Grouping Defined Fixed Unbalanced

Grouping Defined Fixed Unbalanced - Grouping...

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Unformatted text preview: Grouping (Defined/Fixed] Unbalanced) L l Grouping (Defined/Fixed/Unbalancea) Games Questions 7-1 1 Each of five illnessesiJ, K, L, M, and Niis characterized by at least one of the following three symptoms: fever, headache, and sneezing. None of the illnesses has any symptom that is not one of these three. lllness J is characterized by headache and sneezing. lllnesses J and K have no symptoms in common. lllnesses J and L have at least one symptom in common. lllness L has a greater number of symptoms than illness K. lllnesses L and N have no symptoms in common. lllness M has more symptoms than illness J. 7. Which one of the following statements must be false? (A) lllness J has exactly two symptoms. (B) lllness K has exactly one symptom. (C) lllness L has exactly two symptoms. (D) lllness M has exactly three symptoms. (E) lllness N has exactly two symptoms. 8. In which one of the following pairs could the first member of the pair be characterized by exactly the same number and types of symptoms as the second member of the pair? (A) J and N (B) K and L (C) K and N (D) L and M (E) M and N 9. 10. 11. 1f illness L is characterized by a combination of symptoms different from any of the other illnesses, then which one of the following statements must be true? (A) Fever is a symptom of illness L. (B) Sneezing is a symptom of illness L. (C) Headache is a symptom of illness L. (D) lllnesses K and N are characterized by exactly the same symptoms. (E) lllnesses M and N are characterized by exactly the same symptoms. The illnesses in which one of the following pairs must have exactly one symptom in common? (A) J and L (B) J and M (C) J and N (D) K and L (E) M and N If Walter has exactly two of the three symptoms, then he cannot have all of the symptoms of (A) both illness J and illness L (B) both illness J and illness N (C) both illness K and illness L (D) both illness K and illness N (E) both illness L and illness N1 1 PT 4, Game 2 Grouping (Defined/Fixed/Unbalancea) Games I Questions 7-1 1 A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. 7. 8. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available. Which one of the following must be false? (A) Two of the shirts that Casey buys are small and two are red. (B) Two of the shirts that Casey buys are medium and two are red. (C) Two of the shirts that Casey buys are large and two are red. (D) Two of the shirts that Casey buys are small, one is yellow, and one is blue. (E) Two of the shirts that Casey buys are medium, one is yellow, and one is blue. lf Casey buys a small blue shirt, which one of the following must be false? (A) Casey buys two blue shirts. (B) Casey buys two red shirts. (C) Casey buys two yellow shirts. (D) Casey buys two small shirts. (E) Casey buys two medium shirts. 9. 10. 11. 1f Casey does not buy a medium yellow shirt, which one of the following must be true? (A) Casey buys either a medium red shirt or a small blue shirt. (B) Casey buys either a medium red shirt or a medium blue shirt. (C) Casey buys either a large red shirt or a small blue shirt. (D) Casey buys either a large red shirt or a medium red shirt. (E) Casey buys either a large yellow shirt or a small yellow shirt. lf Casey buys exactly one medium shirt and does not buy two shirts of the same color, then she cannot buy which one of the following? (A) a medium red shirt (B) a medium yellow shirt (C) a medium blue shirt (D) a large red shirt (E) a large yellow shirt If neither large red shirts nor small blue shirts are available, which one of the following must Casey buy? (A) a red shirt (B) a medium yellow shirt (C) either a large shirt or a small shirt (D) either a medium red shirt or a medium blue shirt (E) either a large yellow shirt or a medium blue shirt2 2 PT 5, Game 2 I Grouping (Defined/Fixed/Unbalancea) Games Questions 12-17 15. The hobbyist could select any of the following groups of fish for the aquarium EXCEPT A hobbyist is stocking her aquarium with exactly three fish of (A) G K L different types and with exactly two species of plants. The only (B) H’ J ’K fish under consideration are a G, an H, a J, a K, and an L, and (C) H’ J’ L the only kinds of plants under consideration are of the species (D) H’ K’ L W, X, Y, and Z. She will observe the following conditions: (E) J ’K ’L If she selects the G, she can select neither the H nor a Y. ’ ’ She cannm 5616“ the H unless She seleCts the K' 16. 