Grouping Linear Combination

Grouping Linear Combination - Grouping] Linear Combination...

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Unformatted text preview: Grouping] Linear Combination L l Grouping/Linear Combination Games Questions 14-19 At an automobile exhibition, cars are displayed on each floor of a three-floor building. On each floor the cars are either all family cars or all sports cars, either all new or all used, and either all production models or all research models. The following conditions apply to this exhibition: 1f the exhibition includes both family cars and sports cars, then each family car is displayed on a lower numbered floor than any sports car. The exhibition includes no used research models. The exhibition includes no research models that are sports cars. There are new cars on floor 1. There are used cars on floor 3. 14. If there are sports cars on exactly two floors, then which one of the following statements could be true? (A) There are research models on floor 1. (B) There are sports cars on floor 1. (C) There are family cars on floor 2. (D) There are research models on floor 2. (E) There are family cars on floor 3. 15. Which one of the following statements could be true? (A) The exhibition includes new research model sports cars. (B) The exhibition includes used research model family cars. (C) The exhibition includes used research model sports cars. (D) There are research models on exactly one floor. (E) There are research models on all three floors. 16. Which one of the following statements must be true? (A) There are production models on floor 1. (B) There are research models on floor 1. (C) There are production models on floor 2. (D) There are production models on floor 3. (E) There are research models on floor 3. 17. 18. 19. If there are research models on exactly two floors, then which one of the following statements can be false? (A) There are family cars on floor 1. (B) There are research models on floor 1. (C) There are new cars on floor 2. (D) There are research models on floor 2. (E) There are family cars on floor 3. If all the new cars in the exhibition are research models, then which one of the following statements must be true? (A) All the family cars in the exhibition are new. (B) All the family cars in the exhibition are research models. (C) All the family cars in the exhibition are used. (D) All the new cars in the exhibition are family cars. (B) All the production models in the exhibition are family cars. If all the production models in the exhibition are used, then which one of the following statements must be true? (A) There are family cars on floor 1. (B) There are new cars on floor 2. (C) There are research models on floor 2. (D) There are family cars on floor 3. (E) There are sports cars on floor 3.1 1 PT 3, Game 3 Grouping/Linear Combination Games I Questions 6-12 A square parking lot has exactly eight lightsinumbered 1 through 8isituated along its perimeter as diagramed below. North 1.....2.....3 West8 4East 7.....6.....5 South The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on. 6. Which one of the following could be a complete and accurate list of lights that are on together? (A) 1, 3, 5, 7 (B) 2, 4, 6, 8 (C) 2, 3, 5, 6, 8 (D) 3, 4, 6, 7, 8 (E) 1, 2, 4, 5, 6, 8 7. Which one of the following lights must be on? (A) light 2 (B) light 3 (C) light 4 (D) light 5 (E) light 6 10. ll. 12. 1f light 1 is off, which one of the following is a light that must also be off? (A) fight 3 (B) fight 4 (C) fight 5 (D) fight 6 (E) fight 7 Which one of the following statements must be true? (A) If light 2 is on, then light 6 is off (B) If light 3 is on, then light 2 is on. (C) If light 4 is on, then light 3 is off (D) If light 5 is off, then light 4 is on. (E) If light 6 is off, then light 1 is on. If light 5 is on, which one of the following could be true? (A) Light 1 is off and light 6 is off (B) Light 1 is on and light 7 is on. (C) Light 2 is off and light 4 is on. (D) Light 2 is off and light 6 is off (E) Light 6 is on and light 7 is on. If light 4 is on, each of the following statements must be true EXCEPT: (A) Light 1 is on. (B) Light 2 is on. (C) Light 5 is off (D) Light 6 is on. (E) Light 7 is off. Suppose that it is no longer part of the specifications that two lights on the north side be on. If all of the other original specifications remain the same, and if exactly one light on the north side is on, which one of the following statements could be false? (A) Light 1 is off. (B) Light 2 is on. (C) Light 3 is off (D) Light 4 is on. (E) Light 5 is on.2 2 PT 8, Game 2 I Grouping/Linear Combination Games Questions 19724 A soloist will play six different guitar concertos, exactly one each Sunday for six consecutive weeks. Two concertos will be selected from among three concertos by Giulianiifl, J, and K; two from among four concertos by RodrigckM, N, O, and P; and two from among three concertos by Vivaldiix, Y, and Z. The following conditions apply without exception: 19. 