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Basic Linear Unbalanced

# Basic Linear Unbalanced - Basic Linear(Unbalanced I Basic...

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Unformatted text preview: Basic Linear (Unbalanced) I Basic Linear (Unbalancea) Games Questions 6-12 An apartment building has ﬁve ﬂoors. Each ﬂoor has either one or two apartments. There are exactly eight apartments in the building. The residents of the building are J, K, L, M, N, O, P, and Q, who each live in a different apartment. J lives on a ﬂoor with two apartments. K lives on the ﬂoor directly above P. The second ﬂoor is made up of only one apartment. M and N live on the same ﬂoor. 0 does not live on the same ﬂoor as Q. L lives in the only apartment on her ﬂoor. Q does not live on the first or second ﬂoor. 6. Which one of the following must be true? (A) Q lives on the third ﬂoor. (B) Q lives on the ﬁfth ﬂoor. (C) L does not live on the fourth ﬂoor. (D) N does not live on the second ﬂoor. (E) J lives on the ﬁrst ﬂoor. 7. Which one of the following CANNOT be true? (A) K lives on the second ﬂoor. (B) M lives on the ﬁrst ﬂoor. (C) N lives on the fourth ﬂoor. (D) O lives on the third ﬂoor. (E) P lives on the ﬁfth ﬂoor. 8. 1f J lives on the fourth ﬂoor and K lives on the ﬁfth ﬂoor, which one of the following can be true? (A) O lives on the ﬁrst ﬂoor. (B) Q lives on the fourth ﬂoor. (C) N lives on the ﬁfth ﬂoor. (D) L lives on the fourth ﬂoor. (E) P lives on the third ﬂoor. 9. lf 0 lives on the second ﬂoor, which one of the following CANNOT be true? (A) K lives on the fourth ﬂoor. (B) K lives on the ﬁfth ﬂoor. (C) L lives on the ﬁrst ﬂoor. (D) L lives on the third ﬂoor. (E) L lives on the fourth ﬂoor. 10. ll. 12. If M lives on the fourth ﬂoor, which one of the following must be false? (A) O lives on the ﬁfth ﬂoor. (B) J lives on the ﬁrst ﬂoor. (C) L lives on the second ﬂoor. (D) Q lives on the third ﬂoor. (E) P lives on the ﬁrst ﬂoor. Which one of the following must be true? (A) If J lives on the fourth ﬂoor, then Q does not live on the ﬁfth ﬂoor. (B) lf 0 lives on the second ﬂoor, then L does not live on the fourth ﬂoor. (C) If N lives on the fourth ﬂoor, then K does not live on the second ﬂoor. (D) If K lives on the third ﬂoor, then 0 does not live on the ﬁfth ﬂoor. (E) If P lives on the fourth ﬂoor, then M does not live on the third ﬂoor. lf 0 lives on the fourth ﬂoor and P lives on the second ﬂoor, which one of the following must be true? (A) L lives on the ﬁrst ﬂoor. (B) M lives on the third ﬂoor. (C) Q lives on the third ﬂoor. (D) N lives on the ﬁfth ﬂoor. (E) Q lives on the ﬁfth ﬂoor.1 1 PT 2, Game 2 Basic Linear (Unbalancea) Games I Questions 1-5 A gymnastics instructor is planning a weekly schedule, Monday through Friday, of indiVidual coaching sessions for each of six studentsiH, l, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: 1. H’s session must take place at some time before Z’s session. l’s session is on Thursday. K’s session is always scheduled for the day immediately before or the day immediately after the day for which O’s session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled. Which one of the following is a pair of students whose sessions can both be scheduled for Tuesday, not necessarily in the order given? (A) H and U (B) H and Z (C) K and O (D) O and U (E) U and Z If K’s session is scheduled for Tuesday, then which one of the following is the earliest day for which Z’s session can be scheduled? (A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) Friday 3. Which one of the following must be true? (A) If U’s session is scheduled for Monday, H’s session is scheduled for Tuesday. (B) If U’s session is scheduled for Tuesday, O’s session is scheduled for Wednesday. (C) If U’s session is scheduled for Wednesday, Z’s session is scheduled for Tuesday. (D) If U’s session is scheduled for Thursday, Z’s session is scheduled for Friday. (E) If U’s session is scheduled for Friday, Z’s session is