1f the hobbyist selects a Y, which one of the following She cannot select the J unless she selects a W. 9 If she selects the K, she must select an X. muSt be the group Of fiSh She seleCts‘ (A) G, H, K 12. Which one of the following is an acceptable selection of (B) H, J, K fish and plants for the aquarium? (C) H, J, L , (D) H, K, L Fish Plants J, K, L (A) G, H, K w, Y (B) G, J, K W, X 17. The hobbyist could select any of the following plant (C) G, J, L X, Z combinations EXCEPT <3 <A> wandx ( ) = = = (B) W and Y Z 13. 1f the hobbyist selects the H, which one of the following :2, :31: Y must also be true? (E) X and Z3 (A) She selects at least one W. (B) She selects at least one X. (C) She selects the J, but no Y’s. (D) She selects the K, but no X’s. (E) She selects at least one X, but no Y’s. 14. 1f the hobbyist selects both X’s and 2’s, which one of the following could be the group of fish she selects? (A) G, H, K (B) G, J, K (C) G, K, L (D) H, J, L (E) J, K, L 3 PT 5, Game 3 Questions 177 A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids. Which one of the following is an acceptable selection of flowers for the three corsages? Corsage l Corsage 2 Corsage 3 (A) 2 gardenias l orchid l gardenia l rose 1 rose 1 orchid l violet l violet (B) 2 orchids 2 orchids 2 gardenias l rose 1 rose 1 rose (C) 2 orchids 3 roses 1 gardenia l rose 2 violets (D) l gardenia lgardenia l gardenia l orchid l rose 1 rose 1 rose 1 violet l violet (E) l orchid 3 violets 3 gardenias 2 roses The maximum total number of roses that can be used in the three corsages is (A) three (B) four (C) five (D) six (E) seven Grouping (Defined/Fixed/Unbalancea) Games I lf corsage 1 contains two orchids and one rose, what is the maximum total number of violets that the florist can use in making the three corsages? (A) one (B) two (C) three (D) four (E) five lf corsage 2 is exactly the same as corsage 3, the nine flowers used in the corsages can include exactly (A) two orchids (B) three gardenias (C) three roses (D) five roses (E) five violets If two of the corsages contain at least one orchid each, then the flowers in corsage 2 must include at least (A) one gardenia and one orchid (B) one gardenia and one rose (C) one orchid and one rose (D) one orchid and one violet (B) one rose and one violet 1f the greatest possible number of violets is used in the three corsages, the florist must use (A) exactly one rose and exactly one gardenia (B) exactly one orchid and exactly four violets (C) exactly two orchids (D) exactly two roses (E) exactly six violets lf corsage 1 contains at least one gardenia and at least one violet, and if corsage 3 contains three different types of flowers, which one of the following could be used to make corsage 2? (A) one rose, one orchid, and one gardenia (B) one rose and two orchids (C) one rose and two violets (D) two roses and one gardenia (E) two roses and one violet4 4 PT 9, Game 1 a Grouping (Defined/Fixed/Unbalancea) Games Questions 8713 From a group of seven peopleiJ, K, L, M, N, P, and Q7 exactly four will be selected to attend a diplomat’s retirement dinner. Selection must conform to the following conditions: Either J or K must be selected, but J and K cannot both be selected. Either N or P must be selected, but N and P cannot both be selected. N cannot be selected unless L is selected. Q cannot be selected unless K is selected. 8. Which one of the following could be the four people selected to attend the retirement dinner? (A) J, K, M, P (B) J, L, N, Q (C) J, M, N, Q (D) K, M, P, Q (E) L, M, N, P 9. Among the people selected to attend the retirement dinner there must be (A) K or Q or both (B) L or M or both (C) N or M or both (D) N or Q or both (E) P or Q or both 10. Which one of the following is a pair of people who CANNOT both be selected to attend the retirement dinner? (A) J and N (B) J and Q (C) K and L (D) K and N (E) N and Q 11. 12. 13. If M is not selected to attend the retirement dinner, the four people selected to attend must include which one of the following pairs of people? (A) J and Q (B) K and L (C) K and P (D) L and P (E) N and Q If P is not selected to attend the retirement dinner, then exactly how many different groups of four are there each of which would be an acceptable selection? (A) one (B) two (C) three (D) four (E) five There is only one acceptable group of four that can be selected to attend the retirement dinner if which one of the following pairs of people is selected? (A) J and L (B) K and M (C) L and N (D) L and Q (E) M and Q5 5 PT 9, Game 2 Grouping (Defined/Fixed/Unbalancea) Games a Questions 20-24 Five experienced plumbersiF rank, Gene, Jill, Kathy, and Markiand four inexperienced plumbersiRoberta, Sally, Tim, and Vemonimust decide which of them will be assigned to four work teams of exactly two plumbers each. Assignments must meet the following restrictions: Each plumber is assigned to at most one team. At least one plumber on each team must be experienced. Neither Mark nor Roberta nor Vernon can be assigned to a team with Frank. lf Tim is assigned to a team, either Gene or Kathy must be assigned to that team. Jill cannot be assigned to a team with Roberta. 