Must-Do Topics for CAT Quantitative Aptitude
Key topics in QA for CAT are:
Arithmetic: Percentage, Profit and Loss, Simple interest and compound interest, Time and Speed, Time and Work, Average and Mixture, Ratio and Partnership
Number System: HCF and LCM, divisibility rules, Factors, Trailing zeros
Algebra: Linear equations, quadratic equations, functions, polynomials, inequality, Logarithm, surds and Indices, Sequence and Series
Geometry and Mensuration: Triangles, Quadrilaterals, Circles, Polygons, Area and perimeter of 2 D figures, Area and Volume of 3 D figures, Coordinate Geometry
Modern Maths: Permutation and Combinations, Probability
Top 10 Important Topics for CAT QA
As per the previous year’s analysis, top 10 important topics and their key strategies for CAT Quantitative Aptitude are as follows:
1. Percentage and its application in profit and loss, SI and CI
Key Strategies:
(i). Learn the percentage to fractions conversion to solve the questions quickly.
For Ex: 33.33% of a number is calculated by dividing the number by 3. i.e. Fraction of 33.33% is 1/3.
(ii). Understand the key concepts of percentage change and successive change.
(iii). Solve Conceptually rather than using formulas.
(iv). Learn to apply the concept of percentages in the questions of profit and loss, SI and CI.
(v). Practice different kinds of problems.
2. Time, Speed, and Distance
Key Strategies:
(i). Divide questions in the categories of proportionality, Average Speed and Relative Speed.
(ii). Average Speed = $\frac {2S_1S_2}{S_1 + S_2}$
If distances covered with both speeds is same.
(iii). Use the concept of relative speed in solving the questions on Trains.
(iv). Conversion of speeds in appropriate should be done.
(v). Divide questions topic wise and practice different problems based on CAT Previous years questions.
3. Time and work
Key Strategies:
(i). Total work cab be taken as LCM of time taken by all the individuals.
(ii). Dividing questions concept wise may help in preparation.
(iii). Applying the concepts of time and work in the questions of Pipes and Cistern are solved by using the concept of time and work.
(iv). Use the concept of ratio to solve the questions on time and work.
4. Average and Mixtures
Key Strategies:
(i). At the initial stage of preparation, try to solve at-least 4 to 5 questions on averages and mixtures to check your understanding about the concept.
(ii). Learn the basic concept of average, weighted average, rule of allegation and concept of replacements.
(ii). Start with basic questions. (Probably level of difficulty 1)
(iv). After solving basic questions, learn some tricks and special cases to solve the problems quickly.
(v). Start to solve difficult problems from the books which are suggested in this article.
5. Equations and Inequality
Key Strategies:
(i). Use Elimination method by making coefficient of one variable equal in two equations.
(ii). Learn the rules for nature of solutions/roots.
(iii). Try to solve linear equations graphically.
(iv). In case of quadratic equations, check for feasibility of solutions.
(v). Learn important concepts of inequality such as
If -a > -b, then a < b.
If -a < -b, then a > b.
If a > b and c < 0 then ac < bc.
If a > b and c > d then a + c > b + d.
6. Functions
Key Strategies:
(i). Understand all types of functions and their related graphs to solve the questions based on functions effectively.
(ii). Learn the concept of composite Functions
It is function of some other function.
$ (g \circ f)(x) = g [f(x)] $
$ (f \circ g)(x) = f [g(x)] $
(iii). Understand the concept of Domain and Range:
Domain: Set of input values and represented on x-axis of the graph.
Range: Set of output values and represented on y-axis of the graph.
(iv) Practice questions of functions involving modulus function.
7. Logarithm
Key Strategies:
(i). Learn important properties of logarithm are as:
$\log_a (xy) = \log_a x + \log_a y$
$\log_a \left(\frac{x}{y}\right) = \log_a x - \log_a y$
$\log_a (x^n) = n \log_a x$
$\log_a \left( x^{m/n} \right) = \frac{m}{n} \log_a x$
$\log_a x = \frac{1}{\log_x a}$ (Base Change Operation)
$\log_a a = 1$
$\log_a 1 = 0$
$a^{\log_a x} = x$
(ii). Some common mistakes done by students while applying properties of logarithms which should be avoided:
$\log_a (x + y) \neq \log_a x + \log_a y$
$\log_a (xy) \neq (\log_a x)(\log_a y)$
(iii). Apply the concept of logarithm in questions where the number of digits is asked.
