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

Answer: 900 = 22 × 32 × 52. Therefore, any number that is a factor of 900 can have powers of 2 equal to 20, 21 or 22. Similarly, for 3, the powers can be 30, 31, or 32 and for 5 they will be 50, 51, or 52. Writing the powers in a line we have-

Divisors of a Number

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, 21 × 32 × 51 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.

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critical reasoning basics
Critical reasoning

Sometimes it is necessary to ask ‘Big Hairy Audacious Goals (BHAG)’ questions to put your goalposts and milestones in perspective. For example, a CAT 2010 aspirants should regularly question himself “Am I a 100 percentiler yet?” This question has lot more to it than it seems. First, half of you would not even dare to ask this question as you do not possess the belief that you can be a 100 percentiler. That means you would not be even 99 percentiler and the race for CAT is already over for you. For those who DO believe that they can be a 100 percentiler, the question would really make you ask yourself if you are doing enough to become one. You would realize the slackness that you have fallen into or the weak areas that you need to look into. In short, it would bring back the steel that you need so badly. The catch is that if you are not stupid enough to dream to be supreme, the biggest, and the best, do not dare to dream at all. Once you decide to be the best, biggest, or the most famous at what you want, everything else will fall into place.Today’s chapter is a continuation of the critical reasoning series that Kumar Sir has agreed to write. I am loving his simple and lucid way of explanation. I sincerely hope you would too. Please do attempt the subjective questions at the end of the lesson. Good Luck!-

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Today’s article comes from another founding father of TathaGat, Mr. Kumar Abhishek, popularly known as ‘Kumar’ and hands down the best verbal instructor in Delhi. Though he is great fun in his classes, he is a terror if you cross his rules, i.e. forget to submit your weekly book reviews, come without flashcards or The Hindu newspaper in the class, or arrive late for your class. But if you follow all that, you would forget about the time during his classes. He regales the students with his command in both Hindi and English. To quote a student “kumar sir is tough only in the first few classes……then it’s a smooth ride……and keeps the mood of the class light and interactive with his wisecracks and sudden outbursts of unadulterated hindi….like “mera abir balak kahan hai”………and “yatharth ka dharatal”……..”prabal sambhavana” and many more…” For those who would like to know, his favourite words are “Bhasad” and “Hawabaz” which he can be seen quoting once in every 5 sentences. Even his fan club on TG Town is known as ‘Bhasad’. Not to mention that he is extremely famous among his students. Once we were so full of reading his praises on the internet that we started pulling his leg “Aap hi to kahin jakar nahin likhte rahte hain internet par apne bare mein?” 

Logical Reasoning:
Logical Reasoning:


Ramu is a delivery boy at The Queen Hill Hotel. The hotel is peculiar as no road inside the hotel premises is flat; it either goes uphill or downhill. Ramu’s uphill speed is 60m/min and downhill speed is 90m/min. It is also known that he takes 2 minutes to serve the order in the room.

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Need for Speed - DI Set

Huey , Dewey and Louie are the three grandnephews of millionaire Scrooge McDuck. For their 18th birthday, they want a sports car each. Being the stingy uncle that Scrooge is, he has asked them to solve a puzzle, the right answer to which would get them a car each. The puzzle is as follows:

I raced all the 25 cars that I have (C1, C2, C3…C25), 5 at a time, and the results were as shown in the table.

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