basic math tricks

Math Short Tricks (Zero to SSC CGL)

Part 1: Number System

• Divisibility rules (2, 3, 4, 5, 6, 8, 9, 11…)
• Remainder tricks
• Unit digit tricks
• LCM & HCF shortcuts
• Prime numbers
• Factors & Multiples

Part 2: Simplification

• BODMAS
• Squares (1–100)
• Cubes (1–50)
• Square roots
• Cube roots
• Fast calculations

Part 3: Percentage

• Basic concepts
• Fraction ↔ Percentage table
• Percentage increase/decrease
• Successive percentage shortcuts

Part 4: Profit & Loss

• Cost Price & Selling Price
• Discount
• Marked Price
• Successive discounts

Part 5: Ratio & Proportion

Part 6: Average

Part 7: Partnership

Part 8: Time & Work

Part 9: Pipes & Cisterns

Part 10: Time, Speed & Distance

Part 11: Boat & Stream

Part 12: Trains

Part 13: Simple & Compound Interest

Part 14: Algebra

Part 15: Geometry

Part 16: Mensuration

Part 17: Trigonometry

Part 18: Data Interpretation

---

Chapter 1 – Number System (Zero Level to SSC CGL)

Trick 1: Divisibility by 2

Rule: Last digit is even (0, 2, 4, 6, 8).

Example

• 428 ✓
• 915 ✗

---

Trick 2: Divisibility by 3

Rule: Sum of digits is divisible by 3.

Example

• 546
• 5 + 4 + 6 = 15
• 15 ÷ 3 = 5

Therefore 546 is divisible by 3.

---

Trick 3: Divisibility by 4

Rule: Last two digits are divisible by 4.

Examples:

• 1236 → 36 ÷ 4 = 9 ✓
• 4578 → 78 ÷ 4 = 19.5 ✗

---

Trick 4: Divisibility by 5

Rule: Last digit is 0 or 5.

Examples:

• 875 ✓
• 240 ✓
• 453 ✗

---

Trick 5: Divisibility by 6

Rule: Number must be divisible by both 2 and 3.

Example:

• 534
• Even ✓
• Sum = 5+3+4 = 12 ✓

Therefore divisible by 6.

---

Trick 6: Divisibility by 8

Rule: Last three digits are divisible by 8.

Example:

• 7128
• 128 ÷ 8 = 16 ✓

---

Trick 7: Divisibility by 9

Rule: Sum of digits divisible by 9.

Example:
729

7+2+9 = 18

18 divisible by 9

Therefore 729 is divisible by 9.

---

Trick 8: Divisibility by 11

Rule:
Difference between the sum of alternate digits should be 0 or a multiple of 11.

Example:
50644

(5+6+4)=15

(0+4)=4

Difference=11

Therefore divisible by 11.

---

Trick 9: Unit Digit of Powers

Last Digit	Power Pattern
2	2,4,8,6
3	3,9,7,1
4	4,6
5	5
6	6
7	7,9,3,1
8	8,4,2,6
9	9,1

Example

Find the last digit of .

Pattern for 7: 7, 9, 3, 1 (cycle of 4)

103 ÷ 4 leaves remainder 3.

The 3rd number in the cycle is 3.

Answer: 3

---

Trick 10: Squares Ending in 5

Shortcut

Examples:

• 25² = 625
• 35² = 1225
• 45² = 2025
• 95² = 9025

---

Trick 11: Square of Numbers Near 100

Example:
103²

Step 1: Difference from 100 = +3

Step 2:
103+3=106

Step 3:
3²=09

Answer:
10609

---

Example:
97²

Difference=-3

97−3=94

3²=09

Answer:
9409

---

Trick 12: Multiplication by 11

Example:
54 × 11

Write first digit 5

Add digits 5+4=9

Write last digit 4

Answer:
594

---

Example:
72 ×11

7

7+2=9

2

Answer:
792

---

Trick 13: Multiplication by 25

Since

25 = 100 ÷ 4

Example:
84 ×25

84÷4=21

Add two zeros

2100

---

Trick 14: Multiplication by 125

Since

125 =1000÷8

Example:
64×125

64÷8=8

Add three zeros

8000

---

Trick 15: Fast Percentage

Percentage	Shortcut
10%	÷10
5%	Half of 10%
20%	×2 of 10%
25%	÷4
50%	Half
75%	Three-fourths

