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

1. Complete GMAT RC Questions in less than 1 minute and 50 seconds

3. Take Notes Effectively

4. Collect and Interpret Facts

5. Speed up Summary Creation

6. Remember Information

7. Question the Author

9. Learn to Solve GMAT Reading Comprehension Main Idea Question

10.Learn to Solve GMAT Reading comprehension inference question

11. Learn to Solve GMAT Reading Comprehension Detail Questions

12. Learn to Organize passage in GMAT Reading Comprehension

13. Learn to Identify style/tone or attitude of the author

14. Learn to Improve GMAT Reading Comprehension Score

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After you read F1GMAT’s Mastering GMAT Critical Reasoning Guide, you will:

1) Learn to eliminate out of scope answer choices

2) Learn to spot logical fallacies

3) Learn to read questions by focusing on the holy trinity – premise, assumption, and conclusion.

4) Learn to disregard filler information

5) Complete GMAT CR Questions in less than 1 minute and 40 seconds

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