Quantitative Aptitude - Chapters, Notes, Topics, Formulas, Questions & Answers
Imagine you are calculating a discount while shopping, comparing travel time, or managing your monthly budget. Without knowing it, you are already using Quantitative Aptitude skills. Quantitative Aptitude is all about understanding numbers, applying formulas, and solving problems related to arithmetic, algebra, percentages, ratio and proportion, time and work, speed and distance, probability, and data interpretation. This article on Quantitative Aptitude – Chapters, Notes, Topics, Formulas, Questions & Answers will help you build strong numerical ability, improve calculation speed, and master smart problem-solving techniques for exams. Quantitative Aptitude plays a key role in more than 25+ competitive exams like CAT, SSC, IBPS, SBI PO, etc.
What is Quantitative Aptitude?
Quantitative Aptitude refers to a set of numerical and mathematical skills used to evaluate a candidate’s ability to solve arithmetic, algebraic, logical, and analytical problems quickly and accurately. It is one of the most important sections in competitive exams, entrance tests, and placement interviews, as it tests calculation speed, number sense, problem-solving ability, and logical thinking.
Quantitative Aptitude covers major maths topics such as percentages, ratio and proportion, profit and loss, time and work, speed and distance, algebra, probability, statistics, and data interpretation, making it a core subject for exams like SSC, Banking, CAT, XAT, CUET, CLAT, Railways, and Defence exams.
Importance of Quantitative Aptitude in Competitive Exams
Quantitative Aptitude plays a crucial role in determining overall exam performance because it is highly scoring when practiced well and conceptually strong.
Tests numerical ability and analytical skills
Improves calculation speed and accuracy
Helps in solving data interpretation and word problems
Builds strong logical and mathematical reasoning
Real-Life Applications of Quantitative Aptitude
Quantitative Aptitude is not limited to exams; it has wide applications in daily life and professional fields.
Used in finance for budgeting, profit analysis, and investments
Applied in physics and engineering for calculations and measurements
Helpful in business and economics for data analysis and forecasting
Strengthens decision-making using numbers and logic
Mastering Quantitative Aptitude enhances both academic performance and practical numerical skills, making it an essential subject for every competitive exam aspirant.
Quantitative Aptitude Topics
This section covers all the important Quantitative Aptitude topics that are commonly asked in competitive exams. It includes a complete list of chapters from Arithmetic, Algebra, Geometry, Mensuration, Number System, Probability, and Data Interpretation, helping you understand the syllabus clearly and prepare each topic in a structured and exam-focused way.
Classification of Numbers
Numbers are a fundamental concept of Maths. Classification of numbers is one of the topics covered for all competitive exams. A number is denoted by a group of digits called numerals. Classification of Numbers are used to identify and solve on the type of numbers such as natural numbers, whole numbers, Integers, rational numbers, irrational numbers, composite numbers and prime numbers.
Rational Numbers
All integers and fractions are rational numbers. In general, rational numbers are numbers that can be expressed as a fraction in p/q form. This topic of rational numbers in quantitative aptitude is about the operations on rational numbers.
BODMAS and Simplification
The BODMAS rule is the important rule for solving the simplification problems for all competitive exams. It is one of the basic and repeated questions in competitive exams. The BODMAS rule depicts the correct sequence in which the operations are to be executed, so to simplify the given expression. Here, 'B’ stands for Brackets, ‘O’ stands for of, 'D’ for Division, ‘M’ for Multiplications, ‘A’ for Addition and ‘S’ for Subtraction. Simplifying an expression using this rule can give an accurate answer.
Factors
If a number ‘a’ divides another number 'b’ exactly, then the number ‘a’ is called a factor of b. The factors can be found by dividing by each number or by a method called prime factorization.
Perfect squares and perfect cubes
The square of a number is multiplying a number by itself. Similarly, the cube of a number is multiplying a number by itself twice. A number is a perfect square if it is a square of an integer, and a number is a perfect cube if it is a cube of an integer. This topic in quantitative aptitude is about the problems on perfect squares and perfect cubes.
