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:

Click on following links:


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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!!!!

Quantitative Aptitude : Number Systems - 1

Introduction to Number system


Number system is one of the most important topic that has always been asked in ALL the MBA entrance exams and also in GRE/GMAT. It contributes quite considerable portion in quant section. Also number system being a very huge topic examiner always has a variety of questions to ask. number system is not at all difficult but it is sure exhaustive.





Why I am starting with number system?

1. It contributes major section of quant paper.
2. It deals with the basics about numbers which is always required in later concepts.
3. It sets your brain to work in "think out of the box mode".
4. It is really interesting as well as challenging.

Now before I start I would like to highlight the pedagogy that I shall follow here:

1. Concept Notes: first of all we shall assimilate all the concepts that are needed to crack questions based on number system.
2. Practice question: Then I shall post the question along with the answer. Answers of the question along with detailed explanations will also be posted
3. Doubts/Queries: You can always put your doubts and question in comment region.
4. Queries can also be emailed at trushit.vaishnav@gmail.com.

Also I would request you to subscribe to my blog. Its free.Subscribe to CAT-MBA by Email

Group discussion and essay writing : Session 1

Our today's topic is :
"Should foreign universities be allowed to have their campuses in India?"

• First answer the above question in simple terms. Yes/No. That is decide you stand, favor or against.
• If your answer is yes then why it is yes?
• If your answer is no why it is no?

Here I have provided my personal view on this topic:

I believe that foreign universities should be allowed to have their campus in India. 

Primary reason for me to be in support is that it stems out the very serious problem that our country is facing today. That is brain drain. Students of the our country go their and study. And most of them settle there only. As a result India loses its talent.

Second thing I would highlight over is research. Foreign universities provide facilities and encourage research. Against that hardly any research takes place in Indian universities as compared to foreign universities.

Third, it will give us entire new pedagogy.

Fourth, it will give rise to cosmopolitan culture. This is important for a person's personal progress. India is a country of many religions, languages etc. and If a person belong to X state, he will tend to be his own state and will always try to work with the people of his own state. This creates hindrance is his progress. Hence exposure to cosmopolitan culture eliminates this problem.

Thank You! 

Group discussion and essay writing

Group discussions and personal interviews are very powerful as well as frequently used tools. Be it a campus recruitment or be it a admission process to any damn good B school either of two, or may be both of them would me there.

Many students who do well enough at CAT fail to get seat in IIMs or even in few of the top B schools just because of their lack in abilities to express themselves. Just because they can't figure out points in favor or in against the topic stated. Some students make a grave mistake of not making their stand clear and stating their views randomly just for sake of speaking. Actually it is must that you either be in favor or be against.

GDs and and essay writing are undertaken to test you decision making abilities. They want to know how well you can analyze the situation and provide basis for why you took that decision. They are least concerned with what side have you taken...are u against or in favor...that really does not matter at all....  what matters is how well you justify your stand.

We shall see one topic today to get the fair idea about how to tackle the topics. Check out my next post!

Vocabulary session - 3

Our next root is HOSP/HOST means both host or guests.

Words that originate from HOSP/HOST are:

• Hospitality
• Hospice
• Hostel
• Inhospitable
• Hostile
• Hostage

Today I have not provided you with words in context. That is because you can get the meaning of the words without sentences. Give it a try! Don't forget to jot those judged meanings on paper. 

Hospitality :

Hospitality is something that a host is expected to show to its guests. Its a generous and friendly treatment.

Hospice:

It is a place or a program undertaken by few organisations to help terminally ill patients. Usually patients are admitted in hospice when there is no scope of improvement in their health.

Hostel:

It is a supervised place and relatively cheap for the travelers to stay overnight. Now a days it also refers to the place where students stay while they are studying in the place far away from their home.

Inhospitable:

Inhospitable is someone who is unfriendly.

Hostage:

Hostage is someone who is held or exchanged so as to maintain the truce( truce is a small period during which there won't be any violence between two groups). Sometimes kidnappers take people hostage so as to get money or concessions. Obviously hostage are not "guests"!! So etymology may give you wrong meaning over here if you have not know this word. So its better to use etymology to remember meaning of words rather than using it to derive meanings of new unknown words.

That is enough for today!!!! Good day!!!