It is always a fun to play with numbers. Aspirants preparing for Bank exams & other competitive exams have to be quick enough to perform calculations within seconds. If they will follow the basic approach for performing calculations, they will lag behind.

Someone has rightly said,

“Effort is important, but knowing where to make an effort makes all the difference”

Calculation is an important part of Quantitative Aptitude section in every competitive exam. Through this blog, we would like to share with our readers Short-tricks on Squares & Multiplication which will definitely help them to perform quick calculations & save time in the upcoming Bank exams.

 

Shortcut Tricks to solve Squares

Type I: (80-100)

Assume 100 as the base since 80-100 is near to 100.

Example 1: 932

Base = 100

Step 1: Calculate the difference between base and number

100-93 = 7

Step 2: Subtract the difference from the number

93-7= 86

Step 3: Calculate the square of the difference

72 = 49

Answer = 8649

 

Example 2: 822

In order to calculate the square of 82, we will follow similar steps mentioned in example 1:

Base =100

100-82 =18

82-18= 64

182 = 324

This square is 3 digit no., however, we are calculating from 100, where we assumed base which has 2 zeros,

So, the new no. becomes = 64__324

This 3 will be carried forward and will be added to 64.

Therefore, the correct answer is = (64+3)__24

                                                          = 6724

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Type II: 100-120

Example 3: 1032

Step 1: Difference between 103 and 100 (i.e 3)

Step 2: Add this difference to the base i.e 100

             = 100+3

             = 103

Step 3: 103+3

          = 106

Step 3: Calculate the square of the difference

             32 = 9

Note: 9 is a single digit no. and we are assuming 100 as base

Therefore, we will add zero before 9 .

Correct answer = 106_09

 

Example 4:  1142

114+14  = 128

142 = 196

Square is a 3 digit no., however we are calculating assuming the base to be 100

Therefore, we will carry forward the 1 and add it to 128.

Correct answer = (128+1)__96

                             = 12996

 

Type III: 50-70

Base -50 

25 + Difference between given no. & 50_Sqaure of the difference                

Example 5: 542
=(25+4)__42

=2916

 

Example 6: 632

 = (25+13)__(13)2

       = 38__169

1 will be carried forward and added to 38 to reach the correct answer

= (38+1)__69

= 3969

 

Type IV: 30-50

Base- 50

25- difference between the given no. & 50_Sqaure of the difference


Example 7:

472

 = (25-3)__32

 = 2209

 

Example 8:

362

= (25-14)__142

 = 11_196

We will carry forward 1 and add it to 11

Therefore, the correct answer= 12_96

 

Example 9:

322

= (25-18)__182

 = 1024

 

Type V: 71-79

This category can be calculated assuming both the bases 50 as well as 100.

Example 10: 742

i.Base 50

(25+24)_242

49_576 (We will carry forward 5 and add it to 49)

Correct answer =5476

ii.Base 100

(74-26)_262

48_676

We will carry forward 6 and add it to 48.

Correct answer = 5476

 

Tricks to solve Multiplications

 

(A) Multiplication of Numbers having 5 at their unit places

Type I: When the nos. are same

In this if questions, we fix 25 in the end and multiply first digit with the next digit. Let us go through examples to understand it better:

Example 11:

65 *65

=6*7_25

=4225

 

Example 12:

55 * 55

= 5*6_25

=3025

 

Example 13:

125*125

=(12*13)_25

= 15625

 

Type II: When nos. have difference of 10

Example 14:

45*55

(4*6)_75

2475

105*105

= (10*12)_75

=12075

 

Example 15:

185*195

=(18*20)

=36075

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Type III: When nos. have a difference of 20

Example 16:

45*65

= (4*7)_125 (Fix 125 in the last and multiply 4*7)

Note: From 125, we will carry forward 1 to the digits multiplied)

Correct answer = (28+1)_25

                             = 2925

 

Example 17:

95*115

=(9*12)_125

=(108+1)25

=10925

 

Example 18:

185*205

(18*21)_125

(378+1)_25

37925

 

Type IV: When the difference between the nos. is 30

Example 19:

55*85

Fix 175 in the end and multiply 5 and 9.

