## 500 BASIC AND MOST IMPORTANT ESSENTIAL MATHS APTITUDE SHORTCUTS FOR ANY EXAM LIKE BANK,ENTRANCE,CAT,MAT,GATE EXAM. Quantitative-Aptitude-Fast-Quick-Shortcut-steps-Tricks-in pdf-Download | [TUTORIAL 5]

### 1. A number is divisible by 2, if its unit’s place digit is 0, 2, 4, or 8

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2. A number is divisible by 3, if the sum of its digits is divisible by 3

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3. A number is divisible by 4, if the number formed by its last two digits is divisible by 4

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4. A number is divisible by 8, if the number formed by its last three digits is divisible by 8

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5. A number is divisible by 9, if the sum of its digits is divisible by 9

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6. A number is divisible by 11, if, starting from the RHS (Sum of its digits at the odd place) – (Sum of its digits at even place) is equal to 0 or 11x

### 7. (a + b)2 = a2 + 2ab + b2

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8. (a - b)2 = a2 - 2ab + b2

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9. (a + b)2 - (a - b)2 = 4ab

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10. (a + b)2 + (a - b)2 = 2(a2 + b2)

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11. (a2 – b2) = (a + b)(a - b)

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12. (a3 + b3) = (a + b)(a2 - ab + b2)

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13. (a3 – b3) = (a - b)(a2 + ab + b2)

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14. Results on Division:

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**Tutorial Part 1 click here to go**

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**Tutorial Part 2 Click here to Go **

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**Tutorial Part 3 Click here to go **

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**Tutorial Part 4 Click here to go **

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**Tutorial Part 5 Click here to go **

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**Tutorial Part 6 Click here to go**

**Tutorial Part 6 Click here to go**

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