## A man had twelve toothpicks

A man had twelve toothpicks in front of him. He took one away. Now he had nine in front of him. How is this possible?

## What English word is nine letters long?

What English word is nine letters long, and can remain an English word at each step as you remove one letter at a time, right down to a single letter. List the letter you remove each time and the words that result at each step.

## You have a pile of 24 coins

Here is  an interesting mathematical puzzle for you.

You have a pile of 24 coins. Twenty-three of these coins have the same weight, and one is heavier. Your task is to determine which coin is heavier and do so in the minimum number of weighings. You are given a beam balance (scale), which will compare the weight of any two sets of coins out of the total set of 24 coins. How many weighings are required to identify the heavier coin?

## Once upon a time

Once upon a time, an old lady went to sell her vast quantity of eggs at the local market.
Son, I can’t count past 100 but I know that.

If you divide the number of eggs by 2 there will be one egg left.
If you divide the number of eggs by 3 there will be one egg left.
If you divide the number of eggs by 4 there will be one egg left.
If you divide the number of eggs by 5 there will be one egg left.
If you divide the number of eggs by 6 there will be one egg left.
If you divide the number of eggs by 7 there will be one egg left.
If you divide the number of eggs by 8 there will be one egg left.
If you divide the number of eggs by 9 there will be one egg left.
If you divide the number of eggs by 10 there will be one egg left.
Finally. If you divide the Number of eggs by 11 there will be NO EGGS left!

How many eggs did the old lady have?

## Vedic Maths Subtraction

#### Learn Amazingly Fast Vedic Mathematics Subtraction

Very often we have to deduct a number from numbers like 1000, 10000, 100000 and so on.

This Vedic Maths Subtraction method found as sutra in ancient vedas, is given below is very useful for such subtractions.

Memory Trick: ALL FROM 9 AND THE LAST FROM 10

Use the formula all from 9 and the last from 10, to perform instant subtractions.

For example 1000 – 357 = ?      (subtraction from 1000)

We simply take each figure in 357 from 9 and the last figure from 10.
Step 1. 9-3 = 6
Step 2. 9-5 = 4
Step 3. 10-7 = 3

So the answer is 1000 – 357 = 643
And that’s all there is to it!

This always works for subtractions from numbers consisting of a 1 followed by noughts: 100; 1000; 10,000 etc.
Similarly 10,000 – 1049 = 8951      (subtraction from 10000)

9-1 = 8
9-0 = 9
9-4 = 5
10-9 = 1

For 1000 – 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 83 is 083.
So 1000 – 83 becomes 1000 – 083 = 917

Corollary: If last term is 0, keep that last term as 0 and subtract the last non Zero term from 10 .

Illustration: 10000 – 920 = 10000 – 0920 = (9-0) (9-9) (10-2) 0 =9080

Illustration: 100000 – 78010 = (9-7) (9 – 8 ) (9- 0) (10 – 1) 0 = 21990

## MAT SYLLABUS

Management Aptitude Test or MAT Syllabus

MAT is the MBA entrance test conducted country-wide by the Centre for Management Services (CMS) of All India Management Association (AIMA). It is usually conducted four times in a year in February, May, September and December. MAT is conducted in all major cities in the country and in leading cities abroad.

Eligibility

The minimum qualification for appearing in MAT is graduation in any discipline from any recognized University or equivalent recognized degree. A final year student in any undergraduate (i.e., B.A., B.Sc., B.Com., B.Tech., etc.,) can also appear provisionally. Usually, there is a minimum percentage requirement in graduation, which is different for different MIs / University.

MAT Syllabus
The Management Aptitude Test or MAT is the test conducted by All India Management Testing Service for entering into MBA or equivalent post graduate programmes.

There are five papers in MAT:
1. Language Comprehension
2. Mathematical Skills
3. Data Analysis
4. Intelligence & Critical Reasoning
5. Indian & Global Environment Section

Paper Pattern:

Total Questions: 200
Time: 150 minutes

Marks allocation:
Correct attempt: 1 mark
Incorrect attempt: Negative marking not specified

Section Questions
Data Interpretation/Data sufficiency     40
Quantitative Aptitude      40
Logical and Critical reasoning        40
General Awareness**       40
**Scores are based on the first four sections only, the decision to consider scores of the General Awareness section are left to the institutes.

