Quadratic Equations are first taught to us in 6^th or 7^th class and most of us are able to score good marks in it because we are able to solve 90% of the questions by just using that formula. And that formula is:

The above formula gives us the roots of the quadratic equation ax² + bx + c = 0

For this post, I am assuming that you are aware of the basics of quadratic equations and know how to use the above mentioned formula. In case you are not, spending five minutes on the wiki page of Quadratic Equations won’t hurt. Wikipedia can be daunting at times, so come back here as soon as you start feeling woozy.

In this particular post, I am going to discuss ideas related to maxima and minima with respect to equations and quadratic equations in particular.The first thing that you need to understand is that a quadratic equation will either have a maxima or a minima but it cannot have both. The reason for that is, a quadratic equation is shaped like a parabola which is either open upwards or downwards.

As you can see here, the parabola is open upwards and it will only have a minima

The nature of the graph of the quadratic equation is decided by the co-efficient of x².

If the co-efficient of x² is greater than 0, the parabola will be open upwards and hence it will have a minima.

If the co-efficient of x² is less than 0, the parabola will be open upwards and hence it will have a maxima.

Once you have decided whether it will be a maxima or a minima the next task is to figure out two things:

a)     The point at which the maxima / minima occurs

b)     The maximum / minimum value of the quadratic equation

Let us try to figure these values out with the help of an example of both types i.e. when co-efficent of x² is greater than 0 and when it is less than 0

As you might have realised, the above idea of ‘completing a square’ can be used to find out the maximum / minimum value and also the point at which the maxima/minima occurs in any quadratic equation. Based upon the logic given above, there is also a set of formulas that you can use for a quadratic equation represented by ax² + bx + c = 0

Maxima / Minima occurs at –b/2a

 Maximum / Minimum value is (4ac – b²) / 4a

 To make things a little more complicated, you might get a question in which the quadratic equation is in the denominator.  It is sometimes also referred to as the rational function.

Example 1: Constant / Quadratic Rational Function

Find out the maximum or minimum value of 3 / (2x^2 – 5x + 7)

We know that the denominator is a quadratic equation with a > 0

•   The denominator will have a minimum value at –b/2a = 5/2 and the value will be (4ac – b²) / 4a = 31/8
•   The function will have a maximum value at 5/2 and the value will be 3/(31/8) = 24/31

Example 2: Linear / Quadratic Rational Function

Maximum value of the function is 1 and the minimum value of the function is  -1/

Example 3: Quadratic / Quadratic Rational Function

Let me add that it is not necessary that you will always be able to find out the maximum and / or the minimum value of a rational function. 

Introduction to Data Sufficiency

Data Sufficiency questions often involve very simple calculations. This does not mean that the questions are simple. It just means that the chances to make conceptual mistakes and / or silly mistakes are a little higher than usual. You will need to pay attention to detail in such questions.

In Data Sufficiency, you need to figure out whether or not the data given in the question / statements is good enough to find out a unique answer. Once again – is the data enough to find out a unique answer?

 Please note that in Data Sufficiency:

• You do not need to find out the answer
• You need to find out whether or not you can find out the answer

A Data Sufficiency question / question set will contain the following:

• Instructions – they may vary set per set
• Questions (with or without data)
• Two statements (with data – may or may not be sufficient)

A typical set of Instructions (4 options):

1. If one of the statements alone is sufficient
2. If both the statements alone are sufficient
3. If both statements together are sufficient but neither is sufficient alone
4. If both statements together are not sufficient

Let us look at a few simple questions to understand the concept in a better way. Please note that these questions are way too simple to be asked in an exam like CAT, but they are necessary for understanding the idea.

Q1: What is the value of ‘x’, given that it is an integer?

Statement A:                    x < 10

Statement B:                    x > 8

By combining both statements, I can say that x lies between 8 and 10. The only integer between 8 and 10 is 9. So my answer should be Option 3

WRONG!

