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Strategy For Quants

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If you ask the CAT aspirants "Which section of CAT do you think as your weakest section?" more than 85% of them have the same answer: Quant. Quant or Quantitative aptitude as it is generally known has been a nightmare for the majority of the students irrespective of their educational background.

Lets try to understand the reasons behind this. If we look at the type of people writing CAT they are majorly final year graduates or people working for one year or more.

Since CAT is open for all types of educational backgrounds graduates with backgrounds like Arts or Commerce are those who have not done maths for the last 3 - 4 years. And surely a fear about the subject has remained in them right from their school days. So though the syllabus remains to be in the fundamentals of class Xth or XIth level but a change in the approach makes it a whole new learning.

On the other hand students from science background and even engineering have never done any calculation without using a calculator. Throughout their graduation days and beyond they have done even two digit additions with a calculator. So when they find themselves in a situation where calculator is not allowed and u have to do big and bad looking calculations they find themselves lost out. The biggest danger students normally face is that they tend to give up on this section - fallaciously believing that they stand no chance in this area.

Ok dear CAT aspirant let me ask a simple question. The syllabus and the knowledge level required in Quants is surely that of class Xth or XIth right? Then why is that a class tenth boy not eligible to write CAT? Why is that graduation is the minimum criteria for admission in B schools? Don't you think that if knowledge required is same we should actually allow people to become managers right after there Xth class or school?

Bingo! You have got the answer perfectly right. We need a slightly matured head on the shoulders to join as a manager in the big bad corporate world. And surely so are you compared to that kid.

Know what I am driving to? Simple I am just saying we have to deal with quants in a slightly matured manner and not the way a kid does. So throw away that fear and tie your seat belts tight. You have nothing to fear but the fear itself!

Tactics for tackling the QA area of the CAT paper

Solving the QA section in two rounds
One of the best ways of solving the QA section of the CAT paper is by taking sections in two rounds. If we have allocated 37 minutes for a 50- marks section, then dividing the 37 minutes into two parts of 24 minutes and 13 minutes duration will help solve the problems better.

In the first round of 24 minutes each question should be read and it should be checked whether the same can be answered within one to one-and-a-half minutes or not. If so, then we should proceed to solve it and mark the answer or else just leave it and go to the next question. This way we are spending time only on those questions which are direct formula based or direct application of a concept or which are very easy and familiar and can solved by back calculation and numerical substitution.

One point worth mentioning out here. There will be some questions in this 24 minutes which seemed pretty straight forward when you started but soon you understand that it has got more twists than you anticipated. So what do you do if you have already spent two minutes on it?

Don't think. Just leave it and go forward. Please never forget your aim is not to solve the best question in the paper, your aim is to solve as many questions as possible. So forget that special one, lookout for easier ones. Remember you might have a very colorful dish in front of you but that does not mean you continue eating it once you understand that its not edible.

What you ensure in this process is by the 24th minute we should have looked at all the questions in that section, solved all the sitters and enroute had left a mark on all those which you thought were moderately difficult or worth giving a second try. What has automatically happened is you have also recognized those questions which you would not like to solve at all and so do not waste time again when you come back to solve the remaining questions. This way you must have attempted at least 10 - 12 questions in the first round itself.

Now you are left with somewhere around 12 - 13 minutes. You already know your 10 - 15 target questions so attack. Here again make sure you are leaving out those questions where even after 30 - 45 seconds of effort, you do not appear to to be getting anywhere near an answer.

Using this method, we can ensure that we are attempting around 20 - 22 questions in the paper at least. If the questions contain both from 1 marks and 2 marks section what we are talking about is an attempt for around 25 - 27 marks. Assuming an accuracy rate of 80% a person attempting this much should get a net score of 17-18 and if you could do slightly better accuracy even 20 -22.

Dividing the paper into sets
This is another method by which you can ensure that very easy question is solved and the return on time invested is maximized. Lets assume that there are 50 questions and same 37 minutes to solve the questions. Our objective is to that by the end of he section we should have identified and solved all the easy questions as well as ensure that we maximize the output.

First divide the section into 5 different sets of 10 questions each( if there are 35 questions with differential marking we can go with 5 sections of 7 each and so on). Now since we have around 37 minutes we can have around 7 minutes for each of these mini sections. The same procedure that we have applied in the last strategy can also be applied here. Since the frame of reference is only 10 questions now, it is almost impossible to miss out any of the easy questions. In effect, one can ensure that even if there are only three or four or even two in some of those 5 sets, they can be solved with high level of accuracy. We are also not under the pressure to do all the 50 questions at a time.