20. If N is selected, then J is also selected. If M is selected, then neither] nor O can be selected. If X is selected, then neither Z nor P can be selected. If both J and O are selected, then J is played at some time before O. X cannot be played on the fifth Sunday unless one of Rodrigo's concertos is played on the first Sunday. Which one of the following is an acceptable selection of concertos that the soloist could play on the first through the sixth Sunday? lZifiié (A)HZMNYK (B) KJYOZN (C) KYPJZM (D)PYJHXO (E) XNKOJZ 1f the six concertos to be played are J, K, N, O, Y, and Z and if N is to be played on the first Sunday, then which one of the following concertos CANNOT be played on the second Sunday? (A) (B) (C) (D) (E) [Vt-<07?" 21. 22. 23. 24. 1f J, O, and Y are the first three concertos to be played, not necessarily in the order given, which one of the following is a concerto that CANNOT be played on the fifth Sunday? (A) H (B) K (C) N (D) P (E) X If O is selected for the first Sunday, which one of the following is a concerto that must also be selected? (A) J (B) K (C) M (D) N (E) X Which one of the following is a concerto that must be selected? (A) (B) (C) (D) (E) Which one of the following is a concerto that CANNOT be selected together with N? [Vt-<07?" (A) M (B) 0 (C) P (D) X (E) Z3 3 PT 10, Game 4 Grouping/Linear Combination Games I Questions 12-17 An art teacher will schedule exactly six of eight lecturesi fresco, history, lithography, naturalism, oils, pastels, sculpture, and watercolorsifor three daysil , 2, and 3. There will be exactly two lectures each dayimoming and afternoon. Scheduling is governed by the following conditions: 12. 13. Day 2 is the only day for which oils can be scheduled. Neither sculpture nor watercolors can be scheduled for the afternoon. Neither oils nor pastels can be scheduled for the same day as lithography. lf pastels is scheduled for day l or day 2, then the lectures scheduled for the day immediately following pastels must be fresco and history, not necessarily in that order. Which one of the following is an acceptable schedule of lectures for days 1, 2, and 3, respectively? (A) Morning: lithography, history, sculpture Afternoon: pastels, fresco, naturalism (B) Morning: naturalism, oils, fresco Aftemoon: lithography, pastels, history (C) Morning: oils, history, naturalism Afternoon: pastels, fresco, lithography (D) Morning: sculpture, lithography, naturalism Afternoon: watercolors, fresco, pastels (E) Morning: sculpture, pastels, fresco Aftemoon: lithography, history, naturalism lf lithography and fresco are scheduled for the afternoons of day 2 and day 3, respectively, which one of the following is a lecture that could be scheduled for the afternoon of day l? (A) history (B) oils (C) pastels (D) sculpture (E) watercolors 14. 1f lithography and history are scheduled for the mornings 15. l6. 17. of day 2 and day 3, respectively, which one of the following lectures could be scheduled for the morning of day l? (A) fresco (B) naturalism (C) oils (D) pastels (E) sculpture lf oils and lithography are scheduled for the mornings of day 2 and day 3, respectively, which one of the following CANNOT be scheduled for any day? (A) fresco (B) history (C) naturalism (D) pastels (E) sculpture If neither fresco nor naturalism is scheduled for any day, which one of the following must be scheduled for day l? (A) history (B) lithography (C) oils (D) pastels (E) sculpture 1f the lectures scheduled for the mornings are fresco, history, and lithography, not necessarily in that order, which one of the following could be true? (A) Lithography is scheduled for day 3. (B) Naturalism is scheduled for day 2. (C) Fresco is scheduled for the same day as naturalism. (D) History is scheduled for the same day as naturalism. (E) History is scheduled for the same day as oils.4 4 PT 13, Game 3 a Grouping/Linear Combination Games Questions: 7-12 9. Which one of the following must be true? (A) At least one female reptile is alone in a habitat. A zoo s reptile house has a straight row of exactly five (B) At least one male reptile is alone in a habitat. consecutive habitats—numbered 1 through 5 from left to (C) At least one lizard is alone in a habitat. right—for housing exactly seven reptiles—four snakes and (D) At least one lizard is male. three lizards. Five of the reptiles are female and two are male. At least one snake is male. The reptiles must be housed as follows: N0 habltat houses more than two repules' 10. Which one of the following CANNOT be the complete No habitat houses both a snake and a lizard. . . . . . . housing arrangement for habitats 1 and 2? No female snake is housed in a habitat that is immediately next to a habitat housing a male lizard. (A) 1: one female snake; one male snake; 2: one male snake 7. Which one of the following could be a complete and (B) 13 one male nzordi 23 one male snake accurate matching of habitats to reptiles? (C) 13 two female nzardsi 23 one female snake (D) 1: one male snake; 2: empty (A) 1: two female snakes; 2: one male snake; 3: one 1. empty; 2. one female lizard female lizard; 4: one male snake; one female llzard; 5 i one female hzard 11. 