HCF and LCM
If a number ‘a’ divides another number 'b’ exactly, then the number ‘a’ is called a factor of ‘b’ and 'b’ is called the multiple of ‘a’. The HCF (Highest Common Factor) of two or more numbers is the greatest number that divides each of them exactly.
Divisibility Rules
Divisibility rules are used to find by which integer is the given number divisible. These divisibility rules are very important for checking prime numbers, finding factors, simplifying expressions and fractions etc.
Unit Digit
The order of the place value of the digit is calculated from the right side of the number. The first digit on the right side is the unit digit. Finding the unit digit is one of the very fundamental topics which could help solve problems in divisibility rules, finding the factors etc.
Last Two Digits of a Number
The first (one's place) and the second (ten's place) digit on the right side of a number is the last two digit of a number. Finding the last two digits of a number could also help in solving problems related to divisibility rules, finding the factors etc. Solving problems based on finding the last two digits of a number could improve the numerical skills of the candidate.
Remainder Theorem
The number left out after the dividend is completely divided by the divisor is called the remainder. This remainder theorem is used to find the remainder of the given number. Problems based on this enhance logical, analytical and problem-solving skills.
Number of Factors and Number of Trailing Zeros
If a number ‘a’ divides another number 'b’ exactly, then the number ‘a’ is called a factor of b. The factors can be found by dividing by each number or by a method called prime factorization. Finding the number of factors and number of trailing zeros in larger numbers and factorials is very important to solve more complex problems.
Arithmetic Progression
Arithmetic progression is a sequence of numbers where the difference between the consecutive terms is the same. Solving arithmetic progression problems is one of the logical thinking skills.
Geometric Progression
Geometric progression is a sequence of numbers where the ratio between consecutive terms is the same. Solving geometric progression problems also enhances logical thinking skills.
Harmonic Progression
Harmonic progression is a sequence of numbers where each term is the reciprocal of an arithmetic sequence. Solving harmonic progression problems requires good logical thinking skills especially in arithmetic progression.
Relation between Arithmetic Mean, Geometric Mean and Harmonic Mean
It is a repeated topic in competitive exams. The relation between arithmetic mean, geometric mean and harmonic mean (relation between AM, GM and HM) is mainly used in quantitative aptitude topics involving inequalities, speed and distance, etc.
Percentage
Percentage represents a number out of 100. This concept of solving percentages requires logical skills. This is one of the important topics to include in the preparation for competitive exams as it is required to solve problems on other topics like probability, simple and compound interest, profit and loss, etc.
Applications of Percentage
It is important to include application of percentage in the preparation for competitive exams as it is required to solve problems on other topics like probability, simple and compound interest, profit and loss, proportion, discount, loans and installments, data interpretation, mixture and alligations etc.
Profit and Loss
If the selling price of a product is greater than the cost price then it is profit, else it is a loss. Profit and Loss is one of the repeated topics in most competitive exams which requires analytical, logical and problem-solving skills.
Simple Interest
Simple interest is the process of earning a fixed percentage of interest in a specified time with respect to the principal amount. This concept of simple interest is also a repeated topic in quantitative aptitude. Solving problems related to simple interest improves problem solving skills.
Compound Interest
Compound interest is the process of earning a fixed percentage of interest in a specified time with respect to the principal amount and the interest earned in the previous term. It requires problem solving and analytical skills to solve problems related to compound interest.
Loans and Installments
Loans and installments are an important topic in quantitative aptitude which involves a good understanding in the concept of simple and compound interest. Solving problems related to loans and installments could help to enhance the problem solving skills.
Ratio and Proportion
The comparison of two quantities is called a ratio while equating two ratios are called proportion. Understanding the concepts of ratio and proportion is important as it is used in many other topics of quantitative aptitude other than ratio and proportion like trains and streams, mixture and alligations, profit and loss etc.
Proportion and variation
Proportion is equating the ratios of two quantities. Variation is the changes in the proportion of one quantity with respect to another. Solving these problems could help develop problem solving skills.
