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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14 Dec 2009, 16:19
6
14
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..

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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Joined: 14 Aug 2007
Posts: 670
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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16 Nov 2008, 23:45
1
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.
Manager
Joined: 14 Oct 2008
Posts: 149
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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17 Nov 2008, 05:06
1
1
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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Posts: 670
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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17 Nov 2008, 06:19
1
1
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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Joined: 03 Oct 2009
Posts: 78
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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14 Dec 2009, 02:58
1
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..
Math Expert
Joined: 02 Sep 2009
Posts: 53771
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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26 Jul 2010, 02:05
3
2
bibha wrote:
What is the angle between the minute and the hour hand of the clock which shows 12:24?

115
120
124
130
132

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

There is general formula for this, (though no need to memorize):

$$|\frac{11}{2}m - 30h|$$

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.

For our original question:
12:24 --> $$h=0$$ (not 12) and $$m=24$$ --> $$|\frac{11}{2}m - 30h|=|\frac{11}{2}24 - 30*0|=132$$

Hope it's clear.
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Concentration: Strategy, Marketing
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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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30 Sep 2014, 08:01
1
such questions are asked on GMAT? I have never encountered this type in OG, gmatprep or any other test prep material
Math Expert
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Posts: 53771
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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30 Sep 2014, 08:40
3
4
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.

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Posts: 79
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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22 Oct 2016, 06:44
1
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
VP
Joined: 07 Dec 2014
Posts: 1160
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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22 Oct 2016, 12:05
[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°
Manager
Joined: 29 Dec 2014
Posts: 66
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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01 Jan 2017, 19:27
Bunuel wrote:
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..

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.

Please can anyone elaborate on when to assign positive and negative signs when opening the modulus in the general formula given above?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 53771
Re: What is the angle between the minute and the hour hand of the clock wh  [#permalink]

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02 Jan 2017, 04:59
WilDThiNg wrote:
Bunuel wrote:
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..

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.

Please can anyone elaborate on when to assign positive and negative signs when opening the modulus in the general formula given above?

Thanks

You should take the absolute value of $$\frac{11}{2}m - 30h$$, so if $$\frac{11}{2}m - 30h$$ is negative you should make it positive.
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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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02 Jan 2017, 20:36
thanks for clarifying
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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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26 Feb 2019, 05:29
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Re: What is the angle between the minute and the hour hand of the clock wh   [#permalink] 26 Feb 2019, 05:29
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