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In Crescentville there are exactly five record stores, whose names are abbreviated S, T, V, X, and Z. Each of the five stores carries at least one of four distinct types of music: folk, jazz, opera, and rock. None of the stores carries any other type of music. The following conditions must hold: Exactly two of the five stores carry jazz. T carries rock and opera but no other type of music. S carries more types of music than T carries. X carries more types of music than any other store in Crescentville carries. Jazz is among the types of music S carries. V does not carry any type of music that Z carries.
|
200510_4-G_3_13
|
[
"S, V, and Z all carry folk.",
"S, X, and Z all carry jazz.",
"Of the five stores, only S and V carry jazz.",
"Of the five stores, only T and X carry rock.",
"Of the five stores, only S, T, and V carry opera."
] | 3 |
Which one of the following could be true?
|
In Crescentville there are exactly five record stores, whose names are abbreviated S, T, V, X, and Z. Each of the five stores carries at least one of four distinct types of music: folk, jazz, opera, and rock. None of the stores carries any other type of music. The following conditions must hold: Exactly two of the five stores carry jazz. T carries rock and opera but no other type of music. S carries more types of music than T carries. X carries more types of music than any other store in Crescentville carries. Jazz is among the types of music S carries. V does not carry any type of music that Z carries.
|
200510_4-G_3_14
|
[
"S and V carry exactly two types of music in common.",
"T and S carry exactly two types of music in common.",
"T and V carry exactly two types of music in common.",
"V and X carry exactly two types of music in common.",
"X and Z carry exactly two types of music in common."
] | 1 |
If exactly one of the stores carries folk, then which one of the following could be true?
|
In Crescentville there are exactly five record stores, whose names are abbreviated S, T, V, X, and Z. Each of the five stores carries at least one of four distinct types of music: folk, jazz, opera, and rock. None of the stores carries any other type of music. The following conditions must hold: Exactly two of the five stores carry jazz. T carries rock and opera but no other type of music. S carries more types of music than T carries. X carries more types of music than any other store in Crescentville carries. Jazz is among the types of music S carries. V does not carry any type of music that Z carries.
|
200510_4-G_3_15
|
[
"T carries exactly the same number of types of music as V carries.",
"V carries exactly the same number of types of music as Z carries.",
"S carries at least one more type of music than Z carries.",
"Z carries at least one more type of music than T carries.",
"X carries exactly two more types of music than S carries."
] | 2 |
Which one of the following must be true?
|
In Crescentville there are exactly five record stores, whose names are abbreviated S, T, V, X, and Z. Each of the five stores carries at least one of four distinct types of music: folk, jazz, opera, and rock. None of the stores carries any other type of music. The following conditions must hold: Exactly two of the five stores carry jazz. T carries rock and opera but no other type of music. S carries more types of music than T carries. X carries more types of music than any other store in Crescentville carries. Jazz is among the types of music S carries. V does not carry any type of music that Z carries.
|
200510_4-G_3_16
|
[
"S and Z carry no types of music in common.",
"S and V carry at least one type of music in common.",
"S and Z carry at least one type of music in common.",
"T and Z carry at least one type of music in common.",
"T and V carry at least two types of music in common."
] | 2 |
If V is one of exactly three stores that carry rock, then which one of the following must be true?
|
In Crescentville there are exactly five record stores, whose names are abbreviated S, T, V, X, and Z. Each of the five stores carries at least one of four distinct types of music: folk, jazz, opera, and rock. None of the stores carries any other type of music. The following conditions must hold: Exactly two of the five stores carry jazz. T carries rock and opera but no other type of music. S carries more types of music than T carries. X carries more types of music than any other store in Crescentville carries. Jazz is among the types of music S carries. V does not carry any type of music that Z carries.
|
200510_4-G_3_17
|
[
"S and T carry no types of music in common.",
"S and Z carry no types of music in common.",
"T and Z carry no types of music in common.",
"S and Z carry two types of music in common.",
"T and V carry two types of music in common."
] | 1 |
If S and V both carry folk, then which one of the following could be true?
|
Maggie's Deli is open exactly five days every week: Monday through Friday. Its staff, each of whom works on at least one day each week, consists of exactly six people—Janice, Kevin, Nan, Ophelia, Paul, and Seymour. Exactly three of them—Janice, Nan, and Paul—are supervisors. The deli's staffing is consistent with the following: Each day's staff consists of exactly two people, at least one of whom is a supervisor. Tuesday's and Wednesday's staffs both include Ophelia. Of the days Nan works each week, at least two are consecutive. Seymour does not work on any day before the first day Paul works that week. Any day on which Kevin works is the first day during the week that some other staff member works.
|
200510_4-G_4_18
|
[
"Monday: Janice, Kevin Tuesday: Nan, Ophelia Wednesday: Nan, Paul Thursday: Kevin, Paul Friday: Janice, Seymour",
"Monday: Paul, Seymour Tuesday: Ophelia, Paul Wednesday: Nan, Ophelia Thursday: Kevin, Nan Friday: Janice, Seymour",
"Monday: Janice, Kevin Tuesday: Nan, Ophelia Wednesday: Nan, Ophelia Thursday: Kevin, Paul Friday: Paul, Seymour",
"Monday: Janice, Kevin Tuesday: Janice, Ophelia Wednesday: Nan, Ophelia Thursday: Nan, Seymour Friday: Kevin, Paul",
"Monday: Paul, Seymour Tuesday: Ophelia, Paul Wednesday: Nan, Ophelia Thursday: Janice, Kevin Friday: Nan, Paul"
] | 2 |
Which one of the following could be an accurate staffing schedule?
|
Maggie's Deli is open exactly five days every week: Monday through Friday. Its staff, each of whom works on at least one day each week, consists of exactly six people—Janice, Kevin, Nan, Ophelia, Paul, and Seymour. Exactly three of them—Janice, Nan, and Paul—are supervisors. The deli's staffing is consistent with the following: Each day's staff consists of exactly two people, at least one of whom is a supervisor. Tuesday's and Wednesday's staffs both include Ophelia. Of the days Nan works each week, at least two are consecutive. Seymour does not work on any day before the first day Paul works that week. Any day on which Kevin works is the first day during the week that some other staff member works.
|
200510_4-G_4_19
|
[
"Janice",
"Kevin",
"Nan",
"Paul",
"Seymour"
] | 4 |
If Kevin and Paul work Thursday, who must work Friday?
|
Maggie's Deli is open exactly five days every week: Monday through Friday. Its staff, each of whom works on at least one day each week, consists of exactly six people—Janice, Kevin, Nan, Ophelia, Paul, and Seymour. Exactly three of them—Janice, Nan, and Paul—are supervisors. The deli's staffing is consistent with the following: Each day's staff consists of exactly two people, at least one of whom is a supervisor. Tuesday's and Wednesday's staffs both include Ophelia. Of the days Nan works each week, at least two are consecutive. Seymour does not work on any day before the first day Paul works that week. Any day on which Kevin works is the first day during the week that some other staff member works.
|
200510_4-G_4_20
|
[
"Janice works Monday and Tuesday.",
"Kevin and Paul work Friday.",
"Seymour works Monday and Friday.",
"Janice and Kevin work Thursday.",
"Paul works Monday and Friday."
