How do we find divisors of a number? For example, how do we calculate the number of divisors of 900?

Answer: 900 = 2^{2} × 3^{2} × 5^{2}. Therefore, any number that is a factor of 900 can have powers of 2 equal to 2^{0}, 2^{1} or 2^{2}. Similarly, for 3, the powers can be 3^{0}, 3^{1}, or 3^{2} and for 5 they will be 5^{0}, 5^{1}, or 5^{2}. Writing the powers in a line we have-

Now any combination of a power of 2, a power of 3, and a power of 5 will give us a divisor. For example, in the figure, 2^{1} × 3^{2} × 5^{1} will be a divisor of 900. As we can select a power of 2 in 3 ways, a power of 3 in 3 ways, and a power of 5 in 3 ways, the total number of combinations will be 3 × 3 × 3 = 27. Therefore, the number of divisors of 900 is 27.

*The sentences given in the question, when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from the given choices to construct a coherent paragraph.*

**1.**

**A.** It conceived of the gods as blissful and immortal, yet material, beings made of atoms, inhabiting the empty spaces between worlds in the vastness of infinite space, too far away from the earth to have any interest in what man was doing.

**B.** In modern popular usage, an epicure is a connoisseur of the arts of life and the refinements of sensual pleasures, especially of good food and drink, attributable to a misunderstanding of the Epicurean doctrine, as promulgated by Christian polemicists.

**C.** It can be argued that the philosophy is atheistic on a practical level, but avoids the charge of Atheism on the theoretical level, thus avoiding the fate of Socrates, who was tried and executed for the Atheism of his beliefs.

**D.** Epicureanism emphasizes the neutrality of the gods and their non-interference with human lives, although it did not deny the existence of gods, despite some tendencies towards Atheism.

**1.** DACB **2.** ABDC **3.** BADC **4.** DBAC

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Similar triangles present one of the biggest tools students have to solve many geometry questions. And yet, whenever the opportunity arises, the students often fail to spot the similarity between two triangles. Sometime they spot the similarity but fail to apply the ratios correctly. Today we will start with some familiar cases in which we apply similarity of triangles and then move on to some tricky and difficult cases. We hope that after solving all these problems, you’ll not have any issue in spotting and solving similarity.

In practical scenario, we always prove that two triangles are similar by proving that their corresponding angles are equal. For example, look at the very simple figure below:

If you can prove that $\angle BAC$ = $\angle QPR$ and $\angle ABC$ = $\angle PQR$ then $\triangle ABC$ and $\triangle PQR$ are similar. In which case the ratios of the corresponding sides are equal. The best way to write the ratio of the sides is to write both the triangles in the order of the angle which are equal (for example here $\angle A$ = $\angle P$, $\angle B$ = $\angle Q$ and $\angle C$ = $\angle R$ so write ABC and PQR only) and then write the ratio by picking same corresponding points from the two written triangles. Therefore,

*The passage given below is followed by a set of questions. Choose the best answer to each question.*

As I said before, I do not think that the real reason why people accept religion has anything to do with argumentation. They accept religion on emotional grounds. One is often told that it is a very wrong thing to attack religion, because religion makes men virtuous. So I am told; I have not noticed it. You know, of course, the parody of that argument in Samuel Butler’s book, Erewhon Revisited. You will remember that in Erewhon there is a certain Higgs who arrives in a remote country, and after spending some time there he escapes from that country in a balloon. Twenty years later he comes back to that country and finds a new religion in which he is worshiped under the name of the “Sun Child,” and it is said that he ascended to heaven. He finds that the Feast of the Ascension is about to be celebrated, and he hears Professors Heroditus and Panopticon say to each other that they never set eyes on the man Higgs, and they hope they never will; but they are the high priests of the religion of the Sun Child. He is very indignant, and he comes up to them, and he says, “I am going to expose all this humbug and tell the people of Erewhon that it was only I, the man Higgs, and I went up in a balloon.” He was told, “You must not do that, because all the morals of this country are bound round this myth, and if they once know that you did not ascend into Heaven they will all become wicked”; and so he is persuaded of that and he goes quietly away.

[latexpage]

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.

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.

**Read the passage given below and answer the questions that follow:**

There is nothing easy about the adoption of cloud computing. It demands new information-technology (IT) and developer skill sets. It also challenges organizational structure and work practice. But that does not mean, as Bruce Schneier says, that “it’s complicated” or a “maybe”. Companies should make the adoption of the cloud a strategic imperative because it is a vastly superior way to deliver reliable, secure, scalable computing—which is needed to fuel business.

Mr Schneier highlights the potential risks of the cloud, but fails to account for the risk of not adopting it. Businesses exist to deliver value while managing risk. And the broad adoption of cloud computing will dramatically decrease risk and offer incredible opportunities to firms that seek competitive advantage. Mr Schneier neglects to mention the manifest risk inherent in the status quo: a legacy mindset born of well-founded fears. Today’s IT infrastructure is a Swiss cheese of vulnerable networks, operating systems and applications developed before the internet. It is difficult and expensive to keep running—and easy to penetrate. In 2014 Verizon reported more than 2,100 data breaches. The FBI has claimed that every major American company has been compromised by the Chinese—whether they realized it or not. Against this backdrop, it is rational for IT staff to seek greater control by locking down networks and computers, and by prohibiting the use of the cloud.

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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.

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