Applications of Ratios in Partnership
The comparison of two quantities is called a ratio. Ratios are an important concept in partnership as they are used to compare and determine the investment, profit, loss etc. in a partnership. Partnership is a repeated topic covered in quantitative aptitude for competitive exams.
Time and Work
The concept of Time and Work involves calculating the amount of work done with respect to time. It is one of the important topics in Quantitative aptitude for competitive exams. Practicing these topics could enhance problem-solving skills.
Pipe and Cistern
This topic pipe and cistern involves the understanding of rate at which the pipes fill and empty a tank. It is one of the repeated concepts for competitive exams.
Relative and Average Speed
Relative speed is the speed of an object with respect to the other while average speed is the average among the whole journey. This is an important and repeated topic in quantitative aptitude.
Speed, Time and Distance
Problems with speed, time and distance are a repeated topic for all competitive exams which enhance problem-solving skills. This is a fundamental concept for many topics like linear races and circular races etc.
Linear Races and Circular Races
Linear Races are straight tracks used for the races while circular races are oval shaped tracks. Both Linear and circular Races problems can be solved using concepts like speed, time and distance.
Average
Average is the mean value of the given set of numbers. It is one of the fundamental concepts used in many topics like Speed and distance, Time and Work, Sequence and Series, probability etc.
Mixture and Alligations
Mixture and alligations are problems related to mixed quantities with different characteristics. Solving these problems could help enhance analytical, logical and problem-solving skills.
Polynomials
Polynomials are expressions consisting of variables, coefficients and constants. Understanding the types of polynomials is very important as it is a fundamental concept.
Algebraic Identities
Algebraic identities are equations that hold true for all values which are used for solving complex equations and polynomials. Algebraic identities are one of the fundamental concepts used for solving equations, especially in quantitative aptitude.
Maxima and Minima in Polynomials
In a polynomial function, Maxima is the highest point and minima is the lowest point. Understanding the maxima and minima in polynomials is important to solve polynomials.
Linear Equations in One Variable
Linear equation in one variable is a polynomial with degree one. It is an important concept for quantitative aptitude as it is a fundamental concept to solve problems. Solving these equations may improve problem solving skills.
Linear Equations in Two Variables
Linear equations in two variables are a polynomial with degree two. There are many methods to solve these linear equations. Understanding how to solve these equations is important to solve problems in quantitative aptitude involving solution of equations.
Quadratic Equations
Quadratic equations are polynomials with degree two. These quadratic equations can be solved using various methods. Solving questions based on these quadratic equations can improve the analytical and problem-solving skills of the candidate.
Exponent and Surds
The exponent of a real number represents the number of multiplications to be done by the number itself while surds are irrational numbers. Understanding these topics on exponents and surds are very much important for solving problems on other complex topics.
Square Roots and Cube Roots on Surds
Surds are irrational numbers. Finding the square roots and cube roots of surds has many methods. Solving problems related to square roots and cube roots of surds could help improve numerical and analytical skills. These are fundamental concepts to solve complex problems.
Lines and Angles
A line is a straight one-dimensional figure extending on both side and an angle is a turn or rotation between two rays. These concepts require strong logical skills. These are very fundamental concepts which need better understanding to solve problems on other topics like mensuration, etc.
Triangles
Triangles are three-sided shapes made of lines. Understanding the concepts related to triangles like congruence, area etc. is required to understand other topics in coordinate geometry. Working on these topics could help enhance logical and problem-solving skills.
Quadrilaterals
Quadrilaterals are four sided figures made of lines. Knowing about the properties of quadrilaterals could be a great help to solve problems related to quadrilaterals and mensuration. Solving problems in this topic could improve the logical and analytical skills.
Parallelogram and Mid-Point Theorem
Parallelogram is a four-sided quadrilateral whose parallel sides are equal. Mid-point theorem is an important concept for competitive exams. It is used in various topics like geometry, etc.
Rhombus, Square, Rectangle and Trapezium
Rhombus, square, rectangle and trapezium are all four-sided quadrilaterals with different properties. Understanding the different properties of different shapes are important to understand other topics like mensuration. These are one of the fundamental and repeated topics for competitive exams.
