## Sunday, February 15, 2009

## Thursday, August 28, 2008

### The first suthra of vedic maths

The First Sutra: Ekādhikena Pūrvena

The relevant Sutra reads Ekādhikena Pūrvena which rendered

into English simply says “By one more than the previous one”.

Its application and “modus operandi” are as follows.

(1) The last digit of the denominator in this case being 1 and the

previous one being 1 “one more than the previous one”

12

evidently means 2. Further the proposition ‘by’ (in the sutra)

indicates that the arithmetical operation prescribed is either

multiplication or division. We illustrate this example from pp. 1

to 3. [51]

Let us first deal with the case of a fraction say 1/19. 1/19

where denominator ends in 9.

By the Vedic one - line mental method.

A. First method

1/

19

=

.0 5 2 6 315 7 89 4 7 368 4 2 i

1 1 111 1 1 11

B. Second Method

1/

19

=

.0 5 2 6 3 1 5 7 8 / 9 4 7 3 6 8 4 2 i

1 1 11 1 1 1 1 1

This is the whole working. And the modus operandi is

explained below.

A. First Method

Modus operandi chart is as follows:

(i) We put down 1 as the right-hand most digit 1

(ii) We multiply that last digit 1 by 2 and put the 2

down as the immediately preceding digit. 2 1

(iii) We multiply that 2 by 2 and put 4 down as the

next previous digit. 4 2 1

(iv) We multiply that 4 by 2 and put it down thus 8 4 2 1

(v) We multiply that 8 by 2 and get 16 as the

product. But this has two digits. We therefore

put the product. But this has two digits we

therefore put the 6 down immediately to the

left of the 8 and keep the 1 on hand to be

carried over to the left at the next step (as we

13

always do in all multiplication e.g. of 69 × 2 =

138 and so on). 6 8 4 2 1

1

(vi) We now multiply 6 by 2 get 12 as product, add

thereto the 1 (kept to be carried over from the

right at the last step), get 13 as the

consolidated product, put the 3 down and keep

the 1 on hand for carrying over to the left at

the next step. 3 6 8 4 2 1

1 1

(vii) We then multiply 3 by 2 add the one carried

over from the right one, get 7 as the

consolidated product. But as this is a single

digit number with nothing to carry over to

the left, we put it down as our next

multiplicand. 7 3 6 8 4 2 1

1 1

((viii) and xviii) we follow this procedure

continually until we reach the 18th digit

counting leftwards from the right, when we

find that the whole decimal has begun to

repeat itself. We therefore put up the usual

recurring marks (dots) on the first and the last

digit of the answer (from betokening that the

whole of it is a Recurring Decimal) and stop

the multiplication there.

Our chart now reads as follows:

1/

19

= . 0 5 2 6 3 1 5 7 8 / 9 4 7 3 6 8 4 2 i .

1 1 1 1 1 1 / 1 1 1

B. Second Method

The second method is the method of division (instead of

multiplication) by the self-same “Ekādhikena Pūrvena” namely

2. And as division is the exact opposite of multiplication it

14

stands to reason that the operation of division should proceed

not from right to left (as in the case of multiplication as

expounded here in before) but in the exactly opposite direction;

i.e. from left to right. And such is actually found to be the case.

Its application and modus operandi are as follows:

