40 Unofficial Lsat Logic Games for Extra Practice (1)

Buyer: Bryan Duncan ([email protected]) Transaction ID: 4FP0558632323183D

40 Unofficial LSAT Logic Games for Extra Practice

by Alex Green

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Buyer: Bryan Duncan ([email protected]) Transaction ID: 4FP0558632323183D

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Table of Contents Section 1 «««««««««««««««««««««««««««...3 Section 2 «««««««««««««««««««««««««««10 Section 3 ««««««««««««««««««««««««««« 17 Section 4 ««««««««««««««««««««««««««« 23 Section 5 «««««««««««««««««««««««««««29 Section 6 ««««««««««««««««««««««««««« 34 Section 7 «««««««««««««««««««««««««««41 Section 8 ««««««««««««««««««««««««««« 46 Section 9 «««««««««««««««««««««««««««53 Section 10 «««««««««««««««««««««««««««59 Section 1 Answers «««««««««««««««««««««««« 65 Section 2 $QVZHUV««««««««««««««««««««««««66 Section 3 $QVZHUV««««««««««««««««««««««««67 Section 4 $QVZHUV««««««««««««««««««««««««68 Section 5 $QVZHUV««««««««««««««««««««««««69 Section 6 $QVZHUV««««««««««««««««««««««««70 Section 7 $QVZHUV««««««««««««««««««««««««71 Section 8 $QVZHUV««««««««««««««««««««««««72 Section 9 $QVZHUV««««««««««««««««««««««««73 Section 10 $QVZHUV««««««««««««««««««««««« 74 Page  |  2  

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Questions 1-6 A computer technician company is sending seven workers out to a job over the course of seven days. Beginning on Sunday, one technician will work each day. Their names are Adam, Brett, Carly, Daniel, Emmett, Frank, and Gina. They must work under the following conditions: Adam and Brett cannot work consecutive days Frank cannot work before Tuesday Emmett and Carly must both work after Daniel Gina and Daniel cannot have more than one day between their work days Brett cannot work on Friday 1. Which of the following is an acceptable schedule of work days, beginning with Sunday? a. Adam, Emmett, Gina, Daniel, Carly, Frank, Brett b. Gina, Brett, Daniel, Emmett, Frank, Carly, Adam c. Brett, Frank, Gina, Daniel, Emmett, Adam, Carly d. Gina, Adam, Daniel, Emmett, Carly, Brett, Frank e. Daniel, Adam, Carly, Gina, Frank, Emmett, Frank 2. If Adam works on Wednesday, then which of the following must be false? a. Daniel works after Adam b. Gina works after Emmett c. Brett works on Saturday d. Carly works on Friday e. Frank works on Thursday

3. How many different technicians could work on Saturday if Gina works on Tuesday? a. 1 b. 2 c. 3 d. 4 e. 5 4. If Adam works directly before Gina, then each of the following could be true except a. Brett works on Sunday b. Frank works on Wednesday c. Emmett works on Friday d. Gina works on Thursday e. Adam works on Sunday 5. On how many different days could Brett work? a. 3 b. 4 c. 5 d. 6 e. 7 6. Which of the following is not an acceptable arrangement of Adam, Daniel, and Frank, if they are arranged consecutively? a. Daniel, Adam, Frank b. Daniel, Frank, Adam c. Frank, Daniel, Adam d. Frank, Adam, Daniel e. Adam, Daniel, Frank

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Questions 7-11 An eight-car train will travel from Boston to Providence, and then to New York City. On the first half of the trip, when it travels to Providence, four cars need to hold passengers, three need to hold supplies, and one needs to serve food. From Providence to New York, there must be five cars for passengers, two for supplies, and one to serve food. The following conditions apply to the train from the front car (Car 1) to the last car (Car 8): Cars 1 and 3 cannot be changed from one type to another at any time between Boston and New York Car 2 will definitely change from one type to another If Car 5 stays the same type, then so does Car 6 Car 8 is the food car on at least one half of the trip Car 7 will hold supplies for the whole trip 7. If the arrangement of cars from Boston to Providence, front to back, is passenger, supplies, passenger, passenger, food, passenger, supplies, supplies, then which of the following must be true? a. Exactly three of the cars will change type b. Exactly four of the cars will change type c. More odd numbered cars stay the same type than even numbered cars do d. At least four passenger trains will be lined up consecutively e. Exactly three passenger trains will be lined up consecutively

8. If the food car is in the eighth car on the first half of the trip, then in how many different cars could it end up for the second half of the trip? a. 3 b. 4 c. 5 d. 6 e. 7 9. Which of the following cannot be true? a. Car 3 is a food car on the first half of the trip b. Car 2 is a passenger car on the first half of the trip c. Car 1 is a supplies car on the first half of the trip d. Car 4 is a passenger car on the second half of the trip e. Car 5 is a supplies car on the second half of the trip 10. If the arrangement of cars from Providence to New York, front to back, is passengers, supplies, passengers, passengers, passengers, passengers, supplies, food, then which of the following must be false? a. The food car is Car 5 for the first half of the trip b. A supplies car is Car 5 for the first half of the trip c. There are four passenger cars in a row for each half of the trip d. The food car is Car 8 for both halves of the trip e. No supply car on the first half of the trip is adjacent to another supply car

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11. If the supplies cars cannot be directly next to one another on either half of the trip, then which of the following must be false? a. Car 2 is a supplies car for the first half of the trip b. Car 4 is a supplies car for the first half of the trip c. Car 4 is a supplies car for the second half of the trip d. Car 8 is always a food car e. There are four consecutive passenger cars in the first half of the trip

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Questions 12-18 A gardener is planting fruit and vegetable seeds in a straight line in his garden. He has asparagus, broccoli, cucumber, peapod, squash, tomato, watermelon, and zucchini seeds, and he will arrange them from left to right under the following conditions: Watermelon is either on the far left or far right Peapods will grow in one of the middle two spots Squash must come somewhere to the left of the cucumbers Tomatoes will grow to the right of the zucchini The asparagus and broccoli cannot be next to each other 12. Which of the following is an acceptable order of plants, from left to right? a. Squash, asparagus, broccoli, peapods, cucumbers, zucchini, tomatoes, watermelon b. Watermelon, zucchini, asparagus, peapods, squash, cucumbers, tomatoes, broccoli c. Zucchini, asparagus, peapods, tomatoes, broccoli, squash, cucumbers, watermelon d. Watermelon, asparagus, tomatoes, squash, peapods, zucchini, cucumbers, broccoli e. Watermelon, zucchini, asparagus, cucumbers, peapods, squash, broccoli, tomatoes 13. If cucumbers are third from the left, then which of the following must be true? a. Tomatoes are in the right half of the garden b. Watermelon is in the left half of the garden

c. Asparagus is in the right half of the garden d. Broccoli is in the left half of the garden e. The peapods are next to the zucchini 14. How many different plants could be on the far right? a. 2 b. 3 c. 4 d. 5 e. 6 15. If Asparagus in fifth from the left, and broccoli is on the far right, then which of the following pairs cannot be next to one another? a. Squash and cucumbers b. Squash and tomatoes c. Watermelon and zucchini d. Cucumbers and broccoli e. Zucchini and tomatoes 16. If broccoli comes directly between watermelon and squash, then which of the following is a complete and accurate list of plants that could be second from the right? a. Broccoli, tomatoes, cucumbers, zucchini b. Broccoli, tomatoes, cucumbers c. Asparagus, cucumbers, tomatoes d. Asparagus, cucumbers, squash, and zucchini e. Asparagus, tomatoes, cucumbers, and zucchini

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17. How many combinations of the order of plants exist if squash is on the far left and asparagus is fourth from the left? a. 5 b. 6 c. 7 d. 8 e. 9

18. Suppose that the zucchini had to be next to the peapods and that there was only one space between the zucchini and watermelon. Which of the following could not be directly next to the watermelon? a. Tomatoes b. Squash c. Cucumbers d. Broccoli e. Asparagus

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Questions 19-24 A traveling musical group will perform in five different towns, named V, W, X, Y, and Z in five days, Monday through Friday. They will perform at a theater and a school in each town, and the shows will take place either in the afternoon or in the evening. Only one town can be visited each day. The performances will be scheduled under the following conditions: All five towns must host two performances There can be no more than two theater performances in the afternoon Town V hosts a performance before town W In town Z, the group performs in the theater in the afternoon The group visits the theater in town X at the same time of day as they do in town Y Towns X and Z cannot host performances in consecutive days 19. Each of the following could be true except: a. Town X has performances on Wednesday b. Town V has performances on Thursday c. Town Y hosts an evening performance in their school d. Town W hosts an afternoon performance in their theater e. Town X hosts an afternoon performance in their school

20. If Town W is the host on Tuesday, which of the following must be true? a. Town Y hosts a performance on Thursday b. Town Z hosts a performance on Wednesday c. Town W has an afternoon performance in their theater d. Town W has an afternoon performance in their school e. Town X hosts a performance on Friday 21. If Town X hosts the musical group after Towns Z and W, then which of the following is a complete and accurate list of towns that could host on Thursday? a. W & X b. X & Z c. V, X, Y, & Z d. X & Y e. W, X, & Y 22. What is the highest number of consecutive towns that could possibly have a school performance in the afternoon? a. 1 b. 2 c. 3 d. 4 e. 5

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23. Which of the following cannot be true? a. Towns X and Y are on nonconsecutive days b. The town hosting the Wednesday performances has a theater performance in the afternoon c. Town W hosts their performances on Monday d. Town V hosts their performances after towns X and Z e. Towns V and W host their school performances at the same time of day

24. If Town X hosts the musical group on Wednesday, then how many different ways could the five towns be assigned to the days of the week? a. 5 b. 6 c. 7 d. 8 e. 9

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Questions 1-6 Ten camp counselors will be in charge of seven different cabins, numbered 1-7 in order, at a summer camp. Every counselor will cover a FDELQ0DOHFRXQVHORUVPXVWFRYHUWKHER\V¶ cabins, and female counselors must cover the JLUOV¶FDELQV There are an equal number of children in each cabin, but there are more girls at the camp than boys. The male counselors are Josh, Kyle, Liam, and Max, and the female counselors are Natalie, Paula, Rosie, Samantha, Tracy, and Valerie. They are assigned to cabins under the following conditions: Either one or two counselors cover each cabin &DELQLVDER\V¶FDELQ &DELQLVDJLUOV¶FDELQ ([DFWO\RIWKHER\V¶FDELQVDUHDGMDFHQWWR JLUOV¶FDELQV Natalie and Paula cannot cover consecutive cabins Max does not cover a cabin alone 1. Which of the following could be the arrangement of cabins from 1-7? a. Boys, Boys, Girls, Girls, Boys, Boys, Girls b. Girls, Boys, Boys, Girls, Girls, Girls, Girls c. Boys, Girls, Boys, Girls, Girls, Girls, Girls d. Girls, Boys, Girls, Girls, Girls, Girls, Girls e. Boys, Boys, Girls, Girls, Girls, Girls, Boys