1f habitat 3 is empty; and no snake is housed in a habitat (B) 1: empty; 2: two female snakes; 3: two female . , that is immediately next to a habitat containing a snake; lizards; 4: two male snakes; 5: one female lizard then which one of the following could be false? (C) 1: one female snake; one male snake; 2: female . . snakes; 3: one male lizard; 4: one female lizard; (A) All snakes are housed in even-numbered habitats. 5: one female lizard (B) None of the lizards is male. (D) 1: two male snakes; 2: empty; 3: one female (C) No Snake {5 alone 1n.a habnot . lizard; 4: one female lizard; 5: two female (D) No nzard 15 housed In a habnat that 15 snakes, one female lizard immediately next to a habitat containing a lizard. (E) 1: one female snake, one male snake; 2: one Exactly one habitat contains exactly one reptile. female snake; one male snake; 3: one male . lizard; 4: one female lizard; 5: one female lizard 12. If all snakes are female and each of the lizards has a habitat to itself; then which one of the following habitats 8. 1f habitat 2 contains at least one female snake and habitat CANNOT oontaln any snakeS? 4 contains two male lizards; then which one of the (A) habitat 1 following could be true? (3) habitat 2 (A) Habitat 3 contains two reptiles. (C) nabnat 3 (B) Habitat 5 contains two reptiles. (D) nabnat 45 (C) Habitat 1 contains a female lizard. habnat 5 (D) Habitat 2 contains a female lizard. (E) Habitat 5 contains a female lizard. 5 PT 27, Game 2 Questions 6-10 The six messages on an answering machine were each left by one of F leure, Greta, Hildy, Liam, Pasquale, or Theodore, consistent with the following: At most one person left more than one message. No person left more than three messages. If the first message is Hildy’s, the last is Pasquale’s. lf Greta left any message, F leure and Pasquale did also. If F leure left any message, Pasquale and Theodore did also, all of Pasquale’s preceding any of Theodore’s. lf Pasquale left any message, Hildy and Liam did also, all of Hildy’s preceding any of Liam’s. 6. Which one of the following could be a complete and accurate list of the messages left on the answering machine, from first to last? (A) F leure’s, Pasquale’s, Theodore’s, Hildy’s, Pasquale’s, Liam’s (B) Greta’s, Pasquale’s, Theodore’s Theodore’s, Hildy’s, Liam’s. (C) Hildy’s, Hildy’s, Hildy’s Liam’s, Pasquale’s, Theodore’s (D) Pasquale’s, Hildy’s, F leure’s, Liam’s, Theodore’s, Theodore’s (E) Pasquale’s, Hildy’s, Theodore’s, Hildy’s, Liam’s, Liam’s . The first and last messages on the answering machine could be the first and second messages left by which one of the following? (A) F leure (B) Hildy (C) Liam (D) Pasquale (E) Theodore 8. 10. Grouping/Linear Combination Games a lf Greta left the fifth message, then which one of the following messages CANNOT have been left by Theodore? (A) the first message (B) the second message (C) the third message (D) the fourth message (E) the sixth message Each of the following must be true EXCEPT: (A) Liam left at least one message. (B) Theodore left at least one message. (C) Hildy left at least one message. (D) Exactly one person left at least two messages. (E) At least four people left messages. If the only message Pasquale left is the fifth message, then which one of the following could be true? (A) Hildy left the first message. (B) Theodore left exactly two messages. (C) Liam left exactly two messages. (D) Liam left the second message. (E) F leure left the third and fourth messages.6 6 PT 30, Game 2 Grouping/Linear Combination Games Questions 19-23 A crew of up to five workers is to install a partition in at most three days. The crew completes five tasks in this order: framing, wallboarding, taping, sanding, priming. The crew is selected from the following list, which specifies exactly the tasks each person can do: George: taping Helena: sanding, priming lnga: framing, priming Kelly: framing, sanding Leanda: wallboarding, taping Maricita: sanding Olaf: wallboarding, priming The following conditions must apply: At least one task is done each day. Taping and priming are done on different days. Each crew member does at least one task during the installation, but no more than one task a day. Each task is done by exactly one worker, completed the day it is started and before the next task begins. 19. Which one of the following could be a complete and accurate list of the members of the crew? (A) George, Helena, lnga, Kelly (B) George, Helena, Kelly, Leanda (C) Helena, lnga, Kelly, Olaf (D) Helena, lnga, Maricita, Olaf (E) George, Helena, Leanda, Maricita, Olaf 20. 