(i) Dividing 1 (The first digit of the dividend) by

2, we see the quotient is zero and the

remainder is 1. We therefore set 0 down as the

first digit of the quotient and prefix the

remainder 1 to that very digit of the quotient

(as a sort of reverse-procedure to the carrying

to the left process used in multiplication) and

thus obtain 10 as our next dividend. 0

1

(ii) Dividing this 10 by 2, we get 5 as the second

digit of the quotient, and as there is no

remainder to be prefixed thereto we take up

that digit 5 itself as our next dividend. . 0 5

1

(iii) So, the next quotient – digit is 2, and the

remainder is 1. We therefore put 2 down as the

third digit of the quotient and prefix the

remainder 1 to that quotient digit 2 and thus

have 12 as our next dividend. . 0 5 2

1 1

(iv) This gives us 6 as quotient digit and zero as

remainder. So we set 6 down as the fourth

digit of the quotient, and as there is no

remainder to be prefixed thereto we take 6

itself as our next digit for division which gives

the next quotient digit as 3. . 0 5 2 6 3 1

1 1 1

(v) That gives us 1 and 1 as quotient and

remainder respectively. We therefore put 1

down as the 6th quotient digit prefix the 1

thereto and have 11 as our next dividend. . 0 5 2 6 3 1 5

1 1 1 1

15

(vi to xvii) Carrying this process of straight continuous

division by 2 we get 2 as the 17th quotient digit and 0 as

remainder.

(xviii) Dividing this 2 by 2 are get 1 as 18th

quotient digit and 0 as remainder. But this is

exactly what we began with. This means that

the decimal begins to repeat itself from here.

So we stop the mental division process and

put down the usual recurring symbols (dots)

on the 1st and 18th digit to show that the

whole of it is a circulating decimal.

Now if we are interested to find 1/29 the student should

note down that the last digit of the denominator is 9, but the

penultimate one is 2 and one more than that means 3. Likewise

for 1/49 the last digit of the denominator is 9 but penultimate is

4 and one more than that is 5 so for each number the

observation must be memorized by the student and remembered.

The following are to be noted

1. Student should find out the procedure to be followed.

The technique must be memorized. They feel it is

difficult and cumbersome and wastes their time and

repels them from mathematics.

2. “This problem can be solved by a calculator in a time

less than a second. Who in this modernized world take

so much strain to work and waste time over such simple

calculation?” asked several of the students.

3. According to many students the long division method

was itself more interesting.

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Posted by GMAT books at 11:46 AM 7 comments

### Squares

When you think of a square, you probably think of a box-shaped figure with four equal sides

that’s a good way to think about squares and square

roots.

A square of a number is just the number multiplied by itself. So the square of 4 is 4 × 4 = 16. How does

this relate to a square-shaped figure? The area of a square is the amount of space a square takes up. To calculate the area of a square, you multiply the length of one side by itself. That is why the area of a square is sometimes written as s squared, or s2. Any time a number is written with a 2 raised after it, it means to multiply the number by itself, or to square the number.

1. 22

2. 92

3. 162

4. 122

5. 62

6. 52

7. 152

8. 82

9. 32

10. 132

11. 72

12. 262

13. 352

14. 252

15. 912

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Posted by GMAT books at 11:27 AM 1 comments

### 3 digit addition using vedic maths

The strategy for adding 3-digit numbers is the same as for adding 2-digit numbers

you add left to right. After each step, you arrive at a new (and smaller) addition problem

All mental addition problems can be worked using this method. The goal is to

keep simplifying the problem until you are left adding a 1-digit number. It is important to

reduce the number of digits you are manipulating because human short-term memory is

limited to about 7 digits. Notice that 538 + 327 requires you to hold on to 6 digits in your

head, whereas 838 + 27 and 858 + 7 require only 5 and 4 digits, respectively. As you

simplify the problems, the problems get easier

Did you reduce and simplify the problem by adding left to right? After adding the

hundreds digit (623 + 100 = 723), you were left with 723 + 59. Next you should have

added the tens digit (723 + 50 = 773), simplifying the problem to 773 + 9, which you

easily summed to 782

Your mind-talk may not sound exactly like mine, but whatever it is you say to

yourself, the point is to reinforce the numbers along the way so that you don't forget

where you are and have to start the addition problem over again.

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Posted by GMAT books at 11:24 AM 1 comments

### Vedic maths....

I remember the day in third grade when I discovered that it was easier to add and

subtract from left to right than from right to left, which was the way we had all been

taught. Suddenly I was able to blurt out the answers to math problems in class well before

my classmates put down their pencils. And I didn't even need a pencil! The method was

so simple that I performed most calculations in my head. Looking back, I admit I did so

as much tc show off as for any mathematical reason. Most kids outgrow such behavior.

