Numbers set 4 – Practice different types of aptitude test for free, including numerical and verbal tests. All questions come with worked solutions to help you improve.

Formulas to Solve Number System(Aptitude Tests Numbers set 4)

• Number system is a writing system for presenting number on the number line. A number system is a system of writing or expressing numbers.
• There are generally two type of Number 
  • Whole Number
  • Natural Number.

Number System Formulas & Definitions(Aptitude Tests Numbers set 4)

• Natural Numbers
  • All positive integers are called natural numbers. All counting numbers from 1 to infinity are natural numbers. N = {1, 2, 3, 4, 5, 6……….∞}
• Whole Numbers
  • The set of numbers that includes all natural numbers and the number zero are called whole numbers. They are also called as Non-negative integers. W = { 0,1,2,3,4,5,6,7,8,…………..∞}
• Integers
  • All numbers that do not have the decimal places in them are called integers. Z = {∞…….-3, -2, -1, 0, 1, 2, 3………∞}
  • a. Positive Integers: 1, 2, 3, 4….. is the set of all positive integers.
  • b. Negative Integers: −1, −2, −3….. is the set of all negative integers.
  • c. Non-Positive and Non-Negative Integers: 0 is neither positive nor negative.
• Real Numbers
  • All numbers that can be represented on the number line are called real numbers.
• Rational Numbers
  • A rational number is defined as a number of the form a/b where ‘a’ and ‘b’ are integers and b ≠ 0. The rational numbers that are not integers will have decimal values. These values can be of two types
  • a. Terminating decimal fractions: For example: \frac{1}{5}51​ = 0.5,\frac{125}{4}4125​ = 31.25

• b. Non-Terminating decimal fractions: For example:\frac{19}{6}619​ = 3.1666666, \frac{21}{9}921​ = 2.33333
• Irrational Numbers
  •  It is a number that cannot be written as a ratio \frac{x}{y}yx​ form (or fraction). An Irrational numbers are non-terminating and non-periodic fractions. For example: \sqrt{2}2​ = 1.414
• Complex Numbers
  • The complex numbers are the set {a+bi}, where, a and b are real numbers and ‘i’  is the imaginary unit.
• Imaginary Numbers
  • A number does not exist on the number line is called imaginary number. For example square root of negative numbers are imaginary numbers. It is denoted by ‘i’ or ‘j.
• Even Numbers
  • A number divisible by 2 is called an even number.
  • For example: 2, 6, 8, 14, 18, 246, etc.
• Odd Numbers
  • A number not divisible by 2 is called an odd number.
  • For example: 3, 7, 9, 15, 17, 373, etc.
• Prime numbers
  • A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself.
  • For example: 2, 3, 5, 7, 11, 13, 17, etc.
• Composite numbers
  • Numbers greater than 1 which are not prime, are known as composite numbers. For example: 4, 6, 8, 10, etc.

Formulas for Number System and Basic Concept

1. (a – b)(a + b) = (a² – b²).
2. (a + b)² = (a² + b² + 2ab)
3. (a – b)² = (a² + b² – 2ab)
4. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
5. (a³ + b³) = (a + b)(a² – ab + b²)
6.  (a³ – b³) = (a – b)(a² + ab + b²)
7. (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
8. When a + b + c = 0, then a³ + b³ + c³ = 3abc.

Read Also – How to solve number system problems Quickly

Formulas for finding the Squares of a number .

• Squares of numbers 91-100:
• 97²
  Step 1: 100-97 = 3

Step 2: 97-3 = 94

Step 3: 3²= 09

Final result: From step 2 and

Step 3  => 97²= 9409

• 91²

Step 1: 100-9 = 91

Step 2: 91-9 = 82

Step 3: 9² = 81

Final Result: From step 2 and step 3 => 91² = 8281

• Squares of numbers 100-109:
• 102²

Step 1: 102-100 = 2

Step 2: 102 +2 = 104

Step 3: 2² = 04 Final result:

From step 2 and step 3 => 102²=10404

• 107²

Step 1: 107-100 = 7

Step 2: 107+7 = 114

Step 3: 7² = 49

Final Result: From step 2 and step 3 => 107² = 11449

• Squares of numbers 51-60
• 53²

Step 1: 53-50 = 3

Step 2: 25+3 = 28

Step 3: 3² = 09

Final result: From step 2 and step 3 => 53² = 2809.

• 42²

Step 1: 50-42 = 8

Step 2: 25-8 = 17

Step 3: 8² = 1764

Final Result From step 2 and step 3 => 42² = 1764

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