Page 1 Page 1 CAT 2001 Actual Paper Directions for questions 1 to 37: Answer the questions independently. 1. 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 a. 2 b. 3 c. 4 d. 5 2. 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 a. 1 2 2 + b. 1 2 2 + c. 1 â€“ 2 2 d. 1 â€“ 2 2 3. 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? a. y(x â€“ z) 2 is even b. y 2 (x â€“ z) is odd c. y(x â€“ z) is odd d. z(x â€“ y) 2 is even 4. If x > 5 and y < â€“1, then which of the following statements is true? a. (x + 4y) > 1 b. x > â€“4y c. â€“4x < 5y d. None of these 5. 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? a. 30 b. 24 c. 20 d. 60 6. 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 a. 5 b. 103 c. 6 d. Cannot be determined 7. 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? a. 6 km b. 9 km c. 12 km d. None of these Instructions: 1. The Test Paper contains 150 questions. The duration of the test is 120 minutes. 2. The paper is divided into three sections. Section-I: 50 Q:, Section-II: 50 Q:, Section-III: 50 Q. 3. Wrong answers carry negative marks. There is only one correct answer for each question. Page 2 Page 1 CAT 2001 Actual Paper Directions for questions 1 to 37: Answer the questions independently. 1. 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 a. 2 b. 3 c. 4 d. 5 2. 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 a. 1 2 2 + b. 1 2 2 + c. 1 â€“ 2 2 d. 1 â€“ 2 2 3. 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? a. y(x â€“ z) 2 is even b. y 2 (x â€“ z) is odd c. y(x â€“ z) is odd d. z(x â€“ y) 2 is even 4. If x > 5 and y < â€“1, then which of the following statements is true? a. (x + 4y) > 1 b. x > â€“4y c. â€“4x < 5y d. None of these 5. 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? a. 30 b. 24 c. 20 d. 60 6. 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 a. 5 b. 103 c. 6 d. Cannot be determined 7. 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? a. 6 km b. 9 km c. 12 km d. None of these Instructions: 1. The Test Paper contains 150 questions. The duration of the test is 120 minutes. 2. The paper is divided into three sections. Section-I: 50 Q:, Section-II: 50 Q:, Section-III: 50 Q. 3. Wrong answers carry negative marks. There is only one correct answer for each question. Page 2 CAT 2001 Actual Paper 8. AB C D EF In the above diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the areas of ? CEF and that of the rectangle? a. 6 1 b. 8 1 c. 9 1 d. None of these 9. 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? a. A and B b. A and C c. B and C d. A and D 10. 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? a. 5 b. 8 c. 1 d. 4 11. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial 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? a. Rs. 93,300 b. Rs. 93,200 c. Rs. 93,100 d. None of these 12. 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? a. 1050 b. 540 c. 1440 d. 1590 13. 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? a. Rs. 300 b. Rs. 250 c. Rs. 400 d. Rs. 500 14. x and y are real numbers satisfying the conditions 2 < x < 3 and â€“ 8 < y < â€“7. Which of the following expressions will have the least value? a. x 2 y b. xy 2 c. 5xy d. None of these 15. m is the smallest positive integer such that for any integer m n= , the quantity n 3 â€“ 7n 2 + 11n â€“ 5 is positive. What is the value of m? a. 4 b. 5 c. 8 d. None of these 16. 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? a. 10 m b. 15 m c. 20 m d. 17 m Page 3 Page 1 CAT 2001 Actual Paper Directions for questions 1 to 37: Answer the questions independently. 1. 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 a. 2 b. 3 c. 4 d. 5 2. 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 a. 1 2 2 + b. 1 2 2 + c. 1 â€“ 2 2 d. 1 â€“ 2 2 3. 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? a. y(x â€“ z) 2 is even b. y 2 (x â€“ z) is odd c. y(x â€“ z) is odd d. z(x â€“ y) 2 is even 4. If x > 5 and y < â€“1, then which of the following statements is true? a. (x + 4y) > 1 b. x > â€“4y c. â€“4x < 5y d. None of these 5. 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? a. 30 b. 24 c. 20 d. 60 6. 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 a. 5 b. 103 c. 6 d. Cannot be determined 7. 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? a. 6 km b. 9 km c. 12 km d. None of these Instructions: 1. The Test Paper contains 150 questions. The duration of the test is 120 minutes. 2. The paper is divided into three sections. Section-I: 50 Q:, Section-II: 50 Q:, Section-III: 50 Q. 3. Wrong answers carry negative marks. There is only one correct answer for each question. Page 2 CAT 2001 Actual Paper 8. AB C D EF In the above diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the areas of ? CEF and that of the rectangle? a. 6 1 b. 8 1 c. 9 1 d. None of these 9. 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? a. A and B b. A and C c. B and C d. A and D 10. 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? a. 5 b. 8 c. 1 d. 4 11. