Number System Tips, Tricks and Shortcuts

March 6, 2024

Shortcuts and tricks for Number System

On this page we will be telling you about the shortcuts, tricks and tips to solve Number System easily and quickly. Number system is a basic section and one of the main sections in the aptitude. 

Tips and Tricks for Number System

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Number System Tips and Tricks

Number System Examples
Whole Number 0, 1, 2, 3, 4, 5…
Natural Number 1, 2, 3, 4, 5, 6…
Integers …-3, -2, -1, 0, 1, 2, 3, 4, 5,…
Prime Number 3, 5, 7, 11, 13, 17…..
Co-Prime Number HCF = 1
Composite Number 4, 6, 8, 9, 12, 14, 15…..
Even Number 2, 4, 6, 7, 8, 10…
Odd Number 1, 3, 5, 7, 9….
Rational Number In ‘p/q’ form wherein p & q are integers and q is not equal to 0

Tips and Tricks to solve Number System Quickly

Trick to find the square of a Number :

25^{2}

we can write 25 as (20+5)

so, (20+5)^{2}

we will use the formula (a+b)^{2}

20^{2} + 5^{2} + 2*20*5

400 + 25 + 200 = 625 

56^{2}

square the first and second number = 5^{2}= 25  6^{2 } =36 = 2536

Then, multiply the given digit 5*6 = 30 and add 0 at then end = 300,

then multiply it by 2 = 300 * 2 = 600

add both the number = 2536 + 600 = 3136

Trick to solve the Square root of any number 

\sqrt{3136}

We have to see the unit digit of the number that is 6 and 6 is the unit digit of either the square of 4 or 6 

Now see the first two digits, 31 which comes between the square of 4 or 6, so we will take the number 5

Now multiply the number 5 by 4 = 20, it is not possible because it is way less than 31 
5*6 = 30, it is near 31

so 56 is the answer.

Tricks to find the factorial of any number 

n Factorial Formula
The formulas for n factorial are:

  1. n! = n(n-1)(n-2)…………………….(3)(2)(1)
  2. n! = n × (n – 1)!

7! = 7 * 6 * 5 * 4 * 3 * 2 = 5040

Trick to find the multiple square of a number 

\sqrt{5\sqrt{5}\sqrt{5}\sqrt{5}}

we will use the formula, x^{\frac{2^{n}-1}{2^{n}}}

n = number of digits in the square

we have four digits so, n =  4

5^{\frac{2^{4}-1}{2^{4}}}

5^{\frac{15}{16}}

 

Divisibility Rule

Divisibility Rule Definition
Divisibility rule of 2 Any number whose last digit is an even number (0, 2, 4, 6, 8) is divisible by 2
Divisibility rule of 3 A number is divisible by 3 if the sum of its digits is divisible by 3.
Divisibility rule of 4 A number is divisible by 4, if the number formed by the last two digits is divisible by 4.
Divisibility rule of 5 A number is exactly divisible by 5 if it has the digits 0 or 5 at one’s place.
Divisibility rule of 6 A number is exactly divisible by 6 if that number is divisible by 2 and 3 both. It is because 2 and 3 are prime factors of 6.
Divisibility rule of 7 Double the last digit and subtract it from the remaining leading truncated number to check if the result is divisible by 7 until no further division is possible
Divisibility rule of 8 If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.
Divisibility rule of 9 It is the same as of divisibility of 3. Sum of digits in the given number must be divisible by 9.
Divisibility rule of 11 If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11.

Tips and Tricks to solve Number System questions

Question 1 : Simplify the equation, (1/?) × 425 ÷ 5^{–2} = 4 × 156.25

Options

A. 19

B. 34

C. 17

D. 19

Solution:  

(1/?) × 425 ÷ 5^{–2} = 4 × 156.25

625 = (1/?) × 425 × 25

? = (425/25) = 17

Correct option: A

Question 2: How many prime numbers are there from 1 to 50?

Options

A. 20

B. 15

C. 21

D. 25

Solution:    Prime numbers less than 50 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Correct option: B

Question 3: 1198 * 1198 = ?

Options

A. 1435204

B. 1432504

C. 1453204

D. 1435024

Solution:     (1198)²

(1200 – 2)²

We can use the identity: (a-b)²= a² + b² – 2ab

(1200)² + 2² – 2 * 1200 * 2

1440000 + 4 – 4800

1435204

Correct option: A

Question 4: The sum of first five prime numbers is:

Options

A. 20

B. 28

C. 30

D. 25

Solution:     Sum of first five prime numbers is = 2+3+5+7+11 = 28

Correct option: B

Question 5: If x and y are odd numbers, then which of the following is always an even numbers?

Options

A. x + y

B. xy

C. x/y

D. xy + 2

Solution:    The sum of two odd number is always even. So, x + y is even.

Correct option: A

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