Tackling Quant & DI section of CAT

Have you ever wondered how some people score consistently and comfortably in Quant/DI section of MBA exams? Irrespective of the difficulty level and the topic distribution they score well, like a gift. This article is based on the suggestions of some of the best quant minds I know (which includes Quant mentors and folks from top business schools). So here we go!
Conceptual clarity
Let’s take a quiz. How many of the below concepts/formula you are comfortable with
Finding the sum of even factors of a given number
Chinese remainder theorem
Componendo Dividendo
Rule of Alligation
Binomial theorem
n^{th} term of Harmonic progression
Appollonius theorem
Angle bisector theorem
Area of a regular hexagon
The sum of all interior angles for an nsided polygon
Ptolemey’s Theorem
Finding last digit & last two digits of an expression
Sum of the roots of the equation x^{2} + x + 1 = 0 = ???
If we cut a number into equal parts and then multiply those parts together. what size should each piece be for the answer to be as big as possible?
Rght most non zero digit of a factorialSo what’s your score ? This is just the tip of an iceberg. Make a list of all the major concepts/theorems which will be useful for CAT. Work on them until you have the confidence to teach them to any person using simple language without jargons. That’s when you are ready :)
A solid grip on the underlying theory will be very handy while organizing our thoughts while solving a problem. It will help us to connect the dots better and faster. This clarity is the shining armor of the quant knights out there. They clearly understand what is given and what is asked in a given question and most of them told it will take them around 15  30 seconds to connect the ends in a logical way. Lacking the conceptual clarity is also the main reason behind most of our mistakes. Like the ones we make while constructing geometric figures or while forming algebraic equation or while tackling questions that deal with patterns and arrangement. Build your theory before jumping into hectic practice sessions. Also think for 15 seconds before you solve any problem to check whether there are any traps or shortcuts hidden in the given details.
Cheat codes
Given enough time, most of us will score good marks in CAT. But sadly CAT is a time based test. We need to spend our time wisely. And short cuts will come handy here. They help us in saving time and also will protect us from logical errors (as many a times it is just substitution of values in a formula). Dig deep and find all the gems you can find in this area. Revise them regularly and make sure you practice them enough.
Some good ones below, (Thanks Ankan sengupta for the help :) )
Polya's theorem (coloring cube): The formula is (t^{6 }+ 3t^{4} + 12t^{3} + 8t^{2})/24
suppose you want to colour 6 faces of a cube by 2 colours. Put t = 2. Formula is valid up to 4 colorsZellar’s theorem (to find the day): F = K + [(13M  1)/5] + D + [D/4] + [C/4] – 2C
(where K is the date, M is the month code (March =1, April = 2, … Feb = 12), D is the last 2 digits of the year and C is the first 2 digits of century)
for 07/07/2014, K = 7, M = 5, D = 14, C = 20.
F = 7 + 12.x + 14 + 3.x + 5 – 40 = 41 – 40 = 1 (ignore the decimal values)
F = 1 corresponds to Monday, F=2 for Tuesday etc… and if F > 7, take F mod 7.
so 07/07/2014 was a monday.Profit % using false weights = (Claimed weight / Actual weight – 1 ) * 100
For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) and the maximum number of negative roots it can have is the number of sign changes in f(x)
Find the LEAST NUMBER which when divided by x, y and z leaves the remainders a, b and c respectively. It is always observed that (x – a) = (z – b) = (z – c) = K (say).
Required number = (L.C.M. of x, y and z) – K.Again, just the tip of another iceberg. There are many more awesome shortcuts that can save you lot of time (and will also make your preparation more fun)... Best way would be to make a team, split the topics between members and collect the cheat codes / concepts accordingly.. Collate all the gyan and you will have the complete theory you need for CAT in less than 10 days.
Practice… Practice… Practice
CAT wants you to apply your theory and short cuts under time pressure. If you don’t practice, you will choke during exam. It is as simple as that. For next 2 months, pick up any good study material and solve them. MBAtious has a collection of 630 Quant questions and 130 DS questions which are collected from previous CAT papers. Your peers have posted detailed solutions for most of them and you can (and should) also contribute your solutions. Trust me when I say, this collection will be of great help for your preparation in the last 2 months. Practice till you cannot get it wrong. Questions are categorized as set of 10 questions each. Even if you decide to solve one set per day you will need 2 full months for quant alone ;)
DI
There are 10 DI questions waiting for you in section 1. No theory, no formula… just scattered data from which you are asked to find some information. DI skills are easy to hone; Practice a lot. Also make sure you are not wasting time by doing unnecessary calculations. If you can solve using visual inspection, do that. If you can use approximation, use them. DI is your score booster in section 1. Make peace with it.
DI also goes with the same route.
Concepts : So are you thorough with percentage values and commonly used fractions ?
Cheat code : Line method, Approximation etc...
Practice : For DI also, we have a collection of previous CAT DI sets. Happy solving!
Give enough time for DI. It will fetch marks for you!
Relax!
These 2 months will overload your life with lot of stuffs like filling forms, attending mocks, analyzing your scores, revising the concepts and so on. Chances are high that your morale will go down; Peer pressure will be at its peak. It is important to keep your calm. Take regular breaks, have proper sleep and don’t forget food. Try to see CAT as something that holds the key to change your life for better rather than a Math/English test. Enjoy the process.
All the very best and happy learning.
Cheers!