20. Which one of the following is an inexperienced plumber 21. who can be assigned to a team with Frank? (A) Kathy (B) Roberta (C) Sally (D) Tim (B) Vernon Which one of the following is a pair of plumbers who can be assigned together to a team? (A) Frank and Roberta (B) Frank and Vernon (C) Jill and Mark (D) Roberta and Tim (B) Sally and Vernon 22. 23. 24. 1f Tim is assigned to a team, and if Sally is assigned to a team with a plumber who could have been assigned to a team with Tim, then the only plumber with whom Frank could be assigned to a team is (A) Gene (B) J ill (C) Mark (D) Roberta (E) Vernon lf Gene is not assigned to a team, then Jill must be assigned to a team with (A) Vernon (B) Tim (C) Mark (D) Kathy (E) Frank If all of the inexperienced plumbers are assigned to teams, and neither Roberta nor Tim nor Vernon is assigned to a team with Gene, then Sally must be assigned to a team with either (A) Frank or else Gene (B) Frank or else Mark (C) Gene or else Mark (D) Jill or else Kathy (E) Jill or else Mark6 6 PT 15, Game 4 Grouping (Defined/Fixed/Unbalancea) Games Questions 6-12 Exactly six employeesiofficers F, G, and H, and supervisors K, L, and Mimust be assigned to exactly three committeesi Policy, Quality, and Salesiwith exactly three employees per committee. Committee assignments must conform to the following conditions: Each committee must have at least one officer assigned to it. Each employee must be assigned to at least one committee. All three officers must be assigned to the Policy Committee. G cannot be assigned to the same committee as L. K must be assigned to the Sales Committee. 6. Which one of the following is a group of three employees who can be assigned together to the Sales Committee? (A) F, G, and H (B) F, G, and M (C) G, K, and L (D) H, K, and L (E) K, L, and M 7. If H is assigned to exactly one committee, and if no committee has both F and M assigned to it, then it must be true that (A) G and M are both assigned to the Quality Committee (B) K and L are both assigned to the Sales Committee (C) K is assigned to exactly two committees (D) L is assigned to exactly two committees (E) M is assigned to exactly two committees 8. Which one of the following CANNOT be true? (A) F is assigned to exactly one committee. (B) G is assigned to exactly three committees. (C) H is assigned to exactly three committees. (D) K is assigned to exactly one committee. (E) L is assigned to exactly two committees. 9. 10. ll. 12. If F is assigned to exactly three committees, and G is assigned to exactly two committees, then which one of the following must be true? (A) G is assigned to the Quality Committee. (B) G is assigned to the Sales Committee. (C) K is assigned to the Quality Committee (D) L is assigned to the Sales Committee. (E) M is assigned to the Quality Committee. Which one of the following is a group of three employees who can be assigned together to the Quality Committee? (A) F, G, and H (B) F, G, and K (C) G, H, and K (D) G, K, and L (E) H, L, and M lf L is assigned to exactly two committees, which of the following must be true? (A) F is assigned to the Sales Committee. (B) G is assigned to the Sales Committee. (C) H is assigned to the Quality Committee. (D) K is assigned to the Quality Committee. (E) M is assigned to the Quality Committee. Which one of the following CANNOT be true? (A) F and G are each assigned to exactly one committee. (B) F and H are each assigned to exactly one committee. (C) G and H are each assigned to exactly one committee. (D) F and M are both assigned to the Sales Committee. (E) G and K are both assigned to the Quality Committee.7 7 PT 17, Game 2 Grouping (Defined/Fixed/Unbalancea) Games I Questions 6-12 A university library budget committee must reduce exactly five of eight areas of expenditureiG, L, M, N, P, R, S, and Wiin accordance with the following conditions: If both G and S are reduced, W is also reduced. If N is reduced, neither R nor S is reduced. If P is reduced, L is not reduced. Of the three areas L, M, and R, exactly two are reduced. 