Example:
25% of 480

480÷4

=120

---

Important SSC CGL Notes

Memorize these:

Fraction to Percentage

Fraction	Percentage
1/2	50%
1/3	33⅓%
1/4	25%
1/5	20%
1/6	16⅔%
1/8	12.5%
1/10	10%
3/4	75%
2/5	40%
4/5	80%

---

Squares (Must Know)

11²=121

12²=144

13²=169

14²=196

15²=225

…

30²=900

…

50²=2500

---

Cubes (Must Know)

2³=8

3³=27

4³=64

5³=125

…

20³=8000

---

Prime Numbers (1–100)

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

---

Study Plan (30 Days)

1. Number System – 2 days
2. Simplification – 2 days
3. Percentage – 2 days
4. Ratio & Proportion – 2 days
5. Average – 1 day
6. Profit & Loss – 2 days
7. Time & Work – 2 days
8. Time, Speed & Distance – 2 days
9. SI & CI – 2 days
10. Algebra – 4 days
11. Geometry – 4 days
12. Mensuration – 3 days
13. Trigonometry – 2 days
14. Data Interpretation – 2 days

This roadmap takes you from the basics to the level commonly required for SSC CGL, provided you also practice a good number of questions after each chapter.

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50+ Short Tricks

Could you clarify what you mean by “50+ Short Tricks”?

For example, are you looking for:

• Math short tricks (percentages, squares, multiplication, etc.)
• Reasoning tricks (competitive exams)
• English grammar/vocabulary tricks
• General life hacks
• Computer/Excel/MS Word shortcuts
• Science shortcuts
• GK (General Knowledge) tricks

Tell me the topic, and I’ll provide 50+ easy, one-line tricks with examples.

math short Tricks for zero level to SSC CGL LEVEL with example and notes in details

That’s a great topic. A complete guide from Zero Level → SSC CGL Level is much larger than can fit in one response (it would be 200–400+ pages if fully detailed).

A practical approach is to build it chapter by chapter. Here’s the syllabus I recommend:

Math Short Tricks (Zero to SSC CGL)

Part 1: Number System

• Divisibility rules (2, 3, 4, 5, 6, 8, 9, 11…)
• Remainder tricks
• Unit digit tricks
• LCM & HCF shortcuts
• Prime numbers
• Factors & Multiples

Part 2: Simplification

• BODMAS
• Squares (1–100)
• Cubes (1–50)
• Square roots
• Cube roots
• Fast calculations

Part 3: Percentage

• Basic concepts
• Fraction ↔ Percentage table
• Percentage increase/decrease
• Successive percentage shortcuts

Part 4: Profit & Loss

• Cost Price & Selling Price
• Discount
• Marked Price
• Successive discounts

Part 5: Ratio & Proportion

Part 6: Average

Part 7: Partnership

Part 8: Time & Work

Part 9: Pipes & Cisterns

Part 10: Time, Speed & Distance

Part 11: Boat & Stream

Part 12: Trains

Part 13: Simple & Compound Interest

Part 14: Algebra

Part 15: Geometry

Part 16: Mensuration

Part 17: Trigonometry

Part 18: Data Interpretation

---

Chapter 1 – Number System (Zero Level to SSC CGL)

Trick 1: Divisibility by 2

Rule: Last digit is even (0, 2, 4, 6, 8).

Example

• 428 ✓
• 915 ✗

---

Trick 2: Divisibility by 3

Rule: Sum of digits is divisible by 3.

Example

• 546
• 5 + 4 + 6 = 15
• 15 ÷ 3 = 5

Therefore 546 is divisible by 3.

---

Trick 3: Divisibility by 4

Rule: Last two digits are divisible by 4.

