Determining the second last digit and the last two digits

October 10th, 2020 by

Nike caused controversy with its advertising campaign during the 1996 Olympics by using the slogan, "You Don't Win Silver — You Lose Gold." Nike's use of this slogan drew harsh criticism from many former Olympic Silver medallists. In a way, it did undermine the importance of the second position but in Math things are often very different. Figuring out the second last digit is often tougher than figuring out the last digit. It is unlikely but definitely not impossible that in CAT you get a straightforward question that asks you to find out the second last digit of a number (abcpqr). In fe


Number System Concepts for CAT – Even Factors, Odd Factors, Sum of Factors

September 21st, 2020 by

let me first list down the topics that I am going to cover in this particular blogpost: Number of factors of a given number Number of even factors or odd factors of a given number Sum of all factors of a given number Sum of all even factors or odd factors of a given number   We know that a number N can be written as a product of its factors as given below   N = ap x bq x cr … Here a,b,c… are prime factors of N & p,q,r … are the powers of the prime factors of N.   In such a case the number of factors of N are given by the formula &


Divisibility Rules for CAT Quantitative Aptitude Preparation

September 19th, 2020 by

The concept of ‘divide and conquer’, derived from the Latin phrase ‘Divide et impera’, was put into use effectively by everyone from Caesar to Napoleon to The British in India. Even Gaddafi tried using the same but as current events show us – he wasn’t very effective. Dividing rather divisibility rules to be specific can come in really handy at times in solving problems based on Number Systems. The standard rules which nearly all of us are very comfortable with are the ones for 2n and 5n. For these all that one needs to do is look at the last ‘n’ digits of the number. If


Application of LCM (Lowest Common Multiple) in solving CAT Quantitative Aptitude Problems

August 25th, 2020 by

While most students are comfortable with the concept of HCF (Highest Common Factor) and LCM (Lowest Common Multiple), they somehow fail to apply it when required. Sometimes, they do not even realise that it needs to be applied. I sometimes feel sad when students ask me, “Sir, when to apply HCF and when to apply LCM?”. This question is a symbol of everything that is wrong with rote learning. HCF and LCM are concepts that students start learning as early as the 5th class in school (may be even earlier in some cases). The problem occurs because a few of them forget how the concepts need t


Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 2

July 27th, 2020 by

In the previous post we discussed lines, triangles, parallelograms, trapeziums, polygons etc. Now, we will discuss other expanses of geometry which are vital as, the questions on these topics are asked repeatedly in CAT. Let us look at few of the fundas / formulae on these topics that are often neglected by students and can fetch some crucial marks in the exam. Funda 1: Angle made by Secants       2 .   In both these cases, PA * PB = PC * PD   Funda 2: Common Tangents     eg: Note: The two centers


Geometry Fundas for CAT Quantitative Aptitude Preparation – Part 1

July 26th, 2020 by

I got a lot of feedback via emails and texts that people are looking for a post on geometry. I have been avoiding it for sometime because of two main reasons: a)      It is not one of my strong areas. b)      It takes a lot of time to draw the diagrams that are sometimes required to explain the fundas. The questions on geometry are the trickiest and consumes the maximum amount of time as compared to the questions on other topics in Quantitative aptitude that is why, I have compiled a list of fundas that you might find helpful in solving CAT level questions. I am splittin


Cyclicity of Remainders for CAT Exam

July 13th, 2020 by

Cyclicity of Remainders In this post I would like to discuss some of the really fundamental ideas that can be used to solve questions based on remainders. If you have just started your preparation for CAT Exam, you might find this article helpful. First of all, What I am trying to say above is that if you divide a^n by d, the remainder can be any value from 0 to d-1. Not only that, if you keep on increasing the value of ‘n’, you would notice that the remainders are cyclical in nature. What I am trying to say is that the pattern of remainders would repeat. Let me try to


Games and Tournaments for CAT Exam Logical Reasoning – Part 2

June 18th, 2020 by

In our previous post on games and tournaments part-1, we discussed about two of the popular types of questions when it comes to games and tournament questions. So, if you are looking for questions on new types of data representation or questions based on seeding in a tennis tournament, probably you should read that. However, there is another popular type of questions with respect to Games and Tournaments and that is – Football / Hockey tournament questions in which we have to find out Goals scores, winners, ties, etc. In such tournaments, all competitors play a fixed number of matches


Games and Tournaments for CAT Exam Logical Reasoning – Part 1

June 16th, 2020 by

In Logical Reasoning very often we encounter problems based on games and tournaments. The first thing that as a CAT taker you need to realize is that such tournament based format offers the examiner a multitude of options. So, there cannot be a set formula for solving such kind of questions. However, if you look at the CAT papers of past few years – a pattern seems to emerge. Let us discuss couple of them. Type 1: The questions are typically in a set where the data will be either in the standard tabular format or a format which you would never find on Cricinfo or for that matter any o


How to Find Number of Trailing Zeros in a Factorial or Product

June 12th, 2020 by

In this Number of trailing Zeros blog post, We would like to cover these two ideas: Number of trailing zeroes in a Product or Expression Number of trailing zeroes in a factorial (n!) But before I begin, let us first try to understand what exactly are ‘trailing zeroes’. It is nothing else but the number of zeroes at the end. I do not want to sound pedantic but on many occasions when you see a question which asks about, “What is the number of zeroes in ___” it is incorrect, because it should actually say – “What is the number of trailing zeroes?” or “What is the