1f the installation takes three days, and if the same two crew members work on the first and third days, then which one of the following could be the pair of crew members who work on those two days? (A) Helena and lnga (B) lnga and Kelly (C) lnga and Leanda (D) Kelly and Olaf (E) Leanda and Olaf 21. Each of the following could be a complete and accurate list of the members of the crew EXCEPT: (A) Helena, lnga, Kelly, Maricita (B) lnga, Kelly, Leanda, Olaf (C) George, Helena, lnga, Leanda (D) lnga, Leanda, Maricita, Olaf (E) Kelly, Leanda, Maricita, Olaf 22. 1f the installation takes three days, and if the sanding is done on the third day, then which one of the following could be a list of all the crew members who work on the second day? (A) lnga (B) Kelly (C) Olaf (D) George and Helena (E) Leanda and Olaf 23. Which one of the following could be a pair of members of the crew both of whom work on the same days as each other and each of whom could perform two tasks? (A) George and Maricita (B) Helena and Kelly (C) lnga and Leanda (D) Kelly and Leanda (E) Leanda and Olaf7 7PT31,Game4 Questions 1-6 Of the eight studentsiGeorge, Helen, Irving, Kyle, Lenore, Nina, Olivia, and Robertiin a seminar, exactly six will give individual oral reports during three consecutive daysi Monday, Tuesday, and Wednesday. Exactly two reports will be given each dayione in the morning and one in the aftemooniaccording to the following conditions: Tuesday is the only day on which George can give a report. Neither Olivia nor Robert can give an afternoon report. If Nina gives a report, then on the next day Helen and Irving must both give reports, unless Nina’s report is given on Wednesday. Which one of the following could be the schedule of the students’ reports? (A) Mon. morning: Helen; Mon. afternoon: Robert Tues. morning: Olivia; Tues. afternoon: Irving Wed. morning: Lenore; Wed. afternoon: Kyle (B) Mon. morning: Irving; Mon. afternoon: Olivia Tues. morning: Helen; Tues. afternoon: Kyle Wed. morning: Nina; Wed. afternoon: Lenore (C) Mon. morning: Lenore; Mon. afternoon: Helen Tues. morning: George; Tues. afternoon: Kyle Wed. morning: Robert; Wed. afternoon: Irving (D) Mon. morning: Nina; Mon. afternoon: Helen Tues. morning: Robert; Tues. afternoon: Irving Wed. morning: Olivia; Wed. afternoon: Lenore (E) Mon. morning: Olivia; Mon. afternoon: Nina Tues. morning: Irving; Tues. afternoon: Helen Wed. morning: Kyle; Wed. afternoon: George If Kyle and Lenore do not give reports, then the morning reports on Monday, Tuesday, and Wednesday, respectively, could be given by (A) Helen, George, and Nina (B) Irving, Robert, and Helen (C) Nina, Helen, and Olivia (D) Olivia, Robert, and Irving (E) Robert, George, and Helen Grouping/Linear Combination Games I 3. Which one of the following is a pair of students who, if they give reports on the same day as each other, must give reports on Wednesday? (A) George and Lenore (B) Helen and Nina (C) Irving and Robert (D) Kyle and Nina (E) Olivia and Kyle If George, Nina, and Robert give reports and they do so on different days from one another, which one of the following could be true? (A) Helen gives a report on Wednesday. (B) Nina gives a report on Monday. (C) Nina gives a report on Tuesday. (D) Olivia gives a report on Monday. (E) Robert gives a report on Wednesday. If Kyle gives the afternoon report on Tuesday, and Helen gives the afternoon report on Wednesday, which one of the following could be the list of the students who give the morning reports on Monday, Tuesday, and Wednesday, respectively? (A) Irving, Lenore, and Nina (B) Lenore, George, and Irving (C) Nina, Irving, and Lenore (D) Robert, George, and Irving (E) Robert, Irving, and Lenore If Helen, Kyle, and Lenore, not necessarily in that order, give the three morning reports, which one of the following must be true? (A) Helen gives a report on Monday. (B) Irving gives a report on Monday. (C) Irving gives a report on Wednesday. (D) Kyle gives a report on Tuesday. (E) Kyle gives a report on Wednesday.8 8 PT 32, Game 1 PT 3, Game 3 pg. 1 14. 15. 16. 17. 18. 19. >UU1UU> PT 31, Game 4 pg. 7 19. 20. 21. 22. 23. UW>UDU GROUPING/LINEAR COMBINATION GAMES PT 8, Game 2 pg. 2 6. C 7. B 8. B 9. D 10. A 11. B 12. E PT 32, Game 1 pg. 8 1. 0111-wa WU>WUO PT 10, Game 4 pg. 3 19. 20. 21. 22. 23. 24. >meow PT 13, Game 3 pg. 4 12. 13. 14. 15. 16. 17. mwum>w PT 27, Game 2 pg. 5 7. 8. 9. 10. 11. 12. O>Uomw PT 30, Game 2 pg. 6 6. 7. 8. 9. 10. OU>>U ...
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This note was uploaded on 10/02/2010 for the course ACCT 5457 taught by Professor Polm during the Fall '10 term at Rensselaer Polytechnic Institute.

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Grouping Linear Combination - Grouping] Linear Combination...

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