Polygon
Polygon is a closed figure made of lines. Polygons have atleast three sides which is a triangle. There are repeated questions from the topic of polygon in almost every competitive exams. Solving problems related to this topic enhances the logical thinking, analytical and problem-solving skills.
Circle
A circle is a two-dimensional closed, curved surface with an equal distance from the center to every point. There are many properties of circles. This is a very fundamental topic in geometry.
Chord and Angle Subtended by a Chord
A chord is a straight line drawn from one end to another of a circle which divides the circle into two parts. The longest chord dividing the circle into two equal parts is called the diameter. Knowing the properties of the chord helps to solve problems based on it.
Tangents and Secants
Tangent is a line touching the circle at only one point and Secant is a line intersecting the circle at two different points. Understanding the concepts of tangent and secant helps solve problems based on other topics like coordinate geometry.
Surface Area and Volume of a Prism
A prism is a three-dimensional closed figure with five flat faces. Understanding these concepts of surface area and volume of a prism is important to competitive exams.
Surface Area and Volume of a Pyramid
A pyramid is a three-dimensional closed figure with triangular flat faces. Knowing the properties of the pyramid could help in solving the problems based on the topic surface area and volume. Solving problems on these topics improves logical thinking skills.
Cubes, Cuboid and Cylinder
Cubes, cuboid and cylinder are three-dimensional figures with different properties. Problems from these topics are repeatedly asked in the section quantitative aptitude for competitive exams.
Surface Area and Volume of Cone and Frustum
Cone is a three-dimensional figure with a round flat base and one vertex while frustum is the lower part of a cone or pyramid. Understanding the properties of these figures could help to solve problems on mensuration.
Sphere and Hemisphere
Sphere is the three-dimensional figure of a circle while hemisphere is half of the sphere. Working on problems related to this topic sphere and hemisphere could help enhance logical thinking and analytical skills.
Coordinate Geometry
Coordinate geometry is a branch of mathematics involving lines, shapes and graphs. For almost every competitive exam, there are repeated questions from this topic coordinate geometry.
Trigonometry
Trigonometry is a branch of mathematics dealing with the sides and angle of the triangle. This plays a major role in solving problems on other quantitative aptitude topics like mensuration, geometry, etc.
Mean, Median and Mode of Grouped and Ungrouped data
Grouped data is data represented as intervals while ungrouped data is random scattered data. Mean, median and mode are very basic topics in statistics. Understanding these topics helps in solving problems related to data interpretation.
Probability
Probability is a chance for an event to occur. This is one of the repeated topics in almost every competitive exam under quantitative aptitude. Working on this topic could help the aspirants solve problems on other topics like statistics, data interpretation, etc.
Data Interpretation
Data interpretation is analyzing the data represented in different visual forms like bar graphs, histogram, pie chart, etc. There are repeated questions from this topic on almost every competitive exam. Working on these topics could help the candidates enhance their logical thinking skills.
Permutations and Combinations
Permutations are possible arrangements of the given items while combinations are different possible selection from the given items. Permutations and combinations are fundamental topics for various other topics like probability, statistics, etc. Solving problems on these topics could help enhance the problem-solving skills.
Quantitative Aptitude Topics and Subtopics
This section provides a complete and structured breakdown of Quantitative Aptitude topics and subtopics as per the latest competitive exam syllabus. It covers all major areas such as Arithmetic, Algebra, Geometry, Mensuration, Number System, Probability, and Data Interpretation, helping students understand the full scope of the Quantitative Aptitude section.
