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CAT 2019: How to improve your QA percentile – Part III

In the previous two posts, we took a look at the first two building blocks to increase your score and percentile on CAT Quant — Accuracy & Question Selection. In this post, we will look at the third building block — Speed.

Increasing your speed by at least 2x is a function of changing three things in the way you execute a solution:

  • increasing your number-crunching muscle
  • reducing your dependence on writing extensively
  • viewing problems through an alternative lens

Increase your number-crunching muscle

Find (1² + 3² + 4² + 5² + 7² + 8² + 9² + 11² + 12² + 13² + 15² + 16² +…….49²) / 1249  if it is an integer.  (TITA)

This is a question from a SimCAT and most people would have let the question go. Upon reading the solution, they would have become doubly sure that it was a good leave.

But as we have often seen in T20 cricket, guys with huge reach and immense power can send balls, which can be potential dot balls to other batsmen, sailing into the crowd.

I decided to take on the above problem using some number0crunching muscle

Firstly, I knew that this numerator was the sum of the first 49 squares minus the even squares— we just need to substitute n = 49 in the formula, n(n+1)(2n+1) /6 and minus the sum of the missing squares.

49*50*99/6 can be reduced to 49*25*33 which can be approximated to be 50*25*33 = 1250*33 = 12*3 = 36 so a value greater than 36000, also this has to end in a 5 since it is 49*25*33.

If I ignore the values that need to be subtracted — the even squares — and look at the denominator 1249, I know the answer has to be 35 since the value is greater than 36000 and has to end in a 5, 1249 has to be multiplied by a number ending in 5 to get a value ending in 5.

But the catch is that some values are missing from the sum of squares, which I promptly listed:

2² + 6² + 10² + 14² + 18² + 22² + 26² + 30² + 34² + 38² + 42² + 46²

We can quickly estimate the last digit of the sum of these terms — 4,6,0,6,4,4,6,0,6,4,4,6 — 0, so even after subtracting the value has to end in 5 and hence the answer has to end in 5, so if without subtracting it is 35, then after subtracting it has to be 25, 15 or 5.

I set about quickly estimating the value of the above terms by starting from the right end since the squares of the larger number will make up most of the value and the smaller ones can be effectively ignored.

I am writing the approximation as I processed it mentally:

  • 42² + 46² = Two 40s, more than 1600, 1600, so around 3500
  • 30² + 34² + 38² = Three 30s = more than 1000, 1000, 1000 = around 3500
  • 22² + 26² = 400, 600 = more than 1000
  • 2² + 6² + 10² + 14² + 18² = less than 1000

So from a value greater than 36000 I need to subtract around 10000 so it will be around 26000 and hence value greater than 26000 ending in 5 when divided by 1249, to give an integer, has to yield 25 since 12*2 = 24 and 12*3 = 36

Thinking is always faster than writing so the actual time that I took for this crunching process was under 2 minutes.

Given that the CAT is a test of speed, what matters is not knowing how to solve but how quickly you can reach from knowing how to solve to the final answer.

This can only happen if you have some serious number-crunching muscle — extensive conceptual clarity cannot compensate for this muscle. You need to ask your self

  • when the clock is ticking and you are executing a solution, can you break the numbers down or will you buckle under their load?

If your answer is sometimes I can crack, sometimes I buckle or most often I buckle, then you are not yet in shape to take the CAT. But you have three months to build some serious muscle by memorizing all of these:

  • all squares from 2 to 30
  • all cubes from 2 to 12
  • all powers of 2 from 1 to 12
  • all powers of 3 from 1 to 6
  • all fraction and equivalent percentages from 1/2 to 1/11
  • tables from 2*10 to 20*10

Most of you want to do an MBA so that you can do high-quality, high-paying work. If that is the case then you should approach the 180 minutes of the CAT in a such a way that we do only quality work during the 180 minutes of the test.

  • Do you want to be calculating 29², if it is the answer to a TITA question?
  • Do you want to be calculating the value of 2 raised to 8 by starting with 2 raised to 5 in the middle of a problem?

All of these values should already be fed into and so deeply embedded in the system, that there is no gap between retrieving and executing the solution.

In short, you need to be the calculating-equivalent of a T20 big-hitting beast.


Reduce your dependence on writing extensively

A few years back a student came to have a chat with me, he was retaking the CAT and needed a plan. He said he was really good at Math but could not solve more than 22 problems on CAT 2016, which as you know had an easy and hence high-scoring QA. He was working with a good firm and had a good profile and was thus looking at premier schools that needed high percentiles.

