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stringlengths 14
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|---|---|---|---|---|
A critic ranks exactly seven restaurants—Lautrec, Medici, Pastilla, Robusto, Scheherazade's, Tantoko, and Vistula—from highest (best) to lowest (worst). The ranking must meet the following conditions: Pastilla ranks higher than Lautrec but lower than Robusto. Medici ranks higher than Vistula but lower than Tantoko. If Scheherazade's ranks higher than Pastilla, Medici ranks higher than Scheherazade's. If Medici ranks higher than Scheherazade's, Scheherazade's ranks higher than Pastilla. There are no ties.
|
200002_1-G_2_12
|
[
"Lautrec ranked fourth highest.",
"Pastilla is ranked fifth highest.",
"Medici is ranked fifth highest.",
"Scheherazade's is ranked fifth highest.",
"Medici is ranked sixth highest."
] | 1 |
If Tantoko is ranked third highest, then which one of the following CANNOT be true?
|
Each of exactly three parks—Jessup, Island, and Hilltop—has at least one attraction. Each attraction is exactly one of five different types: fountain, garden, museum, playground, or theater. Among the three parks at least one of each type of attraction is included. No two attractions of the same type are included in any park. The following conditions must apply: Each of exactly two parks has a garden. Jessup has a museum but not a theater. Island has exactly one attraction. No park has both a playground and a fountain. Each park that has a theater also has a garden. Each park that has a museum also has a playground.
|
200002_1-G_3_13
|
[
"Jessup: garden, museum; Island: playground; Hilltop: garden, theater",
"Jessup: museum, theater; Island: garden; Hilltop: fountain, garden, playground, theater",
"Jessup: garden, museum, playground; Island: theater; Hilltop: garden, museum, playground",
"Jessup: garden, museum, playground; Island: fountain; Hilltop: garden, theater",
"Jessup: museum, playground; Island: fountain, garden; Hilltop: garden, theater"
] | 3 |
Which one of the following could be a complete and accurate matching of each park to its attractions?
|
Each of exactly three parks—Jessup, Island, and Hilltop—has at least one attraction. Each attraction is exactly one of five different types: fountain, garden, museum, playground, or theater. Among the three parks at least one of each type of attraction is included. No two attractions of the same type are included in any park. The following conditions must apply: Each of exactly two parks has a garden. Jessup has a museum but not a theater. Island has exactly one attraction. No park has both a playground and a fountain. Each park that has a theater also has a garden. Each park that has a museum also has a playground.
|
200002_1-G_3_14
|
[
"Neither Island nor Hilltop has a museum.",
"Neither Island nor Hilltop has a playground.",
"Neither Jessup nor Hilltop has a fountain.",
"Neither Jessup nor Island has a garden.",
"Neither Jessup nor Island has a theater."
] | 3 |
Which one of the following CANNOT be true?
|
Each of exactly three parks—Jessup, Island, and Hilltop—has at least one attraction. Each attraction is exactly one of five different types: fountain, garden, museum, playground, or theater. Among the three parks at least one of each type of attraction is included. No two attractions of the same type are included in any park. The following conditions must apply: Each of exactly two parks has a garden. Jessup has a museum but not a theater. Island has exactly one attraction. No park has both a playground and a fountain. Each park that has a theater also has a garden. Each park that has a museum also has a playground.
|
200002_1-G_3_15
|
[
"Island does not have a fountain.",
"Jessup does not have a garden.",
"Jessup has exactly two attractions.",
"Hilltop has exactly three attractions.",
"Hilltop has exactly four attractions."
] | 3 |
If each of exactly two of the parks has a fountain, then which one of the following could be true?
|
Each of exactly three parks—Jessup, Island, and Hilltop—has at least one attraction. Each attraction is exactly one of five different types: fountain, garden, museum, playground, or theater. Among the three parks at least one of each type of attraction is included. No two attractions of the same type are included in any park. The following conditions must apply: Each of exactly two parks has a garden. Jessup has a museum but not a theater. Island has exactly one attraction. No park has both a playground and a fountain. Each park that has a theater also has a garden. Each park that has a museum also has a playground.
|
200002_1-G_3_16
|
[
"Island only",
"Jessup only",
"Island and Hilltop only",
"Island and Jessup only",
"Jessup, Island, and Hilltop"
] | 1 |
If Jessup has exactly three attractions, then it is possible to determine the exact set of attractions featured by which of the parks?
|
Each of exactly three parks—Jessup, Island, and Hilltop—has at least one attraction. Each attraction is exactly one of five different types: fountain, garden, museum, playground, or theater. Among the three parks at least one of each type of attraction is included. No two attractions of the same type are included in any park. The following conditions must apply: Each of exactly two parks has a garden. Jessup has a museum but not a theater. Island has exactly one attraction. No park has both a playground and a fountain. Each park that has a theater also has a garden. Each park that has a museum also has a playground.
|
200002_1-G_3_17
|
[
"Hilltop has a playground.",
"Island has a museum.",
"Island has a fountain.",
"Island has a garden.",
"Jessup has a garden."
] | 4 |
If the attraction included in Island is of the same type as an attraction included in Jessup, then which one of the following must be true?
|
Each of exactly three parks—Jessup, Island, and Hilltop—has at least one attraction. Each attraction is exactly one of five different types: fountain, garden, museum, playground, or theater. Among the three parks at least one of each type of attraction is included. No two attractions of the same type are included in any park. The following conditions must apply: Each of exactly two parks has a garden. Jessup has a museum but not a theater. Island has exactly one attraction. No park has both a playground and a fountain. Each park that has a theater also has a garden. Each park that has a museum also has a playground.
|
200002_1-G_3_18
|
[
"Both Hilltop and Island have a garden.",
"Both Hilltop and Island have a playground.",
"Both Hilltop and Island have a theater.",
"Both Island and Jessup have a fountain.",
"Both Island and Jessup have a garden."
] | 0 |
Which one of the following could be true?
|
Each of exactly three parks—Jessup, Island, and Hilltop—has at least one attraction. Each attraction is exactly one of five different types: fountain, garden, museum, playground, or theater. Among the three parks at least one of each type of attraction is included. No two attractions of the same type are included in any park. The following conditions must apply: Each of exactly two parks has a garden. Jessup has a museum but not a theater. Island has exactly one attraction. No park has both a playground and a fountain. Each park that has a theater also has a garden. Each park that has a museum also has a playground.
|
200002_1-G_3_19
|
[
"Hilltop has a museum.",
"Hilltop has a playground.",
"Island does not have a fountain.",
"Island has a garden.",
"Jessup has a garden."
] | 0 |
If Hilltop has exactly three attractions, then each of the following could be true EXCEPT:
|
Each year for the next three years, Dynamic Motors will assemble four new automobile models—the Volante, the Whisper, the Xavier, and the Ziggurat—in exactly five of its factories—F, G, H, I, and K. Each factory will assemble exactly one model in each year. Because of contractual obligations Dynamic will assemble all four models each year according to the following constraints: No model is manufactured in the same factory in consecutive years. Neither Volantes nor Whispers are assembled in any factory in which Xaviers were assembled the previous year. Neither Volantes nor Xaviers are assembled in any factory in which Ziggurats were assembled the previous year. In any year, only one factory assembles Zigurats.
|
200002_1-G_4_20
|
[
"year 1: Volantes in F, Ziggurats in G year 2: Xaviers in F, Whispers in G",
"year 1: Whispers in F, Xaviers in G year 2: Whispers in F, Ziggurats in G",
"year 1: Xaviers in F, Volantes in G year 2: Ziggurats in F, Ziggurats in G",
"year 1: Xaviers in F, Xaviers in G year 2: Whispers in F, Ziggurats in G",
"year 1: Ziggurats in F, Whispers in G year 2: Volantes in F, Volantes in G"
] | 0 |
Which one of the following could be the assembly schedule for factories F and G for the first two years?
|
Each year for the next three years, Dynamic Motors will assemble four new automobile models—the Volante, the Whisper, the Xavier, and the Ziggurat—in exactly five of its factories—F, G, H, I, and K. Each factory will assemble exactly one model in each year. Because of contractual obligations Dynamic will assemble all four models each year according to the following constraints: No model is manufactured in the same factory in consecutive years. Neither Volantes nor Whispers are assembled in any factory in which Xaviers were assembled the previous year. Neither Volantes nor Xaviers are assembled in any factory in which Ziggurats were assembled the previous year. In any year, only one factory assembles Zigurats.