Examples:

• 1236 → 36 ÷ 4 = 9 ✓
• 4578 → 78 ÷ 4 = 19.5 ✗

---

Trick 4: Divisibility by 5

Rule: Last digit is 0 or 5.

Examples:

• 875 ✓
• 240 ✓
• 453 ✗

---

Trick 5: Divisibility by 6

Rule: Number must be divisible by both 2 and 3.

Example:

• 534
• Even ✓
• Sum = 5+3+4 = 12 ✓

Therefore divisible by 6.

---

Trick 6: Divisibility by 8

Rule: Last three digits are divisible by 8.

Example:

• 7128
• 128 ÷ 8 = 16 ✓

---

Trick 7: Divisibility by 9

Rule: Sum of digits divisible by 9.

Example:
729

7+2+9 = 18

18 divisible by 9

Therefore 729 is divisible by 9.

---

Trick 8: Divisibility by 11

Rule:
Difference between the sum of alternate digits should be 0 or a multiple of 11.

Example:
50644

(5+6+4)=15

(0+4)=4

Difference=11

Therefore divisible by 11.

---

Trick 9: Unit Digit of Powers

Last Digit	Power Pattern
2	2,4,8,6
3	3,9,7,1
4	4,6
5	5
6	6
7	7,9,3,1
8	8,4,2,6
9	9,1

Example

Find the last digit of .

Pattern for 7: 7, 9, 3, 1 (cycle of 4)

103 ÷ 4 leaves remainder 3.

The 3rd number in the cycle is 3.

Answer: 3

---

Trick 10: Squares Ending in 5

Shortcut

Examples:

• 25² = 625
• 35² = 1225
• 45² = 2025
• 95² = 9025

---

Trick 11: Square of Numbers Near 100

Example:
103²

Step 1: Difference from 100 = +3

Step 2:
103+3=106

Step 3:
3²=09

Answer:
10609

---

Example:
97²

Difference=-3

97−3=94

3²=09

Answer:
9409

---

Trick 12: Multiplication by 11

Example:
54 × 11

Write first digit 5

Add digits 5+4=9

Write last digit 4

Answer:
594

---

Example:
72 ×11

7

7+2=9

2

Answer:
792

---

Trick 13: Multiplication by 25

Since

25 = 100 ÷ 4

Example:
84 ×25

84÷4=21

Add two zeros

2100

---

Trick 14: Multiplication by 125

Since

125 =1000÷8

Example:
64×125

64÷8=8

Add three zeros

8000

---

Trick 15: Fast Percentage

Percentage	Shortcut
10%	÷10
5%	Half of 10%
20%	×2 of 10%
25%	÷4
50%	Half
75%	Three-fourths

Example:
25% of 480

480÷4

=120

---

Important SSC CGL Notes

Memorize these:

Fraction to Percentage

Fraction	Percentage
1/2	50%
1/3	33⅓%
1/4	25%
1/5	20%
1/6	16⅔%
1/8	12.5%
1/10	10%
3/4	75%
2/5	40%
4/5	80%

---

Squares (Must Know)

11²=121

12²=144

13²=169

14²=196

15²=225

…

30²=900

…

50²=2500

---

Cubes (Must Know)

2³=8

3³=27

4³=64

5³=125

…

20³=8000

---

Prime Numbers (1–100)

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

---

Study Plan (30 Days)

1. Number System – 2 days
2. Simplification – 2 days
3. Percentage – 2 days
4. Ratio & Proportion – 2 days
5. Average – 1 day
6. Profit & Loss – 2 days
7. Time & Work – 2 days
8. Time, Speed & Distance – 2 days
9. SI & CI – 2 days
10. Algebra – 4 days
11. Geometry – 4 days
12. Mensuration – 3 days
13. Trigonometry – 2 days
14. Data Interpretation – 2 days

This roadmap takes you from the basics to the level commonly required for SSC CGL, provided you also practice a good number of questions after each chapter.

Simplification basics to the level commonly required for SSC CGL, provided you also practice a good number of questions after each chapter.

