Alphametics The Art of Numbers

As CAT 2018 preparation starts heating up, I am going to flag the race with an oddball topic: Alphametics. What are alphametics or cryptarithms as they are also known?

Alphametics are number puzzles in basic arithmetic operations where digits are represented by alphabets. It is customary that different digits are represented by different alphabets. Why are alphametics relevant? Because they require a good knowledge of the properties of numbers and skill in working with them. Solving alphametics helps you quickly identify the solution to many problems which might otherwise require a good amount of time.

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Noun

This lesson covers the fundamentals and types of nouns, knowledge of which will help you in B-school entrance exams like the NMAT, SNAP and IIFT.

So, let’s get started!

Noun: A noun is a word that is used to name a person, animal, place, thing, or an abstract idea. Nouns tell you about the ‘what’s’ ‘who’s’ and ‘where’s’ of a sentence. Let’s see an example: TG and Dagny went to Maxims to order a chocolate truffle cake.

TG and Dagny are persons, Maxims is a place and chocolate truffle cake is a thing.

Nouns can be broadly classified into

  • Common nouns
  • Proper nouns
  • Concrete Nouns
  • Abstract Nouns
  • Countable Nouns
  • Non-Countable Nouns
  • Collective Nouns
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Some properties of natural numbers :

1•Sum of first n natural numbers : 1 + 2 + 3 +……+ n = n ( n +1)/2

2• Sum of squares of first n natural numbers : 1² + 2² + 3² +……+ n² = n ( n +1) ( 2n +1) /6

3• Sum of cubes of first n natural numbers : 1³ + 2³ + 3³ +……+ n³ = [ n ( n +1)/2]²

4• Sum of first n odd numbers: n²

5• Sum of first n even numbers: n² + n

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Similar Triangles

Similar Triangles

The current article deals with a frequently occurring topic in geometry in CAT- similarity of triangles. Most of you will notice that this topic is coming year after year in CAT and, as geometry questions in CAT are easy compared with other topics, mastering the concept is easier than mastering concepts in Algebra, Permutation, and Combination, or Probability.

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 Divisibility Rules
A. Divisibility by 2, 4, 8, 16, 32.

A number is divisible by 2, 4, 8, 16, 32,.. 2 when the number formed by the last one, two, three, four, five…n digits is divisible by 2, 4, 8, 16, 32,..2 respectively.

Example: 1246384 is divisible by 8 because the number formed by the last three digits i.e. 384 is divisible by 8. The number 89764 is divisible by 4 because the number formed by the last two digits, 64 is divisible by 4.

B. Divisibility by 3 and 9

A number is divisible by 3 or 9 when the sum of the digits of the number is divisible by 3 or 9 respectively.

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LOGARITHM

If a is a positive real number other than 1, and am = x, then we can write: m = logax, and we say that the value of log x to the base a is m.
Examples:

(i) 104 = 10000     log10 10000 = 4.

(ii) 35 = 243     log3 243 = 5.

(iii) (0.1)3 = 0.001     log (0.1) (0.001) = 3.


Properties of Logarithms

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Remainder Theorems

Remainders-CAT-MAT-GMAT

It is uncanny how children pick up a lot of small habits and beliefs of their parents. Even the ones that rebel against their parents bear the subconscious resemblance to their father or mother. There is a lesson for instructors in this. It is important for them to realize that students mirror their feelings about CAT. If the instructor expresses or feels that CAT is tough, or is fearful about CAT, his students will mirror the same feeling and will be less confident. If the instructor is brazen and casual about the paper and scoffs the competition, his students would reflect the same feelings. Also, it is so necessary to have unflinching faith in one’s students. I still remember that during my school days my mother used to proudly proclaim that I was an intelligent kid. I was barely scrapping passing marks in the school exams. If truth be told I was at the bottom of the class, but my mother had her blinkers on. And because of my mother, I also believed that I was second to none. It was only years later, during my boards exams, that I took to studying seriously, and managed to outperform everyone else. I don’t know if it was my mother’s blind love for me or that she could see some bright spark in me that made her claim my intelligence but it really had great effect on my attitude. And attitude, in an exam like CAT, is everything.

Well, it’s almost everything. A keen attitude towards CAT subjects’ fundamentals also plays an important role in one’s performance.

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Counting in Geometry


(a) In a plane, if there are n points of which no three are collinear, then

  1. The number of straight lines that can be formed by joining them is nC2.
  2. The number of triangles that can be formed by joining them is nC3.
  3. The number of polygons with k sides that can be formed by joining them is nCk.

(b) In a plane, if there are n points out of which m points are collinear, then

  1. The number of straight lines that can be formed by joining them is nC2mC2 + 1.
  2. The number of triangles that can be formed by joining them is nC3mC3.
  3. The number of polygons with k sides that can be formed by joining them is nCkmCk.

(c) The number of diagonals of an n sided polygon is nC2 – n = n × (n – 3)/2

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