2. If Josh and Max cover cabin 6, which of the following is possible? a. There are four consecutive cabins of girls b. 1DWDOLH¶VFDELQLVEHWZHHQ.\OH¶V DQG/LDP¶V c. There is a male counselor in cabin 1 d. Liam covers cabin 5 e. Kyle covers cabin 4 3. Which of the following cannot be true? a. Natalie and Paula cover the same cabin b. Kyle covers cabin 3 alone c. Rosie and Tracy cover the same cabin d. A single male counselor covers cabin 2 e. Male counselors cover cabins 4 and 5 4. If Valerie is one of two pairs of females FRYHULQJWKHJLUOV¶FDELQVWKHQKRZ many combinations exist for the arrangement of cabins by gender? a. 4 b. 5 c. 6 d. 7 e. 8 5. If Kyle and Josh cover cabin 3, then which of the following is a complete and accurate list of the cabins that could be covered by Samantha? a. 1, 2, 4, 6, 7 b. 1, 4, 6, 7 c. 1, 5, 6, 7 d. 4, 5, 6, 7 e. 1, 4, 5, 6, 7

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6. If Natalie covers cabin 4 alone, and there DUHWKUHHER\V¶FDELQVWKHQZKLFKRIWKH following must be true? a. Paula covers cabin 7 b. Male counselors cover cabin 6 c. Tracy covers cabin 3 d. Male counselors cover cabin 1 e. Female counselors cover cabin 5

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Questions 7-12 A car dealer is displaying six vehicles on his showroom floor. He is choosing between five cars and four trucks. The cars he can pick from are a convertible, a sedan, a hatchback, a wagon, and a sports car. The trucks he can pick from are a pickup, a sport utility vehicle, a diesel truck, and a dump truck. The owner must choose the vehicles based on the following conditions: The sports car cannot be featured with the pickup truck The diesel truck must be selected if the wagon is selected The convertible must be selected if the dump truck is selected If the dump truck and diesel are selected, then so must the sedan There are more cars than trucks 7. Which of the following could be the arrangement of vehicles on the showroom floor? a. Cars: convertible, sedan, sports car, wagon. Trucks: diesel, pickup b. Cars: convertible, hatchback, sedan, sports car. Trucks: sport utility vehicle, dump truck c. Cars: convertible, sedan, sports, car, wagon, hatchback. Trucks: sport utility vehicle d. Cars: sedan, wagon, hatchback. Trucks: sport utility vehicle, diesel truck, pickup truck e. Cars: sedan, wagon, hatchback, sports car. Trucks: diesel truck, dump truck

8. If the dump truck is selected and the diesel truck is not, which of the following cannot be selected? a. Sport Utility Vehicle b. Convertible c. Hatchback d. Pickup e. Sedan 9. If the sports car is selected for display and the sport utility vehicle is not, then which of the following must be false? a. Five cars are displayed b. Four cars are displayed c. The wagon is not displayed d. The convertible is not displayed e. The hatchback is not displayed 10. If the sport utility vehicle and the wagon are selected, then how many combinations of vehicles can the owner choose from? a. 4 b. 5 c. 6 d. 7 e. 8 11. If the diesel truck is not displayed, then which of the following must be false? a. The sport utility vehicle is displayed b. The dump truck is displayed c. The sedan is displayed d. The pickup is not displayed e. The hatchback is not displayed

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12. Which one of the following pairs of vehicles cannot be displayed together? a. Diesel truck and pickup b. Diesel truck and hatchback c. Pickup and sport utility vehicle d. Sport utility vehicle and diesel truck e. Sport utility vehicle and dump truck

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Questions 13-17 Six friends named Donny, Gary, Jeff, Liam, Smokey, and Walter are in a bowling league. They will bowl on a team according to the following conditions: Exactly four bowlers are on the team If Donny is on the team, then Liam is on the team as well Walter and Gary cannot both be on the team If Gary and Smokey are both on the team, then Gary bowls before Smokey If Liam and Walter are both on the team, then Liam bowls before Walter

16. If Jeff bowls first and Smokey bowls second, then which of the following could be true? a. Walter bowls third b. Gary bowls third c. Walter bowls last d. Donny bowls before Walter e. Liam bowls after Walter 17. If Donny bowls first, how many team members could bowl second? a. 2 b. 3 c. 4 d. 5 e. 6

13. Which of the following is an acceptable order of bowlers on the team, from first to last? a. Jeff, Walter, Liam, Donny b. Donny, Walter, Liam, Gary c. Liam, Smokey, Donny, Gary d. Gary, Jeff, Smokey, Liam e. Walter, Jeff, Smokey, Donny 14. If Walter bowls on the team, then which of the following must be false? a. Donny does not bowl b. Smokey bowls before Jeff c. Donny, Liam, and Jeff bowl d. Donny, Liam, and Smokey bowl e. Walter bowls first 15. Which two bowlers cannot be left off the team together? a. Gary and Walter b. Smokey and Donny c. Jeff and Walter d. Jeff and Gary e. Smokey and Gary

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Questions 18-22 Three friends named Mark, Judy, and Lucy are making sandwiches for a picnic. They will each make their own sandwich with some combination of the following ingredients: the available breads are white, rye, and sourdough, the available meats are roast beef, turkey, and ham, and the available toppings are lettuce, mayonnaise, and pickles. The three sandwiches must be made under the following conditions: Each sandwich has one kind of bread, one kind of meat, and one topping Each of the three friends uses a different kind of bread, a different kind of meat, and a different topping Mark will not make his sandwich with rye bread or with pickles Lucy must have roast beef on her sandwich If Judy has turkey on her sandwich, then she has to use white bread If Lucy has lettuce on her sandwich, then Mark must have mayonnaise on his sandwich 18. If Judy has turkey on her sandwich, each of the following could be true except a. Judy has pickles b. Lucy has pickles c. Mark has white bread d. Mark has lettuce e. Lucy has mayonnaise

20. Which of the following pieces of information will be enough to determine H[DFWO\ZKDWHYHU\RQH¶VVDQGZLFKLV made of? a. Judy has pickles and Lucy has mayonnaise b. Mark has white bread and Lucy has lettuce c. Mark has ham on sourdough bread d. Mark has ham and Lucy has lettuce e. Judy has ham on white bread 21. How many different kinds of sandwiches could Mark have? a. 6 b. 7 c. 8 d. 9 e. 10 22. Which of the following must be true if Mark has ham? a. Lucy has sourdough b. Lucy has pickles c. Judy has mayonnaise d. Mark has lettuce e. Lucy has rye

19. Which of the following must be false? a. Mark has ham on white b. Lucy has lettuce and rye c. Judy has pickles and sourdough d. Judy has Ham e. Mark has mayonnaise and white bread

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Questions 1-6 Dr. Ahteri has seven patients in rooms A, B, C, D, E, F, and G who need treatment. He must help them one at a time, and he must treat them all. The following conditions must be met in the treatment: D must be treated before C G must be treated after A but before B C must be treated before G Patient A is terribly sick, and must be treated either 1st or 2nd Patient B is not terribly sick, and must be treated either 6th or 7th 1. Which of the following is a possible RUGHURISDWLHQWV¶WUHDWPHnts from first to last? a. A, C, E, D, F, B, G b. E, A, F, D, C, G, B c. D, C, A, G, E, F, B d. A, D, C, G, B, F, E e. A, F, D, G, C, E, B 2. Which of the following can NOT be the 5th patient? a. C b. G c. E d. F e. D

3. If Dr. Ahteri treats patients E and F in immediate succession, then each of the following could be false except: a. G is 6th b. A is 1st c. B is 7th d. Either E or F is 3rd e. C is 5th 4. Which of the following must be false? a. Patient E is treated 5th b. Patient F is treated 1st c. Patient B is treated 7th d. Patient C is treated after patient D and E e. Patient C is treated before patient A 5. If patient A is treated directly between patients D and C, then how many combinations of orders of the patients exist? a. 7 b. 8 c. 9 d. 10 e. 11 6. Suppose Dr. Ahteri treated patients D and C in immediate succession. In how many different placements could the pair be treated? a. 1 b. 2 c. 3 d. 4 e. 5

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Questions 7-12 A photographer will take pictures of eight models. There are four men, named Drew, Steve, Terrance, and Joseph, and there are four women, named Ashley, Diana, Haley, and Lucille, who are available to be photographed. They will each be photographed during a fifteenminute session, beginning at 3:00 and ending at 5:30. There are two breaks when nobody will be photographed, for a total of 10 consecutive sessions. The models must schedule their appointments under the following conditions: No more than 2 men can be photographed in consecutive time slots No more than 2 women can be photographed in consecutive time slots Steve is scheduled to be photographed at 4:30 There are no breaks taken after the 4:45 time slot ends Drew must be photographed after Haley Joseph must be photographed before Diana There must be at least three times slots between Steve and Lucille 7. Which of the following is an acceptable order, from start to finish, for the models to attend their appointments? a. Lucille, Haley, Drew, Ashley, Joseph, Steve, Diana, Terrance b. Ashley, Terrance, Drew, Lucille, Steve, Haley, Joseph, Diana c. Joseph, Lucille, Terrance, Diana, Drew, Steve, Haley, Ashley d. Haley, Lucille, Diana, Drew, Ashley, Steve, Joseph, Terrance e. Lucille, Ashley, Terrance, Haley, Steve, Joseph, Drew, Diana

8. If Steve is the sixth model to be photographed, then which of the following pairs of time slots could be breaks? a. 4:00 and 4:15 b. 3:45 and 4:15 c. 3:45 and 5:15 d. 3:00 and 3:15 e. 3:30 and 4:45 9. If Drew is photographed at 3:15, then which of the following must be true? a. Lucille is photographed at 3:30 b. Terrance and Diana are both photographed after 4:00 c. Both breaks come no later than the 4:15 time slot d. Joseph is photographed by 4:00 e. There are two men photographed consecutively 10. Supposing there are consecutive breaks, which of the following must be false? a. Lucille is photographed at 3:30 b. Diana and Drew are photographed consecutively before Steve is c. The breaks come at 3:45 and 4:00 d. Haley is photographed after the 3:30 time slot ends e. There are three women photographed before the breaks 11. Each of the following could be true except a. Exactly three photo shoots occur before Lucille's b. There are six photo shoots in between the breaks c. Diana is photographed before Haley d. Lucille is photographed after Diana e. Joseph is photographed at 5:00