] | 1 |
Each of the following could be true EXCEPT:
|
Maggie's Deli is open exactly five days every week: Monday through Friday. Its staff, each of whom works on at least one day each week, consists of exactly six people—Janice, Kevin, Nan, Ophelia, Paul, and Seymour. Exactly three of them—Janice, Nan, and Paul—are supervisors. The deli's staffing is consistent with the following: Each day's staff consists of exactly two people, at least one of whom is a supervisor. Tuesday's and Wednesday's staffs both include Ophelia. Of the days Nan works each week, at least two are consecutive. Seymour does not work on any day before the first day Paul works that week. Any day on which Kevin works is the first day during the week that some other staff member works.
|
200510_4-G_4_21
|
[
"Janice and Seymour",
"Kevin and Paul",
"Paul and Seymour",
"Nan and Ophelia",
"Janice and Nan"
] | 0 |
Which one of the following CANNOT be the pair of staff that works Monday?
|
Maggie's Deli is open exactly five days every week: Monday through Friday. Its staff, each of whom works on at least one day each week, consists of exactly six people—Janice, Kevin, Nan, Ophelia, Paul, and Seymour. Exactly three of them—Janice, Nan, and Paul—are supervisors. The deli's staffing is consistent with the following: Each day's staff consists of exactly two people, at least one of whom is a supervisor. Tuesday's and Wednesday's staffs both include Ophelia. Of the days Nan works each week, at least two are consecutive. Seymour does not work on any day before the first day Paul works that week. Any day on which Kevin works is the first day during the week that some other staff member works.
|
200510_4-G_4_22
|
[
"Nan works Wednesday and Friday only.",
"Seymour works Monday and Paul works Tuesday.",
"Kevin works Monday, Wednesday, and Friday.",
"Nan works Wednesday with Ophelia and Thursday with Kevin.",
"Ophelia and Kevin work Tuesday."
] | 1 |
Which one of the following could be true?
|
Henri has exactly five electrical appliances in his dormitory room: a hairdryer, a microwave oven, a razor, a television, and a vacuum. As a consequence of fire department regulations, Henri can use these appliances only in accordance with the following conditions: Henri cannot use both the hairdryer and the razor simultaneously. Henri cannot use both the hairdryer and the television simultaneously. When Henri uses the vacuum, he cannot at the same time use any of the following: the hairdryer, the razor, and the television.
|
200512_2-G_1_1
|
[
"the hairdryer and the razor",
"the hairdryer and the television",
"the razor and the television",
"the razor and the vacuum",
"the television and the vacuum"
] | 2 |
Which one of the following is a pair of appliances Henri could be using simultaneously?
|
Henri has exactly five electrical appliances in his dormitory room: a hairdryer, a microwave oven, a razor, a television, and a vacuum. As a consequence of fire department regulations, Henri can use these appliances only in accordance with the following conditions: Henri cannot use both the hairdryer and the razor simultaneously. Henri cannot use both the hairdryer and the television simultaneously. When Henri uses the vacuum, he cannot at the same time use any of the following: the hairdryer, the razor, and the television.
|
200512_2-G_1_2
|
[
"hairdryer",
"razor",
"vacuum",
"hairdryer, razor",
"hairdryer, vacuum"
] | 4 |
Assume that Henri is using exactly two appliances and is not using the microwave oven. Which one of the following is a list of all the appliances, other than the microwave oven, that Henri CANNOT be using?
|
Henri has exactly five electrical appliances in his dormitory room: a hairdryer, a microwave oven, a razor, a television, and a vacuum. As a consequence of fire department regulations, Henri can use these appliances only in accordance with the following conditions: Henri cannot use both the hairdryer and the razor simultaneously. Henri cannot use both the hairdryer and the television simultaneously. When Henri uses the vacuum, he cannot at the same time use any of the following: the hairdryer, the razor, and the television.
|
200512_2-G_1_3
|
[
"Henri uses the hairdryer while using the microwave oven.",
"Henri uses the microwave oven while using the razor.",
"Henri uses the microwave oven while using two other appliances.",
"Henri uses the television while using two other appliances.",
"Henri uses the vacuum while using two other appliances."
] | 4 |
Which one of the following CANNOT be true?
|
Henri has exactly five electrical appliances in his dormitory room: a hairdryer, a microwave oven, a razor, a television, and a vacuum. As a consequence of fire department regulations, Henri can use these appliances only in accordance with the following conditions: Henri cannot use both the hairdryer and the razor simultaneously. Henri cannot use both the hairdryer and the television simultaneously. When Henri uses the vacuum, he cannot at the same time use any of the following: the hairdryer, the razor, and the television.
|
200512_2-G_1_4
|
[
"one",
"two",
"three",
"four",
"five"
] | 0 |
If Henri were to use exactly three appliances, then what is the total number of different groups of three appliances any one of which could be the group of appliances he is using?
|
Henri has exactly five electrical appliances in his dormitory room: a hairdryer, a microwave oven, a razor, a television, and a vacuum. As a consequence of fire department regulations, Henri can use these appliances only in accordance with the following conditions: Henri cannot use both the hairdryer and the razor simultaneously. Henri cannot use both the hairdryer and the television simultaneously. When Henri uses the vacuum, he cannot at the same time use any of the following: the hairdryer, the razor, and the television.
|
200512_2-G_1_5
|
[
"Henri is using the hairdryer.",
"Henri is using the television.",
"Henri is not using the hairdryer.",
"Henri is not using the microwave oven.",
"Henri is not using the vacuum."
] | 0 |
Which one of the following statements, if true, guarantees that Henri is using no more than one of the following: the hairdryer, the razor, the television?
|
Henri has exactly five electrical appliances in his dormitory room: a hairdryer, a microwave oven, a razor, a television, and a vacuum. As a consequence of fire department regulations, Henri can use these appliances only in accordance with the following conditions: Henri cannot use both the hairdryer and the razor simultaneously. Henri cannot use both the hairdryer and the television simultaneously. When Henri uses the vacuum, he cannot at the same time use any of the following: the hairdryer, the razor, and the television.
|
200512_2-G_1_6
|
[
"Henri uses at most three appliances simultaneously.",
"Henri uses at most four appliances simultaneously.",
"Henri uses at most one other appliance while using the microwave oven.",
"Henri uses at most one other appliance while using the razor.",
"Henri uses at least two other appliances while using the hairdryer."
] | 0 |
Which one of the following must be true?
|
A farmer harvests eight separate fields—G, H, J, K, L, M, P, and T. Each field is harvested exactly once, and no two fields are harvested simultaneously. Once the harvesting of a field begins, no other fields are harvested until the harvesting of that field is complete. The farmer harvests the fields in an order consistent with the following conditions: Both P and G are harvested at some time before K. Both H and L are harvested at some time before J. K is harvested at some time before M but after L. T is harvested at some time before M.
|
200512_2-G_2_7
|
[
"J is the first field harvested.",
"K is the second field harvested.",
"M is the sixth field harvested.",
"G is the seventh field harvested.",
"T is the eighth field harvested."
