Quantitative Aptitude for CAT

Cover
About Pearson
Title Page
Copyright
Table of Contents
Preface
CAT Pattern Analysis 2015–2017
	Cat Journey So Far
	Pattern Analysis
		2015
		2016
		2017
Quantitative Aptitude Analysis 2015–2017
	Analysis—2015
	Analysis—2016
	Analysis—2017
Unit 1: Introduction
	Chapter 1: Building Blocks
		Classification of Numbers
		Number Line
		Rules for Divisibility
		Prime Factors
		L.C.M and H.C.F.
		Some Important Points
		The Equation of Division
		Rules Related to the Behaviour of Remainders
		Algebraic Identities and Numerical Expressions
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
	Chapter 2: Speed Maths
		Importance of Calculation Speed
		Additions, Subtractions and Multiplications
			Some Ways of Simplifying Calculations
			Multiplying Two Numbers Both of Which are Close to the Same Power of 10
		Fractions and Percentages
		Reciprocals and Its Multiples
			Percentage Calculations
		Comparison of Fractions
		Approximations
		BODMAS—Hierarchy of Arithmetic Operations
			Squares and Cubes
			Powers of 2 and 3
		Solved Examples
			Exercise-1
			Answer Keys
		Solutions
			Exercise-1
Unit 2: Numbers
	Chapter 1: Numbers
		Basic Arithmetic Operations
			Rule of Signs
		Classification of Real Numbers
			Rational Numbers
			Irrational Numbers
			Integers
			Prime Numbers
			Composite Numbers
			Even and Odd Numbers
			Perfect Numbers
		Hierarchy of Arithmetic Operations
		Recurring Decimals
		Integers
			Properties of Division
			Factors, Multiples and Co-primes
			Rules for Divisibility
		Factors and Co-Primes of a Number
			Number of Factors of a Number
			Number of Ways of Expressing a Given Number as a Product of Two Factors
			Sum of All the Factors of a Number
			Product of All the Factors of a Number
			Number of Ways of Writing a Number as Product of Two Co-primes
			Number of Co-primes to N That Are Less Than N
			Sum of Co-primes to N That Are Less Than N
		Least Common Multiple (L.C.M.) and Highest Common Factor (H.C.F.)
			L.C.M. by Factorization
			L.C.M. by Division
			H.C.F. by Factorization
			H.C.F. by Long Division
			L.C.M. and H.C.F. Models
		Successive Division
			Factorial
			IGP of a Divisor in a Number
			IGP of a Number in N!
		Algebraic Identities
		Some Important Points
		Last Digit of any Power
		Last Digit of a Sum or Product
			Finding the Remainder in Divisions Involving Powers of Numbers
		Last Two Digits of am
		Some Important Theorems
			Binomial Theorem
			Fermat’s Little Theorem
			Wilson’s Theorem
			Remainder of a Number When Divided by 10n ± 1
			Rules Pertaining to an + bn or an - bn
		Some Important Identities
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 2: Number Systems
		Base
		Representation
		Conversions
		Binary Arithmetic
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
	Chapter 3: Simple Equations
		One Equation in One Unknown
		Two Equations in Two Unknowns
		Three Equations in Three Unknowns
		Additional Cases in Linear Equations
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
Unit 3: Arithmetic
	Chapter 1: Ratio, Proportion and Variation
		Ratio
		Proportion
		Variation
			Direct Variation
			Inverse Variation
			Joint Variation
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 2: Percentages, Profit and Loss and Partnerships
		Percentage
		Percentage Points
		Profit and Loss
		Partnerships
		Stocks and Shares
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 3: Special Equations
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
	Chapter 4: Simple Interest andCompound Interest
		Interest
			Simple Interest
			Compound Interest
			Compounding More Than Once a Year
		Present Value
			Present Value Under Simple Interest
			Present Value Under Compound Interest
		Repayment in Equal Instalments—Compound Interest
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 5: Time and Distance
		Speed
		Average Speed
			Relative speed
		Boats and Streams
		Races and Circular Tracks
		Clocks
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 6: Time and Work
		Pipes and Cisterns
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 7: Averages, Mixturesand Alligations
		Averages
			Points to Remember
			An Easy Method to Calculate Averages
			Weighted Average
		Mixtures
		Alligations
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
Unit 4: Geometry
	Chapter 1: Geometry
		Angles and Lines
		Parallel Lines
		Ratio of Intercepts
			Triangles
		Geometric Centres of a Triangle
			Circumcentre
			Incentre and Excentres
			Orthocentre
			Centroid
		Similarity of Triangles
		Congruence of Triangles
		Some More Useful Points About Triangles
			Basic Proportionality Theorem
			Mid-Point Theorem
		Quadrilaterals
		Trapezium
