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500 BASIC AND MOST IMPORTANT ESSENTIAL  MATHS APTITUDE SHORTCUTS FOR ANY EXAM LIKE BANK,ENTRANCE,CAT,MAT,GATE EXAMQuantitative-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:


Tutorial Part 1 click here to go

Tutorial Part 2 Click here to Go 


Tutorial Part 3 Click here to go 

Tutorial Part 4 Click here to go 

Tutorial Part 5 Click here to go 

Tutorial Part 6 Click here to go

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