Intelligent Guessing

©2001 Magical Methods Enterprises

Visit us at: http://www.magicalmethods.com/

Intelligent Guessing

Here I am addressing Most frequently asked question by CAT aspirants i.e. Intelligent

Guessing. I am involved in training CAT aspirants since last six years. Wherever I have gone for

lecture the students have asked me this question.

This article contains my experience with CAT and Intelligent Guessing.

I have divided this article into several parts so that student can have full knowledge of Intelligent

guessing and they can apply it.

Contents:

1. Need of Intelligent Guessing

2. What is intelligent Guessing?

3. When to do Intelligent Guessing?

4. Deterrents of Intelligent Guessing

5. Tools Required for Intelligent Guessing

6. How to take help of your subconscious mind to find the correct answer?

7. Final word: How to avoid costly mistakes?

http://www.magicalmethods.comConfidential 4/7/2023

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By Pradeep Kumar [B. Tech, MBA (IIMB)] Education Consultant, Vedic Math Expert © 2001 Magical Methods Enterpriseshttp://www.magicalmethods.com

http://www.magicalmethods.com/



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Need of Intelligent Guessing

A word about CAT (Common admission Test conducted by IIMs)

CAT is one of the toughest examinations in India. Toughness of CAT lies in the time constraints

and the type of problem asked.

CAT papers can be divided into four parts namely QA, DI, RC and VA. QA is 10 th level

mathematics, which tests calculation and problem solving speed. Apart from QA, DI tests

analytical skills of a student & VA and RC tests knowledge of English language. All these sound

simple.

The complexity arises when all this is constrained by time. Normally CAT comprises of 165-175

problems, which is to be solved in 120 minutes (2 hours). If we try to find out the allocated time

per question then it comes to roughly 40 seconds.

If you have not seen CAT type test papers then it is recommended to go through the CAT bulletin

to have a look at the difficulty level. The level of difficulty can be termed "Very Difficult".

You are a hard worker. You have mastered all the concepts. You have gone through several Full-

length tests organised by so many different CAT/MBA preparation institutes but all those are

insufficient, given the difficulty level you are going to face in CAT. You will be required to do

"Intelligent Guessing" if you wish to enter into IIMs. Frankly speaking a student will be able to

attempt 90 to 100 questions if he/she solves (?) all the problem and mind it that is not sufficient

for gaining entry into IIMs. If you want to fulfill your dream then you should be able to score in that

region (90-100). It means that you should actually answer 120-130 problems. How will you do

that? Where is the time????

To counter these situations experts suggest: do Intelligent Guessing.

Intelligent Guessing? What is this?


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What is Intelligent Guessing?

I hope you must have come across this term. Almost all the aspirants who are planning to take

CAT come across this term while preparing for the CAT.

But the definition of this term is very vague. Everyone talks about it, even the experts but still the

definition of this term is not in sight. While suggesting the students, expert says whenever you are

not able to solve the problem completely, do intelligent guessing.

In this article I will try to define this vague term and try to find out some answer to this complex

problem.

You must have seen several episodes of KBC ("Kaun Banega Krorepati"). You must also have

dreamt of being in hot seat?? Just imagine you are in hot seat facing Mr. Big B, he has put in a

question to you. If you know the answer then you will answer it without using any of your help

lines. If you do not know the answer then you will try to hazard a guess or use help lines.

Your guessing will fall into any of these two categories Blind Guessing and Intelligent

Guessing.

There are several prevalent methods of doing Blind Guessing.

1. Closing your eyes and putting your finger on one of the answer.

2. Tossing a coin

3. Tossing a dice

4. Closing your eyes and catching your left hand finger with your right hand (Fingers pre

designated with a, b, c, d etc.)

5. Making circles on the desk, namely a, b, c, d etc. and putting your finger on to one of these

after closing your eyes.

6. Marking all answers with any one of these a or b or c or d.

There are infinite number of permutations and combinations available to do Blind Guessing. But

how sure you can be of the outcome?


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Believe me nine out of ten cases your answer will be wrong.

In CAT you have negative marking. Normally for every four wrong answer one mark is deducted.

So what will happen to you if you resort to Blind Guessing?

You will end up with negative score.

I hope by now you must have understood the concept of Guessing.

When you try to hazard a guess by resorting to methods described above, you are doing nothing

but Blind Guessing. It's unrelated. You are not bothered about the question being asked and

the options provided.

Intelligent Guessing is related. You read the question and provided options. You work on the

options and try to Eliminate the wrong ones. It requires some working also. Working backward,

moving forward, using tools and techniques etc.

What is the outcome of Intelligent Guessing?

Three out of four cases you will be correct.

Take a minute to compare the outcome of Blind Guessing and Intelligent Guessing:

Particulars % Correct Effect on Exam Performance

Blind Guessing 10 Negative impact on final Score

Intelligent Guessing 75 Positive impact on final score

Facts and figures are in front of you take a look at it and decide yourself what you would like to

do, Blind Guessing or Intelligent Guessing?


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When to do Intelligent Guessing?

Intelligent Guessing can be done with Multiple Choice type of tests only. It is futile to do this with long answer types.In a Multiple choice questions a student is subjected to three kind of situation:1. Know the answer or can work out the answer.2. Do not know the answer and can not work it out.3. In between.

It's easy to deal with first kind of the problem. Work it out.

It's easy to deal with second kind of problems. Leave it.

Problem arises where one comes across a problem, which falls in between. We recommend doing Intelligent Guessing in such scenario.

How to recognise the problem which falls in between?

These problems have some symptoms , which your mind can identify .1. You are aware of some of the terms given in the problem.2. You have done such problem previously but unable to recollect the formula.3. You know that one from these two is the answer but not sure which one.4. You are receiving some sort of cue from your mind about it.

This is very fast and it does not take more than a fraction of a second to know the category in which a given question falls.


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Deterrents of Intelligent Guessing

There are several deterrents of Intelligent Guessing but the biggest one is Exam Anxiety. This takes the sheen away from the examinee. Therefore I will focus on its symptoms and how to handle it.

What is Exam Anxiety?

The term "Exam anxiety" refers to the emotional reactions that some students have to exams. The fear of exams is not an irrational fear - after all, how you perform on exams will shape the whole course of your life. But the excessive fear of exams interferes with your ability to be successful.

