## Hour Clock Arithmetic

Hour Clock Arithmetic is the topic in SAT Preparation and other competitive exams, in which question are frequently asked. When we see a question in this topic, we may find it difficult to solve it. But, the problems in this topic are very easy to be solved, if we know some basic ideas of arithmetic modulo 12.

Basic Concept:

If the divisor m=12, then the arithmetic modulo 12 is called the clock arithmetic. The remainder can be related to hour numbers in a clock where 0 corresponds to the 12 hour.

Problem:1

It is 9 hours now in 12 hours clock.,What will be the time after 18 hours?.

Solution:

Since we are trying to find the time 18 hours after from the time now 9 hours, we have to add 18 to 9.

9 + 18 = 27

In hour clock arithmetic, since the divisor m = 12, we have to divide 27 by 12 and take the remainder.

When we divide 27 by 12, we get the remainder 3

Hence,The time after 18 hours from now ( 9 hours) will be 3 hours.

Problem:2

What was the time 71 hours back.

Solution:

9-71=-62.

-62 can be written as -72+10

So the time before 71 hours was 10 hours.

This is how, we do problems on hour-clock arithmetic based on the techniques explained above in SAT and other competitive exams. When students have this kind of problems in examinations, immediately they would find it difficult to solve and get answer.But when they apply the techniques, and easily they can solve and get answer within in a minute.

So, we can solve this kind of problems very easily within a minute once we know the concept. But we need to spend some time to take practice on these problems.When we keep on practicng, we can be in the position to solve any difficult problem in this topic by using the above techniques.

Hour Clock Arithmetic to SAT Preparation

Math dictionary