| Main Topic | Important Sub-Topics Included |
|---|---|
| Arithmetic | Percentage, Profit and Loss, Simple & Compound Interest, Ratio and Proportion, Average, Time and Work, Time Speed and Distance, Mixtures and Alligation, Partnership, Pipes and Cisterns, Boats and Streams |
| Algebra | Linear Equations, Quadratic Equations, Polynomials, Algebraic Identities, Surds and Indices, Inequalities, Logarithms, Simplification, Equations in One and Two Variables |
| Geometry | Lines and Angles, Triangles, Circles, Polygons, Quadrilaterals, Coordinate Geometry Basics, Properties of Shapes, Theorems and Constructions |
| Mensuration | Area and Perimeter of 2D Shapes, Surface Area and Volume of 3D Shapes, Cube, Cuboid, Cylinder, Cone, Sphere, Hemisphere, Frustum |
| Number System | Types of Numbers, Divisibility Rules, Factors and Multiples, HCF and LCM, Remainders, Base System, Simplification, Unit Digit, Cyclicity |
| Probability | Basic Probability, Classical Probability, Conditional Probability, Independent and Dependent Events, Permutations and Combinations (Basics), Probability Based Word Problems |
| Data Interpretation | Tables, Bar Graphs, Pie Charts, Line Graphs, Caselets, Missing Data, Data Comparison, Percentage Change, Ratio Analysis, Approximation |
Important Quantitative Aptitude Formulae List
This section provides a complete and well-organized Quantitative Aptitude formula list covering all major topics like Arithmetic, Algebra, Geometry, Mensuration, Number System, Probability, and Data Interpretation. It is designed for quick revision, faster problem-solving, and exam-focused preparation, helping students easily recall important formulas during practice and exams.
| Topic | Formula | Use / Application |
|---|---|---|
| Arithmetic | Percentage = $(\frac{\text{Value}}{\text{Total}}) \times 100$ | Increase, decrease, comparison |
| Profit = SP − CP | Profit calculation | |
| Loss = CP − SP | Loss calculation | |
| Simple Interest = $\frac{P \times R \times T}{100}$ | Interest problems | |
| Speed = $\frac{\text{Distance}}{\text{Time}}$ | Time, speed, distance | |
| Average = $\frac{\text{Sum}}{\text{Number}}$ | Mean value | |
| Algebra | $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$ | Quadratic equations |
| $(a+b)^2 = a^2 + 2ab + b^2$ | Expansion | |
| $(a-b)^2 = a^2 - 2ab + b^2$ | Expansion | |
| $a^2 - b^2 = (a-b)(a+b)$ | Factorization | |
| $ax + b = 0 \Rightarrow x = -\frac{b}{a}$ | Linear equations | |
| $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$ | Cubic factorization | |
| Geometry | Area of triangle = $\frac{1}{2}bh$ | Triangle problems |
| $c^2 = a^2 + b^2$ | Pythagoras theorem | |
| Area of circle = $\pi r^2$ | Circle area | |
| Circumference = $2\pi r$ | Circle perimeter | |
| Area of rectangle = $l \times b$ | Plane figures | |
| Area of parallelogram = $b \times h$ | Parallelogram | |
| Mensuration | Volume of cube = $a^3$ | 3D shapes |
| Volume of cuboid = $lbh$ | Storage capacity | |
| Curved surface area of cylinder = $2\pi rh$ | Cylinder problems | |
| Volume of cylinder = $\pi r^2 h$ | Tanks and pipes | |
| Surface area of sphere = $4\pi r^2$ | Sphere surface | |
| Volume of sphere = $\frac{4}{3}\pi r^3$ | Sphere volume | |
| Number System | HCF × LCM = Product of two numbers | Relation of HCF & LCM |
| Number of factors = $(a+1)(b+1)$ | If $n=p^a q^b$ | |
| Sum of first $n$ natural numbers = $\frac{n(n+1)}{2}$ | Series | |
| Sum of first $n$ odd numbers = $n^2$ | Pattern | |
| Sum of first $n$ even numbers = $n(n+1)$ | Pattern | |
| Probability | $P(E)=\frac{\text{Favorable}}{\text{Total}}$ | Basic probability |
| $P(\text{Not }E)=1-P(E)$ | Complement rule | |
| $P(A \cup B)=P(A)+P(B)-P(A \cap B)$ | Union of events | |
| $P(A \cap B)=P(A)\cdot P(B)$ | Independent events | |
| Data Interpretation | Percentage change = $\frac{\text{New−Old}}{\text{Old}} \times 100$ | Growth / decline |
| Average = $\frac{\text{Total}}{n}$ | Data analysis | |
| Ratio = $\frac{a}{b}$ | Comparison | |
| Pie chart angle = $\frac{\text{Value}}{\text{Total}} \times 360^\circ$ | Pie chart questions | |
| Weighted average = $\frac{\sum wx}{\sum w}$ | Combined data analysis |
Step-by-Step Methods to Solve Quantitative Aptitude Questions
A systematic approach is the key to scoring high in Quantitative Aptitude for competitive exams like SSC, Banking, CAT, CUET, and Railways.