What are the Components of Exam Anxiety?There are three components of exam anxiety. The physical component involves the typical bodily reactions to acute anxiety: a knot in the stomach, hand wet and trembling, nausea or "butterflies in the stomach," ache in the shoulders and back of the neck, dry mouth, pounding heart, etc. The emotional component involves fear, panic, or bread - as one student put it, "I know I will not be able to make it!" The mental or cognitive components of exam anxiety involve problems with attention and memory ("My mind jumps from one thing to another"), and worry ("I'm certain to fail").

Symptoms of Exam Anxiety (List)

Fear that you'll forget? Fear that you'll run out of time? Fidget? Experience memory blocks? Experience a change in appetite? Have sweaty palms? Feel angry? Feel confused? Lack the ability to concentrate? Have stomach pains or upsets? Hyperventilate? Feel nervous? Feel your throat tighten?

How to control Exam Anxiety?

Having a positive attitude and knowing that you are organized and have studied effectively is the easiest way to prevent exam anxiety.


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By Pradeep Kumar [B. Tech, MBA (IIMB)] Education Consultant, Vedic Math Expert © 2001 Magical Methods Enterpriseshttp://www.magicalmethods.com/



Visit us at: http://www.magicalmethods.com/I will discuss the methods of controlling exam anxiety based upon the type namely Physical, Emotional and Mental or Cognitive.

Physical Symptoms:When you notice this symptoms or get a cue of physical symptoms use Relaxation Technique suggested below.Learning this is simple, but if you want to be able to do it on your next exam, you will have to practice it a few times beforehand. Follow these six steps:

1. Get comfortable in your chair - slouch down if that helps. 2. Tighten, and then relax different muscle groups or your body, one group at a time. Start

with your feet, then move up your body to your neck and face. 3. Close your eyes. 4. Begin breathing slowly and deeply. 5. Focus your attention on your breath going in and out. 6. Each time you breathe out, say "relax" to yourself.

Emotional Symptoms: An Emotional symptom consists of negative and worrisome thoughts. And our focus should be onreducing the negative and worrisome thoughts that provoke the anxiety. Students who are anxious about exams tend to think or say things to themselves that are negative, depressing, or irrelevant to the task at hand. Research shows that exam anxiety can be reduced if these negative thoughts can be replaced by positive thoughts. In order to do this, you must first become aware of your own thoughts during Full Length Tests, and then decide to practice more positive thoughts during your CAT. Given below is a list of Negative and Positive thoughts. You have to work on your negative thoughts at these three stages and replace it with positive thoughts as suggested.

Negative Thoughts Positive ThoughtsBefore CAT:*I will never pass. *I don't have to be perfect.*I'm going to panic, as usual. *Hurrying won't help anything.*If only I could get out of it. *Try not to take this too seriously.*There's too much to learn. *I can manage the situation.*Why didn't I study more? *Easy does it - it's only a test.During CAT:*Everyone else is working faster than I am. *Don't think about the others; focus on the test.*I am just plain stupid. *I don't need to prove myself.*People will notice my hands trembling. *Just take one step at a time.*My mind is a total blank. *I'm feeling tense - it's time to relax myself.*I might as well give up; what's the use? *Getting upset won't help.*Other students are turning their tests already.

*Use the time that's left - focus on the test.

After CAT:*I knew I would blow it. *I knew I could get though.*I'm going to flunk out. *It could have been a lot worse.*There is something wrong with my mind. *I handled it pretty well.*I don't belong in college. *Good - I did it.*What will my parents say? *I may not be the best, but I'm not the worst


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Visit us at: http://www.magicalmethods.com/either.

Mental Symptoms:

If you frequently experience "mental blocks" during tests, turn your test paper over before taking a test and write down math formulae, key vocabulary terms, key concepts or time lines. Then turn the test paper over and begin. Then if a "block" does occur during the test, turn your paper over and see if your notes trigger your memory.


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Tools Required for Intelligent Guessing

Long time back four men of a village were intensely discussing the alternatives so that they can irrigate their land. Rainy season was passing by. It was already a month into the rainy season. There was hardly any water in the pond they dug up last year. The responsibility of the village was on their shoulder. They thought it over and decided to dig a canal from the nearby river.

To accomplish their task they required several implements. These implements would help them to accomplish their task. They called village blacksmith and asked him to prepare the required implements.

What kind of implements do they require? Earth digging implements.

Terror monger uses their tools i.e. AK-47, Suicide Bombers, Rocket Launchers etc.

In the war against terror America is using a lot of lethal tools. You can name several of them.

Similarly you will also require tools for Intelligent Guessing. What are those tools? And what should they do?

Intelligent Guessing tools should help you out in eliminating wrong answers.

These tools are:

1. Elimination Techniques2. Approximation Technique3. Anxiety Removing Techniques 4. Practice

1. Elimination Techniques:First step to intelligent guessing should be to learn the elimination technique. Here I am providing you a list of method by which you will be able to eliminate wrong answers. Apart from the techniques listed here you can construct your own technique depending upon your experience with such type of tests.

Eliminating wrong answers by Visualization Technique

1. Alternatives with absolute or universal qualifiers are usually wrong (all, every, never, in no

case, in every case, etc.)


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Visit us at: http://www.magicalmethods.com/2. Alternatives that seem impossible or that seem completely unrelated to the question are

usually wrong (watch out for alternatives that are true, but have nothing to do with the

question).

3. If two or more alternatives say the same thing, each is probably wrong (you can have two that

are wrong, but not two that are right on m/c tests).

4. The answer to one question is sometimes given away in another question (tests contain a lot

of information - use it).

5. When 3 or more alternatives deal in different ways with one concept, one of them is usually

right. The instructor usually doesn't waste 3 alternatives on single incorrect concept. In this

case, he or she most likely wants to have you discriminate knowledge.

6. If two answers contain a similar sounding word, such as "subordination" and "subrogation,"

choose one of these.

7. If two answers are almost identical except for a few words, choose one of these.

8. If two answers seem extreme, they should be eliminated, and a guess made as to the

remaining answers. As an example, if the answer is to be a number, and 3, 57, 89, 1103 are

the choices given, you should eliminate the 3 and 1103, and take a guess at one of the

remaining choices.

