CAT concept: Triangles

In most of the CAT or any other MBA questions, geometry remains as significant portion. At same time, most of the question in CAT deals with variety of shapes and not to any particular shape. To deal with such question it is important to understand each shape differently. So we shall focus on different shapes and its characteristics. Failing to understand this is the major reason for not doing well at this section. 

Shape of the day : Triangle

Triangle is a closed figure having three side. We don't need very precise definition. In fact we don't need definition at all! There are three kinds of triangle:

• Acute : If all three angles are less than 90 degree, such triangle is called right triangle

• Obtuse : If any one angle is greater 90 degree, it is called obtuse triagle.

• Right: If any one angle is equal to 90 degree, it is called right triangle.

Sum of all the three angles is 180 degree.

Sum of length of two shorter side is always greater than the longest side.

Area  = 1/2 * base * height

If all the sides are equal then such triangle is called equilateral triangle. Each angle of equilateral triangle is 60 degree.


Angle opposite to the longer side is always greater and angle opposite to smaller site is always smaller.
So we can further conclude that angles opposite to equal sides are equal. A triangle is said to be isosceles if two of the three sides are equal.

If all the three side are different it is called scalene.

Geometry - 1

Geometry has yet another concept that is begin tested each year. And just like any other quant concept, you need to absorb it all inside you. But at same time geometry for quant demands the logical thinking. Simply knowing the rules of geometry that what angle is equal to what is may not help. You need to know ow to apply it?

Many students, particularly who has left geometry long back as they took humanities or commerce may find this bit difficult. But let me tell you - ITS INTERESTING!

Let us start!

This session will be about some basics of angles. Very elementary. But as I can't scan my prepared material due to lack of time (assignments has to be submitted). I will hopefully scan tomorrow.

Alternate interior angles are equal.

Corresponding angles are equal.

Sum of circular angles = 360 degree.

Linear pair => Angle 1 + Angle 2 = 180 degree

Pattern Recognition - 3

Recently I have come across few people who try to cram the pattern that they learn. Grave mistake one can do! CAT-IIM paper setters are too smart and they change the pattern a bit and your approach to that question will change. Obviously, the concept remains same. So instead of cramming one should focus on sharpening the ability to curl out the pattern. Because there are infinite patterns possible and you never know as things are under the sun. CAT tests your ability to understand and observe and not to memorize. Its a matter of  aptitude. 





Anyways, lets us see today's question:

The number of positive integers valued pairs (x , y) satisfying 4x - 17y = 1 and x <=1000 is

• 59
• 57
• 55
• 58

Patter Recognition Question - 2

This question is a simplified version of actual CAT question. Obviously concept remains same. Try out. Check the video for solution.

If A1 = 1 and A(N+1) – 3AN + 2 = 4N for every positive integer N, then A10 = 

•

• 39    -  20
• 310  + 20 
• 39    + 20
• 310  - 20
• 310  /  20 

 

      

Pattern Recognition Question - 1

Pattern recognition as the name implies is the ability to catch the hidden pattern. CAT and other MBA entrances emphasize on this topic due to certain reasons:

• No advanced mathematical skill needed.
• Logic is king.
• You are expected to be a manager in future. Being a manager, it is expected that you can recognize the pattern. Say company makes high profits in September and sales slow down in October, then it is expected from you that you could curl out this pattern. And for this reason pattern recognition has always been there and it can be a decisive area.

We shall see the question on pattern recognition for some days. I do remember that question on number system - base concept are yet to be posted. That I will do it in few days.  

Question:

What would be the sum, in thousands, of all the possible four digits numbers that you could make with the digits 2,3,4,5 and 6.

OPTIONS ARE NOT NEEDED! For solution see this video:

  

Number System : Base concept

CAT (common admission test) always checks your thinking out of the box ability. Today what we shall discuss proves this unparalleled ability of CAT. GRE and GMAT have also used this concept. But most of the books have ignored this topic. But I really can't figure ou why? This concept is being repeatedly put to test several times. And topic is too easy even.



As we all know that we follow decimal number system. But have you ever wondered that can there be other number system too. Say octagonal number system. Have you ever wondered why anything raised to zero is one? If you know this well and good. But if you don't know this....we shall discuss this today.

Tomorrow I am going to post a slideshow with few questions on the concept that we discussed today. 

That is it for today! Thank you!

Do you know this?

CAT IS A MCQ BASED EXAMINATION! Ya ya...you all must be knowing this but many a times we forget this at a time of writing a paper. Options are your best friends. Many of the CAT and other MBA entrance exams questions are designed in such a way that you just can't solve them without use of options. If you try to get you answer by solving questions, I am sorry to say but there is complete likelihood that you will not get correct answer or may be you won't reach any answer! Let us say you are having 2 equations and three unknowns. Maths says you need 3 equations to solve equations having three unknowns. Logic never puts any limitation.

