## Aptitude Tests(number system)

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

### Formulas to Solve Number System(Aptitude Tests)

- 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)

**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, 6â€¦â€¦â€¦.âˆž}**

- All positive integers are called natural numbers. All counting numbers from 1 to infinity are natural numbers.
**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,â€¦â€¦â€¦â€¦..âˆž}**

- 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.
**Integers**- All numbers that do not have the decimal places in them are called integers.
**Z = {âˆžâ€¦â€¦.-3, -2, -1, 0, 1, 2,**3â€¦â€¦â€¦âˆž} - a. Positive Integers: 1, 2, 3, 4â€¦.. is the set of all positive integers.
- b. Negative Integers: âˆ’1, âˆ’2, âˆ’3â€¦.. is the set of all negative integers.
- c. Non-Positive and Non-Negative Integers: 0 is neither positive nor negative.

- All numbers that do not have the decimal places in them are called integers.
**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 â€˜aâ€™ and â€˜bâ€™ are integers and b â‰ 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}51â€‹ = 0.5,\frac{125}{4}4125â€‹ = 31.25

- b. Non-Terminating decimal fractions: For example:\frac{19}{6}619â€‹Â = 3.1666666,Â \frac{21}{9}921â€‹Â = 2.33333
**Irrational Numbers**- Â It is a number that cannot be written as a ratioÂ \frac{x}{y}
*yx*â€‹Â form (or fraction). An Irrational numbers are non-terminating and non-periodic fractions. For example:Â \sqrt{2}2â€‹Â = 1.414

- Â It is a number that cannot be written as a ratioÂ \frac{x}{y}
**Complex Numbers**- The complex numbers are the set {a+bi}, where, a and b are real numbers and â€˜iâ€™Â 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 â€˜iâ€™ or â€˜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

- (a â€“ b)(a + b) = (aÂ² â€“ bÂ²).
- (a + b)Â² = (aÂ² + bÂ² + 2ab)
- (a â€“ b)Â² = (aÂ² + bÂ² â€“ 2ab)
- (a + b + c)Â² = aÂ² + bÂ² + cÂ² + 2(ab + bc + ca)
- (aÂ³ + bÂ³) = (a + b)(aÂ² â€“ ab + bÂ²)
- (aÂ³ â€“ bÂ³) = (a â€“ b)(aÂ² + ab + bÂ²)
- (aÂ³ + bÂ³ + cÂ³ â€“ 3abc) = (a + b + c)(aÂ² + bÂ² + cÂ² â€“ ab â€“ bc â€“ ac)
- When a + b + c = 0, then aÂ³ + bÂ³ + cÂ³ = 3abc.

**Read Also â€“Â How to solve number system problems Quickly**

### Formulas for finding the Squares of a number .

- Squares of numbers 91-100:
- 97
^{2}

Step 1: 100-97 = 3

Step 2: 97-3 = 94

Step 3: 3^{2}= 09

Final result: From step 2 and

Step 3 => 97^{2}= 9409

- 91
^{2}

Step 1: 100-9 = 91

Step 2: 91-9 = 82

Step 3: 9^{2} = 81

Final Result: From step 2 and step 3 => 91^{2} = 8281

- Squares of numbers 100-109:
- 102
^{2}

Step 1: 102-100 = 2

Step 2: 102 +2 = 104

Step 3: 2^{2} = 04 Final result:

From step 2 and step 3 => 102^{2}=10404

- 107
^{2}

Step 1: 107-100 = 7

Step 2: 107+7 = 114

Step 3: 7^{2} = 49

Final Result: From step 2 and step 3 => 107^{2} = 11449

**Squares of numbers 51-60**- 53
^{2}

Step 1: 53-50 = 3

Step 2: 25+3 = 28

Step 3: 3^{2} = 09

Final result: From step 2 and step 3 => 53^{2} = 2809.

- 42
^{2}

Step 1: 50-42 = 8

Step 2: 25-8 = 17

Step 3: 8^{2} = 1764

Final Result From step 2 and step 3 => 42^{2} = 1764