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12. A fifth female model named Nina came in after the scheduling was done, and she will fill in for the second break. If she has to be either the fourth or fifth female to be photographed, which of the following must be true? a. Nina will be photographed in between Steve and Lucille b. Nina will be photographed sometime after Drew c. There is a male model directly before and directly after Nina d. Steve will be directly before or after Nina e. Nina is photographed before Joseph

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Questions 13-17 Teachers are being assigned to a five-day school schedule that is made up of four periods per day, which are called W, X, Y, and Z. There are four teachers named Arnold, Betty, Chuck, and Daphne. Each teacher will work from Monday to Friday under the following conditions: Each teacher gets one period off per day At least one teacher is assigned to each period, each day Arnold has period W off more than anyone else Daphne has period Z off at least twice Betty takes off either period X or Y each day Chuck takes off either period W, Y, or Z each day None of the teachers get the same period off in consecutive days 13. Which of the following is a possible list, in order, of the teachers who have period Y off, from Monday to Friday? a. Betty, Daphne, Arnold, Chuck, Arnold b. Chuck, Betty, Arnold, Betty, Betty c. Chuck, Betty, Chuck, Betty, Chuck d. Betty, Chuck, Arnold, Daphne, Betty e. Betty, Arnold, Betty, Arnold, Chuck 14. Which of the following is enough information to determine the exact schedule for the whole week? a. Betty takes off period X on Monday, Wednesday, and Friday b. Only Arnold and Chuck take period W off c. On Tuesdays and Thursdays, Arnold takes off period X and Chuck takes off period W

d. On Mondays and Wednesdays, Arnold takes off period W and Daphne takes off period Z e. Betty takes off period Y on Monday, Wednesday, and Friday 15. If Daphne takes off period X more times than anyone else, then which of the following must be false? a. Betty takes period Y off more than anyone else b. Arnold takes period W off more than anyone else c. Chuck takes period Z off more than anyone else d. Daphne takes period Y off at least once e. Arnold takes period Y off at least once 16. Which of the following is a complete and accurate list of the teachers who can take period X off on Tuesdays and Thursdays? a. Betty b. Arnold and Betty c. Arnold and Daphne d. Betty and Daphne e. Arnold, Betty, and Daphne 17. Which of the following is not possible? a. Arnold takes off period W only twice b. Chuck takes off period Z three times c. Daphne takes off period X three times d. Three different teachers take off period W e. Three different teachers take off period X

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Questions 18-22 A handyman is organizing his toolbox to keep his work efficient. The box contains tools including a hammer, screwdriver, vice grip, wrench, tape measure, and pliers, and it also contains items including screws, nails, hooks, and rope. The toolbox has two levels, and will be arranged by the following conditions: The nails must be on the same level as the hammer The screws must be on the same level as the screwdriver The four items must not all be together on the same level The rope is on the top level The pliers are not on the same level as the tape measure The wrench and vice grip must be on the same level No tools or items can be left out of the toolbox 18. What is the highest number of tools and items that could be on one level? a. 6 b. 7 c. 8 d. 9 e. 10

19. Which of the following is a possible arrangement of the tools and items? a. Upper level: rope, hooks, screwdriver, screws, vice grip Lower level: hammer, nails, pliers, wrench, tape measure b. Upper level: hammer, tape measure, nails, screwdriver, rope Lower level: pliers, screws, wrench, vice grip, hooks c. Upper level: nails, pliers, hammer, screwdriver, screws Lower level: wrench, vice grip, hooks, rope, tape measure d. Upper level: rope, vice grip, tape measure, wrench, hooks. Lower level: hammer, nails, pliers, screws, screwdriver e. Upper level: pliers, hammer, rope, nails, screwdriver, screws, hooks Lower level: tape measure, wrench, vice grip 20. If the hammer is kept on a different level than the rope and pliers, then how many total tools and items could be on the upper level? a. 5 b. 6 c. 7 d. 8 e. 9

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21. If exactly two items are on the lower level, then which of the following must be false? a. There are four tools on the upper level b. There are four tools on the lower level c. The vice grip and rope are on the same level d. The screws and nails are on the same level e. The hammer and screwdriver are on the upper level

22. If a total of seven tools and items are on the lower level, then which of the following must be true? a. The wrench is on the lower level b. The tape measure is on the top level c. The hammer and screwdriver are on different levels d. The pliers are on the lower level e. Only one item is on the upper level

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Questions 1-5 Amanda is planning a music playlist for her party. She is choosing between Jazz, Heavy Metal, Classic rock, Hip-hop, and Alternative. She will narrow the choices down to three genres, one for each the beginning, middle, and end of the party, according to the following conditions: Heavy Metal and Alternative cannot both be choices Hip-hop and Classic rock cannot both be choices Hip-hop cannot be played before Heavy Metal Jazz, if played, must be played during the beginning of the party Classic rock, if played, must be played during the middle of the party 1. Which of the following is a possible RUGHURIPXVLFJHQUHVIRU$PDQGD¶V party? a. Hip-hop, Classic rock, Alternative b. Jazz, Hip-hop, Heavy Metal c. Jazz, Classic rock, Alternative d. Jazz, Classic rock, Hip-hop e. Hip-hop, Jazz, Alternative 2. If Alternative is played, which of the following cannot be true? a. Classic rock is played second and Heavy metal is played third b. Jazz is played first and Hip-hop is played third c. Classic rock and Jazz are both played d. Hip-hop and Jazz are both played e. Heavy metal and Hip-hop are both played

3. If Heavy metal and Hip-hop are both chosen, how many total arrangements of genres could be made? a. 1 b. 2 c. 3 d. 4 e. 5 4. Which genre must be played at the party? a. Jazz b. Heavy metal c. Classic rock d. Hip-hop e. Alternative 5. If Blues is added as a choice and played in the middle of the party, and all other conditions remain the same, which of the following must be false? a. Jazz and Heavy Metal are both played b. Hip-hop is played c. Alternative and Classic Rock are both played d. Neither Alternative nor Hip-hop is played e. Neither Hip-hop nor Heavy Metal is played

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Questions 6-10 A stable has nine horses, and six of them will be selected to perform in a horse show. The horses are named Bronze, Cinnamon, Domino, Edgar, Firestorm, Gemini, Holyoke, Jupiter, and Kronos. The owner will select the horses according to the following conditions: If Edgar is selected, then so must Holyoke If Gemini is selected, then Jupiter cannot be Cinnamon and Kronos cannot be selected without one another Jupiter or Bronze or both must be selected Firestorm must be selected if Domino is not 6. Which of the following could be the list of horses being taken to the show? a. Edgar, Cinnamon, Holyoke, Firestorm, Jupiter, Bronze b. Gemini, Domino, Cinnamon, Kronos, Jupiter, Firestorm c. Kronos, Holyoke, Bronze, Cinnamon, Firestorm, and Jupiter d. Kronos, Cinnamon, Holyoke, Edgar, Domino, and Gemini e. Kronos, Firestorm, Edgar, Bronze, Cinnamon, Gemini

8. If Cinnamon and Gemini are selected, which of the following must be false? a. Domino and Holyoke are chosen b. Holyoke and Edgar are chosen c. Bronze and Domino are chosen d. Neither Firestorm nor Edgar is chosen e. Neither Jupiter nor Holyoke is chosen 9. How many combinations of selected horses exist if Edgar and Gemini are selected? a. 1 b. 2 c. 3 d. 4 e. 5 10. Suppose the owner were allowed to bring seven horses instead of only six. If all the other conditions stay the same, which of the following could be true? a. Gemini and Holyoke are left out b. Jupiter and Holyoke are left out c. Holyoke and Edgar are left out d. Edgar and Jupiter are left out e. Domino and Firestorm are left out

7. If both Edgar and Domino are selected, then which of the following must be true? a. Cinnamon or Bronze is selected b. Jupiter is selected c. Bronze is selected d. Kronos or Jupiter is selected e. If Firestorm is selected, then Jupiter cannot be

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Questions 11-16 In an elementary school, there are six grades: 1, 2, 3, 4, 5, and 6. The school is hosting a one-hour presentation for each grade, to be held at 8:30, 9:30, 11:00, 12:00, 1:30, and 2:30. The presentations must be scheduled under the following conditions. Grade 6 will see the presentation after Grades 1 and 2 *UDGH¶VSUHVHQWDWLRQZLOOEHJLQWKLUW\PLQXWHV past the hour There is exactly a half hour in between Grade 5 DQG*UDGH¶VSUHVentations Grade 3 cannot have their presentation directly before or directly after Grade 2 does 11. Which of the following is a possible VFKHGXOHIRUHDFKJUDGH¶VSUHVHQWDWLRQV" a. 1, 4, 5, 2, 6, 3 b. 2, 4, 1, 5, 6, 3 c. 1, 2, 4, 3, 5, 6 d. 3, 4, 1, 5, 6, 2 e. 1, 2, 3, 6, 5, 4 12. If Grade 6 sees the presentation at 12:00, then which of the following must be true? a. Only Grade 1 or Grade 2 could see it at 9:30 b. Only Grade 1 or Grade 2 could see it at 11:00 c. Only Grades 2, 3, or 4 could see it at 8:30 d. Only Grade 3 or Grade 4 could see it at 2:30 e. Grade 1 sees it before Grade 4 does

13. How many combinations exist for the schedule if Grade 5 sees the presentation at 1:30? a. 6 b. 7 c. 8 d. 9 e. 10 14. Which of the following pieces of information is enough to determine the full schedule for the presentations? a. Grade 4 sees the presentation directly after Grade 5 b. Exactly two Grades see the presentation between Grade 1 and Grade 5 c. Exactly two Grades see the presentation between Grade 3 and Grade 6 d. Grades 2 and 3 are the first and last to see the presentation e. Grades 1 and 4 are the first and last to see the presentation 15. Which of the following pairs of Grades cannot be the first and last to see the presentation? a. 1 & 4 b. 2 & 4 c. 4 & 3 d. 2 & 3 e. 1 & 3

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16. Each of the following could be true except a. Grade 4 sees the presentation at 8:30 b. Grade 3 sees the presentation at 9:30 c. Grade 1 sees the presentation at 11:00 d. Grade 5 sees the presentation at 12:00 e. Grade 4 sees the presentation at 2:30  

