Solved Examples

Sitting Arrangements-Linear and Circular


Sitting arrangement is one of the popular topics of LRDI section for any competitive exam. The best thing about this topic is that you don’t need to apply any out of the box thinking but to process and write down all the information that is given to solve the questions. Sometimes you will feel that given information is not enough to complete the arrangements but remember your job is to solve the questions not to complete the arrangement.

Here I am giving you some sets of linear and circular arrangements, try to solve them and then match your answers with the given solution.

Direction for question number 1 to 4: Four couples A,B,C,D,E,F,G and H are sitting together on a bench facing towards north not necessarily in the same order. It is also known that

I. A,C,E,G are females who are sitting immediate left of their husbands.
II. G is sitting immediate right of H who is sitting three places away to the left of C.
III. A is sitting five places to the left of B who is sitting 3rd from extreme right.

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Line Graph – Data Interpretation for CAT

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As the name suggests, data interpretation is all about logical interpretation of the given data and answering questions. Data interpretation carries the same weightage in third section of CAT as reading comprehension in verbal section or geometry and algebra in quant section. For the past two years (CAT 2014 & CAT 2015), CAT carries approximately 20 questions on data interpretation. If you haven’t been serious about this topic till now, there is never a better day than today to start!

Data can be represented in many ways, some of the most common ways are tables, bar graphs, Line Graphs, paragraphs, pie charts etc… This article will focus on LINE GRAPHS and will introduce you with the most basic aspects of a line graph.

line graph basic example

above is one of the basic example of a line graph and its various component are as follows:

Title : The title of the graph tells us what the graph is about
Label : Horizontal and vertical labels tell us about type of the data
Axis : X and Y axises tell us about the unit of the data.
Dots : Dots on the line graph tell us combination of X and Y axis data.
Line : The blue line connecting the dots in the above graph gives a visual representation of the data, and its variation.

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The Theory of Equations- Properties of Roots

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theory of equationsIn CAT and other MBA entrance exams, there are many questions which fall in the domain of equations (quadratic, cubic, quartic..) and the properties of their roots. Deriving these properties will not only help us remember them but also give us the basic concepts to solve all kinds of equations and their problems. In this chapter we shall learn how the properties of roots of a general polynomial equation are derived. So let’s begin!

Let’s take a polynomial P(x) in a single variable x:

Let $P(x) = a_0(x)^n + a_1(x)^{n-1} + a_2(x)^{n-2} + … + a_{n-1}x + a_n$ where $a_1$, $a_2$ etc. are constants (associated with decreasing powers of x) and n, n-1, etc. are the whole number powers of the variable x. The highest power of the variable x is known as the ‘degree’ of the polynomial P(x).

For example, $P(x) = x^5 – 3x + 1$ is a polynomial with degree 5 with $a_0 = 1, a_1 = 0, a_2 = 0, a_3 = 0, a_4 = -3, a_5 = 1$

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