A very commonly asked question is about the relative importance given to different topics in the QA section of the CAT. The unpredictability of the CAT has been one of the reasons that make it difficult to bell.
The following chart shows us how much percent of the QA section of CAT 2004 to CAT 2008 was Arithmetic, Algebra, Geometry and Modern Maths.
Apart from the reducing importance of Arithmetic, no clear pattern emerges from this. More importantly, no topics can be completely ignored for your preparation.
Going into greater detail, it is possible to identify the concepts that are most important in CAT - going by the number of times that they have appeared from 2004 onwards.
Number Theory accounted for almost 26% of the 127 quant questions. Circles and Functions followed with 18% and 12% respectively.
Here is the complete list of concepts that appeared in these five years, along with the number of questions from that topic.
NOTE: A question that requires the application of more than one concept has been counted only once, under the central, primary concept area being tested. For instance, a question classified under the Number Theory concept could also require basic knowledge and application of percentages, averages and quadratic equations, but we count it only once, under the concept Number Theory. Or a functions question could test your knowledge of higher order algebraic equations or set theory.
Let's discuss the most important concepts:
Number Theory
Number Theory questions usually are based on classification of numbers (even-odd, prime-composite), HCF, LCM, divisibility, reversal of numbers, factorials, squares, cubes and base conversions.
Many of these questions can be solved by testing different sets of numbers to satisfy conditions or by plugging in values in options. Some others can be easily solved if you know divisibility rules for numbers like 2, 3, 4, 5, 8, 9, 11, 16 etc.
Having knowledge of the Fundamental Principle of Counting, applications of the Binomial theorem to divisibility problems and notations of Set theory will definitely help.
Remember that on the difficulty scale these questions rank very low, but practice alone can make you comfortable with these questions. Use the Skill Builder and the huge resource (72 questions) of Past CAT Questions in Number Systems and Number Theory for gaining confidence that you can handle this concept.
Circles
Here you need to apply basic formulae like area of circles, triangles, Pythagoras theorem, mid-point theorem and know the definitions and properties of tangents, chords and arcs. As mentioned earlier, there may be sub-concepts in a Circles question. Basics of geometry, triangles, coordinate geometry, and arithmetic and geometric progressions very often feature in these questions. More often than not, a fair amount of visualisation is important.
There are only a few fundamentals to master in plane geometry, but an endless variety of questions. CBSE/NCERT textbooks of standards VIII, IX and X are a great place to learn the basics and past CAT questions a great place to apply them.
Functions
This is probably the most feared concept. You should know how functions are represented analytically (algebraically) and graphically. Number theory, algebraic equations, inequalities and co-ordinate geometry are concepts that are generally required to answer these questions.
Functions have an uncanny knack of appearing difficult when they are absolutely not. Do not decide whether to attempt a Functions question based on how it appears at the first glance.
Time and Distance
Time × Speed = Distance
We learn this in the third standard. The faster you run, the faster you reach. The slower you run, more is the time you take to reach. If two trains run towards each other, they collide with each other faster than they would, if one was stationary and the other running. This is common sense, right? Well this is what Time and Distance questions in CAT are all about.
You need to understand the concept of relative speed very well. You should know what average speed means and if you understand variation well, Time and Distance questions will be a cakewalk for you.
Permutations and Combinations
This is one topic where most students falter, partly because it is generally taught in classes XI and XII, after which it is not really used, and partly because students have a preconception that this is a very tough topic. Well, Permutations and Combinations can be rated as the most entertaining concept, if you get the hang of it.
You can start with simple applications of the Fundamental Principle of counting, which you will find in any good text book and slowly graduate to solving relatively complex questions on permutations and combinations. Past CAT questions will give you an idea of what kind of questions you can expect in the exam.
Do not take the risk of neglecting this concept. As mentioned earlier, this concept is very frequently useful in Number Theory.
Sequences, Progressions and Series
This concept covers mainly two types of questions. One involves identifying sequences of numbers that do not follow any predefined patterns using logic and the other involves use of arithmetic, geometric and harmonic progressions. The application of this concept also features in Functions, Geometry, Number Theory, and Time and Distance.
As you go through the Past CAT questions you will see that there is hardly any topic that is completely absent. A single question may need an understanding of 3-4 different concepts. Therefore, not knowing one concept may put you at the risk of losing out on the choice of attempting a number of questions.
Hence, it is important to get the basics right across the concepts, and then focus on the ones that you know are important.
If you keep practicing new examples, you will master all fundamentals easily. The best way to learn is by doing, rather than learning by rote.
The following chart shows us how much percent of the QA section of CAT 2004 to CAT 2008 was Arithmetic, Algebra, Geometry and Modern Maths.
Apart from the reducing importance of Arithmetic, no clear pattern emerges from this. More importantly, no topics can be completely ignored for your preparation.