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Questions 17-22 A coffee shop is preparing coffee for a group of six customers. They want different combinations of added ingredients. Each guest wants a particular combination of sugar, cream, and vanilla flavoring. Each of the guests may also choose either Regular or Decaffeinated (Decaf) coffee. The coffee shop worker will make them according to the following conditions. Guest 1 wants regular if Guest 2 wants regular, and he wants decaf if Guest 2 wants decaf Guest 4 will at least add sugar to his regular coffee Guest 5 has no added ingredients that Guest 6 chooses Guest 3 will have regular if Guest 6 has decaf, DQGKH¶OOKDYHGHFDILI*XHVWKDVUHJXODU coffee No more than one guest can have their coffee without any ingredients Guest 2 wants only cream and sugar added There are more regular coffees ordered than there are decaffeinated coffees ordered 17. Which of the following is a complete and accurate list of the guests who may want decaf? a. 1, 2, 3, 5, 6 b. 1, 2, 3, 6 c. 3, 4, 6 d. 3, 5, 6 e. 1, 2, 3, 4, 6

18. How many different combinations exist IRU*XHVW¶VFRIIHH" a. 3 b. 4 c. 5 d. 6 e. 7 19. If Guest 6 has a regular coffee with cream and sugar, then which of the following must be false? a. Guest 1 drinks his coffee without added ingredients b. Guest 3 has a decaf with sugar c. Guests 2 and 5 both have at least one added ingredient in common d. Guests 1 and 4 have at least one added ingredient in common e. Guest 5 drinks a decaffeinated coffee 20. Which of the following must be false if none of the guests drink their coffee without added ingredients? a. Guest 4 adds two ingredients to his coffee b. Guest 3 drinks regular coffee c. Guests 1, 4, and 5 drink coffee with only one ingredient d. Guest 6 drinks his coffee with cream, sugar, and vanilla flavoring e. Two of the guests drink their coffee decaffeinated

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21. If Guest 3 has vanilla flavoring and cream in his decaf coffee, then which of the following could be true? a. Guest 3 has both ingredients that Guest 2 has b. Five guests have vanilla flavoring in their coffee c. Guest 6 has sugar in his decaf coffee d. Guests 2, 5, and 6 all have the same number of added ingredients e. Every guest has two ingredients in his coffee

22. If honey was added as another ingredient, but all the original conditions stayed the same, how many guests could add honey to their coffee on the same occasion? a. 2 b. 3 c. 4 d. 5 e. 6    

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Questions 1-5 On seven consecutive days, starting on Sunday and ending on Saturday, a painting company will paint seven different houses. The houses are labeled A, B, C, D, E, F, and G. Some houses will be painted white, and others will be painted red. The painters must organize their schedule according to the following conditions. No two houses can be painted red consecutively Exactly two houses that are painted before B are white D must be painted before A is painted but after E is painted C is painted on Wednesday, and G is painted before it There are more white houses than there are red houses House A is painted red 1. Which of the following is a possible order of how the houses are painted? a. G, E, A, C, D, B, F b. F, E, D, C, G, A, B c. E, G, D, C, B, A, F d. E, B, G, C, D, F, A e. E, G, D, A, C, F, B

3. Which of the following pairs of houses cannot be painted consecutively? a. B & G b. C & A c. C & F d. A & G e. D & A 4. If D is painted red, then which of the following could not be true? a. A is painted on Friday b. E is painted on Thursday c. D is painted on Tuesday d. B is painted on Tuesday e. E is painted on Sunday 5. In how many different locations can house F be located? a. 2 b. 3 c. 4 d. 5 e. 6

2. If house G is red, and D is white, then which of the following must be false? a. B is painted before Thursday b. E is painted on Tuesday c. G is painted on Monday d. E is painted before G e. E is painted red

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Questions 6-12 A cook is organizing her spice rack, which includes basil, cinnamon, dill, garlic, oregano, paprika, sage, and thyme. There are three shelves, and the spices are arranged under the following conditions: There are at least two spices on each shelf Basil and thyme must be on the same shelf Cinnamon is above oregano Basil is not below dill Dill and garlic cannot be on the same shelf Sage is on the middle shelf Paprika is not on the top shelf 6. Which of the following is a possible arrangement of spices on the rack? a. Lower shelf: oregano, dill, paprika. Middle shelf: garlic, sage, cinnamon. Upper shelf: basil, thyme b. Lower shelf: oregano, paprika. Middle shelf: basil, thyme, sage. Upper shelf: dill, cinnamon, garlic c. Lower shelf: paprika, dill. Middle shelf: sage, oregano, thyme. Upper shelf: basil, cinnamon, garlic d. Lower shelf: basil, thyme paprika. Middle shelf: sage, cinnamon, dill. Upper shelf: garlic, oregano e. Lower shelf: dill, oregano, basil, thyme. Middle shelf: sage, cinnamon. Upper shelf: garlic, paprika

7. If basil is on the middle shelf, which of the following must be true? a. Dill is on the middle shelf b. Dill and oregano are on the same shelf c. Cinnamon and garlic are on the upper shelf d. Paprika and oregano are on the lower shelf e. Dill is on the lower shelf 8. How many of the eight spices could possibly be on the upper shelf? a. 3 b. 4 c. 5 d. 6 e. 7 9. If paprika and cinnamon are on the same shelf, then which of the following must be true? a. Paprika is on the lower shelf b. Dill is on the upper shelf c. Oregano and dill are on the same shelf d. Sage and cinnamon are on different shelves e. Basil is on the upper shelf 10. Which of the following trios of spices cannot be on the same shelf? a. Basil, sage, and cinnamon b. Oregano, dill, and paprika c. Sage, basil, and paprika d. Garlic, oregano, and paprika e. Cinnamon, dill, and thyme

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11. Which of the following is a complete and accurate list of the spices that can be next to Oregano? a. Garlic, paprika, basil, thyme b. Garlic, paprika, basil, thyme, sage c. Garlic, paprika, basil, thyme, sage, cinnamon d. Garlic, paprika, basil, thyme, sage, dill e. Garlic, paprika, basil, thyme, sage, dill, cinnamon

12. If the cook decided to add nutmeg to the shelf, a spice that had to be next to the sage, and all of the original conditions remained the same, then which of the following would have to be false? a. The lower shelf has five spices b. The middle shelf has five spices c. The upper shelf has five spices d. Basil and oregano are below the nutmeg e. Dill and paprika are below the nutmeg

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Questions 13-17 A little league baseball tournament is taking place. The competing teams are called the Astros, Bears, Cougars, Diamonds, Eagles, Flyers, Giants, and Hammerheads. The tournament will be single elimination, and there are no ties. In the first round, all eight teams will play. In the second round, the four winners of the first round will play. In the championship, the two winners of the second round will play. They will play according to the following conditions: The Hammerheads cannot beat the Cougars The Astros cannot defeat the Flyers The Bears will not play the Eagles or the Hammerheads The Giants will play the Bears in the first round The Hammerheads will lose in the second round The Diamonds will defeat the team they play in the first round The Eagles and Diamonds will not win the championship 13. If the Eagles win in the first round, which of the following must be false? a. The Giants will defeat the Eagles in the championship b. The Bears lose in the second round c. The Eagles will defeat the Hammerheads d. The Eagles will defeat the Cougars e. The Hammerheads will defeat the Flyers

14. How many teams could beat the Flyers in the second round? a. 2 b. 3 c. 4 d. 5 e. 6 15. If the Astros win in the first round, but lose in the second, which of the following is a complete and accurate list of the teams that could beat them? a. Bears, Diamonds, Giants b. Diamonds, Giants c. Diamonds, Eagles, Giants d. Bears, Eagles, Giants e. Bears, Diamonds, Eagles, Giants 16. If the Eagles beat the Cougars, then which of the following must be true? a. The Flyers win in the first round b. The Cougars win in the first round c. The Giants win in the first round d. The Eagles win in the second round e. The Diamonds win in the second round 17. Which of the following teams could beat the Cougars in the second round? a. Astros b. Flyers c. Eagles d. Diamonds e. Hammerheads

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Questions 18-23 Six athletes are competing in a multi-sport competition. There are three male athletes, Andrew, Bob, and Charlie, and three female athletes, Morgan, Nancy, and Polly. They are competing in soccer, golf, track, and archery. Each of the athletes competes in exactly three of the sports, and they are chosen under the following conditions: Exactly two of the male athletes play golf Exactly two of the female athletes compete in archery Charlie and Polly do not compete in the same three sports More athletes play soccer than any other sport in the competition If Bob runs track, then so does Nancy Morgan does not compete in track 18. If archery is played more than track or golf, then which of the following is a complete and accurate list of the male athletes who compete in it? a. Andrew and Bob b. Bob and Charlie c. Andrew, Bob, and Charlie d. Andrew and Charlie e. Charlie 19. How many athletes play soccer? a. 2 b. 3 c. 4 d. 5 e. 6

20. Which of the following must be false? a. Nancy and Polly compete in archery b. Bob and Charlie compete in track c. Four athletes compete in the same three sports as each other d. One sport is played only twice e. More male athletes play archery than females do 21. If Andrew and Charlie compete in track, and Nancy and Morgan compete in the same exact sports as each other, then which of the following could be false? a. Andrew plays golf b. Polly plays golf c. Charlie plays golf d. Bob plays archery e. Charlie plays archery 22. Which of the following is a complete and accurate list of sports that can be played by exactly three athletes? a. Track b. Archery and Golf c. Track and Golf d. Archery and Track e. Archery, Track, and Golf 23. If Nancy competes in archery and track, then how many athletes¶VSRUWVVFKHGXOHV can be fully calculated? a. 1 b. 2 c. 3 d. 4 e. 5

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Questions 1-6 Lockers A, B, C, D, E, F, and G are aligned in a locker room. A, B, and C are red, while D, E, F, and G are green. They are arranged from left to right under the following conditions: A is to the left of C B is to the left of D D is to the right of C F is to the right of E There is a green locker on each end of the row The locker in the very middle is red The three red lockers are not all lined up consecutively 1. Which of the following is a possible arrangement of the lockers? a. E, A, G, C, B, D, F b. G, A, B, C, E, D, F c. G, A, E, B, D, C, F d. E, F, B, G, A, C, D e. E, B, F, C, A, G, D 2. Which of the following must be false? a. Locker F is the second from the right b. Locker E is the second from the left c. Locker D is the third from the right d. Locker G is on the very left edge e. Locker C is in the very middle