Particularly in case of DI and LR and sometimes in QUANT even, options are to be used inevitably. And sometimes, question become easier if we use options. Let us see one examples to see what wonders options can do: 

Question:

Three friends, returning from a movie, stopped to eat at a restaurant Sita took 1/3 of mint but returned 4 because of a momentary pang of guilt. Fatima then took 1/4 of what was left but returned three for similar reason. Eswari then took half of the remainder but threw 2 back to the bowl. Only 17 mints are left now. Determine original number of mints.

options : A)27 B)30 C)48 D)36

Solution: You can always use equations. But process will be time consuming. Let me tell you a logic behind this that CAT wants to check. No one will ever take mind in fractions. they will always take in whole numbers.

If option 1 were true then sita will take 1/3 *27 = 9. Left in bowl = 18. Then she returned 4. So 18 + 4=22 mints were left in bowl. But if 22 are left for fatima and she takes 1/4  *22 then fatima will take 5.5 which is a fraction. Options 1 is eliminated here.

If option 2 were true then sita will take 1/3*30 = 10. Left in bowl = 20. Then she returned 4. So 20+4= 24 mints were left in bowl. Now fatima will take 1/4*24 =6. So mints left in bowl  = 18. Then fatima returned 3. So 18+3=21 mints were left in the bowl. Eswari took 1/2 of 21. That is 10.5. Fraction! eliminated!

If option 3 were true then sita will take 1/3*48 = 16. Left in bowl = 32.then she returned 4. So 32+4=36. Now fatima will take 1/4 * 36 =9. So mints left in bowl  = 27.Then fatima returned 3. So 3+27 = 30 were left in bowl.  Eswari took 1/2 of 30. That is 15. Then Eswari returned 2. That makes 15 + 2 =17. That exactly matches the given data in the question. So our answer is option3. 


We need not to look any further option. This process may look long because I have explained it to you. But try to apply this yourself. You will realize that it takes hardly one minute.

Thank you!

CAT: FasTrack

Are you appearing for CAT 2011? You have less than two months time!! No matter how well you are prepared CAT has a power to make you feel low confident. CAT has always been know for its element of surprise! And this seems to be a valid reason to be worried!?

Well, My answer is a big NO! Because I personally believe in a theory. This theory may not help you get into IIM but it will surely help you to manage your stress (Little bit of stress in good by the way!!) See if you have prepared well....if you have been working hard enough...then there is no need to worry...You have given your best and still you have a one month time to improve. And if you did not work hard then please just stop worrying. If you did not bother to care before then why such trepidation now!! There is no point. Better work hard next time! For those who think they have worked hard but still can't score well. Don't worry! If you have worked hard in right direction (hard and smart work...both are necessary) you will come out with flying colors. You have time! This was my personal advice! 

I said all this because many of my friends who are appearing for CAT this year feel stressed. Some curse their teachers...few say that material was not good...some say CAT is not their piece of cake....etc.... excuses don't let us get anything.

Anyways still we should try to absorb most out of this remaining time. I am just trying to give you an outline to work with.

- Sleep : at least 7 hours (must).If you don't sleep enough you may go blank at CAT paper! Nothing can be worse than this!

-Mocks : Appear for maximum number of mocks. But don't over stress. If your friend appears 7 papers a week...that really does not mean that you have to appear 14 a week. Its ok even if you appear 3. Quality outweighs quantity! Also try to form your strategy!

-Revision: You better start revising your concept! That is must!

-Vocabulary : Just go through word power made easy! (you must know it by heart by now)....And standard word lists.

-Believe in yourself : I don't have anything to tell you about this!

ONCE YOU APPEAR FOR CAT, PLEASE SHARE YOUR VALUABLE EXPERIENCE OF TAKING CAT WITH US, NO MATTER IF YOU CRACK IT OR NOT!

CAT concept: Squares

CAT (common admission test) and other MBA entrance exam use simple sounding topics like square and cubes. But still most of us find it difficult to solve questions about them. Let us see few underlying concepts.



It is advised that once you learn this fundamental, you apply this to original CAT question. Also try to appy them in your day to day practice.

check out this video:

Question of the day - 2

Today's question deals with geometry!




The diameter of a hollow cone is equal to the diameter of a spherical ball. If the ball is placed at the base of a cone, what portion of ball will be outside the cone?

• <50%
• 50%
• >50%
• 100%

Solution :

Key concept  : Tangent and radius are perpendicular to each other at point of contact.

