|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.
By what number should we multiply -1/5 so that the product may be 9/25?
|Profit and Loss|
A person sells an article for Rs 550, gaining 1/10 of its cost price. Its gain percentage is.
If 3x + 2y = 12 and xy = 6, then 9x2 + 4y2 = ______.
|Volume and Surface Area|
In a temple there are 25 cylindrical pillars. The radius of each pillar is 28cm and height 4m. The total cost of painting the curved surface area of pillars at the rate of Rs. 8 per m2 is:
|Problems on Ages|
After 12 years, I shall be 3 times as old as I was 4 years ago. My present age is:
|Square and Cube Root|
The smallest number by which 1100 must be multiplied so that the product becomes a perfect square is____.
What is the probability that a number selected from the numbers 1, 2, 3,…….,25 is a prime number, when each of the given numbers is equally likely to be selected?
|Square and Cube Root|
What is the smallest number by which 3087 must be divided so that the quotient is a perfect cube?
The most comfortable distance at which one can read with a normal eye is:
Cholera is caused by:
Write the name of reptile with four chambered heart?
Raj borrowed Rs. 5000 at 10% per annum on simple interest and lent the same amount at 15% per annum on compound interest. At the end of 2 years, he would ?
If the area of a square is 16 cm2, then the area of the square joining the mid-points of the sides is?
|General Knowledge of MP|
Vidisha is situated on the banks of river?
|General Knowledge of World|
When is the Human Rights Day celebrated?
|Profit and Loss|
By selling coconuts at the rate of Rs. 6/- each, a trader gained 20%. Find the cost of 100 coconuts?
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