My first instinct was to give him a piece of paper and a problem just to watch how he solved it. He wrote down around 10 steps on the paper and solved the problem and that was the exact reason why he was only able to attempt 22 questions.

Writing and executing the entire solution of a problem is the biggest speed-breaker or decelerator in front of you. Each one of you will have varying degrees of dependence on writing. Sometimes, the more diligent the aspirant, the more steps he or she will write (systematically and without clutter) while solving a question.

The problem is that this method will result in fewer than 15 attempts in 60 minutes and when coupled with a few mistakes will end up in a percentile that is perennially hovering in the 85 range.

So if you are among those who write diligently then you need to drastically change your approach to increase your percentiles and understand than

  • you are used to writing because you are used to submitting homework
  • you are used to writing because missing steps can mean fewer marks being awarded
  • you are used to writing neatly because so far good, clutter-free writing fetched you higher marks

None of the things listed above applies to CAT Math — just like none of the rules of test cricket applies to T20 — no marks for handwriting, no marks for steps

How do you decrease the amount of writing you do? Start with the following steps

  • do not duplicate information from the screen on to your rough sheet
    • a man does a piece of work in 20 days, then do not write 20 or t = 20 on your paper, you are just executing robot-like steps without getting any closer to solving the problem
  • do not write what you need to execute
    • if you need to calculate the average of five numbers then there is no way you are writing 5 numbers with plus sign and then drawing a line underneath them and writing a five; you need to just get adding and dividing without writing anything
  • start skipping writing down steps by executing intermediate steps mentally
    • if you have to solve 1/(x+1)  + 1/(x+2) = 2, then maybe the next step you should write is 2x + 3 = 2x² + 6x + 4

In short, write only if you cannot process the information in your head!

This is a question in one of this year’s SimCATs that I solved purely mentally when an aspirant who is working with us in the content team came to me and asked me to solve a  paper live to see how I approach a section to learn selection and speed.

The function F is defined as F(k) = 2k³ – 3k² – 5k + 7 and the function G is defined as G(k) = 2k³ + 1k² + 7k + 15. Find the product of all values of ‘k’ for which F(k) and G(k) are equal.

I knew that I had to equate the two since that is when they will become equal, the cubes cancel themselves out and if I take the remaining terms to one side, it becomes a quadratic with 4,12, and 8, which gets reduced to 1,3, and, 2, whose roots will be 1 and 2, making their product 2. This took about 60 seconds or fewer mentally.

Even if you take more time, the key is that there is no need to write. Some of you might say that if I do it this way, I’ll be making mistakes, it is like saying if I drive faster I will crash, but then you won’t win the race — it is about driving the fastest you can with control.

This is easier said than done though since we have been conditioned over years to equate writing with thinking and solving, so like the legendary dog of Pavlov, we start writing the moment we start reading a problem.

To practice the above steps consciously you should try a few special practice sessions.

  • Take a section test or an area test or the Quant section of a take-home SimCAT with your hands folded or your palms locked in front of you.
  • Have a pen and paper handy on the table to write only if the need arises
  • Force yourself to execute a few steps mentally
  • Do not be bothered about time running out, do not be bothered about the score

If you do not try out these things during practice you will keep doing the same thing over and over again and keep expecting different results, which alas is a non-sequitor (CR enthusiasts should check what this means).


Viewing problems through an alternate lens

The above heading might seem as if there is a standard lens and there is an alternate lens. In fact, nothing could be farther from the truth. What always matters is the most optimal solution to a problem. Why do we not find the optimal solution?

Reject the formula-first approach

Our gut reaction to solving a problem is to try to immediately fit it to a formula. In fact, when faced with a question we immediately ask ourselves — what formula do I know that can help me solve this.

A formula is only one of the tools that you will use to reach the solution that you have devised; they are similar to a surgeon’s or a mechanic’s tools. A surgeon does not decide on the kind of surgery to be done based on the tools he has, neither does mechanic decide on how he is going to fix a vehicle based on the tool he has!

So do not make formula-fitting your first step.

Do not algebraify a problem by force

If we do not go to a formula, we start taking the first thing we encounter as X and we try to form an equation.

We feel that if we can convert English into Algebra, we have done our job but Algebra is just another language like English. What you have to convert it into is logical language, which can still be in English but uses words or Algebra that uses symbols.

