Quantitative Aptitude

                                1.Number System

  • Numbers are the collection of certain symbols or figures called digits
  • The common number system in use is the decimal number system.
  • In this system we use digits as 0,1,2,3,4,5,6,7,8 and 9.

        A combination of these digits representing a number is called a Numeral.

FACE VALUE AND PLACE VALUE

  • Face value is equal to the value of the digit itself.

Example face value of 3 in 47326          = 3

Face value of 7 in 47326                          = 7

  • Place value is equal to the place of the given digit .

We begin from the extreme right as unit’s place, ten’s place, hundred’s place, thousand’s place and so on.

Ten ThousandThousandHundredTensUnit Place
    6    2    5    1    8

 

Place value of 5 = 5 x 100 =      500

Place value of 1 = 1×10             =  10

Eg: 276345

276345Face ValuePlace Value
1) 444×10   = 40
2) 333×100  =300
3) 666×1000 =6000
4) 222×10000 = 20000


TYPES OF NUMBERS


1. Natural Numbers (N)

Counting numbers such as  1,2,3,4………… are called natural numbers.

Eg:  N =1,2,3,4,……. ()infinity

2. Whole Numbers (W)

Includes all natural numbers and zero.

Eg.  W = 0,1,2,3,……. ()infinity

3. Even Natural Numbers

These are the numbers which are completely divisible by 2.

Eg:  2,4,6,8……………

4. Odd Natural Numbers

Numbers which are not divisible by 2.

Eg:  1,3,5,7,………………

Note:  Zero is an exception to the even – odd classification.

5. Integers     (I)

    Includes  all whole numbers along with negative numbers.

    Eg:   I …….-2,-1,0,1,2,…………. .(infinity)

Positive Integers

This includes all natural numbers.

Eg:  1,2,3………. (infinity)

Negative Integers

  This includes -1,-2……….. (infinity)

  Note:    Zero is neither positive nor negative.

6. Rational Numbers:

Real numbers which are expressed in the form of fractions like ‘a/b ‘ where a and b are integers and b not equal to Zero are called rational numbers.

Eg:  3/7, 8/5 , 3 (3/1), -9 (-9/1)

7. Irrational numbers 

Real numbers which cannot be expressed in the form of fractions like a/b, where b not equal to 0 are called irrational numbers.

Eg:  7,3,√5

8. Prime Numbers

Numbers with only two factors   → 1 and that number itself.

Eg:  2,3,5,7,11

2 = 1×2

3 =1×3

5 =1×5

  CODE

41 to 10
410 to 20
220 to 30
230 to 40
340 to 50
250 to 60
260 to 70
370 to 80
280 to 90
190 to 100

 

1  to 25                                              – 9 prime numbers
1 to 50                                               – 15 prime numbers
1 to 100                                             – 25 prime numbers
50 to 100                                           – 10 prime numbers


Prime numbers between 1 and 100

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97

Prime Number

 1 Digit2 Digits3 Digits4 Digits
Least2111011009
Greatest7979979973

 

9 .Composite Numbers

Numbers with more than 2 factors.

Eg:  4,6,8,9,10,12,14,……………..

 4   = 1 x 4               3 factors = 1,2,4

      =  2 x 2

9    = 1 x 9

      = 3 x 3

10. Square Numbers

1,4,9,16,25,36

12  = 1

22  = 4

11. Cube Numbers

1,8,27,64,125

13 =  1

23 =  8

33 = 27

12. Perfect Numbers

Sum of all the factors of a number except the number, is the number itself is called perfect number.

Eg.1)        6 – Factor of 6  = 1,2,3,6

                               6 =   1 x6

                               6 =   3 x2

Sum of factors except 6   = 1+2+3 = 6 (The Number itself)

Eg:2)  Factors of 28  = 1,2,4,7,14,28

                              28   = 1 x 28

                              28   = 14 x 2

                              28   = 7 x  4

Sum of factors except 28   = 1+2+4+7+14 = 28

13. Armstrong Numbers

            153,370,371,407 are Armstrong Numbers.

153   =   13 + 53 + 33       = 1+125+27          = 153
370   = 33  + 73+ 03     = 9 + 343 + 0        = 370
371   = 33  + 73  + 13    = 9 + 343 + 1        = 371
407   = 43  + 03  + 73     = 64 + 0 + 343      = 407


14. Ramanujan Number

Ramanujan Number       —–  1729

1729       —-  It is the smallest number expressible as the sum of two (positive)  cubes in two different ways.

          1729    = 103  + 93  = 1000 + 729  = 1729

          1729     = 123   + 13  = 1728 + 1      = 1729

The second number which is in the form of the Ramanujan number is 4104.