Read the question carefully and identify the topic (Arithmetic, Algebra, Geometry, Probability, or DI).
Write down the given values and required result clearly.
Select the correct formula or concept related to the question.
Substitute values step by step to avoid calculation mistakes.
Simplify using basic arithmetic rules and shortcuts.
Recheck your answer by approximating or reversing the calculation.
This step-by-step method improves accuracy, clarity, and confidence in quantitative problem-solving.
Shortcuts and Tricks for Faster Calculation
Using smart tricks can significantly boost your speed in Quantitative Aptitude.
Use percentage-to-fraction conversions like 25% = 1/4, 50% = 1/2, 20% = 1/5.
Learn squares and cubes up to 30 for faster mental calculation.
Apply ratio simplification techniques before multiplying big numbers.
Use approximation methods in Data Interpretation questions.
Remember Vedic maths multiplication tricks for quick results.
Cancel common factors early to reduce calculation load.
These shortcuts help you solve more questions in less time during exams.
Common Mistakes to Avoid in Quantitative Aptitude
Avoiding common errors can greatly improve your exam accuracy.
Using the wrong formula for a given problem type.
Ignoring units in speed, time, and distance questions.
Making sign mistakes in algebraic expressions.
Rushing calculations without proper simplification.
Not reading the question completely, missing conditions.
Skipping revision of basic formulas.
Staying alert to these mistakes improves your Quantitative Aptitude performance.
Quantitative Aptitude Preparation Strategy
A smart strategy makes your preparation more exam-oriented and result-driven.
Divide your syllabus into Arithmetic, Algebra, Geometry, Number System, Probability, and DI.
Study one topic daily with formulas and 20–30 practice questions.
Revise formulas regularly using a formula sheet.
Solve previous year questions to understand exam patterns.
Take weekly mock tests to measure progress.
Focus equally on speed and accuracy.
Daily Study Plan for Quantitative Aptitude
A balanced daily routine ensures steady improvement.
20 minutes: Revise important Quantitative Aptitude formulas
40 minutes: Practice topic-wise questions
20 minutes: Solve mixed practice or DI sets
10 minutes: Analyze mistakes and note weak areas
This routine builds strong numerical ability and problem-solving skills.
Time Management Tips for Quantitative Aptitude
Time management is crucial for cracking competitive exams.
Attempt easy questions first to secure quick marks.
Do not spend more than 1–1.5 minutes on a single question.
Skip lengthy calculations initially and return later.
Use approximation in Data Interpretation questions.
Practice with a timer to simulate real exam conditions.
Keep the last 5 minutes for review and corrections.
With the right time strategy, Quantitative Aptitude becomes one of the highest-scoring sections in any competitive exam.
Frequently Asked Questions (FAQs)
Quantitative Aptitude is defined as a set of topics used to analyze the ability of a candidate to solve numerical, logical and analytical problems.
With regular and consistent practice, you can improve the required skills for quantitative aptitude.
No. Formulas are important, but understanding when and how to apply them is more important. Concept clarity combined with formula usage gives better results.
The syllabus for quantitative aptitude includes classification of numbers, ratio and proportion, sequence and series, average, profit and loss, etc. Refer the above article for the topics on quantitative aptitude.
Arithmetic usually carries the highest weight, especially topics like percentage, profit and loss, ratio and proportion, time and work, and time-speed-distance.