Do not convert all problems into Algebra, especially the Arithmetic ones.

Move to the question first approach

Put the question and what is finally asked in the question as the first and most important thing. Work backward from there to determine what you really need instead of trying to build towards the answer from the first bits of information.

Do not treat the given information passively

On most good questions, the given information itself holds more than meets the eye, provided you are willing to at least turn it over in your palm to see a small latch that you can pull.

If you take it just the way it is and do not try to even squeeze a wee bit or cut it then a lemon is as good or bad as a stone or softball (in fact not even as good as those).

The methods we know of are a function of the teachers we have had

We are more or less a function of what we have been taught and made to do; there are always a very small few who can see things by themselves but there are a great many who can do much better than what they if someone points the way.

How many really high-quality teachers have we had (and I do not mean by good because of their nature; I will prefer a horrible person who teaches stuff with fresh eyes to a good human being who teaches stuff in the most mundane of ways; there a few who combine the best qualities of the two types and I have had the pleasure of knowing two of them) ?

I started looking at problems differently after I encountered my colleague pulling off some amazing solutions (go through all of them); it did not feel like it was way above my league since it was more a question of approach and attitude rather than some genius intuition (which he does have) because it was something that was easily understood.

I figured that it was more about my ability to let go of my conditioned responses and less about my ability to find alternate solutions.

To find a new road, you have to first get off the old one!

 

 

 

 

 

 

 

 

 

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12 Comments

  1. Hello Sir,

    I have a query regarding work experience while filling the CAT form.

    Currently, I am working in my own registered partnership firm.
    I have been Working on the startup since my graduation i.e July 2018
    But got it officially registered in June 2019.
    So what should I do while filling up the work experience details??
    And also what official documents do I have to present later in order to prove the same??
    I have currently Partnership Deed, Shop act licence and company PAN.

    Like

    • Hi Divyanshu,

      You can show work-ex only from the date of official registration since that is the only thing that you can prove on paper.

      The documents you mentioned above should suffice. If there are any details about the Financial transactions of the company such as bank statements and stuff, they should come in handy as well.

      Hope this clarifies,

      All the best!

      Like

      • Sir, I have contacted IMS support regarding the same.
        They are saying I can mention the work experience from July 2018(when I started work) as the start date.

        I am getting really confused and worry that my form may get canceled at the time of admission if I fill this wrong.
        Please kindly help me with this…

        I am coping the transcript of the Email I have received from IMS support.

        Dear Student,

        Thank you for writing to us.

        “You can mention July 2018 (when you started work) as the start date.

        The mentioned documents should be enough. If you are withdrawing any remuneration, bank statements would help (but not mandatory)”

        Please feel free to revert to this mail for any further assistance required.

        You can also call us at IMS Head Office(Mumbai) between Monday to Friday from 10 am to 6 pm on 022-66170000 (Extn: 218/219) for any help.

        Do mention your Permanent IMS Number (PIN) for all the future communications with us.

        Warm Regards,
        Student Convenience Team
        IMS Corporate Office – Mumbai

        Like

      • Hi Divyanshu,

        Firstly, your application will not be cancelled at the time of admission!

        The process is that at the time of the interview, they will check your documents, to see if the details you mentioned in the CAT form are corroborated by marks lists and employment letters. In the case of self-employed individuals or start-ups, it is always a grey area since in India partnerships need not be registered. So you can put in 2018, it will not cause any problem other than the questions they will ask you at the time of verification and during the interview. If they deem your case genuine, which seems to be the case, then there should not be any problem, which seems to be the case. So you can go ahead and enter 2018 (I had mentioned 2019 just be on the safer side but in that case, you will not be getting any marks for work-ex.

        Hope this clarifies,

        All the best!

        Like

  2. Gaurav says

    Again a supercalifragilisticexpialidocious post sir in the Quant row! The points you mentioned are very relatable with the common conundrum. Hoping a similar post for LRDI section as well .

    Like

  3. Sanya Mehta says

    Hi Sir,
    Despite giving SIMCATs regularly, I am not able to get more than 5 questions net correct in quant. How should I proceed further?
    And how should I now study for Quant to get good percentile considering that now I am short on time.
    Thank You

    Like

    • Hi Sanya,

      I hope you have read the other two posts in the series, especially the first post. If yes, then based on the post, you need to figure out where the problem lies with respect to accuracy. If that is the main problem is not accuracy but attempts then it can be due to one of three things: selecting the wrong questions, which is covered in the second post, one of speed, which is addressed in this post, or a much bigger problem — not knowing enough concepts to attempt more questions.

