Keep your cool!

I believe the most important virtue of the people who clear CAT is their ability to have a cool head. CAT is all about your ability to handle change and pressure.

I remember my high-pressure D-Day in 1996, when I was appearing for CAT. In the chilling December cold in Lucknow, when the temperatures go down to 5-8 deg C, it was an instant "hot" shock when we looked at the test paper. We were ready for a 4-section test with an open 2-hour period. Suddenly, we were told that we were supposed to do only English sections (Verbal and RC) in the first one hour, and then Quant+DI in the latter half. I, for one, was decided on spending only about 45 mins in English.

The change in CAT pattern inevitably results in lower cutoffs in the affected sections or the overall one. So I was pretty confident that I was not the only one who was in shock. The key was to get over the shock and come out a winner. So I did extremely well in the English with 15 mins extra. And since I expected the Math + DI cutoffs to be slightly lower, I did the right selection of questions, and maximized my scores there as well. I guess some people who were otherwise sharper than me, couldn't cope well with the pressure and got behind me. How else could I explain my IIM Seat when others, who were consistently better than me, couldn't!

I can relate to the situation better with a really motivating advertisement from Accenture. The inimitable Tiger Woods is shown trying to hit a ball stuck in deep pit with all his usual concentration. Many other players would have lost half of the game in this situation, but Tiger Woods' name is synonymous with Winning! The tag line puts it appropriately for the champion..."Conditions Change, Results Shouldn't".

So, while we start the countdown to CAT, don't forget that There Is But One Seat Reserved For You at the IIMs. You only have to make sure YOU get in it, NO MATTER WHAT!

Be A Winner!

Quantitative Ability – POINTS TO REMEMBER(Algebra)

Quantitative Ability – POINTS TO REMEMBER

1.If an equation (i.e. f(x) = 0) contains all positive co-efficients of any powers of x, it has no positive roots.
Eg: x^3+3x^2+2x+6=0 has no positive roots

2.For an equation, if all the even powers of x have same sign coefficients and all the odd powers of x have the opposite sign coefficients, then it has no negative roots.

3.For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x)

4.Complex roots occur in pairs, hence if one of the roots of an equation is 2+3i, another has to be
2-3i and if there are three possible roots of the equation, we can conclude that the last root is real. This real root could be found out by finding the sum of the roots of the equation and subtracting (2+3i)+(2-3i)=4 from that sum.

5.For a cubic equation ax^3+bx^2+cx+d=o
Sum of the roots = - b/a
Sum of the product of the roots taken two at a time = c/a
Product of the roots = -d/a

6.For a bi-quadratic equation ax^4+bx^3+cx^2+dx+e = 0
Sum of the roots = - b/a
Sum of the product of the roots taken two at a time = c/a
Sum of the product of the roots taken three at a time = -d/a
Product of the roots = e/a

7.If an equation f(x)= 0 has only odd powers of x and all these have the same sign coefficients or if f(x) = 0 has only odd powers of x and all these have the same sign coefficients, then the equation has no real roots in each case (except for x=0 in the second case)

8.Consider the two equations
a1x+b1y=c1
a2x+b2y=c2
Then,
If a1/a2 = b1/b2 = c1/c2, then we have infinite solutions for these equations.
If a1/a2 = b1/b2 <> c1/c2, then we have no solution.
If a1/a2 <> b1/b2, then we have a unique solution.

9.a + b = a + b if a*b>=0
else, a + b >= a + b

10.The equation ax^2+bx+c=0 will have max. value when a<0>0. The max. or min. value is given by (4ac-b^2)/4a and will occur at x = -b/2a

11.If for two numbers x + y=k (a constant), then their PRODUCT is MAXIMUM if x=y (=k/2). The maximum product is then (k2)/4.

12. If for two numbers x*y=k (a constant), then their SUM is MINIMUM if x=y (=root(k)). The minimum sum is then 2*root (k).

13.Product of any two numbers = Product of their HCF and LCM. Hence product of two numbers = LCM of the numbers if they are prime to each other.

14. For any 2 numbers a, b where a>b
a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic means respectively)
(GM)^2 = AM * HM

15.For three positive numbers a, b, c
(a + b + c) * (1/a + 1/b + 1/c)>=9

16.For any positive integer n
2<= (1 + 1/n)^n <=3

17. a^2 + b^2 + c^2 >= ab + bc + ca
If a=b=c, then the case of equality holds good.