Going into greater detail, it is possible to identify the concepts that are most important in CAT - going by the number of times that they have appeared from 2004 onwards.
Number Theory accounted for almost 26% of the 127 quant questions. Circles and Functions followed with 18% and 12% respectively.
Here is the complete list of concepts that appeared in these five years, along with the number of questions from that topic.
| Concept | Percentage of Questions |
| Number Theory | 26 |
| Circles | 18 |
| Functions | 12 |
| Time and Distance | 10 |
| Permutations and Combinations | 10 |
| Sequences, Progressions and Series | 10 |
| Quadratic and Higher Order Equations | 8 |
| Linear Equations | 5 |
| Triangles | 4 |
| Inequalities | 3 |
| Logarithms | 3 |
| Mensuration | 3 |
| Sets | 3 |
| Algebraic Formulae and Operations | 2 |
| Co-ordinate Geometry | 2 |
| Quadrilaterals and Other Polygons | 2 |
| Surds and Indices | 1 |
| Averages | 1 |
| Mixtures and Alligation | 1 |
| Ratio and Proportion | 1 |
| Time and Work | 1 |
| Basics of Geometry | 1 |
NOTE: A question that requires the application of more than one concept has been counted only once, under the central, primary concept area being tested. For instance, a question classified under the Number Theory concept could also require basic knowledge and application of percentages, averages and quadratic equations, but we count it only once, under the concept Number Theory. Or a functions question could test your knowledge of higher order algebraic equations or set theory.
Let's discuss the most important concepts:
Number Theory
Number Theory questions usually are based on classification of numbers (even-odd, prime-composite), HCF, LCM, divisibility, reversal of numbers, factorials, squares, cubes and base conversions.
Many of these questions can be solved by testing different sets of numbers to satisfy conditions or by plugging in values in options. Some others can be easily solved if you know divisibility rules for numbers like 2, 3, 4, 5, 8, 9, 11, 16 etc.
Having knowledge of the Fundamental Principle of Counting, applications of the Binomial theorem to divisibility problems and notations of Set theory will definitely help.
Remember that on the difficulty scale these questions rank very low, but practice alone can make you comfortable with these questions. Use the Skill Builder and the huge resource (72 questions) of Past CAT Questions in Number Systems and Number Theory for gaining confidence that you can handle this concept.
Circles
Here you need to apply basic formulae like area of circles, triangles, Pythagoras theorem, mid-point theorem and know the definitions and properties of tangents, chords and arcs. As mentioned earlier, there may be sub-concepts in a Circles question. Basics of geometry, triangles, coordinate geometry, and arithmetic and geometric progressions very often feature in these questions. More often than not, a fair amount of visualisation is important.
There are only a few fundamentals to master in plane geometry, but an endless variety of questions. CBSE/NCERT textbooks of standards VIII, IX and X are a great place to learn the basics and past CAT questions a great place to apply them.
Functions
This is probably the most feared concept. You should know how functions are represented analytically (algebraically) and graphically. Number theory, algebraic equations, inequalities and co-ordinate geometry are concepts that are generally required to answer these questions.
Functions have an uncanny knack of appearing difficult when they are absolutely not. Do not decide whether to attempt a Functions question based on how it appears at the first glance.
Time and Distance
Time × Speed = Distance
We learn this in the third standard. The faster you run, the faster you reach. The slower you run, more is the time you take to reach. If two trains run towards each other, they collide with each other faster than they would, if one was stationary and the other running. This is common sense, right? Well this is what Time and Distance questions in CAT are all about.
You need to understand the concept of relative speed very well. You should know what average speed means and if you understand variation well, Time and Distance questions will be a cakewalk for you.
Permutations and Combinations
This is one topic where most students falter, partly because it is generally taught in classes XI and XII, after which it is not really used, and partly because students have a preconception that this is a very tough topic. Well, Permutations and Combinations can be rated as the most entertaining concept, if you get the hang of it.
You can start with simple applications of the Fundamental Principle of counting, which you will find in any good text book and slowly graduate to solving relatively complex questions on permutations and combinations. Past CAT questions will give you an idea of what kind of questions you can expect in the exam.
Do not take the risk of neglecting this concept. As mentioned earlier, this concept is very frequently useful in Number Theory.
Sequences, Progressions and Series
This concept covers mainly two types of questions. One involves identifying sequences of numbers that do not follow any predefined patterns using logic and the other involves use of arithmetic, geometric and harmonic progressions. The application of this concept also features in Functions, Geometry, Number Theory, and Time and Distance.
As you go through the Past CAT questions you will see that there is hardly any topic that is completely absent. A single question may need an understanding of 3-4 different concepts. Therefore, not knowing one concept may put you at the risk of losing out on the choice of attempting a number of questions.
Hence, it is important to get the basics right across the concepts, and then focus on the ones that you know are important.
If you keep practicing new examples, you will master all fundamentals easily. The best way to learn is by doing, rather than learning by rote.
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