# SSC CGL Short Tricks Tier II

SSC CGL Short Tricks Tier II – Solve squares, cubes and multiply numbers in seconds.

## SSC CGL Short Tricks Tier II

SSC CGL Short Tricks Tier II – Hacks to save time.

SSC CGL short tricks tier II will be extremely beneficial in scoring high marks in competitive exams. These helps you save time and attempt more questions, thus increasing the overall score.

It will help you immensely in solving simplification problems, which is an important topic of the quantitative aptitude section.

### SSC CGL Short Tricks Tier II to Calculate Squares

**Type I:**

For digits starting from 80 to 100, let the base be 100. As there are 2 digits in the base, maximum 2 digits can be added.

Example I:

a) Find the square of 97

Solution:

1. Calculate the difference between base and number i.e. 100 – 97 = 3.

2. Subtract the difference from the number i.e. 97 – 3 = 94. This will be the first 2 digits of the solution.

3. Then, calculate square of the difference i.e. 3^{2} = 09.

4. The final solution is 9409.

Example II:

b) Find the square of 87

Solution:

1. Calculate the difference between base and number i.e. 100 – 87 = 13.

2. Subtract the difference from the number i.e. 87 – 13 = 74. This will be the first 2 digits of the solution.

3. Then, calculate square of the difference i.e. 13^{2} = 169.

4. 169 is a 3 digit number and we need only 2 digits. We’ll transfer the 1 at hundred’s place to 74 i.e. 74 + 1 = 75.

5. And the solution is 7569.

**Type II:**

For numbers starting from 100 to 120, the base is still assumed to be 100.

Example I:

Solution:

a) Find 107^{2}

1. Calculate the difference between base and number i.e. 107 – 100 = 7.

2. Add this difference with the number i.e. 107 + 7 = 114.

3. Calculate the square of the difference i.e. 7^{2 }= 49.

4. The solution is 11449.

b) Find 112^{2}

1. Calculate the difference between base and number i.e. 112 – 100 = 12.

2. Add this difference with the number i.e. 112 + 12 = 124.

3. Calculate the square of the difference i.e. 12^{2 }= 144.

4. 144 is a 3 digit number and we need only 2 digits. We’ll transfer the 1 at hundred’s place to 124 i.e. 124 + 1 = 125.

5. And the solution is 12544.

**Type III:**

For numbers starting between 50 to 70, we assume the base to be 50. Here, the formula to calculate squares is:

25 + Extra from the base_square of extra value

Examples:

1. 51^{2 }= 25 + (51 – 50) _(51 – 50)^{2 }= 25 + 1_01 = 26_01 = 2601.

2. 59^{2 }= 25 + 9_81 = 3481

3. 62^{2} = 25 + 12_144 = 37_144

Here, since 144 is a 3 digit number, we’ll transfer the 1 from hundred’s place to 37 i.e. 37 + 1 = 38.

The solution is 3844.

**Type IV:**

Similarly, for numbers between 30 to 50, the base is assumed to be 50. Here, the formula to calculate squares is:

25 – less from the base _ square of less value

Examples:

1. 46^{2 }= 25 – (50 – 46)_(50 – 46)^{2 }= 25 – 4_16 = 2116

2. 49^{2} = 25 – 1_01 = 2401

3. 43^{2} = 25 – 7_49 = 1849

4. 34^{2} = 25 – 16_256 = 9256

Here, since 256 is a 3 digit number, we’ll transfer the 2 from hundred’s place to 9 i.e. 9 + 2 = 11.

The solution is 1156.

**Type V:**

For numbers between 71 to 79, the solution can be found by using both the 50 base and 100 base method.

### SSC CGL Short Tricks Tier II to Calculate Cubes

Simplifying a problem involving cubes can take a lot of time. Therefore, it’s beneficial to learn shortcut tricks to save precious time.

1) Write down the cube of ten’s place digit in a row of four figures. The next 3 numbers in the row should be written in a geometrical ratio and should be in the exact proportion that exists between the digits.

2) Write down the two times of 2^{nd} and 3^{rd} number just below the 2^{nd} and 3^{rd} number in the next row.

3) Then add the two rows to get the answer.

