Dear Readers, in continuation to our previous post on Basic Concepts & Short Tricks on Number System in Quant Section, here is the Part II of the same providing you some more details of the topic and making the Quant Section and calculation more easy for you all to understand. We hop you all will like the post.

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 50^th 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 a 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.