Formula List for 13th May 2009

------------------------------------------
THEORY OF EQUATIONS
------------------------------------------

(1) 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

(2) For a biquadratic equation ax^4+bx^3+cx^2+dx+e = 0

sum of the roots = - b/a
sum of the product of the roots taken three at a time = c/a
sum of the product of the roots taken two at a time = -d/a
product of the roots = e/a

(3) 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.

(4) Besides Complex roots , even irrational roots occur in pairs. Hence if 2+root(3) is a root , then even 2-root(3) is a root .
(All these are very useful in finding number of positive , negative , real ,complex etc roots of an equation )

Announcing First Mock CAT

Dear Friends,
I hope that you enjoyed solving the tests I uploaded before. But you can analyze your performance only when you take a test similar to the actual entrance test.
So here I announce First Mock CAT. I shall upload it tomorrow. All the instructions will be given in the test. For your conveyance I shall give the rapidshare link so that you can download that test and solve it in your home.
Best of Luck Friends.

*Note:- The answers for DI exercise will be uploaded on 19th May 2009.
Do Comment either you like something or hate something.
Thank You.

Answers of Quant Injection for 11th May 2009

Answers
1. 2
2. 4
3. 3
4. 4
5. 4
6. 2
7. 3
8. 3
9. 4
10. 3
11. 4
12. 3
13. 2
14. 3
15. 2
16. 4
17. 2
18. 3
19. 3

New Quant injection will be uploaded tomorrow.
Best of luck.

Answers of Reading Comprehension Exercise(11th May 2009)

Passage 1

1. B 2. E 3. C 4. A 5. C
6. B 7. E 8. C


Passage 2

1. A 2. B 3. C 4. E 5. B
6. C 7. B 8. C 9. D


New RC passages will be uploaded tomorrow. So keep checking the site.
Best of luck.

Data Interpretation(DI) Practice for 11th may 2009 -25th may 2009

I have given the link for the DI test for 11th may 2009-25th may 2009. I shall post its answer keys after 1 week.
Because this is very long test so you cannot solve it in 1 day even you should not try to solve it in one day. Take at least 1 weak to solve it and then ask me for the answers.

http://rapidshare.com/files/231877093/DI_test.rar

Quant Injection for 11th May 2009

There are 19 questions. Solve them according to your own timing. Answers will be given after 24 hours i.e. with next Quant Injection

DIRECTIONS for questions 1 and 2: These questions are based on the following data.

Rama went to the market and bought some apples, mangoes and bananas. He bought 42 fruits in all. The number of bananas is less than half the number of apples; the number of mangoes is more than one-third the number of apples and the number of mangoes is less than three-fourths the number of bananas.

1. How many apples did Rama buy?

(1) 20 (2) 23 (3) 26 (4) 28

2. How many bananas did Rama buy?

(1) 8 (2) 9 (3) 10 (4) 11

DIRECTIONS for questions 3 to 5: These questions are based on the data given below.

Everyday, Saddam, the office attender fetches water for the office in container A which has certain rated capacity.

However, because of a dent at the bottom of the container, only 80% of the rated capacity of the container can be used to fill water. This water is transferred periodically into a smaller container B - for people in the office to use this water for drinking. There is an outlet (a faucet) in B from which water is let out. Since the faucet is fixed at a level above the base of B, water upto 10% of the rated capacity of B cannot be let out through the faucet. Everyday in the morning, after Saddam fetches water in container A, he cleans B and fills B to the brim by pouring water from A into B. Whenever the water level falls to the faucet level in B, he again fills B to the brim by pouring water from A into B. The questions in this set are independent of each other.

3. On a particular day, Saddam finds that he filled B five times (including the first time) and at the end of the day, A was empty. The water level in B reached the faucet level. What is the ratio of the rated capacities of A and B?

(1) 4.6 : 1 (2) 5 : 1 (3) 5.75 : 1 (4) 6.25 : 1

4. If Saddam gets the dent in container A removed (so that water can be fetched in this container to its rated capacity) how many times can he fill container B (including the first time in the morning) given that the rated capacities of the two containers are in the ratio 10 : 1?

(1) 9 times (2) 10 times (3) 12 times (4) 11 times

5. Saddam gets the dent in container A removed. He also gets the faucet in container B refixed so that all the water filled into B can be used. He keeps filling B from A everytime B gets emptied. After he pours out water from A into B the last time (i.e., A gets emptied), what percentage of B is empty? The ratio of the rated capacities of A and B is 7.5 : 1?

(1) 0% (2) 331/3% (3) 25% (4) 50%

DIRECTIONS for questions 6 and 7: These questions are based on the following data.

Amar, Akbar and Anthony sold their three cycles manufactured in different years to Mr.Kishanlal. Mr.Kishanlal gave a total of Rs.1700 to the three and said that Amar should get about one-half of the total amount as his cycle was used less. Akbar’s cycle being used more than Amar’s, he should get about one-third of the total amount and the last one gets about one-ninth. Each individual gets his amount only in denominations of Rs.100.

