In the run up to CAT, there are a lot of aspects that one needs to keep in mind. Five well-known, but often overlooked aspects of improving your problem solving skills in Quantitative aptitude are provided here with live examples of how to use some of them in a typical CAT scenario.

A. Judicious choice of questions

i) You need to choose questions that give you maximum marks in the given time. Ideally, you should attempt questions from the areas that you are more comfortable with. Also, do not try to evaluate the difficulty of a question without reading it completely.

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For instance, CAT 2007 had a number of questions which were relatively simple and which should have been attempted. A lot of test takers avoided them because they appeared difficult at a cursory glance. In the current CAT scenario where you have more time per question, you can afford to give a good look at all the questions before freezing in on the questions to be attempted. Consider it time invested, not wasted. A lot of test takers miss a call from the IIMs because they are penny wise, pound foolish.

ii) Consider this: if you had a 100 per cent accuracy rate, you needed to attempt only 50 per cent of the CAT 2007 paper in order to get a call from an IIM. This means the average time per question you had was four minutes. Even with an accuracy rate of 80 per cent, the average time per question you had was just under three minutes. Remember, haste makes waste.

B. Prioritising topics according to their weightage in CAT

Though it is difficult to say which topics are important from the CAT point of view, we can always draw some conclusions from the past CATs. If you closely examine the previous CATs, you would see that Number Theory, Data Sufficiency, Functions, Circles, Permutations and Combinations, Sequences and Series, Time, Speed and Distance were some of the important topics.

Topics like Probability, Profit and Loss, Clocks, Interest and Growth rates seemed to be of lesser importance. It pays to spend most of your time honing your skills in these important topics in the run up to CAT 2008.

C. Intelligent guessing

Though it is advisable not to guess, it probably can be done in a smart way. When you are able to narrow down the answer to two options, the laws of probability state that it pays off to mark one of the options.

D. Substitution to simplify

There are many ways in which you can use substitution in order to cut down the time taken to solve questions, especially with options which have variables. Here you may substitute the variables with values to arrive at the answer. Sometimes, the options are values of the variable(s) in the question.

Consider this question from CAT 2007:

Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.

Option A: Invest in a public sector bank. It promises a return of +0.10%

Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of -3%

Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of -2.5%, while a fall will entail a return of +2%

1. The maximum guaranteed return to Shabnam is:

(1) 0.25%              (2)0.10%                     (3) 0.20%         (4) 0.15%              (5) 0.30%

2. What strategy will maximize the guaranteed return to Shabnam?

(1) 100% in A            (2) 36% in B and 64% in C                (3)64% in B and 36% in C                                           

(4) 1/3 in each of the three options                                     (5) 30% in A, 32% in B and 38% in C

Solution:

One way to solve this question is by the rigorous long drawn method.
An effective way is to substitute the values given in the options for the second question.

Consider option 3. When Shabnam would invest 64% in B and 36% in C the return she would get in the case of rise in the stock market would be 64 x 0.05 + 36 x (-0.025) = 2.3%. Similarly the return in case of fall would be 64 x (-0.03) + 36 x (0.02) =  -1.2%. In this way we can calculate the returns in the cases of fall and rise for all the options and construct the following table.

Now the guaranteed return in a case is the minimum of the two returns in the case of rise and fall (for example in option 4, the guaranteed return is -3.3 %). From this table one can deduce that the maximum guaranteed return is highest in case of the second option and is 0.2%. Hence the correct answer is option 2.

Once the second question is solved, the answer to the first question is also determined = 0.20%, and hence the right answer is option 3.

E. Learning Formulae and tables

This is what is called sticking to the basics. You can substantially cut down on your time by using formulae and you still have time to master them, if you haven't already. This is especially helpful in geometry questions. In an actual exam environment it takes a lot of time to work out the solutions, if you do not know the formulae. The same can be said about tables. Consider this question from CAT 2006.

A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting its circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semi-circle (in sq. cm.) will be:

1. 32TT                                  2. 50TT              3. 40.5TT                      

4. 4. 81TT                               5. Cannot be determined

Solution

In this question, we can use the property AC x BC = CD2. From this relation we get BC = 18 cm. From this we get the diameter as 20 cm and hence the area of the semi-circle as 50TT which is option 2. The relevant formula is all that one needed in order to solve this question. God lies in the details. So does an IIM call.

Good luck!

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