scheduled for Thursday. Scheduling Z’s session for which one of the following days determines the day for which U’s session must be scheduled? (A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) Friday . lf H’s session is scheduled as the next session after U’s session, which one of the following could be true about H’s session and U’s session? (A) U’s session is scheduled for Monday, and H’s session is scheduled for Tuesday. (B) U’s session is scheduled for Thursday, and H’s session is scheduled for Friday. (C) They are both scheduled for Tuesday. (D) They are both scheduled for Thursday. (E) They are both scheduled for F riday.2 2 PT 8, Game 1 I Basic Linear (Unbalanceo) Games Questions 6712 Six reviewersiFrank, George, Hilda, Jackie, Karl, and Lenaiwill review four moviesiMystery, Retreat, Seasonings, and Wolvesiaccording to the following conditions: Each reviewer reviews exactly one movie, and each movie is reviewed by at least one of the six reviewers. Hilda reviews the same movie as Frank. Lena reviews the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves. 13. 1f Lena reviews Seasonings, which one of the following must be true? (A) Hilda reviews Retreat. (B) Jackie reviews Seasonings. (C) Karl reviews Mystery. (D) Karl reviews Retreat. (E) Karl reviews Wolves. 14. 1f Karl does not review Seasonings, which one of the following must be true? (A) Lena reviews Mystery. (B) Lena reviews Retreat. (C) Lena reviews Seasonings. (D) Frank and Hilda review Retreat. (E) Frank and Hilda review Seasonings. 18. 15. Which one of the following is a complete and accurate list of the movies each of which could be the movie that Lena reviews? (A) Mystery, Retreat (B) Retreat, Seasonings (C) Mystery, Seasonings, Wolves (D) Retreat, Seasonings, Wolves (E) Mystery, Retreat, Seasonings, Wolves 16. Which one of the following can be true? (A) Frank and George review Mystery. (B) Frank and Lena review Wolves. (C) George and Jackie review Mystery. (D) Karl reviews Wolves and Lena reviews Mystery. (E) Lena reviews Retreat and Frank reviews Seasonings. l7. Lena can review any of the following EXCEPT (A) (B) (C) (D) (E) Mystery with George Mystery with Karl Retreat with Karl Seasonings with Karl Wolves with Jackie lf Karl reviews the same movie as exactly one other reviewer, which one of the following is a complete and accurate list of the movies any one of which could be the movie that these two reviewers review? (A) (B) (C) (D) (E) Mystery, Retreat Mystery, Seasonings Retreat, Seasonings Mystery, Seasonings, Wolves Retreat, Seasonings, Wolves 19. Which one of the following is an acceptable assignment of reviewers to movies? Mystery (A) George (B) George (C) George (D) George, Karl (E) Jackie Retreat Frank, Hilda Frank, Hilda Karl, Lena Frank, Hilda George, Lena 3 PT 10, Game 2 Seasonings Wolves Jackie, Lena Karl Karl, Lena Jackie Jackie Frank, Hilda Lena Jackie Frank, Hilda Karl3 Basic Linear (Unbalancea) Games I Questions 14-19 Four peopleiFritz, Gina, Helen, and J erryihave formed a car pool to commute to work together six days a week from Monday through Saturday. Each day exactly one of the people drives. The schedule of the car pool’s drivers for any given week must meet the following conditions: Each person drives on at least one day. No person drives on two consecutive days. Fritz does not drive on Monday. Jerry drives on Wednesday or Saturday or both, and he may also drive on other days. If Gina drives on Monday, then Jerry does not drive on Saturday. 14. Which one of the following could be the schedule of drivers for one week, for the days Monday through Saturday, respectively? (A) Gina, Fritz, Jerry, Helen, Gina, Gina (B) Gina, Fritz, Jerry, Helen, Fritz, Jerry (C) Helen, Fritz, Gina, Jerry, Helen, Fritz (D) Helen, Gina, Jerry, Fritz, Helen, Fritz (E) Helen, Gina, Jerry, Helen, Jerry, Gina 15. Which one of the following could be true of one week’s schedule of drivers? (A) Fritz drives on both Wednesday and Saturday. (B) Gina drives on both Monday and Wednesday. (C) Jerry drives on both Tuesday and Friday. (D) Gina drives on Monday and Jerry drives on Thursday. (E) Jerry drives on Wednesday and Gina drives on Saturday. 