## Simplification Techniques and Tricks

Simplification is one of the most important part of Quantitative Aptitude section of any competitive exam. Today I am sharing all the techniques to solve Simplification questions quickly.

## Rules of Simplification

V → Vinculum
B → Remove Brackets – in the order ( ) , { }, [ ]
O → Of
D → Division
M → Multiplication

S → Subtraction

## Important Parts of Simplification

• Number System
• HCF & LCM
• Square & Cube
• Fractions & Decimals
• Surds & Indices

## Number System

• Classification
• Divisibility Test
• Division& Remainder Rules
• Sum Rules

## Classification

 Types Description Natural Numbers: all counting numbers ( 1,2,3,4,5….∞) Whole Numbers: natural number + zero( 0,1,2,3,4,5…∞) Integers: All whole numbers including Negative number + Positive number(∞……-4,-3,-2,-1,0,1,2,3,4,5….∞) Even & Odd Numbers : All whole number divisible by 2 is Even (0,2,4,6,8,10,12…..∞) and which does not divide by 2 are Odd (1,3,5,7,9,11,13,15,17,19….∞) Prime Numbers: It can be positive or negative except 1, if the number is not divisible by any number except the number itself.(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61….∞) Composite Numbers: Natural numbers which are not prime Co-Prime: Two natural number a and b are said to be co-prime if their HCF is 1.

## Divisibility

Numbers IF A Number Examples
Divisible by 2 End with 0,2,4,6,8 are divisible by 2 254,326,3546,4718 all are divisible by 2
Divisible by 3 Sum of its digits  is divisible by 3 375,4251,78123 all are divisible by 3.  [549=5+4+9][5+4+9=18]18 is divisible by 3  hence 549 is divisible by 3.
Divisible by 4 Last two digit divisible by 4 5648 here last 2 digits are 48 which is divisible by 4 hence 5648 is also divisible by 4.
Divisible by 5 Ends with 0 or 5 225 or 330 here last digit digit is 0 or 5 that mean both the numbers are divisible by 5.
Divisible by 6 Divides by Both 2 & 3 4536 here last digit is 6 so it divisible by 2 & sum of its digit (like 4+5+3+6=18) is 18 which is divisible by 3.Hence 4536 is divisible by 6.
Divisible by 8 Last 3 digit divide by 8 746848 here last 3 digit 848 is divisible by 8 hence 746848 is also divisible by 8.
Divisible by 10 End with 0 220,450,1450,8450 all numbers has a last digit zero it means all are divisible by 10.
Divisible by 11 [Sum of its digit in
odd places-Sum of its digits
in even places]= 0 or multiple of 11
Consider the number 39798847
(Sum of its digits at odd places)-(Sum of its digits at even places)(7+8+9+9)-(4+8+7+3)
(23-12)

23-12=11, which is divisible by 11. So 39798847 is divisible by 11.

## Division & Remainder Rules

Suppose we divide 45 by 6 hence ,Represent it as:
dividend = ( divisor✘quotient ) + remainder
or
divisior= [(dividend)-(remainder] / quotient
could be write it as
x = kq + r where (x = dividend,k = divisor,q = quotient,r = remainder)

### Example:

On dividing a certain number by 342, we get 47 as remainder. If the same number is divided by 18, what will be the remainder ?
Number = 342k + 47
( 18 ✘19k ) + ( 18 ✘2 ) + 11
18 ✘( 19k + 2 ) +11.
Remainder = 11