# How To Crack Quantitative Aptitude- A Complete Guide

**Want to do MBA and get that package you were always earning for? Well now is the time to start preparing for it. CAT is a Common Admission Test exam that is required for you to be given.**

If you wish to be selected by the best MBA institutes you will have to earn a 99%ile in the exam. There are three subjects in all the exams.

**The first one is Verbal Ability Reading Comprehension (VARC), Data Interpretation Logical Reasoning (DILR), and lastly Quantitative Aptitude (QA). In this article, we are going to learn how you can crack Quantitative Aptitude and earn that 99%ile for yourself.**

Quantitative Aptitude is considered the toughest subject for students who are not from an engineering background. It’s easier for them as this subject is mostly based on Mathematics.

The engineers can crack it quicker than the rest of them. Don’t worry if you’re not from that background. With your knowledge, skills, and hard work, you will also crack this section.

All you have to do is remember and revise the basics of Mathematics we learned in school and college. It has also been seen that the students who are weak in this section can also gain a 99%ile with proper planning and strategy.

**Prepare QUANTS through IIM SKILLS Online CAT Coaching**

The marking system for this section a total of **34.**

The topics for Quantitative Aptitude are as follows:-

· Number System

· Averages

· LCM & HCF

· Percentages

· Speed, Time and Distance

· Profit, Loss, and Discount

· Simple Compound Interest

· Ratio & Proportion

· Linear and Quadratic Equations

· Sequences & Series

· Logarithm

· Binomial Theorem

· Set Theory

· Inequalities

· Mixtures and Allegations

· Probability

· Trigonometry

· Permutation and Combination

· Mensuration

· Surds and Indices

· Coordinate Geometry

Along with these topics here’s an overview of what you can expect from each topic and gain the marks you require.

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**Numbering System**

This topic is one of the easiest to solve. Students have the full opportunity to score the marks they have lost. For solving these questions you need a combination of mathematical knowledge and logical skills. It includes

- Digital root
- Prime numbers
- Divisibility rules
- Real numbers
- Unit’s digits
- Number of zeros
- Natural numbers
- Reminders
- Whole numbers.

TIPS to Remember

- Gets your basics straight, revise the rules and formulas that are required.
- Figure out the difference between all the numbers.
- Know all the prime numbers till 100, for the advanced topics like divisibility rules get them covered thoroughly.
- Practice the topics referring to what was asked in the previous years of the CAT exam

**Averages, LCM & HCF**

Averages are the sums that are intensive in calculations and tricky in nature. The formula for it is

**Averages = Sum of Observations/Number of Observations**

Usually, 1-2 questions are asked from this topic. The basics points you need to remember for Averages are these:-

- Averages are a set of numbers that you have to crack by calculations.
- The lowest number on the set always lies beneath the highest number on the set
- There are weighted average and average age sums to be solved.
- This is a standard approach and deviation approach to solve the sums.
- Keep this in mind whenever you increase or decrease a certain quantity/observation i.e Y, then the mean will also increase/decrease by the same quantity/observation i.e N.
- When the average of numbers i.e Y is multiplied by certain numbers then the outcome will also say that the mean is also multiplied by the same quantity ie N. ( Y x N)
- Same way when the average of numbers ie Y is divided by certain numbers then the mean is also divided by N to get a new average. (Y/N)
- The average numbers are added or subtracted ie Y then the numbers will also be added or subtracted by N to get the average that is required. (Y + N) (Y – N)

LCM (Lowest Common Factor) and HCF (Highest Common Factor) are the basics we were taught in school. Use the formulas and methods to solve the questions.

Figure out where you are supposed to apply LCM or HCF by practicing the questions in mock tests and past papers of the CAT exam.

**Speed, Time, and Distance**

Questions from these sections come from various areas like calculate the speed, distance, and time of races, train, bus, cyclist, swimming, and much more.

It covers relative time, average speed, total time, total distance. The formulas are easy but when to apply part gets a little tricky for the students.

Understand the question that is asked, read it thoroughly, apply the formula then go for the options. Remember these points:-

- When the Speed is constant, Distance is directly proportional to Time.
- When Distance is constant, Speed is inversely proportional to Time.