9. If you are unable to eliminate any answer on a 4-answer question, choose the third.

Experience has shown that it has a better than 25% chance of being the correct answer.

10. Never argue with a question. Accept it at face value.

11. When all else fails:

a. Choose the alternative that makes the best sentence, when added to the open-ended

question.

b. Look for subject-verb agreement.

c. Know the instructor's quirks of language.

d. Choose the longer answer. The instructor may have used more words to make the

answer precise; thus the most correct.

12. If two items are correct and there is only one possible answer, then the answer must be "all of

the above."

13. If alternative e appears less than 10% of the time, it will be correct at least 80% of the time.

14. None of these rules works all the time, so use them only if you have to.

Eliminating wrong answers by Working Backward (Answer to Question)


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Visit us at: http://www.magicalmethods.com/During your test you will come across problems which is going to take a lot of time if TOP DOWN

approach is adopted. In such scenario working backward is suggested.

What is working backward?

You are said to be working backward on Multiple Choice Questions when you test the alternatives

one by one on for correctness. This way you are able to eliminate wrong alternatives. You may be

first time lucky or you may be required to test all but one of the alternatives. God forbid if you

have to test three alternatives to eliminate them. This operation is going to take a lot of time. But

who has the time? You are reading this because you would like to solve more in less time. My

dear friends it totally depends upon you whether you always want to be first time lucky or…

Secret of being first time lucky has been given here, go through it, practice it and obtain a

mastery over it. Success is waiting for you.

At this juncture you will certainly ask me: sir, what is the secret? My dear friends you can always

be first time lucky if you use this method in conjunction with the "Visualisation" method described

above. How?

First eliminate the answers using Vilualisation technique then use Working Backward. I bet you

will be correct 5 out of 6 times.

Approximation Techniques

Finding Squares, Multiplication, Addition, Subtraction, Division, Fractions, Cubes, Square Roots,

Cube Roots, Percentage Calculation.

Finding Squares: This is most important area from any examination or competition point of view.

Students do everything but when he encounters a square in the last step he leaves it. And this is

one of the demons, which appears without warning. To counter this demon coaching institutes

ask students to memorise squares up to 100. We do not recommend cramming. It simply takes

your disk space and when you want to retrieve the information, it fails.

To counter this demon I am presenting here two techniques: One is Yavdunam sutra from

Magical Methods and another is one efficient technique.

YAVDUNAM

This sutra function over a base value. The bases may be 10, multiples of 10 or 100, multiples of 100 or 1000, multiples of 1000.

For this discussion we will limit ourselves to base 10, multiples of 10 and 100, multiples of 100.

Use of Yavdunam Sutra for finding square of a number near 100.


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Say you want to find square of a number near 100 or multiples of 100. First we will discuss how to find square of a number which is near 100.

Let the number be 98.

In conventional method, you will be required to multiply 98 by 98 as shown below: -

98 X 98 ---------- 784 882 ----------- 9604 -----------

The answer comes to 9604. But it is a good deal of work.

Are you interested in something really fast? Faster than computer then learn this formula.

The formula says whatever be the difference of the number from the base add (if the number is more than the base) or subtract (if the number is less than the base) that much to the number and on the right hand side set the square of the difference. This is your answer.

Let us start working from base 100.

Say you want to find out 982

982 = 98 - 2/ 022 = 96/04 = 960498 is 2 away (less) from 100 therefore 2 is reduced from 98 in L.H.S. and on the R.H.S. square of 2 is set.

Solved Examples; -

1. 972 = 97 - 3/ 032 = 94/09 = 9409

2. 952 = 95 - 5/ 52 = 90/25 = 9025

3. 922 = 92 - 8/ 82 = 84/64 = 8464

4. 892 = 89 - 11/ 112 = 78 / 121 = 7921

Slash (/) is used here to separate the left-hand side and the right hand side of the number. You will be required to keep in mind that when you set your base as 10, 100 or 1000, number of digits on right should be equal to number of zeros in the base.

You have seen how quickly you can find square of a number which is less than 100. Can we apply the same technique for digits more than 100?

Let us try this


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Visit us at: http://www.magicalmethods.com/Say you want to find out 1022

1022 = 102+2/022 = 10404

Kind in mind, since 102 is 2 more than 100 therefore we have added 2 here as per the Sutra and on the right hand side we set square of 2. Also on R.H.S. there will be two digits.

Solved Examples: -

1. 1032 = 103+3/032 = 106/09 = 10609

2. 1072 = 107+7/72 = 114/49 = 11449

3. 1112 = 111+11/112 = 122 / 121 = 12321

4. 1162 = 116+16/162 = 132 / 256 = 13456

You have learned the super-fast method of calculating squares of a number near 100. Now let us expand this technique and learn to calculate squares of a number near 50, near 200, near 150, near 300 etc.

Yavdunam Sutra for finding squares of a number near 50.

Can we write 50 = 100/2? All of you will say yes! Aren’t you wondering why I am asking you this simple question? My dear friend we will use this to find squares of a number near 50.

Say you want to find 482

Can we proceed as given below? Taking distance from 50.

482 = 48-2/022 = 46/04 = 4604.

Now let us multiply 48 by 48

4848

-------------- 384 192-------------- 2304

The answer should be 2304 but what we are getting after using the formula is 4604. Answer is not correct! Why? Have we left out something?

In the beginning I asked you can we write 50 = 100/2 all of you said yes! Now the tine has come to use this.

To get the correct answer do this, divide the L.H.S. number by 2. Why? Because 50 = 100/2


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Visit us at: http://www.magicalmethods.com/482 = 48-2/022 = 46/04 divide L.H.S. by2.

We get 2304, which is the right answer.

Solved Examples: -

1. 472 = 47-3 / 032 = 44 / 09 = 2209 2 2

2. 462 = 46-4 / 042 = 42 / 16 = 2116 2 2

3. 532 = 53+3/ 032 = 56 / 09 = 2809 2 2

4. 522 = 52+2/ 022 = 54 / 04 = 2704 2 2

Uses of Yavdunam Sutra for finding squares of a number near 200.

I am asking you again that can we write: 200 = 100 x 2 ?

If you have gone through the previous explanation carefully then I am sure that you have understood the above clue. If you haven’t, then I would like you to go through the previous explanation before you read on. Let me ask you are you ready to take plunge? You have the clue?