Simplification (Basic to SSC CGL Level)

Complete Notes + Short Tricks + Examples + Practice

Simplification is one of the highest-scoring topics in SSC CGL. Most questions are based on BODMAS, fractions, decimals, powers, roots, and fast calculations.

---

Chapter 1: BODMAS Rule

BODMAS means:

Letter	Meaning
B	Brackets
O	Orders (Power, Square, Cube, Root)
D	Division
M	Multiplication
A	Addition
S	Subtraction

Order of solving:

Brackets → Powers → Division → Multiplication → Addition → Subtraction

---

Example 1

20 + 10 × 5

Wrong:
(20+10)×5 =150 ❌

Correct:

20 + 50

=70 ✅

---

Example 2

72 ÷ 8 × 3

Division and Multiplication are solved from Left to Right.

72÷8=9

9×3=27

Answer = 27

---

Example 3

18−6÷3

6÷3=2

18−2=16

Answer = 16

---

Chapter 2: Brackets Priority

Priority:

1. ( )
2. { }
3. [ ]

Example:

20−{5+(12−8)}

=20−{5+4}

=20−9

=11

---

Chapter 3: Fractions

Addition

LCM =6

=3/6+2/6

=5/6

---

Subtraction

=5/6−2/6

=3/6

=1/2

---

Multiplication

=(4×5)/(5×6)

Cancel 5

=4/6

=2/3

SSC Trick: Always cancel common factors before multiplying.

---

Division

=3/4×5/2

=15/8

---

Chapter 4: Decimal Tricks

Trick

0.25=1/4

0.5=1/2

0.75=3/4

0.125=1/8

0.2=1/5

Memorize these.

---

Example

25% of 480

=480÷4

=120

---

Example

12.5% of 800

=800÷8

=100

---

Chapter 5: Squares (Must Learn)

Number	Square
11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400

Continue memorizing up to 50².

---

Chapter 6: Squares Near 100

Formula

(100+a)²

=(100+a+a) followed by a²

---

Example

104²

104+4=108

4²=16

Answer

10816

---

Example

97²

97−3=94

3²=09

Answer

9409

---

Chapter 7: Squares Ending in 5

Formula

Examples

35²

3×4=12

Answer=1225

---

65²

6×7=42

Answer=4225

---

95²

9×10=90

Answer=9025

---

Chapter 8: Cube Tricks

Learn cubes up to 20.

Examples

5³=125

8³=512

12³=1728

15³=3375

20³=8000

---

Chapter 9: Square Root Tricks

Example

√144

Since

12×12=144

Answer=12

---

Perfect Squares

1,4,9,16,25,36,49,64,81,100,121,144,169,…

---

Chapter 10: Cube Root Tricks

Example

∛729

9×9×9=729

Answer=9

---

Chapter 11: Powers

Rule 1

a²×a³=a⁵

---

Rule 2

a⁵÷a²=a³

---

Rule 3

(a²)³=a⁶

---

Example

2³×2⁴

=2⁷

=128

---

Chapter 12: Multiplication Tricks

Multiply by 11

54×11

5 (5+4) 4

Answer

594

---

87×11

8 (8+7=15)

Carry 1

Answer

957

---

Multiply by 25

25=100÷4

Example

84×25

84÷4=21

Answer

2100

---

Multiply by 125

125=1000÷8

64×125

64÷8=8

Answer

8000

---

Multiply by 5

Multiply by 10 then divide by 2.

Example

76×5

760÷2

=380

---

Multiply by 50

Multiply by 100 then divide by 2.

Example

84×50

8400÷2

=4200

---

Chapter 13: Division Tricks

Example

560÷5

Multiply numerator by 2

1120÷10

=112

---

Example

240÷25

Multiply numerator by 4

960÷100

=9.6

---

Chapter 14: Percentage Shortcuts

Percentage	Shortcut
10%	÷10
20%	÷5
25%	÷4
50%	Half
75%	Three-fourths
12.5%	÷8
5%	Half of 10%
1%	÷100

---

Example

75% of 800

=(3/4)×800

=600

---

Chapter 15: Fraction–Percentage Table

Fraction	Percentage
1/2	50%
1/3	33⅓%
2/3	66⅔%
1/4	25%
3/4	75%
1/5	20%
2/5	40%
3/5	60%
4/5	80%
1/8	12.5%
3/8	37.5%
5/8	62.5%
7/8	87.5%

Memorize this table.