Nowhere in the question it is mentioned that x is an integer / natural number. Until and unless that is specified, we cannot uniquely determine the value of ‘x’. It can take any value from 8 to 10 {eg: 8.1, 8,2, 9.999, etc.}

So, the correct answer would be Option 4

Q2 What is the value of ‘x + y’?

Statement A:                     3x + 7y = 10

Statement B:                     2x + 9y = 8

Two equations, two variables. I can solve the equations to find out the values of x & y and hence, I can find out the value of ‘x+y’ Option 3

Q3 What is the value of ‘x + y’?

Statement A:                     3x –  7y = 10

Statement B:                     14y = 6x + 19

By combining the two statements I get – Two equations, two variables. I can solve the equations to find out the values of x & y. Hence, I can find out the value of ‘x+y’ Option 3

 WRONG!

These two equations represent a set of parallel lines. They are  inconsistent with each other. I will not be able to determine the values of x & y. Hence, I cannot find out the value of ‘x+y’ Option 4

 Q4 What is the value of x?

Statement A:                     x^2 – 5x + 6 = 0

Statement B:                     x^2 – 6x + 8 = 0

From the first statement, I get the values of x as 2 & 3. I do not have a unique answer.

From the second statement, I get the values of x as 2 & 4. I do not have a unique answer.

After combining the two statements, I get the unique value of x as 2. Option 3

Q5 What is the value of x?

Statement A:                     x^2 – 5x + 6 = 0

Statement B:                     x^2 – 4x + 4 = 0

From the first statement, I get the values of x as 2 & 3. I do not have a unique answer.

From the second statement, I get the value of x as 4. I have a unique answer so there is no need to combine the two statements. Option 1

 Q6 What is the value of x?

Statement A:                     x^2 – 9x + 9 = 0

Statement B:                     x^2 – 4x + 4 = 0

From the first statement, I get the value of x as 3. I have a unique answer.

From the second statement, I get the value of x as 4. I have a unique answer.

I am getting a unique answer from both the statements individually. Option 2

Now some of you might be thinking that we have got a different answer from both the statements and so the answer is not unique. Well, that thinking is incorrect. We have to figure out whether or not the given data was sufficient. When I am looking at Statement A, I am just looking at Statement A. If I can get a unique answer from Statement A, I will not even bother with what is going on in Statement B.

Q7 Is ‘x’ a prime number?

Statement A:                     x^2 – 5x + 6 = 0

Statement B:                     x^2 – 10x + 24 = 0

From the first statement, I get the values of x as 2 & 3.

From the second statement, I get the values of x as 4 & 6.

But that is not what the question is. The question is whether or not x is a prime number. My answers should not be values of ‘x’, they should be ‘Yes’ or ‘No’ or ‘Can’t Say’.

So, let us calculate again.

From the first statement, I get the values of x as 2 & 3. So, x is a prime number. I can answer the question and my answer is YES.

From the second statement, I get the values of x as 4 & 6. So, x is not a prime number. I can answer the question and my answer is NO.

I am getting a unique answer from both the statements individually. Option 2

I hope you would be comfortable with Data Sufficiency questions now. I would like to repeat that the questions mentioned above are on the simpler side and probably you should practice some real Data Sufficiency question to get a hang of the topic.

General Awareness – Awards, Medals and Prizes (Part 1)

In philosophy, the study of knowledge is called epistemology, and the philosopher Plato famously defined knowledge as “justified true belief.” There is however no single agreed upon definition of knowledge, and there are numerous theories to explain it. When it comes to studying or preparing ‘General Knowledge / Awareness’ for a competitive exam, there are some broad based theories or guidelines which a student can use. I hope you understand that preparing for General Awareness is not an exact science like mathematics and will never be. But we can make an educated guess. A topic which has been very popular in CMAT and other management exams has been Awards / Medals / Prizes.  Although information about awards and awards winners is readily available on the interwebz, the problem is that there is too much information. Most students get bogged down looking at long lists. So, I have filtered that information and made shortened lists which would be easier to go through and remember. So, here we go.