3. In how many different spaces can locker E be placed? a. 1 b. 2 c. 3 d. 4 e. 5 4. If locker A is in the very center of the row, and no red lockers are directly next to one another, then how many combinations exist for the arrangement of the lockers? a. 2 b. 3 c. 4 d. 5 e. 6 5. If locker F is on the very right side of the row, then which of the following is a complete and accurate list of the spaces, from left to right, that could have a red locker? a. 2, 4, 6 b. 2, 3, 4, 5 c. 2, 3, 5 d. 2, 4, 5, 6 e. 2, 4, 5 6. If locker G has to be to the left of locker E, then which of the following must be true? a. Locker D is to the left of locker F b. Locker C is to the right of locker B c. The locker that is second from the left is green d. The locker that is second from the left is red e. Locker G is the first locker

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Questions 7-11 The president of an outdoorsman club is picking out kayaks for his eight members. Four of the members are men, and four are women. The president is choosing from red, yellow, and green kayaks, which can be either long or short. He must choose them under the following conditions: The women choose either yellow or green kayaks There is at least one of each color kayak chosen More members choose long kayaks than short kayaks There are no short green kayaks No more than one red kayak is long At least two women choose short kayaks The men and women cannot have the same number of green kayaks No more than five kayaks can be the same color 7. If only one red kayak is chosen, and it is short, then which of the following could be false? a. Exactly three men choose long kayaks b. Exactly two women choose long kayaks c. At least one man chooses a green kayak d. The women choose at least two yellow kayaks e. There are a different number of yellow and green kayaks

8. Each of the following could be true except: a. There are a total of five green kayaks b. There are a total of five yellow kayaks c. There are a total of three red kayaks d. There are more red kayaks than green kayaks e. There are only two short kayaks 9. If the men do not select any yellow kayaks, which of the following must be true? a. The men have more green kayaks than the women do b. The men have fewer green kayaks than the women do c. The women have exactly two yellow kayaks d. The men have only one red kayak e. The men have no short kayaks 10. If the men choose more yellow kayaks than either red or green kayaks, which of the following could be false? a. The women choose at least two green kayaks b. The women choose at least two yellow kayaks c. The men choose one red kayak d. The men choose one green kayak e. There are more yellow kayaks between men and women than any other color

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11. Suppose blue kayaks became available to the women but they must have the same number of blue kayaks as yellow kayaks. If all other conditions remain the same, then how many color combinations are available to the women? a. 2 b. 3 c. 4 d. 5 e. 6

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Questions 12-17 A police force is scheduling assignments for its officers, and will divide up into five sections labeled A, B, C, D, and E. The officers will handle traffic, robberies, noise complaints, parking violations, and accidents. The police sections will be assigned to the different tasks according to the following conditions: Each police section will cover two different tasks Section C will cover noise complaints If section D covers accidents, then section A will cover traffic Sections B and A cover completely different tasks Section E will cover at least one task in common with section C All tasks must be covered twice 12. Which of the following is a possible schedule for the five police sections? a. Section A - accidents and noise complaints Section B ± parking violations and robberies Section C ± noise complaints and traffic Section D ± parking violations and accidents Section E ± traffic and robberies b. Section A ± parking violations and accidents Section B ± noise complaints and traffic Section C ± noise complaints and robberies Section D ± traffic and robberies Section E ± parking violations and accidents

c. Section A ± robberies and parking violations Section B ± accidents and noise complaints Section C ± accidents and traffic Section D ± parking violations and robberies Section E ± noise complaints and traffic d. Section A ± traffic and noise complaints Section B ± parking violations and robberies Section C ± noise complaints and accidents Section D ± robberies and traffic Section E ± accidents and parking violations e. Section A ± traffic and parking violations Section B ± accidents and traffic Section C ± robberies and noise complaints Section D ± accidents and parking violations Section E ± noise complaints and robberies 13. If sections D and A both cover accidents, then which of the following is a complete and accurate list of the sections that could have four different tasks assigned to them? a. Section C b. Section E c. Section C and E d. Section D, and E e. Section C, D, and E

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14. If section E covers accidents and traffic, then which of the following must be true? a. Section D covers parking violations and robberies b. Section A covers robberies and noise complaints c. Section B covers parking violations and traffic d. Section C covers traffic e. Section C covers accidents

17. Which of the following pairs of police sections could have the same two assignments? a. D and E b. A and C c. B and C d. B and D e. A and E

15. Which of the following must be false? a. Section C covers robberies b. Section D covers noise complaints c. Section E covers accidents d. Section A covers traffic e. Section A covers noise complaints 16. Which of the following choices provides enough information to determine the exact assignments of the different police sections? a. Section A covers robberies and section D covers traffic and parking violations b. Section D covers accidents and parking violations and section A covers robberies c. Section A covers accidents and traffic and section E covers accidents and robberies d. Section D covers accidents and parking violations and Section A covers accidents e. Section A covers noise complaints and traffic and section E covers parking violations and accidents

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Questions 18-22 A student is taking classes on Tuesdays, Wednesdays, and Thursdays, both in the morning and the evening. He will take a total of six classes per week, exactly one on each morning and evening of those three days. The classes he will take are Biology, Chemistry, English, French, Geometry, and History, and they must be scheduled under the following conditions: English and French cannot be on the same day Biology and Chemistry cannot be on the same day Geometry must come sometime after English each week Chemistry must be taken in the morning History must be taken on Wednesday evening 18. Which of the following is a possible schedule of classes? a. Tuesday: morning ± Chemistry, evening ± English Wednesday: morning ± History, evening ± French Thursday: morning ± Geometry, evening ± Biology b. Tuesday: morning ± Biology, evening ± Geometry Wednesday: morning ± English, evening ± History Thursday: morning ± Chemistry, evening ± French c. Tuesday: morning ± Chemistry, evening ± English Wednesday: morning ± Geometry, evening ± History Thursday: morning ± French, evening ± Biology

d. Tuesday: morning ± English, evening ± Geometry Wednesday: morning ± French, evening ± History Thursday: morning ± Chemistry, evening ± Biology e. Tuesday: morning ± Biology, evening ± English Wednesday: morning ± French, evening ± History Thursday: morning ± Geometry, evening ± Chemistry 19. If Geometry is taken on Tuesday evening, which of the following cannot be true? a. Biology is taken on the same day as French b. Chemistry is taken on the same day as French c. Biology and French are taken on consecutive mornings d. Chemistry is taken before History e. French is taken Thursday morning 20. If English is taken on Thursday morning, which of the following must be true? a. French is taken on Tuesday b. Chemistry is taken on Wednesday c. Biology is taken on Tuesday d. Biology is taken at the same time of day as Geometry e. French is taken at the same time of day as English

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21. How many combinations of class schedules are possible if English is taken on Wednesday morning? a. 1 b. 2 c. 3 d. 4 e. 5

22. If Japanese was added as a course option instead of French, and it could be taken at any time after Geometry but not on the same day as Geometry, then which of the following could be true? a. Japanese is taken on Wednesday b. English is taken on Wednesday c. Chemistry is taken directly after Biology d. Japanese is taken directly after Geometry e. Biology is taken on Tuesday

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Questions 1-6 An entrepreneur will set up seven shops in a row, including a clothing store, a deli, a fast food restaurant, a grocery store, an ice cream shop, a jewelry store, and a liquor store. They will be placed from left to right, the far left being first and the far right being last. She will arrange them according to the following conditions: The jewelry store and the liquor store must be next to one another The clothing store must be second or sixth The grocery store and ice cream shop cannot be next to one another The fast food restaurant comes somewhere before the deli The liquor store and grocery store have no more than two other shops between them 1. Which of the following is an acceptable order of the shops, from first to last? a. Jewelry, clothing, fast food, liquor, ice cream, deli, grocery b. Fast food, ice cream, jewelry, liquor, grocery, clothing, deli c. Ice cream, clothing, deli, fast food, liquor, jewelry, grocery d. Grocery, fast food, deli, ice cream, clothing, liquor, jewelry e. Liquor, jewelry, fast food, ice cream, deli, clothing, grocery 2. If the jewelry store is last in the line, then how many different arrangements of the shops are possible? a. 4 b. 5 c. 6 d. 7 e. 8

3. If the deli comes third and the jewelry store comes fourth, then which of the following cannot be true? a. The clothing store is second b. The clothing store is sixth c. The liquor store is after the grocery store d. The ice cream shop is first e. The fast food restaurant is second 4. How many shops could possibly come last? a. 3 b. 4 c. 5 d. 6 e. 7 5. If the deli comes before the liquor store and there are exactly two shops between them, then which of the following must be false? a. The liquor store comes sixth b. The grocery store comes last c. The ice cream shop comes third d. The fast food restaurant comes third e. The fast food restaurant comes second 6. If the ice cream shop is first and the grocery store is last, then which of the following is enough information to fill in the rest of the shop locations? a. The jewelry store is fourth b. The deli is fourth c. The clothing store is sixth d. The liquor store is sixth e. The fast food restaurant is second

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Questions 7-11 A group of students on field trips will visit five places. There is a museum, a park, an aquarium, a historical site, and a zoo. The students are split into three groups, named 1, 2, and 3. Each group will visit each of the five sites separately, and they will do so under the following conditions: Group 1 will start at the zoo Group 2 will visit the aquarium after Group 1 visits it Group 3 will visit the historical site after group 2 visits it The park cannot be the last place visited by Group 3 While Group 1 is at the museum, Group 2 is at the park None of the groups visit the historical site and the zoo consecutively No more than one group visits the same place at the same time 7. Which of the following must be false? a. Group 1 visits the park after visiting the museum b. Group 2 begins at the park c. Group 2 visits the aquarium before Group 3 does d. Group 3 visits the historical site second e. Group 1 visits the museum third 8. Which of the following is an acceptable order of events for Group 3? a. park, zoo, museum, historical site, aquarium b. zoo, museum, park, historical site, aquarium

c. historical site, aquarium, zoo, park, museum d. museum, historical site, aquarium, zoo, park e. museum, park, historical site, zoo, aquarium 9. If the historical site is the third visit for Group 3, then which of the following must be true? a. Group 2 visits the aquarium third b. Group 3 visits the park fourth c. Group 2 visits the zoo fourth d. Group 1 visits the park after the aquarium e. Group 1 visits the historical site after the aquarium 10. All of the following could be true except a. Group 1 visits the historical site third b. Group 1 visits the aquarium fourth c. Group 2 visits the aquarium second d. Group 2 visits the park fourth e. Group 3 visits the museum fourth 11. If Group 2 visits the museum second, then how many different ways could they visit the five locations? a. 3 b. 4 c. 5 d. 6 e. 7

