How to Solve GMAT Clock Angle Problems

Clock based math problems are among the most challenging and interesting problems to crack.

Basics
  
For every 60 units that a minute hand move in an hour , the hour hand moves 5 units.

For 12 hours the hour hand completes 360 degrees

1 hour  =  360/12 = 30 degrees
60 minutes = 30 degrees
Degrees turned by hour hand in 1 minute = 0.5 degrees

For 1 hour the minute hand completes 360 degrees

1 hour = 360 degrees
60 minutes = 360 degrees
Degrees turned by minute hand in 1 minute = 6 degrees

Lets test what we have learned:

Q) Find the degree between hour hand and minute hand at 3:32'

Hour hand = 3

1 minute ( hour hand) = 0.5 degrees
3 hours = 3*0.5*60(1 hour= 60 minutes)
3 hours ( 3'o clock) = 90 degrees

Minute Hand = 32'

1 minute(minute hand) = 6 degrees
32 minutes(minute hand) = 32*6 = 192 degrees

For the 32 minutes, the hour hand moves by an additional 16 degrees
 = 32*0.5

So Hour hand at 32 minutes = 90+16=106 degrees

Degrees between minute hand and hour hand at 3:32' = 192-106
=86 degrees

Number of right angles

1) A clock makes two right angles between 2 hours
2) The clock does not makes 48 right angles in 24 hours( 1 day)

P.S: Between 2 -4 and 8-10 there are 3 right angles and not 4

The first right angle between 3 - 4 (9-10)  and second right angle bw:
2-3(8-9) are the same.

Q) At what time between 3 and 4 p.m is the first right angle formed

At 3 p.m

 No of units that the hour hand is ahead of the minute hand = 15 units
 For 90 degrees the minute hand should be 15 units ahead of hour hand
 No of units that the minute hand has to cover = 15+15 = 30 units

Distance covered by minute hand over hour hand in one hour = 55 units
1 hour = 55 units
x hour = 30 units

x = 30/55 = 6/11 of an hour

So first right angle between 3 and 4 is at 6/11 of an hour
Converting 6/11 to minutes = 6/11 * ( 60) minutes
                              = 360/11 minutes
                              = 32 ( 8/11) minutes
Converting 8/11 minutes to seconds = 8/11*(60) = 480/11 = 43.6363..

So the first right angle is at 3 : 32 : 43.64

Learn how to Solve Tricky Clock Angle Math Problems