How to Prepare for Quantitative Aptitude for the CAT Common Admission Test

1. Master Fundamental Arithmetic Skills for Quantitative Dominance

Addition being the mother of all calculations has the potential of giving you the extra edge you require to dominate this all important examination.

Addition is foundational. The ability to perform rapid and accurate addition is the bedrock of quantitative aptitude. Proficiency in addition directly impacts performance in various calculation-intensive areas, including basic numeracy, data interpretation, and commercial arithmetic.

Beyond carry-over methods. Traditional carry-over methods are often slow and require writing down intermediate steps. Instead, cultivate mental strategies like thinking on the number line, which eliminates the need for carry-overs and promotes faster calculations. For example, adding 78 and 88 can be visualized as 78 + 80 + 8, avoiding the need to write down the carry-over.

Practice for speed and accuracy. Consistent practice is essential to develop the ability to react to two-digit numbers with their sums instantaneously. Regular exercises, such as daily 10x10 addition tables, can significantly improve calculation speed and accuracy. The goal is to reach a point where adding multiple two-digit numbers becomes automatic, freeing up mental resources for problem-solving.

2. Strategic Block-Wise Preparation is Key to Conquering the CAT

It is in this context and for this precise reason that I have divided this book into six manageable blocks—the approach being rationalising the chapters and grouping them according to the amount of shared concepts these chapters have amongst each other.

Divide and conquer. Instead of being overwhelmed by the vast syllabus, divide the quantitative aptitude section into manageable blocks based on shared concepts. This approach makes the preparation process less daunting and more focused. The book is divided into six blocks: Number Systems and Progressions, Averages and Alligations, Arithmetic and Word-based Problems, Geometry, Algebra, and Counting.

Prioritize based on exam trends. Allocate study time based on the relative importance of each block in the CAT and other management entrance exams. For example, Number Systems and Progressions, Geometry, and Algebra are typically high-priority areas for the CAT. However, it's crucial to be well-versed in at least four blocks to ensure a balanced preparation.

Develop intuitive knowledge. Don't just focus on studying the theory in each area; develop an intuitive understanding of all problem scenarios that emerge from each block. This involves working through a variety of questions and developing the ability to recognize and apply the appropriate logic in different contexts.

3. Ratio and Percentage Proficiency: Cornerstones of Quantitative Problem Solving

In my view, percentage rule (as I call it) is one of the best ways to calculate percentages since it gives you the flexibility to calculate the percentage value up to as many digits after decimals as you are required to and at the same time allows you to stop the moment you attain the required accuracy range.

Master the percentage rule. Develop the ability to calculate percentages through additions and subtractions, removing 100%, 50%, 10%, 1%, 0.1%, and so forth of the denominator from the numerator. This method allows for flexible and efficient percentage calculations, stopping when the required accuracy is achieved.

Ratio comparison techniques. Learn and practice various methods for comparing ratios, including cross-multiplication, percentage value comparison, and numerator-denominator percentage change. The numerator-denominator percentage change method is particularly powerful for comparing close ratios.

Percentage Change Graphic (PCG). Utilize the PCG to calculate the value of percentage changes in ratios, successive changes, and product changes. This visual tool simplifies complex calculations and provides a clear understanding of the relationships between different variables.

4. Geometry and Mensuration: Visualizing Solutions for Aptitude Success

You sit in front of your CAT question paper and the first question comes in front of you. If you have identified the logic of the question or seen the question itself earlier, your entire QA preparation is fructified.

Prioritize key formulas. Focus on mastering a core set of geometrical formulas and theorems, including those related to lines, polygons, triangles, quadrilaterals, circles, cones, cylinders, spheres, and frustums. Understanding and applying these fundamental concepts is more important than memorizing obscure formulas.

Develop visualization skills. Cultivate the ability to visualize geometrical figures and solids, even when they are not explicitly provided in the question. This skill is crucial for understanding the relationships between different elements and identifying the appropriate formulas to apply.

Employ reverse flowcharting. Instead of directly trying to find the required value, identify related values that can be more easily calculated. This approach can simplify complex problems and lead to a more efficient solution.

5. Functions, Equations, and Inequalities: Bridging Algebra and Graphical Intuition

The whole battle for QA preparation in the CAT can be essentially summarised in terms of the quality of pre formed logic that you have to the specific questions that you are going to face in the exam.

Connect analytical and graphical representations. Develop a strong understanding of how algebraic expressions translate into graphical representations. This involves visualizing the shapes of linear, quadratic, and cubic functions and understanding how changes in the equation affect the graph's position and orientation.

