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# M12-26

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Math Expert
Joined: 02 Sep 2009
Posts: 50544

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15 Sep 2014, 23:47
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:22) correct 33% (01:04) wrong based on 97 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: 50544

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15 Sep 2014, 23:47
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.

_________________
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 422
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)

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21 Jan 2015, 09:01
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
Intern
Joined: 27 Jul 2016
Posts: 14

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01 Sep 2016, 19:34
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
Current Student
Joined: 17 Apr 2014
Posts: 11
Location: India
Concentration: Technology, Operations
GMAT 1: 660 Q49 V31
WE: Information Technology (Computer Software)

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25 Sep 2016, 22:45
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: 8

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10 Sep 2017, 19:36
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
Math Expert
Joined: 02 Sep 2009
Posts: 50544

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10 Sep 2017, 20:37
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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Intern
Joined: 09 Aug 2014
Posts: 8

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10 Sep 2017, 20:47
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...
Manager
Joined: 29 May 2016
Posts: 104

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10 Sep 2017, 21:39
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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Posts: 30
Location: Uzbekistan
Schools: Babson '21
GMAT 1: 690 Q47 V37
GPA: 4
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14 Nov 2017, 16:54
Very good question!
Thank you Bunuel!
Re: M12-26 &nbs [#permalink] 14 Nov 2017, 16:54
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# M12-26

Moderators: chetan2u, Bunuel

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