Solved Example #16

February 19th, 2013 by

Question : Find the No of zeroes at the end of 25! +26! + 27! + 28! + 30!   Answer :  To understand this, let us understand the basic idea first What will be the number of 0s at the end of a + b + c would depend upon the least number of 0s that any one of a or b or c has. For eg: 300 + 120000 + 17272730 will end in 1 zero But, if they have the same number of zeroes, we will also have to consider the last non-zero digit. For eg: 12000 + 161237000 + 1212331000 will not end in 3 zeroes but in 4 zeroes because the last non-zero digits 2, 7 and 1 will add up to generate an extra zero.

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Cubes and Matchstick Problems

February 16th, 2013 by

Cubes and Matchstick Problems   ‘If it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.’ – Tweedledee in Lewis Caroll’s Through the Looking Glass. If the above line confused you, trust me – you are not alone. Even God can vanish in a puff of logic. To know how, you can probably jump to the end of this post. To those who choose not to skip – let us discuss few common types of Logical Reasoning problems.   Type 1:  Cube problems:  A cube is given with an edge of unit ‘N’. It is painted on all faces. It is cut i

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Basic Functions and Modifications of Graphs

February 16th, 2013 by

Basics of functions and modifications of graphs   XAT’s Quant is always a little bit on the tougher side. It is said that the paper would be do-able and the level of difficulty will see a dip. That does not mean that the difficulty level would suddenly drop to the standard of elementary mathematics. XAT traditionally focuses more on topics like functions, probability, permutation & combination, etc. more than the CAT exam. In this post we will discuss some basic tips about functions and how graphs of functions change. Let us see what the function y = f(x) = x3 + 7 looks like:

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Remainders Advanced

February 15th, 2013 by

REMAINDERS ADVANCED   In previous posts, we have already discussed how to find out the last two digits and basic ideas of remainders. However, there are theorems by Euler, Fermat & Wilson that make calculation of remainders easier. Let’s have a look at them.   Funda 1 – Euler:   A very common mistake that students tend to make while using Euler’s Theorem in solving questions is that they forget M and N have to be co-prime to each other. There is another set of students (like me in college) who don’t even understand what to do with the theorem or

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Basic Application of Remainder Theorem

February 15th, 2013 by

Basic Applications of Remainder Theorem     In my previous post, we discussed the cyclical nature of the remainders when an is divided by d. In this post, we will see how problems on finding out the remainder can be broken down into smaller parts.   Funda 1: Remainder of a sum when it is being divided is going to be the same as the sum of the individual remainders.   Let us look at an example for this case: Eg: Find out the remainder when (79+80+81) is divided by 7. If we add it up first, we get the sum as 240 and the remainder as 2 as shown bel

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Cyclicity of Remainders

February 15th, 2013 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. On the other hand, if you are looking for some advance stuff, I suggest that you check out some of my posts from last year on the same topic. 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

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Solved Example #10

February 11th, 2013 by

Question : 100 million bacteria can completely decompose a garbage dump in 15 days and 60 million can do so in 30 days. If same quantity of garbage is added to the initial quantity of the dump everyday , how many bacteria will be required to completely decompose the dump in 10 days?       Answer : Let us say 1 Million bacteria can clear 1 unit of garbage in 1 day. Initially there were 'x' units of garbage and everyday 'y' units of garbage gets added.   Case 1 : 100 M bacteria can decompose in 15 days. Total garbage present = Total garbage decompo

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Solved Example #9

February 11th, 2013 by

Question : A student was given 8 two-digit numbers to add,by a teacher.If the student reversed each number and added the results,the sum of the numbers would be 36 more than the actual sum.Find the excess of the sum of the units digits over that of the ten digits.     Answer :  Let us say that the 8 numbers are a1 b1, a2 b2, a3 b3 ... a8 b8 ...{eg: 38} They actually represent a1*10 + b1, a2*10 + b2 ... a8*10 + b8 ...{eg: 3*10 + 8} Sum of the numbers = (a1 + a2 + a3 .. a8)*10 + (b1 + b2 + b3 .. b8)   Reversed numbers will be b1 a1, b2 a2, ... b8 a8 Sum

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Solved Example #8

February 11th, 2013 by

Question : Without stoppage, a train travels at an average speed of 75km/h. With stoppages it covers the same distance at an average speed of 60 km/h. How many minutes per hour does the train stop?     Answer :  This seems like a pretty straightforward question but can confuse because of the way it is asked. The best way to understand it, in my opinion, is to assume a distance. Let us say that the distance that the train covers is 300 km. (I am taking 300 km because it is divisible by both 75 & 60)   Case 1: Time taken without stoppages = 300 / 75 = 4

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Solved Example #7

February 9th, 2013 by

Question : Find the number of ternary sequences of length 4 where 0 is not followed by 1 and 1 is not followed by 2. (Ternary sequence of length n is a sequence having n terms and each term is either 0,1 or 2) a. 47 b.37 c. 72 d.54 e.44   Answer :   Total ternary sequences possible = 3^4 = 81 {There are 4 positions and 3 choices for each position}   Invalid sequences: Sequences which contain 01. The location for 01 can be selected in 3C2 or 3 ways. {01xx, x01x, xx01} The other two digits can be selected in 3*3 or 9 ways. {Filling up

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