**Ratio & Proportion**

All 2-3 questions are asked in the exam from this section. It’s a basic concept which we all have learned in school and college. For example, if the cost of a laptop is Rs. 75,000 and the cost of a phone is Rs. 25,000.

Comparing the difference we understand that the difference is Rs. 50,000. When we divide them in ratios we get 75,000/25,000 = 3/1. So we can say that the cost of the laptop is 3 times more than a phone.

When we say two ratios are equal it means they are in proportion. Learn the formulas well, practice the test questions and paper. You will be all ready to crack this topic as it is quite easy.

**Linear and Quadratic Equations**

A standard equation is this **ax2+bx+c = 0, where a, b and c are known values. But if the value of a is 0 then it will become a linear equation. Then you have to decide whether it’s maxima or minima. **

**Usually, Maxima/Minima occurs at –b/2a **

**Maximum/minimum value is (4ac – b2) / 4a**

**Sequences & Series**

Sequences and series are some of the topics students love to solve. For those who have a knack for puzzles, this is a treat. This topic is vital in the exams. First, let’s learn the difference between Sequences and Series is all about.

This is called a sequence {1, 2, 4, 8, 16, 32, …}.

In this example, you see that every term doubles as it increases. It is also called an infinite sequence.

This is known as a series ¼ + 1/16 + 1/64 + 1/256 + …= 1/3

It is called an infinite series.

**Logarithm and Binomial Theorem **

Logarithm one of the simplest topic yet one of the most haunting ones for the students, as many of the students, don’t know where to apply it. They get all confused and fumble over them which causes them to lose marks.

A logarithm is ax = b, where x is the logarithm of b, it comes as a base and is written like log a b = x. Practice these sums and will get a hang of them soon.

As for the Binomial Theorem, its application is wide. Binomial means the sum or difference of two terms. The positive integer n is the index of binomial.

Some of the formulas are:-

· nC0 = 1

· nC1 = n

· nC2 = n (n – 1)/2

· nC3 = n (n – 1) (n – 2)/ 3!

They are Binomial Coefficients. They are the coefficients of the power x and y. The expansion is (x + y)n. These terms will remain the same depending on the positive-negative signs and the number being odd or even in the sum. The (n + 1) is the term for expansion.

**Set Theory **

A set is a group of objects that includes numbers, letters, colors. It’s written using braces and denoted with Capital Letters. Usually, students are comfortable when there are sets till 3 when it goes beyond that they start to get confused over it.

At least 2 sets are always asked, so you need to get a grip on the sets more than 3. Solve them focus and note down a number one by one keeping in mind you don’t miss any.

A Set Equality is termed when both Sets A and B are equal, meaning the same number of elements. They are written as (A = B).

A Null Set is an empty set that has no elements. You denote the Null Set as {}.

Then there is a union of sets A and B denoted as A U B.

The Intersection of Sets A and B is written as A ∩ B.

The difference in Sets A and B is denoted as A – B.

**Inequalities **

Inequalities do include LHS and RHS but they are not equal. Inequalities are of two types Linear and Quadratic. Basic rules to remember while solving the sums are as follows:-

§ Arithmetic Mean > = Geometric Mean for any set of +ve numbers.

§ Modulus functions are the magnitude of variable and not any sign |4| = 4, |-4| = 4.

§ Maximum and minima concepts deal with products and sum.

For this, you simply have to Equate the inequalities, then mark the Correct Option, and go for the next one. Avoid leaving any questions in this section.

**Probability**

Probability is one of the most painless topics for students. All they have to do is apply the required formula and see if their guess was right. Probability is a chance that a particular event might occur.

There is sample space, certain and impossible events, exhaustive events, mutually exclusive events, independent events.

**Trigonometry**

Trigonometry is a study of angular relationships with three-dimensional figures. It deals with the relationships between sides and angles of a triangle.

It is used to find out the unknown elements of a triangle, especially the ones that have a 90o angle. In trigonometry, you use the basics of the mensuration approach which defines the six trigonometric ratios in terms of angles.

Complimentary Angles are these

- Sin (90 – A) = cos A
- Cos (90 – A) = sin A
- Tan (90 – A) = cot A
- Cot (90 – A) = tan A
- Sec (90 – A) = cosec A
- Cosec (90 – A) = sec A

Identities

- sin2Ꝋ + cos2Ꝋ = 1
- tan2Ꝋ + 1 = sec2Ꝋ
- cot2Ꝋ + 1 = cosec2Ꝋ

Remember these important things and solve the questions accordingly.

