[latexpage] Problems related to escalators baffle a lot of students preparing for CAT. Probably because not much time has been devoted to explaining this simple concept. Although we keep telling in our CAT classrooms continuously that escalator questions are similar to ‘upstream’ ‘downstream’ questions that students solve in time, speed and distance, the future MBAs still get confused because of the way that the questions are put. Today, we are going to see the theory behind escalator questions and solve them through both equations and ratios. In order to benefit the most, please solve these questions on your own before looking at the solutions.

An escalator is a moving stair, i.e. it moves continuously up or down. At any given point in time, the total number of stairs are fixed in an escalator. For example, for an escalator going up that is showing 50 steps, if 2 stairs disappear at the top, 2 stairs come out at the bottom. Most of the escalator questions involve people moving on an escalator. Remember that the speed of climbing stairs for a person does not vary whether the escalator is moving or still. For example, if Bantu can climb stairs at 2 stairs per second, his speed of climbing stairs on a moving escalator would stay the same.

[latexpage] In 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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