6. Which one of the following could be a complete and accurate list of the areas of expenditure reduced by the committee? (A) G, L, M, N, W (B) G: L, M, P, W (C) G: M, N, R, W (D) G, M, P, R, s (E) L, M, R, s, W 7. 1f W is reduced, which one of the following could be a complete and accurate list of the four other areas of expenditure to be reduced? (A) G, M, P, S (B) L, M, N, R (C) L, M, P, s (D) M, N, P, s (E) M, P, R, s 8. If P is reduced, which one of the following is a pair of areas of expenditure both of which must be reduced? (A) G, M (B) M, R (C) N, R (D) R, S (E) s, w 9. 10. ll. 12. If both L and S are reduced, which one of the following could be a pair of areas of expenditure both of which are reduced? (A) G, M (B) G, P (C) N, R (D) N, W (E) P, S If R is not reduced, which one of the following must be true? (A) G is reduced. (B) N is not reduced. (C) P is reduced. (D) S is reduced. (E) W is not reduced. If both M and R are reduced, which one of the following is a pair of areas neither of which could be reduced? (A) (B) (C) (D) (E) G,L G,N L,N L,P s P, Which one of the following areas must be reduced? (A) (B) (C) (D) (E) G L N P W8 8 PT 20, Game 2 n Grouping (Defined/Fixed/Unbalancea) Games Questions 20-24 Exactly six of seven jugglersiG, H, K, L, N, P, and Q are each assigned to exactly one of three positionsifront, middle, and rearion one of two teamsiteam l and team 2. For each team, exactly one juggler must be assigned to each position according to the following conditions: If either G or H or both are assigned to teams, they are assigned to front positions. lf assigned to a team, K is assigned to a middle position. If assigned to a team, L is assigned to team 1. Neither P nor K is on the same team as N. P is not on the same team as Q. If H is on team 2, then Q is assigned to the middle position on team 1. 20. Which one of the following is an acceptable list of 21. assignments of jugglers to team 2? (A) front: Q; middle: K; rear: N (B) front: H; middle: P; rear: K (C) front: H; middle: L; near: N (D) front: G; middle: Q; rear: P (E) front: G; middle: Q; rear: N If H is assigned to team 2, which one of the following is an acceptable assignment of jugglers to team 1? (A) front: G; middle: K; rear: L (B) front: G; middle: K; rear: N (C) front: L; middle: K; rear: P (D) front: L; middle: Q; rear: G (E) front: L; middle: Q; rear: N 22. 23. 24. Which one of the following is an acceptable list of assignments of jugglers to team 1? (A) front: G; middle: K; rear: L (B) front: G; middle: K; rear: P (C) front: L; middle: K; rear: Q (D) front: Q; middle: K; rear: P (E) front: Q; middle: L; rear: N If G is assigned to team 1, which one of the following is a pair of jugglers who could also be assigned to team 1? (A) H and N (B) K and L (C) K and P (D) L and N (E) L and Q If G is assigned to team 1 and K is assigned to team 2, which one of the following must be assigned the rear position on team 2? (A) H (B) L (C) N (D) P (E) (29 9 PT 22, Game 4 Grouping (Defined/Fixed/Unbalancea) Games n Questions 12-18 Exactly six of seven researchersithree anthropologists: Franklin, Jones, and Marquez; and four linguists: Neil, Osborne, Rice, and Samuelsiwill be included in two three- person teamsiteam l and team 2. No researcher will be included in more than one team. Each team must include at least one anthropologist and at least one linguist. The teams’ composition must conform to the following conditions: Neither team includes both Franklin and Samuels. Neither team includes both Neil and Rice. If a team includes Marquez, it includes neither Rice nor Samuels. lf team 1 includes Jones, team 2 includes Rice. 12. Which one of the following could be the list of the researchers on the two teams? (A) team 1: Franklin, Marquez, Osborne team 2: Jones, Neil, Rice (B) team 1: Franklin, Neil, Samuels team 2: Jones, Osborne, Rice (C) team 1: Franklin, Osborne, Rice team 2: Jones, Neil, Samuels (D) team 1: Jones, Marquez, Neil team 2: Osborne, Rice, Samuels (E) team 1: Jones, Osborne, Rice team 2: Franklin, Marquez, Neil 13. 1f Jones is on team 1, which one of the following is a pair of researchers that must be on team 2 together? (A) Franklin and Rice (B) Marquez and Osborne (C) Neil and Osborne (D) Osborne and Samuels (E) Rice and Samuels 14. 1f Neil is on team 1, which one of the following is a pair of researchers that could be on team 1 together with Neil? (A) Franklin and Jones (B) Jones and Osborne (C) Jones and Rice (D) Jones and Samuels (E) Osborne and Samuels 15. l6. 17. 18. 