Quantitative Aptitude Important Formulas Logical ReasoningGeneral Knowledge of MPGeneral Knowledge of India |
Percentage - Important Formulas,Tricks and Examples |
X percent means X hundredths, written as X% => X/100 If X % of Y = X * Y/100 If the price of the commodity decreases by R%,then the increase in consumption If the price of a commodity increases by R%, then the reduction in consumption If the present population of the town is P now and it increases at the rate of R% per annum, then: If the present population of the town is P now and it decreases at the rate of R% per annum, then: If the present value of a machine is P now and it depreciates at the rate R% per annum, then: If a number A is increased successively by x% followed by y% and then by z%, If A is R% more than B, then B is less than A by [R/(100+R))*100]%. If A is R% less than B, then B is more than A by [(R/(100-R)*100]%. If the value of a number is first increase by x% and later decrease by x% , then the net effect is always a decrease (x/10)2 %. If the value of a number is first changed ( increased +ve or decreased -ve) by x% and then changed (increased or decreased ) by y% ,then net change % = { ± x ± y + [(±x±y)/100]} % |
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Numbers - Important Formulas,Tricks and Examples |
The common number system is decimal number system. Types of Numbers Natural Numbers:The numbers that are used for counting called Natural Numbers.These are infinite and start from the number 1 . Whole numbers:The whole numbers are just all the natural numbers plus zero. Integers: Integers incorporate all positive and negative numbers with zero. 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. 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. Real numbers: Real numbers include counting numbers, whole numbers, integers, rational numbers and irrational numbers. 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. Composite Number: A Composite Number is a number which can be divided evenly. Any composite number has additional factors than 1 and itself. 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) Twin Primes: A pair of prime numbers is said to be twin primes if they differ by 2. Algebra (a+b)2 = a2 + 2ab + b2 (a+b)2 - (a-b)2 = 4ab a2-b2 = (a-b)(a+b) (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) 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 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. |