Those who don't probably become either teachers or magicians.

These mental skills are not only

important for doing the tricks in this book but are also indispensable in school or at work,

or any time you use numbers. Soon you will be able to retire your calculator and use the

full capacity of your mind as you add, subtract, multiply, and divide 2-digit, 3-digit, and

even 4-digit numbers.

LEFT-TO-RIGHT ADDITION

There are many good reasons why adding left to right is a superior method for

mental calculation. For one thing, you do not have to reverse the numbers (as you do

when adding right to left). And if you want to estimate your answer, then adding only the

leading digits will get you pretty close. If you are used to working from right to left on

paper, it may seem unnatural to add and multiply from left to right. But with practice you

will find that it is the most natural and efficient way to do mental calculations.

With the first set of problems—2 digit addition—the left to right method may not

seem so advantageous. But be patient. If you stick with me, you will see that the only

easy way to solve 3-digit and larger addition problems, all subtraction problems, and

most definitely all multiplication and division problems, is from left to right. The sooner you get accustomed to computing this way, the better

2-DIGIT ADDITION

My assumption is that you know how to add and subtract 1-digit

numbers. We will begin with 2-digit addition, something I suspect you can already do

fairly well in your head. The following exercises are good practice, however, because you

will use the 2-digit addition skills you polish here for larger addition problems, as well as

virtually all multiplication problems in later chapters. It also illustrates a fundamental

1

principle of mental arithmetic—namely, to simplify your problem by breaking it into

smaller, more manageable components to success—simplify, simplify, simplify.

The easiest 2-digit addition problems, of course, are those that do not require you

to cany any numbers.

To add 32 to 47, you can simplify by treating 32 as 30 + 2, add 30 to 47 and then

add 2. In this way the problem becomes 77 + 2, which equals 79.

Adding from left to right, you can simplify the problem by adding 67 + 20 = 87;

then 87 + 8 = 95

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Posted by GMAT books at 11:10 AM 1 comments

## Wednesday, August 13, 2008

### CliffsQuickReview

lgebra II (Cliffs Quick Review)

ISBN: 0764563718

Author: Edward Kohn David Alan Herzog

Publisher: Cliffs Notes

Publication Date: 2001-05-29

Number Of Pages: 272

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Posted by GMAT books at 3:32 AM 2 comments

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### Schaum's Outline of Theory and Problems

Schaum's Outline of Theory and Problems of Geometry

Schaum's Outline of Theory and Problems of Geometry: Includes Plane, Analytic, Transformational, and Solid Geometries (Schaum's Outline)

ISBN: 0070522464

Author: Barnett Rich Philip A. Schmidt

Publisher: McGraw-Hill

Publication Date: 1989-02

Number Of Pages: 272

Schaum's Outline of Geometry is a revised edition of this very successful solved-problem outline first published in 1963. "Measure of an angle" terminology and metric as well as customary units are used throughout. Dates and amounts, sections on quantifiers, and laws of reasoning have been updated. Analytic geometry and transformational geometry has been added and the section on solid geometry shortened in line with the recent national curriculum changes. The book integrates plane geometry with arithmetic, algebra, numerical trigonometry, analytic geometry, and simple logic. For plane geometry courses in high schools and colleges and for those who want independent self study. 712 Solved Problems are included. Additionally, this book includes hundreds of supplementary problems.

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Posted by GMAT books at 3:28 AM 1 comments

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## Saturday, June 14, 2008

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## Tuesday, April 22, 2008

### Idioms and phrases in GMAT

a consequence of

enough X that Y

a debate over

except for

a responsibility to

fascinated by

allows for

identical with

as X as to Y

in contrast to

ask X to Y

in danger of

associate with

independent from

based on

indifferent towards

believed X to be Y

insist that

better served by X than by Y

interaction of

centers on

just as X, so Y

compare to (similarities)

mandate that

compare with (differences)

mistake X for Y

concerned with

modeled after

consider X Y (without 'to be')

not so much X as Y

contend that

not X but rather Y

contrast X with Y

noted that

credited with

potential to

declare X Y

rates for (not 'of')

declare Y X

requiring that X Y

demand that

requiring X to Y

depends on whether

resulting in

determined by

retroactive to

differ from

so as not to be hindered by

different from

so X s to (be) Y

disagree with

so X as to constitute Y

dispute whether

the more X the greater Y

distinguish between X and Y

X enough to Y

distinguish X from Y

X out of Y (numbers)

doubt that

X regarded as Y

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Posted by GMAT books at 5:34 AM 11 comments

