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**

- F1GMAT's Blog
- 6408 reads

**Download Essential GMAT Reading Comprehension Guide**

F1GMAT has created an extensive Guide that will improve your speed and accuracy in GMAT Reading Comprehension Section. **You will learn To: **

1) Take Notes Effectively using keywords and mnemonics

2) Remember Relevant Information and Skip Facts that slows you down

3) Use Speed Reading Techniques

4) Solve Tough GMAT 800 Reading Comprehension Questions by using Process of Elimination

5) Question the Author and Find Logical Fallacies in the arguments**Download GMAT RC Guide»**