If you are ready to take the plunge then let us start with an example: -

Say you want to find out 2012 can we write

2012 = 2 x (201+1)/012 = 2 x (202)/01 = 40401

Why we multiplied by 2 here because 200 = 2 x 100.

Let us multiply 201 by 201 and verify

201 201 -----------

201 000 402 -----------

40401


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Visit us at: http://www.magicalmethods.com/Hurrah! Our answer is correct.

Solved Examples: -

1. 2022 = 2 x (202 + 2)/022 = 40804

2. 2032 = 2 x (203+3)/032 = 41209

3. 2072 = 2 x (207+7)/072 = 42849

4. 1982 = 2x (198-2)/022 = 39204

5. 1922 = 2 x (192 - 8)/82 = 36864

Can you apply the technique learned here to find square of digits near 150, 250, 350 etc? Try ----

Finding square of a Number Near 50. (Second Method)

I have described several methods of finding square of a number but it's my feeling that without this the thing will not be complete.

Say you want to find 512 It can be given by

512 = 52 + 1/012 = 25+1/01 = 2601

and 522 = 52 + 2/022 = 25+2/04 = 2704

and 482 = 52 - 2/022 = 25-2/04 = 2304

and 472 = 52 - 3/032 = 25-3/09 = 2209

and 462 = 52 - 4/042 = 25-4/16 = 2116

and 492 = 52 - 1/012 = 2401

and 482 = 52 - 2/022 = 2304

and 472 = 52 - 3/032 = 2209

and 462 = 52 - 4/042 = 2116

and 442 = 52 - 6/062 = 1936

and 422 = 52 - 8/082 = 1764

and 532 = 52 + 3/032 = 2809

and 552 = 52 + 5/052 = 3025

and 562 = 52 + 6/062 = 3136

and 572 = 52 + 7/072 = 3249

and 582 = 52 + 8/082 = 3364


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Visit us at: http://www.magicalmethods.com/and 592 = 52 + 9/092 = 3481

and 612 = 52 + 11/112 = 36/121 =3721

and 642 = 52 + 14/142 = 39/196 =4096Can you think why this relation is possible with numbers near to 50 only?

Finding Square of any two-digit number. : This is one smart technique, which I was talking. This formula is very potent formula. This formula will solve your problems in minutes and it may lead to a total shift in your working method.

You may always use this formula instead of using any other because this is quick and simple. Also this formula has been derived from a simple formula known to every student above class V.

You know that (a + b)2 = a2 + 2ab + b2. But tell me where can you use this? Think about it. I will say that the use is limited. And I am going to describe the way by which you can make it unlimited. Interested?

Let us use the above formula as taught to us

Say 722 = (70 + 2)2 = 702 + 2 x 70 x 2 + 22

= 4900 + 280 + 4 = 5184

or say 662 = (60 + 6)2 = 3600 + 2 x 60 x 6 + 36= 3600 + 720 + 36= 4356

Now try to understand the method, which I am going to describe

(a + b)2= a2 + 2ab + b2

Say you want to find 722 by this method

7 22 put 7 as a and 2 as b a b

722 = a2 2ab b2

49/ 28/ 4 = 51 84 2

Separate a2, 2ab and b2 as shown above start from Right, put 4 as answer digit, No remainder put 8 as next answer digit, Remainder = 2 Add the remainder to left most number 49 + 2 = 51Thus you got the answer = 5184

The answer is the same what you have got in the first case. How do you feel now? If you have understood the steps then you will jump but let us take a few more examples

Solved Examples: -


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1. 6 62 = a2 2ab b2

a b = 36/ 72/ 36 = 4 3 5 6 7 3

Here again we have proceeded in the same way described above. Let us understand this

Start from the right,

Put 6 as answer digit & 3 as remainder Add 3 to 72 you get 75, put 5 as answer digit and 7 as a remainder, Add 7 to leftmost digit i.e. 36 + 7 you get 4356 as answer.

2. 432 = a2 2ab b2

ab = 16/ 24/ 9 = 1 8 4 9 2

3. 362 = 9/ 36/ 36 = 1 2 9 6 3 3

4. 542 = 25/ 40/ 16 = 2 9 1 6 4 1

5. 642 = 36/ 48/ 16 = 4 0 9 6 4 1

6. 872 = 64/ 112/ 49 = 7 5 6 9 11 4

7. 282 = 4/ 32/ 64 = 7 8 4 3 6

8. 332 = 9/ 18/ 9 = 1 0 8 9 1

9. 752 = 49/ 70/ 25 = 5 6 2 5 7 2

10. 892 = 64/ 144/ 81 = 7 9 2 1 15 8

How to gain the speed?

I hope by now you have fully understood the technique you can now do away with the intermediate steps and write the answers directly.


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Visit us at: http://www.magicalmethods.com/Solved Examples:-

1. 342 = 11 5 6ab 2 1

Explanation:-

First find b2 put the unit digit as answer and the tens digit as remainder, then find 2ab add the remainder to it, put the unit digit of the resultant as answer digit and other digits as remainder.

Finally find a2 and add remainder to it. You have got the answer.

It took me a lot of words to explain but it's really very easy:

2. 432 = 1 8 4 9 2

3. 572 = 3 2 4 9 7 4

4. 382 = 1 4 4 4 5 6

5. 562 = 3 1 3 6 6 3

Multiplication: Addition and subtraction is quite fast and students do not find any difficulty with

addition and subtraction. They can even do it with jet set speed. But when it comes to

multiplication they develop cold feet. Here I will be discussing few techniques, which is very

simple to adopt. You can find More techniques in our course Calculation Speed Builder.

Probably you must be aware of the policies of British Empire, which they used so effectively to

gain and retain power in India for more than 200 years. Probably you have recollected it, the

policy is very famous and this can be stated as "Divide and Rule".

You may wonder why I am describing this policy here and what is its relation with multiplication.

You do not have to wait long for understanding why I have talked about that policy here. Like

British Empire you have to use that policy to fathom calculation. This policy can be applied in all

sorts of calculation. So what I am suggesting? I am suggesting that whenever in difficulty break it

and rule over it. How?

Example:


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Visit us at: http://www.magicalmethods.com/17 16 = ?

