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Number System Tricks Questions & Notes

Number System in Quantitative Aptitude

In this article,we study about the topic & shortcut tricks used in the quantitative aptitude for bank exams i.e. “Number System”.You can solve the question based on the topic by practicing regularly. Candidate those who are preparing for the IBPS Exam (Clerk, PO, SO) and others can use these tricks. Candidate can do download in PDF format.


Types of Numbers

  1. Natural Numbers(N)

    It is a set of natural numbers then N={1,2,3,4,5,…}

  2. Whole Numbers(W)

    It is a set of whole number then W={0,1,2,3,4,5,6,….}

  3. Integers(I)

    It is the set of positive and negative numbers then I={-3,-2,-1,0,+1,+2,+3……..}

  4. Real Number

    Real number includes both rational and irrational numbers.

  5. Rational Number

    It is in the form of p/q where p and q are both integers and q is not equal to 0. 

  6. Irrational Numbers

    Irrational Numbers Non-recurring and non-terminating decimals are called irrational numbers.

  7. Even Numbers

    Divided by 2.

  8. Odd Numbers

    Not Divided by 2.

  9. Prime Numbers

    Numbers which divide by one and itself.

Divisibility Test for numbers

Divisibility by 2

A number is divisible by 2 when the digit at ones place is 0, 2, 4, 6 or 8.

Divisibility by 3

A number is divisible by 3 when sum of all digits of a number is a multiple of 3.

Divisibility by 4

A number is divisible by 4, if the number formed with its last two digits is divisible by 4.

Divisibility by 5

A number is divisible by 5 if its last digit is 0 or 5.

Divisibility by 6

A number is divisible by 6, if it is divisible both by 2 and 3.

Divisibility by 7

A number is divisible by 7 when the difference between twice the digit at ones place and the number formed by other digits is either zero or a multiple of 7.

Divisibility by 8

A number is divisible by 8, if the number formed by the last 3 digits of the number is divisible by 8.

Divisibility by 9

A number is divisible by 9, if the sum of all the digits of a number is a multiple of 9.

Divisibility by 10

A number is divisible by 10, if its last digit is 0.

Divisibility by 11

When the difference between the sum of its digits in odd places and in even places is either 0 or a multiple of 11.


Division on Numbers

In a sum of division, we have four quantities.
They are (i) Dividend, (ii) Divisor, (iii) Quotient and (iv) Remainder. These quantities are connected by a relation.
(a) Dividend = Divisor × Quotient + Remainder.
(b) Divisor = (Dividend – Remainder) ÷ Quotient.
(c) Quotient = (Dividend – Remainder) – Divisor.

Rules for numbers

  1. Sum of all n first natural numbers=n(n+1)2
  2. Sum of n odd numbers=n^2.
  3. Sum of n even numbers=n(n+1).
  4. Sum of square of first n natural numbers=n(n+1)(2n+1)6
  5. Sum of cubes of first n natural numbers =(n(n+1)2)^2

Thing to remember

  1. The smallest natural number is 1.
  2. The smallest whole number is 0.
  3. 2 is the only even prime number.
  4. 1 is not a prime number because it has two equal factors.
  5. Every prime number greater than 3 can be written in the form of (6K + 1) or (6K – 1) where K is an integer.
  6. There are 15 prime numbers between 1 and 50 and 10 prime numbers between 50 and 100.
Questions & Answers
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