---

SSC CGL Simplification Short Tricks

1. Cancel common factors before multiplication.
2. Convert decimals into fractions whenever possible.
3. Memorize squares (1–50).
4. Memorize cubes (1–20).
5. Learn common square roots.
6. Apply BODMAS strictly.
7. Solve multiplication/division from left to right.
8. Use multiplication shortcuts (×11, ×25, ×125, ×5, ×50).
9. Learn fraction-to-percentage conversions.
10. Estimate the answer first to avoid calculation errors.

---

Practice Questions

Easy

1. 15 + 25 ÷ 5 = ?
2. 12 × 8 − 20 = ?
3. 3/4 + 1/4 = ?
4. 25% of 480 = ?
5. √225 = ?

---

Moderate

6. (24 ÷ 6) × (18 − 12) = ?
7. 84 × 25 = ?
8. 96 × 125 = ?
9. 3/5 + 7/10 = ?
10. 95² = ?

---

SSC CGL Level

11. 72 ÷ 8 × 9 − 12 = ?
12. (5² + 7² − 6²) ÷ 2 = ?
13. 12.5% of 640 + 25% of 240 = ?
14. √324 + ∛512 = ?
15. (3/4 × 16) ÷ (2/5) = ?

---

Answer Key

1. 20
2. 76
3. 1
4. 120
5. 15
6. 24
7. 2100
8. 12000
9. 13/10
10. 9025
11. 69
12. 19
13. 140
14. 26
15. 30

---

7-Day Simplification Study Plan

Day	Topics	Practice
1	BODMAS, Brackets	50 questions
2	Fractions, Decimals	50 questions
3	Squares, Cubes, Roots	75 questions
4	Powers & Indices	50 questions
5	Percentage & Fraction Conversion	75 questions
6	Calculation Shortcuts	100 questions
7	Mixed SSC CGL Simplification Test	100 questions

Target: Solve a typical SSC CGL simplification question in 20–30 seconds with 90%+ accuracy. Focus on mastering the basic rules first, then build speed through regular timed practice.

Top of Form

Bottom of Form

quares, Cubes & Roots (Zero to SSC CGL Level)

Complete Notes + Short Tricks + Examples

This chapter is extremely important for SSC CGL, CHSL, CPO, MTS, Banking, Railways, and State Exams. Around 2–5 questions in every paper are directly or indirectly based on squares, cubes, and roots.

---

Part 1: Squares (n²)

What is a Square?

The square of a number means multiplying the number by itself.

Examples:

• 5² = 5 × 5 = 25
• 12² = 12 × 12 = 144
• 25² = 25 × 25 = 625

---

Squares from 1 to 30 (Must Memorize)

Number	Square	Number	Square
1	1	16	256
2	4	17	289
3	9	18	324
4	16	19	361
5	25	20	400
6	36	21	441
7	49	22	484
8	64	23	529
9	81	24	576
10	100	25	625
11	121	26	676
12	144	27	729
13	169	28	784
14	196	29	841
15	225	30	900

SSC Tip: Memorize squares at least up to 50².