|
200002_1-G_4_21
|
[
"Volantes and Whispers",
"Whispers and Volantes",
"Whispers and Ziggurats",
"Ziggurats and Whispers",
"Ziggurats and Ziggurats"
] | 1 |
If in the first year Volantes and Whispers are assembled in F and G, respectively, the models that are assembled in the second year in F and G, respectively, could be
|
Each year for the next three years, Dynamic Motors will assemble four new automobile models—the Volante, the Whisper, the Xavier, and the Ziggurat—in exactly five of its factories—F, G, H, I, and K. Each factory will assemble exactly one model in each year. Because of contractual obligations Dynamic will assemble all four models each year according to the following constraints: No model is manufactured in the same factory in consecutive years. Neither Volantes nor Whispers are assembled in any factory in which Xaviers were assembled the previous year. Neither Volantes nor Xaviers are assembled in any factory in which Ziggurats were assembled the previous year. In any year, only one factory assembles Zigurats.
|
200002_1-G_4_22
|
[
"Xaviers are assembled in exactly two of the factories in the first year.",
"Xaviers are assembled in exactly one of the factories in the second year.",
"Xaviers are assembled in exactly two of the factories in the second year.",
"Xaviers are assembled in exactly one of the factories in the third year.",
"Xaviers are assembled in exactly two of the factories in the third year."
] | 1 |
Which one of the following must be true?
|
Each year for the next three years, Dynamic Motors will assemble four new automobile models—the Volante, the Whisper, the Xavier, and the Ziggurat—in exactly five of its factories—F, G, H, I, and K. Each factory will assemble exactly one model in each year. Because of contractual obligations Dynamic will assemble all four models each year according to the following constraints: No model is manufactured in the same factory in consecutive years. Neither Volantes nor Whispers are assembled in any factory in which Xaviers were assembled the previous year. Neither Volantes nor Xaviers are assembled in any factory in which Ziggurats were assembled the previous year. In any year, only one factory assembles Zigurats.
|
200002_1-G_4_23
|
[
"Volantes are assembled in exactly one of the factories in the third year.",
"Whispers are assembled in exactly one of the factories in the third year.",
"Volantes are assembled in F in the first year.",
"Whispers are assembled in F in the first year.",
"Xaviers are assembled in F in the first year."
] | 4 |
If in the second year Ziggurats are assembled in F, which one of the following must be true?
|
Each year for the next three years, Dynamic Motors will assemble four new automobile models—the Volante, the Whisper, the Xavier, and the Ziggurat—in exactly five of its factories—F, G, H, I, and K. Each factory will assemble exactly one model in each year. Because of contractual obligations Dynamic will assemble all four models each year according to the following constraints: No model is manufactured in the same factory in consecutive years. Neither Volantes nor Whispers are assembled in any factory in which Xaviers were assembled the previous year. Neither Volantes nor Xaviers are assembled in any factory in which Ziggurats were assembled the previous year. In any year, only one factory assembles Zigurats.
|
200002_1-G_4_24
|
[
"Whispers and Volantes",
"Whispers and Xaviers",
"Xaviers and Volantes",
"Xaviers and Ziggurats",
"Ziggurats and Volantes"
] | 0 |
If in the second year Volantes and Whispers are assembled in F and G, respectively, the models that are assembled in the first year in F and G, respectively, could be
|
Each of seven television programs—H, J, L, P, Q, S, V—is assigned a different rank: from first through seventh (from most popular to least popular). The ranking is consistent with the following conditions: J and L are each less popular than H. J is more popular than Q. S and V are each less popular than L. P and S are each less popular than Q. S is not seventh.
|
200012_4-G_1_1
|
[
"J, H, L, Q, V, S, P",
"H, L, Q, J, S, P, V",
"H, J, Q, L, S, V, P",
"H, J, V, L, Q, S, P",
"H, L, V, J, Q, P, S"
] | 2 |
Which one of the following could be the order of the programs, from most popular to least popular?
|
Each of seven television programs—H, J, L, P, Q, S, V—is assigned a different rank: from first through seventh (from most popular to least popular). The ranking is consistent with the following conditions: J and L are each less popular than H. J is more popular than Q. S and V are each less popular than L. P and S are each less popular than Q. S is not seventh.
|
200012_4-G_1_2
|
[
"J is second.",
"J is third.",
"L is third.",
"Q is third.",
"P is seventh."
] | 0 |
If J is more popular than L, and S is more popular than P, then which one of the following must be true of the ranking?
|
Each of seven television programs—H, J, L, P, Q, S, V—is assigned a different rank: from first through seventh (from most popular to least popular). The ranking is consistent with the following conditions: J and L are each less popular than H. J is more popular than Q. S and V are each less popular than L. P and S are each less popular than Q. S is not seventh.
|
200012_4-G_1_3
|
[
"L",
"J",
"Q",
"V",
"P"
] | 4 |
Which one of the following programs CANNOT be ranked third?
|
Each of seven television programs—H, J, L, P, Q, S, V—is assigned a different rank: from first through seventh (from most popular to least popular). The ranking is consistent with the following conditions: J and L are each less popular than H. J is more popular than Q. S and V are each less popular than L. P and S are each less popular than Q. S is not seventh.
|
200012_4-G_1_4
|
[
"P is more popular than S.",
"S is more popular than V.",
"P is more popular than L.",
"J is more popular than V.",
"Q is more popular than V."
] | 3 |
If V is more popular than Q and J is less popular than L, then which one of the following could be true of the ranking?
|
Each of seven television programs—H, J, L, P, Q, S, V—is assigned a different rank: from first through seventh (from most popular to least popular). The ranking is consistent with the following conditions: J and L are each less popular than H. J is more popular than Q. S and V are each less popular than L. P and S are each less popular than Q. S is not seventh.
|
200012_4-G_1_5
|
[
"H is first.",
"L is fourth.",
"V is not fourth.",
"J is not third.",
"Q is third."
] | 1 |
If Q is more popular than L, then each of the following must be true of the ranking EXCEPT:
|
Bird-watchers explore a forest to see which of the following six kinds of birds—grosbeak, harrier, jay, martin, shrike, wren—it contains. The findings are consistent with the following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are.
|
200012_4-G_2_6
|
[
"jays, shrikes",
"harriers, grosbeaks",
"grosbeaks, jays, martins",
"grosbeaks, martins, shrikes, wrens",
"martins, shrikes"
] | 3 |
Which one of the following could be a complete and accurate list of the birds NOT in the forest?
|
Bird-watchers explore a forest to see which of the following six kinds of birds—grosbeak, harrier, jay, martin, shrike, wren—it contains. The findings are consistent with the following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are.
|
200012_4-G_2_7
|
[
"Shrikes are the only other birds in the forest.",
"Jays are the only other birds in the forest.",
"The forest contains neither jays nor shrikes.",
"There are at least two other kinds of birds in the forest.",
"There are at most two other kinds of birds in the forest."
] | 4 |
If both martins and harriers are in the forest, then which one of the following must be true?
|
Bird-watchers explore a forest to see which of the following six kinds of birds—grosbeak, harrier, jay, martin, shrike, wren—it contains. The findings are consistent with the following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are.
|
200012_4-G_2_8
|
[
"Martins are in the forest.",
"Harriers are in the forest.",
"Neither martins nor harriers are in the forest.",
"Neither martins nor shrikes are in the forest.",
"Harriers and shrikes are the only birds in the forest."
] | 3 |
If jays are not in the forest, then which one of the following must be false?
|
Bird-watchers explore a forest to see which of the following six kinds of birds—grosbeak, harrier, jay, martin, shrike, wren—it contains. The findings are consistent with the following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are.
|
200012_4-G_2_9
|
[
"two",
"three",
"four",
"five",
"six"
] | 2 |
Which one of the following is the maximum number of the six kinds of birds the forest could contain?
|
Bird-watchers explore a forest to see which of the following six kinds of birds—grosbeak, harrier, jay, martin, shrike, wren—it contains. The findings are consistent with the following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are.
|
200012_4-G_2_10
|
[
"jays, wrens",
"jays, shrikes",
"shrikes, wrens",
"jays, martins",
"shrikes, martins"
] | 0 |
Which one of the following pairs of birds CANNOT be among those birds contained in the forest?
|
Bird-watchers explore a forest to see which of the following six kinds of birds—grosbeak, harrier, jay, martin, shrike, wren—it contains. The findings are consistent with the following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are.
|
200012_4-G_2_11
|
[
"Shrikes are in the forest.",
"Wrens are in the forest.",
"The forest contains both wrens and shrikes.",
"At most two kinds of birds are in the forest.",
"At least three kinds of birds are in the forest."
