CAT: focus areas for Quant
The Quantitative Aptitude (QA) section in the CAT draws upon theory learnt in school up to Class XII, so it is theory that every one of us has learnt at some point of time or the other. Therefore, there is absolutely no need to pick up textbooks with advanced engineering mathematics to crack Quant in the computer-based CAT. Textbooks I would recommend for theory are the NCERT for Class IX to XII, and a personal favourite of mine -- Higher Algebra by Hall and Knight. All of these are very reasonably priced.
The most important part of preparation for QA in CBT-CAT is practice tests. I would recommend taking every mock test as seriously as the real CAT. Time yourself for every test that you take and have a target time in which you have to finish the test. For engineering students or students currently in college who may be familiar with the theory, it is okay to start off with tests immediately. However, for working professionals who may be out of touch with academics, I would recommend taking at least a couple of weeks to look at some of the formulae and theorems that you will require for your CBT-CAT.
Start off with topic tests in the initial stage of preparation. When you gain confidence in several topics, it is time to start taking a couple of full-length QA tests. After you have gained confidence in QA, merge individual sectional tests and start taking CAT-type full length test papers containing all three sections. Always analyse your performance with the help of detailed personalised reports after every test you take and use the mock tests as a valuable feedback mechanism. If you feel the need, keep going back to topics which you feel require more work and take one or two more area-specific tests in that topic. An important thing you need to work on is the judicious selection of questions. Utilise practice tests for this purpose.
Most importantly, try and ensure that you do not have more than one really weak topic which you wish to avoid, as you never know which areas the CAT will test you on. It is okay to have one dodgy area, but you will still be taking a risk, and need to be that much better in the other topics. Therefore, I would recommend working hard in every area, so that you have the luxury of having all the questions to select from on the day of CAT.
Quantitative Aptitude for CBT-CAT can be broadly divided under three main heads:
Geometry, coordinate geometry and mensuration
I have grouped these topics together since they deal with the portion of QA that can be visualised. Of the three, maximum weightage is given to geometry, although every CAT paper will have three or four questions on mensuration, as well as a couple of questions on coordinate geometry, totalling about 25-30 per cent of questions in the QA section.
Topics that need to be covered in geometry are basic theorems involving triangles, circles and parallel lines. A common type of question that is often asked in CAT is to find the value of certain angles or length of certain sides. Therefore, make sure that you cover topics such as congruency and similarity of triangles.
The only things that you need to do in coordinate geometry are straight lines and circles. Don't go into conic sections and other advanced topics. More importantly, do not try and solve IIT-JEE level questions in coordinate geometry. Given the equation of a circle, you should be able to comment on the centre and radius of the circle and draw it on a piece of graph paper, and nothing more. Similarly, you should know what the slope and y-intercept of a given straight line equation is, and be able to draw the line on a piece of graph paper.
For mensuration, flip through a school-level textbook for basic formulae on areas, surface areas and volumes of triangles, circles, cylinders, cones, cuboids and spheres. Mensuration problems are calculation-intensive, and require lots of practice, especially this year as you no longer have the luxury of doing calculations just next to the questions on the computer screen.
NCERT textbooks will suffice for this head.
Algebra and Number Theory
Algebra and number theory provide the major chunk of questions in any CAT QA section -- 55-60 per cent. Topics that you need to look at are Permutations and Combinations, Probability (very basic, including die and card problems and perhaps Bayes' theorem), Functions, Progressions (AP, GP, HP and AGP), Logarithms, Equations (Quadratic and Linear/Simultaneous) and, most importantly, Number Theory.
Number theory problems are usually very simple, if you know how to do them. They require certain tricks that you can pick up from any good textbook. Having said that, number theory contributes three or four questions to every CAT, and so it is a very important topic. You should be comfortable solving numbers in their algebraic form (eg a three-digit number having digits xyz can be represented as 100x + 10y + z). You should also learn about divisibility tests and the 'modulo' notation and its applications (for programmers, 10%5=0 is also referred to as 10 modulo 5 is 0, that is, the remainder when 10 is divided by 5, is zero).
A textbook I would recommend for algebra and number theory is Higher Algebra by Hall and Knight, which is available at any bookstore that sells textbooks for IIT-JEE.
Arithmetic and miscellaneous
About 15-20 per cent of the questions in previous CATs came from this head and I will be very surprised if the trend does not continue in the CBT-CAT. Major topics that you need to cover are Set Theory (especially Venn diagrams) and problems on Time, Speed and Distance, both of which are always asked. Both of these topics are covered as part of the school syllabus, but may need some brushing up. Sometimes, questions on topics such as Linear Programming are also asked. An NCERT textbook is enough to study from for this head.
Miscellaneous problems are those problems that do not fall under any head. They are rarely asked, and even when they do appear in CAT, they do not number more than one or two. They are purely tests of mathematical aptitude, and you cannot learn how to solve them. The only advice I can give for dealing with these problems is to try back-substitution of answer choices, or to avoid these problems altogether.
An area that had a high concentration of questions in CAT 2007 was Data Sufficiency. Data Sufficiency problems can come from any of the three heads, and are in the form of a question followed by two statements. You need to answer whether you can solve the problem using the statements individually, or using both, or whether you cannot solve the problem using the information provided. The key to answering such problems is to pretend as if one statement does not exist, and then try and solve the problem, then pretend as if the other statement does not exist and try and solve the problem again. These problems are generally tricky, and I would recommend lots of practice and perhaps solving them near the end of your QA section, after you have solved the other problems.
Although there is absolutely no substitute for knowing your theory, and practice, in the QA section, there are some question-solving strategies that you may use. They are:
~ Substitution of numbers for variables in algebraic problems, which may make the problem simpler. Remember, however, that this usually does not work when the answer choices are also in terms of variables.
~ Back-substitution of answers into the problem in order to solve it, ie assume one of the answer choices to be the answer and then solve the problem. If the problem cannot be solved or reduces to the trivial case, repeat for another answer choice until you stumble on the correct answer choice.
~ Substituting variables for numbers in the answer choices. This usually works for progression problems. Let's say the nth term of a progression is given in terms of n and some other terms. You are then asked to find the 100th term in the progression. The answer choices are of the form 2100, 299 -- 1 etc (for instance). Then, you can start with the first answer choice, assume that the nth term will be 2n, solve the first few terms of the progression and find if this is indeed the case (let's say it's easy calculating the 3rd term, which you find to be 8 or 23. Hence the 100th term will be 2100). If it is not, assume that the nth term is 2n-1 -- 1 and repeat, until you get to the correct answer choice.
~ Solving coordinate geometry algebraically, or vice versa. Often a complicated algebra problem involving several equations can be solved very easily if you draw the corresponding figures on an imaginary graph paper. Similarly, coordinate geometry problems can often be solved by writing corresponding algebraic equations. Always remember the correspondence between algebra and coordinate geometry.
~ If you can eliminate all options except two, guess. The CAT rewards educated guessing. Look at it this way: if you have two questions, probability states that you will get one of these wrong and the other right. The expected number of marks you will get is +4 and -1, which translates to +3 for both the questions combined, or +1.5 per question answered. If you do this for a significant number of questions, unless you are exceptionally unlucky, the benefits of not wasting time solving every problem completely will far outweigh the loss of marks due to some incorrect answers.
To summarise, the most important part of your QA preparation is PRACTICE. The theory is not too tough, so practice as much as you can. QA has been an area where students have done well in the last two CATs, so you should look at it as an area where you can also improve your overall score in the CBT-CAT.
source: rediff
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