Quantitative Aptitude Important Formulas

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.

Latest Updates

Height and Distance

An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60º and 45º respectively. What is the height of the lower plane from the ground?

From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30º and 45º respectively. What is the height of the tree?

Trigonometry

What is the value of sinx √( 1 /1+cosx + 1 /1-cosx ) ?

What is cos4 A - sin4 A / cos2 A - sin2 A equal to?

If 7sin2 x +3cos2 x = 4, 0 < x < 90º ,then what is the value of tan x?

If x = a cosθ + b sinθ and y = a sinθ - b cosθ then what is x2 + y2 equal to?

Average

The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number?

The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are?

In an asymmetrical distribution, of the mean and median of the distribution are 270 and 220 respectively, then the mode of the data is?

Let a, b, c, d, e, f, g be consecutive even numbers and j, k, l, m, n be consecutive odd numbers. What is the average of all the numbers?

Alligation or Mixture

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is the ratio 1 : 2 and the amount of lead and tin in the alloy Y is in the ratio 2 : 3, then what is the ratio of lead to tin in the mixture?

Simplification

The ratio of two numbers is 1 : 5 and their product is 320. What is the difference between the square of these two numbers?

Trigonometry

What is the value of cot 4π/3 ?

Indian Politics

Article-24 of the Indian Constitution ‘Prohibition of employment of children in factories, etc’ deals with?

Article-134A of the Indian Constitution ‘Certificate for appeal to the Supreme Court’ deals with?

Chemistry

Who invented Aspirin?

Physics

A larger force on a rotating body results in larger?

What is the unit of the physical quantity, magnetic flux density?