		Parallelogram
		Rhombus
		Rectangle
		Square
		Polygon
		Circles
		Arcs and Sectors
		Areas of Plane Figures
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 2: Mensuration
		Areas of Plane Figures
			Triangles
			Quadrilaterals
			Circle
			Ellipse
			Areas and Volumes of Solids
			Prism
			Cuboid or Rectangular Solid
			Cube
			Cylinder
			Pyramid
			Cone
			Cone Frustum
			Frustum of a Pyramid
			Torus
			Sphere
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 3: Coordinate Geometry
		Rectangular coordinates
		Ordered Pair
		X-coordinate and Y-coordinate
		The Straight Line
		Equations of Lines
		Angle Between Two Lines
		Some Formulae to Remember
		Locus
		Pair of Straight Lines
			Change of Axes
			Translation of Axes
			Rotation of Axes
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 4: Trigonometry
		Measurement of Angles
		Basic Co nversions
		Important Conversions
			Signs of Trigonometric Ratios
			Maximum and Minimum Values of Trigonometric Ratios
			Graphs of Sine, Cosine and Tangent Functions
			Some Important Trigonometric Identities
			Addition and Subtraction Formulae
			Double Angle Formulae
			Half-angle Formulae
			Triple Angle Formulae
			Formulae for Changing the Product into Sum or Difference
			Formulae for Changing the Sum orDifference into Products
		Other Standard Results
		Heights and Distances
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
Unit 5: Algebra
	Chapter 1: Sequences and Series
		Progressions
			Arithmetic Progression
			Geometric Progression
			Infinite Geometric Progression
			Harmonic Progression
		Some Important Results
		Sequences and Series
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 2: Indices and Surds
		Indices
		Surds
			Rationalization of a Surd
			Square Root of a Surd
			Comparison of Surds
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 3: Logarithms
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
	Chapter 4: Quadratic Equations
		Quadratic Equations
			Finding the Roots by Factorization
			Finding the Roots by Using the Formula
		Sum and Product of Roots of Aquadratic Equation
		Nature of the Roots
		Signs of the Roots
		Constructing a Quadratic Equation
			Constructing a New Quadratic Equationby Changing the Roots of a GivenQuadratic Equation
		Maximum or Minimum Value of Aquadratic Expression
			Polynomials and Polynomial Equations
			Division of a Polynomial by a Polynomial
			Relations between Roots and Coefficients
			Roots of Equations and Descartes’ Rule
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 5: Inequalities and Modulus
		Symbols and Notations
		Absolute Value
			Properties of Modulus
		Interval Notation
		Some Useful Models
			Model 1
			Model 2
			Model 3
			Model 4
			Model 5
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5 Based on Data Sufficiency
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Exercise-5
	Chapter 6: Functions
		Sets
			Some Definitions
			Basic Set Operations
		Relations
		Functions
			Ways of expressing Functions
			Some Properties of Functions
			Some Types of Functions
			Functional Equations
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
	Chapter 7: Graphs
		Line Graphs
			Shifting of Graphs
		Graphs of Commonly Used Functions
			Floor and Ceiling (or Ceil) Functions
			Exponential Function (eax)
			Signum Function
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
	Chapter 8: Operator-Based Questions
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
Unit 6: Modern Maths
	Chapter 1: Permutations and Combinations
		Permutations
		Combinations
			Total Number of Combinations
			Dividing Given Items into Groups
		Circular Permutations
			Sum of All Numbers Formed from Given Digits
			Rank of a Word
		Some Additional Points
		Selections
		Arrangements
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
	Chapter 2: Probability
		Probability
			Equally Likely Outcomes
			Mutually Exclusive Events
			Collectively Exhaustive Events
		Addition Theorem of Probability
			Conditional Probability and the Multiplication Theorem of Probability
			Pairwise Independence and Mutual Independence
			Bayes’ Theorem
		Expected Value
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
	Chapter 3: Statistics
		Measures of Central Tendencies
			Arithmetic Mean (A.M.)
			Geometric Mean (G.M.)
			Harmonic Mean (H.M.)
			Median
			Mode
		Measures of Dispersion
			Range
			Quartile Deviation (Q.D.) or Semi-interquartile Range
			Mean Deviation (M.D.)
			Standard Deviation (S.D.)
		Solved Examples
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
			Answer Keys
		Solutions
			Exercise-1
			Exercise-2
			Exercise-3
			Exercise-4
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