FIVE THINGS TO YOU KNOW IMPROVE YOUR SELF iN THE QUANTITATIVE APTITUDE

 FIVE THINGS TO YOU KNOW IMPROVE YOUR SELF iN THE QUANTITATIVE APTITUDE

 1.BASICS
2.DAILY Practice
3.Solving the  different different problems
4.Time management
5.practice websites are so many in the internet 
so practice well..
Practicing problems on numbers systems not only helps in improving your speed but also provides a strong base for solving other quantitative aptitude sections like HCF and LCM,averages, percentages, time and speed, pipes and cisterns etc as well. In this tutorial let's look at how to solve number system problems easily and quickly.

1. 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
2. (1² + 2² + 3² + ..... + n²) = n ( n + 1 ) (2n + 1) / 6
3. (1³ + 2³ + 3³ + ..... + n³) = (n(n + 1)/ 2)²
4. Sum of first n odd numbers = n²
5. Sum of first n even numbers = n (n + 1)

1. (a + b)(a - b) = (a² - b²)
2. (a + b)² = (a² + b² + 2ab)
3. (a - b)² = (a² + b² - 2ab)
4. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
5. (a³ + b³) = (a + b)(a² - ab + b²)
6. (a³ - b³) = (a - b)(a² + ab + b²)
7. (a³ + b³ + c³ - 3abc) = (a + b + c)(a² + b² + c² - ab - bc - ac)
8. When a + b + c = 0, then a³ + b³ + c³ = 3abc
9. (a + b)ⁿ = aⁿ + (ⁿC₁)a^n-1b + (ⁿC₂)a^n-2b² + … + (ⁿC_n-1)ab^n-1 + bⁿ
10.  
    1. A number is divisible by 2, if its unit's digit is any of 0, 2, 4, 6, 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 the last two digits is divisible by 4.
    4. A number is divisible by 5, if its unit's digit is either 0 or 5.
    5. A number is divisible by 6, if it is divisible by both 2 and 3.
    6. A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8.
    7. A number is divisible by 9, if the sum of its digits is divisible by 9.
    8. A number is divisible by 10, if it ends with 0.
    9. A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.
    10. A number is divisible by 12, if it is divisible by both 4 and 3.
    11. A number is divisible by 14, if it is divisible by 2 as well as 7.
    12. Two numbers are said to be co-primes if their H.C.F. is 1. To find if a number, say y is divisible by x, find m and n such that m * n = x and m and n are co-prime numbers. If y is divisible by both m and n then it is divisible by

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