] | 0 |
If grosbeaks are in the forest, then which one of the following must be true?
|
Bird-watchers explore a forest to see which of the following six kinds of birds—grosbeak, harrier, jay, martin, shrike, wren—it contains. The findings are consistent with the following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are.
|
200012_4-G_2_12
|
[
"The forest contains both jays and shrikes.",
"The forest contains both wrens and shrikes.",
"The forest contains both martins and shrikes.",
"Jays are not in the forest, whereas martins are.",
"Only two of the six kinds of birds are not in the forest."
] | 1 |
Suppose the condition is added that if shrikes are in the forest, then harriers are not. If all other conditions remain in effect, then which one of the following could be true?
|
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three—F, G, and H—are rubies; three—J, K, and M—are sapphires; and four—W, X, Y, and Z—are topazes. The selection of stones must meet the following restrictions: At least two of the topazes are selected. If exactly two of the sapphires are selected, exactly one of the rubies is selected. If W is selected, neither H nor Z is selected. If M is selected, W is also selected.
|
200012_4-G_3_13
|
[
"F, G, H, M, X, Y",
"F, G, J, K, M, W",
"F, G, J, K, W, X",
"G, H, J, X, Y, Z",
"G, H, K, W, X, Z"
] | 3 |
Which one of the following could be the selection of stones?
|
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three—F, G, and H—are rubies; three—J, K, and M—are sapphires; and four—W, X, Y, and Z—are topazes. The selection of stones must meet the following restrictions: At least two of the topazes are selected. If exactly two of the sapphires are selected, exactly one of the rubies is selected. If W is selected, neither H nor Z is selected. If M is selected, W is also selected.
|
200012_4-G_3_14
|
[
"G is selected.",
"J is selected.",
"X is selected.",
"Of at least one of the three types of stones, exactly one stone is selected.",
"Of at least one of the three types of stones, exactly three stones are selected."
] | 4 |
Which one of the following most be true?
|
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three—F, G, and H—are rubies; three—J, K, and M—are sapphires; and four—W, X, Y, and Z—are topazes. The selection of stones must meet the following restrictions: At least two of the topazes are selected. If exactly two of the sapphires are selected, exactly one of the rubies is selected. If W is selected, neither H nor Z is selected. If M is selected, W is also selected.
|
200012_4-G_3_15
|
[
"All three of the sapphires are selected.",
"Both J and M are selected.",
"Both K and M are selected.",
"None of the rubies is selected.",
"None of the sapphires is selected."
] | 4 |
If Z is selected, which one of the following could be true?
|
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three—F, G, and H—are rubies; three—J, K, and M—are sapphires; and four—W, X, Y, and Z—are topazes. The selection of stones must meet the following restrictions: At least two of the topazes are selected. If exactly two of the sapphires are selected, exactly one of the rubies is selected. If W is selected, neither H nor Z is selected. If M is selected, W is also selected.
|
200012_4-G_3_16
|
[
"H is selected.",
"J is selected.",
"Z is selected.",
"Exactly one sapphire is selected.",
"Exactly two topazes are selected."
] | 3 |
If exactly two rubies are selected, which one of the following must be true?
|
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three—F, G, and H—are rubies; three—J, K, and M—are sapphires; and four—W, X, Y, and Z—are topazes. The selection of stones must meet the following restrictions: At least two of the topazes are selected. If exactly two of the sapphires are selected, exactly one of the rubies is selected. If W is selected, neither H nor Z is selected. If M is selected, W is also selected.
|
200012_4-G_3_17
|
[
"The selection of stones includes at least one ruby.",
"The selection of stones includes at most two rubies.",
"The selection of stones includes either F or Z, or both.",
"The selection of stones includes either X or Y, or both.",
"The selection of stones includes either X or Z, or both."
] | 3 |
Which one of the following must be true?
|
From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three—F, G, and H—are rubies; three—J, K, and M—are sapphires; and four—W, X, Y, and Z—are topazes. The selection of stones must meet the following restrictions: At least two of the topazes are selected. If exactly two of the sapphires are selected, exactly one of the rubies is selected. If W is selected, neither H nor Z is selected. If M is selected, W is also selected.
|
200012_4-G_3_18
|
[
"F and G are both selected.",
"F and X are both selected.",
"G and H are both selected.",
"G and K are both selected.",
"Y and Z are both selected."
] | 1 |
If J and M are the only sapphires selected, which one of the following could be true?
|
There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions: No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street. Red lights decorate store 4. Yellow lights decorate store 5.
|
200012_4-G_4_19
|
[
"green, red, green, red, green",
"green, red, green, yellow, red",
"green, red, yellow, red, green",
"yellow, green, red, green, red",
"yellow, red, green, red, yellow"
] | 1 |
Which one of the following could be an accurate list of the colors of the lights that decorate stores 2, 4, 6, 8, and 10, respectively?
|
There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions: No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street. Red lights decorate store 4. Yellow lights decorate store 5.
|
200012_4-G_4_20
|
[
"Green lights decorate store 2.",
"Green lights decorate store 10.",
"Red lights decorate store 8.",
"Red lights decorate store 9.",
"Yellow lights decorate store 2."
] | 3 |
If green lights decorate store 7, then each of the following statements could be false EXCEPT:
|
There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions: No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street. Red lights decorate store 4. Yellow lights decorate store 5.
|
200012_4-G_4_21
|
[
"Green lights decorate store 10.",
"Red lights decorate store 1.",
"Red lights decorate store 8.",
"Yellow lights decorate store 8.",
"Yellow lights decorate store 10."
] | 1 |
Which one of the following statements must be true?
|
There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions: No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street. Red lights decorate store 4. Yellow lights decorate store 5.
|
200012_4-G_4_22
|
[
"Green lights decorate store 9.",
"Red lights decorate store 2.",
"Red lights decorate store 7.",
"Red lights decorate store 10.",
"Yellow lights decorate store 8."
] | 4 |
If green lights decorate five stores on the street, then which one of the following statements must be true?
|
There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions: No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street. Red lights decorate store 4. Yellow lights decorate store 5.
|
200012_4-G_4_23
|
[
"Green lights decorate store 1.",
"Red lights decorate store 7.",
"Red lights decorate store 10.",
"Yellow lights decorate store 2.",
"Yellow lights decorate store 8."
] | 3 |
Suppose that yellow lights decorate exactly two stores, not just one, on the south side of the street and decorate exactly one store on the north side. If all of the other conditions remain the same, then which one of the following statements must be true?
|
Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively 1 through 9 from one end of the store 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: 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.
|
200106_4-G_1_1
|
[
"Jill",
"Kurt",
"Larisa",
"Manny",
"Olga"
] | 2 |
Which one of the following clerks could stock two consecutive aisles?
|
Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively 1 through 9 from one end of the store 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: 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.
|
200106_4-G_1_2
|
[
"Jill and Manny",
"Kurt and Olga",
"Larisa and Manny",
"Kurt and Manny",
"Larisa and Olga"
] | 4 |
Which one of the following is a pair of clerks, neither of whom could stock aisle 5?
|
Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively 1 through 9 from one end of the store 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: 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.
|
200106_4-G_1_3
|
[
"Jill, Kurt, Larisa",
"Jill, Larisa, Manny",
"Jill, Larisa, Olga",
"Jill, Kurt, Larisa, Manny",
"Jill, Kurt, Larisa, Olga"
] | 1 |
Which one of the following is a complete and accurate list of clerks, any one of whom could stock aisle 3?
|
Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively 1 through 9 from one end of the store 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: 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.
|
200106_4-G_1_4
|
[
"1, 3, 4, 5",
"3, 5, 7, 9",
"3, 4, 5, 6",
"3, 4, 5, 6, 7",
"3, 5, 7"
] | 3 |
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?
|
Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively 1 through 9 from one end of the store 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: 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.
|
200106_4-G_1_5
|
[
"Jill stocks aisle 6.",
"Manny stocks aisle 7.",
"Both of Jill's aisles are numbered lower than Olga's.",
"Jill stocks only even-numbered aisles.",
"Only one clerk stocks a higher numbered aisle than Olga does."