] | 2 |
Which one of the following could be true?
|
A farmer harvests eight separate fields—G, H, J, K, L, M, P, and T. Each field is harvested exactly once, and no two fields are harvested simultaneously. Once the harvesting of a field begins, no other fields are harvested until the harvesting of that field is complete. The farmer harvests the fields in an order consistent with the following conditions: Both P and G are harvested at some time before K. Both H and L are harvested at some time before J. K is harvested at some time before M but after L. T is harvested at some time before M.
|
200512_2-G_2_8
|
[
"H",
"J",
"K",
"L",
"P"
] | 1 |
If M is the seventh field harvested, then any one of the following could be the fifth field harvested EXCEPT:
|
A farmer harvests eight separate fields—G, H, J, K, L, M, P, and T. Each field is harvested exactly once, and no two fields are harvested simultaneously. Once the harvesting of a field begins, no other fields are harvested until the harvesting of that field is complete. The farmer harvests the fields in an order consistent with the following conditions: Both P and G are harvested at some time before K. Both H and L are harvested at some time before J. K is harvested at some time before M but after L. T is harvested at some time before M.
|
200512_2-G_2_9
|
[
"G",
"J",
"M",
"P",
"T"
] | 2 |
Which one of the following CANNOT be the field that is harvested fifth?
|
A farmer harvests eight separate fields—G, H, J, K, L, M, P, and T. Each field is harvested exactly once, and no two fields are harvested simultaneously. Once the harvesting of a field begins, no other fields are harvested until the harvesting of that field is complete. The farmer harvests the fields in an order consistent with the following conditions: Both P and G are harvested at some time before K. Both H and L are harvested at some time before J. K is harvested at some time before M but after L. T is harvested at some time before M.
|
200512_2-G_2_10
|
[
"L is the first field harvested.",
"H is the second field harvested.",
"T is the fourth field harvested.",
"K is the seventh field harvested.",
"M is the eighth field harvested."
] | 4 |
If J is the third field harvested, then which one of the following must be true?
|
A farmer harvests eight separate fields—G, H, J, K, L, M, P, and T. Each field is harvested exactly once, and no two fields are harvested simultaneously. Once the harvesting of a field begins, no other fields are harvested until the harvesting of that field is complete. The farmer harvests the fields in an order consistent with the following conditions: Both P and G are harvested at some time before K. Both H and L are harvested at some time before J. K is harvested at some time before M but after L. T is harvested at some time before M.
|
200512_2-G_2_11
|
[
"G is harvested at some time before T.",
"H is harvested at some time before K.",
"J is harvested at some time before M.",
"K is harvested at some time before J.",
"T is harvested at some time before K."
] | 3 |
If H is the sixth field harvested, then which one of the following must be true?
|
A farmer harvests eight separate fields—G, H, J, K, L, M, P, and T. Each field is harvested exactly once, and no two fields are harvested simultaneously. Once the harvesting of a field begins, no other fields are harvested until the harvesting of that field is complete. The farmer harvests the fields in an order consistent with the following conditions: Both P and G are harvested at some time before K. Both H and L are harvested at some time before J. K is harvested at some time before M but after L. T is harvested at some time before M.
|
200512_2-G_2_12
|
[
"J is harvested at some time before G.",
"J is harvested at some time before T.",
"K is harvested at some time before T.",
"M is harvested at some time before H.",
"M is harvested at some time before J."
] | 4 |
If L is the fifth field harvested, then which one of the following could be true?
|
In a repair facility there are exactly six technicians: Stacy, Urma, Wim, Xena, Yolanda, and Zane. Each technician repairs machines of at least one of the following three types—radios, televisions, and VCRs—and no other types. The following conditions apply: Xena and exactly three other technicians repair radios. Yolanda repairs both televisions and VCRs. Stacy does not repair any type of machine that Yolanda repairs. Zane repairs more types of machines than Yolanda repairs. Wim does not repair any type of machine that Stacy repairs. Urma repairs exactly two types of machines.
|
200512_2-G_3_13
|
[
"one",
"two",
"three",
"four",
"five"
] | 2 |
For exactly how many of the six technicians is it possible to determine exactly which of the three types of machines each repairs?
|
In a repair facility there are exactly six technicians: Stacy, Urma, Wim, Xena, Yolanda, and Zane. Each technician repairs machines of at least one of the following three types—radios, televisions, and VCRs—and no other types. The following conditions apply: Xena and exactly three other technicians repair radios. Yolanda repairs both televisions and VCRs. Stacy does not repair any type of machine that Yolanda repairs. Zane repairs more types of machines than Yolanda repairs. Wim does not repair any type of machine that Stacy repairs. Urma repairs exactly two types of machines.
|
200512_2-G_3_14
|
[
"Of the types of machines repaired by Stacy there is exactly one type that Urma also repairs.",
"Of the types of machines repaired by Yolanda there is exactly one type that Xena also repairs.",
"Of the types of machines repaired by Wim there is exactly one type that Xena also repairs.",
"There is more than one type of machine that both Wim and Yolanda repair.",
"There is more than one type of machine that both Urma and Wim repair."
] | 0 |
Which one of the following must be true?
|
In a repair facility there are exactly six technicians: Stacy, Urma, Wim, Xena, Yolanda, and Zane. Each technician repairs machines of at least one of the following three types—radios, televisions, and VCRs—and no other types. The following conditions apply: Xena and exactly three other technicians repair radios. Yolanda repairs both televisions and VCRs. Stacy does not repair any type of machine that Yolanda repairs. Zane repairs more types of machines than Yolanda repairs. Wim does not repair any type of machine that Stacy repairs. Urma repairs exactly two types of machines.
|
200512_2-G_3_15
|
[
"Exactly one of the six technicians repairs exactly one type of machine.",
"Exactly two of the six technicians repair exactly one type of machine each.",
"Exactly three of the six technicians repair exactly one type of machine each.",
"Exactly one of the six technicians repairs exactly two types of machines.",
"Exactly three of the six technicians repair exactly two types of machines each."
] | 3 |
Which one of the following must be false?
|
In a repair facility there are exactly six technicians: Stacy, Urma, Wim, Xena, Yolanda, and Zane. Each technician repairs machines of at least one of the following three types—radios, televisions, and VCRs—and no other types. The following conditions apply: Xena and exactly three other technicians repair radios. Yolanda repairs both televisions and VCRs. Stacy does not repair any type of machine that Yolanda repairs. Zane repairs more types of machines than Yolanda repairs. Wim does not repair any type of machine that Stacy repairs. Urma repairs exactly two types of machines.
|
200512_2-G_3_16
|
[
"Stacy and Urma",
"Urma and Yolanda",
"Urma and Xena",
"Wim and Xena",
"Xena and Yolanda"
] | 2 |
Which one of the following pairs of technicians could repair all and only the same types of machines as each other?
|
In a repair facility there are exactly six technicians: Stacy, Urma, Wim, Xena, Yolanda, and Zane. Each technician repairs machines of at least one of the following three types—radios, televisions, and VCRs—and no other types. The following conditions apply: Xena and exactly three other technicians repair radios. Yolanda repairs both televisions and VCRs. Stacy does not repair any type of machine that Yolanda repairs. Zane repairs more types of machines than Yolanda repairs. Wim does not repair any type of machine that Stacy repairs. Urma repairs exactly two types of machines.
|
200512_2-G_3_17
|
[
"There is exactly one type of machine that both Urma and Wim repair.",
"There is exactly one type of machine that both Urma and Xena repair.",
"There is exactly one type of machine that both Urma and Yolanda repair.",
"There is exactly one type of machine that both Wim and Yolanda repair.",
"There is exactly one type of machine that both Xena and Yolanda repair."