1f Franklin is on the same team as Marquez, which one of the following could be true? (A) Jones is on team 1. (B) Rice is on team 1. (C) Samuels is on team 2. (D) Both Neil and Osborne are on team 1. (E) Both Neil and Osborne are on team 2. Each of the following is a pair of researchers that could be on team 2 together EXCEPT: (A) Franklin and Jones (B) Franklin and Marquez (C) Franklin and Rice (D) Jones and Marquez (E) Jones and Rice Which one of the following could be true? (A) Franklin is on team 1 and Neil is on team 2. (B) Franklin is on team 2 and Jones is not on any team. (C) Franklin is on team 2 and Marquez is on team 2. (D) Franklin is not on any team and Jones is on team 1. (E) Jones is on team 1 and Neil is on team 2. 1f Marquez is on team 2, which one of the following must also be on team 2? (A) Franklin (B) J ones (C) Osborne (D) Rice (E) Samuels10 1° PT 23, Game 3 n Grouping (Defined/Fixed/Unbalancea) Games Questions 18-23 Nine different treatments are available for a certain illness: three antibioticsiF, G, and Hithree dietary regimensiM, N, and Oiand three physical therapiesiU, V, and W. For each case of the illness, a doctor will prescribe exactly five of the treatments, in accordance with the following conditions: If two of the antibiotics are prescribed, the remaining antibiotic cannot be prescribed. There must be exactly one dietary regimen prescribed. lf 0 is not prescribed, F cannot be prescribed. lf W is prescribed, F cannot be prescribed. G cannot be prescribed if both N and U are prescribed. V cannot be prescribed unless both H and M are prescribed. 18. Which one of the following could be the five treatments prescribed for a given case? (A) F, G, H, M, V (B) F, G, M, o, v (C) F, H, M, o, W (D) G, H, N, U, W (B) G, H, 0, U, W 19. Which one of the following could be the antibiotics and physical therapies prescribed for a given case? (A) F, G, H, W (B) F a G, U, V (C) F, U, v, W (D) G, U, v, W (B) H, U, v, W 20. lf 0 is prescribed for a given case, which one of the following is a pair of treatments both of which must also be prescribed for that case? (A) F, M (B) G, V (C) N, U (D) U, V (E) U, W 21. 22. 23. If G is prescribed for a given case, which one of the following is a pair of treatments both of which could also be prescribed for that case? (A) F, M (B) F, N (C) N, v (D) o, v (F) v, W Which one of the following is a list of three treatments that could be prescribed together for a given case? (A) F, M, U (B) F, o, W (C) G, N, v (D) G, v, W (B) H, N, v Which one of the following treatments CANNOT be prescribed for any case? (A) G (B) M (C) N (D) U W11 “ PT 24, Game 4 Grouping (Defined/Fixed/Unbalancea) Games n Questions 19-24 In each of two years exactly two of four lawmakers—Feld, Gibson, Hsu, and lvins—and exactly two of three scientists—Vega, Young, and Zapora—will serve as members of a four-person panel. In each year, one of the members will be chairperson. The chairperson in the first year cannot serve on the panel in the second year. The chairperson in the second year must have served on the panel in the first year. Service on the panel must obey the following conditions: 19. 20. 21. Gibson and Vega do not serve on the panel in the same year as each other. Hsu and Young do not serve on the panel in the same year as each other. Each year, either lvins or Vega, but not both, serves on the panel. Which one of the following could be the list of the people who serve on the panel in the first year? (A) F eld, Gibson, Vega, Zapora (B) F eld, Hsu, Vega, Zapora (C) F eld, lvins, Vega, Zapora (D) Gibson, Hsu, lvins, Zapora (E) Hsu, lvins, Young, Zapora lf Vega is the chairperson in the first year, which one of the following is a pair of people who must serve on the panel in the second year? (A) Gibson and Young (B) Gibson and Zapora (C) Hsu and lvins (D) lvins and Young (E) Vega and Young lf Hsu is the chairperson in the first year, which one of the following could be the chairperson in the second year? (A) F eld (B) Gibson (C) Hsu (D) lvins (E) Young 22. 23. 24. If F eld serves on the panel in a given year, any one of the following could serve on the panel that year EXCEPT: (A) Gibson (B) Hsu (C) lvins (D) Vega (E) Young lf lvins is the chairperson in the first year, which one of the following could be the chairperson in the second year? (A) F eld (B) Gibson (C) Hsu (D) Vega (E) Young Which one of the following must be true? (A) F eld is on the panel in the second year. (B) Hsu is on the panel in the first year. (C) lvins is on the panel in both years. (D) Young is on the panel in both years. (E) Zapora is on the panel in the second year. 12 12 PT 26, Game 4 n Grouping (Defined/Fixed/Unbalancea) Games Questions 6-12 To prepare for fieldwork, exactly four different researchers—a geologist, a historian, a linguist, and a paleontologist—will learn at least one and at most three of four languages—Rundi, Swahili, Tigrinya, and Yoruba. They must learn the languages according to the following specifications: Exactly one researcher learns Rundi. Exactly two researchers learn Swahili. Exactly two researchers learn Tigrinya. Exactly three researchers learn Yoruba. Any language learned by the linguist or paleontologist is not learned by the geologist. Any language learned by the geologist is learned by the historian. 