---

Trick 1: Numbers Ending in 5

Formula

If the number is a5, then:

1. Multiply a × (a + 1)
2. Write 25 at the end.

Examples

25²

• 2 × 3 = 6
• Answer = 625

35²

• 3 × 4 = 12
• Answer = 1225

85²

• 8 × 9 = 72
• Answer = 7225

95²

• 9 × 10 = 90
• Answer = 9025

---

Trick 2: Squares Near 100

Formula

If the number is 100 + a:

Square = (Number + a) | a²

Example

103²

Difference = +3

103 + 3 = 106

3² = 09

Answer = 10609

---

Example

108²

Difference = +8

108 + 8 = 116

8² = 64

Answer = 11664

---

Example

97²

Difference = −3

97 − 3 = 94

3² = 09

Answer = 9409

---

Trick 3: Square Near 50

Example: 52²

= (50 + 2)²

= 2500 + 200 + 4

= 2704

Example: 48²

= (50 − 2)²

= 2500 − 200 + 4

= 2304

---

Part 2: Cubes (n³)

What is a Cube?

Cube means multiplying the number three times.

Example:

• 3³ = 3 × 3 × 3 = 27
• 5³ = 5 × 5 × 5 = 125

---

Cubes from 1 to 20 (Must Memorize)

Number	Cube
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000
11	1331
12	1728
13	2197
14	2744
15	3375
16	4096
17	4913
18	5832
19	6859
20	8000

---

Trick 4: Cube Near 10

Formula

(10 + a)³ = 1000 + 300a + 30a² + a³

Example

12³

=1000+600+120+8

=1728

---

Part 3: Square Roots (√)

What is Square Root?

A square root is the number which, when multiplied by itself, gives the original number.

Examples:

• √49 = 7
• √81 = 9
• √144 = 12

---

Perfect Squares

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400…

---

Trick 5: Find √ of Perfect Squares

Example

√729

Since

27 × 27 = 729

Answer = 27

---

Last Digit Trick

If a square ends with:

Ends With	Root Ends With
1	1 or 9
4	2 or 8
5	5
6	4 or 6
9	3 or 7
0	0

---

Example

√1764

1. Last digit = 4 → Root ends with 2 or 8
2. Remove last two digits → 17
3. Largest square ≤ 17 is 16 = 4²
4. First digit = 4
5. Possible answers: 42 or 48
6. Since 48² = 2304 (too large), the answer is 42.

---

Part 4: Cube Roots (∛)

A cube root is the number that, when multiplied three times, gives the original number.

Examples:

• ∛8 = 2
• ∛27 = 3
• ∛125 = 5
• ∛512 = 8
• ∛729 = 9

---

Trick 6: Cube Root of Perfect Cubes

Example

∛2744

Last digit = 4

Only 14³ ends with 4.

Answer = 14

---

Example

∛2197

Last digit = 7

Only 13³ ends with 7.

Answer = 13

---

Cube Last Digit Table

Cube Ends With	Root Ends With
0	0
1	1
2	8
3	7
4	4
5	5
6	6
7	3
8	2
9	9

Memorize this table—it helps solve cube root questions in seconds.

---

Important SSC CGL Facts

Squares Ending Digits

A square number can end only with:

0, 1, 4, 5, 6, 9

It never ends with:

2, 3, 7, 8

---

Cubes Ending Digits

A cube can end with any digit (0–9).

---

Number of Digits in Squares

• 2-digit number → square has 3 or 4 digits
• 3-digit number → square has 5 or 6 digits

---

Practice Questions

Easy

1. 17² = ?
2. 25² = ?
3. 13³ = ?
4. √625 = ?
5. ∛343 = ?

Moderate

6. 96² = ?
7. 104² = ?
8. √1764 = ?
9. ∛4096 = ?
10. 18³ = ?

SSC CGL Level

11. √2025 = ?
12. √3969 = ?
13. ∛6859 = ?
14. 99² = ?
15. 125² = ?

---

Answer Key

1. 289
2. 625
3. 2197
4. 25
5. 7
6. 9216
7. 10816
8. 42
9. 16
10. 5832
11. 45
12. 63
13. 19
14. 9801
15. 15625

---

Memory Tips

• Squares: Learn 1² to 50² by heart.
• Cubes: Learn 1³ to 20³ by heart.
• Square roots: Recognize all perfect squares up to 2500.
• Cube roots: Recognize all perfect cubes up to 8000.
• Practice 20–30 questions daily to improve both speed and accuracy. These shortcuts become much more effective with regular practice.

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