16. If during one week Jerry drives on Wednesday and Saturday only, which one of the following must be true of that week? (A) Fritz drives on Tuesday. (B) Gina drives on Friday. (C) Helen drives on Monday. (D) Fritz drives on exactly two days. (E) Helen drives on exactly two days. 17. 18. 19. If during one week Gina drives on Monday and Saturday only, which one of the following must be true of that week? (A) One other person besides Gina drives on exactly two days. (B) The person who drives on Wednesday does not drive on Friday. (C) Helen drives on a day immediately before a day on which Fritz drives. (D) Either Fritz or Helen drives on Friday. (E) Either Helen or Jerry drives on Tuesday. Which one of the following CANNOT be true of on week’s schedule of drivers? (A) Fritz drives on Tuesday and Gina drives on Friday. (B) Gina drives on Monday and Jerry drives on Tuesday. (C) Gina drives on Monday and Jerry drives on Friday. (D) Helen drives on Monday and Jerry drives on Tuesday. (E) Helen drives on Tuesday and Jerry drives on Friday. If during one week Fritz drives exactly twice but he drives on neither Tuesday nor Wednesday, which one of the following could be true of that week? (A) One person drives exactly three times during the week. (B) Three people drive exactly one time each during the week. (C) Jerry drives on no day that is immediately before a day on which Fritz drives. (D) Gina drives on Wednesday. (E) Jerry drives on F riday.4 4 PT 15, Game 3 a Basic Linear (Unbalancea) Games Questions 7-11 9. There is exactly one possible color sequence of the three lights if which one of the following is true? A worker will insert colored light bulbs into a billboard (A) Light 1 is purple equipped with exactly three light sockets, which are labeled (B) Light 2 is purple. lights 1, 2, and 3. The worker has three green bulbs, three (C) Light 2 is yellow' purple bulbs, and three yellow bulbs. Selection of bulbs for the (D) Light 3 is purple' sockets is governed by the following conditions: (E) Light 3 is yellow' Whenever light 1 is purple, light 2 must be yellow. ' \$323: g \$316; llghiel 0:111:51: :Vgrleierﬁ't 2 must be 10. If no green bulbs are selected, there are exactly how many purple g purp y ’ g possible different color sequences of the three lights? (A) one 7. Which one of the following could be an accurate list of (B) tWO the colors of light bulbs selected for lights 1, 2, and 3, (C) three respectively? (D) four (E) ﬁve (A) green, green, yellow (B) purple, green, green 11 (C) purple, purple, green (D) yellow, purple, green (E) yellow, yellow, yellow . If no two lights are assigned light bulbs that are the same color as each other, then which one of the following could be true? (A) Light 1 is green, and light 2 is purple. 8. 1f light 1 is yellow, then any of the following can be true, (B) Light 1 is green, and light 2 is yellOW. EXCEPT: (C) Light 1 is purple, and light 3 is yellow. (A) Light 2 is green. (D) Light 1 is yellow, and light 2 is green. (B) Light 2 is purple Light 1 is yellow, and light 3 is purple.5 (C) Light 3 is green. (D) Light 3 is purple. (E) Light 3 is yellow. 5PT21,Garne2 Basic Linear (Unbalancea) Games a Questions 20-24 Exactly six piano classes are given sequentially on Monday: two with more than one student and four with exactly one student. Exactly four femalesiGimena, Holly, lyanna, and Kateiand ﬁve malesiLeung, Nate, Oscar, Pedro, and Sauli attend these classes. Each student attends exactly one class. The following must obtain: lyanna and Leung together constitute one class. Pedro and exactly two others together constitute one class. Kate is the ﬁrst female, but not the ﬁrst student, to attend a class. Gimena’s class is at some time after lyanna’s but at sometime before Pedro’s. Oscar’s class is at some time after Gimena’s. 20. Which one of the following students could attend the ﬁrst class? (A) Holly (B) Leung (C) Oscar (D) Pedro (E) Saul 21. Which one of the following is a complete and accurate list of classes (A) the fourth, the ﬁfth (B) the fourth, the sixth (C) the second, the fourth, the ﬁfth (D) the third, the ﬁfth, the sixth (E) the second, the third, the fourth 22. 