Example 1:

Find the cube of 13.

Solution:

1) Write down the cube of ten’s place that is 1. You can also observe that the ratio between 1 and 3 is 1:3.

2) So, we can write down the 1^{st} row as 1 3 (3×3) (3x3x3) i.e. 1 3 9 27.

3) Then, find the double of the 2^{nd} & 3^{rd} number in the row that is 3 & 9. The doubled up numbers are 3×2 = 6 and 9×2 = 18.

4)Write down these numbers exactly below the 1^{st} row:

1 3 9 27

6 18

5)Then, add the two rows:

1 3 9 27

__+ 6 18 __

6) The ten’s place number i.e. 2 from number 27 is carried forward to the sum of 9 and 18: 9+18+2 = 29.

7) Similarly, the ten’s place number from 29 i.e. 2 is carried forward.

8) Adding up all the numbers in a similar fashion, we get the solution as 1197.

### SSC CGL Short Tricks Tier II to Multiply Numbers

**To multiply numbers having 5 at the unit’s place:**

**Type I:** When numbers are same

65×65 = (6×7)_25 = 4225 (Keep 25 in the end, multiply 6 from 7 that is 42)

85×85 = (8×9)_25 = 7225 (Keep 25 in the end, multiply 8 from 9 that is 72)

115×115 = (11×12)_25 = 13225 (Keep 25 in the end, multiply 11 from 12 that is 132)

**Type II: **When numbers have difference of 10

65×75 = (6×8)_75 = 4875 ( Keep 75 in the end, multiply 6 from 8 that is 48)

85×95 = (8× 10)_75 = 8075 ( Keep 75 in the end, multiply 8 from 10 that is. 80)

115×125 = (11×13)_75 = 14375 (Keep 75 in the end, multiply 11 from 13 that is 143)

**Type III: **When numbers have difference of 20

65×85 = (6×9)_125 = 54_125 (Keep 125 in the end and multiply 6 from 9 that is 54)

Note: In this, 1 from 125 has to be transferred to 54 i.e. 54 + 1 = 55. So, answer will be 5525.

85×105 = (8×11)_125 = 88_125 = 8925

115×135 = (11×14)_125 = 154_125 = 15525

**Type IV: **When numbers have difference of 30

65×95 = (6×10)_175 = (Keep 175 in the end and multiply 6 from 10 that is 60)

In this, 1 from 175 has to be transferred to 60 i.e. 60+1 = 61. So answer will be 6175

85×115 = (8×12)_175 = 96_175 = 9775

**To multiply other numbers:**

**Type I: **When the difference of two numbers is even

Multiplication = (Middle number)^{2 }– (Difference between the numbers/2)^{2 }= (Sum of the numbers/2) ^{2 }– (Difference between the numbers/2)^{2}

19×21 = 20^{2} – (2/2)^{2 }= 400-1 = 399

47×53 = 50^{2} – (6/2)^{2} = 2500-9 = 2491

73×77 = 75^{2} – (4/2)^{2} = 5625-4 = 5621

**Type II: **Consecutive number multiplication

Square of small number + small number

12×13 = 12^{2}+12 = 144+12 = 156

48×49 = 48^{2}+48 = 2304+48 = 2352

Formula derivation:

12×13 = 12×(12+1)= 12× 12+12 = 12^{2}+12

**Type III:** Different numbers (more than 100)

103×108

+8 +3

(103+8)_ (+3)×(+8) = 11124 or (108+3)_8×3 = 11124

109×117

+17 +9

(109+17)_(+9)×(+17) = 126_153 = 12753

**Type IV: **Different numbers (less than 100)

96×91

-9 -4

(96-9)_(-9)×(-4) = 8736 or (91-4)_9×4 = 8736

92×87

-13 -8

(92-13)_(-13)×(-8) = 79_104 = 8004

**Type V: **Different numbers (one more than and one less than 100)

103×96

-4 +3

(103-4)_(-4×3) = 99_ (-12) = 9900-12= 9888

Or (96+3)_(-4×3) = 99_-12 = 9900-12 = 9888

Dear candidates, we’re sure that utilizing these tricks will help you manage your time better and score more.

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