M12-26

Question

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

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

Bunuel · Accepted Answer

Official Solution:

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

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

Starting from the 12:00 position, where both hands are vertical, we note that the hour hand moves  \frac{360}{12*60}=0.5  degrees per minute and the minute hand moves  \frac{360}{60}=6  degrees per minute.
 
Consequently, at 12:24, 24 minutes after 12:00, the hour hand will have shifted  24*0.5=12  degrees from the vertical position and the minute hand will have moved  24*6=144  degrees from the vertical position.
 
The angle between the two hands would therefore be  144-12=132  degrees.

Answer: E

pacifist85 · Answer

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

wainsdaylion · Answer

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

nish0912 · Answer

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

BobsterGMAT · Answer

Very good question! 
Thank you Bunuel!

ocelot22 · Answer

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.

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

M12-26

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