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Questions 12-16 A bakery will sample two different pies for their customers in each season of one particular year: Winter, Spring, Summer, and finally Fall. The pies are apple, blueberry, cherry, lemon, pecan, pumpkin, rhubarb, and strawberry. Each season two pies will be sampled, and they must follow these conditions: Pecan and pumpkin will not be in the same season Apple must be in the same season, or in a consecutive season, as rhubarb If lemon is sampled in the springtime, then so is strawberry If blueberry is sampled in the summer, then cherry is sampled in the fall Pumpkin will be sampled in either the summer or fall 12. Which of the following could be the order of samples, beginning with winter and ending in the fall? a. Apple & rhubarb, lemon & strawberry, pumpkin & cherry, pecan & blueberry b. Lemon & pecan, rhubarb & strawberry, blueberry & cherry, pumpkin & apple c. Apple & pecan, rhubarb & lemon, strawberry & pumpkin, blueberry & cherry d. Rhubarb & lemon, apple & pumpkin, blueberry & pecan, cherry & strawberry e. Blueberry & cherry, apple & rhubarb, pumpkin & pecan, lemon & strawberry

13. If apple and blueberry are sampled in the summer, which of the following could be false? a. Pumpkin and cherry are sampled together b. Lemon is sampled in the winter c. Rhubarb is sampled in the spring d. Strawberry is sampled in the spring e. Pumpkin is sampled in the fall 14. If lemon is sampled in the spring, then how many pies could be sampled in the winter? a. 2 b. 3 c. 4 d. 5 e. 6 15. Which of the following is a complete and accurate list of pies that could be sampled in the spring if apple and cherry are sampled in the winter? a. Rhubarb, pecan b. Rhubarb, strawberry c. Rhubarb, lemon, strawberry, blueberry d. Rhubarb, lemon, strawberry, pecan e. Rhubarb, blueberry, strawberry, pecan

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16. If strawberry and cherry had to be sampled during the winter, then which of the following would have to be false? a. Pecan and blueberry are both sampled in the fall b. Lemon and blueberry are both sampled in the summer c. Rhubarb and blueberry are both sampled in the spring d. Apple is sampled in the summer e. Pumpkin and lemon are both sampled in the summer

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Questions 17-22 A soda manufacturer is filling a vending machine with the various sodas that they make. The eight flavors that they will stock are cola, lemon-lime, root beer, ginger ale, diet, orange, tonic, and vanilla. He will stock them from top to bottom according to the following conditions: Cola is either on the top or the bottom Ginger ale is next to lemon-lime Root beer must be stocked somewhere above the diet soda There is exactly one space between orange and tonic There is more than one space between lemon-lime and cola 17. Which of the following is an acceptable order of sodas from bottom to top? a. Cola, root beer, ginger ale, lemon-lime, diet, orange, vanilla, tonic b. Cola, diet, orange, lemonlime, ginger ale, tonic, vanilla, root beer c. Ginger ale, lemon-lime, orange, diet, tonic, root beer, vanilla, cola d. Orange, diet, tonic, lemonlime, vanilla, ginger ale, root beer, cola e. Cola, vanilla, lemon-lime, ginger ale, diet, orange, root beer, tonic 18. If orange soda is next to lemon-lime, then which of the following spaces could orange occupy? a. The bottom b. Second from the bottom c. Third from the bottom d. The top e. Second from the top

19. If lemon-lime is third from the top and next to vanilla, then which of the following must be true? a. Either orange or tonic is third from the bottom b. Root beer is third from the bottom c. Cola is on top d. Tonic is next to cola e. Diet is third from the bottom 20. How many different spaces could be occupied by ginger ale? a. 2 b. 4 c. 5 d. 7 e. 8 21. If root beer is directly above vanilla, then which of the following must be false? a. Root beer is fourth from the top b. Lemon-lime is third from the top c. Diet is fourth from the bottom d. Tonic is third from the bottom e. Tonic is second from the bottom 22. Which of the following is a pair of sodas that cannot be consecutive in the machine? a. Root beer and cola b. Cola and ginger ale c. Diet and orange d. Lemon-lime and orange e. Tonic and diet

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Questions 1-7 Two friends decide to take a road trip to seven states in seven days. They begin on a Sunday, traveling until the following Saturday. The seven states they visit are New York, Connecticut, Rhode Island, Massachusetts, Vermont, New Hampshire, and Maine. They only visit one state per day, and do not skip any days or states. They must plan the trip according to the following conditions: Connecticut and Maine cannot be visited in consecutive days New York must be visited after Rhode Island New Hampshire and Vermont must be visited consecutively There is exactly one day between Massachusetts and New York Vermont cannot be visited on Thursday 1. Which of the following could be the order of the states, from Sunday through Saturday? a. Vermont, New Hampshire, Massachusetts, Maine, Rhode Island, New York, Connecticut b. Connecticut, Rhode Island, New Hampshire, New York, Maine, Massachusetts, Vermont c. Rhode Island, New York, Maine, Massachusetts, Vermont, New Hampshire, Connecticut d. Massachusetts, Connecticut, New York, Vermont, New Hampshire, Rhode Island, Maine e. Rhode Island, Vermont, New Hampshire, New York, Maine, Massachusetts, Connecticut

2. If the friends visit Massachusetts on Friday, then which of the following must be true? a. Rhode Island is visited on Sunday b. Rhode Island is visited on Tuesday c. New Hampshire is visited between Rhode Island and Vermont d. Massachusetts is visited between Connecticut and Maine e. Maine is not visited the day after New York 3. If Rhode Island is visited on Wednesday, then which of the following is a pair of states that could possibly be visited on Friday and Saturday? a. New York and Vermont b. New York and New Hampshire c. Maine and New York d. Maine and Vermont e. Connecticut and Vermont 4. How many states could be visited on Saturday if New Hampshire is visited on Friday? a. 1 b. 2 c. 3 d. 4 e. 5

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5. Which of the following pieces of information is enough to determine with certainty that either Maine or Connecticut is visited on Wednesday? a. Massachusetts is visited on Monday b. New York is visited on Tuesday c. New Hampshire is visited on Thursday d. Massachusetts is visited on a Friday e. Connecticut is visited on a Saturday 6. How many ways could the schedule be arranged if New York is visited on Monday? a. 4 b. 5 c. 6 d. 7 e. 8 7. Which of the following is a complete and accurate list of states that could come before both Rhode Island and Connecticut? a. Maine, Massachusetts b. Maine, Connecticut, New Hampshire c. Maine, Massachusetts, Vermont, New Hampshire d. New Hampshire, Vermont e. New Hampshire, Vermont, Maine

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Questions 8-12 Seven boys named Craig, Eric, Jimmy, Kyle, Leopold, Stan, and Timmy are planning a ski trip. Some of the boys will travel to Denver to ski while the rest will travel to Boulder. The following conditions apply to the trip: Eric travels to a different city than Kyle Jimmy travels to a different city than Timmy If Stan travels to Boulder, then Leopold travels to Boulder If Kyle travels to the same city as Stan, then Craig travels to the same city as Eric 8. If Stan and Kyle travel to Boulder, then which of the following could be true? a. Leopold travels to Denver b. Craig travels to Boulder c. Exactly three boys travel to Boulder d. Eric travels to Boulder e. Jimmy travels to Boulder 9. Which of the following trios cannot travel to Boulder together? a. Eric, Jimmy, and Leopold b. Craig, Kyle, and Stan c. Kyle, Jimmy, and Leopold d. Craig, Eric, and Jimmy e. Eric, Leopold, and Timmy

10. If Jimmy and Leopold travel to Denver, then which pair of boys cannot travel together? a. Timmy and Stan b. Craig and Eric c. Leopold and Stan d. Eric and Stan e. Eric and Timmy 11. Which of the following is a complete and accurate list of boys that could travel to Denver if Jimmy and Craig travel to Denver? a. Craig, Eric, Jimmy, Stan b. Craig, Eric, Jimmy, Kyle, Stan c. Craig, Eric, Jimmy, Kyle, Leopold, Stan d. Craig, Jimmy, Kyle, Leopold e. Craig, Jimmy, Kyle, Leopold, Stan 12. If five boys travel to one city, then how many of the boys could potentially be in the pair that travels to the other city? a. 2 b. 3 c. 4 d. 5 e. 6

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Questions 13-18 A local museum is opening a reptile exhibit and needs to decide how to arrange their animals. The available reptiles to be displayed are alligators, chameleons, geckos, iguanas, komodo dragons, snakes, and turtles. The reptiles will be arranged in two displays marked A and B, and each display will be arranged from left to right. No animals will be featured in both displays. The following conditions must apply to their arrangement: The alligators and turtles must be in separate displays The chameleons and iguanas must be in the same display The geckos are to the left of the komodo dragons if they are in the same display The snakes must be directly next to the alligators if they are in the same display There are no more than four animals in each display 13. Which of the following could be the arrangement, from left to right, of Display B? a. Komodo dragons, Geckos, Alligators b. Alligators, Snakes, Komodo dragons, Chameleons c. Alligators, Snakes, Komodo dragons, Turtles n d. Snakes, Iguanas, Chameleons, Turtles e. Komodo dragons, Turtles

14. If only the Turtles, Iguanas, and Chameleons are in Display A, then how many different ways can Display B be arranged from left to right? a. 4 b. 5 c. 6 d. 7 e. 8 15. If the Geckos and Komodo dragons are in different displays, which of the following must be false? a. The Iguanas and Snakes are in the same display b. The Komodo dragons and Alligators are in the same display c. The Snakes and Turtles are in the same display d. The Geckos and Alligators are in the same display e. The Komodo dragons and Turtles are in the same display 16. Which of the following trios of animals cannot be displayed together? a. Geckos, Alligators, and Komodo dragons b. Chameleons, Alligators, and Snakes c. Snakes, Komodo dragons, and Iguanas d. Geckos, Turtles, and Snakes e. Snakes, Alligators, and Geckos

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17. If the Chameleons are one of only three animals in Display A, which of the following could be true? a. The Geckos are in the rightmost space in Display B b. The Geckos are directly next to the Chameleons c. The Komodo dragons are directly next to the Iguanas d. The Snakes are in the rightmost space of their display e. The Komodo dragons are in the left-most space of their display

18. If Monitor lizards are added to the exhibit, and they cannot be displayed with Geckos, then which of the following must be true? a. The Iguanas are displayed with the Komodo Dragons b. The Snakes are displayed with the Komodo Dragons c. The Chameleons are displayed with the Alligators d. The Monitor lizards are displayed with the Snakes e. The Geckos are displayed with the Snakes