] | 0 |
If Larisa's aisles are separated by the maximum number of aisles that could separate her aisles, which one of the following could be true?
|
Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively 1 through 9 from one end of the store 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: 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.
|
200106_4-G_1_6
|
[
"Jill stocks aisle 9.",
"Kurt stocks aisle 6.",
"Larisa stocks aisle 4.",
"Manny stocks aisle 4.",
"Olga stocks aisle 6."
] | 4 |
If Jill stocks aisle 3, then which one of the following CANNOT be true?
|
Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively 1 through 9 from one end of the store 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: 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.
|
200106_4-G_1_7
|
[
"Jill stocks aisle 3.",
"Olga stocks aisle 6.",
"Olga stocks the only aisle between the two aisles that Jill stocks.",
"Kurt stocks only even-numbered aisles.",
"One of Larisa's aisles is immediately next to Olga's."
] | 1 |
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 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: 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.
|
200106_4-G_2_8
|
[
"The first speaker lectures on Mill.",
"The second speaker lectures on Mill.",
"The second speaker lectures on Nietzsche.",
"The fifth speaker lectures on Nietzsche.",
"The fifth speaker lectures on Ockham."
] | 4 |
Which one of the following statements could be true?
|
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: 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.
|
200106_4-G_2_9
|
[
"2",
"3",
"4",
"5",
"6"
] | 0 |
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 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: 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.
|
200106_4-G_2_10
|
[
"the weeks that Kant, Locke, and Mill are lectured on",
"the weeks that Kant, Mill, and Nietzsche are lectured on",
"the weeks that Kant, Mill, and Ockham are lectured on",
"the weeks that Mill, Nietzsche, and Ockham are lectured on",
"the weeks that Mill, Nietzsche, and Plato are lectured on"
] | 2 |
Which one of the following, if known, would allow one to determine the entire lecture schedule and identify for each week the philosopher who is lectured on that week?
|
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: 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.
|
200106_4-G_2_11
|
[
"The first and fourth speakers lecture on British philosophers.",
"The first and fourth speakers lecture on German philosophers.",
"The second and third speakers lecture on British philosophers.",
"The third and fourth speakers lecture on German philosophers.",
"The fourth and fifth speakers lecture on British philosophers."
] | 3 |
Assume that, of the six philosophers, Kant and Nietzsche are the only German philosophers, and Locke, Mill, and Ockham are the only British philosophers. Each of the following statements could be true EXCEPT:
|
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: 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.
|
200106_4-G_2_12
|
[
"Mill is lectured on in the first lecture and Nietzsche in the fourth.",
"Mill is lectured on in the second lecture and Nietzsche in the third.",
"Mill is lectured on in the second lecture and Nietzsche in the fourth.",
"Mill is lectured on in the fourth lecture and Nietzsche in the fifth.",
"Nietzsche is lectured on in the second lecture and Mill in the fourth."
] | 1 |
Suppose the third speaker were a specialist not only in Mill and Nietzsche, but also in Sartre. If all of the other conditions remained the same, then each of the following could be true EXCEPT:
|
Exactly seven different trains—Quigley, Rockville, Sunnydale, Tilbury, Victoria, Wooster, and York—arrive at Middlebrook Station on Saturday. The following conditions govern their arrivals: The trains arrive one at a time. Either the York or the Wooster arrives fourth. The Sunnydale arrives at some time after the Wooster but at some time before the York. Both the Tilbury and the Victoria arrive at some time after the Rockville. The Tilbury does not arrive next after the Victoria; nor does the Victoria arrive next after the Tilbury.
|
200106_4-G_3_13
|
[
"Rockville, Tilbury, Victoria, Wooster, Sunnydale, York, Quigley",
"Rockville, Wooster, Quigley, York, Tilbury, Sunnydale, Victoria",
"Rockville, Tilbury, Quigley, Wooster, Sunnydale, York, Victoria",
"Quigley, Rockville, Wooster, Sunnydale, Victoria, York, Tilbury",
"Tilbury, Rockville, Quigley, Wooster, Sunnydale, York, Victoria"
] | 2 |
Which one of the following could be the order in which the trains arrive, from first to last?
|
Exactly seven different trains—Quigley, Rockville, Sunnydale, Tilbury, Victoria, Wooster, and York—arrive at Middlebrook Station on Saturday. The following conditions govern their arrivals: The trains arrive one at a time. Either the York or the Wooster arrives fourth. The Sunnydale arrives at some time after the Wooster but at some time before the York. Both the Tilbury and the Victoria arrive at some time after the Rockville. The Tilbury does not arrive next after the Victoria; nor does the Victoria arrive next after the Tilbury.
|
200106_4-G_3_14
|
[
"four",
"five",
"six",
"seven",
"eight"
] | 0 |
If the Wooster arrives at some time before the Rockville, then exactly how many different orders are there in which the seven trains could arrive?
|
Exactly seven different trains—Quigley, Rockville, Sunnydale, Tilbury, Victoria, Wooster, and York—arrive at Middlebrook Station on Saturday. The following conditions govern their arrivals: The trains arrive one at a time. Either the York or the Wooster arrives fourth. The Sunnydale arrives at some time after the Wooster but at some time before the York. Both the Tilbury and the Victoria arrive at some time after the Rockville. The Tilbury does not arrive next after the Victoria; nor does the Victoria arrive next after the Tilbury.
|
200106_4-G_3_15
|
[
"The first train to arrive is the Rockville.",
"The Quigley arrives at some time before the Sunnydale.",
"The Rockville arrives at some time before the Wooster.",
"The Victoria arrives at some time before the York.",
"The Wooster arrives at some time before the York."
] | 4 |
Which one of the following must be true?
|
Exactly seven different trains—Quigley, Rockville, Sunnydale, Tilbury, Victoria, Wooster, and York—arrive at Middlebrook Station on Saturday. The following conditions govern their arrivals: The trains arrive one at a time. Either the York or the Wooster arrives fourth. The Sunnydale arrives at some time after the Wooster but at some time before the York. Both the Tilbury and the Victoria arrive at some time after the Rockville. The Tilbury does not arrive next after the Victoria; nor does the Victoria arrive next after the Tilbury.
|
200106_4-G_3_16
|
[
"The Sunnydale is the next train to arrive after the Quigley.",
"The Rockville is the next train to arrive after the Sunnydale.",
"The Rockville is the next train to arrive after the Tilbury.",
"The Quigley is the next train to arrive after the Sunnydale.",
"The Quigley is the next train to arrive after the Wooster."
] | 1 |
Which one of the following could be true?
|
Exactly seven different trains—Quigley, Rockville, Sunnydale, Tilbury, Victoria, Wooster, and York—arrive at Middlebrook Station on Saturday. The following conditions govern their arrivals: The trains arrive one at a time. Either the York or the Wooster arrives fourth. The Sunnydale arrives at some time after the Wooster but at some time before the York. Both the Tilbury and the Victoria arrive at some time after the Rockville. The Tilbury does not arrive next after the Victoria; nor does the Victoria arrive next after the Tilbury.
|
200106_4-G_3_17
|
[
"The sixth train to arrive is the Sunnydale.",
"The sixth train to arrive is the Tilbury.",
"The third train to arrive is the Rockville.",
"The second train to arrive is the Sunnydale.",
"The first train to arrive is the Rockville."