## Multiply 2 numbers, sum of whose unit places is 10

Vedic Multiplication: This method of multiplication which is from Vedic Maths will make it very easy to multiply two numbers when sum of the last digits is 10 and previous parts are the same

You will get the answer in two parts.

First part, to get left hand side of the answer: multiply the left most digit(s) by its successor

Second part, to get right hand side of the answer: multiply the right most digits of both the numbers.

Example

First part: 4 x (4+1)

Second part: (4 x 6)

Combined effect:  (4 x 5)  | (4 x 6) = 2024

*| is just a separator. Left hand side denotes tens place, right hand side denotes units place

More Examples

37 x 33 = (3 x (3+1)) |  (7 x 3) = (3 x 4) | (7 x 3) = 1221

11 x 19 = (1 x (1+1)) |  (1 x 9) = (1 x 2)  | (1 x 9) = 209

As you can see this method is corollary of  “Squaring number ending in 5”

It can also be extended to three digit numbers like :

E.g. 1: 292 x 208.

Here 92 + 08 = 100, L.H.S portion is same i.e. 2

292 x 208 = (2 x 3) x 10 | 92 x 8  (Note: if 3 digit numbers are multiplied, L.H.S has to be multiplied by 10)

60 | 736 (for 100 raise the L.H.S. product by 0) = 60736.

E.g. 2: 848 X 852

Here 48 + 52 = 100,

L.H.S portion is 8 and its next number is 9.

848 x 852 = 8 x 9 x 10 | 48 x 52 (Note: For 48 x 52, use methods shown above)

720 | 2496

= 722496.

[L.H.S product is to be multiplied by 10 and 2 to be carried over because the base is 100].

Eg. 3: 693 x 607

693 x 607 = 6 x 7 x 10 | 93 x 7 = 420 / 651 = 420651.

Note: This Vedic Maths method can also be used to multiply any two different numbers, but it requires several more steps and is sometimes no faster than any other method. Thus try to use it where it is most effective

## How to Quickly Find Square of Any Number Ending in 5

Finding square of any number with unit’s digit being 5 is the most common, yet very interesting trick of Vedic Maths.  Using this technique you can find the square of any number ending in 5 very easily.  Also explore a quick method of squaring numbers ending in 9. Given below is the step by step explanation of this Vedic Maths Method.

Let us take a 2 digit number in generic form, say the number is a5 (=10a+5), where a is the digit in ten’s place

Square of a5= a x (a+1) | 25

That means a is multiplied by the next higher number, i.e. (a+1). Now let’s take example of a real number ending in 5, say 45.

452 = Left hand side of the answer will be 4 multiplied by its successor i.e. 5 and the right hand side part will always be 25 for squares of numbers of which the unit’s digit is 5.

Giving the answer a x (a+1) | 25 ( |     stands for concatenation}

i.e. 4  x  (4+1) | 25 = 4 x 5 | 25 = 2025

Similarly we can proceed for 3 digit numbers ending in 5

Few more examples:

952=9 x 10 | 25 =9025

1252 = 12 x 13 | 25 = 15625

5052 = 50 x 51 | 25 = 255025

Test yourself

Find out the square of 85, 245, 145, 35, 15, and 95?