6. Which one of the following could be true? (A) The linguist learns three languages—Rundi, Swahili, and Tigrinya. (B) The linguist learns three languages—Swahili, Tigrinya, and Yoruba. (C) The historian learns three languages—Rundi, Swahili, and Tigrinya. (D) The historian learns three languages Swahili, Tigrinya, and Yoruba. (E) The paleontologist learns three languages—Rundi, Swahili, and Tigrinya. 7. 1f the linguist learns three of the languages, then which one of the following must be true? (A) The linguist learns Tigrinya. (B) The linguist learns Rundi. (C) The linguist learns Swahili. (D) The paleontologist learns Rundi. (E) The paleontologist learns Swahili. 8. Each of the following could be true of the researcher who learns Rundi EXCEPT: (A) The researcher also learns Tigrinya but not Swahili. (B) The researcher learns neither Tigrinya nor Swahili. (C) The researcher also learns Tigrinya but not Yoruba. (D) The researcher also learns both Tigrinya and Yoruba. (E) The researcher also learns Yoruba but not Tigrinya. 9. 10. ll. 12. Each of the following could be a complete and accurate list of the researchers who learn both Swahili and Yoruba EXCEPT: (A) the historian (B) the paleontologist (C) the historian, the linguist (D) the historian, the paleontologist (E) the linguist, the paleontologist 1f the geologist learns exactly two of the languages, then which one of the following could be true? (A) The paleontologist learns Rundi. (B) The paleontologist learns Swahili. (C) The historian learns Rundi. (D) The paleontologist learns exactly three of the languages. (E) The historian learns exactly two of the languages. Which one of the following must be true? A Fewer of the lan ua es are learned by the g g historian than are learned by the paleontologist. (B) Fewer of the languages are learned by the geologist than are learned by the historian. (C) Fewer of the languages are learned by the geologist than are learned by the linguist. (D) Fewer of the languages are learned by the paleontologist than are learned by the linguist. (E) Fewer of the languages are learned by the paleontologist than are learned by the historian. lf exactly two of the languages are learned by the historian, then which one of the following must be true? (A) The paleontologist does not learn Rundi. (B) The geologist does not learn Swahili. (C) The linguist does not learn Rundi. (D) The historian does not learn Rundi. (E) The paleontologist does not learn Swahili.l3 13 PT 28, Game 2 Grouping (Defined/Fixed/Unbalancea) Games n Questions 7-13 Two mannequinsil and 2iwill be dressed for display in outfits chosen from ten articles of clothing. Each article is in exactly one of three colors: navy, red, or yellow. There are three hatsione in each color; three jacketsione in each color; three skirtsione in each color; and one red tie. Each mannequin wears exactly one of the hats, one of the jackets, and one of the skirts. Furthermore, their outfits must meet the following restrictions: Neither mannequin wears all three colors. Each mannequin wears a hat in a different color from the jacket it wears. Mannequin 2 wears the navy skirt. Mannequin 1 wears the tie. 7. Which one of the following could be complete outfits for the two mannequins? (A) mannequin 1: navy hat, red jacket, yellow skirt, red tie mannequin 2: red hat, navy jacket, navy skirt (B) mannequin 1: red hat, red jacket, yellow skirt, red tie mannequin 2: yellow hat, navy jacket, navy skirt (C) mannequin 1: red hat, yellow jacket, red skirt, red tie mannequin 2: yellow hat, navy jacket, yellow skirt (D) mannequin 1: yellow hat, red jacket, yellow skirt, red tie mannequin 2: red hat, navy jacket, navy skirt (E) mannequin 1: yellow hat, yellow jacket, red skirt mannequin 2: red hat, navy jacket, navy skirt 8. Which one of the following could be true of the mannequins’ outfits? (A) Mannequin 1 wears the navy jacket and the yellow skirt. (B) Mannequin 2 wears the red hat and the red jacket. (C) Mannequin 1 wears exactly one red article of clothing. (D) Mannequin 1 wears exactly three yellow articles of clothing. (E) Mannequin 2 wears no red articles of clothing. 