It should be borne in mind that when you are considering only a small set of questions, the pressure or tension is much less and you may be land up solving most of those 10 questions. Once the first 7 minutes are over ,then its very important that you break free form the you first set and move to he next. There is no rule or statistics which the first 10 questions are easy then next 10 will be difficult or vice versa. Infact our study says in CAT easy questions are distributed throughout like peals in a jungle. Hence the benefits of this tactics will be evident, only when after first 7 minutes are over, you go to the next set and then again after 7 minutes to the next and so on.

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We can clearly see the advantages now. Assuming you need 20 - 30 seconds to read a question mathematically you should be able to read and attempt atleast 4 - 5 out of those 10 questions but with now a higher degree of accuracy. Which means at the end of those 37 minutes you have an attempt of around 20 - 22 and a score of not less than 18.

Back Substitution/ Numerical Substitution/Mental calculation

These are three very potent methods of solving questions in QA. There are quite a number of questions in the CAT paper of the last ten years where, instead of solving the question in the traditional equation solving way, a simple substitution of the answer choices would have given you an instant answer. There are also cases where the problems involve variables and we have to prove the validity of the expression. In such cases, the best method of solving them would be assume values like 0, 1, 2, etc for each of the variables given and substitute these in the expression. More often than not, this method will yield correct results in the fastest possible speed. Also by simply doing some mental maths a huge of time of writing down equations can be saved.

For what type of questions should I use these methods?

Let's take two simple examples from some recent CAT papers to illustrate what I just said.

CAT 2004:
If a man cycles at 10km/hr, then he arrives at a certain place at 1 pm. If he cycles at 15 km/hr, he will arrive at the same place at 11 am. At what speed should he cycle to reach there at noon?

1. 11 km/hr 2.12 km/hr 3. 13 km/hr 4. 14km/hr

Solution:
Since at 10 km/hr he reaches at 1 pm and at 15 km/hr he reaches at 11 am therefore to reach at exactly mid of this time period he has adopt the average of the two speeds. Average of speeds is Harmonic Mean and so it has to be less than the Arithmetic Mean of the two speeds (i.e. 12.5 km/hr).

It's anybody's guess that average speed of 10 km/hr and 15 km/hr having covered the same distance cannot be 11 km/hr and so answer is 12 km/hr.

Even if you want to avoid any iota of doubt finding out HM of 10 and 15 is hardly 10 seconds job.

CAT 2000:
This question was thought to be difficult and highly mathematical and left out by many students.

Directions: For three distinct real numbers x, y, z let

f(x, y, z) = min(max(x,y),max(y,z),max(z,))
g(x, y, z) = max(min(x,y),min(y,z),min(z,x))
h(x, y, z) = max(max(x,y),max(y,z),max(z,x))
j(x, y, z) = min(min(x,y), min(y,z),min(z,x))
m(x, y, z) = max(x,y,z)
n(x,y,z) = min(x,y,z)

Q1. Which one of the following is necessarily greater than 1?

1.(h(x,y,z) - f(x,y,z)) / j(x,y,z)
2.j(x,y,z)/h(x,y,z)
3.f(x,y,z)/g(x,y,z)
4.(f(x,y,z) + h(x,y,z) - g(x,y,z))/ j(x,y,z)

The above question can be solved in the traditional mathematical way. But a much simpler way is take some easy to handle values of x, y and z.

Without loss of generality let us take x = 1, y = 2 and z= 3. If we put these values in the given expressions we get f = 2, g = 2, h= 3 , j = 1, m= 3 , n = 1.

Substituting these in the four choices yield

1. = 1
2. = 1/3
3. = 1
4. = 3

Thus its clear that 4th is the right answer. In fact in CAT 2000 there were 3 questions given from the same set and simple numerical substitution like above could have helped solve the whole set in less than 2 minutes. Many students however lost these opportunity.

The best thing about the QA section is that you do not need too many marks in this section to clear the cutoff. If you look at the last three or four years paper the cutoff for IIMs will be in the range of 9 to 14 based on varying difficulty levels and may be even lower for other institutes that use CAT. So do not set unrealistic targets for yourself and then panic when you do not achieve them. If a thorough analysis of the paper is done there are always 15 - 20 problems which can be solved easily and 10 to 15 which are of moderate difficulty. Hence the entire endeavour is to to pick and choose those easy questions and avoid spending too much time on any single question.

Just a last word. It seems that number of questions has been concistently decreasing in CAT and time has been increased to 2.5 hours. Though the time may remain same but number of questions is never a guarantee. As such prepare for anything and do not go to write CAT with mindsets. Remember getting adapted to the change is the rule of the game.

So cheer up and go solving. Remember, we need not be mathematicians we only need to be CATs.

(T.I.M.E.)