We would not be as strong as what we could have been. We could never fly!

A man found a cocoon of a butterfly. One day a small opening appeared. He sat and watched the butterfly for several hours as it struggled to force its body through that little hole. Then it seemed to stop making any progress. It appeared as if it had gotten as far as it could, and it could go no further. So the man decided to help the butterfly. He took a pair of scissors and snipped off the remaining bit of the cocoon. The butterfly then emerged easily. But it had a swollen body and small, shriveled wings. The man continued to watch the butterfly because he expected that, at any moment, the wings would enlarge and expand to be able to support the body, which would contract in time. Neither happened! In fact, the butterfly spent the rest of its life crawling around with a swollen body and shriveled wings. It never was able to fly. What the man, in his kindness and haste, did not understand was that the restricting cocoon and the struggle required for the butterfly to get through the tiny opening were God's way of forcing fluid from the body of the butterfly into its wings so that it would be ready for flight once it achieved its freedom from the cocoon. Sometimes struggles are exactly what we need in our lives. If God allowed us to go through our lives without any obstacles, it would cripple us. We would not be as strong as what we could have been. We could never fly!

I asked for Strength......... And God gave me Difficulties to make me strong.

I asked for Wisdom......... And God gave me Problems to solve.

I asked for Prosperity......... And God gave me Brain and Brawn to work.

I asked for Courage......... And God gave me Danger to overcome.

I asked for Love......... And God gave me Troubled people to help.

I asked for Favors......... And God gave me Opportunities.

I received nothing I wanted ........ I received everything I needed!

So don’t worry even if you mess up with your CAT paper, God is just making you strong to Fly......

Here is overview of CAT and Expected cut offs for different Institutes:

CAT is finally OUT!

With limited access to CAT-related news in my hand, I thought the best way to help anyone interested in knowing about today's CAT test is to divert you to our mothership. Logon to www.careerlauncher.com for all the action.

All the best with the post-mortem :-)

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