10. 11. 12. 13. 1f mannequin 1 wears the navy jacket, which one of the following could be true? (A) Mannequin 1 wears the yellow hat. (B) Mannequin 1 wears the yellow skirt. (C) Mannequin 2 wears the red hat. (D) Mannequin 2 wears the yellow hat. (E) Mannequin 2 wears the yellow jacket. If all four of the red articles of clothing are included in the two mannequins’ outfits, which one of the following must be true? (A) Mannequin 1 wears the red hat. (B) Mannequin 1 wears the yellow jacket. (C) Mannequin 2 wears the navy jacket. (D) Mannequin 1 wears no navy articles of clothing. (E) Mannequin 2 wears no yellow articles of clothing. lf mannequin 2 wears the red jacket, then mannequin 1 must wear the (A) navy hat (B) red hat (C) yellow hat (D) red skirt (E) yellow skirt If all three of the yellow articles of clothing are included in the two mannequins’ outfits, which one of the following could be true? (A) Mannequin 1 wears the navy jacket. (B) Mannequin 1 wears the yellow jacket. (C) Mannequin 1 wears the red skirt. (D) Mannequin 2 wears the red hat. (E) Mannequin 2 wears the red jacket. lf mannequin 1 wears the skirt that is the same color as the jacket that mannequin 2 wears, which one of the following must be true? (A) Mannequin 1 wears the yellow hat. (B) Mannequin 1 wears the yellow jacket. (C) Mannequin 2 wears the navy hat. (D) Mannequin 2 wears the red hat. (E) Mannequin 2 wears the red jacket. ’4 1“ PT 29, Game 2 fl Grouping (Defined/Fixed/Unbalancea) Games Questions 1-5 This morning, a bakery makes exactly one delivery, consisting of exactly six loaves of bread. Each of the loaves is exactly one of three kinds: oatmeal, rye, or wheat, and each is either sliced or unsliced. The loaves that the bakery delivers this morning must be consistent with the following: There are at least two kinds of loaves. There are no more than three rye loaves. There is no unsliced wheat loaf. There is at least one unsliced oatmeal loaf. If two or more of the loaves are unsliced, then at least one of the unsliced loaves is rye. 1. Which one of the following could be a complete and accurate list of the loaves that the bakery delivers? (A) six unsliced oatmeal loaves (B) five unsliced oatmeal loaves, one sliced rye loaf (C) five unsliced oatmeal loaves, one unsliced wheat loaf (D) four unsliced oatmeal loaves, two unsliced rye loaves (E) four unsliced oatmeal loaves, two sliced wheat loaves 2. Each of the following could be a complete and accurate list of the unsliced loaves that the bakery delivers EXCEPT: (A) three oatmeal loaves (B) three oatmeal loaves, one rye loaf (C) two oatmeal loaves, two rye loaves (D) two oatmeal loaves, three rye loaves (B) one oatmeal loaf, one rye loaf 3. Which one of the following statements CANNOT be true? (A) The only unsliced loaves are oatmeal loaves. (B) The only sliced loaves are rye loaves. (C) The only unsliced loaves are rye loaves. (D) The number of sliced loaves is exactly one greater than the number of sliced oatmeal loaves. (E) The number of unsliced loaves is exactly one greater than the number of unsliced oatmeal loaves. 4. Which one of the following statements must be true? (A) At least one of the loaves is rye. (B) At least one of the loaves is wheat. (C) At least one of the loaves is sliced. (D) No more than four oatmeal loaves are sliced. (E) No more than four wheat loaves are sliced. 5. 1f the bakery delivers exactly four wheat loaves, then the bakery could also deliver (A) one sliced rye loaf and one unsliced rye loaf (B) one sliced oatmeal loaf and one unsliced oatmeal loaf (C) two unsliced rye loaves (D) two unsliced oatmeal loaves (E) two sliced oatmeal loaves 15 15 PT 30, Game 1 Grouping (Defined/Fixed/Unbalancea) Games n Questions 1-5 From among eight candidates, four astronauts will be selected for a space flight. Four of the candidatesiF, J, K, and Liare experienced astronauts and fouriM, N, P, and Tiare inexperienced astronauts. F, M, P, and T are geologists whereas J, K, L, and N are radiobiologists. The astronauts must be selected according to the following conditions: 1. Exactly two experienced astronauts and two inexperienced astronauts are selected. Exactly two geologists and two radiobiologists are selected. Either P or L or both are selected. Which one of the following is an acceptable selection of astronauts for the space flight? (A) F, J, N, andT (B) F, L, M, and P (C) F, M,N, andP (D) J, L, M, and T (E) K, L, N, and T If F and P are selected for the space flight, the other two astronauts selected must be (A) a radiobiologist who is an experienced astronaut