] | 2 |
Which one of the following must be true?
|
Three folk groups—Glenside, Hilltopper, Levon—and three rock groups—Peasant, Query, Tinhead—each perform on one of two stages, north or south. Each stage has three two-hour performances: north at 6, 8, and 10; south at 8, 10, and 12. Each group performs individually and exactly once, consistent with the following conditions: Peasant performs at 6 or 12. Glenside performs at some time before Hilltopper. If any rock group performs at 10, no folk group does. Levon and Tinhead perform on different stages. Query performs immediately after a folk group, though not necessarily on the same stage.
|
200512_2-G_4_18
|
[
"Glenside, Levon, Query",
"Glenside, Query, Hilltopper",
"Hilltopper, Query, Peasant",
"Peasant, Levon, Tinhead",
"Peasant, Query, Levon"
] | 0 |
Which one of the following could be a complete and accurate ordering of performances on the north stage, from first to last?
|
Three folk groups—Glenside, Hilltopper, Levon—and three rock groups—Peasant, Query, Tinhead—each perform on one of two stages, north or south. Each stage has three two-hour performances: north at 6, 8, and 10; south at 8, 10, and 12. Each group performs individually and exactly once, consistent with the following conditions: Peasant performs at 6 or 12. Glenside performs at some time before Hilltopper. If any rock group performs at 10, no folk group does. Levon and Tinhead perform on different stages. Query performs immediately after a folk group, though not necessarily on the same stage.
|
200512_2-G_4_19
|
[
"Glenside",
"Hilltopper",
"Levon",
"Peasant",
"Tinhead"
] | 0 |
Which one of the following groups must perform earlier than 10?
|
Three folk groups—Glenside, Hilltopper, Levon—and three rock groups—Peasant, Query, Tinhead—each perform on one of two stages, north or south. Each stage has three two-hour performances: north at 6, 8, and 10; south at 8, 10, and 12. Each group performs individually and exactly once, consistent with the following conditions: Peasant performs at 6 or 12. Glenside performs at some time before Hilltopper. If any rock group performs at 10, no folk group does. Levon and Tinhead perform on different stages. Query performs immediately after a folk group, though not necessarily on the same stage.
|
200512_2-G_4_20
|
[
"Glenside",
"Hilltopper",
"Levon",
"Query",
"Tinhead"
] | 0 |
Which one of the following groups could perform at 6?
|
Three folk groups—Glenside, Hilltopper, Levon—and three rock groups—Peasant, Query, Tinhead—each perform on one of two stages, north or south. Each stage has three two-hour performances: north at 6, 8, and 10; south at 8, 10, and 12. Each group performs individually and exactly once, consistent with the following conditions: Peasant performs at 6 or 12. Glenside performs at some time before Hilltopper. If any rock group performs at 10, no folk group does. Levon and Tinhead perform on different stages. Query performs immediately after a folk group, though not necessarily on the same stage.
|
200512_2-G_4_21
|
[
"Glenside, Levon, Query",
"Peasant, Hilltopper, Tinhead",
"Peasant, Tinhead, Glenside",
"Peasant, Tinhead, Hilltopper",
"Peasant, Tinhead, Levon"
] | 3 |
If Query performs at 12, then which one of the following could be an accurate ordering of the performances on the north stage, from first to last?
|
Three folk groups—Glenside, Hilltopper, Levon—and three rock groups—Peasant, Query, Tinhead—each perform on one of two stages, north or south. Each stage has three two-hour performances: north at 6, 8, and 10; south at 8, 10, and 12. Each group performs individually and exactly once, consistent with the following conditions: Peasant performs at 6 or 12. Glenside performs at some time before Hilltopper. If any rock group performs at 10, no folk group does. Levon and Tinhead perform on different stages. Query performs immediately after a folk group, though not necessarily on the same stage.
|
200512_2-G_4_22
|
[
"A folk group performs at 6.",
"A folk group performs at 8.",
"A folk group performs at 12.",
"A rock group performs at 8.",
"A rock group performs at 12."
] | 1 |
If a rock group performs at 10, then which one of the following must be true?
|
During an international film retrospective lasting six consecutive days—day 1 through day 6—exactly six different films will be shown, one each day. Twelve films will be available for presentation, two each in French, Greek, Hungarian, Italian, Norwegian, and Turkish. The presentation of the films must conform to the following conditions: Neither day 2 nor day 4 is a day on which a film in Norwegian is shown. A film in Italian is not shown unless a film in Norwegian is going to be shown the next day. A film in Greek is not shown unless a film in Italian is going to be shown the next day.
|
200606_1-G_1_1
|
[
"French, Greek, Italian, Turkish, Norwegian, Hungarian",
"French, Hungarian, Italian, Norwegian, French, Hungarian",
"Hungarian, French, Norwegian, Greek, Norwegian, Italian",
"Norwegian, Turkish, Hungarian, Italian, French, Turkish",
"Turkish, French, Norwegian, Hungarian, French, Turkish"
] | 4 |
Which one of the following is an acceptable order of films for the retrospective, listed by their language, from day 1 through day 6?
|
During an international film retrospective lasting six consecutive days—day 1 through day 6—exactly six different films will be shown, one each day. Twelve films will be available for presentation, two each in French, Greek, Hungarian, Italian, Norwegian, and Turkish. The presentation of the films must conform to the following conditions: Neither day 2 nor day 4 is a day on which a film in Norwegian is shown. A film in Italian is not shown unless a film in Norwegian is going to be shown the next day. A film in Greek is not shown unless a film in Italian is going to be shown the next day.
|
200606_1-G_1_2
|
[
"French",
"Greek",
"Hungarian",
"Norwegian",
"Turkish"
] | 3 |
If two films in Italian are going to be shown, one on day 2 and one on day 5, then the film shown on day 1 could be in any one of the following languages EXCEPT:
|
During an international film retrospective lasting six consecutive days—day 1 through day 6—exactly six different films will be shown, one each day. Twelve films will be available for presentation, two each in French, Greek, Hungarian, Italian, Norwegian, and Turkish. The presentation of the films must conform to the following conditions: Neither day 2 nor day 4 is a day on which a film in Norwegian is shown. A film in Italian is not shown unless a film in Norwegian is going to be shown the next day. A film in Greek is not shown unless a film in Italian is going to be shown the next day.
|
200606_1-G_1_3
|
[
"A film in French is shown on day 3.",
"A film in Greek is shown on day 1.",
"A film in Hungarian is shown on day 6.",
"A film in Norwegian is shown on day 5.",
"A film in Turkish is shown on day 4."