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial 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? a. Rs. 93,300 b. Rs. 93,200 c. Rs. 93,100 d. None of these 12. 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? a. 1050 b. 540 c. 1440 d. 1590 13. 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? a. Rs. 300 b. Rs. 250 c. Rs. 400 d. Rs. 500 14. x and y are real numbers satisfying the conditions 2 < x < 3 and â€“ 8 < y < â€“7. Which of the following expressions will have the least value? a. x 2 y b. xy 2 c. 5xy d. None of these 15. m is the smallest positive integer such that for any integer m n= , the quantity n 3 â€“ 7n 2 + 11n â€“ 5 is positive. What is the value of m? a. 4 b. 5 c. 8 d. None of these 16. 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? a. 10 m b. 15 m c. 20 m d. 17 m Page 3 CAT 2001 Actual Paper 17. 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? a. 38 b. 31 c. 41 d. None of these 18. If 09/12/2001(DD/MM/YYYY) happens to be Sunday, then 09/12/1971 would have been a a. Wednesday b. Tuesday c. Saturday d. Thursday 19. In a number system, the product of 44 and 11 is 3414. The number 3111 of this system, when converted to the decimal number system, becomes a. 406 b. 1086 c. 213 d. 691 20. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour? a. 3 7 b. 3 4 c. 3 5 d. 3 8 21. Every 10 years the Indian Government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri. Chota Hazri has 4,522 fewer males than Mota Hazri. Mota Hazri has 4,020 more females than males. Chota Hazri has twice as many females as males. Chota Hazri has 2,910 fewer females than Mota Hazri. What is the total number of males in Chota Hazri? a. 11,264 b. 14,174 c. 5,632 d. 10,154 22. Three classes X, Y and Z take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes? a. 81 b. 81.5 c. 82 d. 84.5 23. Two sides of a plot measure 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. 25 25 24 32 Page 4 Page 1 CAT 2001 Actual Paper Directions for questions 1 to 37: Answer the questions independently. 1. 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 a. 2 b. 3 c. 4 d. 5 2. 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 a. 1 2 2 + b. 1 2 2 + c. 1 â€“ 2 2 d. 1 â€“ 2 2 3. 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? a. y(x â€“ z) 2 is even b. y 2 (x â€“ z) is odd c. y(x â€“ z) is odd d. z(x â€“ y) 2 is even 4. If x > 5 and y < â€“1, then which of the following statements is true? a. (x + 4y) > 1 b. x > â€“4y c. â€“4x < 5y d. None of these 5. 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? a. 30 b. 24 c. 20 d. 60 6. 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 a. 5 b. 103 c. 6 d. Cannot be determined 7. 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? a. 6 km b. 9 km c. 12 km d. None of these Instructions: 1. The Test Paper contains 150 questions. The duration of the test is 120 minutes. 2. The paper is divided into three sections. Section-I: 50 Q:, Section-II: 50 Q:, Section-III: 50 Q. 3. Wrong answers carry negative marks. There is only one correct answer for each question. Page 2 CAT 2001 Actual Paper 8. AB C D EF In the above diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the areas of ? CEF and that of the rectangle? a. 6 1 b. 8 1 c. 9 1 d. None of these 9. 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? a. A and B b. A and C c. B and C d. A and D 10. 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? a. 5 b. 8 c. 1 d. 4 11. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial 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? a. Rs. 93,300 b. Rs. 93,200 c. Rs. 93,100 d. None of these 12. 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? a. 1050 b. 540 c. 1440 d. 1590 13. 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? a. Rs. 300 b. Rs. 250 c. Rs. 400 d. Rs. 500 14. x and y are real numbers satisfying the conditions 2 < x < 3 and â€“ 8 < y < â€“7. Which of the following expressions will have the least value? a. x 2 y b. xy 2 c. 5xy d. None of these 15. m is the smallest positive integer such that for any integer m n= , the quantity n 3 â€“ 7n 2 + 11n â€“ 5 is positive. What is the value of m? a. 4 b. 5 c. 8 d. None of these 16. 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? a. 10 m b. 15 m c. 20 m d. 17 m Page 3 CAT 2001 Actual Paper 17. 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? a. 38 b. 31 c. 41 d. None of these 18. If 09/12/2001(DD/MM/YYYY) happens to be Sunday, then 09/12/1971 would have been a a. Wednesday b. Tuesday c. Saturday d. Thursday 19. In a number system, the product of 44 and 11 is 3414. The number 3111 of this system, when converted to the decimal number system, becomes a. 406 b. 1086 c. 213 d. 691 20. