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M12-26

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Math Expert
Joined: 02 Sep 2009
Posts: 58306

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16 Sep 2014, 00:47
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Difficulty:

35% (medium)

Question Stats:

70% (01:59) correct 30% (02:03) wrong based on 63 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

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Math Expert
Joined: 02 Sep 2009
Posts: 58306

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16 Sep 2014, 00:47
Official Solution:

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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21 Jan 2015, 10:01
2
Hey Bunuel,

Could we just say that the clock can be divided into four 90 degree quadrants (or eight 45 degree quadrants). The 24th minute is in the second quadrant, just a tick before the 3rd 45 degree angle.

What this means is that the angle is 90+LT45 = LS135. Only E is a good enough approximation, as the hand is almost on the 3rd 45 degree angle.

I hope I am making myself clear.

Just because your solution is amazing, but it would require more calcualation probably.

Thanks,
Natalia
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Joined: 27 Jul 2016
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01 Sep 2016, 20:34
My figuring was a little more muddled but the same answer.

A clock is 360 degrees. 60 minutes, so each minute is 6 degrees.
24 minutes = 144 degrees from 12.

12 hours so each hour is 30 degrees.
At :24 then 24 minutes of an hour = 24/60 = 2/5. 2/5 of 30 degrees = 12
144-12 = 132

Pretty similar
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25 Sep 2016, 23:45
1
Theres a far more better way to solve these kinds of problems:

Angle=11/2m - 30h
where m is minutes and h is hours
points to be noted:1. if h=12,then put h=0 in the equation
2. if answer comes to be more than 180,subtract it from 360 to get the answer(as a straight angle cannot have an angle more than 180)

Coming back to the original question,
angle = 11/2 * 24 -30 * 0 = 132

Please correct me If I am wrong
Intern
Joined: 09 Aug 2014
Posts: 7

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10 Sep 2017, 20:36
Hi Bunuel,

Isn't this question open to interpretation?

Practically, the hour hand is not exactly vertical when the clock is at 12:24. It would be tilted slightly right.

In such a case the angle would be slightly less than 132.

Regards
Srinath
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10 Sep 2017, 21:37
krsrinath wrote:
Hi Bunuel,

Isn't this question open to interpretation?

Practically, the hour hand is not exactly vertical when the clock is at 12:24. It would be tilted slightly right.

In such a case the angle would be slightly less than 132.

Regards
Srinath

The solution does not say that the hour hand will be vertical at 12:24. It accounts for the moving of the hour hand from vertical position at 12:00 in 24 minutes: 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...
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10 Sep 2017, 21:47
1
Apologies! Just realized!

Bunuel wrote:
krsrinath wrote:
Hi Bunuel,

Isn't this question open to interpretation?

Practically, the hour hand is not exactly vertical when the clock is at 12:24. It would be tilted slightly right.

In such a case the angle would be slightly less than 132.

Regards
Srinath

The solution does not say that the hour hand will be vertical at 12:24. It accounts the moving of the hour hand from vertical position at 12:00 in 24 minutes: 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...
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Joined: 29 May 2016
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10 Sep 2017, 22:39
when min hand goes 60 min = 360 degree
1 min = 6 degree
24 min = 6*24 = 144 degree ...ideally, but at the same time hour hand will rotate with some angle to reduce the degree
for 360 degree= hours hand will go 360/12 = 30degree
for 144 min => 30/360 *144 = 12

so 144-12= 132 E
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14 Nov 2017, 17:54
Very good question!
Thank you Bunuel!
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10 Jan 2019, 16:52
I had difficulty with this question, until I realized that both the minute and the hour hand are moving. The minute hand is moving every minute, and the hour hand is moving every fraction of an hour. Without having to consider the rates of movement of both hands, I realized that we can think of this problem in terms of total time elapsed. From the 12 position to the 24 minute position 4 hours and 24 minutes have elapsed = 4(60) +25 = 264 minutes elapsed. Now, in the entire clock there should be 12*60 = 720 minutes total 264/720 gives us the fraction of the circle that has revolved. Therefore
(264 min)/(720 min) *360 degrees = 264/2 =132 degrees. The time units cancelling out is typically a sign that I set up my calculations correctly. The answer is E.
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26 Apr 2019, 00:53
Hi,

360/12 = 30 degrees each hour
30*4= 120 degrees

4 minutes more is left. cant we convert these 4 minutes into hr and then multiply by 30 degrees
4/60*30 = 2

so, 120 + 2 = 122

please let me know where my understanding is incorrect.

thanks a lot!
Re: M12-26   [#permalink] 26 Apr 2019, 00:53
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