http://wordseveryday.blogsome.com/

THIS IS THE NEW UPGRADED SITE FOR YOUR QUANT QUESTIONS

Sequence: A succession of numbers formed and arranged in a definite order according to a certain definite rule, is called a sequence.

Any number occurring at the nth place of a sequence is called its nth term.

Progression: If the terms of a sequence increases or decreases continuously, then such a sequence is called a progression.

Arithmetic progression: If each term precedes its next term by a constant, then such a progression is called an arithmetic progression.

An A.P with first term a ; and a common difference d is given by- a, (a+d), (a+2d), (a+3d),…

The nth term of an A.P with 1^st term a and common difference d is given by

Tn=a +(n-1)d.

The sum of terms of an A.P is Sn=n/2[2a+(n-1)d] = n/2 (first term + last term).

Geometric Progression: Where every term bears a constant ratio with its preceding term, is called a GP.

A GP with 1^st term a and common ratio r is given by: a, ar, ar square , ar cube….

Tn= ar to the power n-1 .

Sum of GP is Sn= a(1-r to the power n)/ (1-r).

Harmonic Progression:  Numbers a1,a2,a3.. are said to be in HP, if 1/a1,1/a2,1/a3… are in AP. 

      #There are 25 prime nos. between 1 and 100#

      #To find if a number is prime or not#

          – Ex. To find if 165 is prime or not.

            > Take the nearest value of √165 is 13

                 that is 13>√165.       

            > So test the divisiblity of 165 by each of  the prime numbers less than 13.

            > If it is divisible any of those nos. then it is not prime.(Here 165 is divisible by 11; hence not prime).

            > If it is not divisible by any of those nos. then it is a prime no.

• Composite Numbers: Numbers greater than 1 which are not prime nos. are called composite nos.

      # 1 is neither prime nor composite#

      # 2 is the only even prime number#

• Division on Numbers:

       Division Algorithm:

Formula: Dividend=(Divisor*Quotient) +Remainder.

Ex: When 123 is divided by 16, we have

       Dividend= 123.

       Divisor= 16

       Quotient= 7

       Remainder= 11

       Therefore, 123=16*7+11.

• Tests of Divisibility.

1. Divisibility by 2: A number is divisible by 2 if its units digit is divisible by 2. Ex: 4326894.
2. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3 .  Ex:693258.
3. Divisibility by 4: A number is divisible by 4 if its last two digits is divisible by 4. Ex: 738924.
4. Divisibility by 5: A number is divisible by 5 if its unit digit is either 0 or 5.
5. Divisibility by 8: A number is divisible by 8 if its last three digits is divisible by 8.Ex: 73512.
6. Divisibility by 9: A number is divisible by  if its sum of all digits is divisible by 9. Ex: 1458.
7. Divisibility by 11: A number is divisible by 11 if the difference of the sum of digits at odd places and sum of digits at even places is either 0 or is dividible by 11. Ex: 684387.

Part I

Go to WordsEveryday

To master this chapter it is very essential to know the basics thoroughly.

NUMBERS.

Types of Numbers.

• Natural numbers: The counting nos. are called natural nos.

      N={1,2,3,4,5,6,….} is a set of all natural nos.

• Whole numbers: All counting numbers together with zero form a set of whole nos.

      W={0,1,2,3,4,5,6,…} is a set of all whole nos.

       #Every natural no. is a whole no, but every whole no is not a natural no.# zero is not a natural no.

• Integers: The set of all natural nos, zero and negatives of counting numbers is the set of all integers.

      I={…..-3,-2,-1,0,1,2,3,…..} is the set of all integers.

     -  Positive integers: The set I={1,2,3,4,5,6,…}

     – Negative integers: The set I={-1,-2,-3,……..}

      # zero is neither negative nor postive#

• Rational numbers: The nos. of the form p/q; where p and q are integers and q not equal to zero, are known as rational nos.

      Ex. 2/3 ; 3/5 ;  129/-12 etc.,

       #Every natural no. is a rational no.#

       #Every natural no. can be written as a/1#

       #Every integer is a rational no.#

• Irrational Numbers:  All numbers which are expressed in decimal form are in non-terminating and non-repeating form, are called irrational nos.

      Ex.√2,√3,√7 etc.,

•       Real numbers: The total of all rational and all irrational nos. forms a set of all real nos.

     #The sum of a rational and an irrational no. is irrational#

     #The product of a rational and an irrational no. is irrational#

Go back to WordsEveryday