**Mensuration**

This topic can be cracked by lots of practice and importantly being consistent in them. Remember the formulas and revise them regularly.

The topics in mensuration are cubes, cone, sphere, pyramid, cuboid, polygon, cylinder, frustum, prism, and more. Keep in mind the length, dimension of a cuboid/cube, slant surface/ frustum of a pyramid.

You can also solve these questions with the help of Symmetry. It makes the solving part a piece of cake for the students.

**Surds and Indices**

Surds are referred to as rational and irrational numbers, which are also called audible and inaudible. Surd is the root of a whole number. An index number is a number as it is raised to a power.

It tells you how many times you have to multiply the number by itself.

**Coordinate Geometry**

Coordinate Geometry uses graphs and coordinates to find measurements about geometric figures. You will encounter 2-3 questions on this topic. Coordinates are grinds that have their rows and columns labeled.

The equation of a line is Ax + By = C, then the slope-intercept forms y = MX + c where (c is y-intercept). The point-slope is y – y1 = m( x – x1) where (m is the slope of the line).

The two point formula is (y – y1) / (y2 – y1) = (x – x1) / (x2 – x1).

The last one is the intercept formula which is x / a + y / b = 1.

Practice as many questions as you can and make your base stronger.

Now that you have gotten an overview of the syllabus Quantitative Aptitude has to offer. Let’s move on to the part where we learn how to crack QA and secure good marks for ourselves. These are a few tips you can follow:-

**Don’t Skip Any Topic **

Students tend to talk with friends and trying to analyze by looking at past papers. All that hustle for trying to guess which topics could come in the exam.

So they could skip a topic they find difficult to deal with. Since the topics are vast and the questions are limited to 2-3 it allows the students to gamble among the topics.

I would suggest NO skipping any topic because you might never know which ones they would suddenly decide to include. You could lose marks if you take this kind of risk.

Imagine getting a child’s play question from Permutation from which you could easily obtain your 3 marks. Then realizing the fact that you skipped that topic because you felt it was a complicated topic or not a vital one in your eyes.

It will make a huge impact on your negative marking system. Thus, resulting in an effect on your final percentile. Before you see the question paper in the exam you can’t predict where you will get a simple question.

Be comfortable with every topic, practice them with sheer focus and determination. Cover your basics, understand the topics, get the concepts right, rectify your mistakes in the mock tests.

Solve as many as papers possible in the period of time given. Get proper guidance from your tutors, the online classes you attend. Prepare every topic thoroughly and will surely obtain the marks you acquire in this section with ease.

**Consistence Practice**

Practice is what is going to make you perfect in every topic. Without that, of course, you don’t stand a chance to clear any exam.

Every student practices yet they don’t seem to achieve the marks they desire. Why? Because they are not consistent in their practice, solving questions for 2-3 days is not going to you anywhere.

You need to work hard every day to achieve the marks you aspire for.

Solve sums every day even if it’s an hour a day. Don’t break the habit or else it will be difficult to get back on it. I understand things can get a little monotonous after while switching up the topics, try a different way, but don’t give up and hang in there.

Correct the mistakes you make in these practice questions. Make sure you don’t repeat it twice.

**Making the timetable**

Make sure you give at least 2 weeks to one subject. Start with basics then move to the advanced topics. You still have a lot of time to work on all areas.

Keep an aim to devote at least 2-3 hours per subject in a day. As the portion is vast you will need to study more to cover it all in time for your exams.

**Study Material **

A lot of study material is available in the market for CAT exams. From books to question banks, preparation books, sample question papers are available in the market and online stores.

Getting the right study material is crucial for clearing your exams with good grades. The papers that you solve will tell you what your weaknesses and strengths are. The books that are well known for Quantitative Aptitude:-

How to Prepare for Quantitative Aptitude for CAT and Teach Yourself Quantitative Aptitude by Arun Sharma

The book How to Prepare for Quantitative Aptitude contains comprehensive theory as per the latest theory and syllabus. Covers, all the past papers for CAT. Tips and techniques for solving sums quickly.