For example: find the number of digits in $2^{12}$
$\log 2^{12} = 12 \log 2 = 12 \times 0.3010 = 3.612$
Therefore, the number of digits in $2^{12}$ will be $(3 + 1) = 4$
8. Geometry and Mensuration
Key Strategies:
(i). Learn important properties of triangles such as Similarity, congruency, geometrical centres, sine rule, exterior angle property etc.
(ii). Learn to apply the formula of area of triangle in different scenarios.
(iii). Memorize Pythagoras triplets.
(iv). Learn important properties related to quadrilaterals and in what circumstances the properties are applied.
(v). Practice questions based on exterior and interior angle of regular polygons.
(vi). Practice questions on chords, tangents and secants, sectors and segments.
(vii). Understand difference between 2-D and 3-D figures.
(viii). Memorize all the formulas related to surface area and volume.
(ix). Use method of symmetry to solve the questions related to geometry and mensuration.
(x). Practice questions on coordinate geometry. Concept of symmetry plays an important role in solving the questions on coordinate geometry.
9. Sequence and Series
Key Strategies:
(i). Learn to apply the formula to find $n^{th}$ term and sum of $n$ terms.
(ii). Use some specific tricks such as
An AP of odd number of terms is to be assumed as
…, $a - 2d$, $a - d$, $a$, $a + d$, $a + 2d$, … [common difference $d$]
An AP of even number of terms is to be assumed as
…, $a - 3d$, $a - d$, $a + d$, $a + 3d$, … [common difference $2d$]
A GP of odd number of terms is to be assumed as
…, $\frac{a}{r}$, $a$, $ar$, … [common ratio $r$]
A GP of even number of terms is to be assumed as
…, $\frac{a}{r^3}$, $\frac{a}{r}$, $ar$, $ar^3$, … [common ratio $r^2$]
AM $\times$ HM = GM$^2$
AM $\geq$ GM $\geq$ HM
(iii). Practice Previous Years Questions to get an idea of questions.
10. Permutation and Combination
Key Strategies:
(i). Learn the concept of factorial.
(ii). Understand the conceptual clarity of permutations and combinations. You should be very clear about the uses of permutations and combinations in questions.
(iii). You can use following tricks and formulas
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The number of permutations of $n$ distinct items taking $r$ items at a time is
$nP_r = \frac{n!}{(n-r)!}$
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$nP_n = n!$
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$nC_r = nC_{n-r}$
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Out of $n$ given things, the number of ways of selecting any number = $2^n - 1$.
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Dividing $n$ items into two groups of $p$ and $q$ items = $\frac{n!}{q! , p!}$
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If $p = q$ and two groups are not identical; the number of groups will be $\frac{n!}{{p!}^2}$
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If $p = q$ and two groups are identical; number of groups will be $\frac{n! , 2!}{{p!}^2}$.
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The number of diagonals in an $n$-sided regular polygon $= \binom{n}{2} - n$
(iv). Divide questions of distributions in following categories while solving:
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Identical Objects Identical Places
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Identical Objects Distinct Places
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Distinct Objects Identical Places
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Distinct Objects Distinct Places
(v). Solve questions conceptually rather than using formulas.
Why Trigonometry is essential for CAT QA
Although the direct questions from trigonometry are rarely asked, it is very crucial for CAT QA. It is essential because
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You may find questions in geometry where the trigonometric ratios are required.
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It is required in the questions of height and distance.
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Trigonometric ratios are required in the questions of sector and segment, area using sine rule.
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Trigonometric ratios are useful for quick calculations.
How to Approach These Topics
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Developing Conceptual Strength: A strong knowledge of application of basic concepts to be developed.
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Rigorous Practice on daily basis: Include practice sessions on QA in study plan on daily basis build speed and accuracy.
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High-Weightage Topics first: As per the analysis of CAT previous years question papers focus on topics which constitutes highest weightage.
