While the previous three posts on Accuracy, Selection, and Speed are more than comprehensive in terms of what is needed to push your score north, I still keep getting messages from students who are unable to come to terms with QA. They say they have done concepts and enough practice as well but none of it seems to be pushing the scores up and the confidence levels are pretty low.

It was only a few years ago, that I figured out the core issue with these students when I was sitting with one — he was preparing for the GMAT and had a decent amount of work-ex and by the time I had met him he was already through with two attempts spread over two years with sub-par scores. He was willing to put in another attempt and a year more if required to get a par score.

I gave him some broad guidelines and assigned a personal mentor to him, and met with him regularly on overall prep strategy, some specific pointers, and test-taking strategies. But at the end of another year the score was the same.

I could not figure it out — the guy was very professional, super-committed (something you would have figured by now), doing reasonably well in his job, and super-positive despite everything.

It was when he came to meet me again that I threw a few questions at him, questions that I had solved in class and he had attended multiple times, and his reaction to them and the way he reacted when I told him the solution — Oh, ya, ya, ya, ya! — that I figured the core problem — he was mugging up Math!

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Do you learn Math the same way you did for your X & XII exams?

This I realise is a bigger problem than what is assumed. Students whose only interaction with Math has been for their X and XII exams, who have never prepared for an aptitude test before, and took extensive tuitions for their school exams, do not even know that the Math they did then and Math they have to do now is the same but the way it is tested cannot be more different.

Those papers needed parrots, parrots who could replicate things step by step and with good handwriting.

And nothing could be more different from that than a CAT paper.

So ask yourself that question, do you mug-up concepts or do you actually understand why a^x.a^y = a^x+y

If you do memorise and have always done so then you need to really start from scratch and it is not easy and you will definitely need to do approach it more holistically.

I suggest doing this free course by Barbara Oakley — she had a BA in literature and worked in the defence services before taking up engineering later than others — https://www.coursera.org/learn/learning-how-to-learn

Read this book by her as well — A Mind for Numbers

Another thing to keep in mind is that even if you somehow mug stuff up, get a bit lucky, and manage to get into an IIM, the first-year course will be as tough, if not tougher than CAT Math — you will be graded relative to others and the others is everybody who has cracked the CAT (the only reprieve is that time is not a constraint). A lot of the students who are unable to complete the MBA Program or finish it over a longer period — would have failed in the first-year Math subjects.

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Do you know basic concepts but have no clue how advanced concepts came about?

Do you know how the formula for the number of total factors of a number — a^m.bⁿ — (m+1)(n+1) — came about?

Those who know how this came about will know how to solve this question discussed in Part-II of this series:

How many factors of 1080000 are not divisible by 40?

I am sure there are many who know the formula but yet not know how to answer the question. If they happen to read the solution they wonder why it did not strike them.

It need not be that you have this issue in the whole of QA. It can be that you have this problem only in some areas — Numbers and Geometry or Geometry and Modern Math. — or only on specific topics such as P&C and Logarithms.

If you are in this bucket then you need to focus on understanding how formulas came about so that you develop the ability to solve such questions.

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Do you try to memorise patterns?

The last category is test-takers who are good at Math but their approach to prep is to memorise as many different patterns and endless sub-formulas (formulas derived for an endless list of special cases) as possible.

The problem with the approach is that whenever they are faced with a problem the first instinct to try to map it to a formula or a pattern they have solved before.

It is not that there are no patterns, there are patterns and in recent years CAT has become more pattern-based than before. But all that needs to happen is for 8-10 problems that do not fall into a pattern but are otherwise solvable to appear in the paper and these test-takers will not be able to handle them. If a few of these problems turn up at the beginning of the section then the confidence can take a major hit.

Another issue with mugging patterns is that you need to keep a lot of your brain space free for all of these patterns and sub-formulas. Those who have exceptional storage and memory between their ears can afford to follow this approach. I prefer to have only the bare minimum of formulas and patterns in my head and go by pure logic — the lower the fuel in the car the faster it can go. I think the golden mean between the two where you know the patterns but are willing to look at a problem first up with fresh eyes is crucial.