23. 24. Which one of the following pairs of students could be in the class with Pedro? (A) Gimena and Holly (B) Holly and Saul (C) Kate and Nate (D) Leung and Oscar (E) Nate and Saul lf Oscar and Pedro do not attend the same class as each other, then which one of the following could be true? (A) Gimena attends the ﬁfth class. (B) Holly attends the third class. (C) lyanna attends the fourth class. (D) Nate attends the ﬁfth class. (B) Saul attends the second class. Suppose the condition that Oscar attends a class after Gimena is replaced with the condition that Oscar attends a class before Gimena and after Kate. If all the other conditions remain the same, then which class must Holly attend? (A) the second (B) the third (C) the fourth (D) the ﬁfth (E) the sixth6 6 PT 29, Game 4 Basic Linear (Unbalancea) Games Questions 14-18 During a single week, from Monday through Friday, tours will be conducted of a company’s three divisionsiOperations, Production, Sales. Exactly ﬁve tours will be conducted that week, one each day. The schedule of tours for the week must conform to the following restrictions: Each division is toured at least once. The Operations division is not toured on Monday. The Production division is not toured on Wednesday. The Sales division is toured on two consecutive days, and on no other days. If the Operations division is toured on Thursday, then the Production division is toured on Friday. 14. Which one of the following CANNOT be true of the week's tour schedule? (A) The division that is toured on Monday is also toured on Tuesday. (B) The division that is toured on Monday is also toured on Friday. (C) The division that is toured on Tuesday is also toured on Thursday. (D) The division that is toured on Wednesday is also toured on Friday. (E) The division that is toured on Thursday is also toured on Friday. 15. If in addition to the Sales division one other division is toured on two consecutive days, then it could be true of the week's tour schedule both that the (A) Production division is toured on Monday and that the Operations division is toured on Thursday (B) Production division is toured on Tuesday and that the Sales division is toured on Wednesday (C) Operations division is toured on Tuesday and that the Production division is toured on Friday (D) Sales division is toured on Monday and that the Operations division is toured on Friday (E) Sales division is toured on Wednesday and that the Production division is toured on Friday l6. 17. 18. If in the week's tour schedule the division that is toured on Tuesday is also toured on Friday, then for which one of the following days must a tour of the Production division be scheduled? (A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) Friday If in the week's tour schedule the division that is toured on Monday is not the division that is toured on Tuesday, then which one of the following could be true of the week's schedule? (A) A tour of the Sales division is scheduled for some day earlier in the week than is any tour of the Production division. (B) A tour of the Operations division is scheduled for some day earlier in the week than is any tour of the Production division. (C) The Sales division is toured on Monday. (D) The Production division is toured on Tuesday. (E) The Operations division is toured on Wednesday. If in the week's tour schedule the division that is toured on Tuesday is also toured on Wednesday, then which one of the following must be true of the week's tour schedule? (A) The Production division is toured on Monday. (B) The Operations division is toured