] | 4 |
If exactly one of the trains arrives after the Wooster but before the York, then which one of the following could be true?
|
Exactly seven different trains—Quigley, Rockville, Sunnydale, Tilbury, Victoria, Wooster, and York—arrive at Middlebrook Station on Saturday. The following conditions govern their arrivals: The trains arrive one at a time. Either the York or the Wooster arrives fourth. The Sunnydale arrives at some time after the Wooster but at some time before the York. Both the Tilbury and the Victoria arrive at some time after the Rockville. The Tilbury does not arrive next after the Victoria; nor does the Victoria arrive next after the Tilbury.
|
200106_4-G_3_18
|
[
"second",
"third",
"fourth",
"fifth",
"sixth"
] | 2 |
If the Quigley arrives at some time before the Rockville, then the Wooster must arrive
|
Each of exactly six doctors—Juarez, Kudrow, Longtree, Nance, Onawa, and Palermo—is at exactly one of two clinics: Souderton or Randsborough. The following conditions must be satisfied: Kudrow is at Randsborough if Juarez is at Souderton. Onawa is at Souderton if Juarez is at Randsborough. If Longtree is at Souderton, then both Nance and Palermo are at Randsborough. If Nance is at Randsborough, then so is Onawa. If Palermo is at Randsborough, then both Kudrow and Onawa are at Souderton.
|
200106_4-G_4_19
|
[
"Juarez, Kudrow, Onawa",
"Juarez, Nance, Onawa, Palermo",
"Kudrow, Longtree, Onawa",
"Nance, Onawa",
"Nance, Palermo"
] | 1 |
Which one of the following could be a complete and accurate list of the doctors that are at Souderton?
|
Each of exactly six doctors—Juarez, Kudrow, Longtree, Nance, Onawa, and Palermo—is at exactly one of two clinics: Souderton or Randsborough. The following conditions must be satisfied: Kudrow is at Randsborough if Juarez is at Souderton. Onawa is at Souderton if Juarez is at Randsborough. If Longtree is at Souderton, then both Nance and Palermo are at Randsborough. If Nance is at Randsborough, then so is Onawa. If Palermo is at Randsborough, then both Kudrow and Onawa are at Souderton.
|
200106_4-G_4_20
|
[
"Juarez is at Randsborough.",
"Kudrow is at Randsborough.",
"Longtree is at Souderton.",
"Nance is at Randsborough.",
"Onawa is at Randsborough."
] | 0 |
If Palermo is at Randsborough, then which one of the following must be true?
|
Each of exactly six doctors—Juarez, Kudrow, Longtree, Nance, Onawa, and Palermo—is at exactly one of two clinics: Souderton or Randsborough. The following conditions must be satisfied: Kudrow is at Randsborough if Juarez is at Souderton. Onawa is at Souderton if Juarez is at Randsborough. If Longtree is at Souderton, then both Nance and Palermo are at Randsborough. If Nance is at Randsborough, then so is Onawa. If Palermo is at Randsborough, then both Kudrow and Onawa are at Souderton.
|
200106_4-G_4_21
|
[
"zero",
"one",
"two",
"three",
"four"
] | 2 |
What is the minimum number of doctors that could be at Souderton?
|
Each of exactly six doctors—Juarez, Kudrow, Longtree, Nance, Onawa, and Palermo—is at exactly one of two clinics: Souderton or Randsborough. The following conditions must be satisfied: Kudrow is at Randsborough if Juarez is at Souderton. Onawa is at Souderton if Juarez is at Randsborough. If Longtree is at Souderton, then both Nance and Palermo are at Randsborough. If Nance is at Randsborough, then so is Onawa. If Palermo is at Randsborough, then both Kudrow and Onawa are at Souderton.
|
200106_4-G_4_22
|
[
"Juarez is at Souderton.",
"Kudrow is at Souderton.",
"Palermo is at Randsborough.",
"Four doctors are at Souderton.",
"Four doctors are at Randsborough."
] | 0 |
If Nance and Onawa are at different clinics, which one of the following must be true?
|
Each of exactly six doctors—Juarez, Kudrow, Longtree, Nance, Onawa, and Palermo—is at exactly one of two clinics: Souderton or Randsborough. The following conditions must be satisfied: Kudrow is at Randsborough if Juarez is at Souderton. Onawa is at Souderton if Juarez is at Randsborough. If Longtree is at Souderton, then both Nance and Palermo are at Randsborough. If Nance is at Randsborough, then so is Onawa. If Palermo is at Randsborough, then both Kudrow and Onawa are at Souderton.
|
200106_4-G_4_23
|
[
"Juarez and Kudrow",
"Juarez and Palermo",
"Kudrow and Onawa",
"Nance and Onawa",
"Nance and Palermo"
] | 4 |
Which one of the following CANNOT be a pair of the doctors at Randsborough?
|
Each of exactly six doctors—Juarez, Kudrow, Longtree, Nance, Onawa, and Palermo—is at exactly one of two clinics: Souderton or Randsborough. The following conditions must be satisfied: Kudrow is at Randsborough if Juarez is at Souderton. Onawa is at Souderton if Juarez is at Randsborough. If Longtree is at Souderton, then both Nance and Palermo are at Randsborough. If Nance is at Randsborough, then so is Onawa. If Palermo is at Randsborough, then both Kudrow and Onawa are at Souderton.
|
200106_4-G_4_24
|
[
"Juarez is at Souderton.",
"Nance is at Souderton.",
"Onawa is at Randsborough.",
"Palermo is at Souderton.",
"Palermo is at Randsborough."
] | 1 |
If Kudrow is at Souderton, then which one of the following must be true?
|
From among eight candidates, four astronauts will be selected for a space flight. Four of the candidates—F, J, K, and L—are experienced astronauts and four—M, N, P, and T—are 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: 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.
|
200110_3-G_1_1
|
[
"F, J, N, and T",
"F, L, M, and P",
"F, M, N, and P",
"J, L, M, and T",
"K, L, N, and T"
] | 3 |
Which one of the following is an acceptable selection of astronauts for the space flight?
|
From among eight candidates, four astronauts will be selected for a space flight. Four of the candidates—F, J, K, and L—are experienced astronauts and four—M, N, P, and T—are 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: 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.
|
200110_3-G_1_2
|
[
"a radiobiologist who is an experienced astronaut and a radiobiologist who is an inexperienced astronaut",
"a radiobiologist who is an experienced astronaut and a geologist who is an inexperienced astronaut",
"a radiobiologist and a geologist, both of whom are experienced astronauts",
"two radiobiologists, both of whom are experienced astronauts",
"two radiobiologists, both of whom are inexperienced astronauts"
] | 0 |
If F and P are selected for the space flight, the other two astronauts selected must be
|
From among eight candidates, four astronauts will be selected for a space flight. Four of the candidates—F, J, K, and L—are experienced astronauts and four—M, N, P, and T—are 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: 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.
|
200110_3-G_1_3
|
[
"K",
"L",
"M",
"N",
"T"
] | 3 |
If F and J are selected for the space flight, which one of the following must also be selected?
|
From among eight candidates, four astronauts will be selected for a space flight. Four of the candidates—F, J, K, and L—are experienced astronauts and four—M, N, P, and T—are 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: 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.
|
200110_3-G_1_4
|
[
"F",
"J",
"L",
"N",
"P"
] | 1 |
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?
|
From among eight candidates, four astronauts will be selected for a space flight. Four of the candidates—F, J, K, and L—are experienced astronauts and four—M, N, P, and T—are 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: 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.
|
200110_3-G_1_5
|
[
"F",
"J",
"L",
"M",
"T"
] | 0 |
If N is selected for the space flight, which one of the following must also be selected?
|
A showroom contains exactly six new cars—T, V, W, X, Y, and Z—each 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.
|
200110_3-G_2_6
|
[
"two",
"three",
"four",
"five",
"six"
] | 2 |
For exactly how many of the six cars is it possible to determine exactly which options each one has?
|
A showroom contains exactly six new cars—T, V, W, X, Y, and Z—each 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.
|
200110_3-G_2_7
|
[
"Exactly five of the six cars have leather interiors.",
"Exactly five of the six cars have sunroofs.",
"Exactly four of the six cars have leather interiors.",
"Exactly four of the six cars have power windows.",
"Exactly four of the six cars have sunroofs."
] | 0 |
Which one of the following must be false?
|
A showroom contains exactly six new cars—T, V, W, X, Y, and Z—each 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.
|
200110_3-G_2_8
|
[
"T has power windows.",
"T has a sunroof.",
"V has power windows.",
"Z has power windows.",
"Z has a sunroof."
] | 4 |
If all the cars that have leather interiors also have power windows, which one of the following must be false?
|
A showroom contains exactly six new cars—T, V, W, X, Y, and Z—each 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.
|
200110_3-G_2_9
|
[
"T has power windows.",
"Z has a sunroof.",
"Exactly four of the six cars have power windows.",
"Exactly four of the six cars have leather interiors.",
"Exactly four of the six cars have sunroofs."
] | 3 |
If 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 showroom contains exactly six new cars—T, V, W, X, Y, and Z—each 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.
|
200110_3-G_2_10
|
[
"Exactly three of the six cars have power windows.",
"Exactly four of the six cars have power windows.",
"Exactly three of the six cars have sunroofs.",
"Exactly four of the six cars have sunroofs.",
"Exactly four of the six cars have leather interiors."
