Here is a little trick.
Convert time into mins. 4:40 = 4(60)+40 = 280
The angle between min n hour handle = arccos(cos(5.5*above))
5.5* 280 = 1540, get the remainder wrt 360 = 1540 - 360(4) = 1540 - 1440 = 100
Answer is 100 degrees
----------------------------------explanation---------------------------
In an hour, minutes hand travels 360 degrees; but hours hand travels 30 degrees.
The relative speed: 330 degrees per hour or 330/60 degrees per min or 5.5 degrees per min
4:40 = 280 mins.
280 * relative speed = 280*5.5 = 1440
get rid of multiples of 360.
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angle in a clock
Source: Beat The GMAT — Problem Solving |
That was quite an explanation but one should stay away from this kind of complex calculation in order to find a solution of the problem.
I found an easier formula for this:
Angle = |30*H - (11/2)*M|, where H is the hours hand and M is the minutes hand
in this case: H = 4, M= 40
30*4 - (11/2)*40 = 120 - 220 = -100 = |-100| = 100
I found an easier formula for this:
Angle = |30*H - (11/2)*M|, where H is the hours hand and M is the minutes hand
in this case: H = 4, M= 40
30*4 - (11/2)*40 = 120 - 220 = -100 = |-100| = 100
hey RoadtoIvy,
I didn't get your explanation.Could you elaborate?GMAT destroyer's explanation just went over my head!
I didn't get your explanation.Could you elaborate?GMAT destroyer's explanation just went over my head!
Here you go:MG368 wrote:hey RoadtoIvy,
I didn't get your explanation.Could you elaborate?GMAT destroyer's explanation just went over my head!
H = represents hours hand
M = minutes hand
So when you say 4.40, it means: H = 4 and M =40
Now use this expression to find the angle:
mode of(30*H - (11/2) * M) = mode of(30*4 - (11/2) * 40) = |120 - 220| = |-100| = 100
Hope it is more clear now.
[/u]Another less advanced solution than those posted:
The minute hand travels 360 deg i one hour. The hour hand travels (360/60)*5 =30 deg in one hour (360/60 is 6 degrees pr minute and in one hour the hour hand passes 5 minute markers).
If you assume the minute hand is at 40 min and hour hand is at exactly 4, the angle between the hands is (20/60)*360=120
But you obviously know this is to much since the hour hand has moved. All you need to do is subtract the degrees the hour hand has moved from 4 to 4:40, which is 30*(40/60)=20. (30 degrees per hour times 4/6 of an hour)
So the answer is 120-20=100.
The minute hand travels 360 deg i one hour. The hour hand travels (360/60)*5 =30 deg in one hour (360/60 is 6 degrees pr minute and in one hour the hour hand passes 5 minute markers).
If you assume the minute hand is at 40 min and hour hand is at exactly 4, the angle between the hands is (20/60)*360=120
But you obviously know this is to much since the hour hand has moved. All you need to do is subtract the degrees the hour hand has moved from 4 to 4:40, which is 30*(40/60)=20. (30 degrees per hour times 4/6 of an hour)
So the answer is 120-20=100.