(5*9)_175

From this 175, 1 will be carried forward to the digits multiplied to find the correct answer.

Correct answer = 4675

 

Example 20:

125*155

=(12*16)-175

=19375

 

(B) Multiplication by 25                                                                                                             

Whenever we have to multiply by 25,instead of directly multiplying by 25, we should rather multiply by 100 and divide by 4 in order to follow an easy approach.

Let us understand it with the help of examples:

Example 21

52*25

=52*100/4

=1300

 

Example 22:

112*25

=112*100/4

=2800

 

(C) Multiplication by 50

Whenever we have to multiply by 50, we should multiply by 100 and divide by 2 in order to make our calculations easy.

Example 23:

28*50

=28*100/2

=1400

 

(D) Multiplication using Multiples

Directly multiplying 2 nos. is time consuming, so we must follow multiples approach wherever it is suitable so make our calculations easy.

Example 24:

15*18

=15*6*3 (Here we have split 18 into 6*3)

= 180

 

(E) Consecutive Number Multiplication

Square of smaller number + Smaller number


Example 25:

25*26

= (25)2 + 25

= 625 + 25

= 650

 

(F) Rule of Multiply of 100(+)

This rule is used where the nos. to be multiplied are more than 100

Example 26:

105*109

+9       +5   and 9*5=45

(105+9)_(+9)*(+5)                      OR (109+5)_(+5)*(+9)

114_45                                               =114_45

11445                                                 =11445

 

Example 27:

1009*1012

Here, we will take Base as 1000 instead of 100 since the no. is a 4-digit number.

1009* 1012

+12        +9   and 12*9 =108

(1009+12)_(12*9)

1021_108

1021108

 

(G) Rule of Multiply of 100(-)

Example 28:

94*96

-4    -6 and (-4)*(-6)

(94-4)_24

90_24

=9024

 

Example 29:

494*483

Here the digits are near 500. So we assume base to be 500

494*483

(-17)   (-6) and (-17)*(-6)

(494-17)_102

477_102

Important Note: We have taken Base-500 instead of 100 i.e 5 times of 100. So, now we multiply 477 with 5 which amounts to 2385.

2385_102 (Since the base as 2 zeros we will carry forward 1 from 102 and add it to 2385)

So, the correct answer is (2385+1)_02

                                            =238602

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(H) Rule of Multiply of 100(+) and 100 (-)

Example 30:

96*107

(+7)   (-4)  and (+7)*(-4)

(96+7)_(-28)

103_(-28)

=10300-28

=10272

 

Example 31:

91*116

+16    -9

(91+16) and (+16)*(-9)

107_(-144)

10700-144

=10556

 

(I) Unit’s digit 10

We use this approach when the sum of unit’s digit is 10 and ten’s digit is same.

Let us understand it with the help of an example:

Example 32:

46*44

Here the sum of unit’s digits (i.e 6+4 =10) is 10 and tenis digit is same i.e 4.

4*5_6*4 (We have multiplied the units digit with the next consecutive no. and ten’s digit of  both the nos.)

20_24

2024

 

Example 33:

52*58

5*6_2*8

=3016

 

(I) Multiplication by 11

Type 1: If sum of digits is greater than 10

Example 34:

67*11

=6_7

Therefore, middle no. is 6+7 =13

Since middle no. is more than 10, use 3 and add then add 1 to the first term

737

 

Type 2: If sum of digits is less than 10

Example 35:

52*11

5_2

Sum of middle terms = 5+2

                                   =7

Place the middle between 5 and 2

Correct answer= 572

 

We hope we have made it easy for all the aspirants to calculate squares and solve multiplication. It is sincere advice, if you want to use these short-tricks at exam time, keep practicing these tricks on daily basis.

Good Luck

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