Ratio and Proportion – Concepts, Properties, and CAT Questions

April 20th, 2019 by

Ratio and Proportions is one of the easiest concepts in CAT. It is just an extension of high school mathematics. Questions from this concept are mostly asked in conjunction with other concepts like similar triangles, mixtures and allegations. Hence fundamentals of this concept are important not just from a stand-alone perspective, but also to answer questions from other concepts 1.  Ratio (Concepts and Properties) Many a times we compare two data values of the same type. One way to do this is to find out the difference (a-b). Other method of comparison could be by division or finding ou

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Pipes and Cisterns (Concepts, Properties and CAT Questions)

April 17th, 2019 by

A pipe is connected to a tank or cistern. It is used to fill or empty the tank; accordingly, it is called an inlet or an outlet. Inlet: A pipe which is connected to fill a tank is known as an inlet. Outlet: A pipe which is connected to empty a tank is known as an outlet. Problems on pipes and cisterns are similar to problems on time and work. In pipes and cistern problems, the amount of work done is the part of the tank of filled or emptied. And, the time taken to do a piece of work is the time take to fill or empty a tank completely or to a desired level. Pipes and Cisterns Po

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Remainder Concepts for CAT – How to Find Out Remainder of a Number with Power?

April 15th, 2019 by

Figuring out the last digit is the same as figuring out the remainder of a number when divided by 10, but I guess you already know that. Figuring out the last two digits is the same as figuring out the remainder of a number when divided by 100. However, if you wish to figure the remainder when the divisor is not 10 or 100, I suggest you read on. Funda 1 of Remainders:  Basic idea of remainders can be used to solve complicated problems.     There is nothing special or unique about this idea. At first glance it seems like something really obvious. But it is it

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Quadratic Equations – Concepts and Questions with Solutions for CAT Exam

April 9th, 2019 by

Quadratic Equations are first taught to us in 6th or 7th class and most of us are able to score good marks in it because we are able to solve 90% of the questions by just using that formula. And that formula is: The above formula gives us the roots of the quadratic equation ax2 + bx + c = 0 For this post, I am assuming that you are aware of the basics of quadratic equations and know how to use the above mentioned formula. In case you are not, spending five minutes on the wiki page of Quadratic Equations won’t hurt. Wikipedia can be daunting at times, so come back here as soon a

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

April 3rd, 2019 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

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Factorial Concepts for CAT – Rightmost digit, Ending Zeroes, Power of a Prime

March 15th, 2019 by

We all know what factorials (n!) are. They look friendly and helpful but looks can be deceiving, as many quant problems have taught us. Probably it is because that Factorials are simple looking creatures, most students prefer attempting questions based on them rather than on Permutation & Combination or Probability. I will cover P&C and Probability at a later date but in today’s post I would like to discuss some fundas related to factorials, which as a matter of fact form the basis of a large number of P&C and Probability problems.   Some of the factorials that mig

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Time Speed Distance – Motion of Two Bodies in a Straight Line

March 13th, 2019 by

There are some topics in Quantitative Aptitude, like Permutation & Combination,  where you can easily find out the answer and the answer you calculate is there in the options but it turns out to be wrong. And then there are some topics in which you read the question, understand it but cannot even begin solving it. You get stuck at the first step and you have no idea about how to even approach the question. The irritating fact is that you understood the question properly. It happens very frequently with questions on Time Speed & Distance (TSD). I have always been a big advocate of

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Determining the second last digit and the last two digits

March 1st, 2019 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

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

February 22nd, 2019 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 &

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Divisibility Rules for CAT Quantitative Aptitude Preparation

February 20th, 2019 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

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