and a radiobiologist who is an inexperienced astronaut (B) a radiobiologist who is an experienced astronaut and a geologist who is an inexperienced astronaut (C) a radiobiologist and a geologist, both of whom are experienced astronauts (D) two radiobiologists, both of whom are experienced astronauts (E) two radiobiologists, both of whom are inexperienced astronauts If F and J are selected for the space flight, which one of the following must also be selected? (A) K (B) L (C) M (D) N (E) T If M and T are selected for the space flight, which one of the following could be, but need not be, selected for the flight? (A) F (B) J (C) L (D) N (E) P If N is selected for the space flight, which one of the following must also be selected? (A) F (B) J (C) L (D) M T16 1" PT 35, Game 1 Grouping (Defined/Fixed/Unbalancea) Games Questions 6-12 A showroom contains exactly six new carsiT, V, W, X, Y, and Zieach equipped with at least one of the following three options: power windows, leather interior, and sunroof. No car has any other options. The following conditions must apply: V has power windows and a sunroof W has power windows and a leather interior. W and Y have no options in common. X has more options than W. V and Z have exactly one option in common. T has fewer options than Z. 6. For exactly how many of the six cars is it possible to determine exactly which options each one has? (A) two (B) three (C) four (D) five (E) six 7. Which one of the following must be false? (A) Exactly five of the six cars have leather interiors. (B) Exactly five of the six cars have sunroofs. (C) Exactly four of the six cars have leather interiors. (D) Exactly four of the six cars have power windows. (E) Exactly four of the six cars have sunroofs. 8. If all the cars that have leather interiors also have power windows, which one of the following must be false? (A) T has power windows. (B) T has a sunroof (C) V has power windows. (D) Z has power windows. (E) Z has a sunroof 9. 1f Z has no options in common with T but has at least one option in common with every other car, then which one of the following must be false? (A) T has power windows. (B) Z has a sunroof (C) Exactly four of the six cars have power windows. (D) Exactly four of the six cars have leather interiors. (E) Exactly four of the six cars have sunroofs. 10. Suppose that no two cars have exactly the same options as 11. 12. one another. In that case, each of the following could be true EXCEPT: (A) Exactly three of the six cars have power windows. (B) Exactly four of the six cars have power windows. (C) Exactly three of the six cars have sunroofs. (D) Exactly four of the six cars have sunroofs. (E) Exactly four of the six cars have leather interiors. lf exactly four of the six cars have leather interiors, and exactly four of the six cars have power windows, then each of the following must be true EXCEPT: (A) T and V have no options in common. (B) T and Y have no options in common. (C) T and Z have exactly one option in common. (D) W and Z have exactly one option in common. (E) Y and Z have no options in common. Suppose that the condition requiring that X has more options than W is replaced by a new condition requiring that X and W have exactly two options in common. If all of the other original conditions remain in effect, which one of the following must be false? (A) T and X have no options in common. (B) V and X have exactly one option in common. (C) V and X have exactly two options in common. (D) X and Z have no options in common. (E) X and Z have exactly two options in common. 17 17 PT 35, Game 2 PT 4, Game 2 pg. 1 7. E 8. C 9. A 10. E 11. E PT 17, Game 2 pg. 7 6. D 7. C 8. B 9. E 10. E 11. E 12. B PT 28, Game 2 pg. 13 6. D 7. B 8. C 9. B 10. A 11. B 12. D GROUPING (DEFINED/FIXED/UNBALANCED) GAMES PT 5, Game 2 pg. 2 7. A 8. B 9. B 10. B 11. D PT 20, Game 2 pg. 8 6. A 7. E 8. B 9. A 10. A 11. C 12. E PT 29, Game 2 pg. 14 7. D 8. E 9. E 10. E 11. B 12. B 13. C PT 5, Game 3 pg. 3 12. 13. 14. 15. 16. 17. WUOOWW PT 22, Game 4 pg. 9 20. E 21. E 22. E 23. E 24. D PT 30, Game 1 pg. 15 1. D A C D B PT 9, Game 1 pg. 4 1. qomgww >UO>WUO PT 23, Game 3 pg. 10 12. 13. 14. 15. 16. 17. 18. W>WOU>O PT 35, Game 1 PT 9, Game 2 pg. 5 8. 9. 10. 11. 12. 13. WOWWWU PT 24, Game 4 pg. 11 18. 19. 20. 21. 22. 23. OUU‘JU‘JU‘JU‘J PT 35, Game 2 pg. 17 6. 7. 8. 9. 10. 11. 12. UUOUFU>O PT 15, Game 4 pg. 6 20. C 21. C 22. B 23. A 24. A PT 26, Game 4 pg. 12 19. 20. 21. 22. 23. 24. m>>>Uw ...
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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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