NUMBER SYSTEM

QUANTITATIVE APTITUDE

Introduction• Real Numbers : Decimals (fractions),

Integers (No Decimals)• Decimals : RATIONAL – Finite (Terminating

Decimal 2.7, 3.4) Infinite (Non Terminating

Repeating Decimal 2.1212, 2.66) IRRATIONAL – Non terminating Non repeating decimal 2.5813, ∏

Introduction

• Integers : Negative, Zero, Positive• Natural Numbers : Positive Integers

1,2,3,4..• Whole Numbers : Includes 0.. 0,1,2,3…• 1 = Neither prime Nor Composite

Introduction

• Face Value : 1, 2, 3 is face value. In 34562 the face value of 2 and 3 is 2 and 3 respectively.

• Place Value : In 34562 the place value of 2 and 3 is 2 and 30000 respectively and 5 is 500.

Formulae

• Sum of first N natural numbers : Sn = n(n+1) / 2

• Sum of squares first N natural numbers : Sn = n(n+1)(2n +1) / 6

• Sum of cubes first N natural numbers : Sn = [n(n+1) / 2]2

• Sum of first N odd natural numbers : Sn = [n]2

• Sum of first N even natural numbers :Sn = n(n+1)

Formulae

Tips

• (xn – an) is completely divisible by (x + a) when n is even number.

• (xn + an) is completely divisible by (x + a) when n is odd number.

• What is the remainder when 17200 is divided by 18?(17200 – 1200) is completely divisible by (17 + 1) as 200 is even number. So when 17200 is divided by 18 remainder is 1.

Contd..

• If 232 + 1 is completely divisible by a whole number, which number is completely divisible by this number?

• Lets assume 232 + 1 = x + 1 296 + 1 = {(232 ) 3 + 1} = (x 3 + 1)

= (x + 1)(x2 – x + 1)

Contd..

• What is the common factor of (22121 + 19121 ) and (22231 + 19231 )

• Answer will be 22+19 = 41. • Since 121 and 231 are odd.

Some shortcuts

• Multiplication with base 100 :• 98*115 =?• -2*15=-30• 115-2=98+15=113• (113*100)-30 = 11300 – 30 = 11270

Some shortcuts

• Multiplication with base 300 :• 297*292 =?• -3*-8=24• 297-8=292-3=289• (289 * 300) + 24 = 86700 + 24 = 86724

Some shortcuts

• Multiplication with base 1000 :• 997*983 =?• -3*-17=51• 997-17=983-3=980• (980*1000)+51 = 980000 + 51 = 980051

Problem

• What will be the remainder when (6767 + 67) is divided by 68?

• (xn + an) is completely divisible by (x + a) when n is odd number.

• So (6767 + 1) + 66 is when divided by 67+1 (68)• So remainder will be 66 as (6767 + 1) is

completely divided by 68.