Consider the following image in which 50% of ball is inside. This is possible only in case of cylinder. Because then only radius and tangent will be perpendicular. Consider the radius ( or diameter) passing through center and completely horizontal. This divides the ball in two equal halves. It can be easily understood that only in case of cylinder 50 % of ball will be in side.

Now in case of cone what will happen is very clear from figure itself. Tangent touches the ball at the point that is in the lower halve. So ball is less than 50 % inside. So more than 50 % of ball will remain outside.

So option 3.

Question of the day - 1

Q ) How many pair of natural numbers are such that difference between their squares is 39?


Options:

• 1
• 2
• 3
• 4

Now before you proceed further, just try to solve it by your own. Kindly post your solution in comment area. There are always many different ways in which question can be cracked but here we will see the shortest and most efficient method. If you have any better method, your suggestions are welcome. 

Solution:

Natural numbers are all positive numbers greater then 0.

A² - B² = 39
(A-B) (A+B) = 39

Now 39 can be factorized as

• 1 * 39
• 3 * 13
• 13 * 3
• 39 * 1

So we get for cases:

Case 1 :

A - B = 1

A + B = 39

So A = 20 and B = 19

Case 2:

A - B = 39

A + B = 1

So A = 20 and B = -19

Case 3:

A - B = 3

A + B = 13

So A = 8 and B = 5

Case 4:

A - B = 13

A + B = 3

A = 8 and B = -5

Now from all the above four cases, only two are positive pairs. So our answer is two. Option 2.

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Question of the day!

Hi,

Almost every alternate day I post a session on vocabulary. And I guess its helping you out. But to prepare a quant concept session in one day is bit difficult. I have come up with an idea. I will post one quant question every day. The question will pertain purely to simple but profound logic. This will help you develop think out of the box ability which is must for cracking exams like CAT. Moreover, there are many website that provide "question of the day" facility. But most of them provide the questions of the kind that are almost not asked in actual exams. Before using any source, you must realize that what it provides and is it relevant with the exam. If you see the past years question papers, you will see that not even a single question can be solved with the formula that we have learned in our school days. Yes, formula can be used as a tool but at a same time logic is must. And that is what we shall develop here. Many books and websites provide questions that are typical maths problems. If you are practicing those sums then you are actually doing nothing. 

I will try to provide you an idea of what kind of logic you may need to crack the quant part of the CAT. Hope this will help you. All the best! 

Vocabulary session - 8

Today we will discuss words about love and hate. According to me love and hate are two most strongest emotions (intense feelings). And we all know the meanings of these two words. But there are several other words that are related to these words. Some are synonyms, while others have a bit different shade of meaning but still they are about feelings. And believe me, you can learn thousands of words only by learning words relating to emotions. You will see in few days!

Love according to me is one of the most innocent, clean and pure feeling. But still each person has his own way of loving.

• If you love someone selflessly, with no expectations, you have respect and regards for that person, you just want that person to be happy. This kind of love is called agape. You can say that this love is spiritual (unworldly, unearthly) in nature. Agape also means love of god towards mankind or human race. Another shade of agape, entirely different from this one is to look at something/someone with your mouth open due to something that was unexpected, awesome, surprising, shocking, starling, stunning, astonishing and amazing. For example if you see someone solving entire CAT paper in 15 minutes you may agape at him/her.

• Have you ever wondered how child love his/her parents! Complete innocence. They are so innocent that they sometimes don't even know the meaning of innocence. This love shown by child for his/her parents is called Filial love.

• Have you ever had crush on someone? Please don't say no...that would be a lame lie. When you have crush on someone, you have a lower degree of madness in you. Intense feeling of love, affection and philia. This kind of feeling is called ardor. But again ardor is platonic (free from physical desire). If a boy and a girl always be together, like each other or even love each other but have no physical desire towards each other then this kind of relation is called platonic relation.

• amorousness/enamoredness  :  These words means the same and have two shades. One is to have the feeling of fondness for someone. Other is the feeling of sexual desire. Other words that have same meaning as the second shade is carnality, prurience, eros and concupiscence. 

The most popular antonym of love is hate.

Hate does not have many different shades. Hate means to dislike someone. But many words are synonyms of hate. These are detest, hatred, loathe, execrate, abhor ( higher degree of hatred), disgust, odium (hate coupled with disgust), repugnant (offensive to your mind). 

That's all for today!! Thank you. Good day!

A word of apology!

Sorry for not posting for almost 20 days. One rat had invaded my room and cut my computers wire. Finally, I got rid of it today. So i ll be regular as I was. Sorry once again.!! 

Vocabulary session - 7

Today we will discuss the words about belief and disbelief.

