# Concept & Tricks on Number System, Study Notes, Material - All Teaching Exam

By Ashish Kumar|Updated : June 17th, 2021

In this article, we should read related to the  Concept & Tricks on Number System Important for the CTET Paper-1 & 2. (All Teaching Exam).

• We use numbers and know many things about them.
• Numbers help us count concrete objects.
• They help us to say which collection of objects is bigger and arrange them in order e.g., first, second, etc.
• Numbers are used in many different contexts and in many ways.

### Basic Formula of Number System:

1. Sum of all the first n natural numbers =

For example:  1+ 2 +3 +…..+105=

2. Sum of first n odd numbers =

For example 1+3+5+7==16(as there are four odd numbers)

3. Sum of first n even numbers = n (n+1)

For example : 2+4+6+8+….+100 (or 50th even number) = 50×(50+1)= 2550

4. Sum of squares of first n natural numbers =

For example:

5. Sum of cubes of first n naturals numbers =

For example:

Example:

(1) What is the total of all the even numbers from 1 to 400?

Solution:

From 1 to 400, there are 400 numbers. So, there are 400/2= 200 even numbers.

Hence, sum = 200(200+1) = 40200     (From Rule III)

(2) What is the total of all the even numbers from 1 to 361?

Solution:

From 1 to 361, there are 361, there are 361 numbers; so there are even numbers. Thus, sum = 180(180+1)=32580

(3) What is the total of all the odd numbers from 1 to 180?

Solution:

Therefore are 180/2 = 90 odd numbers between the given range. So, the sum =

(4) What is the total of all the odd numbers from 1 to 51?

Solution

There are odd numbers between the given range. So, the sum =

(5) Find the of all the odd numbers from 20 to 101.

Solution:

The required sum = Sum of all the odd numbers from 1 to 101.

Sum of all the odd numbers from 1 to 20

= Sum of first 51 odd numbers – Sum of first 10 odd numbers

=

Miscellaneous

1. In a division sum, we have four quantities – Dividend, Divisor, Quotient, and Remainder. These are connected by the relation.

Dividend = (Divisor × Quotient) + Remainder

2. When the division is exact, the remainder is zero (0). In this case, the above relation becomes

Dividend = Divisor × Quotient

Example: 1: The quotient arising from the divisor of 24446 by certain numbers is 79 and the remainder is 35; what is the divisor?

Solution:

Divisor × Quotient = Dividend -  Remainder

79×Divisor = 24446 -35 =24411

Divisor = 24411 ÷ 79 = 309.

Example: 2: A number when divided by 12 leaves a remainder of 7. What remainder will be obtained by dividing the same number by 7?

Solution:

We see that in the above example, the first divisor 12 is not a multiple of the second divisor 7. Now, we take the two numbers 139 and 151, which when divided by 12, leave 7 as the remainder. But when we divide the above two numbers by 7, we get the respective remainder as 6 and 4. Thus, we conclude that the question is wrong.

This article tends to be beneficial for the following exams - REETUPTETCTETSuper TETDSSSBKVS, etc.

Note: All the study notes are available in Hindi as well as English language. Click on A/अ to change the language.

 Serial No. Book Name Author Name 1. The Pearson Guide To Quantitative Aptitude For Competitive Examination Dinesh Khattar 2. Quantitative Aptitude Quantum CAT Sarvesh K. 3. Teach Yourself Quantitative Aptitude Arun Sharma

Thanks

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## FAQs

• The weightage of the Mathematics Section in CTET Paper 1 & 2 is 30 marks.

• In a division sum, we have four quantities – Dividend, Divisor, Quotient, and Remainder. These are connected by the relation.

• Sum of all the first n natural numbers =

• Sum of first n odd numbers =

For example 1+3+5+7==16(as there are four odd numbers)

### CTET & State TET Exams

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