# Numbers

The number of divisors the form 4n +1, n ≥0, of the number 10^{10} × 11^{11} × 13^{13}

__________

A. 256

B. 924

C. 1024

D. 512

E. None of these

The number of divisors the form 4n +1, n ≥0, of the number 10^{10} × 11^{11} × 13^{13}

__________

A. 256

B. 924

C. 1024

D. 512

E. None of these

In the figure, ABCD is a rhombus. Point E is on the diagonal AC such that AE = 41, EC = 9 and measure of ∠ABE = 90º. Find the area of this rhombus.

**About XAT: **

The Xavier’s Aptitude Test is a national level management aptitude test conducted by Xavier Association of Management Institution on behalf of XLRI. XAT is usually held in the month of January and over top 150 MBA colleges consider the XAT scores for their management programs. It is the oldest B-school entrance exam of the nation. XAT went online for the first time in January 2018 in its 60 years of legacy. It is the second most important exam after the CAT for management courses in India.

I am dividing this method into four parts and we will discuss each part one by one:

a. Last two digits of numbers which end in one

b. Last two digits of numbers which end in 3, 7 and 9

c. Last two digits of numbers which end in 2

d. Last two digits of numbers which end in 4, 6 and 8

Before we start, let me mention binomial theorem in brief as we will need it for our calculations.

**Last two digits of numbers ending in 1**

Let’s start with an example.

**What are the last two digits of 31 ^{786}?**

CAT is a national level MBA entrance exam for admission into the business administration programs of the Indian Institutes of Management (IIMs). Apart from the IIMS, hundreds of other leading business schools such as FMS Delhi, SPJIMR Mumbai, JBIMS Mumbai, MDI Gurgaon, IITs, IMT, IMI, XIMB, TAPMI and others accept the CAT score as the admission criterion.

CAT is an online computer-based test conducted in the month of November/December every year. Approximately 2 lakhs students take the exam for close to 5000 seats.

There have been questions, in recent years CAT’s quant and data interpretation sections, based on some mathematical strategy games. These questions do not require much mathematical expertise but seek for your hidden intelligence. Just like many things which you might have studied at your degree college are practical i.e. useful but not practicable i.e. feasible. Also in a business school, you learn so much business jargon and tactics but how much is practicable you learn only after getting out of school and enter the business. The exactly same way you may know ‘n’ amount of mathematics but that sharp intelligence, aptitude to solve problems is the key which CAT is looking for.

All of us know that mathematics can be learned but there are no courses for learning intelligence (* leave Artificial Intelligence for the time being). But we can nurture and nourish intelligence by using it. So let’s do it.

Hello World!! Now that you are well set on your journey of grammar, here’s a small lesson for you on one of the most frequent error zones in grammar- Modifiers.

Oh, by the way! Do you like coffee? It might not be a bad idea to keep a steaming mugful by your side as you read the lesson. Sip along!

**Modifiers- Dangling and Misplaced:**

A modifier describes, clarifies, or gives more detail about a word or a word group. A dangling modifier is a phrase that modifies the wrong word or phrase because of the absence of the word or phrase it is supposed to modify. In other words, the modifier is left “dangling”. A misplaced modifier is placed incorrectly in the sentence such that it modifies the wrong word and makes the sentence sound illogical.

The rules of business can be applied to any competitive environment. Just as businesses keep trying to achieve an extra edge and sell more and more products so do students preparing for competitive exams such as CAT 2018. The focus should always be on trying to achieve more and more. For CAT aspirants, this is the golden rule- always be focused on your goal. That means giving away all your distractions: that movie which other friends are going to watch, those phone calls, whatsapp, facebook, or twitter, those sms, those days of boredom when you do not want to study, and so much more. For every second, minute, hour or day that you lose, someone is trying to get ahead of you. The fact is that you are not going to become a CAT cracker overnight; you will have to grow inch by inch. And the other fact is that it is easier to increase your percentile to 95 or 97 from 70 or 80 percentile but it is much much tougher to increase it further to 99+. So the more you are at the top, the harder it is to grow further. And it takes focus and dedication climb day by day.

I am very fond of today’s chapter. These tricks are used by me off an on and I teach them in my first class also. The result is that all my students are able to work out calculations mentally by the end of the class. The sad fact is that they do not continue it once they get home, which is a pity. If they keep up the practise for 3 or 4 months, they would see themselves doing wonders, as I saw with myself. But practicing it day in and day out again takes focus and vision of one’s goal.

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