• Have you ever came across a person who is too frank to be artificial. A person who has no pretense or artificiality. He don't have even minuscule amount of qualities like guile, guise, feigning, hoax etc. He is far from craftiness, deceitfulness, deceptiveness, goldbricking. A person who is away from chicanery and dissimulation ( to show some other feeling other than what you have). 

The adjective to describe such kind of person is ingenuous. Very similar sounding word is ingenious which means shrewd, cunning, inventive, adroit ( incidentally droit means right hand in french), adept.

• Our words that are synonyms of ingenuous is naive, credulous and gullible. But ingenuous is a complimentary term where as remaining there are derogatory in meaning. Let us see their meanings:
• naive means unworldly. Unknown to how this evil world works. They are innocent. They get convinced too easily. They are inexperienced, unsophisticated (-sophos- means wisdom) and ignorant.  
• credulous is from -credo- meaning to believe. 
• credibility, credit, incredible are all from the same root.
• gullible are fools. They can be convinced to believe something that is too fantastic for others to believe.
• Few more words that means the same are :
• unworldly
• unsophisticated
• fleeceable
• naif
• green
• dewy eyed
• rounded eyed.
• All the above words have similar meaning. So you are requested to get acquainted with these words. Do speak them a loud in your own voice. Get used to its appearance. Read a lot.

Thank you!!    

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A word from you...

Hello friends,

I have been uploading posts on my blog since days. But off late I have got an idea. Obviously, I will continue uploading even more material. But at the same time it would help me serve better if you tell me what you need...be it videos, concepts, roots etc.

You can send your suggestions on http://www.facebook.com/groups/133844183364374?ap=1. This is our group, strictly focused on CAT and MBA entrance examination preparation.

Benefits of joining the group:

• We get a platform to discuss and interact.
• Not only me, but all of us can discuss about concepts that are published on this blog and also about the doubts that you encounter in your day to day practice. 
• You can share links to free resources.
• You can always share your interest.
• We can have discussion and share our views on current affairs.

Come and join!

Thank you!

Vocabulary session - 6

Our today's root is VITA (life) or VIVO (to live). It is a latin root that has given birth to many important English words. Let us see few of them today. We shall also see some related words.

Have you ever encountered someone who, when you met him/her for first time are seemed to be knowing you since days?! The words that describe this kind of person is friendly, extroverted, outgoing, happy to go with. They are full of life. They are sociable,amiable, affable, cordial, genial, congenial, companionable, clubbable, forthcoming. All these words mean same.

They are convivial. (con means together + viva means life). These are the people who love to live together.



Few other words are:

• vivacious 
•  Something that has quality of life. Full of life. Something that is spirited or vibrant, animated, peppy.
• vivid  
• Vivid means fresh, sharp, strong, lively, bright, realistic, clear. It also means intense or saturated. (e.g. vivid green).
• revive: 
• re (back, again) +  vive (to live) = to bring back to life. To improve, to resuscitate, improve, resurrect, redux, upraise, rejuvenate.
• vivisection: 
• Cutting live animals to study the cause of disease.

• vital: 
• essential to life, needed, crucial, critical, indispensable.
• devitalize and revitalize (judge their meanings???)
• vitamin is also from this root.

Revise this an many times as you can! have fun and take care.

  

Number system: The Last Digit Concept

Last digit concept is one of the few important concepts that has been put to test. It deals with following two fundamentals:

• Division by 10 to know the unit place of expression. In this case it is the extension of remainder theorem.
• Representation of any number in form of 4n + x . This is used when a number is raised to some huge power is given.

See this video to understand the concept in detail:

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Number System : Remainder theorem

Remainder theorem is one of the most important concept of that has been repeatedly put to test is all the MBA entrance exams. Remainder theorem used in conjunction with "pattern of 1" is very powerful tool to determine the remainder of huge numbers.



I have a video lecture on remainder theorem that I have uploaded on my youtube channel. I have embedded that video below. Have a look. Almost all the concepts of remainder theorem has been discussed in the video.

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Thank you!

Vocabulary session - 5

Today we shall take up the root EGO. Ego is well know english word but very few of you would be knowing that EGO is one of the latin roots. EGO is one of the most selfish roots one can ever come across.

EGO means I.

Words that originated from root EGO:

• Egoistic
• Egotist
• Egocentric
• Egomaniac
• Alter Ego

Here also I don't think contextual usage is need to judge the meaning. 

Meanings:

• Egoistic: Someone who is full of ego.
• Egotist: Someone who talks about his own achievements to obnoxious degree.
• Egocentric: Someone who thinks about everything putting himself at center. Someone who is selfish.
• Egomaniac: Someone who is impulsive for his ego. A kind of madness. These kind of people can be dangerous.  

Now lets call it a day!!! See you tomorrow!!!!