] | 2 |
Suppose that no two cars have exactly the same options as one another. In that case, each of the following could be true EXCEPT:
|
A showroom contains exactly six new cars—T, V, W, X, Y, and Z—each 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.
|
200110_3-G_2_11
|
[
"T and V have no options in common.",
"T and Y have no options in common.",
"T and Z have exactly one option in common.",
"W and Z have exactly one option in common.",
"Y and Z have no options in common."
] | 3 |
If 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 showroom contains exactly six new cars—T, V, W, X, Y, and Z—each 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.
|
200110_3-G_2_12
|
[
"T and X have no options in common.",
"V and X have exactly one option in common.",
"V and X have exactly two options in common.",
"X and Z have no options in common.",
"X and Z have exactly two options in common."
] | 3 |
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?
|
Quentin, Robert, Shiro, Tony, and Umeko are the only members of the Kim family who attend an opera. Each of them sits in a separate seat in either row G or row H, and each sits in a seat numbered 1, 2, or 3. Consecutively numbered seats within each row are adjacent. Each member of the Kim family sits in a seat adjacent to, and in the same row as, at least one other member of the family. Tony and Umeko sit in row H. Shiro and Umeko sit in lower numbered seats than does Tony. Robert sits in the same row as Quentin or Shiro or both. Robert sits in a seat numbered 2.
|
200110_3-G_3_13
|
[
"Seat G3 is empty.",
"Seat H2 is empty.",
"Shiro sits in a seat numbered 3.",
"Tony sits in a seat numbered 1.",
"Umeko sits in a seat numbered 3."
] | 0 |
Which one of the following statements could be true?
|
Quentin, Robert, Shiro, Tony, and Umeko are the only members of the Kim family who attend an opera. Each of them sits in a separate seat in either row G or row H, and each sits in a seat numbered 1, 2, or 3. Consecutively numbered seats within each row are adjacent. Each member of the Kim family sits in a seat adjacent to, and in the same row as, at least one other member of the family. Tony and Umeko sit in row H. Shiro and Umeko sit in lower numbered seats than does Tony. Robert sits in the same row as Quentin or Shiro or both. Robert sits in a seat numbered 2.
|
200110_3-G_3_14
|
[
"Robert sits in row H.",
"Shiro sits in row H.",
"Quentin sits in the same row as, and in a seat adjacent to, Shiro.",
"Robert sits in the same row as, and in a seat adjacent to, Tony.",
"Robert sits in the same row as, and in a seat adjacent to, Umeko."
] | 1 |
Which one of the following statements could be true?
|
Quentin, Robert, Shiro, Tony, and Umeko are the only members of the Kim family who attend an opera. Each of them sits in a separate seat in either row G or row H, and each sits in a seat numbered 1, 2, or 3. Consecutively numbered seats within each row are adjacent. Each member of the Kim family sits in a seat adjacent to, and in the same row as, at least one other member of the family. Tony and Umeko sit in row H. Shiro and Umeko sit in lower numbered seats than does Tony. Robert sits in the same row as Quentin or Shiro or both. Robert sits in a seat numbered 2.
|
200110_3-G_3_15
|
[
"Quentin sits in a seat numbered 3.",
"Umeko sits in a seat numbered 1.",
"Quentin sits in the same row as, and in a seat adjacent to, Robert.",
"Robert sits in the same row as, and in a seat adjacent to, Shiro.",
"Tony sits in the same row as, and in a seat adjacent to, Umeko."
] | 2 |
If Tony sits in a seat numbered 2, then which one of the following statements could be false?
|
Quentin, Robert, Shiro, Tony, and Umeko are the only members of the Kim family who attend an opera. Each of them sits in a separate seat in either row G or row H, and each sits in a seat numbered 1, 2, or 3. Consecutively numbered seats within each row are adjacent. Each member of the Kim family sits in a seat adjacent to, and in the same row as, at least one other member of the family. Tony and Umeko sit in row H. Shiro and Umeko sit in lower numbered seats than does Tony. Robert sits in the same row as Quentin or Shiro or both. Robert sits in a seat numbered 2.
|
200110_3-G_3_16
|
[
"G1, G3",
"G3, H1",
"H1, H3",
"G1, G3, H1",
"G1, G3, H1, H3"
] | 4 |
Considering only the six seats in which members of the Kim family could sit, which one of the following is a complete and accurate list of those seats any one of which could be empty?
|
Quentin, Robert, Shiro, Tony, and Umeko are the only members of the Kim family who attend an opera. Each of them sits in a separate seat in either row G or row H, and each sits in a seat numbered 1, 2, or 3. Consecutively numbered seats within each row are adjacent. Each member of the Kim family sits in a seat adjacent to, and in the same row as, at least one other member of the family. Tony and Umeko sit in row H. Shiro and Umeko sit in lower numbered seats than does Tony. Robert sits in the same row as Quentin or Shiro or both. Robert sits in a seat numbered 2.
|
200110_3-G_4_17
|
[
"Quentin",
"Shiro, Umeko",
"Robert, Shiro, Umeko",
"Tony, Shiro, Umeko",
"Quentin, Shiro, Tony, Umeko"
] | 4 |
Which one of the following is a complete and accurate list of those members of the Kim family any one of whom could sit in seat H2?
|
Exactly seven professors—Madison, Nilsson, Orozco, Paton, Robinson, Sarkis, and Togo—were hired in the years 1989 through 1995. Each professor has one or more specialities, and any two professors hired in the same year or in consecutive years do not have a specialty in common. The professors were hired according to the following conditions: Madison was hired in 1993, Robinson in 1991. There is at least one specialty that Madison, Orozco, and Togo have in common. Nilsson shares a specialty with Robinson. Paton and Sarkis were each hired at least one year before Madison and at least one year after Nilsson. Orozco, who shares a specialty with Sarkis, was hired in 1990.
|
200110_3-G_4_18
|
[
"Nilsson, Orozco, Robinson",
"Orozco, Robinson, Sarkis",
"Nilsson, Orozco, Paton, Robinson",
"Nilsson, Orozco, Paton, Sarkis",
"Orozco, Paton, Robinson, Sarkis"
] | 2 |
Which one of the following is a complete and accurate list of the professors who could have been hired in the years 1989 through 1991?
|
Exactly seven professors—Madison, Nilsson, Orozco, Paton, Robinson, Sarkis, and Togo—were hired in the years 1989 through 1995. Each professor has one or more specialities, and any two professors hired in the same year or in consecutive years do not have a specialty in common. The professors were hired according to the following conditions: Madison was hired in 1993, Robinson in 1991. There is at least one specialty that Madison, Orozco, and Togo have in common. Nilsson shares a specialty with Robinson. Paton and Sarkis were each hired at least one year before Madison and at least one year after Nilsson. Orozco, who shares a specialty with Sarkis, was hired in 1990.
|
200110_3-G_4_19
|
[
"Madison and Paton share a specialty.",
"Robinson and Sarkis share a specialty.",
"Paton was hired exactly one year after Orozco.",
"Exactly one professor was hired in 1994.",
"Exactly two professors were hired in 1993."
] | 0 |
If exactly one professor was hired in 1991, then which one of the following could be true?
|
Exactly seven professors—Madison, Nilsson, Orozco, Paton, Robinson, Sarkis, and Togo—were hired in the years 1989 through 1995. Each professor has one or more specialities, and any two professors hired in the same year or in consecutive years do not have a specialty in common. The professors were hired according to the following conditions: Madison was hired in 1993, Robinson in 1991. There is at least one specialty that Madison, Orozco, and Togo have in common. Nilsson shares a specialty with Robinson. Paton and Sarkis were each hired at least one year before Madison and at least one year after Nilsson. Orozco, who shares a specialty with Sarkis, was hired in 1990.
|
200110_3-G_4_20
|
[
"Nilsson was hired in 1989.",
"Paton was hired in 1990.",
"Paton was hired in 1991.",
"Sarkis was hired in 1992.",
"Togo was hired in 1994."
] | 4 |
Which one of the following must be false?
|
Exactly seven professors—Madison, Nilsson, Orozco, Paton, Robinson, Sarkis, and Togo—were hired in the years 1989 through 1995. Each professor has one or more specialities, and any two professors hired in the same year or in consecutive years do not have a specialty in common. The professors were hired according to the following conditions: Madison was hired in 1993, Robinson in 1991. There is at least one specialty that Madison, Orozco, and Togo have in common. Nilsson shares a specialty with Robinson. Paton and Sarkis were each hired at least one year before Madison and at least one year after Nilsson. Orozco, who shares a specialty with Sarkis, was hired in 1990.
|
200110_3-G_4_21
|
[
"Orozco was hired before Paton.",
"Paton was hired before Sarkis.",
"Sarkis was hired before Robinson.",
"Robinson was hired before Sarkis.",
"Madison was hired before Sarkis."