## Monday, April 21, 2008

### Common pitfalls in GMAT RC

Principle: something fundamental that we do not question. This would be somewhat stronger than a fact because it is not specific to a limited number of cases but instead, apply to a broader range of scenarios(and often deeper in meaning). For instance, you will not talk about the principle that crime is increasing in large cities. Instead, it is a fact which applies to large cities. However, you will talk about the principles of Physics or the fundamental principles of Human Rights. I believe principles convey a stronger connotation than mere facts.

Fact: something taken as true at face value (stats, historical events)

Evidence: what is used to support a conclusion (examples, stats, historical events). Although these may include facts, it is usually stronger than facts because they are direct elements needed for the conclusion to stand whereas facts are not necessary for the latter to stand

Pre-evidence: This is a bit of a stretch. It will not often be on the test but it seems very similar to "background" information as described below.

Background: Elements needed to put the evidence into context but which, as stand alone pieces of information, might not constitute what is called an evidence necessary to arrive at a conclusion. For instance, blood tests performed on one thousand persons may reveal that 35% of those persons were HIV infected. However, the background information could be that the test was performed in more underinformed regions of the world where AIDS knowledge is at a minimum. As you can see, the fact that the test was performed in more underinformed regions is not in and of itself an evidence because it does not allow us to come to a conclusion. Instead, the 35% stats, as a stand-alone piece of info, is what will lead us to the conclusion we want. However, the background info is also crucial and cannot be omitted; it is required background info.

Consideration: Something which was taken into account or given some thought before arriving to the conclusion.

Premise: This is usually a required statement to arrive at a conclusion. Evidence and facts want to prove something to you whereas premises are there to logically lead you to a conclusion. The best example of premises is the ones included in syllogisms. For instance, you can say that(premise1) when it rains, you go outside. Then, it rains(premise2). You have to be outside(conclusion).

Assumption: Unstated information which will link the argument to a logical conclusion. Without this, the argument falls apart.

Conclusion: Self-explanatory

Inference: Something that might not be explicitly stated or proved. For instance, you may say that 95% of GMAT test-takers have over 340. We can reasonably infer that Anthony will get more than 340 on his GMAT based on the fact given. I think the main difference b/w an inference and a conclusion is that the former might not be the final line of an argument. For instance, there could be facts/evidence given, an inference in b/w, and then the conclusion. An inference can be an intermediate step before the conclusion which will sum up the whole passage. Also, a conclusion seems to be stronger because it is based on stronger facts/evidence. As in my previous example, we can reasonably infer that Anthony got 340+ on his GMAT but we cannot conclude that he got 340+. See the nuance?

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Posted by GMAT books at 5:44 AM 9 comments

## Friday, February 29, 2008

### SC Question of the day...........

1. A collection of 38 poems by Phillis Wheatley, a slave, was published in the 1770’s, the first book by a Black woman and __it was only the second published by an American woman__.

(A) it was only the second published by an American woman

(B) it was only the second that an American woman published

(C) the second one only published by an American woman

(D) the second one only that an American woman published（E）

(E) only the second published by an American woman Read more!

Posted by GMAT books at 1:20 AM 9 comments

## Thursday, February 28, 2008

### will sent u within this monday or atmost first march....

Posted by GMAT books at 8:11 AM 22 comments

## Sunday, February 24, 2008

### Which books is best?????

This strange question is asked by each and every GMAT test taker........

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3.Princeton

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Posted by GMAT books at 2:22 AM 85 comments

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Posted by GMAT books at 2:14 AM 126 comments