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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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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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

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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

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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

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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

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Understanding Percentage The word “Percent” can be understood as “per 100” or “out of 100”. Percentage in itself is a dimensionless number used to tell how many parts per hundred are being considered. It is often denoted using the percent sign, "%". The reference point for calculating percentage is taken as 100. If in a class of 100 students, 90 students passed in a subject then the percentage of students who passed in the exam is 90%. Had the total number of students been 200, the percentage would have reduced to 45%. This is because 45 students out of every 100 students pas

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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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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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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

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