It's slightly difficult to write the answer directly. But if you apply divide and rule policy here you can

do it mentally. How? The above multiplication can be broken as given below.

17 (10 + 6) =

Now you can work with this very easily. And write the answer as 272.

You can also break them as follows:

(20-3) 16 = 320 - 48 = 272

It is suggested that you should break the numbers into two parts in such a way that one part is

multiple of 10 and another part is small addition or subtraction. Try to choose nearest multiple of

10 as one part, this will reduce your burden considerably.

In our course Calculation Speed Builder we have provided the techniques by which you will be

able to multiply any digit with any other digit within no time. Three techniques have been

explained there namely First Formula, Quick Formula and Criss-Cross Technique. I will give

you a glimpse of First Formula here.

I have called this “First Formula” because in my opinion a person willing to learn “Magical methods of Fast calculation” should start from here. Formula will be explained by taking various examples.

Two-digit number multiplied by two-digit number.

Let us start with an example: -

35 35

How would you multiply this in conventional way?

Let us solve it: -

35 35

175 105

1225

What are the steps you took here? 1. First you multiplied 35 by 5 and wrote it below the line (175). 2. Then you multiplied 35 by 3 and wrote it below the first row leaving one space from right

(105).


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Visit us at: http://www.magicalmethods.com/3. You added the numbers in first row with the numbers in the second row by first putting

right most digit down and adding other digits thereafter conventionally. 4. You got 1225 as answer.

Now let us do it by magical method: -

35 35

1225

What did we do here?1. We multiplied 5 by 5 and put 25 as right hand side of the answer. 2. We added 1 to the top left digit 3 to make it 4. 3. We then multiplied it (4) by bottom left digit 3 and get 12, this is left hand side of the

answer. 4. We arrived at our desired answer 1225.

Did you get it?

Let us do some more by the method learned just now!

75 75

5625

Let me explain the method again !!1. We multiplied 5 by 5 and put 25 on the right hand side. 2. We added 1 to the top left digit 7 to make it 8. 3. We then multiplied 8 by bottom left digit 7 and kept 56 on left-hand side. 4. We arrived at our desired answer 5625.

Now the method should be crystal clear to you.

In the same manner, we can multiply the following: - 15 by 15, 25 by 25, 35 by 35, 45 by 45, 55 by 55, etc.

I understand, you are getting inquisitive here and planning to ask a loaded question. Your question is whether the applicability of the formula is limited to a number ending with 5 only? My answer is no, its not like that. Let us expand the formula……………….We can apply this formula to find multiplication of a good amount of two digit, three digit numbers.

Preconditions are: -


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Left-hand digits should be same and addition of right hand digits should be 10.





Let us take an example: -

66 64

4224

In this example left-hand digits are same i.e. 6 and addition of right-hand digits are 10. So we can apply this formula here.

Can we apply the same formula to the following: -

(1) 67 (2) 68 (3) 69 63 62 61

4221 4216 4209

Yes, We can apply the same formula to all these since their left-hand digits are same and addition or right hand digits are 10. Here another question may creep into your mind that in the third one above when 9 is multiplied by 1 then it gives 9, but how come we are putting 09 there. The answer is simple, from all above examples we have learned that the right hand side should have two digits but we are getting only one digit i.e. 9 so what to do? How can we use this harmlessly without changing its value? You know it, add 0 to the left. Now see whether your formula is applicable to the given examples: -

(1) 46 (2) 47 (3) 48 (4) 49 44 43 42 41

I know that, your answer is affirmative and you can write the answers as 2024, 2021, 2016 and 2009. This is just a small part of First Formula. It can be applied to three digit numbers also. There are

lots of applications of this formula, which you can find in our course Calculation Speed Builder.

(SHYSCSB)

Addition: This is a very slow process and scope of innovation is limited. But you have come

across a proverb "When there is a will there is a way". I had a way and I am suggesting you to


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Visit us at: http://www.magicalmethods.com/take two at a time. Are you perplexed? You want to put a query to me. Sir, what do you mean by

taking two at a time? Let me explain it by one small example.

Suppose you have to add the following:

345 +378 = ?

In this example let us try to take two at a time.

34 / 5 +37/ 8 = ?

Let us bifurcate the numbers into two parts. 345 can be bifurcated as 34 and 5. Similarly 378 can

be bifurcated into 37 and 8 as shown above. I have used slash (/) mark as bifurcation symbol.

Now we have two separate parts for addition: 34 +37 and 5 + 8. After separate addition they have

been written as below.

34/ 5 +37/ 8 = 71 / 13

Now how to get the final result?

On the right hand side you have two digits but there should be only one digit because after

bifurcating the numbers you have kept only one digit on the right. (Long explanation is given in

our course Magical Methods and its Application in Data Interpretation).

On the right hand side we have 13 but we should have only one digit as we have deduced. So

what should we do?

Add left most digit of RHS to left hand side i.e. carry over 1 of 13 and add it to 71. Your answer is

71 / 13 = 72 / 3 = 723

You can follow the same principle of addition with four digit numbers.

Suppose you have to add

2345 +346 = ?

Bifurcation can be done as follows:

23 / 45 +3 / 46 =

Or

234/ 5 +34/ 6 =


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Visit us at: http://www.magicalmethods.com/Only thing you have to keep in mind is the number of digits taken on the right side of the

bifurcation should be same for both the numbers and also in the answer. If you are getting more

than two digits then you should adjust the number of digits accordingly.

There is one more technique of addition i.e. adding from Left. Details are given in our course.

Magical Methods and its application in Data Interpretation.

Taking two at a time involves addition of one two digit number with another two digit number. You

will be required to do a little practice for taking two at a time. Practice material for taking two at a

time is available in our package Calculation Speed Builder.

Subtraction:

The principal you have applied above can be utilised very well for subtraction also. In this case

the process will be slightly different. Have you ever wondered how easy it is to add or subtract

numbers ending with zero? Why so?

Its because you have to work with one digit less.

This principle we will apply in our subtraction problems and see to it if this has become slightly

easier.

Suppose you have to do the following problem.

2345 - 348 = ?

If you will do it using conventional method it will take time. As it involves several carry digits.

Try the following:

The above problem can be bifurcated as shown below:

2345 - 345 - 3 =

2000 - 3 = 1997

This exercise is a mental exercise and does not require any pen and paper operation.

