Numbers System Aptitude Questions and Answer – Quantitative Aptitude

Numbers System Aptitude Questions and Answer – Formulas & Tricks

Number Theory – Tips

• Sum of natural numbers form 1 to n = (n * (n + 1) / 2)
• Sum of squares of first n natural number is = (n * (n + 1) * (2n + 1)) / 6
• Sum of the squares of first n even natural numbers is = ((2 / 3) * n * (n + 1) (2n + 1))
• Sum of Cubes of first n natural numbers is = [(n * (n + 1) / 2)]²
• Any Number N can be represented in the decimal system of number as N = n_k10^_k + n_k-110^k-1 + n … + n_i10 + n₀

Types of Numbers

1. Natural Numbers : The counting numbers which are used for counting are known as natural numbers
   • 1, 2, 3, 4, 5, 6, 7, …
2. Whole Numbers: All counting numbers along with zero from a set of whole numbers.
   • 0, 1, 2, 3, 4, 5, 6 ….
3. Integers: The whole numbers including the negative numbers and excluding fractions are known as integer.
   • …. -3, -2, -1, 0, 1, 2, 3, 4, 5….
4. Prime Numbers: A whole number which is greater than 1 and is divisible by 1 and itself is a prime number
   • 2, 3, 5, 7, 11,….
5. Co-Prime Numbers: Two natural numbers p and q are said to be co-prime if their HCF is 1
   • (2, 3)(4, 5)(7, 9)(11, 9)
6. Composite Numbers: It refers to a whole number which is greater than 1 and is not a prime number. It can be divided by numbers other than 1 and itself
   • 4, 6, 8, 9, 10, 12
7. Even Number: An integer which is divisible by 2 is known as Even Number
   • 2, 4, 5, 8, 10
8. Odd Number: An integer which is not divisible by 2 is known as Odd Number
   • 1, 3, 5, 7, 9
9. Consecutive Numbers: It is a serious of numbers in which the numbers follow each other in an order, that is there is a difference of 1 between two successive numbers or each number is greater than the preceding number 1.
10. Rational Number: The number in the form of P/Q where P and Q are integer and Q can? be zero are known as Rational Numbers.
11. Irrational Numbers: The numbers which when written in decimal form do not terminate and repeat are known as irrational numbers. These Numbers cannot be expressed as a ratio of integer or a fraction.
12. Real Numbers: The number which can e found on the number line and include both rational and irrational numbers are known as Real Numbers.
13. Face Value: It is the actual value of a digit. It remains definite and does not change with the digit’s place.
14. Place Value: The place value of a digit depends on its place or position in the number. It is the product of its place and face value. Each place in a number has a value of 10 times the place to its right.
15. Unit Digit: The unit digit is the ones place digit of a number

Numbers System Aptitude Questions and Answer With Detailed Explanation – Quantitative Aptitude