6. What is the difference between the amounts received by Amar and Anthony?

(1) Rs.900 (2) Rs.700 (3) Rs.800 (4) Rs.600

7. The amount that Amar has is how much more than what Akbar and Anthony together have?

(1) Rs.200 (2) Rs.300 (3) Rs.100 (4) Rs.400

Directions for questions 8 to 12: Select the correct alternative from the given choices.

8. A, B and C start running simultaneously from the points P, Q and R respectively on a circular track. The distance (when measured along the track) between any two of the three points P, Q and R is L and the ratio of the speeds of A, B and C is 1 : 2 : 3. If A and B run in opposite directions while B and C run in the same direction, what is the distance run by C before A , B and C meet for the first time?

(1)10/3L (2)11/3 L

(3) All three of them will never meet. (4) Cannot be determined

9. A circle of radius 1cm circumscribes a square. A dart is thrown such that it falls within the circle. What is the

probability that it falls outside the square?

(1) 1/2π (2) (2π - 1) /2π (3) (π - 1) /π (4) (π - 2) /π

10. Fifteen boys went to collect berries and returned with a total of 80 berries among themselves. What is the minimum number of pairs of boys that must have collected the same number of berries?

(1) 0 (2) 1 (3) 2 (4) 3

11. A cube of edge 12 ft is placed on the floor with one of its faces touching a wall. A ladder of length 35 ft is resting against that wall and is touching an edge of the cube. Find the height at which the top end of the ladder touches the wall, given that it is more than the distance of the foot of the ladder from the wall?

(1) 11 ft (2) 23 ft (3) 21 ft (4) 28 ft

12. Two circles touch each other externally. One of the circles is 300% more in area than the other. If A is the centre of the larger circle and BC is the diameter of the smaller circle and either AB or AC is a tangent to the smaller circle, then find the ratio of the area of the triangle ABC to that of the smaller circle?

(1) 2 : π (2) 3 : π (3) 2 Ö2 : π (4) π : 4Ö2

DIRECTIONS for questions 13 and 14: Select the correct alternative from the given choices.

13. a1, a2, a3, a4 and a5 are five natural numbers. Find the number of ordered sets (a1, a2, a3, a4, a5) possible such that a1 +a2 + a3 + a4 + a5 = 64.

(1) ⁶⁴C₅ (2) ⁶³C₄ (3) ⁶⁵C₄ (4) None of these

14. In the above question if a1, a2, a3, a4 and a5 are non-negative integers then find the number of ordered sets (a1, a2, a3, a4 and a5) that are possible.

(1) ⁶⁴C₅ (2) ⁶³C₄ (3) ⁶⁸C₄ (4) None of these

DIRECTIONS for questions 15 to 17: Each question gives certain information followed by two quantities A and B.

Compare A and B, and then

Mark 1 if A > B

Mark 2 if B > A

Mark 3 if A = B

Mark 4 if the relationship cannot be determined from the given data.

15. A baker had a certain number of boxes and a certain number of cakes with him. Initially he distributed all the cakes equally among all the boxes and found that there was no cake left without a box. He later found that he had one more box with him and so he redistributed all the cakes equally among all the boxes and found that there was one cake less per box than initially and one cake was left without a box with the baker.

A. The number of cakes per box in the first case.

B. The total number of boxes with the baker.

16. A trader gives a discount of r% and still makes a profit of r%. A second trader marks up his goods by r% and gives a discount of r%.

A. The cost price of the first trader.

B. The cost price of the second trader.

17. A piece of work is carried out by a group of men, all of equal capacity, in such a way that on the first day one man works and on every subsequent day one additional man joins the work. A group of women, all of equal capacity is engaged to carry out a second piece of work with ten women starting the work on the first day and one woman leaving the work at the end of everyday. The second piece of work is thrice as time consuming as the first piece of work while each man is thrice as efficient as each woman. It is known that one man working alone can complete the first piece of work in 6 days.

A. Number of days in which the first piece of work is completed.

B. Number of days in which the second piece of work is completed.

DIRECTIONS for questions 18 and 19: Select the correct alternative from the given choices.

18. A number when divided by a certain divisor, left a remainder of 8. When the same number was multiplied by 12 and then divided by the same divisor, the remainder is 12. How many such divisors are possible?

(1) 1 (2) 2 (3) 4 (4) 5

19. Consider the equation x² + y² + z² = 1. Let (x1, y1, z1) and (x2, y2, z2) be two sets of values of (x, y, z) satisfying the given equation and let A = (x1 – x2)² + (y1 – y2) ² + (z1 – z2)². What is the maximum possible value that A can assume?(assume that all the quantities involved are real numbers)

(1) 1 (2) 2 (3) 4 (4) 6

Answers of above questions

Formula List for 11th May 2009

THEORY OF EQUATIONS:
-----------------------------

(1) If an equation (i:e f(x)=0 ) contains all positive co-efficients of any powers of x , it has no positive roots then.
eg: x^4+3x^2+2x+6=0 has no positive roots .

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

(3)Summarising DESCARTES RULE OF SIGNS:

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) .
Hence the remaining are the minimum number of imaginary roots of the equation(Since we also know that the index of the maximum power of x is the number of roots of an equation.)


(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 roots could be found out by finding the sum of the roots of the equation and subtracting (2+3i)+(2-3i)=4 from that sum. (More about finding sum and products of roots next time )