18.a^4 + b^4 + c^4 + d^4 >= 4abcd (Equality arises when a=b=c=d=1)

19.(n!)^2 > n^n

20.If a + b + c + d=constant, then the product a^p * b^q * c^r * d^s will be maximum if a/p = b/q = c/r = d/s

21.x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + .......+ a^(n-1) ) ......Very useful for finding multiples. For example (17-14=3 will be a multiple of 17^3 - 14^3)

22.e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ........to infinity
Note: 2 < e < 3

23.log(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 .........to infinity [Note the alternating sign . .Also note that the logarithm is with respect to base e]

24.(m + n)! is divisible by m! * n!

25.When a three digit number is reversed and the difference of these two numbers is taken, the middle number is always 9 and the sum of the other two numbers is always 9.

26.Any function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y)

The sum of first n natural numbers = n(n+1)/2

The sum of squares of first n natural numbers is n(n+1)(2n+1)/6

The sum of cubes of first n natural numbers is (n(n+1)/2)2/4

The sum of first n even numbers= n (n+1)

The sum of first n odd numbers= n^2

Test on numbers(10Q)

DIRECTIONS for Questions 1 and 2: Answer the questions on the basis of the information given below.
N is a natural number such that 300 < N < 750. P is the sum of the number N and the number formed by reversing the digits of N, even if upon reversing, it becomes a two-digit or a single-digit number. P is also equal to ‘K’ times the sum of the digits of the number N.

1. Find the minimum possible value of ‘K’.
1. 28.5 2. 32.75 3. 37.5 4. 40.25 5. 43.5

2. If ‘K’ = (96*4)/17, then find the remainder when N is divided by the sum of its digits.

1. 9 2. 12 3. 11 4. 5 5. 6

3. What is the product of all factors of the number N = 6^4 * 10^2 which are divisible by 5?
2^210 * 3^102 * 5^140
2^210 * 3^140 * 5^105
2^140 * 3^210 * 5^102
2^140 * 3^102 * 5^210
2^102 * 3^210 * 5^140

4 .If the product of four positive integers is 10! Then what is the smallest possible value their sum can have?

1. 180 2. 181 3. 175 4. 176 5 . 174

5. 3^36 – 1 = 1A009463A296999120, where A is a single digit whole number, then the value of A is

1. 1 2. 2 3. 8 4. 5 5. 6

6. Out of the 200 even natural numbers. How many even numbers exit having even number of factors?

1. 90 2. 10 3. 190 4. None of these

7. Let d1,d2….dk be all the factors of a positive integer n in ascending order including 1 and n. Supposed d1+d2+d1……..+dk = 72
Then the value of 1/d1 + 1/d2 + 1/d3……….+1/dk is

1. N^2/ 72 2. N/72 3. 72/n 4.d36/ n

8. N = 2^15* 3^7* 5^10 . How many factors of N are multiples of 360 but not multiples of 10800?

1. 402 2. 240 3. 204 4. 420


9. A = 626!-625! How many consecutive zeros would be there at the end of A?

1. 156 2. 160 3. 1 4. None of these

10. A = 4^86 – 2^171. How many digits would be there in binary notation of A?

1. 171 2. 172 3. 87 4. 88

EXISTENTIALISM SIMPLIFIED!

Well the mercury is rising everyone...CAT is just a month away!Lately I have been thinking that although we talk a lot about the reasoning and verbal section of CAT, we focus hardly on the most ubiquitous section in CAT English i.e.Reading Comprehension.We know different terms like eclectic reading ,nuances of reading,mind mapping et al but truly speaking hardly a few must have seriously done any of these.I call RC your best buddy in CAT because you can rely on it even if you have not put in a lot of effort. Over the years,CAT has had comprehensions from various realms like philosophy,history,religion,psychology etc.The passages based on philosophy are the eyesore of everybody as the pressure of the CAT environment doesn't let anybody concentrate and get to the crux of the matter.My suggestion would be to skip such passages but you should have a little insight on them , in case you have no better option.

Today one of my students asked me about EXISTENTIALISM.Though I had a preliminary idea about it and knew about Sartre,Kierkegaard and Nietzsche et al but then I wanted to simplify the entire concept....so Google came to my rescue.I read a few things which I wanted to share with all of you.Existentialistic ideas came out of a time in society when there was a deep sense of despair following the Great Depression and World War II. There was a spirit of optimism in society that was destroyed by World War I and its mid-century calamities. This despair has been articulated by existentialist philosophers well into the 1970s and continues on to this day as a popular way of thinking and reasoning.

