The Pearson Guide to Quantitative Aptitude and Data Interpretation for the CAT

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Cover Contents Preface Acknowledgements CAT Demystified How to Prepare for QA How to Use This Book About the Author Part 1: Quantitative Aptitude Module 1: Numbers and their Properties Chapter 1: Vedic Mathematics Introduction to the Topic Types of Calculations Vedic Math Techniques in Multiplication Squaring Properties of a Square Number Odd and Even Square Numbers Methods of Squaring Cubing Properties of a Cube Methods of Cubing Vedic Maths Techniques in Algebra Chapter 2: Number System Introduction to the Topic Types of Questions Classification of Numbers/Integers Natural Numbers Whole Numbers Integers Number Line Prime Numbers and Composite Numbers Properties of Prime Numbers Even and Odd Numbers Comparing Integers Questions Based on Concepts LCM and HCF Summarizing LCM and HCF Questions Based on Standard Application of LCM and HCF Divisibility Rules (for Decimal System) Number of Divisors/Factors Condition for Two Divisors of any Numbern to be Co-Prime to Each Other Sum of Divisors Remainders Basics of Remainder Concept of Successive Division Derivations Unit Digit Tens’ Digit Number of Exponents Types of Questions Base System Decimal Calculation Basic Algebraic Calculations Involvingbase Systems Comparison of Different Base Systems Divisibility Rules for Systems Other than Decimal System Pigeon-Hole Principle Practice Exercises Warm Up Foundation Moderate Advanced True/False Answers Hints and Solutions Benchmarking Test 1 Answers Module 2: Arithmetic Chapter 3: Percentage Introduction to the Topic What is Percentage? Percentage as a Common Platform Percentage as a Rate Measurer Successive Percentage Change Percentage–Ratio Equivalence Product Stability Ratio Extension of Product Stability Ratio Application of Percentage 1. Simple Interest and Compound Interest 2. Simple Annual Growth Rate (SAGR) Andcompounded Annual Growth Rate (CAGR) 3. Calculation Practice Exercises Warm Up Foundation Moderate Advanced True/False Answers Hints and Solutions Chapter 4: Profit, Loss and Discount Introduction to the Topic Terminology Cost Price Selling Price Marked Price List Price Margin Calculating CP/SP Profit % or Loss % Profit Generation Honest Ways Dishonest Ways Practice Exercises Warm Up Foundation Moderate Advanced Answers Hints and Solutions Chapter 5: Average and Its Applications Introduction to the Topic Average Central Value Meaning of Average Properties of Average Some Special Cases Weighted Average Mixtures Mixing Without Replacement Practice Exercises Warm Up Foundation Moderate Advanced True/False Answers Hints and Solutions Chapter 6: Ratio, Proportion and Variation Introduction to the Topic Ratio 1. Ratio as a Bridging Element 2. Ratio as a Multiplier Comparison of Ratio Ratio, Proportion and Variation Proportion Standard Results/Definitions on Ratio/Proportion Variation Direct Proportion Inverse Proportion Direct Relation Application of Ratio, Proportion and Variation Practice Exercises Warm Up Foundation Moderate Advanced Answers Hints and Solutions Chapter 7: Time and Work Introduction to the Topic Time and Work Time–Work Equivalence Individual Work and Individual Efficiency Collective Work And Collective Efficiency Extension of the Concept of Time and Work Practic Eexercis Warm Up Foundation Moderate Advanced Answers Hints and Solutions Chapter 8: Time, Speed and Distance Introduction to the Topic Relationship Between Time, Speed and Distance Distance Time Speed Motion in a Straight Line Boats and Streams/Escalator Basic Terminology Races Basic Statements Circular Motion Trains Some Special Cases Clocks Degree Concept of Clocks Important Derivations Practice Exercises Warm Up Foundation Moderate Advanced True/False Answers Hints and Solutions Benchmarking Test 2 Answers Module 3: X+2 Maths Chapter 9: Basics of Algebra Introduction to the Topic What is Algebra? Algebraic Notations and Operations System of Two Linear Equations in Two Unknowns Solving a System of Lineare Quations (I) Graphical Method (II) Elimination Method Remainder and Factor Theorem (I) Remainder Theorem (II) Factor Theorem Practice Exercises Answers Hints and Solutions Chapter 10: Equations Introduction to the Topic Definitions Polynomials Degree of a Polynomial Polynomial Equation Polynomial Inequation Roots of an Equation Quadratic Equation Geometrical Meaning of Roots Factorization of a Quadratic Equation Properties of the Roots Descartes’ Rule of Signs of Roots Roots of a Quadratic Equation and