] | 0 |
If two films in Italian are shown during the retrospective, which one of the following must be false?
|
During an international film retrospective lasting six consecutive days—day 1 through day 6—exactly six different films will be shown, one each day. Twelve films will be available for presentation, two each in French, Greek, Hungarian, Italian, Norwegian, and Turkish. The presentation of the films must conform to the following conditions: Neither day 2 nor day 4 is a day on which a film in Norwegian is shown. A film in Italian is not shown unless a film in Norwegian is going to be shown the next day. A film in Greek is not shown unless a film in Italian is going to be shown the next day.
|
200606_1-G_1_4
|
[
"day 1, day 3, day 5",
"day 2, day 4, day 5",
"day 2, day 5, day 6",
"day 1, day 3",
"day 2, day 4"
] | 1 |
Which one of the following is a complete and accurate list of the days, any one of which is a day on which a film in Italian could be shown?
|
During an international film retrospective lasting six consecutive days—day 1 through day 6—exactly six different films will be shown, one each day. Twelve films will be available for presentation, two each in French, Greek, Hungarian, Italian, Norwegian, and Turkish. The presentation of the films must conform to the following conditions: Neither day 2 nor day 4 is a day on which a film in Norwegian is shown. A film in Italian is not shown unless a film in Norwegian is going to be shown the next day. A film in Greek is not shown unless a film in Italian is going to be shown the next day.
|
200606_1-G_1_5
|
[
"a film in French, a film in Turkish",
"a film in Greek, a film in Hungarian",
"a film in Italian, a film in Norwegian",
"a film in Norwegian, a film in Turkish",
"a film in Turkish, a film in Greek"
] | 3 |
If two films in French are going to be shown, one on day 3 and one on day 5, which one of the following is a pair of films that could be shown on day 1 and day 6, respectively?
|
During an international film retrospective lasting six consecutive days—day 1 through day 6—exactly six different films will be shown, one each day. Twelve films will be available for presentation, two each in French, Greek, Hungarian, Italian, Norwegian, and Turkish. The presentation of the films must conform to the following conditions: Neither day 2 nor day 4 is a day on which a film in Norwegian is shown. A film in Italian is not shown unless a film in Norwegian is going to be shown the next day. A film in Greek is not shown unless a film in Italian is going to be shown the next day.
|
200606_1-G_1_6
|
[
"A film in Norwegian is shown on day 1.",
"A film in Norwegian is shown on day 5.",
"A film in Turkish is shown on day 4.",
"A film in Hungarian or else a film in Norwegian is shown on day 3.",
"A film in Hungarian or else a film in Turkish is shown on day 2."
] | 4 |
If neither a film in French nor a film in Italian is shown during the retrospective, which one of the following must be true?
|
During an international film retrospective lasting six consecutive days—day 1 through day 6—exactly six different films will be shown, one each day. Twelve films will be available for presentation, two each in French, Greek, Hungarian, Italian, Norwegian, and Turkish. The presentation of the films must conform to the following conditions: Neither day 2 nor day 4 is a day on which a film in Norwegian is shown. A film in Italian is not shown unless a film in Norwegian is going to be shown the next day. A film in Greek is not shown unless a film in Italian is going to be shown the next day.
|
200606_1-G_1_7
|
[
"day 1",
"day 3",
"day 5",
"day 1 or else day 3",
"day 3 or else day 5"
] | 3 |
If a film in Greek is going to be shown at some time after a film in Norwegian, then a film in Norwegian must be shown on
|
There are exactly five pieces of mail in a mailbox: a flyer, a letter, a magazine, a postcard, and a survey. Each piece of mail is addressed to exactly one of three housemates: Georgette, Jana, or Rini. Each housemate has at least one of the pieces of mail addressed to her. The following conditions must apply: Neither the letter nor the magazine is addressed to Georgette. If the letter is addressed to Rini, then the postcard is addressed to Jana. The housemate to whom the flyer is addressed has at least one of the other pieces of mail addressed to her as well.
|
200606_1-G_2_8
|
[
"Georgette: the flyer, the survey Jana: the letter Rini: the magazine",
"Georgette: the flyer, the postcard Jana: the letter, the magazine Rini: the survey",
"Georgette: the magazine, the survey Jana: the flyer, the letter Rini: the postcard",
"Georgette: the survey Jana: the flyer, the magazine Rini: the letter, the postcard",
"Georgette: the survey Jana: the letter, the magazine, the postcard Rini: the flyer"
] | 1 |
Which one of the following could be a complete and accurate matching of the pieces of mail to the housemates to whom they are addressed?
|
There are exactly five pieces of mail in a mailbox: a flyer, a letter, a magazine, a postcard, and a survey. Each piece of mail is addressed to exactly one of three housemates: Georgette, Jana, or Rini. Each housemate has at least one of the pieces of mail addressed to her. The following conditions must apply: Neither the letter nor the magazine is addressed to Georgette. If the letter is addressed to Rini, then the postcard is addressed to Jana. The housemate to whom the flyer is addressed has at least one of the other pieces of mail addressed to her as well.
|
200606_1-G_2_9
|
[
"the postcard",
"the letter, the postcard",
"the letter, the survey",
"the magazine, the survey",
"the letter, the magazine, the postcard"
] | 1 |
Which one of the following is a complete and accurate list of the pieces of mail, any one of which could be the only piece of mail addressed to Jana?
|
There are exactly five pieces of mail in a mailbox: a flyer, a letter, a magazine, a postcard, and a survey. Each piece of mail is addressed to exactly one of three housemates: Georgette, Jana, or Rini. Each housemate has at least one of the pieces of mail addressed to her. The following conditions must apply: Neither the letter nor the magazine is addressed to Georgette. If the letter is addressed to Rini, then the postcard is addressed to Jana. The housemate to whom the flyer is addressed has at least one of the other pieces of mail addressed to her as well.
|
200606_1-G_2_10
|
[
"the flyer, the letter, the magazine",
"the flyer, the letter, the postcard",
"the flyer, the letter, the survey",
"the flyer, the magazine, the postcard",
"the flyer, the magazine, the survey"
] | 4 |
Which one of the following CANNOT be a complete and accurate list of the pieces of mail addressed to Jana?
|
There are exactly five pieces of mail in a mailbox: a flyer, a letter, a magazine, a postcard, and a survey. Each piece of mail is addressed to exactly one of three housemates: Georgette, Jana, or Rini. Each housemate has at least one of the pieces of mail addressed to her. The following conditions must apply: Neither the letter nor the magazine is addressed to Georgette. If the letter is addressed to Rini, then the postcard is addressed to Jana. The housemate to whom the flyer is addressed has at least one of the other pieces of mail addressed to her as well.
|
200606_1-G_2_11
|
[
"the magazine, the postcard",
"the letter, the survey",
"the letter, the magazine",
"the flyer, the magazine",
"the flyer, the letter"
] | 1 |
Which one of the following CANNOT be a complete and accurate list of the pieces of mail addressed to Rini?
|
There are exactly five pieces of mail in a mailbox: a flyer, a letter, a magazine, a postcard, and a survey. Each piece of mail is addressed to exactly one of three housemates: Georgette, Jana, or Rini. Each housemate has at least one of the pieces of mail addressed to her. The following conditions must apply: Neither the letter nor the magazine is addressed to Georgette. If the letter is addressed to Rini, then the postcard is addressed to Jana. The housemate to whom the flyer is addressed has at least one of the other pieces of mail addressed to her as well.
|
200606_1-G_2_12
|
[
"The survey is addressed to Georgette.",
"The postcard is addressed to Rini.",
"The magazine is addressed to Jana.",
"The letter is addressed to Rini.",
"The flyer is addressed to Jana."
