Quantitative Aptitude - Chapters, Notes, Topics, Formulas, Questions & Answers

Quantitative aptitude is a major part of almost every competitive exam and interview. It includes various topics in logical, numerical and analytical problems which are used to test the candidates' logical, numerical and analytical skills. It represents the Problem-Solving skills of the candidate.

What is Quantitative Aptitude?

Quantitative Aptitude is defined as a set of topics used to analyze the ability of a candidate to solve numerical, logical and analytical problems. It is a major part of almost every competitive exam and interview. Apart from academics, quantitative aptitude has various real-life applications in mathematics, physics, finance, etc.

Why is Quantitative Aptitude important?

Quantitative aptitude for a candidate is important to crack a competitive exam or an interview. Apart from this, quantitative aptitude has many applications in real-life like interest calculations, time and work calculations, to find the area and volume of a shape, to calculate the profit and loss, data interpretation etc.

The important topics to be covered in quantitative aptitude for the preparation of competitive exams are,

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.