their Nature Graph of a Quadratic Equation Maxima and Minima of a Quadratic Equation Algebraic Calculations on Roots Quadratic Equation Cubic Equation Bi-Quadratic Equation Formation of Quadratic Equation from its Roots Solution of Inequations Worked-Out Problems Practice Exercises Warm Up Foundation Moderate Advanced Answers Hints and Solutions Chapter 11: Sequence and Series Introduction to the Topic Sequence and Series 1. Arithmetic Progression 2. Geometric Progression 3. Harmonic Progression Arithmetico Geometric Series Means Arithmetic Mean Geometric Mean Harmonic Mean Worked-Out Problems Practice Exercises Warm Up Foundation Moderate Advanced True/False Answers Hints and Solutions Chapter 12: Function Introduction to the Topic Function Some Special Functions Modulus Function Greatest Integer Value Function Logarithmic Function Exponential Function Constant Function Ways of Representing Functions Nature of a Function (in Terms of Equation) Even Function Odd Function Neither Odd Nor Even Function Nature of Function (in Terms of a Graph) Even Function Odd Function Composite Function Inverse Function Injective, Surjective and Bijective Functions Practice Exercises Warm Up Foundation Moderate Advanced Answers Hints and Solutions Chapter 13: Graphs and Maxima Minima Introduction to the Topic Maximum and Minimum Value Maximum Value Minimum Value Finding Maxima and Minima in Some Typical Cases Graphs Sketching a Graph Some Standard Graphs Shifting of a Graph Area of a Graphs Practice Exercises Warm Up Foundation Moderate Answers Hints and Solutions Chapter 14: Logarithm Introduction to the Topic Logarithm Some Important Properties Characteristics and Mantissa Practice Exercises Foundation Moderate Answers Hints and Solutions Chapter 15: Permutation and Combination Introduction to the Topic Meaning of Permutation and Combination Fundamental Principles of Counting : Two Basic Theorems Permutations Combinations Approaching a Problem Meaning and Derivation of NPR and NCR Some Important Derivations Total Number of Combinations Some Standard Formats of Questions Word Formation Number Formation Circular Permutation Clockwise and Anti-Clockwise Circular Arrangements Permutation and Combination in Geometry Finding the Rank of a Word Practice Exercises Warm Up Foundation Moderate Advanced Answers Hints and Solutions Chapter 16: Probability Introduction to the Topic Probablity and its Application Trial and Elementary Events Compound Events Exhaustive Number of Cases Mutually Exclusive Events Equally Likely Events Favourable Number of Cases Independent Events Sample Space Odds in Favour and Odds Against Addition Theorem Conditional Probability Practice Exercises Warm Up Foundation Moderate Advanced Answers Hints and Solutions Benchmarking Test 3 Answers Module 4: Measurement Chapter 17: Geometry Introduction to the Topic Lines and their Properties a) Different Angles and Pairs of Angles b) Angles Associated with Two or More Straight Lines c) Angles Associated with Parallel Lines Polygons and their Properties Area and Perimeter of a Regular Polygon Properties of a Polygon Some Frequently Used Polygons Triangles and their Properties Properties of a Triangle Classification of Triangles Based Upon Sides Based Upon Angles Pythagoras Theorem Proofs of Pythagoras Theorem Summarizing the Above Classification Circumcentre Incentre Centroid Orthocentre Important Theorems Related to Triangle Congruency of Triangles Similarity of the Triangles Theorems for Similarity Similar Polygons Some Important Points Quadrilaterals and their Properties Different Types of Quadrilaterals Area of Shaded Paths Some Important Points Circles and their Properties Common Tangents and Secants of Circles Direct Common Tangents and Transverse Common Tangents Cyclic Quadrilateral Circle Packing Circles Inside Circles Ptolemy’s Theorem of Cyclic Quadrilateral Some Important Points Practice Exercises Warm Up Foundation Moderate Advanced Answers Hints and Solutions Chapter 18: Mensuration Introduction to the Topic Solids Euler’s Rule Cube Right Circular Cylinder Prism Right Circular Cone Frustum of Cone Pyramid Frustum of Pyramid Sphere Hemisphere Some More Solids Visual Mensuration Formulae Solved Examples Practice Exercises Warm Up Foundation Moderate Advanced Answers Hints and Solutions Chapter 19: Co-Ordinate Geometry Introduction to the Topic Consider the Following Case Co-Oridnate Axes and Representation of a Point Sign Convention Equation and Graph of Co-Ordinate Axes The Image of a Point Along the Mirror Place on a Straight Line Foot of the Perpendicular