The other book Teach Yourself Quantitative Aptitude is known as one of the best books for this section. It contains past papers, questions. The entire syllabus is comprised of elaborately lucid language.

Quantitative Aptitude for Competitive Examinations by R.S. Aggarwal

The book has been revised by the author many times to keep it updated for every student. It includes more than 5500 questions including past CAT exams. With its simple language, it’s a good book for every CAT aspirant.

Quantitative Aptitude Quantum CAT by Sarvesh K. Verma

This book is a guide to all CAT aspirants. With over 300 concepts and over 400 solved questions, it allows you to practice thoroughly for the CAT exam.

It has shortcut tips and techniques, an analytical approach, and an inspirational approach to crack the exam with a good percent.

Wiley’s Quantitative Aptitude Book by P.A. Anand

This book is not only a recommended one for Quantitative Aptitude but it also serves as a guide for the banking sector, civil services. A collection of questions, and past papers to help prepare you for the exam in a systematic manner.

**Mock Tests**

These form a huge part of your way to a good percentile in the CAT exam. The tests will show you a mirror image of where you stand on this journey of your exams. Which areas you need to work on, look out for the mistakes you make, mark your key areas.

Start with solving 1-2 tests a week as per the topics you have finished at the start. Then gradually move on to 3-4 tests a week to make a better grip on the syllabus you have covered.

As this topic is based on Mathematics, students are bound to make silly mistakes during calculations or as simple as forgetting to put a negative sign.

Read the questions with full focus and understand it to not make any mistakes. See what is asked in the question, do your calculations, and will get your correct answers in the options provided below.

**Group Study or a Lone Warrior**

A lot of students are always debating whether they should study alone or in a group. The choice is entirely up to you. You could sit at home alone and learn online with peace. Then you could solve mock tests with your friends and compare which questions you got wrong.

This all brings a sense of competition among the students and also provides a friendly environment for the students to study without getting bored.

You could prepare better, discuss your problems, solve questions together and help each other in the topic you are weak in.

But if you lose your concentration in a split second by the tiniest thing then a group study could prove to be a dangerous idea for you. Chose wisely what is good for you, just don’t lose focus on the goals you aim for.

**Study Online**

Technology is increased to a level where you can now learn from the best teachers by sitting in the comfort of your homes. Make a schedule, decide a time that’s perfect for you and start learning.

Going and coming from coaching classes disrupts your time more than you can imagine. You could ask your doubts there and then by emailing the concerned professor or any other information that is provided by them.

And get your queries solved in a nick of time. Take advantage of the facilities available to you and focus on your preparation easily.

**Curb the Distractions**

Although with advanced technology we can do things on the tip of our fingers it has also become a big distraction for the students. Our generation’s half of the day, are consumed by WhatsApp forwards and Facebook posts. These are the biggest hurdles a CAT aspirant has to get past them.

More than that the continuous notifications to the curiosity as to who has completed how much also consumes a lot of your valuable time. The vital thing to understand is we don’t need to know who has prepared how much we just need to focus on our share of studies.

Fake news and Whatsapp forwards become common during exam times. It could add a lot of pressure along with the stress you already have.

Students panic over this data start referring to things said or written in the article. Instead of actually, focusing on the topics that are of more importance. Try to stay away from such news for the sake of your sanity.

Don’t fall prey to such news until it is announced by the actual university, don’t take it seriously. Remain calm and watch out for these things.

**Some Tips for you to score a 99%ile in the QA section**

- Prepare a strategy that works the best for you, according to your strengths and weakness.
- Attempt minimum questions but chose the ones you know the right answers to.
- Learn to increase your accuracy day by day to gain your aim.
- Memorizing is not always necessarily what you have to do is understand the concepts instead of blankly mugging them up.
- Keep a time constraint for yourself when you are solving mock tests and papers, it will help you solve your paper in the exam on time.
- Solving mock tests and past papers is the key to securing that 99%ile.
- Seek the help of experts in time of need, they will guide you.
- Stick to the books from which have studied from the start, don’t go around studying from new books in the end.
- You can study rigorously for 3-4 hours a day and it will be enough.
- Make sure to shut off all the distractions before you open your books to study.
- In the end, HARD WORK is the key to cracking every exam.
- Take care of your health and sleep well.

ALL THE BEST for your Exams, ace them with confidence.

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