CAT2001 Related Question Answers
3.
Directions for the following two questions: Answer the questions based on the following information.The batting average (BA) of a Test batsman is computed from runs scored and innings played — completed innings and incomplete innings (not out) in the following manner:$$r_1 =$$ Number of runs scored in completed innings$$n_1 =$$ Number of completed innings$$r_2 =$$ Number of runs scored in incomplete innings$$n_2 =$$ Number of incomplete innings$$BA=\frac{r_1+r_2}{n_1}$$To better assess a batsman’s accomplishments, the ICC is considering two other measures $$MBA_1$$ and $$MBA_2$$ defined as follows:$$MBA_1 = \frac{r_1}{n_1} + \frac{n_2}{n_1}*max[0,(\frac{r_2}{n_2}-\frac{r_1}{n_1})]$$$$MBA_2 = \frac{r_1 + r_2}{n_1 + n_2}$$Based on the above information which of the following is true?
4. An experienced cricketer with no incomplete innings has BA of 50. The next time he bats, the innings is incomplete and he scores 45 runs. It can be inferred that
5.
Directions for the following two questions: Answer the questions based on the following information.The petrol consumption rate of a new model car ‘Palto’ depends on its speed and may be described by the graph below.The axis represents the speed and the Y axis represents the Fuel Consumption (Liters per hour)
Manasa makes a 200 km trip from Mumbai to Pune at a steady speed of 60 km/hr. What is the volume of petrol consumed for the journey?[CAT 2001]
6. Manasa would like to minimize the fuel consumption for the trip by driving at the appropriate speed. How should she change the speed?[CAT 2001]
7. A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is
8. A square, whose side is 2 m, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres, is
9. Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?
11. A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?
12. Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least
13. A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, 3 km north of the north gate, and it can just be seen from a point 9 km east of the south gate. What is the diameter of the wall that surrounds the city?
14. In the given diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the areas of CEF and that of the rectangle?
15. A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work. Which is the first pair?
16. In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?
17. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial monthly salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial monthly salary of Rs. 200 with a rise of Rs. 15 every 6 months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?
18. Anita had to do a multiplication. In stead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?
19. A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited?
20. x and y are real numbers satisfying the conditions 2 < x < 3 and - 8 < y < -7. Which of the following expressions will have the least value?
21. $$m$$ is the smallest positive integer such that for any integer $$n \geq m$$, the quantity $$n^3 - 7n^2 + 11n - 5$$ is positive. What is the value of $$m$$?
22. A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?
23. Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for similar reason. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?
25. In a number system the product of 44$$_{10}$$ and 11$$_{10}$$ is 3414. The number 3111 of this system, when converted to the decimal number system, becomes
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