Nobel Prizes :

In exams, the probability of a question on Nobel Prizes is reasonably high. Having said that, it would be a waste of time to go through the entire list. It would make a lot more sense if you looked at the past couple of years and / or Indian winners.

Given below is a list of Nobel Prize Winners for 2011 / 12

Indian Nobel Prize Winners

Given below is a list of Nobel winners from India or those who have some connection with India.

Booker Prizes

In 1993 to mark the 25th anniversary it was decided to choose a Booker of Bookers Prize. Three judges chose Salman Rushdie’s Midnight’s Children (the 1981 winner) as “the best novel out of all the winners.”

A similar prize known as The Best of the Booker was awarded in 2008 to celebrate the 40th anniversary of the prize. A shortlist of six winners was chosen and the decision was left to a public vote. The winner was again Midnight’s Children

Pulitzer Prize

Pulitzer Prize is a U.S. award for achievements in newspaper and online journalism, literature and musical composition. It was established in 1917 by provisions in the will of American (Hungarian-born) publisher Joseph Pulitzer, and is administered by Columbia University in New York City.

Gobind Behari Lal won the Pulitzer Prize for journalism in 1937.

Jhumpa Lahiri won the Pulitzer Prize for fiction for her book “Interpreters of Maladies” in 2000.

Geeta Anand was awarded a Pulitzer Prize in 2003 for her work on Pompe Disease, a muscular condition, which was made into a movie, “Extraordinary Measures”, and later a book, “The Cure”.

Siddhartha Mukherjee won the Pulitzer Prize for general non-fiction in 2011 for his book, “The Emperor of All Maladies: A Biography of Cancer”.

I hope you enjoyed this post and hopefully you will be able to better in CMAT because of this. In my next post, I would cover other important awards like Bharat Ratna, Padma Awards, Ramon Magsaysay Awards, etc.

General Awareness – Awards, Medals and Prizes (Part 2)

In my previous post, we talked about the Nobel Prize, the Booker Prize and the Pulitzer Prize. In this post, I would like to cover other important awards like Bharat Ratna, Padma Awards and Ramon Magsaysay Awards. Although there as hundreds, if not thousands, of people who have won these awards – it is not possible to remember all their names. I have filtered out a few for you. These have a higher probability of being asked.

Ramon Magsaysay Award

The Ramon Magsaysay Award is an annual award established to perpetuate former Philippine President Ramon Magsaysay’s example of integrity in government, courageous service to the people, and pragmatic idealism within a democratic society. The Ramon Magsaysay Award is often considered Asia’s Nobel Prize.

There have been ~50 Indians who have been awarded the Prize. The prominent / recent ones are:

Bharat Ratna

Bharat Ratna is the Republic of India’s highest civilian award, for performance of highest order in any field of human endeavor.

It was first awarded in 1954 to C. Rajgopalachari, C V Raman & S Radhakrishnan. It was last awarded in 2008 to Bhimsen Joshi.

Of the 41 awards so far, there has been one award to a naturalized Indian citizen, Mother Teresa (1980), and to two non-Indians, Khan Abdul Ghaffar Khan (1987) and Nelson Mandela (1990).

In 2011, the Government of India modified the eligibility criteria to allow sportspersons to receive the award.

Living recipients:

• Nelson Mandela (1990)
• A. P. J. Abdul Kalam (1997)
• Ravi Shankar (1999)
• Amartya Sen (1999)
• Lata Mangeshkar (2001)

Other Awards

-          Padma Vibhushan is the highest civilian honor after Bharat Ratna

-          Rajiv Gandhi Khel Ratna is the highest sporting honor

-          Dhyan Chand Award is highest award for lifetime achievement in sports and games.

-          Dadasaheb Phalke Award is the highest award for lifetime achievement in cinema.

-          Bhartiya Gnanpith Award is a literary award.

