M12 Q 26 : Retired Discussions [Locked]
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# M12 Q 26

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Senior Manager
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03 Jan 2010, 18:21
What is the angle between the minute and the hour hand of the clock which shows 12:24?

115
120
124
130
132

I got 144 degrees but can not find the right answer choice among the answers.
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22 Feb 2010, 11:56
1
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Expert's post
Igor010 wrote:
Bunuel wrote:
There is general formula for this:

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

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

Hey Bunuel!
I still don't understand how this formula works. Please, explain in more details with the numbers from this problem.

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

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03 Jan 2010, 19:04
mirzohidjon wrote:
What is the angle between the minute and the hour hand of the clock which shows 12:24?

115
120
124
130
132

I got 144 degrees but can not find the right answer choice among the answers.

the minute hand at 24 will cover angle (24/60) * 360 = 144. However during the same time the hour hand will not remain stuck/constant at 12. It will also move towards 1. So angle covered by hour hand for 24mins will be
(24/60) * 30 = 12 [Note: 30 degree is angle between each hour of the clock]
so angle b/w hour hand and minute hand will be 144 - 12 = 132

Ans - E - 132
Math Expert
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03 Jan 2010, 23:13
mirzohidjon wrote:
What is the angle between the minute and the hour hand of the clock which shows 12:24?

115
120
124
130
132

I got 144 degrees but can not find the right answer choice among the answers.

There is general formula for this:

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

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.
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04 Jan 2010, 08:27
Thank you for explanation, now I got it.
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22 Feb 2010, 01:39
Bunuel wrote:
There is general formula for this:

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

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

Hey Bunuel!
I still don't understand how this formula works. Please, explain in more details with the numbers from this problem.
Manager
Joined: 13 Dec 2009
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22 Feb 2010, 13:57
Thank you! Got it!
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26 Feb 2010, 02:27
Minute hand moves 360/60 i.e. 6 degrees in 1 minute
Hour hand moves 360/60/12 i.e. 0.5 degrees in 1 minute

therefore at 24 minutes minute hand has moved 24*6 = 144 degrees
hour hand at 12 has moved 24 * 0.5 = 12 degrees

Therefore the angle b/w two hands is 144-12 = 132 degrees

Hope this helps

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Re: M12 Q 26   [#permalink] 26 Feb 2010, 02:27
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# M12 Q 26

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