Master inequality-solving techniques. Learn to solve inequalities by identifying critical points, testing intervals, and considering the sign of the expression. Understand how the discriminant of a quadratic expression determines the nature of its roots and the behavior of the corresponding inequality.

Develop mental structures. Create mental structures for specific mathematical situations, allowing you to quickly recognize and apply the appropriate logic in the exam. This involves developing "thought algorithms" for standard and non-standard mathematical situations related to various chapters and concepts.

6. Permutations, Combinations, and Probability: Mastering the Art of Counting

Your battle for CAT would be won if you get a “YES I KNOW THIS PATTERN/LOGIC” reaction to 50–60% of the questions in your test.

Build a counting toolbox. Familiarize yourself with a set of fundamental counting situations and the tools used to solve them, including combinations (nCr), permutations (nPr), the multiplication principle, and the addition principle. Understand the specific conditions under which each tool is applicable.

Treat P&C and Probability as language chapters. Focus on translating the language of the question into the language of the answer. This involves identifying the key elements, connecting them with conjunctions like "AND" and "OR," and then applying the appropriate counting tools.

Master the art of event definition. In probability problems, clearly define the event whose probability is to be found. Break down complex events into simpler, mutually exclusive events and connect them using "AND" and "OR" to calculate the overall probability.

7. Averages and Alligations: Mastering Mixtures and Distributions

My experience shows that very often students look at the vast number of chapters and concepts to be studied for QA and get disheartened.

Understand the meaning of averages. View averages as representative values that can be used to replace each number in a set without changing the total. This perspective simplifies problem-solving and allows for intuitive calculations.

Master the weighted average formula. Learn to calculate weighted averages when combining groups with different sizes and averages. This is a fundamental skill for solving problems involving mixtures, distributions, and other real-world scenarios.

Utilize the alligation method. Understand the alligation method as a shortcut for solving weighted average problems involving two groups. Learn to represent alligation problems graphically and apply the straight-line approach for efficient calculations.

8. Time, Speed, and Distance: Mastering Motion and Relative Speed

The quality of the questions asked in the CAT over the past couple of years has become extremely good—requiring an upgradation of your grasp of concepts and understanding of each particular topic to a level not required before.

Master the fundamental equation. Understand the relationship between speed, time, and distance (Speed × Time = Distance) and its implications for problem-solving. Recognize the direct and inverse proportionalities that arise from this equation.

Apply relative speed concepts. Learn to calculate relative speeds for objects moving in the same and opposite directions. This is crucial for solving problems involving trains, boats, and other scenarios involving relative motion.

Develop mental structures. Create mental structures for specific problem types, such as those involving trains, boats and streams, and circular motion. This involves understanding the key variables and relationships and developing efficient solution strategies.

9. Deciphering Number Systems: Prime Numbers, LCM, HCF, and Beyond

You sit in front of your CAT question paper and the first question comes in front of you. If you have identified the logic of the question or seen the question itself earlier, your entire QA preparation is fructified.

Master prime number properties. Understand the definition of prime numbers and their unique properties, including divisibility rules and the distribution of primes. Learn efficient methods for checking whether a number is prime.

Understand LCM and HCF concepts. Learn to calculate the Least Common Multiple (LCM) and Highest Common Factor (HCF) of numbers using prime factorization and shortcut methods. Recognize the relationship between LCM, HCF, and the product of the numbers.

Develop a strong foundation in number types. Familiarize yourself with different types of numbers, including integers, decimals, rational numbers, irrational numbers, and mixed fractions. Understand their properties and how they relate to each other.

10. Conquering Quantitative Aptitude: A Holistic Approach

Your battle for CAT would be won if you get a “YES I KNOW THIS PATTERN/LOGIC” reaction to 50–60% of the questions in your test.

Focus on process over perfection. Aim to develop a thorough understanding of the underlying concepts and problem-solving strategies, rather than striving for perfect knowledge of every topic. This approach allows you to adapt to unfamiliar questions and apply your knowledge creatively.

Develop confidence in your problem-solving processes. Cultivate the belief that if your process is correct, your answer will also be correct. This involves thoroughly reviewing your logic and identifying potential errors before checking the answer.

Embrace a learning mindset. Approach each question as an opportunity to learn and refine your understanding. Focus on clearly understanding the interpretation of each sentence and the underlying concepts, rather than simply memorizing formulas and procedures.

Last updated: April 3, 2025