] | 4 |
If the magazine and the survey are both addressed to the same housemate, then which one of the following could be true?
|
A summer program offers at least one of the following seven courses: geography, history, literature, mathematics, psychology, sociology, zoology. The following restrictions on the program must apply: If mathematics is offered, then either literature or sociology (but not both) is offered. If literature is offered, then geography is also offered but psychology is not. If sociology is offered, then psychology is also offered but zoology is not. If geography is offered, then both history and zoology are also offered.
|
200606_1-G_3_13
|
[
"history, psychology",
"geography, history, literature",
"history, mathematics, psychology",
"literature, mathematics, psychology",
"history, literature, mathematics, sociology"
] | 0 |
Which one of the following could be a complete and accurate list of the courses offered by the summer program?
|
A summer program offers at least one of the following seven courses: geography, history, literature, mathematics, psychology, sociology, zoology. The following restrictions on the program must apply: If mathematics is offered, then either literature or sociology (but not both) is offered. If literature is offered, then geography is also offered but psychology is not. If sociology is offered, then psychology is also offered but zoology is not. If geography is offered, then both history and zoology are also offered.
|
200606_1-G_3_14
|
[
"Sociology is offered.",
"History is not offered.",
"Mathematics is not offered.",
"A total of two courses are offered.",
"Zoology is not offered."
] | 2 |
If the summer program offers literature, then which one of the following could be true?
|
A summer program offers at least one of the following seven courses: geography, history, literature, mathematics, psychology, sociology, zoology. The following restrictions on the program must apply: If mathematics is offered, then either literature or sociology (but not both) is offered. If literature is offered, then geography is also offered but psychology is not. If sociology is offered, then psychology is also offered but zoology is not. If geography is offered, then both history and zoology are also offered.
|
200606_1-G_3_15
|
[
"literature",
"mathematics",
"psychology",
"sociology",
"zoology"
] | 0 |
If history is not offered by the summer program, then which one of the following is another course that CANNOT be offered?
|
A summer program offers at least one of the following seven courses: geography, history, literature, mathematics, psychology, sociology, zoology. The following restrictions on the program must apply: If mathematics is offered, then either literature or sociology (but not both) is offered. If literature is offered, then geography is also offered but psychology is not. If sociology is offered, then psychology is also offered but zoology is not. If geography is offered, then both history and zoology are also offered.
|
200606_1-G_3_16
|
[
"Literature is offered.",
"Psychology is offered.",
"Sociology is offered.",
"At least three courses are offered.",
"At most four courses are offered."
] | 3 |
If the summer program offers mathematics, then which one of the following must be true?
|
A summer program offers at least one of the following seven courses: geography, history, literature, mathematics, psychology, sociology, zoology. The following restrictions on the program must apply: If mathematics is offered, then either literature or sociology (but not both) is offered. If literature is offered, then geography is also offered but psychology is not. If sociology is offered, then psychology is also offered but zoology is not. If geography is offered, then both history and zoology are also offered.
|
200606_1-G_3_17
|
[
"Both geography and psychology are offered.",
"Both geography and mathematics are offered.",
"Both psychology and mathematics are offered.",
"Both history and mathematics are offered.",
"Both geography and sociology are offered."
] | 4 |
Which one of the following must be false of the summer program?
|
Exactly eight computer processor chips—F, G, H, J, K, L, M, and O—are ranked according to their speed from first (fastest) to eighth (slowest). The ranking must be consistent with the following: There are no ties. Either F or G is ranked first. M is not the slowest. H is faster than J, with exactly one chip intermediate in speed between them. K is faster than L, with exactly two chips intermediate in speed between them. O is slower than both J and L.
|
200606_1-G_4_18
|
[
"F is ranked first and M is ranked eighth.",
"G is ranked fifth and O is ranked eighth.",
"J is ranked third and L is ranked seventh.",
"K is ranked second and H is ranked third.",
"M is ranked seventh and L is ranked eighth."
] | 1 |
Which one of the following could be true?
|
Exactly eight computer processor chips—F, G, H, J, K, L, M, and O—are ranked according to their speed from first (fastest) to eighth (slowest). The ranking must be consistent with the following: There are no ties. Either F or G is ranked first. M is not the slowest. H is faster than J, with exactly one chip intermediate in speed between them. K is faster than L, with exactly two chips intermediate in speed between them. O is slower than both J and L.
|
200606_1-G_4_19
|
[
"second",
"third",
"fourth",
"fifth",
"sixth"
] | 4 |
H CANNOT be ranked
|
Exactly eight computer processor chips—F, G, H, J, K, L, M, and O—are ranked according to their speed from first (fastest) to eighth (slowest). The ranking must be consistent with the following: There are no ties. Either F or G is ranked first. M is not the slowest. H is faster than J, with exactly one chip intermediate in speed between them. K is faster than L, with exactly two chips intermediate in speed between them. O is slower than both J and L.
|
200606_1-G_4_20
|
[
"G",
"H",
"M",
"J",
"L"
] | 1 |
If O is faster than F, then which one of the following chips could be ranked second?
|
Exactly eight computer processor chips—F, G, H, J, K, L, M, and O—are ranked according to their speed from first (fastest) to eighth (slowest). The ranking must be consistent with the following: There are no ties. Either F or G is ranked first. M is not the slowest. H is faster than J, with exactly one chip intermediate in speed between them. K is faster than L, with exactly two chips intermediate in speed between them. O is slower than both J and L.
|
200606_1-G_4_21
|
[
"second",
"third",
"fourth",
"fifth",
"sixth"
] | 3 |
If M is faster than J, then the fastest ranking J could have is
|
Exactly eight computer processor chips—F, G, H, J, K, L, M, and O—are ranked according to their speed from first (fastest) to eighth (slowest). The ranking must be consistent with the following: There are no ties. Either F or G is ranked first. M is not the slowest. H is faster than J, with exactly one chip intermediate in speed between them. K is faster than L, with exactly two chips intermediate in speed between them. O is slower than both J and L.
|
200606_1-G_4_22
|
[
"J is ranked no faster than fifth.",
"K is ranked no faster than third.",
"L is ranked no faster than fifth.",
"M is ranked no faster than third.",
"O is ranked no faster than eighth."
] | 2 |
Which one of the following must be true?
|
At each of six consecutive stops—1, 2, 3, 4, 5, and 6—that a traveler must make in that order as part of a trip, she can choose one from among exactly four airlines—L, M, N, and O—on which to continue. Her choices must conform to the following constraints: Whichever airline she chooses at a stop, she chooses one of the other airlines at the next stop. She chooses the same airline at stop 1 as she does at stop 6. She chooses the same airline at stop 2 as she does at stop 4. Whenever she chooses either L or M at a stop, she does not choose N at the next stop. At stop 5, she chooses N or O.
|
200609_3-G_1_1
|
[
"L, M, M, L, O, L",
"M, L, O, M, O, M",
"M, N, O, N, O, M",
"M, O, N, O, N, M",
"O, M, L, M, O, N"
] | 3 |
Which one of the following could be an accurate list of the airlines the traveler chooses at each stop, in order from 1 through 6?
|
At each of six consecutive stops—1, 2, 3, 4, 5, and 6—that a traveler must make in that order as part of a trip, she can choose one from among exactly four airlines—L, M, N, and O—on which to continue. Her choices must conform to the following constraints: Whichever airline she chooses at a stop, she chooses one of the other airlines at the next stop. She chooses the same airline at stop 1 as she does at stop 6. She chooses the same airline at stop 2 as she does at stop 4. Whenever she chooses either L or M at a stop, she does not choose N at the next stop. At stop 5, she chooses N or O.