Always visualise yourself in front a problem as a doctor faced with a patient. What does a great doctor do? Listen to you fully, ask the right questions; suggest the right tests, if required; figure out the exact problem; and suggest the least medication possible.

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The different kinds of mugging listed above are reasons behind you truly not solving a problem.

If you are truly honest with yourself about this part of your prep then you will be able to make the changes necessary to achieve a good score on QA and as I mentioned before it is not just CAT QA that is on the line but also Quant in the MBA Program.

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You need to always start with the WHAT and move to the HOW

Some students have written saying that when they try to not copy-paste patterns they find that their mind is blank and they do not know what to do.

Imagine a F1 driver going to drive on relatively unknown tracks every time he goes out to drive — the key word is “relatively” not completely unknown. He or she will draw upon the experiences but still drive as if it were new.

It is exactly like sport, you practice in the nets but every pitch, every match, every ball is different.

This is exactly what makes the Big 3 matches in tennis so interesting, they have played each other million times but they know that every match can be won by either of them. this despite knowing everything inside out.

And what is different?

Each and every time the questions asked of them by their opponent will be different.

WHAT is being asked is different.

If Nadal is hitting the ball closer to the lines, Djoker knows he is being asked a different question and he knows that has to find a response in real-time while drawing on the past.

If Federer is just creaming winners off the forehand then Nadal knows he is being asked a different question.

The first task always is to figure out the WHAT and the move to the HOW instead of thinking about the HOW.

When students say nothing strikes them it is because they are thinking that the HOW will come and strike them. Nothing strikes you if you are not looking for it, except lightning!

Let us take a question to see what I mean by figuring out the WHAT and moving to the HOW.

Question 1

If all the factors of 5040 are arranged in descending order then which will be the fifth factor?

We know that the greatest factor of the number is the number itself — 5040.

WHAT — But we need to factorise this first since we need to find the top 5 factors.

HOW — 5040 – 2⁴*3²*5*7

WHAT — If this is the highest one then what is the one after this?

HOW — I need to remove the smallest possible factor from this?

What is the smallest possible factor that I can remove? 2

So, the next factor in descending order will be 2³*3²*5*7

For the third one, we remove a 3 — 2⁴*3¹*5*7

For the fourth one, we remove a 4 — 2²*3²*5*7

For the fifth one, we remove a 5 — 2⁴*3²*7 — which is what the question is asking us for.

What if the question is tweaked?

Question 2

If all the factors of 5040 are arranged in ascending order then which one will be the 56^th factor?

When I read this with fresh eyes, I know that this seems crazy, am I really supposed to write all the factors from 1 to 55? Surely, you must be joking Mr.Question-man!

There must be another way — they won’t be paying an average salary of Rs.25 LPA at IIM-A for someone to do such donkey work!

WHAT — Before I go ahead I need to know how many factors are there and where does 55 stand?

HOW — To find out the number of factors I need to factorise the number

5040 – 2⁴*3²*5*7

The number of factors — what you will know from all your of previous practice — 5*3*3*2 — 60

There are 60 factors and they are asking me for the 55^th, so, instead of going from 1 to 56 I can come down from 60 to 56.

From here the problem becomes the same as the previous one.

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For some this might be a huge change since you have to undo all your previous mode of dealing with Math, for others it might turn on a switch that they never thought they had, but for everyone there is no other way.

The weird part is that even those who have made it to the IITs do not seem to get this. I had a student from IIT-Ropar in one of my GMAT classes and he was like — you must know all the patterns by now, so you can answer all questions!

It is like saying Kohli knows to play all shots, so every time he goes out he will make a 100! It does not work that way.

Yes, teaching helps, but every teacher does not get a 100 every year in QA right?

On good exams, one gets rewarded for thinking nor regurgitating!

So, stop mugging, start solving!