Turkish wrote:

What is the measure of the smaller angle between the hour and the minute hand of a clock at 6.40pm?

a. 30

b. 35

c. 40

d. 50

e. 60

These questions can be easily done once you understand the concept of speed of hour hand and speed of minute hand.

An hour hand covers 360 degrees (the full circle) in 12 hours ( = 720 mins). So it covers 1/2 degree every minute.

A minute hand covers 360 degrees every hour ( = 60 mins). So it covers 360/60 = 6 degrees every minute.

So the minute hand covers 5(1/2) = 11/2 degrees more than hour hand every minute. So the relative speed of the minute hand with reference to the hour hand is 11/2 degrees every minute. Now just use the relative speed concepts and you can find the angle between the two hands at any given time, even if the time given is not very easy to calculate.

Say what is the angle between them at 6:22?

At 6 o clock, the angle between them is 180 degrees. Say this is the distance between them initially - 180 degrees

In 22 minutes, the minute hand covers 11/2 * 22 = 121 degrees of distance between them.

So distance between them now = 180 - 121 = 59 degrees.

Similarly, take the case of 6:40

At 6 o clock, the angle between them is 180 degrees.

In 40 minutes, the minute hand covers 11/2 * 40 = 220 degrees of distance between them.

So distance between them now = 220 - 180 = 40 degrees.

Check out this post for more examples of this concept:

http://www.veritasprep.com/blog/2012/09 ... clockwork/
_________________

Karishma

Veritas Prep GMAT Instructor

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