Now let us take another example:

3245 - 308 = ?

The above problem can be bifurcated as shown below:


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Visit us at: http://www.magicalmethods.com/32 / 45 - 3 / 08 =

Let us now work with these bifurcation i.e. 32-3 = 29 and 45-8 = 37

32 / 45 - 3 / 08 = 29 / 37 = 2937

Your answer is 2937.

You can construct your own methods of bifurcation. There can be many such methods. Again it

requires a little effort from your side.

It's very difficult to force a change on any body. But you must adopt a promising technique.

We have provided a lot of practice material in our course Calculation Speed Builder.

Division: I have classified division into two main types from examination point of view. One

where the dividend is large and divisor is small for example:

3786 128 =?

and another where dividend is small and the divisor is large (Fractions) for example:

86 129 =?

In the example where dividend is large and divisor is small you can obtain the approximate

answer as given below.

Remove last digit from the dividend and the divisor. The above example

3786 128 =?

Can be written as

379 13 =

Divide it and you will get very close answer. This has given you 29.2 as approximate answer

379 13 = 29. 2

Now let us try to find out exact answer:

3786 128 =29.58

The difference between the exact answer and the approximate answer is not much and you can

very well use this principal.

If you wish to know how to find exact answer then you should go through our package

Calculation Speed Builder. In this package we have described the shortcut process of finding

exact answer to a division problem.


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Fractions:

Now let us come to the second type, where the dividend is small and divisor is large. I have called

this system "Real Magic". This is a very potent method and very useful for intelligent guessing.

Real Magic.

I am certain that you will experience thrill after learning and understanding these methods. You will find this magical. Also you will find this very easy to work with. Try to teach these methods to as many persons as you can.

4.1.1 Denominator ending with 9.

Find 73 up to 5 places of decimals. Let us try to solve it first by conventional method: - 139

139) 730 (0 . 5 2 5 1 7 695

350 278

720 695

250 139

1110 973

137

You people are well verse with conventional method so I am skipping the explanation.

Now, Let us see the magical method: -

73 = 7.3 7.3 = 0. 5 2 5 1 7 - Answer


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Visit us at: http://www.magicalmethods.com/139 13.9 14 3 7 2 11 - Remainders

Check, whether two answers are same (?)

By conventional method our answer to 5 places of decimal is 0.52517.By magical method also our answer is 0.52517.

There is no difference between the answers, however the procedure adopted in both the methods is different. One is more cumbersome than the other. Let me explain the steps.

Steps: -

1. 73 is divided by 139 (a digit ending with 9)2. 73 is reduced to 7. 3 or 7.3

139 13.9 14 3. Start dividing 73 by 14. 4. Put the decimal point first, divide 73 by 14, 5 is Quotient and 3 is remainder, 5 is written

after the decimal and 3 is written in front of 5 below it as shown. 5. Our next gross number is 35, divide 35 by 14. Quotient = 2 and Remainder = 7. Q = 2 is

written after 5 and R = 7 before 2 (below it)6. Our next gross number is 72, divide 72 by 14. Q = 5 and R = 2, Q = 5 is written after 2

and R = 2 before 5 (below it). 7. Our Next gross number = 25, divide 25 by 14. Quotient = 1 and remainder = 11. Q = 1 is

written after 5 and R = 11 before 1 (below it).8. We have already found answer up to four decimal places, our next dividend is 111, divide

by 14. Quotient = 7, thus we have completed finding the answer up to five places of decimal.

9. Repeat the above steps if you want to find the values further.

You have learned the steps required to solve such kind of problems where the denominator ends with 9. Let us take some more examples to make our understanding clear.

Examples: -

1. 75 = 7.5 75 = 0. 5 3 9 5 6 8- Answer 139 13.9 14 5 13 7 9 11 - Remainders

2. 63 = 6.3 6.3 = 0. 4 2 2 8 1 8 7 - Answer 149 14.9 15 3 4 12 2 13 11 - Remainders

3. 83 8.3 = 0. 4 3 9 1 5 3 - Answer 189 19 7 17 2 10 6 8 - Remainders

Denominator digit ending with 8.


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Visit us at: http://www.magicalmethods.com/You will ask me a question, whether the process is applicable only if a denominator ends with 9. Answer is no. We can apply this technique to digits ends with 8, 7, 6 etc. but with slight change.

Let us see it for denominator ending with 8: - +5+2 +8+9 73 = 7.3 7.3 = 0.5 2 8 9 8 - Answer

138 13.8 14 3 12 12 10 - Remainders

In case of denominator digits ending with 8 (one less than 9) the steps are as follows: -

1. Placing of Remainder infront of Quotient remains same as explained in the case 73 or 139

denominator digit ending with 9. 2. In the Quotient digit 1 time (9 – 8= 1) of the Quotient digit is added at every step and

divided by the divisor for finding out the answer.

As in this case we found our first Q1 = 5 and R1 = 3, Our gross dividend comes out to be 35 in which we added 5 to make it 40 then divided by 14. In the next step Q2 = 2 and R2 = 12 Our gross dividend at step 2 becomes 122 + Q2 = 124. Divide this by 14.

The procedure is repeated to find the solution to required number of decimal places.

Let us take some more examples so that we can understand it better: - +4 +4 +6+4 +21. 75 = 7.5 7.5 = 0.4 4 6 4 2 8

168 16.8 17 7 10 6 4 14 +4 +6 +6 +22. 83 = 8.3 8.3 = 0.4 6 6 2 9

178 17.8 18 11 10 4 16 +1+6 +4 +8 3. 31 = 3.1 3.1 = 0.1 6 4 8 9

188 18.8 19 12 8 16 16

Denominator ending with other digits.

After learning this magical method for denominator digits ending with 8, you would like to learn for denominator digits ending with 7.

Let me take one example: - +10 +6 +4 +16 +8

73 = 7.3 7.3 = 0 . 5 3 2 8 4 137 13.7 14 3 3 11 4 6

Once you see the operation you know instantaneously that in this case Quotient digit is multiplied by 2 (9 – 2 = 2) and added to the quotient all other operations remains same as earlier.


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Can you guess what happens in case of denominator digit ends with 6?

