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QA Revision I

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## QA Revision I

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1. QA Revision I CAT 2013 Batch

2. Areas Covered • RATIO, PROPORTION, VARIATION • %, PROFIT & LOSS • TIME & DISTANCE • TIME & WORK • AVERAGES, MIXTURES, ALLEGATIONS • Target: Appx 130 problems from • Original CAT papers, • Vistamind Handouts • Vistamind OST’s

3. CATalogue...

4. 1999: • 1. The speed of a railway engine is 42 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour with 9 compartments are attached, the maximum number of compartments carried by the engine is: • 49 (2) 48 (3) 46 (4) 47 • 2. Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs.700 when there are 25 boarders and Rs.600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders? • (1) 550 (2) 560 (3) 540 (4) None of these • 3. Forty percent of the employees of a company are men, and 75 percent of the men earn more than Rs.25,000 per year. If 45 percent of the company's employees earn more than Rs.25,000 per year, what fraction of the women employed by the company earn Rs.25,000 per year or less? • (1) 2/11 (2) 1/4 (3) 1/3 (4) 3/4 • 4. In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the 3 proposals. • (1) 10 (2) 12 (3) 17 (4) 22

5. 1999: A young girl Roopa leaves home with x flowers, goes to the bank of a near-by river. On the bank of the river, there are four places of worship standing in a row. She dips all the x flowers into the river. The number of flowers doubles. Then she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the second place of worship, offers y flowers to the deity. She dips the remaining flowers into the river and again the number of flowers doubles. She goes to the third place of worship and offers y flowers to the deity. She dips the remaining flowers into the river again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand. 5. If Roopa leaves home with thirty flowers, the number of flowers that she offers to each deity is (1) 30 (2) 31 (3) 32 (4) 33 6. The minimum number of flowers that could be offered to each deity is (1) 0 (2) 15 (3) 16 (4) Cannot be determined 7. The minimum number of flowers with which Roopa leaves home is (1) 16 (2) 15 (3) 0 (4) Cannot be determined Directions for questions 81 and 82: The following table presents the sweetness of different items relative to sucrose, whose sweetness is taken to be 100. 8. What is the minimum amount of sucrose (to the nearest gram) that must be added to one-gram of saccharin to make a mixture that will be at least 100 times as sweet as glucose? (1) 7 (2) 8 (3) 9 (4) 100 9. Approximately how many times sweeter than sucrose is a mixture consisting of glucose, sucrose and fructose in the ratio of 1 : 2 : 3? (1) 13 (2) 1 (3) 0.6 (4) 23

6. 2000: • A truck travelling at 70 kilometres per hour uses 30% more diesel to travel a certain distance than it does when it travels at the speed of 50 kilometres per hour. If the truck can travel 19.5 kilometres on a litre of diesel at 50 kilometres per hour, how far can the truck travel on 10 litres of diesel at a speed of 70 kilometres per hour? • (1) 130 (2) 140 (3) 150 (4) 175 • 2. The table below shows the age-wise distribution of the population of Reposia. The number of people aged below 35 years is 400 million. • If the ratio of females to males in the 'below 15 years' age group is 0.96, then what is the number of females (in millions) in that age group? • (1) 82.8 (2) 90.8 (3) 80.0 (4) 90.0 `

7. 2000: There are five machines A, B, C, D and E situated on a straight line at distances of 10 metres, 20 metres, 30 metres, 40 metres and 50 metres respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw material is located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot-station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of the message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin. If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the next message(s) is received. 3. Suppose on a certain day, machines A and D have sent the first two messages to the origin at the beginning of the first second, and C has sent a message at the beginning of the 5th second and B at the beginning of the 6th second, and E at the beginning of the 10th second. How much distance in metres has the robot travelled since the beginning of the day, when it notices the message of E? Assume that the speed of movement of the robot is 10 metres per second. (1) 140 (2) 80 (3) 340 (4) 360 4. Suppose there is a second station with raw material for the robot at the other extreme of the line which is 60 metres from the origin, that is, 10 metres from E. After finishing the services in a trip, the robot returns to the nearest station. If both stations are equidistant, it chooses the origin as the -5 station to return to. Assuming that both stations receive the messages sent by the machines and that all the other data remains the same, what would be the answer to the above question? (1) 120 (2) 140 (3) 340 (4) 70

8. 2001: • A student took 5 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% is • (1) 2 (2) 3 (3) 4 (4) 5 • 2. A red light flashes 3 times per minute and a green light flashes 5 times in • two minutes at a regular intervals. If both lights start flashing at the same • time, how many times do they flash together in each hour? • (1) 30 (2) 24 (3) 31 (4) 60 • 3. 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 • (1) 5 (2) 103 (3) 6 (4) Cannot be determined • 4. A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of Band 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 cork. Which is the first pair? • (1)A,B (2)A,C (3)B,C (4)A,D

9. 2001: 5. 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 six months. Assure 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? (1) Rs.93,300 (2) Rs. 93,200 (3) Rs.93,100 (4) None of these 6. Anita had to do a multiplication. Instead 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? (1) 1050 (2) 540 (3) 1440 (4) 1590 7. 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 of 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? (1) Rs.300 (1) Rs.250 (1) Rs.400 (3) Rs. 500 8. 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 1/3 of the mints, but returned four because she had a momentary pang of guilt. Fatima then took 1/4th of what was left but returned three for similar reasons. 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? (1) 38 (2) 31 (3) 41 (4) None of these