      So till you are able to diagnose the problem, it will be impossible for me to give you a generic plan to say do this for the next three months and your problem will be sorted.

      Also, please understand that this is not at all like a school or college exam, so the first managerial ability you will need to demonstrate is to identify where you are going wrong since you know what you are doing better than anyone else. If you are unable to do this by yourself, please fix up a one-on-one myPLAN session with your mentor (if you are an IMS student).

      Hope this clarifies,

      All the best!

      Like

  4. Jaiyant Gopal says

    Hi sir,

    Thank you for your great posts, they really help a lot. I have a doubt, for PnC and Probability is it that a preparation in the level of IITJEE is required or the basics is enough? Though not being an IITian myself , I can see in the level of toughness in the questions that I faced during my IIT prep in PnC is way higher than for CAT. Should I look into IIT coaching lectures for these topics or should I just solve the CAT materials.

    And, the yoga and meditation tips that you gave in another post on how to prepare for CAT while doing a job are really working out well and I feel a lot of difference after following them up. Thanks for that sir.

    Thank you.

    Like

    • Hi Jayant,
      Glad you find the blog useful and that it helped you navigate your prep well.

      For the two areas you mentioned, you do not need to go to the JEE books, the CAT that way has become pretty mild, there were no questions on probability last year and barely any in the last few years.

      The best resource would be cat100percentile.com. Go through the tag list on the right hand side and look at the posts related to PnC, Probability, and Partitioning, those should more than suffice.

      All the best!

      Like

  5. thank you sir for such an excellent article on quants it addressed all my worries except one, I am not able to do geometry no matter how much I try I have read all theories and formulas from different sources maybe 5 times and have also solved problems but there is a kind of phobia which just doesn’t go whenever I see a geometry based problem in Simcats first thought which comes to mind is to leave and thus even after scoring good in other sections percentile in quants is not increasing thereby reducing overall performance.How should I tackle this?

    thank you

    Like

    • Hi Abhi,

      Glad you liked the article.

      As you rightly figured, unless you crack Geometry your scores are not going to improve. Last year, there were about 6-7 easy and medium questions on Geometry.

      Many monsoons ago, even I had a similar problem but my bugbear was Modern Math, functions, in particular, I would not even glance at a problem that had f(x).

      But when I did not make it the first time, I told myself that there is no way around things I do not like.

      The first thing I did was approach questions from areas I did not like not as academic subjects but as puzzles. I told myself that just like chess has certain rules, each game/puzzle has certain rules, knowing the rules in itself does not make one a great chess player one needs to play the game.

      In your head, Geometry is 50-60 formulas that you cannot remember, it is something abstract. But we are using Geometry indirectly all the time, intuitively taking particular angles when we drive, recognising something is close to perfect circle or not without really measuring it, we also see how tiles of different kinds fit into each other on the floor etc.

      You need to thus see Geometry as the symmetry hidden in nature and the symmetry made by man to build things, the most important one — a house!

      Treat Geometry as a visual puzzle.

      Spend one full-week doing only Geometry but not mugging up the formulas but learning the derivations starting from lines angles triangles.

      Try to use your visual intuition to grasp a few rules.

      Let’s take a small example.

      Imagine two sticks of equal length. Imagine them parallel to each other horizontally. Imagine breaking (not separating, say the way you would break a broomstick or a twig) the stick on top into two parts of unequal or equal length. Now bend the stick at the breaking point trying to form a triangle with the stick on the bottom as the base. Will you be able to touch the end-points of the stick at the top to those of the stick at the bottom.

      You will see that the end-points of the stick at the top will land inside the end-points of the stick at the bottom. The only way you can make the ends touch is if the stick at the top is longer. You break the longer stick and you can me the end-points touch. This is nothing but sum of two sides of a triangle should always be greater than the third side.

      Only after you learn the derivation of each formula will you get better at Geometry since I am sure you do not remember anything from school.

      And what phobias are we talking about, the only thing you need to fear is death if it appears all of a sudden an unexpectedly.

      Most of our other phobias are stories we tell ourselves, there is no logical reason for someone to be afraid of Geometry.

      Hope this helps,

      All the best!

      Like

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