+15 +9 +18 +21Say 73 = 7.3 = 0. 5 3 6 7 6

136 14 3 8 8 6

In this case thrice of Q digit has been added (9-6=3).

Till now you have seen explanations of the following: -73 , 73 , 73 , 73 139 138 137 136

What will you do in the case of 73 , 73 , 73 , 73 and 73 ? 135 134 133 132 131

Let us take the above mentioned cases one by one: -

73 Multiply numerator & denominator by 2 to get the answer. 135 73 2 = 146 = 146 = 1 146

135 2 270 270 10 27

73 Multiply numerator & denominator by 5 to reduce the divisor. 134 73 5 = 365 = 1 365

134 5 670 10 67

73 , Multiply numerator & denominator by 3. Apply the principle explained for denominator 133 ending with 9.

73 3 = 219 = 21.9 = 21.9 = 0 . 5 4 8 8 7133 3 399 39.9 40 19 35 34 28 8

73 , Multiply numerator & denominator by 5 to reduce the divisor. 132 73 5 = 365 = 1 365

132 5 660 10 66

73 , This case is slightly different here we reduce 1 from both numerator and denominator. 131 4 4 2 7

73 -1 = 72 = 7.2 = 7.2 = 0 . 5 5 7 2131 - 1 130 13 13 7 9 3 6

In this case we proceed as explained previously but our gross dividend changes.

Earlier our gross dividend used to be Remainder Quotient. Here in this case our gross dividend is Remainder (9 – Quotient) As shown in the example our first gross number should have been 75 but it is 7 (9 – 5) = 74.

Let me take a few examples to clarify: - 4 7 9 3

63 = 62 – 1 62 = 6.2 = 0 . 5 2 0 6 6 121 121 – 1 120 12 2 0 7 7 1

6 5 4 9 7 59 5.8 = 0. 3 4 5 0 2 9171 17 7 8 0 4 15


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Numerator having more than one digits after decimal.

Will we be able to apply the same technique when digits after the decimal are more than 1 ?

Say 738 = 7.38 = 7.38 = 0. 52/ 75 /1399 13.99 14 10 / 2

In the case explained above we bring the remainder forward after completion of two operations. Now you will ask me what shall we do when the number of the digits after the decimal places is three? Should we bring the remainder forward after completion of three operations? Yes you are right.

Every thing remains same as explained earlier only the operation related to remainder changes.

Square Roots: This is one of the tedious operations, which requires a lot of patience from the students. Still they are unable to fathom it. It is very very time consuming. So what is the solution to this tedious problem?I am giving you some technique here, If you learn these you will not find it difficult.

For finding square roots we are should have a little knowledge about its behavior. What do I mean by behavior? Nothing much, Infact I mean that you should know how many digits will be there in the square root as soon as you see a number. How will you deduce this?

This is very simple. If you can find out the number of digits in the problem you can find out the number of digits in the square roots. Therefore I said that this is very simple. You can find the number of digits in a given number (?) It can be one digit, two digits, three digits, four-digit or x digit number. What I mean to say is it will either have odd number of digits or even number of digits. Say you represent the number of digits by n,then

Number of digits in a square root will be n for even number of digits in problem and 2

(n+1) for odd number of digits in the problem 2

Once you have the above formula, you know how many digits exactly will be there in the square roots. This is not sufficient, you will also be required to know few more things before we can start


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Visit us at: http://www.magicalmethods.com/finding square roots. You will be required to understand this table. This table tells you what you should put in your answer if you see a digit in the problem.

Last Digit 12 = 1 1

22 = 4 4 32 = 9 9

42 = 16 6 52 = 25 5 62 = 36 6 72 = 49 9 82 = 64 4 92 = 81 1 102 = 100 00

On seeing the above illustration you can say that perfect squares end with 1, 4, 5, 6, 9 and 00. Or a perfect squares does not end with 2, 3, 7 and 8.

Also you can say that square of 2 and 8 ends with 4, square of 3 and 7 ends with 9, square of 4 and 6 ends with 16, square of 1 and 9 ends with 1 and square of 5 ends with 5.

This is very important deduction.

Now in a square root problem (we are dealing with perfect squares only) if you see 9 in the end you can be sure that the square root of this is ending with 3 or 7. But how to become sure that this is ending with 3 not 7 and what is the exact value?

For this you can take help of your mind capacity. Your mind is a very big computer. It stores a large amount of data and helps you in your day to day life. Here also you will take help of your this resource and find square root of the problems. In my opinion you all know this only some direction is required.

You can easily find out square of a number ending with 0 say 10, 20, 30 etc.Also you can easily find out square of a number ending with 5 (if you forgot this technique then refer to First Formula).

Let me take an example:Example: 1 - Find out square root of 529


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Visit us at: http://www.magicalmethods.com/529 is more than 400 (sq. root is 20) and less than 625 (sq. root 25). It means the square root of this very number will fall between 20 and 25.

By seeing the last digit of this number you know that the square root of this number will end with either 3 or 7.

This number falling between 20 and 25 can end with 3 only, therefore your answer will be 23.

Example: 2Find Square Root of 5041

5041is more than 4900 (sq. root is 70) and less than 5625 (sq. root 75). It means the square root of this very number will fall between 70 and 75.

By seeing the last digit of this number you know that the square root of this number will end with either 1 or 9.

This number falling between 70 and 75 can end with 1 only, therefore your answer will be 71.

I hope you have understood the concept. Apply it to get the desired result.

You have learned this technique but I am sure that your mind must be persuading you to ask something. That something I have faced in a lot of my workshops.

Students ask me what if it is not a perfect square? Do you have some technique for that?

My answer is: Yes we do have a technique, by which you can find square root of any number even in decimals. You can refer to our package Calculation Speed Builder to learn this.

Cube Roots

Finding cube root of a number is one of the very difficult tasks one can encounter with. The only method known to us till date is to find the factors of a number and then group the factors taking three at a time and take out one number from a group of three. Let us explain this with the help of an example:

Example: 1Find cube root of 1728

2 17282 8642 4322 2162 1082 543 273 9


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Visit us at: http://www.magicalmethods.com/ 3

We have found the factors now. The next step is to make a group of taking three numbers together.

