Quants Notes | Simplification / Approximation

In this, a topic the questions asked is related to the BODMAS rule. This rule is very common in mathematics. It stands for Bracket Of Division Multiplication Addition and Subtraction. Two tier of examination pattern in bank and insurance exam. i.e. Prelims and Mains. Most of them have changed their exam patterns and set a sectional timing of 20 minutes on each section. Quantitative aptitude is important for every exam because proper strategy and enough practice can help you score full marks in this section. There may not be assured in the language section and you may be stuck while solving reasoning questions but quants is a scoring subject and assure full marks if the calculation is correct.

Remember : you always apply BODMAS on simplification .

So we are providing some example with basic and trick shortcut. It is helpful for your exam

Addition

1. Basic
Eg.  321+467+2311

2. Unit digit

Notes : Most prefer to solve using digit sum. Easy and save your precious time during the examination.

Eg2.   321 + 467 + 2311 = 3099

3. Digital sum

This method is called as nines remainder method.

1 How to solve digit sum

32102= 3+2+1+0+2=8

2 We are always reduce digit sum to a single figure.

 3218 = 3+2+1+8

=14

=5

3 Note- In adding across a number we may drop out 9, 9 doesn't count on digit sum.

eg1: digit sum of 9902 is (0+2) =  2.

eg2: digit sum of 2529 is (2+5+2+9) = 0 here digit sum of (2,5,2) makes 9.

4. for decimals we work exactly the same way, but we don't pay attention to the decimal points.

the digit sum of 6.236 is (6+2+3+6)=8, neglect 9= digit sum is 8

Subtraction 

1. Basic

Eg. 3455-456-4891+4521=2629

2. Unit Digit

Eg. 3455-456-4891+4521=2629

3. Digit sum

Eg.  3455-456-4891+4521=2629

LHS=RHS

LHS

(3+4+5+5)-(4+5+6)-(4+8+9+1)+(4+5+2+1)

=8-6-4+3

=11-10

=2-1 =

2629=2+6+2+9=10=1

LSH=RHS    1=1

Multiplication
Structure of 2digit number
 

43*56 =   20  (24+15)   1 8 =   2408

Breaking Method
43 * 56=43(50+56) = 2408

2. Multiplication of 3 digit

carry forward to next

Multiplication of random number
234 * 42 = 42(200+30+4)=
                  or
234 *(40+2) = 9828

Divison
 1. Basic
eg. 45625/4= 11413
eg. 240108/12=20009

2. Unit digit
eg. 240108/12=20009

20004  wrong       

           or             

20009  right,  because it is nearest value  20009

 ➩Divisibility rule

Number	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.

➩Table: you should remember  table at least up to 1 to 25 

➩Square: also remember square atleast upto 1-40.

square of two digit number
 1. Method

 

➩Cube of number

Using formula to find cube
a³ + b³ = a³ +b³+3 a² b +3a b²  

Eg. 13³
(1+ 3)³ = | 1³ |  | 3 x 1² x 3 |  | 3 x 1 x 3²  |  | 3³ |
=| 1 |   | 9 |   | 27 |    | 27  |=2197