] | 3 |
Which one of the following must be true?
|
Exactly seven professors—Madison, Nilsson, Orozco, Paton, Robinson, Sarkis, and Togo—were hired in the years 1989 through 1995. Each professor has one or more specialities, and any two professors hired in the same year or in consecutive years do not have a specialty in common. The professors were hired according to the following conditions: Madison was hired in 1993, Robinson in 1991. There is at least one specialty that Madison, Orozco, and Togo have in common. Nilsson shares a specialty with Robinson. Paton and Sarkis were each hired at least one year before Madison and at least one year after Nilsson. Orozco, who shares a specialty with Sarkis, was hired in 1990.
|
200110_3-G_4_22
|
[
"Orozco, Paton, and Togo share a specialty.",
"Madison, Paton, and Togo share a specialty.",
"Exactly two professors were hired in 1991.",
"Exactly two professors were hired in 1993.",
"Paton was hired in 1991."
] | 0 |
If exactly two professors were hired in 1992, then which one of the following could be true?
|
Exactly seven professors—Madison, Nilsson, Orozco, Paton, Robinson, Sarkis, and Togo—were hired in the years 1989 through 1995. Each professor has one or more specialities, and any two professors hired in the same year or in consecutive years do not have a specialty in common. The professors were hired according to the following conditions: Madison was hired in 1993, Robinson in 1991. There is at least one specialty that Madison, Orozco, and Togo have in common. Nilsson shares a specialty with Robinson. Paton and Sarkis were each hired at least one year before Madison and at least one year after Nilsson. Orozco, who shares a specialty with Sarkis, was hired in 1990.
|
200110_3-G_4_23
|
[
"Nilsson does not share a specialty with Paton.",
"Exactly one professor was hired in 1990.",
"Exactly one professor was hired in 1991.",
"Exactly two professors were hired in each of two years.",
"Paton was hired at least one year before Sarkis."
] | 4 |
If Paton and Madison have a specialty in common, then which one of the following must be true?
|
A fruit stand carries at least one kind of the following kinds of fruit: figs, kiwis, oranges, pears, tangerines, and watermelons. The stand does not carry any other kind of fruit. The selection of fruits the stand carries is consistent with the following conditions: If the stand carries kiwis, then it does not carry pears. If the stand does not carry tangerines, then it carries kiwis. If the stand carries oranges, then it carries both pears and watermelons. If the stand carries watermelons, then it carries figs or tangerines or both.
|
200112_4-G_1_1
|
[
"oranges, pears",
"pears, tangerines",
"oranges, pears, watermelons",
"oranges, tangerines, watermelons",
"kiwis, oranges, pears, watermelons"
] | 1 |
Which one of the following could be a complete and accurate list of the kinds of fruit the stand carries?
|
A fruit stand carries at least one kind of the following kinds of fruit: figs, kiwis, oranges, pears, tangerines, and watermelons. The stand does not carry any other kind of fruit. The selection of fruits the stand carries is consistent with the following conditions: If the stand carries kiwis, then it does not carry pears. If the stand does not carry tangerines, then it carries kiwis. If the stand carries oranges, then it carries both pears and watermelons. If the stand carries watermelons, then it carries figs or tangerines or both.
|
200112_4-G_1_2
|
[
"figs",
"oranges",
"pears",
"tangerines",
"watermelons"
] | 3 |
Which one of the following could be the only kind of fruit the stand carries?
|
A fruit stand carries at least one kind of the following kinds of fruit: figs, kiwis, oranges, pears, tangerines, and watermelons. The stand does not carry any other kind of fruit. The selection of fruits the stand carries is consistent with the following conditions: If the stand carries kiwis, then it does not carry pears. If the stand does not carry tangerines, then it carries kiwis. If the stand carries oranges, then it carries both pears and watermelons. If the stand carries watermelons, then it carries figs or tangerines or both.
|
200112_4-G_1_3
|
[
"kiwis, tangerines",
"tangerines, watermelons",
"figs, kiwis, watermelons",
"oranges, pears, tangerines, watermelons",
"figs, kiwis, oranges, pears, watermelons"
] | 4 |
Which one of the following CANNOT be a complete and accurate list of the kinds of fruit the stand carries?
|
A fruit stand carries at least one kind of the following kinds of fruit: figs, kiwis, oranges, pears, tangerines, and watermelons. The stand does not carry any other kind of fruit. The selection of fruits the stand carries is consistent with the following conditions: If the stand carries kiwis, then it does not carry pears. If the stand does not carry tangerines, then it carries kiwis. If the stand carries oranges, then it carries both pears and watermelons. If the stand carries watermelons, then it carries figs or tangerines or both.
|
200112_4-G_1_4
|
[
"The stand carries kiwis.",
"The stand carries at least two kinds of fruit.",
"The stand carries at most three kinds of fruit.",
"The stand carries neither oranges nor pears.",
"The stand carries neither oranges nor kiwis."
] | 2 |
If the stand carries no watermelons, then which one of the following must be true?
|
A fruit stand carries at least one kind of the following kinds of fruit: figs, kiwis, oranges, pears, tangerines, and watermelons. The stand does not carry any other kind of fruit. The selection of fruits the stand carries is consistent with the following conditions: If the stand carries kiwis, then it does not carry pears. If the stand does not carry tangerines, then it carries kiwis. If the stand carries oranges, then it carries both pears and watermelons. If the stand carries watermelons, then it carries figs or tangerines or both.
|
200112_4-G_1_5
|
[
"The stand does not carry figs.",
"The stand does not carry tangerines.",
"The stand does not carry pears.",
"The stand carries pears but not oranges.",
"The stand carries pears but not tangerines."
] | 4 |
If the stand carries watermelons, then which one of the following must be false?
|
A fruit stand carries at least one kind of the following kinds of fruit: figs, kiwis, oranges, pears, tangerines, and watermelons. The stand does not carry any other kind of fruit. The selection of fruits the stand carries is consistent with the following conditions: If the stand carries kiwis, then it does not carry pears. If the stand does not carry tangerines, then it carries kiwis. If the stand carries oranges, then it carries both pears and watermelons. If the stand carries watermelons, then it carries figs or tangerines or both.
|
200112_4-G_1_6
|
[
"pears",
"figs, pears",
"oranges, pears, watermelons",
"figs, pears, watermelons",
"figs, oranges, pears, watermelons"
] | 2 |
If the condition that if the fruit stand does not carry tangerines then it does carry kiwis is suspended, and all other conditions remain in effect, then which one of the following CANNOT be a complete and accurate list of the kinds of fruit the stand carries?
|
A radio talk show host airs five telephone calls sequentially. The calls, one from each of Felicia, Gwen, Henry, Isaac, and Mel, are each either live or taped (but not both). Two calls are from Vancouver, two are from Seattle, and one is from Kelowna. The following conditions must apply: Isaac's and Mel's calls are the first two calls aired, but not necessarily in that order. The third call aired, from Kelowna, is taped. Both Seattle calls are live. Both Gwen's and Felicia's calls air after Henry's. Neither Mel nor Felicia calls from Seattle.
|
200112_4-G_2_7
|
[
"Isaac's, Henry's, Felicia's, Mel's, Gwen's",
"Isaac's, Mel's, Gwen's, Henry's, Felicia's",
"Mel's, Gwen's, Henry's, Isaac's, Felicia's",
"Mel's, Isaac's, Gwen's, Henry's, Felicia's",
"Mel's, Isaac's, Henry's, Felicia's, Gwen's"
] | 4 |
Which one of the following could be an accurate list of the calls, listed in the order in which they are aired?
|
A radio talk show host airs five telephone calls sequentially. The calls, one from each of Felicia, Gwen, Henry, Isaac, and Mel, are each either live or taped (but not both). Two calls are from Vancouver, two are from Seattle, and one is from Kelowna. The following conditions must apply: Isaac's and Mel's calls are the first two calls aired, but not necessarily in that order. The third call aired, from Kelowna, is taped. Both Seattle calls are live. Both Gwen's and Felicia's calls air after Henry's. Neither Mel nor Felicia calls from Seattle.
|
200112_4-G_2_8
|
[
"Felicia's call airs fifth.",
"Gwen's call airs first.",
"Henry's call airs second.",
"Isaac's call airs third.",
"Mel's call airs fifth."