           4104      = 153  + 93   =  3375 + 729   = 4104

           4104       = 163  + 23  = 4096 + 8        = 4104

15. Numbers with Roman Representation

12345678910
 I II III IV V VI VII VIII IX X

 

102030405060708090100
 X XX XXX XL L LX LXX LXXX XC C

 

1002003004005006007008009001000
 C CC CCC CD D DC DCC DCCC CM M

 

1
5
10
50
100
500
1000 

 

  V   = 5 X 1000    = 5000 
  X   =  10 X1000   = 10000 
L     =  50 X 1000    = 50000 
  C   =  100 X 1000   = 100000 
D   =  500 X 1000   = 500000 
M   =  1000 X 1000  = 1000000 


Eg:  15 =     10 + 5           =XV

       64  =   50 + 10 + 4     = L X IV

       167 =    100 + 60 + 7  = C LX VII

        99  =   90 + 9            = XC IX

       33  =   30 + 3           = XXX III

Million    = 106    = 10 lakhs  

Billion      = 109    = 100 Crores  

Trillion     = 1012  =   Lakh Crores  

 

Googole   = 10100


Sum of ‘n’ Numbers

  • Sum of first ‘n’ natural numbers   =   n(n+1)/2
 ie; 1+2+3…………   = n(n+1)/2
  • Sum of first ‘n’ odd numbers   = n2
n   = no. of terms


ie;

1+3+5+…………  = n2
  • Sum of first ‘n’ even numbers   = n (n+1)

   ie;

2 + 4 + 6 +……………     = n(n+1)
  • Sum of  squares of first ‘n’ natural  numbers = 1/6n (n + 1)(2n +1)
12+22+32 +……….. = 1/6n (n+1) (2n +1)

ie ,

  • Sum of cubes of first ‘n’ natural numbers  = (n(n+1)/2)2

    ie,  13  + 23 + 33 +…………….=     (n(n+1)/2)2        =   1/4(n(n+1)/2)

 

                                2.Divisibilty

  • Divisibility by 2

            A number is divisible by 2 , if it’s unit digit is any of  0,2,4,6 and 8.

            Eg;  362, 200, 124

  • Divisibility by 3

           A number is divisible by 3, it the sum of it’s digit is divisible by 3.

           Eg; 321 = 3+2+1     =6 (divisible by3)

          So 321 is divisible by 3.

          Eg;   27356312 =  2+7+3+5+6+3+1+2   = 29

          29 ( not divisible by 3)

          So 27356312   is not divisible by 3.

  • Divisiblity by 4

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

          divisible by  4 or the last two digits are zeros.

           Eg;   600 :   Since last two digits are zeros

                       Therefore, 600 is divisible by 4.

           Eg;  4528 :   Since 28 is divisible by 4.

                          Therefore, 4528 is divisible by 4.

  • Divisibility by 5

           A number  which is divisible by 5, if its unit’s digit ie either 5 or zero.

           Eg;  3775, 4050

  • Divisibility by 6

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

           Eg;   612 : Divisible by both 2 and 3.                      612 ÷ 2 = 306

                       So divisible by 6.                                             612 ÷ 3 = 204

          Eg;   328 : Divisible by 2 but not by 3.

          So not divisible by 6                                                    328 ÷ 2 = 164

                                                                                                 328  ÷ 3 = 109.333

  • Divisible by 8 

           A   number  is divisible by 8, if the  last 3 digits is divisible by 8 or

           the last 3 digits are zeros.

           Eg;   34000   : Last 3 digits are zeros                        34000 ÷ 8 = 4250

                              So divisible by 8.

128 ÷ 8 = 16

            62128 : Last 3 digits =128

                              So   62128 is divisible by 8.

  • Divisibility by 9                

            A number is divisible by 9, if the sum of its digits is divisible by 9.

             Eg;   864 =  8 + 6 + 4

                        = 18  ( 18 ÷ 9 =  2 )

            2763  = 2 + 7 + 6 + 3

                        = 18 ( Divisible by 9)

             324     = 3 + 2 + 4  =9

  • Divisibility by 10

            A number is divisible by 10 if its unit digit  is 0.

            Eg;  520 , 65320.

  • Divisibility by 11

           A number is divisible by 11 if the difference of the sum of  its digits at

           odd places and the sum of its digits at even places is either 0 or a

           number  divisible by 11.

           Eg;  231 -Sum of digits at odd  places = 1 + 2

                     Sum of digits at even places =  3 (here only one digit).

               Difference  3-3 =0

  • Divisibility by 12

          A number is divisible by 12 if it is divisible by both  3 & 4

          Eg;    10224 , 672                                           10224   3 =     3408

                                                                                    10224  ÷ 4 =    2556

  • Divisibilty by 14

           A number is divisible by 14, if it is divisible by both  2 and 7.

           Eg:   39200,   1988                                   39200 ÷ 2 = 19600

              39200 ÷ 7 =     5600

  • Divisibilty by 16

           A number is divisible by 16,  if the last 4 digits are divisible by 16 or it is

           either  ‘0000’ .

           Eg;   10000,  60 5024 5024 ÷  16  = 314

  • Divisibilty by 18

           A number is divisible by 18 if it is divisible by both 2 and 9.

×

Hello!

Click one of our representatives below to chat on WhatsApp or send us an email to info@c4competition.com

× Whatsapp
© 2020 All Rights Reserved, c4competition
Powered by