Number System

NUMBERS-:

Natural Number-: Except ‘0’ all no. are called natural no.

                          (1,2,3,4,…………………..n)

 

Whole Number-: Add the ‘0’ in natural no. is called whole no.

                        (0,1,2,3,4,…………………..n)

 

Even Number-:  The no. are divisible by 2, that all are no. is called Even no.

                        (2,4,6,8,10,…………………n)

 

Odd Number-:  The no. are not divisible by 2, that all are no. is called Odd no.

                        (1,3,5,7,9,………………….n)

 

Prime Number-:  Only two factor which no. is called prime no.

                        (2,3,5,7,11,13……………..n)

 

Co-prime Number-:  Two no. whose HCF of 1, are called Co-prime number.

                             (2,3) (5,9) (8,19)

 

Composite Number-:  A number whose factor more than 2, is called composite no.

 

Rational Number-:  Rational is, which is fully divisible till decimal point.

 

Irrational Number-:  Irrational no. is, which is not fully divisible till decimal point.

 

DIVISIBILITY

Divisibility by 2-: If unit digit of any no. is ‘0’ or even no., then the no. are divisible by 2.

Divisibility by 3-: If the sum of total digit of the given no. is divided by 3, then the no. will be divisible by 3.

Divisibility by 4-: If last two digits fully divisible by 4. Then the no. will be divisible by 4.

Divisibility by 5-: Unit digit of any no. ‘0’ or ‘5’, then the no. is fully dividable by 5.

Divisibility by 6-: A number, which is fully divisible by 2 or 3, then the no. is divisible by 6.

Divisibility by 7-: Multiply in unit digit by 5 of any no. & add the product in remaining no. This process will be continuing, when no. comes two digits. If the new two digit no. divisible by 7, then the given no. will be fully divisible by 7.

Divisibility by 8-: If the last three digits fully divisible by 8, then the no. will be divisible by 8.

Divisibility by 9-: Same process as 3.

Divisibility by 11-: The difference between , the sum of even place digits & odd place digits of given no. is either ‘0’ or divisible by 11, then the given no. will be divisible by 11.

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• (n3-n) always divisible by 6.

• If any three digits no. which all digits are same, then will be always divisible by 3, 37 & 111.

• If any six digits no. which is two digit no. repeated by three times, then will be divisible by 3, 7, 13, 37, 111.

• If any three digit no. repeated by two times, then will be always divisible by 7 & 11.

 

MAGIC OF 9 & 11

Magic of 9-: The difference between, a two digits no. & its reverse no. is always divisible by 9. The quotient after dividing by 9 is equal to the difference of the digit in the number.

Magic of 11-: The sum of, a two digits no. & its reverse no. is always divisible by 11. The quotient after dividing by 11 is equal to the sum of the digit in the number.

 

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​1.         The difference between a two digit no. & the no. obtained by interchanging the digit is 36.  What is the difference of two digit of the number?

(A) 6        

(B) 5          

(C) 4          

(D) 3

 

2.         The difference between a two digit no. & the no. obtained by interchanging the digit is 18.  What is the sum of two digit of the number?

(A) 6        

(B) 8         

(C) 4           

(D) CND

 

3.         The sum & the difference of a two digit no. & the no. obtained interchanging the digit are  88  & 36 respectively and unit place digit is more than ten’s place digit. Find the number?

(A) 25      

(B) 32       

(C) 62        

(D) 26

 

4.         If 27 added in the age of ‘A’ the age of ‘B’ obtained, which is obtained by interchanging the digit of the age of ‘A’. The sum of the digit of the age of ‘A; is 5. Find the age of ‘A’?

(A) 14      

(B) 41       

(C) 51        

(D) CND

 

5.         When 18 is added in a two digit number, a number is obtained, which is obtained by  interchanging the digit of that no. Find the number?

(A) 46      

(B) 36       

(C) 64        

(D) CND

 

6.         Which of the following is a prime number?

(A) 161    

(B) 221     

(C) 373     

(D) 437

 

7.         Find the sum of all natural number divisible by 3, between 250-1000?

(A) 671535    

(B) 167535     

(C) 135675      

(D) 165375

 

8.         When a number is divided by 6, 4 & 3 successively, it gives remainder 3, 2 & 1 respectively. Find the least number?

(A) 93      

(B) 111        

(C) 113        

(D) 123

 

9.         Find the unit place digit of (326)928?

(A) 4        

(B) 3          

(C) 6         

(D) 5   

 

10.       When 75% of 1st number added to 2nd number. The 2nd number becomes 1.6 time of itself. What will be the half in product of the sum & difference of both numbers? When 1st number is 44.

(A) 544.5     

(B) 554.5      

(C) 555.5      

(D) 545.5        

 

11.       25% of a number is equal to half of another number. If these number are ratio of 2:1. Find the value of first number?

(A) 38      

(B) 34       

(C) 36       

(D) 32

 

12.       The sum of all digit in three digit number is 12, Digit in middle is 1/5th of other two digit's  sum. It 1st and 3rd digits Interchanged, the number increased by 396. Find out that Number ?

(A) 345     

(B) 336      

(C) 327      

(D) 318

 

13.       The sum of Squares of two consecutive numbers is 7321. Find out the square of sum of both numbers.

(A) 14641    

(B) 15625     

(C) 12321    

(D) 17161 

 

14.       When 25 reduced from a number and multiplied to 4, it becomes 1.5 times of itself, find out 335% of that number.

(A) 238      

(B) 334       

(C) 424       

(D) 144 

 

15.       The sum of first and last numbers in 90 in five consecutive odd numbers and multiple of  Second and fourth numbers is 2021. The sum of all numbers will be equal of 5 times of which number, in these five numbers.

(A) First     

(B) Third      

(C) Second     

(D) Fifth

 

16.       4 times of first number of four consecutive even numbers gives sum of all the four numbers  when 12 is added to it. If the square of sum of first and last number is 3844, then what will be the 35%in square of 25% of Multiplication in third and second numbers?

(A)  21060    

(B) 20610     

(C) 20160     

(D) 21600 

 

17.       Three times of sum of two, three digit Numbers is 3156. It 25%of one of these numbers is 97, and then find the value of second number.

(A) 546      

(B) 664       

(C) 564       

(D) 646

 

18.       If the sum of two Numbers of two digit written three times & added, then we find 276,  which is 12 times of first Number, what is the product of these numbers.

(A) 2197     

(B) 1297     

(C) 1587     

(D) 1478

 

19.       The sum of two consecutive numbers is 23 more than the average of these two numbers  and next third number, what will be the sum of first & third number.

(A) 44       

(B) 46          

(C) 48         

(D) 42

 

20.       When 25%of any two digit number is subtracted from it and the remainder added by 150% of original number then what will be the ratio of new number and previous number.

(A) 8 : 5     

(B) 9 : 4      

(C) 8 : 7      

(D) 7 :  4

 

21.       On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digit of N is?

(A) 10       

(B) 11         

(C) 12        

(D) 13

 

22.       How many 3 digit number are completely divisible by 6?

(A) 149       

(B) 150        

(C) 151         

(D) 166