Centroid of a Triangle Incentre of a Triangle Area of Triangle Equation of a Curve Straight Line Different Forms of Representing a Straight Line Angle Between Two Intersecting Lines Condition for Two Straight Lines to be Paralle Condition for Two Straight Lines to be Perpendicular Point of Intersection of Two Lines Condition of Concurrency of Three Lines Length of Perpendicular Distance Between Two Parallel Lines Conditions for Points to be Collinear Worked Out Problems Practice Exercises Foundation Moderate Answers Benchmarking Test 4 Answers Module 5: Miscellaneous Chapter 20: Set Theory Introduction to the Topic Set Theory Types of Sets Operations on Sets Algebraic Laws in Set Theory Maxima and Minima in Set Theory Practice Exercises Warm Up Foundation Moderate Advanced Answers Hints and Solutions Chapter 21: Miscellaneous Introduction to the Topic Calendar Finding Day of a Date by Using a Reference Date Inequalities Tools of Inequality Standard Definitions Number Line Cauchy–Schwarz Inequality Heights and Distances General Theory on Heights and Distances Some Trigonometric Ratios and Formulae Practice Exercises Foundation Moderate Advanced Answers Chapter 22: Managerial Decision Making Introduction to the Topic When Decisions are Made Types of Decision Making Let us have a Look At the Questions from Cat 2007: Basics of Linear Programming (LP) Formulation of LP Process to Solve: Scheduling The Resources are: Practice Exercises Warm Up Hints and Solutions Part 2: Data Interpretation Module 1: Data Interpretation Chapter 1: Introduction to Data Interpretation What is Data Interpretation? What is Data? Significance of Organized Data Different Ways of Representing Data Narration Based Pictorial Line Chart/X–Y Chart Types of Line Charts Radar Diagram Area Diagram Practice Exercise Bar Chart Pie Chart Line Chart Table Answers Hints and Solutions Chapter 2: Developing the Skills Constituents of Data Interpretation (DI) Data-Set Explanations and Restrictions Skill-Set Required Skill 1—Knowing the Terminology Skill 2—Knowing the Different Formats of Presenting the Data Skill 3—Knowing What is to be Found Out Calculation Techniques Addition Subtraction Multiplication Ratio Comparison Pie Chart Calculation Technique Line Chart/Bar Chart Connecting Different Data-Sets Practice Exercise Chapter 3: Foundation Exercises Practice Exercise 1 Answers Hints and Solutions Practice Exercise 2 Answers Hints and Solutions Practice Exercise 3 Answers Hints and Solutions Practice Exercise 4 Answers Hints and Solutions Practice Exercise 5 Answers Hints and Solutions Practice Exercise 6 Answers Hints and Solutions Practice Exercise 7 Answers Hints and Solutions Practice Exercise 8 Answers Hints and Solutions Practice Exercise 9 Answers Hints and Solutions Chapter 4: Moderate Exercises Practice Exercise 1 Answers Hints and Solutions Practice Exercise 2 Answers Hints and Solutions Practice Exercise 3 Answers Hints and Solutions Practice Exercise 4 Answers Hints and Solutions Practice Exercise 5 Answers Hints and Solutions Chapter 5: Advanced Exercises Practice Exercise 1 Answers Hints and Solutions Practice Exercise 2 Answers Hints and Solutions Practice Exercise 3 Answers Hints and Solutions Practice Exercise 4 Answers Hints and Solutions Chapter 6: Mastering Data Interpretation Practice Exercise 1 Answers Hints and Solutions Practice Exercise 2 Answers Hints and Solutions Practice Exercise 3 Answers Hints and Solutions Module 2: Test Your Mettle Benchmarking Test 1 Answers Hints and Solutions Benchmarking Test 2 Answers Hints and Solutions Benchmarking Test 3 Answers Hints and Solutions Benchmarking Test 4 Answers Hints and Solutions Module 3: Data Sufficiency Chapter 7: Data Sufficiency Data Sufficiency Questions Significance of Data Sufficiency Various Do’s and Don’ts of Data Sufficiency Practice Exercise 1 Answers Hints and Solutions Practice Exercise 2 Answers Hints and Solutions Practice Exercise 3 Answers Hints and Solutions Part 3: Cat Papers Cat 2002 Answers Hints and Solutions Cat 2003 Leaked Paper Answers Hints and Solutions Retest Paper Answers Hints and Solutions Cat 2004 Part—A Part B—Number of Questions = 15 Answers Hints and Solutions Cat 2005 Part—A Part—B Answers Hints and Solutions Cat 2006 Section III Answers Hints and Solutions Cat 2007 Part—A Answers Hints and Solutions Cat 2008 Section I Answers Hints and Solutions Part 4: Section Tests Section Test 1 Answers Hints and Solutions Section Test 2 Answers Hints and Solutions Section Test 3 Answers Hints and Solutions Section Test 4 Answers Hints and Solutions