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Aptitude of Mathematics

By

Prabu Krishna

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Chapter 1:

1. GENERAL NUMBERS

Concepts

Place value or local value of a digit in numeral.

Concept 1:-

In the numeral 68974532, we have

Place value of 2 is 2 units = 2

Place value of 3is 3 tens = 30

Place value of 4 is 4 thousands = 4000

Place value of 7 is 7 ten thousands = 70000

The face value of a digit in a numerical is the value if the digit

itself at whatever place it may be.

Concept 2:-

In the above numeral, the face value of 2 is 2. And the face

value of 3 is 3 and so on

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Prime number

Concept 3:-

A number which is divisible by 1 and itself.

Prime numbers less than 100 are

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

89,97.

Prime numbers larger than 100

Let P be a given number. Find a whole number nearly greater

than the square root of P.

Test

Let k>P

Test whether P is divisible by any prime number less than K. ifyes, then P is not prime otherwise P is Prime.

For Eg.

i) Clearly 14>191Prime numbers less than 14 are 2,3,5,7,9,11.

191 is not divisible by any of them.So, 191 is a prime number.

ii) 20391Prime numbers less than 20 are 2,3,5,7,11,13,17,19.

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We find that 391 is divisible by 17.

So 391 is not a prime number.

Co-prime:-

Concept 4:-

The numbers are said to be co-prime if their H.C.F is 1.

Eg:- (2,3),(4,5),(7,9),(8,11) etc are co-prime.

Formulae:

Concept 5:-

1.( + )2 = 2 + 2 + 22.( )2 = 2 + 2 23.(2 + 2) (2 2) = 44.(2 2) = ( + )( )5.(3 + 3) = ( + )(2 + 2 )6.(3 + 3) = ( )(2 + 2 + )7.(2 + 2) (2 2) = 2(2 + 2)8.( ) = 9.( + ) = +

Distributive law

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If we divide a given number by another number then

Concept 6:-

Divideend= (divisor quotient) + Remainder

Progression

Concept 7:-

A succession of numbers formed and arranged in a definite

order according to certain definite rule is called a progression.

A.P:- (Arithmetic Progression (A.P))

If each term of a progression doffers from its proceeding term

by a constant, then such a progression is called an arithmeticalprogression is called the common difference of the A.P.

An A.P. with first term a and common difference d is given by

A, a+d,a+2d,a+3d,

term = tn

The sum of n terms of this A.P

= a+(n-1)d.

Sn=

2[2a+(n-1)d]=

2[a+l]

Where

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a= first term

l= last term

i. 1+2+3+.+.n=(+1)2

Concept 8:-

ii. (12 + 22 + 32 + + 2)= (+1)(2 +1)6

iii. (13 + 23 + 33 + + 3)= 2(n+1)24

A progression of number in which every term bears a constant

ratio with its proceeding term is called a geometrical

progression.

Concept 9:-

The constant ratio is called the common ratio of the G.P.

A G.P with first term a and common ratio r is a, ar,

a2, 3.

= 1

Sum of the n terms Sn=(1 )

1.