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour? a. 3 7 b. 3 4 c. 3 5 d. 3 8 21. Every 10 years the Indian Government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri. Chota Hazri has 4,522 fewer males than Mota Hazri. Mota Hazri has 4,020 more females than males. Chota Hazri has twice as many females as males. Chota Hazri has 2,910 fewer females than Mota Hazri. What is the total number of males in Chota Hazri? a. 11,264 b. 14,174 c. 5,632 d. 10,154 22. Three classes X, Y and Z take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes? a. 81 b. 81.5 c. 82 d. 84.5 23. Two sides of a plot measure 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. 25 25 24 32 Page 4 CAT 2001 Actual Paper What is the area of the plot? a. 768 2 m b. 534 2 m c. 696.5 2 m d. 684 2 m 24. All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice? a. 44 b. 45 c. 10 d. 12 25. Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyomâ€™s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up? a. 40 b. 50 c. 60 d. 80 26. At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries? a. Rs. 31 b. Rs. 41 c. Rs. 21 d. Cannot be determined 27. If a, b, c and d are four positive real numbers such that abcd = 1, what is the minimum value of (1 + a)(1 + b)(1 + c)(1 + d)? a. 4 b. 1 c. 16 d. 18 28. Thereâ€™s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, thereâ€™s still the potatoes and gravy, yams, salad, and cranberries, not to mention setting the table. Three friends â€” Asit, Arnold and Afzal â€” work together to get all of these chores done. The time it takes them to do the work together is 6 hr less than Asit would have taken working alone, 1 hr less than Arnold would have taken alone, and half the time Afzal would have taken working alone. How long did it take them to do these chores working together? a. 20 min b. 30 min c. 40 min d. 50 min 29. Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side? a. 260 b. 250 c. 240 d. 270 30. For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of 7th and 6th terms of this sequence is 517, what is the 10th term of this sequence? a. 147 b. 76 c. 123 d. Cannot be determined 31. Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes? a. 2 kg b. 2.4 kg c. 2.5 kg d. None of these 32. Train X departs from station A at 11 a.m. for station B, which is 180 km so far. Train Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stop for 15 min at station C, which is 60 km away from station B enroute to station A. Ignoring the lengths of the trains, what is the distance, to the nearest kilometre, from station A to the point where the trains cross each other? a. 112 km b. 118 km c. 120 km d. None of these Page 5 Page 1 CAT 2001 Actual Paper Directions for questions 1 to 37: Answer the questions independently. 1. 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 a. 2 b. 3 c. 4 d. 5 2. 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 a. 1 2 2 + b. 1 2 2 + c. 1 â€“ 2 2 d. 1 â€“ 2 2 3. 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? a. y(x â€“ z) 2 is even b. y 2 (x â€“ z) is odd c. y(x â€“ z) is odd d. z(x â€“ y) 2 is even 4. If x > 5 and y < â€“1, then which of the following statements is true? a. (x + 4y) > 1 b. x > â€“4y c. â€“4x < 5y d. None of these 5. 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? a. 30 b. 24 c. 20 d. 60 6. 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 a. 5 b. 103 c. 6 d. Cannot be determined 7. 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? a. 6 km b. 9 km c. 12 km d. None of these Instructions: 1. The Test Paper contains 150 questions. The duration of the test is 120 minutes. 2. The paper is divided into three sections. Section-I: 50 Q:, Section-II: 50 Q:, Section-III: 50 Q. 3. Wrong answers carry negative marks. There is only one correct answer for each question. Page 2 CAT 2001 Actual Paper 8. AB C D EF In the above diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the areas of ? CEF and that of the rectangle? a. 6 1 b. 8 1 c. 9 1 d. None of these 9. 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? a. A and B b. A and C c. B and C d. A and D 10. 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? a. 5 b. 8 c. 1 d. 4 11. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial 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? a. Rs. 93,300 b. Rs. 93,200 c. Rs. 93,100 d. None of these 12. 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? a. 1050 b. 540 c. 1440 d. 1590 13. 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? a. Rs. 300 b. Rs. 250 c. Rs. 400 d. Rs. 500 14. x and y are real numbers satisfying the conditions 2 < x < 3 and â€“ 8 < y < â€“7. Which of the following expressions will have the least value? a. x 2 y b. xy 2 c. 5xy d. None of these 15. m is the smallest positive integer such that for any integer m n= , the quantity n 3 â€“ 7n 2 + 11n â€“ 5 is positive. What is the value of m? a. 4 b. 5 c. 8 d. None of these 16. 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? a. 10 m b. 15 m c. 20 m d. 17 m Page 3 CAT 2001 Actual Paper 17. 