] | 0 |
Which one of the following could be true?
|
A radio talk show host airs five telephone calls sequentially. The calls, one from each of Felicia, Gwen, Henry, Isaac, and Mel, are each either live or taped (but not both). Two calls are from Vancouver, two are from Seattle, and one is from Kelowna. The following conditions must apply: Isaac's and Mel's calls are the first two calls aired, but not necessarily in that order. The third call aired, from Kelowna, is taped. Both Seattle calls are live. Both Gwen's and Felicia's calls air after Henry's. Neither Mel nor Felicia calls from Seattle.
|
200112_4-G_2_9
|
[
"Felicia's call is the next call aired after Isaac's.",
"Henry's call is the next call aired after Felicia's.",
"Henry's call is the next call aired after Mel's.",
"Henry's call is the next call aired after Isaac's.",
"Isaac's call is the next call aired after Mel's."
] | 2 |
If the first call aired is from Seattle, then which one of the following could be true?
|
A radio talk show host airs five telephone calls sequentially. The calls, one from each of Felicia, Gwen, Henry, Isaac, and Mel, are each either live or taped (but not both). Two calls are from Vancouver, two are from Seattle, and one is from Kelowna. The following conditions must apply: Isaac's and Mel's calls are the first two calls aired, but not necessarily in that order. The third call aired, from Kelowna, is taped. Both Seattle calls are live. Both Gwen's and Felicia's calls air after Henry's. Neither Mel nor Felicia calls from Seattle.
|
200112_4-G_2_10
|
[
"Felicia's call airs fourth.",
"Gwen's call airs fifth.",
"A taped call airs second.",
"A taped call airs third.",
"A taped call airs fourth."
] | 2 |
If a taped call airs first, then which one of the following CANNOT be true?
|
A radio talk show host airs five telephone calls sequentially. The calls, one from each of Felicia, Gwen, Henry, Isaac, and Mel, are each either live or taped (but not both). Two calls are from Vancouver, two are from Seattle, and one is from Kelowna. The following conditions must apply: Isaac's and Mel's calls are the first two calls aired, but not necessarily in that order. The third call aired, from Kelowna, is taped. Both Seattle calls are live. Both Gwen's and Felicia's calls air after Henry's. Neither Mel nor Felicia calls from Seattle.
|
200112_4-G_2_11
|
[
"Gwen's call is live.",
"Henry's call is live.",
"Mel's call is live.",
"Felicia's call is taped.",
"Isaac's call is taped."
] | 0 |
Which one of the following must be true?
|
A radio talk show host airs five telephone calls sequentially. The calls, one from each of Felicia, Gwen, Henry, Isaac, and Mel, are each either live or taped (but not both). Two calls are from Vancouver, two are from Seattle, and one is from Kelowna. The following conditions must apply: Isaac's and Mel's calls are the first two calls aired, but not necessarily in that order. The third call aired, from Kelowna, is taped. Both Seattle calls are live. Both Gwen's and Felicia's calls air after Henry's. Neither Mel nor Felicia calls from Seattle.
|
200112_4-G_2_12
|
[
"one",
"two",
"three",
"four",
"five"
] | 0 |
If no two live calls are aired consecutively and no two taped calls are aired consecutively, then in exactly how many distinct orders could the calls from the five people be aired?
|
A radio talk show host airs five telephone calls sequentially. The calls, one from each of Felicia, Gwen, Henry, Isaac, and Mel, are each either live or taped (but not both). Two calls are from Vancouver, two are from Seattle, and one is from Kelowna. The following conditions must apply: Isaac's and Mel's calls are the first two calls aired, but not necessarily in that order. The third call aired, from Kelowna, is taped. Both Seattle calls are live. Both Gwen's and Felicia's calls air after Henry's. Neither Mel nor Felicia calls from Seattle.
|
200112_4-G_2_13
|
[
"The first call aired is from Seattle.",
"The first call aired is from Vancouver.",
"The fourth call aired is from Seattle.",
"The fifth call aired is from Seattle.",
"The fifth call aired is from Vancouver."
] | 1 |
If a taped call airs second, then which one of the following CANNOT be true?
|
Gutierrez, Hoffman, Imamura, Kelly, Lapas, and Moore ride a bus together. Each sits facing forward in a different one of the six seats on the left side of the bus. The seats are in consecutive rows that are numbered 1, 2, and 3 from front to back. Each row has exactly two seats: a window seat and an aisle seat. The following conditions must apply: Hoffman occupies the aisle seat immediately behind Gutierrez's aisle seat. If Moore occupies an aisle seat, Hoffman sits in the same row as Lapas. If Gutierrez sits in the same row as Kelly, Moore occupies the seat immediately and directly behind Imamura's seat. If Kelly occupies a window seat, Moore sits in row 3. If Kelly sits in row 3, Imamura sits in row 1.
|
200112_4-G_3_14
|
[
"Imamura sits in row 2, whereas Kelly sits in row 3.",
"Gutierrez sits in the same row as Kelly, immediately and directly behind Moore.",
"Gutierrez occupies a window seat in the same row as Lapas.",
"Moore occupies an aisle seat in the same row as Lapas.",
"Kelly and Moore both sit in row 3."
] | 4 |
Which one of the following could be true?
|
Gutierrez, Hoffman, Imamura, Kelly, Lapas, and Moore ride a bus together. Each sits facing forward in a different one of the six seats on the left side of the bus. The seats are in consecutive rows that are numbered 1, 2, and 3 from front to back. Each row has exactly two seats: a window seat and an aisle seat. The following conditions must apply: Hoffman occupies the aisle seat immediately behind Gutierrez's aisle seat. If Moore occupies an aisle seat, Hoffman sits in the same row as Lapas. If Gutierrez sits in the same row as Kelly, Moore occupies the seat immediately and directly behind Imamura's seat. If Kelly occupies a window seat, Moore sits in row 3. If Kelly sits in row 3, Imamura sits in row 1.
|
200112_4-G_3_15
|
[
"Moore occupies the aisle seat in row 3.",
"Imamura occupies the window seat in row 3.",
"Gutierrez sits in the same row as Kelly.",
"Gutierrez sits in the same row as Moore.",
"Moore sits in the same row as Lapas."
] | 0 |
If Lapas and Kelly each occupy a window seat, then which one of the following could be true?
|
Gutierrez, Hoffman, Imamura, Kelly, Lapas, and Moore ride a bus together. Each sits facing forward in a different one of the six seats on the left side of the bus. The seats are in consecutive rows that are numbered 1, 2, and 3 from front to back. Each row has exactly two seats: a window seat and an aisle seat. The following conditions must apply: Hoffman occupies the aisle seat immediately behind Gutierrez's aisle seat. If Moore occupies an aisle seat, Hoffman sits in the same row as Lapas. If Gutierrez sits in the same row as Kelly, Moore occupies the seat immediately and directly behind Imamura's seat. If Kelly occupies a window seat, Moore sits in row 3. If Kelly sits in row 3, Imamura sits in row 1.
|
200112_4-G_3_16
|
[
"Hoffman sits in row 2.",
"Imamura sits in row 2.",
"Imamura sits in row 3.",
"Kelly sits in row 1.",
"Lapas sits in row 3."
] | 3 |
If Moore sits in row 1, then which one of the following must be true?
|
Gutierrez, Hoffman, Imamura, Kelly, Lapas, and Moore ride a bus together. Each sits facing forward in a different one of the six seats on the left side of the bus. The seats are in consecutive rows that are numbered 1, 2, and 3 from front to back. Each row has exactly two seats: a window seat and an aisle seat. The following conditions must apply: Hoffman occupies the aisle seat immediately behind Gutierrez's aisle seat. If Moore occupies an aisle seat, Hoffman sits in the same row as Lapas. If Gutierrez sits in the same row as Kelly, Moore occupies the seat immediately and directly behind Imamura's seat. If Kelly occupies a window seat, Moore sits in row 3. If Kelly sits in row 3, Imamura sits in row 1.
|
200112_4-G_3_17
|
[
"Gutierrez sits in the same row as Imamura.",
"Hoffman sits in the same row as Lapas.",
"Lapas occupies a window seat.",
"Moore occupies a window seat.",
"Gutierrez sits in row 1."
] | 1 |
If Kelly occupies the aisle seat in row 3, then each of the following must be true EXCEPT:
|
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