-          Shahitya Academy Fellowship is the highest literary honour conferred by the Government of India. In 2010, 5 people were honored with the Sahitya Akademi Fellowships. – Dr. Bholabhai Patel, Sri Kunwar Narain, Sri Khushwant Singh, Prof. Kedar Nath Singh & Chandranath Mishra ‘Amar’.

Fundas for SNAP

Symbiosis National Aptitude (SNAP) Test is a common and mandatory written test for the admission to all the Post-Graduate Institutes of Symbiosis International University.

The structure of this year’s paper is given below:

The above information is via www.snaptest.org I would also recommend that you join the official SNAP Facebook page if you haven’t done it already. They keep posting questions / information about the exam which might come in handy.

Few basic things that you should note based upon the official information available and papers from last two years are:

a)      It is a two-hour exam with 150 questions.

b)      All questions are of 1 mark except of ‘Analytical & Logical Reasoning’ that are 2 marks each. This means, that there will be 40 questions each in English, Quant & General Awareness and 30 in LR.

c)      Each wrong answer attracts 25% negative marks. So, avoid blind guesses.

In this post we would discuss a little about the General Awareness section. GA is a scoring area because it does not need any specific talent. Also, you need not devote too much time to this section. The questions are ‘either-you-know-or-you-don’t’ category and hence spending too much time on these would not be a good idea. Let’s face it – you cannot work out or calculate who is the Paramount Leader of China. I recommend a maximum of 20 minutes to go through this section. 30 seconds per question might sound a little optimistic but if you go through some of the sample papers for GA – you will realize that it is enough.

Given below is a broad categorization of questions that have come in the exam in the past three years (2008 / 09 / 10).

Topic-wise distribution:

Time-wise distribution:

There are few things that I will like to point out from the above data:

1. Questions on Business / Economy dominate the test. Reading business magazines of second-half of 2011 might be a good idea.
2. There are lot of questions on Science & IT as well but let me assure you that the exam-setters do not go into too much detail but it would help if you know what did Watson & Crick do.
3. The importance of current affairs has increased over the years. It would help to know who Arvind Kejriwal and Dhanush are.

There is no substitute or short cut to keeping yourself up-to-date and reading newspapers / magazines regularly. However, sample papers and old SNAP papers will come in handy in such situations.

You can download a chapter (link this to the PDF) from my book – Biz World. It won’t be much but it will help you get started.

– Month Before CAT

Dear Student,

The most common question that I face these days is “What should I do in the next few weeks before CAT”. Given below is the best possible approach in my opinion.

The Quantitative Aptitude section is the one that most non-mathematics students fear. You should first divide your study time in two parts. As of now, I would recommend a 50-50 allocation to funda-prep and test-prep. A plan to tackle the same should involve the following:

• Students should revise the basics across all chapters. You can do that from the revision section of minglebox [Please provide the appropriate link] and also from my website. This is recommended because CAT has over the years tested students on their ability to comprehend basics rather than the ability to tackle advanced problems.
• While solving advance level questions the focus should not be on time taken to solve the question but rather on the understanding of the method used to solve it.
• You should also try out a few topic tests. When you gain confidence in several topics, it will be time to start taking a couple of full-length QA tests. I would recommend taking every mock test as seriously as the real CAT. Time yourself for every test that you take and have a target time in which you have to finish the test.
• You can also revisit the mock tests which you have given in the past. I recommend that you spend a few hours to analyse the tests you have already given. Try and figure out the topics that you are doing well in. Also, try and figure out the topics in which you are not performing well. I recommend while doing this analysis, you divide the Quantitative Aptitude in these categories:

a)      Number System

b)      Geometry

c)      Arithmetic and Algebra

d)      Modern Maths (P&C, Functions, Probability, etc.)

If you notice that you are messing up in one particular category, you still have time to repair that chink in your armour.

With this I would like to wrap up this session of Handa Ka Funda. Until next time, Shine On!!!

