M25-12

Question

Between 12:24 and 14:36 the hour hand of the clock turns by

A. 60 degrees
B. 66 degrees
C. 72 degrees
D. 74 degrees
E. 76 degrees

Bunuel · Accepted Answer

Official Solution:

Between 12:24 and 14:36 the hour hand of the clock turns by

A. 60 degrees
B. 66 degrees
C. 72 degrees
D. 74 degrees
E. 76 degrees

In one hour, the hour hand moves by  \frac{360}{12} = 30  degrees. In one minute, the hour hand moves by  \frac{30}{60} = \frac{1}{2}  degrees. The difference between 12:24 and 14:36 is 2 hours and 12 minutes. Thus, the hand moved by  2*30 + 12*0.5 = 66  degrees.

Answer: B

bsmith37 · Answer

good solutions, definitely the safer bet to do it that way.

i did: from 12:24 to 14:24 would be exactly 2 hours, so the hour hand moved 2/12 = 1/6 of 360 degrees = 60 degrees. Then there are about 10 more minutes, so slightly above 60 is 66. (Or ~10 minutes = 1/6 of 1 hour. Since 2 hours was 60 degrees, one hour is 30 and 1/6 of that is 5. So we come out to 65 degrees because of our rounding.)

manpreetsinghkohli · Answer

Total minutes between 14:36 and 12:24 = 2 hours + 12 minutes = 120 + 12 = 132

The hour hand rotates 360 degrees in 12 hours. Or 360 degrees in 720 minutes.
So in one minute it rotates = 720/360 = 1/2 degrees

1/2 degrees in a minute, so it will move 132/2 degrees in 132 minutes. The answer is 132/2 = 66 degrees.

ND9129 · Answer

The hour hand moves by a unit (if we consider total sixty units in the clock) every 12 minutes, as when the hour hand moves from 12 to 1(covering 5 units) the minute hand covers the whole circle(i.e. 60 units), so for every unit on the hour hand the minute hand equals 60/5 = 12 units. i.e. every time the hour hand moves by 1 unit the minute hand covers 12 units(i.e. 12 minutes)
This means that from 12:24 to 14:36 we had 2 hours(10 units on the hour hand) and 12 minutes (i.e. 1 unit on the hour hand). = 2+1/5 units or hours.

Or in a simpler way we can see that the amount of time spent is 2 + 1/5 hours.

and each hour contributes to 30 degrees (360/12). (as 360 = total angle at the center, 12 = number of hours swept in that much time by the hour hand)
 Hence we have 2*30 = 60 + 30*1/5 =60 +6 =66 degrees

ajdse22 · Answer

Awesome problem:---Even though I got this wrong, I made a second attempt and understood why the correct answer is correct. When I got this wrong, I started off from 12:00 and reached to 14:36 ..

Yikes!! But anyway the question asks if the clock moves from 12:24 to 14:36, how many degrees does the hour hand moves. Two things have to be done in order to solve this problem. First how many degrees does the hour hand move if it moves one tick among the 60 ticks .. Well that is equal to (360/60) 6 degrees. So if we go from 12:24 to 14:24, we should move 10 ticks -- so the answer is going to be somewhat greater than 60. Will it go to 72 ? Well 72 is another 2 ticks away. Does the hour hand move that much for 12 extra minutes of minute hand? Let us see The ratio is 5/60= hticks/12, Cancelling we see that hticks = 1. So it is just one tick and so the answer is 60+6 = 66

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M25-12

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