|
200609_3-G_1_2
|
[
"L, M, N",
"L, O, N",
"M, L, N",
"M, L, O",
"N, O, N"
] | 1 |
If the traveler chooses N at stop 5, which one of the following could be an accurate list of the airlines she chooses at stops 1, 2, and 3, respectively?
|
At each of six consecutive stops—1, 2, 3, 4, 5, and 6—that a traveler must make in that order as part of a trip, she can choose one from among exactly four airlines—L, M, N, and O—on which to continue. Her choices must conform to the following constraints: Whichever airline she chooses at a stop, she chooses one of the other airlines at the next stop. She chooses the same airline at stop 1 as she does at stop 6. She chooses the same airline at stop 2 as she does at stop 4. Whenever she chooses either L or M at a stop, she does not choose N at the next stop. At stop 5, she chooses N or O.
|
200609_3-G_1_3
|
[
"M, O, and N",
"M, N, and O",
"N, M, and O",
"N, O, and M",
"O, M, and N"
] | 2 |
If the only airlines the traveler chooses for the trip are M, N, and O, and she chooses O at stop 5, then the airlines she chooses at stops 1, 2, and 3, must be, respectively,
|
At each of six consecutive stops—1, 2, 3, 4, 5, and 6—that a traveler must make in that order as part of a trip, she can choose one from among exactly four airlines—L, M, N, and O—on which to continue. Her choices must conform to the following constraints: Whichever airline she chooses at a stop, she chooses one of the other airlines at the next stop. She chooses the same airline at stop 1 as she does at stop 6. She chooses the same airline at stop 2 as she does at stop 4. Whenever she chooses either L or M at a stop, she does not choose N at the next stop. At stop 5, she chooses N or O.
|
200609_3-G_1_4
|
[
"L, M",
"L, O",
"M, L",
"M, O",
"O, N"
] | 4 |
Which one of the following CANNOT be an accurate list of the airlines the traveler chooses at stops 1 and 2, respectively?
|
At each of six consecutive stops—1, 2, 3, 4, 5, and 6—that a traveler must make in that order as part of a trip, she can choose one from among exactly four airlines—L, M, N, and O—on which to continue. Her choices must conform to the following constraints: Whichever airline she chooses at a stop, she chooses one of the other airlines at the next stop. She chooses the same airline at stop 1 as she does at stop 6. She chooses the same airline at stop 2 as she does at stop 4. Whenever she chooses either L or M at a stop, she does not choose N at the next stop. At stop 5, she chooses N or O.
|
200609_3-G_1_5
|
[
"M, N",
"N, L",
"N, O",
"O, L",
"O, N"
] | 1 |
If the traveler chooses O at stop 2, which one of the following could be an accurate list of the airlines she chooses at stops 5 and 6, respectively?
|
The members of a five-person committee will be selected from among three parents—F, G, and H—three students—K, L, and M—and four teachers—U, W, X, and Z. The selection of committee members will meet the following conditions: The committee must include exactly one student. F and H cannot both be selected. M and Z cannot both be selected. U and W cannot both be selected. F cannot be selected unless Z is also selected. W cannot be selected unless H is also selected.
|
200609_3-G_2_6
|
[
"F, G, K, L, Z",
"F, G, K, U, X",
"G, K, W, X, Z",
"H, K, U, W, X",
"H, L, W, X, Z"
] | 4 |
Which one of the following is an acceptable selection of committee members?
|
The members of a five-person committee will be selected from among three parents—F, G, and H—three students—K, L, and M—and four teachers—U, W, X, and Z. The selection of committee members will meet the following conditions: The committee must include exactly one student. F and H cannot both be selected. M and Z cannot both be selected. U and W cannot both be selected. F cannot be selected unless Z is also selected. W cannot be selected unless H is also selected.
|
200609_3-G_2_7
|
[
"U and X",
"K and L",
"G and M",
"G and K",
"F and G"
] | 3 |
If W and Z are selected, which one of the following is a pair of people who could also be selected?
|
The members of a five-person committee will be selected from among three parents—F, G, and H—three students—K, L, and M—and four teachers—U, W, X, and Z. The selection of committee members will meet the following conditions: The committee must include exactly one student. F and H cannot both be selected. M and Z cannot both be selected. U and W cannot both be selected. F cannot be selected unless Z is also selected. W cannot be selected unless H is also selected.
|
200609_3-G_2_8
|
[
"F and G",
"F and M",
"G and K",
"H and L",
"M and U"
] | 1 |
Which one of the following is a pair of people who CANNOT both be selected?
|
The members of a five-person committee will be selected from among three parents—F, G, and H—three students—K, L, and M—and four teachers—U, W, X, and Z. The selection of committee members will meet the following conditions: The committee must include exactly one student. F and H cannot both be selected. M and Z cannot both be selected. U and W cannot both be selected. F cannot be selected unless Z is also selected. W cannot be selected unless H is also selected.
|
200609_3-G_2_9
|
[
"F",
"G",
"L",
"M",
"Z"
] | 0 |
If W is selected, then any one of the following could also be selected EXCEPT:
|
The members of a five-person committee will be selected from among three parents—F, G, and H—three students—K, L, and M—and four teachers—U, W, X, and Z. The selection of committee members will meet the following conditions: The committee must include exactly one student. F and H cannot both be selected. M and Z cannot both be selected. U and W cannot both be selected. F cannot be selected unless Z is also selected. W cannot be selected unless H is also selected.
|
200609_3-G_2_10
|
[
"K",
"L",
"M",
"U",
"X"
] | 4 |
If the committee is to include exactly one parent, which one of the following is a person who must also be selected?
|
The members of a five-person committee will be selected from among three parents—F, G, and H—three students—K, L, and M—and four teachers—U, W, X, and Z. The selection of committee members will meet the following conditions: The committee must include exactly one student. F and H cannot both be selected. M and Z cannot both be selected. U and W cannot both be selected. F cannot be selected unless Z is also selected. W cannot be selected unless H is also selected.
|
200609_3-G_2_11
|
[
"F and G",
"G and H",
"H and K",
"K and U",
"U and X"
] | 1 |
If M is selected, then the committee must also include both
|
Within a five-year period from 1991 to 1995, each of three friends—Ramon, Sue, and Taylor—graduated. In that period, each bought his or her first car. The graduations and car purchases must be consistent with the following: Ramon graduated in some year before the year in which Taylor graduated. Taylor graduated in some year before the year in which he bought his first car. Sue bought her first car in some year before the year in which she graduated. Ramon and Sue graduated in the same year as each other. At least one of the friends graduated in 1993.
|
200609_3-G_3_12
|
[
"Ramon: 1991; Sue: 1991; Taylor: 1993",
"Ramon: 1992; Sue: 1992; Taylor: 1993",
"Ramon: 1992; Sue: 1993; Taylor: 1994",
"Ramon: 1993; Sue: 1993; Taylor: 1992",
"Ramon: 1993; Sue: 1993; Taylor: 1995"
] | 1 |
Which one of the following could be an accurate matching of each friend and the year in which she or he graduated?
|
Within a five-year period from 1991 to 1995, each of three friends—Ramon, Sue, and Taylor—graduated. In that period, each bought his or her first car. The graduations and car purchases must be consistent with the following: Ramon graduated in some year before the year in which Taylor graduated. Taylor graduated in some year before the year in which he bought his first car. Sue bought her first car in some year before the year in which she graduated. Ramon and Sue graduated in the same year as each other. At least one of the friends graduated in 1993.
|
200609_3-G_3_13
|
[
"Ramon graduated.",
"Ramon bought his first car.",
"Sue graduated.",
"Sue bought her first car.",
"Taylor graduated."