2 2 2 2 2 2 3 3 3

Now if you take out one number from a group of three numbers then you will get :2 2 3 = 12

You have got your answer as 12

Example: 2Find cube root of 9261

3 92613 30873 10297 3437 49

7We have found the factors now. The next step is to make a group of taking three numbers together.

3 3 3 7 7 7 Now if you take out one number from a group of three numbers then you will get

3 7 = 21

You have got your answer as 21Finding factors of a number is a cumbersome task. This takes a lot of time. In contrast Magical Methods provides you with a one-line answer and anybody can find cube root of a number mentally once he/she understands the technique.

Cube Roots (Magical Methods)Finding Cube Roots requires some background

Background Last digit13 = 1 123 = 8 833 = 27 743 = 64 4

53 = 125 5

63 = 216 673 = 343 383 = 512 293 = 729 9


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Visit us at: http://www.magicalmethods.com/From the above illustration we can take out that last digit of 23 is 8, 33 is 7 and vice-versa. All other repeats itself.Procedure of finding a cube: -

Start from right and put a comma when three digits are over Examples: -

9,2611,72832,768

175,616 After putting the comma see the last digit of the number; compare that with table provided

above. You get the last digit. Now see the first group of numbers and ascertain cube of which number is less than the

group. That number is your first digit. You have thus found first digit and last digit.

Let us take an example: -9,261 2 1

Steps: -

Counting from last we put comma after 9. By seeing the last digit we ascertain that last digit of cube root will be 1. Now we see 9 and ascertain that 23 = 8, is less than 9 and 33 = 27 is more.

Our first digit thus comes to 2, and the answer is 21. Another Example: -

32,768 3 2

By seeing last digit we find last digit of cube root is equal to 2. By seeing 32 we put 3, as our first digit as 33 = 27 is less than 32 and 43 = 64 is more. Our answer is 32.

You may visit Guest Book section at www.magicalmethods.com to understand what people say about these methods.

Percentage Calculation: You encounter percentage calculation at several places namely profit

and loss, percentage, partnership, ratio proportion and variation, simple and compound interest,

time and distance, time and work and in several other topic. It simply depends upon the mood of

the examiner where he wants to put it. In-fact percentage is so versatile that it can be put in any

condition. Simplicity in the problem framework brings an enormous amount of difficulty for the

students, as it is never easy to solve problems involving percentage. The percentage calculation

can be termed as difficult because the amount of calculation involved. My endeavor is to reduce

the difficulty.


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How to reduce the difficulty?

Before starting the work on this, let us analyse the way this operation is being carried out.

Suppose I have to find out x% of Y then the operation will contain x multiplied by Y and whole

divided by 100. This will give us the desired answer. It seems very simple. Then where is the

difficulty?

The difficulty arises when you are required to find say 62.5 % of some number. In this case if you

do not know the shortcuts then you will multiply 62.5 with the number and divide that by 100. The

shortcut is to replace 62.5 by some fraction. I am giving below a list of commonly occurring

percentages and their equivalent replacement.

Percentages Equivalent replacement

5 % 1 / 2010 % 1/ 10

11 1/9 % 1/ 912.5 % 1/ 8

16 2/3 % 1/ 617.5 % 7/ 4020 % 1/ 525 % 1/ 4

33 1/3 % 1/ 337.5% 3 / 840% 2 / 550 % 1/ 2

62.5 % 5/ 875 % 3/ 4

87.5 % 7/ 8

Apart from the replacement suggested above you can use 10 % method. What is this?

Can you find 10% of a number?

It’s the easiest % one can find. If you can find 10% of a number then you are through. How?

Convert % into multiples of 10%.

Let us take an example.


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Visit us at: http://www.magicalmethods.com/Find 16.5% of 3365

= 504.75 + 50.475 = 555.225

What about 9%

SOLVED EXAMPLES

1. Find 68.5% of 4326

2. Find 7.6% of 383

3. Find 22% of 8742


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4. Find 22.25% of 731

5. Find 33% of 768

6. Find 6% of 1764

Anxiety Removing Techniques: We have already discussed it.

How to take help of your subconscious mind to find the correct answer? We can divide our mind

into two parts one is conscious and another is subconscious. I hope that you would be aware

that only 10% (by weight) of our brain forms conscious part and 90%(by weight) forms

subconscious part. Conscious brain is limited by logic. Subconscious is vast. It records


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Visit us at: http://www.magicalmethods.com/everything. But its up to you whether you want to take help of subconscious or not. It works

wonderfully if utilised properly. You can utilize your mind's capacity in complex situation to find the

correct answer. Chances of getting it right is more than 75%.

Technique: Use visualization and elimination technique to eliminate two choices. After

eliminating two choices you are left with two choices in which one choice is correct. Mark the

choice, which your mind hints first. (Caution: Do this only after you have reduced the number of

choices to two).

Costly Mistakes: Over Confidence : This is the worst enemy any student can have. Confidence is fine but over confidence is dangerous. I have met so many students who think that he will do it but when he actually faces it he falls flat.

Over Looking : This is most dangerous trap in which one can fall. In my experience I have seen a lot of students falling into this trap. The question says something but he understands something else. And the obvious result is wrong answer. The students even do not read the instructions carefully before proceeding to problem solving. They do not want to waste their precious time in reading instructions. They just assume the instructions (?). You may also do this if you wish to.

Over Learning : This is a case of breakdown maintenance, which is prevalent in India. People who own a vehicle take it to the mechanic when it starts giving a problem. Before the problem he does not bother about it although he could have undertaken periodic maintenance. Similarly, students put time in preparation only in the last moment (Normally last month). Some students remain awake for few continuous days before the exam (called nightouts) hoping to learn everything in that little time. This is impossible.You can learn only in short intervals. You should not put more than 2 - 3 hrs at a stretch. And a day before any important exam one should just relax.

Over Reaction : Over Reaction leads to Exam Anxiety. Due to this phenomenon I have found a lot of students change their answers frequently. They feel that their changed answer is correct but I have altogether different experience. Usually their changed answer is wrong. So it is strongly recommended that do not change your answer unless you have very strong reason to do so.

Over Drive : On road it can kill somebody. Similarly it can seal an examinee's fate. Over Drive means switching between sections frequently. If in your CAT examination you are doing this then you are trying to over drive yourself. Avoid it. You should put in first 10 minutes into going through the paper so that you can plan your time.


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