# DAY ARITHMETIC

Day arithmetic :

7 day clock arithmetic is one of the sub topics of Modular Arithmetic  which plays a major role in quantitative aptitude test.

It is bit difficult to score marks in competitive exams without knowing the shortcuts related to 7 day clock arithmetic, We have already learned this topic in our lower classes.

Even though we have been already taught this topic in our lower classes, we need to learn some more short cuts which are being used to solve the problems in the above topic.

The only thing we have to do is, we need to apply the appropriate short cut and solve the problems in a limited time. This limited time will be one minute or less than one minute in most of the competitive exams.

## Shortcuts we use to solve the problems

BASIC CONCEPT

In modular arithmetic, if the divisor is 7, it is called as day clock arithmetic. Since the divisor is 7, the remainders must be less than or equal to 6. So, the remainder are 0,1,2,3,4,5,6.

"0" corresponds to "Sunday"

"1" corresponds to "Monday"

"2" corresponds to "Tuesday"

"3" corresponds to "Wednesday"

"4" corresponds to "Thursday"

"5" corresponds to "Friday"

"6" corresponds to "Saturday"

Here, we have some problems on 7 day clock arithmetic. You can check your answer online and see step by step solution.

## Day arithmetic - Examples

Question 1 :

A work was assigned to John on a Tuesday.He took 72 days to complete this work.On what day did he complete the work?

Solution :

Tuesday corresponds to 2 in 7 day clock arithmetic.

We want to know the day which is 72 days after Tuesday.

To get answer for our question, we have to do the following steps.

Step 1 :

Step 2 :

Divide the result by the divisor 7

Step 3 :

Take the remainder

72 + 2 = 74

When 74 is divided by 7, the remainder is 4

4 corresponds to Thursday

Hence, John completed the work on Thursday. day arithmetic

Question 2 :

What was the day 23 days before Monday?

Solution :

Monday corresponds to 1 in 7 day clock arithmetic.

We want to know the day which is 23 days before Monday.

To get answer for our question, we have to do the following steps.

Step 1 :

Subtract 23 from 1. That is, 1-23 = -22

Step 2 :

Find the next integer after 22 which is exactly divisible by 7. That is 28.

Step 3 :

Now -22 can be written as -22 = -28 + 6

6 corresponds to Saturday.

Hence, the day 23 days before Monday was Saturday

Question 3 :

What will be the day 20 days after Monday?

Solution :

Monday corresponds to 1 in 7 day clock arithmetic.

We want to know the day which is 20 days after Monday.

To get answer for our question, we have to do the following steps.

Step 1 :

Step 2 :

Divide the result by the divisor 7

Step 3 :

Take the remainder

20+1 = 21

When 21 is divided by 7, the remainder is 0.

0 corresponds to Sunday.

Hence, the day 20 days after Monday will be Sunday.

Question 4 :

Michael was assigned a work on Thursday. He agreed to complete the work after 25 days. But he took two more days to complete the work. On what day did he complete the work?

Solution :

Thursday corresponds to 4 in 7 day clock arithmetic.

We want to know the day which is (25+2=) 27 days after Thursday.

To get answer for our question, we have to do the following steps.

Step 1 :

Step 2 :

Divide the result by the divisor 7

Step 3 :

Take the remainder

27 + 4 = 31

When 31 is divided by 7, the remainder is 3.

3 corresponds to Wednesday.

Hence, Michael completed the work on Wednesday.

Question 5 :

Mr. Lenin's birthday was on Monday. He visited Newyork 28 days before his birthday. On what day, did he visit Newyork?

Solution :

Lenin's birthday was on Monday. Monday corresponds to 1 in 7 day clock arithmetic

We want to know the day which was 28 days before Monday.

To get answer for our question, we have to do the following steps.

Step 1 :

Subtract 28 from 1. That is, 1-28 = -27

Step 2 :

Find the next integer after 27 which is exactly divisible by 7. That is 28.

Step 3 :

Now -27 can be written as -27 = -28 + 1

1 corresponds to Monday.

Hence, Lenin visited Newyork on Monday. After having gone through the stuff given above, we hope that the students would have understood "Day arithmetic"

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