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Questions 19-23 Nine salespersons are filling out a three day schedule. The men are named Frank, Henry, Isaac, James, and Kiel, while the women are named Gayle, Lea, Marissa, and Nicki. They are assigned to days from Monday through Wednesday. No more than three people can work each day. The schedule is made under the following conditions:

21. Which of the following pairs cannot work on the same day? a. Marissa and Lea b. Henry and James c. Isaac and James d. Marissa and Gayle e. Isaac and Gayle

Exactly two men must work on Monday At least one man works on each day Kiel does not work after James or Lea Marissa and Nicki must work on different but consecutive days Gayle works on Tuesday If Isaac works on the same day a Kiel, then Lea must work on the same day as Henry Henry and Frank work on different days

22. Which of the following pieces of information must be false? a. Henry and Nicki both work on Tuesday b. Marissa and James both work on Monday c. James works on Tuesday and Nicki works on Wednesday d. Frank and Nicki work on Wednesday e. Isaac works on Monday and Marissa works on Wednesday

19. If Marissa and James work on Monday, then each of the following must be true except a. Nicki works on Tuesday b. Lea works on Wednesday c. Isaac works on Wednesday d. Henry works on Tuesday e. Kiel works on Monday

23. If Kiel works on Tuesday, how many different people could possibly work on Wednesday? a. 3 b. 4 c. 5 d. 6 e. 7

20. Which of the following must be false? a. Kiel works on Tuesday b. Henry works on Monday c. Lea works on Tuesday d. James and Lea work before Gayle e. Isaac can work any of the three days

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Questions 1-5 A pet shop is having a sale. The manager must advertise kittens, puppies, fish, lizards, and birds in two local papers, named Paper X and Paper Z. The manager must decide which paper is best to advertise each pet, but she will not advertise one animal in both papers. She must do so according to the following conditions: Each pet must be advertised at least once There are seven total ads between the two papers Paper X cannot have more pet ads than Paper Z The kittens and puppies cannot both be advertised twice The fish and lizards are advertised together in exactly one paper The birds are only advertised once If the puppies are advertised in Paper X, then the kittens must be advertised in Paper Z If the lizards are advertised in Paper Z, then the birds must be advertised in Paper X 1. If the birds are advertised in Paper Z, then which of the following could be true? a. Fish are advertised only once b. Lizards are advertised twice c. Kittens are advertised in Paper X only d. Puppies are advertised in Paper X only e. Puppies are advertised in Paper Z only

2. Which of the following is a pair of pets that cannot both be advertised only once? a. Kittens and lizards b. Puppies and fish c. Fish and kittens d. Fish and lizards e. Birds and fish 3. If the birds are advertised in Paper X, then how many different ways can the advertisements be arranged? a. 4 b. 5 c. 6 d. 7 e. 8 4. Each of the following must be false except a. All five pets are advertised in Paper Z b. Puppies and birds are advertised in Paper Z only c. Fish and birds are advertised in Paper Z only d. Lizards and birds are advertised in the same exact way e. Kittens and puppies are both advertised in just one paper 5. Which of the following is a complete and accurate list of pets that cannot be advertised in Paper X only? a. Kittens and puppies b. Kittens, fish, and lizards c. Kittens, puppies, fish, and lizards d. Kittens, puppies, and fish e. Kittens, puppies, and lizards

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Questions 6-11 A baker is making a four-level wedding cake with different ingredients. There are three icings to choose from: White, Red, and Pink. There are also four different flavors of cake to choose from: Chocolate, Vanilla, Strawberry, and Marble. The baker must make it according to the following conditions: The bottom, or first level, must have red icing The top, or fourth level, must have strawberry cake Pink icing cannot go with marble cake Chocolate cake must have white icing covering it Red icing can only cover strawberry cake or vanilla cake No icing or cake flavor can be used more than twice 6. Which of the following is a possible arrangement of the cake layers, from bottom to top? a. 1. Red icing, strawberry cake; 2. Pink icing, chocolate cake; 3. Red icing, vanilla cake; 4. White icing, strawberry cake b. 1. Red icing, strawberry cake; 2. White icing, chocolate cake; 3. Pink icing, marble cake; 4. Pink icing, strawberry cake c. 1. Red icing, vanilla cake; 2. Red icing, marble cake: 3. White icing, chocolate cake; 4. Red icing, strawberry cake

d. 1. Red icing, vanilla cake; 2. Pink icing, strawberry cake; 3. White icing, chocolate cake; 4. Red icing, marble cake e. 1. Red icing, strawberry cake; 2. White icing, chocolate cake; 3. Pink icing, vanilla cake; 4. Pink icing, strawberry cake 7. If the second level has marble cake, then which of the following must be true? a. There is white icing directly above red icing b. There is chocolate cake on the third level c. There are two levels of either vanilla cake or strawberry cake d. There is at least one level with pink icing e. Strawberry cake is found directly above chocolate cake 8. If red icing is found directly above pink icing, then which of the following could be true? a. Strawberry cake is found on the third level b. Marble cake is found on the third level c. There is a level of chocolate cake and a level of marble cake d. There are two levels of marble cake e. Chocolate cake is found on the third level

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9. Which of the following is a complete and accurate list of cake flavors and icings that will not necessarily be used? a. Icings: white. Flavors: chocolate, marble b. Icings: white, pink. Flavors: chocolate, marble c. Icings: white. Flavors: chocolate, marble, vanilla d. Icings: white, pink. Flavors: chocolate, marble, vanilla e. Icings: white, pink. Flavors: chocolate, vanilla

11. Which of the following must be false? a. There is white icing on the fourth level of the cake b. There is pink icing on the fourth level of the cake c. There is exactly one level of vanilla and there is white icing on all strawberry levels d. There is a level of cake with pink icing between two strawberry levels e. There are two levels of vanilla cake

10. If there are two levels of chocolate cake, then how many different levels could be marble cake? a. 0 b. 1 c. 2 d. 3 e. 4

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Questions 12-17 A library is sorting a special collection of documents about the following Presidents: Eisenhower, Ford, Garfield, Harrison, Jackson, Lincoln, Roosevelt, and Taylor. Each of the eight collections will be displayed on one of three floors of the library according to the following conditions: Each floor of the library has at least two collections The Eisenhower collection cannot be on the same floor as the Ford collection The Ford collection cannot be on the same floor as the Lincoln collection The Roosevelt collection must be on the same floor as the Harrison collection If The Roosevelt collection is on the same floor as the Jackson collection, then the Taylor collection must be on the same floor as the Garfield collection The Harrison collection cannot be on the third floor 12. Which of the following is a possible arrangement for the library? a. First floor: Ford, Garfield± Second floor: Eisenhower, Jackson± Third floor: Roosevelt, Harrison, Lincoln, Taylor b. First floor: Roosevelt, Harrison± Second floor: Garfield, Lincoln, Ford ± Third floor: Jackson, Taylor Roosevelt c. First floor: Roosevelt, Jackson, Eisenhower- Second floor: Harrison, Lincoln, Third floor: Garfield, Taylor, Ford d. First floor: Roosevelt, Harrison- Second floor: Eisenhower, Jackson, Ford-

Third floor: Lincoln, Garfield, Taylor e. First floor: Harrison, Jackson, Roosevelt- Second floor: Eisenhower, Lincoln- Third floor: Garfield, Taylor, Ford 13. If the Roosevelt and Jackson collections are both on the first floor, which of the following must be false? a. Harrison is on the same floor as Ford b. Taylor, Garfield, and Ford are on the same floor c. Eisenhower is directly above Garfield d. Four collections occupy the third floor e. Four collections occupy the first floor 14. If the Lincoln collection is on the first floor, and the Eisenhower is on the second floor, then which of the following is a complete and accurate list of collections that could be on the third floor? a. Ford and Jackson b. Ford, Taylor, Garfield, and Jackson c. Ford, Taylor, Jackson, and Roosevelt d. Ford, Garfield, and Jackson e. Ford, Taylor, and Jackson 15. If the Harrison collection is on the same floor as the Jackson collection, how many combinations of collections exist for the library to choose from? a. Two b. Four c. Six d. Eight e. Ten Page  |  56    

 

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16. If there are four collections displayed on the first floor, then how many of the eight collections are eligible to be displayed there? a. Four b. Five c. Six d. Seven e. Eight

17. If the Taylor, Jackson, and Garfield collections are together on a floor, which of the following is a complete and accurate list of the collections that individually could also be on that floor? a. Ford b. Ford and Eisenhower c. Eisenhower and Lincoln d. Lincoln e. Eisenhower

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Questions 18-22 Five musicians are needed for a three-set concert. All five musicians may or may not be used for the concert, but the music itself has already been chosen, and the following instruments are needed: For the first set, percussion and woodwinds, for the second set, brass, and for the third set, piano and strings. The following musicians are available, with their talents listed: Pauline: brass Ricky: woodwinds, piano Sal: strings, piano Trey: percussion, strings Vanessa: percussion, brass Wally: woodwinds, percussion Yasmine: piano, brass The following conditions apply for the performers to be chosen: No more than one musician will play each kind of instrument in each set No musician will play more than once in the concert Trey cannot play a set with Yasmine Ricky cannot play a set with Vanessa 18. Which of the following could be a list of the performers? a. 1st set: Vanessa, Ricky, 2nd set: Yasmine, 3rd set: Trey, Sal b. 1st set: Vanessa, Wally, 2nd set: Pauline, 3rd set: Trey, Yasmine c. 1st set: Wally, Ricky, 2nd set: Vanessa, 3rd set: Pauline, Trey d. 1st set: Vanessa, Wally, 2nd set: Pauline, 3rd set: Yasmine, Sal e. 1st set: Trey, Ricky, 2nd set: Yasmine, 3rd set: Sal, Vanessa

19. If Vanessa plays during the first set, then which of the following must be true? a. Sal plays in the third set b. Wally plays in the first set c. Ricky plays in the third set d. Pauline plays in the concert e. Yasmine plays in the concert 20. If Trey does not play in the concert, all of the following could be true except a. Vanessa plays in the second set b. Vanessa plays with Wally c. Yasmine plays piano d. Sal plays piano e. Ricky plays piano 21. If Vanessa, Wally, Trey, Sal, and Ricky are the performers, then how many combinations of musicians to instruments could be assembled? a. 1 b. 2 c. 3 d. 4 e. 5 22. If percussion is added to the second set along with Brass, but Pauline cannot perform, then which of the following cannot be true? a. Wally plays during the first set b. Trey plays during the first set c. Vanessa plays during the first set d. Sal does not play strings e. Trey does not play percussion