Existentialism in the broader sense is a 20th century philosophy that is centered upon the analysis of existence and of the way humans find themselves existing in the world. The notion is that humans exist first and then each individual spends a lifetime changing their essence or nature. In simpler words, existentialism is a philosophy concerned with finding self and the meaning of life through free will, choice, and personal responsibility. The belief is that people are searching to find out who and what they are throughout life as they make choices based on their experiences, beliefs, and outlook. And personal choices become unique without the necessity of an objective form of truth. An existentialist believes that a person should be forced to choose and be responsible without the help of laws, ethnic rules, or traditions. Existentialism stresses that a person's judgment is the determining factor for what is to be believed rather than by arbitrary religious or secular world values.

An existentialist could either be a religious moralist, agnostic relativist, or an amoral atheist. Kierkegaard, a religious philosopher, Nietzsche, an anti-Christian, Sartre, an atheist, and Camus an atheist, are credited for their works and writings about existentialism. Jean-paul Sartre is noted for bringing the most international attention to existentialism in the 20th century. Each basically agrees that human life is in no way complete and fully satisfying because of suffering and losses that occur when considering the lack of perfection, power, and control one has over their life. Perhaps the most prominent theme in existentialist writing is that of choice. Humanity's primary distinction, in the view of most existentialists, is the freedom to choose. Existentialists have held that human beings do not have a fixed nature, or essence, as other animals and plants do; each human being makes choices that create his or her own nature. According to Sartre,choice is central to human existence, and it is inescapable; even the refusal to choose is a choice. Freedom of choice entails commitment and responsibility. Because individuals are free to choose their own path, existentialists have argued, they must accept the risk and responsibility of following their commitment wherever it leads.

Kierkegaard held that it is spiritually crucial to recognize that one experiences not only a fear of specific objects but also a feeling of general apprehension, which he called dread. He interpreted it as God's way of calling each individual to make a commitment to a personally valid way of life. The word anxiety (Angst) has a similarly crucial role in the work of Martin Heidegger; anxiety leads to the individual's confrontation with nothingness and with the impossibility of finding ultimate justification for the choices he or she must make. In the philosophy of Sartre, the word nausea is used for the individual's recognition of the pure contingency of the universe, and the word anguish is used for the recognition of the total freedom of choice that confronts the individual at every moment.

Existentialism is a vast and profound subject but I have tried to highlight the main points and the pillars of the philosophy. It is a very interesting area if you get into the details , nevertheless if you get a comprehension based on it,I am sure you will be able to sail through atleast a couple of questions.

Another topic of interest is the Civil Wars...so my next post shall carry some gyan on that.In the meantime all of you are free to ask about any other topic.Till then Happy Reading!!!

Difficult AR

Answer the questions on the basis of the information given below:
Atul and his four friends share a single room in a hostel. They have always been encouraged by their class teacher to develop their own interests. As a result, they boys started playing different games, studying different forms of literature and collecting different things. It is known that one of them plays cricket, one study poems and one collects coins. Following additional information is also available.

The boy who is studying stories collects Stamps.
The boy who plays football studies dramas.
Sachin collects buttons.
Mohit, who plays hockey, doesn’t study novels.
The boy who collects leaves plays tennis.
Raghu studies Autobiographies of the great leaders.
One Sunday, Deepak and the boy who collects pebbles went shopping together, the one who plays tennis went to practice, and the one who studies-novels remained in the hostel with the fellow student who plays Chess.

1. Who among the following plays Football?
a. Sachin b. Atul c. Deepak d. Raghu e. None of these

2. What does Deepak collect?
a. Leaves b. Stamps c. Pebbles d. Coins e. None of these

3. Which of the following statements is definitely true?
a. Raghu collects pebbles.
b. The boy, who collects coins, does not study dramas.
c. Atul plays cricket and studies poems.
d. The person who plays cricket studies novels.
e. Atul plays tennis.

4. Who among the following studies poems?

a. Atul b. Mohit c. Deepak d. Sachin e. Raghu

Some interesting Math facts...

1. If you join together the feet of the altitudes of a triangle, they make another triangle called the pedal triangle, and the orthocentre is the incentre of this pedal triangle.

2. The orthocentre, circumcentre and centroid are collinear (Euler’s line) and the centroid is two thirds the distance from the orthocenter to the circumcenter. The incenter is not on the Euler line except when the triangle is isosceles. When the triangle is isosceles, the Euler Line also passes through one of the vertices!

3. Take a triangle with vertices at A, B and C, and let H be its orthocenter. The orthocenter for any of the triangles formed from three of these four points is the fourth point. (4 points which satisfy this condition are called an orthocentric set.)

4. The distance from the orthocenter to a vertex is twice the distance from the circumcenter to the opposite side of the vertex.

One great math site that I love to visit frequently is www.mathforum.org and it is rich with all the knowledge that you will ever need!