10. 2001: 9. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hrs less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 mile 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? (1) 7/3 (2) 4/3 (3) 5/3 (4) 8/3 10. Every ten 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? (1) 11,264 (2) 14,174 (3) 5,632 (4) 10,154 11. Three maths 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? (1) 81 (2) 81.5 (3) 82 (4) 84.5 12. Shyam and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyam takes three steps for every two of Vyom's steps. Shyam 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? (1) 40 (2) 50 (3) 60 (4) 80

11. 2001: 13. At a certain fast food restaurant, Brain 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 fries? (1) Rs.31 (2) Rs.41 (3) Rs.21 (4) Cannot be determined 14. There's a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, there's still the 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 it takes them to do the work together is 6 hrs less than Asit would have taken 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? (1) 20 minutes (2) 30 minutes (3) 40 minutes (4) 50 minutes 15. 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? (1) 2 kgs (2) 2.4 kgs (3) 2.5 kgs (4) None of these 16. A train X departs from station A at 11.am for station B, which is 180 km away. Another train Y departs from station B at 11.am 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 50 km/hr, but has to stop for 15 minutes at station C, which is 60 km away from station B en-route to station A. Ignoring the lengths of the trains, what is the distance to the nearest km, from station A to the point where the trains cross each other? (1) 112 (2) 118 (3) 120 (4) None of these

12. 2001: 17. 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 second up-down cycle, the painting was sold for Rs1,944.81. What was the original price of the painting? (1) 2256.25 (2) 2256.25 (3) 2500 (4) 2000 18. Three runners A, Band C run a race with runner A finishing 12 meters ahead of Band 18 meters ahead of runner C, while runner B finishes 8 meters ahead of runner C. Each runner travels the entire distance the entire distance at a constant speed. What was the length of the race? (1) 36 meters (2) 48 meters (3) 60 meters (4) 72 meters 19. Ashish is given Rs.158 is one rupee denomination. He has been asked to allocate them into a number of bags such that any amount required between Re.1 and Rs.158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required? (1) 11 (2) 12 (3) 13 (4) None of these 20. A change making machine contains 1 rupee, 2 rupees and 5 rupee coins. The total number of coins is 300. The amount is Rs.960. If the number of 1 rupee coins and number of 2 rupee coins are interchanged, the value comes down by Rs40. The total number of 5 rupee coins is (1) 100 (2) 140 (3) 60 (4) 150

13. 2002: 1. Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, if we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of mother of the younger boy. The mother of the younger boy is younger to his father, by 3 years. Then, what is the age of the younger boy? (1) 3 (2) 4 (3) 2 (4) None of these 2. Flights A and B are scheduled from an airport within the next one hour. All the booked passengers of the two flights are waiting in the boarding hall after check-in. The hall has a seating capacity of 200, out of which 10% remained vacant. 40% of the waiting passengers are ladies. When boarding announcements came, passengers of flight A left the hall and barded the flight. Seating capacity of each flight is two-third of the passengers who waited in the waiting hall for both the flights put together. Half the passengers who boarded flight A are women. After boarding for flight A, 60% of the waiting hall seats became empty For every twenty of those who are still waiting in the hall for flight B, there is one airhostess in flight A. Then, what is the ratio of empty seats in flight B to number of airhostesses in flight A? (1) 10 : 1 (2) 5 : 1 (3) 20 : 1 (4) 1 : 1

14. 2003: • 1. A test has 50 questions. A student scores 1 mark for a correct answer, -1/3 for a wrong answer, and -1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than • (1) 6 (2) 12 (3) 3 (4) 9 • 2. Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be • (1) 85.5 (2) 92.5 (3) 90.5 (4) 87.5 • 3. Twenty-seven persons attend a party. Which one of the following statements can never be true? • There is a person in the party who is acquainted with all the twenty-six others, (2) Each person in the party has a different number of acquaintances, (3) There is a person in the party who has an odd number of acquaintances, (4) In the party, there is no set of three mutual acquaintances. • A leather factory produces two kinds of bags, standard and deluxe. The profit margin is Rs.20 on a standard bag and Rs.30 on a deluxe bag. Every bag must be processed on machine A and on machine B. The processing times per bag on the two machines are as follows. • The total time available on machine A is 700 hours and on machine B is 1250 hours. Among the following production plans, which one meets the machine availability constraints and maximizes the profit? • (1) Standard 75 bags, Deluxe 80 bags, (2) Standard 100 bags, Deluxe 60 bags, (3) Standard 50 bags, Deluxe 100 bags, (4) Standard 60 bags, Deluxe 90 bags

15. 2003: 5. In a 4000 m race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race? (1) 20 min (2) 15 min (3) 10 min (4) 5 min 6. At the end of the year 1998, Shepard bought nine dozen goats, Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > O. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true? (1) p = q (2) P < q (3) p> q (4) P = q/2 A certain perfume is available at a duty-free shop at the Bangkok international airport. It is priced in the Thai currency Baht but other currencies are also acceptable. In particular, the shop accepts Euro and US Dollar at the following rates of exchange: US Dollar 1 = 41 Bahts; Euro 1 = 46 Bahts The perfume is priced at 520 Bahts per bottle. After one bottle is purchased, subsequent bottles are available at a discount of 30%. Three friends S, Rand M together purchase three bottles of the perfume, agreeing to share the cost equally. R pays 2 Euros. M pays 4 Euros and 27 Thai Bahts and S pays the remaining amount in US Dollars. 7. How much does R owe to S in Thai Baht? (1) 428 (2) 416 (3) 334 (4) 324 8. How much does M owe to S in US Dollars? (1)3 (2)4 (3)5 (4)6