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? a. 38 b. 31 c. 41 d. None of these 18. If 09/12/2001(DD/MM/YYYY) happens to be Sunday, then 09/12/1971 would have been a a. Wednesday b. Tuesday c. Saturday d. Thursday 19. In a number system, the product of 44 and 11 is 3414. The number 3111 of this system, when converted to the decimal number system, becomes a. 406 b. 1086 c. 213 d. 691 20. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour? a. 3 7 b. 3 4 c. 3 5 d. 3 8 21. Every 10 years the Indian Government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri. Chota Hazri has 4,522 fewer males than Mota Hazri. Mota Hazri has 4,020 more females than males. Chota Hazri has twice as many females as males. Chota Hazri has 2,910 fewer females than Mota Hazri. What is the total number of males in Chota Hazri? a. 11,264 b. 14,174 c. 5,632 d. 10,154 22. Three classes X, Y and Z take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes? a. 81 b. 81.5 c. 82 d. 84.5 23. Two sides of a plot measure 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. 25 25 24 32 Page 4 CAT 2001 Actual Paper What is the area of the plot? a. 768 2 m b. 534 2 m c. 696.5 2 m d. 684 2 m 24. All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice? a. 44 b. 45 c. 10 d. 12 25. Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyomâ€™s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up? a. 40 b. 50 c. 60 d. 80 26. At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries? a. Rs. 31 b. Rs. 41 c. Rs. 21 d. Cannot be determined 27. If a, b, c and d are four positive real numbers such that abcd = 1, what is the minimum value of (1 + a)(1 + b)(1 + c)(1 + d)? a. 4 b. 1 c. 16 d. 18 28. Thereâ€™s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, thereâ€™s still the potatoes and gravy, yams, salad, and cranberries, not to mention setting the table. Three friends â€” Asit, Arnold and Afzal â€” work together to get all of these chores done. The time it takes them to do the work together is 6 hr less than Asit would have taken working alone, 1 hr less than Arnold would have taken alone, and half the time Afzal would have taken working alone. How long did it take them to do these chores working together? a. 20 min b. 30 min c. 40 min d. 50 min 29. Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side? a. 260 b. 250 c. 240 d. 270 30. For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of 7th and 6th terms of this sequence is 517, what is the 10th term of this sequence? a. 147 b. 76 c. 123 d. Cannot be determined 31. Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes? a. 2 kg b. 2.4 kg c. 2.5 kg d. None of these 32. Train X departs from station A at 11 a.m. for station B, which is 180 km so far. Train Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stop for 15 min at station C, which is 60 km away from station B enroute to station A. Ignoring the lengths of the trains, what is the distance, to the nearest kilometre, from station A to the point where the trains cross each other? a. 112 km b. 118 km c. 120 km d. None of these Page 5 CAT 2001 Actual Paper 33. A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 17 7 35 . What was the number erased? a. 7 b. 8 c. 9 d. None of these 34. In DDEF shown below, points A, B and C are taken on DE, DF and EF respectively such that EC = AC and CF = BC. If 0 D40 ?= , then ACB ? = A B C D EF a. 140 b. 70 c. 100 d. None of these 35. The owner of an art shop conducts his business in the following manner: every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X%. After one such up- down cycle, the price of a painting decreased by Rs. 441. After a second up-down cycle the painting was sold for Rs. 1,944.81. What was the original price of the painting? a. Rs. 2,756.25 b. Rs. 2,256.25 c. Rs. 2,500 d. Rs. 2,000 36. Three runners A, B and C run a race, with runner A finishing 12 m ahead of runner B and 18 m ahead of runner C, while runner B finishes 8 m ahead of runner C. Each runner travels the entire distance at a constant speed. What was the length of the race? a. 36 m b. 48 m c. 60 m d. 72 m 37. Let x and y be two positive numbers such that x + y = 1. Then the minimum value of 2 2 y 1 y x 1 x ? ? ? ? ? ? ? ? + + ? ? ? ? ? ? + is a. 12 b. 20 c. 12.5 d. 13.3 Directions for questions 38 and 39: Answer the questions based on the following information. The batting average (BA) of a T est batsman is computed from runs scored and innings played â€” 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 1 2 1 n r r BA + =Read More

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

3 videos|49 docs|43 tests

### CAT Past Year Question Paper Solution - 2001

- Doc | 13 pages
### CAT Past Year Question Paper - 2000

- Doc | 44 pages
### CAT Past Year Question Paper Solution - 2000

- Doc | 10 pages
### CAT Past Year Question Paper - 1999

- Doc | 40 pages
### CAT Past Year Question Paper Solution - 1999.

- Doc | 21 pages
### CAT Past Year Question Paper - 1998

- Doc | 43 pages

- CAT Past Year Question Paper Solution - 2002
- Doc | 12 pages
- CAT Past Year Question Paper - 2002
- Doc | 40 pages