Answer: 7225, 60025, 21025, 1225, 225, 9025

Please let us know if you like this Vedic Maths trick

## CAT SYLLABUS

Syllabus for CAT 2009

There is no prefixed pattern for CAT.Â  The syllabus given below is based on the experience of previous CATs. The list may not be exhaustive but almost the entire gamut is covered. CAT 2009 will be online

QUANTITATIVE:

Ratios and Proportion, Ratios, Percentages, In-equations , Quadratic and linear equations, Algebra, Profit & Loss, Averages, Percentages, Partnership, Time-Speed-Distance, Work and time, Number system, HCF, LCM, Geometric Progression, Arithmetic progression, Arithmetic mean, Geometric mean , Harmonic mean, Median, Mode, Number Base System, BODMAS, Mensuration, Alligation & Mixtures, Work, Pipes and Cisterns, Simple Interest & Compound Interest, Set Theory, Venn Diagram, Installment Payments, Partnership, Clocks, Probability, Permutations & Combinations, Trigonometry, Vectors, Binomial Expansion, Co-ordinate geometry, Geometry (Lines, angles, Triangles, Spheres, Rectangles, Cube, Cone etc), Logarithm, Calendar, Maxima & Minima Progression, Surds & Indices and Complex numbers, Pipes and Cisterns, Functions etc.

DATA INTERPRETATION:

Data Interpretation based on text, Data Interpretation based on graphs and tables. Graphs can be Column graphs, Bar Graphs, Line charts, Pie Chart, Graphs representing Area, Venn Diagram, Data Sufficiency etc.

REASONING:

Critical reasoning, Visual reasoning, Assumption-Premise-Conclusion, Assertion and reasons, Statements and assumptions, identifying valid inferences , identifying Strong arguments and Weak arguments, Statements and conclusions, Cause and Effect, Identifying Probably true, Probably false, definitely true, definitely false kind of statement, Linear arrangements, Matrix arrangements, Puzzles, Family tree problem , Symbol Based problems, Coding and decoding , Sequencing , identifying next number in series etc.

ENGLISH:

Comprehension of passage, Verbal Reasoning, Syllogisms , Contextual usage, Analogies, Antonyms, Fill In the Blanks, Jumbled paragraphs with 4 or 5 sentences, Foreign language words used in English, Sentence completion, Sentence correction, odd man out, idioms, one word substitution, Different usage of same word, Errors in word choice, mania & phobia, Incorrect words, Mood, Conditionals & Multiple Usage , Punctuation, Proverb, Phrasal verb etc.

## Vedic Mathematics Course

Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). The aim of such sutra is to simplify the entire calculations and arithmetical operations.

Vedic Maths Course

There are 16 sutras in vedic mathematics as per Sri Bharati Krsna Tirthaji Maharaj.  The below mentioned list of topics (course content) is how I look at it.

2. Vedic Subtraction
1. All from 9 and the last from 10
2. Various other methods
3. Multiplication (inclusive of mental multiplication)
1. “By one more than the previous one”
2. Multiplication by 9, 99,  ( and so on), 11, 111, (and son on..)
3. Base method of multiplication and many more
4. Vertically and crosswise multiplications – criss-cross method
4. Part of Division (you will be amazed)
1. “Transpose and apply”
2. Special division cases
5. Squaring (it’s so simple) : More than 10 different methods will be discussed for different cases
6. Square root of perfect squares and imperfect squares.
7. Cubing(using things differently)
8. Cube Roots (by seeing only & not by working on it). Different methods for perfect cube and non-perfect cube
9. Dates and calendar
10. Magic Square
11. Special mathematical tricks and techniques
12. Application of vedic mathematics in trigonometry, geometry, algebra and calculus
13. Value (finding and remembering) of fractions
14. Checking the accuracy of different mathematical operations
15. Differential calculus
16. Solving an algebraic equation of one variable
1. “Transpose and adjust (the coefficient)”
17. Solving simultaneous equation and quadratic equation
1. “If the Samuccaya is the same (on both sides of the equation, then) that Samuccaya is (equal to) zero”
2. By the Paravartya rule
3. “If one is in ratio, the other one is zero.”
18. Solving cubic equation
19. Solving fractional equation
1. “The ultimate (binomial) and twice the penultimate (binomial) (equals zero),”

Through www.QuickerMaths.com (QM) I’ll try to cover all the above vedic maths related topics. Lot of other topics, techniques, shortcuts will be part of QM. Mathematical games, puzzles, riddles, etc. are also included to make every kid sharp.