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  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, thecandidate obtained 60% of the total marks. Then the number of papers in which he got more than50% marks isa. 2b. 3c. 4d. 52.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, isa. 122 + b. 122 + c. 1  –  22d. 1  –  223.Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Whichone of the following statements cannot be true?a. y(x  –   z) 2  is evenb. y 2 (x  –   z) is oddc. y(x  –   z) is oddd. z(x  –   y) 2  is even4.If x > 5 and y <  –  1, then which of the following statements is true?a. (x + 4y) > 1b. x >  –  4yc.  –  4x < 5yd. None of these5.A red light flashes three times per minute and a green light flashes five times in 2 min at regularintervals. If both lights start flashing at the same time, how many times do they flash together ineach hour?a. 30b. 24c. 20d. 606.Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number ofboxes containing the same number of oranges is at leasta. 5b. 103c. 6d. Cannot be determined7.A certain city has a circular wall around it, and this wall has four gates pointing north, south, eastand west. A house stands outside the city, 3 km north of the north gate, and it can just be seen froma point 9 km east of the south gate. What is the diameter of the wall that surrounds the city?a. 6 kmb. 9 kmc. 12 kmd. None of these8. ABCDEF 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. 61b. 81c. 91d. None of these    CAT 2001 Paper CATsyllabus.com  9.A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double thatof B, and D takes double that of C to complete the same task. They are paired in groups of twoeach. One pair takes two-thirds the time needed by the second pair to complete the work. Which isthe first pair?a. A and Bb. A and Cc. B and Cd. A and D10.In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of thefirst and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twicethe sum of the other 2 digits. What is the third digit of the number?a. 5b. 8c. 1d. 411.Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X askedfor an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary ofRs. 200 with a rise of Rs. 15 every 6 months. Assume that the arrangements remained unaltered tillDecember 31, 1959. Salary is paid on the last day of the month. What is the total amount paid tothem as salary during the period?a. Rs. 93,300b. Rs. 93,200c. Rs. 93,100d. None of these12.Anita had to do a multiplication. In stead of taking 35 as one of the multipliers, she took 53. As aresult, the product went up by 540. What is the new product?a. 1050b. 540c. 1440d. 159013.A college has raised 75% of the amount it needs for a new building by receiving an average donationof Rs. 600 from the people already solicited. The people already solicited represent 60% of thepeople the college will ask for donations. If the college is to raise exactly the amount needed for thenew building, what should be the average donation from the remaining people to be solicited?a. Rs. 300b. Rs. 250c. Rs. 400d. 50014.x and y are real numbers satisfying the conditions 2 < x < 3 and  –   8 < y <  –  7. Which of the followingexpressions will have the least value?a. x 2 yb. xy 2 c. 5xyd. None of these15.m is the smallest positive integer such that for any integer mn  ≥ , the quantity n 3    –   7n 2  + 11n  –   5 ispositive. What is the value of m?a. 4b. 5c. 8d. None of these16.A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When thebottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against thefoot of the wall. What is the length of the ladder?a. 10 mb. 15 mc. 20 md. 17 m17.Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their billand noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned fourbecause she had a momentary pang of guilt. Fatima then took one-fourth of what was left butreturned three for similar reason. Eswari then took half of the remainder but threw two back into thebowl. The bowl had only 17 mints left when the raid was over. How many mints were srcinally in thebowl?a. 38b. 31c. 41d. None of these  18.If 09/12/2001(DD/MM/YYYY) happens to be Sunday, then 09/12/1971 would have been aa. Wednesdayb. Tuesdayc. Saturdayd. Thursday19.In a number system the product of 44 and 11 is 3414. The number 3111 of this system, whenconverted to the decimal number system, becomesa. 406b. 1086c. 213d. 69120.At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than ittakes him to travel the same distance upstream. But if he could double his usual rowing rate for this24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream12 miles. What is the speed of the current in miles per hour?a. 37b. 34c. 35d. 3821.Every 10 years the Indian Government counts all the people living in the country. Suppose that thedirector of the census has reported the following data on two neighbouring villages Chota Hazri andMota 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. 11,264b. 14,174c. 5,632d. 10,15422.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. 81b. 81.5c. 82d. 84.523.Two sides of a plot measure 32 m and 24 m and the angle between them is a perfect right angle. Theother two sides measure 25 m each and the other three angles are not right angles. 25252432 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 wasadded twice by mistake. The sum obtained was 1000. Which page number was added twice?a. 44b. 45c. 10d. 12  25.Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constantspeed. Shyama takes three steps for every two of Vyom ’ s steps. Shyama gets to the top of theescalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do alittle more of the work) takes only 20 steps to reach the top. If the escalator were turned off, howmany steps would they have to take to walk up?a. 40b. 50c. 60d. 8026.At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries forRs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one orderof fries. How much would it cost for an ordinary meal of one burger, one shake, and one order offries?a. Rs. 31b. Rs. 41c. Rs. 21d. Cannot be determined27.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. 4b. 1c. 16d. 1828.There ’ s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, there ’ s stillthe potatoes and gravy, yams, salad, and cranberries, not to mention setting the table.Three friends  —  Asit, Arnold and Afzal  —  work together to get all of these chores done. The time ittakes them to do the work together is 6 hr less than Asit would have taken working alone, 1 hr lessthan Arnold would have taken alone, and half the time Afzal would have taken working alone. Howlong did it take them to do these chores working together?a. 20 minb. 30 minc. 40 mind. 50 min29.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 theprevious two terms in that sequence. If the difference in squares of 7th and 6th terms of this sequenceis 517, what is the 10th term of this sequence?a. 147b. 76c. 123d. Cannot be determined31.Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. Whatis the weight of dry grapes available from 20 kg of fresh grapes?a. 2 kgb. 2.4 kgc. 2.5 kgd. None of these32.Train X departs from station A at 11 a.m. for station B, which is 180 km so far. Train Y departs fromstation B at 11 a.m. for station A. Train X travels at an average speed of 70 km/hr and does not stopanywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stopfor 15 min at station C, which is 60 km away from station B enroute to station A. Ignoring the lengthsof the trains, what is the distance, to the nearest kilometre, from station A to the point where thetrains cross each other?a. 112 kmb. 118 kmc. 120 kmd. None of these33.A set of consecutive positive integers beginning with 1 is written on the blackboard. A student camealong and erased one number. The average of the remaining numbers is 17735. What was thenumber erased?a. 7b. 8c. 9d. None of these
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