on Tuesday. (C) The Sales division is toured on Wednesday. (D) The Sales division is toured on Thursday. (E) The Production division is toured on F riday.7 7PT31,Garne3 Basic Linear (Unbalancea) Games I Questions 1-7 Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively I thought 9 from one end of the sore to the other. Each aisle is stocked by exactly one clerk and no clerk stocks more than two aisles. Stocking assignments must meet the following conditions: 1. Olga stocks exactly one aisle. Kurt stocks aisle 2. Manny does not stock aisle 1. Jill does not stock consecutive aisles. Kurt stocks the only aisle between the two aisles Manny stocks. Exactly one of Larisa’s aisles is an end aisle. Olga’s aisle is numbered higher than either of Kurt’s aisles, and lower than at least one of Larisa’s. Which one of the following clerks could stock two consecutive aisles? (A) J ill (B) Kurt (C) Larisa (D) Manny (E) Olga Which one of the following is a pair of clerks, neither of whom could stock aisle 5? (A) Jill and Manny (B) Kurt and Olga (C) Larisa and Manny (D) Kurt and Manny (E) Larisa and Olga Which one of the following is a complete and accurate list of clerks, any one of whom could stock aisle 3? (A) Jill, Kurt, Larisa (B) Jill, Larisa, Manny (C) Jill, Larisa, Olga (D) Jill, Kurt, Larisa, Manny (E) Jill, Kurt, Larisa, Olga 4. Which one of the following is a complete and accurate list of aisles, any one of which could be one of the aisles Manny stocks? (A) 1, 3, 4, 5 (B) 3, 5, 7, 9 (C) 3, 4, 5, 6 (D) 3, 4, 5, 6, 7 (E) 3, 5, 7 . lf Larisa’s aisles are separated by the maximum number of aisles that could separate her aisles, which one of the following could be true? (A) Jill stocks aisle 6. (B) Manny stocks aisle 7. (C) Both of Jill’s aisles are numbered lower than Olga’s. (D) Jill stocks only even-numbered aisles. (E) Only one clerk stocks a higher numbered aisle than Olga does. . lf Jill stocks aisle 3, then which one of the following CANNOT be true? (A) Jill stocks aisle 9. (B) Kurt stocks aisle 6. (C) Larisa stocks aisle 4. (D) Manny stocks aisle 4. (E) Olga stocks aisle 6. Suppose that, rather than just one, Larisa stocks both end aisles; all other conditions remaining in effect, which one of the following CANNOT be true? (A) Jill stocks aisle 3. (B) Olga stocks aisle 6. (C) Olga stocks the only aisle between the two aisles that Jill stocks. (D) Kurt stocks only even-numbered aisles. (B) One of Larisa’s aisles is immediately next to Olga’s.8 8 PT 34, Game 1 I Basic Linear (Unbalancea) Games Questions 8-12 A ﬁve-week adult education course consists of exactly ﬁve lectures with a different lecture given each week. No lecture is given more than once. Each lecture is delivered by a different speaker. The following conditions are true about the speakers and their lectures: 10. Each speaker lectures on a philosopher in whom he or she specializes. No two speakers lecture on the same philosopher. The ﬁrst week’s speaker specializes in Kant, Locke, and Mill, and no other philosophers. The second week’s speaker specializes in Kant, Locke, Mill, and Nietzsche, and no other philosophers. The third week’s and fourth week’s speakers each specialize in Mill and Nietzsche, and no other philosophers. The ﬁfth week’s speaker specializes in Nietzsche, Ockham, and Plato, and no other philosophers. Which one of the following statements could be true? (A) The ﬁrst speaker lectures on Mill. (B) The second speaker lectures on Mill. (C) The second speaker lectures on Nietzsche. (D) The ﬁfth speaker lectures on Nietzsche. (E) The ﬁfth speaker lectures on Ockham. What is the maximum possible number of different schedules for the ﬁve lectures in which those philosophers who are discussed are discussed in alphabetical order? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Which one of the following, if known, would allow one to determine the entire lecture schedule and identify for e...
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