500 MOST IMPORTANT MATHS APTITUDE SHORTCUTS ESSENTIAL HAND BOOKS PRINTABLE FORMAT|Quantitative-Aptitude-Fast-Quick-Shortcut-steps-Tricks-in pdf-Download | [TUTORIAL 5]

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

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

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

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

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

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

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

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

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

11. (a2 – b2) = (a + b)(a - b)

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

13. (a3 – b3) = (a - b)(a2 + ab + b2)

14. Results on Division:

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Tutorial Part 3 Click here to go 

Tutorial Part 4 Click here to go 

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Tutorial Part 6 Click here to go

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