Do`s and don`ts – Week Before CAT

Dear Student,

With just couple of weeks left to the big day, given below are seven suggestions.

1) You should not fiddle with your test-taking strategy at this stage. As long as you know that the strategy you are using is giving you rewards, don’t change it.

2) Do not over prepare. You should not take more than 5-6 full length tests in the remaining time. In the last one week you should ideally take only test.

3) The IRMA and IIFT entrance exams are scheduled for 8^th November and 22^nd November respectively. Normally, these exams are scheduled after CAT but as CAT is no longer a one-day test, they had to prepone. Do not let your performance in these two exams effect your CAT performance in a negative way. Some students get disheartened if they perform badly in couple of tests. On the other hand, some become complacent because of their performance in an exam. Make sure you are not a victim of the phenomenon mentioned above.

4) Avoid random guessing. I have never seen it work and I don’t think that you are a special child of Goddess Fortuna. However, intelligent guessing is a smart idea. If you are down to two options, you should definitely go for it.

5) If you have practiced enough amount of variety, CAT DI should not be tough to tackle. And out of a set of five questions, at least three are bound to be easy. Learn the art of skipping questions in DI. The misconception is that you have to solve the whole set before you move on to the next set. I think this is the time which you should devote to DI more than anything else. The return on time invested is going to be the highest.

6) Know your limitations. If your percentiles in the Simulated CATs that you have taken are consistently below 80%ile then you should not attempt a large number of questions.

7) It happens often that high potential students fail to perform because of the pressure. So, I suggest that you unwind, go for movies, hangout with friends. Let me be a little more specific here, non CAT taking friends and the movie should be anything other than London Dreams. It is quite possible that you shoot yourself after watching that absurdity. J

With this I would like to wrap up this session of Handa Ka Funda. Cheers!

Two Days Before CAT !!!

Dear Students,

The most neglected thing during the exam week is to be normal. I know it is easier said than done. For the week before and during the exam, life should be as normal as possible. A clear head is important for taking the exam efficiently.

Do you believe that you can tramp the last mile? What is your response?

-          ‘I am doing great ; bring on the CAT’

-          ‘I am doing great, but I hope I don’t stumble now’

-          ‘Man! I am sure I can crack the CAT. If only Math would stop killing me’

-          ‘When is SNAP??’

Whatever is your response, to tramp the last mile – Have a fresh outlook

* Rejuvenate

• Imagine you have just started your prep
• Imagine the last comprehensive test you took is your first test

* Re-focus

• The Goal  : The CAT
• The Time  : Few days to go
• The Attitude  : Everything to gain and nothing to lose

Few other suggestions:

# During the last week of the exam, students often resort to junk food, but if you really want to maintain your confidence it is extremely important to maintain the right kind of diet. Research shows that eating smaller meals more frequently is vital to maintaining high energy levels. Avoid foods with high sugar and fat – they will make you sluggish. Eat a nutritious breakfast (or meal) before the exam, but do not overeat.

# The most common mistake that we commit during last week’s preparation is by skipping the problems that we are unable to solve because of time-shortage. Make sure that your have instant access to a knowledge base. Your trainers are the best knowledge base that you have. Call them whenever you want to have the problem solved right away. You can mail me at ravihanda@gmail.com for similar stuff.

Heads of Bodies – National and International

When it comes to MBA entrance exams life CMAT, IIFT, SNAP, etc. the knowledge of the heads of important organizations is really helpful. More often than not, you will end up getting couple of questions on these. There is also a reasonable chance that you will get a question of Match-The-Following type where this information would be really useful.

I have compiled a list of the current heads of important bodies and divided into two parts: India & International. Both of them are given below. (F) indicates that the person is a female.

India/ National:

International:

I hope you will find this list useful. This list was last checked / updated on 18^th February 2013.

Question : Find the Remainder when 101010…(94 digits) is divided by 375

a. 10

b. 320

c. 40

d. None of these

Answer : 

375 = 125*3