This is a copy of the preface from the book on quantitative aptitude for CAT. The book can be bought on Flipkart here .
The CAT is a wonderful exam because it aims to create challenging questions based on simple frameworks. In recent years, the paper has become far tougher, but examiners have ensured that the syllabus is simple. This is an often-forgotten, but key, idea that should set the tone for your preparation.
To my mind, this gives us two key guidelines
- Learn from first principles to ensure that you do not ‘plateau’ out in some topics
- Do not bother with really tough questions; do not agonize over speed of computation
To have a preparation strategy that keeps these aspects in mind, I have followed some simple thumb-rules. I have adhered to these rules while building content; my advice would be for students to stick to it as well.
Ø Start from scratch (and then increase difficulty level slowly): The first few questions are beguilingly simple. The plan is to provide a framework for students to handle tougher questions. The most instructive way to learn is by discovering ideas. Every chapter is broken into theory, exercise and CAT-level questions. The idea is to provide a framework with simple questions and ‘push’ students to discover some thought processes while handling CAT-level questions.
Ø Focus on building the thought process, and less on getting answers: Let me illustrate with a simple example. There is a rule that goes like this – For a prime p greater than 3, p2 – 1 is always a multiple of 24. Many CAT aspirants might have seen this rule, but few might know the basis behind this rule. p2 -1 = (p -1) (p + 1). Now, if p is a prime > 3, p is odd. p-1 and p+1 are consecutive even numbers, which implies one of them will be a multiple of 4 and the other a multiple of 2. Or, (p-1) (p +1) will be a multiple of 8. Now, p-1, p, p+1 are three consecutive integers, implying that one of these has to be a multiple of 3. p is prime; so one of p -1 or p + 1 has to be a multiple of 3. This is why, p2 – 1 is a multiple of 24. If you have gone through this process and you see the next rule to be – If p is a prime > 3, p has to be of the form 6k + 1(where k is a natural number), it becomes far easier to establish.
The entire book is built on the premise that it is the ability to figure out newer frameworks that distinguishes the best from the merely good, not a vast knowledge base that comprises many frameworks. Almost every question in the book has detailed solutions; in some answers, we revisit key bits from the theory in order to build the thought process.
Ø Stay away from get-high-scores-quickly schemes: I have consciously stayed away from short-cuts and other over-simplifications to ensure a stubborn focus on fundamentals. Many guys who crack CAT will tell you that the exam is about speed and good time management. They are correct. However, the ‘speed’ that they refer to is the ease with which you can zone in on the best method for a particular question, not necessarily the speed at which you can plug in a shortcut. I have appeared for the CAT multiple times and I can assert that if you ‘pick’ the best method as soon as you read the question, you’ll be able to approach all questions with time to spare. So, work on building that clarity. Many a time, this quest for speed is a distraction. If your fundamentals are sound, you will have time to burn.
Ø Assess where you stand every now and then: Each topic ends with a set of CAT-level questions that acts as a benchmark for students. Innumerable books shoot either too low or too high when it comes to CAT preparation; I have taken enormous effort to ensure that CAT-level questions fall by and large into the band of difficulty that one is likely to encounter in the exam. If a student can confidently approach 80% of the questions in this category, he/she can be confident that this particular topic has been well covered. Barring the topic on combinatorics (where I have included a few tougher questions because learning by enumeration can be very instructive), almost every other question has been designed to be around the difficulty level one can expect in CAT.
I have made it a point to categorize questions into two levels of difficulty – Level 1 are questions that you should see in a CAT paper; Level 2 are those that you should skip in the first round. I have limited the classification to two because when faced with a question in CAT, the only decision a student has to take is ‘now or later?’. It is that simple. Also, to aid this decision-making, I have made it a point to provide the level of difficulty only in the solutions section, thus giving students practice in this decision-making.
Ø Prepare with intensity, but enjoy the process: CAT tests intensity and stamina as much as it does application. Completing a 140-minute exam without concentration ‘drops’ is not easy. It takes immense practice. So, set yourself targets of 20 or 25 minutes for intense preparation and build up from there. Contrary to popular perception, this is not an exam that one should prepare for eight hours a day. If you study with intensity, it is difficult to spend more than two-three hours a day on CAT preparation. And, if you can do two hours a day with intensity for 90- 100 days, you will be in great shape for the exam. Focus on intensity, not time. Intensity can be built up without a feeling of being burdened by it only if you enjoy this process at some level. Looked at differently, CAT preparation can be seen as being similar to solving Sudoku or math puzzles along with some general reading. If your attitude is correct, this can be a lot of fun.
What does the book provide?
There are 27 chapters in math, with each topic containing theory with solved examples, exercise questions and CAT-level questions. All questions have detailed solutions. The level of difficulty of the CAT-level questions is mentioned where solutions are provided. This is supplemented with CAT papers of 2006, 2007 and 2008 (with solutions provided for the first two). There are also three mock CAT papers for the Quant section, again with solutions provided for the first two.
I enjoyed creating the content for this book. Although a fairly arduous task, what started off as just another interesting project soon became a labor of love. I have a lot of fun when I am in a class or when interacting with students. I realized that my maiden venture as an author for a publishing house was also very enjoyable! It is my hope and expectation that students will find it useful and also fun. Mathematics is best understood when learnt with a certain sense of wonder and joy.
Finally, to the caveat emptor – notwithstanding the meticulous efforts undertaken by the team in putting together this book, it is possible that a few errors have crept in. Kindly bring it to our notice in case you notice any. This will help us improve our next edition. I can be reached at firstname.lastname@example.org
What does the book not provide?
I have always believed that it is crucial to know what is not in any book. This book provides a good framework and detailed thought process for a number of challenging questions. However, the book does not provide what I would call “The Grind”.
Students are expected to know the simple basics of the topics being covered. In case you feel like a particular topic is too complex, please look into NCERT class VI, VII or VIII text books and get an understanding of the fundamentals.
While learning some topics, we are more receptive of tougher ideas after we have internalized the simpler ones well and practiced plenty of questions on these. The pace of learning is determined by the amount of “Grind” required to be receptive to the next idea. As my mentor K S Baskar never tires of saying, each person should do the level of “Grind” required for him/her (and not get carried away with doing only as many as the best student in your peer group requires). So, if you feel like you require more practice of simpler questions before going to CAT-level questions, please suspend pride and pick up the NCERT class VI, VII or VIII books and have a go at them.
Best wishes for the CAT and other competitive exams.
I would like to convey my sincere thanks to my colleagues, who painstakingly reviewed most of the content. Special thanks are due to Shivaram (faculty at 2iim Chennai who is now off to IIM-A for his PGDM); Naveenan Ramachandran (IIM-A alumnus, who runs 2iim Mumbai); Vimal Gopinath (XIMB alumnus, who runs 2iim Bangalore); K.S. Baskar (IIMC alumnus, who is the founder of 2iim); Naveen (quant faculty at 2iim Chennai); and Mr. G R K Murthy (IIT Kanpur alumnus, who runs 2iim at Mylapore, Chennai).
I am grateful to Ranjini for her enormous help in formatting and verifying content. I am thankful to Mr. Periyathambi Srinivasan for ensuring that our office functioned smoothly enough when we were wholly occupied with the book.
I also acknowledge the contribution of Mr. Biju Kumar and his entire team at Access Publishing for the editing, proof-checking and general guidance they have provided. This has been invaluable.
Finally, I am indebted to Ms. Ranjeetha Shivakumar (alumnus of Great Lakes, Chennai) for verifying parts of the content. As the author’s better half, Ranjeetha had the unenviable task of having to get her hands dirty with what was not really in her comfort zone.