|Quantitative Aptitude Important Formulas Logical ReasoningGeneral Knowledge of MPGeneral Knowledge of India|
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.
(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.
The rate of simple interest on a sum of money is 6 percent per annum for first 3 years, 8 percent per annum for the next 5 years and 10 percent per annum for period beyond 8 years. If simple interest accrued by the sum for a total period of 10 years is Rs 1560, What is the sum?
Shirin went to a bakery and bought items worth Rs 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Pointing to a photograph, a man said, "I have no brother or sister but that man’s father is my father’s son." Whose photograph was it?
Introducing a man to her husband, a woman said "His brother's father is the only son of my grandfather". How is the woman related to the man ?
What is the difference between Apache Tomcat server and Apache web server?
What is the full form of DOS?
Explain the use of help DOS Command?
How we can create a directory in DOS?
|Pipes and Cistern|
A tank can be filled by one tap in 10 minutes and by another in 30 minutes. Both the taps are kept open for 5 minutes and then the first one is shut off. In how many minutes more is the tank completely filled?
Assume that a sum of money is divided equally among n girls. Each girl will receive $60. If another girl is added to the group and the sum is divided equally among all the girls, each child girl gets a $50 share. What is the sum of money?
|Problems on Trains|
A 300 meter long metro train crosses a platform in a metro station in 39 seconds while it crosses a lamp post in 18 seconds. What is the length of the platform?
|Problems on Ages|
In a group of 7 people, the average age is found to be 17 years. Two more people joined with an average age 19 years. One person left the group whose age was 25 years. What is the new average age of the group?
|Profit and Loss|
Irvin sold a book at a profit of 12%. If Irvin had sold it for Rs 18 more, then 18% would have been gained. Find the cost price?
Non stick cooking utensils are coated with?
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|Jobs in Punjab|
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|Jobs in Chhattisgarh|
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|Jobs in Madhya Pradesh|
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