Cover Contents Preface to the Fourth Edition Preface to the First Edition Acknowledgement ComPetitive eXaminations: an overview Chapter 1: Numbers Introduction Number System Natural Numbers Whole Numbers Irrational numbers real numbers even numbers odd numbers Prime numbers composite numbers Basic Formulae AddItIon and SubtractIon Multiplication Squares Division Short-Cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers ExercIse-1 Exercise-2 (Based on Memory) Chapter 2: H.C.F. and L.C.M. of Numbers Common Factor Highest Common Factor Methods of Finding H.C.F. Common Multiple Least Common Multiple Methods of Finding L.C.M. Short-Cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 3: Square Root and Cube Root Square Exercise-1 Exercise-2 (Based on Memory) Answer Keys Expalantory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 4: Simplification Simple Arithmetic Operations Bodmas Short-cut Methods Exercise–1 Exercise 2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise–2 (Based on Memory) Chapter 5: Percentage Introduction Basic Formulae Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 6: Percentage Introduction Basic Formulae Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 6: Average Introduction Basic Formulae Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 7: Ratio and Proportion Ratio Types of Ratios Proportion Basic Formulae Short-cut Methods Exercise-1 Exercise-2 (Based on Memory Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 8: Partnership Introduction Basic Formulae Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 9: Profit and Loss Introduction Basic Formulae Some Useful Shortcut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 10: Time and Work, Work and Wages Introduction Basic Formulae Exercise 1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 11: Pipes and Cisterns Introduction Basic Formulae Some Useful Shortcut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 12: Time and Distance Introduction Basic Formulae Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 13: Boats and Streams Basic Formulae Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 14: Races and Games of Skill Introduction Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 15: Alligation or Mixture Introduction Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 16: Problems on Ages Introduction Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 17: Simple Interest Introduction Basic Formulae Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 18: Compound Interest Introduction Basic Formulae Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 19: Logarithms Introduction Laws of Logarithms Short-cut Methods Exercise-1 Answer Keys Explanatory Answers Exercise-1 Chapter 20: Stocks, Shares and Debentures Introduction Type of Shares Face Value and Market Value of Share Stocks and Brokerage Computation of Investment or Market Value of a Stock Computation of Gain or Loss in the Sale and Purchase of a Stock Change in Income on sale or Reinvestment Debentures Difference between Share Sandebentures Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 21: Discount (True and Banker’s) Introduction Basic Formulae Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 22: Binary Number System Introduction Exercise-1 Answer Keys Explanatory Answers Exercise-1 Chapter 23: Series Introduction Series Number series Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 24: Clocks and Calendar Clocks Some Basic Facts Short-cut Methods Some Basic Facts Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 25: Polynomials Polynomial Some Basic Theorems Some Useful Results and Formulae A Useful Thortcut Method Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 26: H.C.F. and L.C.M. of Polynomials Introduction Exercise-1 Answer Keys Explanatory Answers Exercise-1 Chapter 27: Linear Equations Linear Equation in one Variable Linear Equation in Two Variables Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 28: Quadratic Equations Introduction Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-2 (Based on Memory) Chapter 29: Progression Introduction Sequence Progressions Series Arithmetic Progression (A.P.) General Term of an A.P. Geometric Progression General Term of a G.P. Harmonic Progression Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 30: Set Theory Introduction Set Representation of Sets Finite and Infinite Sets Empty Set (or Null Set) Singleton Equal Sets Equivalent Sets Subset of a Set Power Set Comparable Sets Universal Set Venn Diagrams Complement of a Set Cartesian Product of Sets Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 31: Permutations and Combinations Introduction Factorial Notation Some Basic Results Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 32: Probability Introduction Probability of an Event Independent Events Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 33: Mensuration I: Area and Perimeter Introduction Some Basic Facts Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 34: Mensuration II: Volume and Surface Area Introduction Basic Formulae Solids Inscribed/Circumscribing other Solids Short-cut Methods Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 35: Trigonometric Ratios Introduction Exercise-1 Exercise-2 (Based on Memory) Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 36: Heights and Distance Introduction ExercIse-1 ExercIse-2 (Based on Memory) Answer Keys Explanatory Answers ExercIse-1 Exercise-2 (Based on Memory) Chapter 37: Plane Geometry Section 1: Lines and Angles Section 2: Triangles Key Results to Remember Section 3: Quadrilaterals and Parallelograms Key Results to Remember Section 4: Polygons Key Results to Remember Section 5: Circles and Tangents Key Results to Remember Theorems on Tangents Some Useful Results Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 38: Co-ordinate Geometry Introduction Basic Formulae Shortcut Method for Finding the Area Exercise-1 Exercise-2 (Based on Memory) Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory) Chapter 39: Data Interpretation Introduction Share Value in Rupees Exercise-1 Exercise-2 (Based on Memory) Recent Years’ Questions Answer Keys Explanatory Answers Exercise-1 Exercise-2 (Based on Memory ) Recent Years’ Questions Chapter 40: Data Sufficiency Introduction Exercise-1 Answer Keys Explanatory Answers Exercise-1