# Quantitative Aptitude Important Formulas

 Compound Interest - Important Formulas,Tricks and Examples Let Principal = P, Rate = R% per annum, Time = n years. Compound Interest, CI=P(1+ R/100)n - P = P[(1+ R/100)n - 1] Amount = P[1+ (R/100) ]n , if interest is payable annually Amount = P[1+ (R/2)/100]2n , if interest is payable half-yearly Amount = P[ 1+ (R/4)/100]4n , if interest is payable quarterly When time is fraction of a year, say 4(3/4) years, then Amount= P(1+ R/100)4 x (1+ (3R/4)/100) When Rates are different for different years, say, R1, R2, R3 for 1st , 2nd & 3rd years respectively then, Amount = P(1+ R1/100)(1+ R2/100)(1+ R3/100) Post/View Answer Post comment Cancel Thanks for your comment.! Write a comment(Click here) ...
 Numbers - Important Formulas,Tricks and Examples The common number system is decimal number system. The Decimal number system used base (or radix) as 10 . This means that the system has ten symbols or numerals to represent any quantity. These symbols are called Digits and they are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Types of Numbers Natural Numbers:The numbers that are used for counting called Natural Numbers.These are infinite and start from the number 1 . Ex : 1, 2, 3, 4, 5, 6 ........ Whole numbers:The whole numbers are just all the natural numbers plus zero. Ex : 0, 1, 2, 3, 4, 5 ............. Integers: Integers incorporate all positive and negative numbers with zero. Ex : .... –3, –2, –1, 0, 1, 2, 3 ..... Even Numbers: An even number is one that can be divided evenly by two leaving no remainder, such as 2, 4, 6, and 8. Odd Numbers: An odd number is one that does not divide evenly by two, such as 1, 3, 5, and 7. Rational Numbers: All numbers of the form p/q where p and q are integers (q ≠ 0) called Rational numbers. Ex : 4, 3/4, 0, …. Irrational Numbers: Irrational numbers are the opposite of rational numbers. An irrational number cannot be written as a fraction as p/q where a and b are integers. the decimal values for irrational numbers never end and do not have a repeating pattern in them.please note ‘pi’ has never ending decimal places, is irrational. Ex : pi, 2^1/2 , 3^1/2, 5^1/2 , 7^1/2 .......... Real numbers: Real numbers include counting numbers, whole numbers, integers, rational numbers and irrational numbers. Ex : 8, 6, 2, (3)^1/2 , 3/5 etc. Prime Number: A prime number is a number which can be divided only by 1 and itself. The prime number has only two factors, 1 and itself. Ex : 2, 3, 7, 11, 13, 17, …. are prime numbers. Composite Number: A Composite Number is a number which can be divided evenly. Any composite number has additional factors than 1 and itself. Ex : 4, 6, 8, 9, 10 ….. Co-primes or Relatively prime numbers: A pair of numbers not having any common factors other than 1 or –1. (Or alternatively their greatest common factor is 1 or –1) Ex : 15 and 28 are co-prime, because the factors of 15 (1,3,5,15) , and the factors of 28 (1,2,4,7,14,28) are not in common (except for 1) . Twin Primes: A pair of prime numbers is said to be twin primes if they differ by 2. Ex : (3,5) , (5,7) , (11,13) , … Algebra (a+b)2 = a2 + 2ab + b2 (a-b)2 = a2 - 2ab + b2 (a+b)2 - (a-b)2 = 4ab (a+b)2 + (a-b)2 = 2 (a2 + b2) a2-b2 = (a-b)(a+b) (a+b)3 = a3+b3+3ab(a+b) = a3+b3+3a2b+3ab2 (a-b)3 = a3-b3-3ab(a-b) = a3-b3-3a2b+3ab2 a3+b3 =(a+b)3-3ab(a+b) = (a+b)(a2-ab+b2) a3-b3 =(a-b)3+3ab(a-b) = (a-b)(a2+ab+b2) Test of Divisibility Divisibility By 2 : A number is divisible by 2, if its unit's digit is zero or even (2, 4, 6, 8..). Divisibility By 3 : A number is divisible by 3, if the sum of its digits is divisible by 3. Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4. Divisibility By 5 : A number is divisible by 5, if its unit's digit is either 0 or 5. Divisibility By 6 : A number is divisible by 6, if it is divisible by both 2 and 3. Divisibility By 8 : A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8. Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible by 9. Divisibility By 10 : A number is divisible by 10, if it ends with 0. Divisibility By 11 : 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. Divisibility By 12: A number is divisible By 12 if the number is divisible By both 4 and 3. Divisibility By 13: A number is divisible By 13 if its unit’s place digit is multiplied By 4 and added to the remaining digits and the number obtained is divisible By 13. Divisibility By 14: A number is divisible By 14 if the number is divisible By both 2 and 7. Divisibility By 15: A number is divisible By 15 if the number is divisible By both 3 and 5. Divisibility By 16: A number is divisible By 16 if its last 4 digits is divisible By 16 or if the last four digits are zeros. Divisibility By 17: A number is divisible By 17 if its unit’s place digit is multiplied By 5 and subtracted from the remaining digits and the number obtained is divisible By 17. Divisibility By 18: A number is divisible By 18 if the number is divisible By both 2 and 9. Divisibility By 19: A number is divisible By 19 if its unit’s place digit is multiplied By 2 and added to the remaining digits and the number obtained is divisible By 19. Divisibility By 20: A number is divisible by 20 if it is divisible by 10 and the tens digit is even.