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Questions 1-6 A gardener is arranging flowers in front of his house, and he will choose from daisies, lilacs, petunias, roses, sunflowers, tulips, and violets. He will arrange the flowers from left to right, according to the following conditions: The roses cannot be on either end of the line of flowers The petunias cannot be next to the tulips The violets are on one end of the line of flowers There are at least two kinds of flowers between the daisies and lilacs The sunflowers must be somewhere to the left of the tulips All seven types of flowers must be planted 1. Which of the following could be the order of the flowers in the bed, from left to right? a. Violets, daisies, sunflowers, lilacs, tulips, roses, petunias b. Violets, daisies, sunflowers, tulips, petunias, roses, lilacs c. Sunflowers, lilacs, roses, tulips, violets, daisies, petunias d. Daisies, roses, sunflowers, petunias, lilacs, tulips, violets e. Violets, petunias, lilacs, tulips, roses, sunflowers, daisies

2. If the tulips are planted second from the left, which of the following must be true? a. Either daisies or lilacs are planted third from the left b. Petunias are planted fourth from the left c. Roses are planted fourth from the left d. Violets are planted on the far left e. Roses are planted to the left of the lilacs 3. How many flowers could be fourth from the left if sunflowers are third from the left? a. 1 b. 2 c. 3 d. 4 e. 5 4. If the violets are directly next to the sunflowers, then each of the following could be true except a. The tulips are on the far right b. The lilacs are fifth from the left c. The violets are to the left of the sunflowers d. The roses are to the right of the lilacs e. The roses are directly next to the petunias

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5. If the petunias are on the very left, and the lilacs are third from the left, then how many combinations exist for the gardener to plant his flowers? a. 1 b. 2 c. 3 d. 4 e. 5

6. Which of the following must be false if roses and lilacs are in the first two spots on the left? a. The daisies are to the left of the petunias b. The daisies are to the left of the tulips c. The petunias are third from the left d. The petunias are third form the right e. The tulips are third from the right

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Questions 7-12 Different colored balloons are being arranged for a holiday display. There is an upper row and a lower row of balloons, containing six balloons each. The different colors are Red, Blue, Green, Yellow, Orange, and Violet, and two of each color is displayed. The following conditions must be met in their arrangement: No balloon can be directly next to, above, or below the other balloon of its color Both of the Green balloons must be in the upper row and not on an end Both of the Blue balloons must be in the lower row There must be one Red, Orange, and Violet balloon on the top and bottom row Both Orange balloons must be next to Violet balloons Both Yellow balloons must be at a spot on an end of the display The Yellow balloons cannot be above or below Blue balloons 7. Which of the following is a possible combination of balloons on the lower row of the display? a. Yellow, Blue, Orange, Violet, Red, Blue b. Orange, Violet, Blue, Red, Blue, Yellow c. Yellow, Orange, Violet, Blue, Red, Yellow d. Yellow, Blue, Violet, Blue, Orange, Red e. Violet, Orange, Blue, Blue, Red, Yellow

8. How many combinations exist for the locations of the two Green balloons? a. 1 b. 2 c. 3 d. 4 e. 5 9. Which of the following must be false? a. The red balloons are both on an edge b. The two balloons in the center of the top row and the center of the bottom row are all Orange and Violet c. The Yellow balloons are on the same level as one another d. At least one green balloon is directly above a blue balloon e. An Orange balloon is on an edge of the display 10. If the upper Red balloon is not above either of the Blue balloons, which of the following must be true? a. At least one Green balloon is above a Blue balloon b. Either Violet or Orange is on an edge c. At least one Red balloon is not on an edge d. There are two or more spaces between the Green balloons e. Orange and Red balloons are adjacent on at least one of the two rows

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11. Which of the following is a complete and accurate list of balloons that can be placed on an edge of the display? a. Yellow, Orange, and Violet b. Yellow, Red, and Green c. Yellow, Orange, Violet, Red d. Yellow, Red, and Violet e. Yellow, Orange, and Green

12. If no Orange balloon is directly above or below a Violet balloon, which of the following must be true? a. A Violet balloon is on an edge of the display b. The Yellow balloon on the top row must be on the left side of the display c. The Orange and Violet balloons occupy the four very center spaces of the display d. At least one Orange or Violet balloon is on an edge e. Both Blue balloons are under either Violet or Orange balloon

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Questions 13-18 A swimming instructor is dividing his eight new students into four age groups. The students are Joseph, Kira, Leslie, Maria, Nathan, Otto, Pamela, and Roger. The groups are named A, B, C, and D, with A being the oldest and D being the youngest. Two people are in each age group, but they are not necessarily the same exact age. The ages of the new students follow these conditions: Joseph is older than Maria Maria is older than both Otto and Pamela Roger is younger than Leslie, but older than Pamela Leslie and Roger cannot be in the same age group Nathan and Kira are in the same age group Nathan is not in group C 13. Which of the following could be the RUGHURIWKHVWXGHQWV¶DJHVIURP oldest to youngest? a. Leslie, Joseph, Roger, Maria, Otto, Pamela, Nathan, Kira b. Joseph, Maria, Nathan, Kira, Leslie, Roger, Pamela, Otto c. Leslie, Maria, Nathan, Kira, Roger, Joseph, Pamela, Otto d. Nathan, Kira, Leslie, Otto, Joseph, Maria, Roger, Pamela e. Joseph, Leslie, Nathan, Maria, Otto, Kira, Roger, Pamela

15. Which of the following is a complete and accurate list of students who could be in group D? a. Roger, Peter, Otto b. Peter, Otto, Nathan, Kira c. Peter, Nathan, Kira d. Peter, Roger, Nathan, Otto, Kira e. Nathan, Kira, Peter, Otto 16. Which of the following pairs of students cannot be in the same age group? a. Pamela and Otto b. Joseph and Roger c. Maria and Roger d. Roger and Peter e. Maria and Otto 17. If Roger and Maria are together in group B, then how many combinations exist for the placement of the students in each group? a. 1 b. 2 c. 3 d. 4 e. 5 18. Which of the following pairs cannot be in consecutive groups? a. Maria and Joseph b. Joseph and Otto c. Roger and Otto d. Leslie and Otto e. Joseph and Peter

14. Which of the following must be false? a. Otto is older than Roger b. Leslie and Maria are in the same group c. Maria is in group B d. Roger and Pamela are in group D e. Nathan is younger than Kira Page  |  63      

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Questions 19-23 Seven groomsmen are picking out ties and belts for a wedding in which they will take part. The ties are green, pink, and purple, and the belts have either steel buckles or leather buckles. The groomsmen are named Alex, Chris, Harold, Jon, Kyle, Matt, and William. They will pick out their outfits according to the following conditions: Alex and Harold have the same color ties Chris and Kyle have the same belts Matt and Jon have either the same color ties or same belts, but not both None of the groomsmen wear both a leather buckle and purple tie William wears a steel belt buckle Chris wears a green tie At least two groomsmen wear each color tie At least two groomsmen wear a pink tie with a leather buckle 19. Which of the following cannot be true? a. Matt and Jon both wear pink ties b. Kyle and Matt wear the only two pink ties c. William wears a pink tie d. Six groomsmen wear the same kind of buckle e. Three groomsmen wear purple ties

20. Each of the following could be true except a. Kyle wears a green tie b. Harold wears a green tie c. Kyle wears a steel buckle d. Chris wears a leather buckle e. Alex wears a leather buckle 21. If three groomsmen wear green ties, which of the following is a complete and accurate list of those who could wear a green tie? a. Chris, Jon, and William b. Chris, Jon, Kyle, and William c. Chris, Kyle, Matt, and William d. Chris, Kyle, and Matt e. Chris, Jon, Kyle, Matt, and William 22. If Alex wears a purple tie, then which of the following must be true? a. William wears a purple tie b. Matt wears a pink tie c. Jon wears a pink tie d. Harold wears a leather buckle e. Kyle wears a leather buckle 23. How many total combinations of ties and belts exist if William and Harold wear purple ties? a. 1 b. 2 c. 3 d. 4 e. 5

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Answers Section 1 1. 2. 3. 4. 5. 6.

B A E D D D

7. 8. 9. 10. 11.

C C A E E

12. 13. 14. 15. 16. 17. 18.

B A D B E E C

19. 20. 21. 22. 23. 24.

C A E D C B

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Section 2 1. 2. 3. 4. 5. 6.

B C E A E D

7. 8. 9. 10. 11. 12.

B D D A E C

13. 14. 15. 16. 17.

D E B C C

18. 19. 20. 21. 22.

C A D A E

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Section 3 1. 2. 3. 4. 5. 6.

B E C E D C

7. 8. 9. 10. 11. 12.

A E A B A E

13. 14. 15. 16. 17.

C C D E A

18. 19. 20. 21. 22.

C D C E A

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Section 4 1. 2. 3. 4. 5.

C A A A C

6. 7. 8. 9. 10.

C A B A D

11. 12. 13. 14. 15. 16.

B D A C A B

17. 18. 19. 20. 21. 22.

D B C D A C

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Section 5 1. 2. 3. 4. 5.

C A D B E

6. 7. 8. 9. 10. 11. 12.

A C C E A D C

13. 14. 15. 16. 17.

B B A C D

18. 19. 20. 21. 22. 23.

C E A C D C

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Section 6 1. 2. 3. 4. 5. 6.

A C C B E E

7. 8. 9. 10. 11.

C C A D A

12. 13. 14. 15. 16. 17.

D E A B C D

18. 19. 20. 21. 22.

C C A D E

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Section 7 1. 2. 3. 4. 5. 6.

B B A C E D

7. 8. 9. 10. 11.

B A E C D

12. 13. 14. 15. 16.

A D D E B

17. 18. 19. 20. 21. 22.

C C E E A B

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Section 8 1. 2. 3. 4. 5. 6. 7.

E D C A B C C

8. 9. 10. 11. 12.

E B A C B

13. 14. 15. 16. 17. 18.

D C A C D B

19. 20. 21. 22. 23.

D C A E B

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Section 9 1. 2. 3. 4. 5.

E D A B D

6. 7. 8. 9. 10. 11.

E A A D A C

12. 13. 14. 15. 16. 17.

E D B D E A

18. 19. 20. 21. 22.

D B D B C

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Section 10 1. 2. 3. 4. 5. 6.

D A E B C D

7. 8. 9. 10. 11. 12.

B C C A C D

13. 14. 15. 16. 17. 18.

A B D B A E

19. 20. 21. 22. 23.

D B E E B

 

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