] | 1 |
Which one of the following could have taken place in 1995?
|
Within a five-year period from 1991 to 1995, each of three friends—Ramon, Sue, and Taylor—graduated. In that period, each bought his or her first car. The graduations and car purchases must be consistent with the following: Ramon graduated in some year before the year in which Taylor graduated. Taylor graduated in some year before the year in which he bought his first car. Sue bought her first car in some year before the year in which she graduated. Ramon and Sue graduated in the same year as each other. At least one of the friends graduated in 1993.
|
200609_3-G_3_14
|
[
"Two of the friends each bought his or her first car in 1991.",
"Two of the friends each bought his or her first car in 1992.",
"Two of the friends each bought his or her first car in 1993.",
"Two of the friends each bought his or her first car in 1994.",
"Two of the friends each bought his or her first car in 1995."
] | 2 |
Which one of the following must be false?
|
Within a five-year period from 1991 to 1995, each of three friends—Ramon, Sue, and Taylor—graduated. In that period, each bought his or her first car. The graduations and car purchases must be consistent with the following: Ramon graduated in some year before the year in which Taylor graduated. Taylor graduated in some year before the year in which he bought his first car. Sue bought her first car in some year before the year in which she graduated. Ramon and Sue graduated in the same year as each other. At least one of the friends graduated in 1993.
|
200609_3-G_3_15
|
[
"None of the three friends graduated in 1991.",
"None of the three friends graduated in 1992.",
"None of the three friends bought his or her first car in 1993.",
"None of the three friends graduated in 1994.",
"None of the three friends bought his or her first car in 1995."
] | 0 |
Which one of the following must be true?
|
Within a five-year period from 1991 to 1995, each of three friends—Ramon, Sue, and Taylor—graduated. In that period, each bought his or her first car. The graduations and car purchases must be consistent with the following: Ramon graduated in some year before the year in which Taylor graduated. Taylor graduated in some year before the year in which he bought his first car. Sue bought her first car in some year before the year in which she graduated. Ramon and Sue graduated in the same year as each other. At least one of the friends graduated in 1993.
|
200609_3-G_3_16
|
[
"Sue bought her first car in 1991.",
"Ramon graduated in 1992.",
"Taylor graduated in 1993.",
"Taylor bought his first car in 1994.",
"Ramon bought his first car in 1995."
] | 4 |
If Taylor graduated in the same year that Ramon bought his first car, then each of the following could be true EXCEPT:
|
Within a five-year period from 1991 to 1995, each of three friends—Ramon, Sue, and Taylor—graduated. In that period, each bought his or her first car. The graduations and car purchases must be consistent with the following: Ramon graduated in some year before the year in which Taylor graduated. Taylor graduated in some year before the year in which he bought his first car. Sue bought her first car in some year before the year in which she graduated. Ramon and Sue graduated in the same year as each other. At least one of the friends graduated in 1993.
|
200609_3-G_3_17
|
[
"Sue bought her first car in 1991.",
"Ramon bought his first car in 1992.",
"Ramon bought his first car in 1993.",
"Taylor bought his first car in 1994.",
"Taylor bought his first car in 1995."
] | 4 |
If Sue graduated in 1993, then which one of the following must be true?
|
A child eating alphabet soup notices that the only letters left in her bowl are one each of these six letters: T, U, W, X, Y, and Z. She plays a game with the remaining letters, eating them in the next three spoonfuls in accord with certain rules. Each of the six letters must be in exactly one of the next three spoonfuls, and each of the spoonfuls must have at least one and at most three of the letters. In addition, she obeys the following restrictions: The U is in a later spoonful than the T. The U is not in a later spoonful than the X. The Y is in a later spoonful than the W. The U is in the same spoonful as either the Y or the Z, but not both.
|
200609_3-G_4_18
|
[
"first: Y second: T, W third: U, X, Z",
"first: T, W second: U, X, Y third: Z",
"first: T second: U, Z third: W, X, Y",
"first: T, U, Z second: W third: X, Y",
"first: W second: T, X, Z third: U, Y"
] | 1 |
Which one of the following could be an accurate list of the spoonfuls and the letters in each of them?
|
A child eating alphabet soup notices that the only letters left in her bowl are one each of these six letters: T, U, W, X, Y, and Z. She plays a game with the remaining letters, eating them in the next three spoonfuls in accord with certain rules. Each of the six letters must be in exactly one of the next three spoonfuls, and each of the spoonfuls must have at least one and at most three of the letters. In addition, she obeys the following restrictions: The U is in a later spoonful than the T. The U is not in a later spoonful than the X. The Y is in a later spoonful than the W. The U is in the same spoonful as either the Y or the Z, but not both.
|
200609_3-G_4_19
|
[
"The Y is in the first spoonful.",
"The Z is in the first spoonful.",
"The T is in the second spoonful.",
"The X is in the second spoonful.",
"The W is in the third spoonful."
] | 3 |
If the Y is the only letter in one of the spoonfuls, then which one of the following could be true?
|
A child eating alphabet soup notices that the only letters left in her bowl are one each of these six letters: T, U, W, X, Y, and Z. She plays a game with the remaining letters, eating them in the next three spoonfuls in accord with certain rules. Each of the six letters must be in exactly one of the next three spoonfuls, and each of the spoonfuls must have at least one and at most three of the letters. In addition, she obeys the following restrictions: The U is in a later spoonful than the T. The U is not in a later spoonful than the X. The Y is in a later spoonful than the W. The U is in the same spoonful as either the Y or the Z, but not both.
|
200609_3-G_4_20
|
[
"The T is in the second spoonful.",
"The U is in the third spoonful.",
"The W is in the first spoonful.",
"The W is in the second spoonful.",
"The X is in the third spoonful."
] | 4 |
If the Z is in the first spoonful, then which one of the following must be true?
|
A child eating alphabet soup notices that the only letters left in her bowl are one each of these six letters: T, U, W, X, Y, and Z. She plays a game with the remaining letters, eating them in the next three spoonfuls in accord with certain rules. Each of the six letters must be in exactly one of the next three spoonfuls, and each of the spoonfuls must have at least one and at most three of the letters. In addition, she obeys the following restrictions: The U is in a later spoonful than the T. The U is not in a later spoonful than the X. The Y is in a later spoonful than the W. The U is in the same spoonful as either the Y or the Z, but not both.
|
200609_3-G_4_21
|
[
"T",
"T, W",
"T, X",
"T, W, Z",
"T, X, W, Z"
] | 3 |
Which one of the following is a complete list of letters, any one of which could be the only letter in the first spoonful?
|
A child eating alphabet soup notices that the only letters left in her bowl are one each of these six letters: T, U, W, X, Y, and Z. She plays a game with the remaining letters, eating them in the next three spoonfuls in accord with certain rules. Each of the six letters must be in exactly one of the next three spoonfuls, and each of the spoonfuls must have at least one and at most three of the letters. In addition, she obeys the following restrictions: The U is in a later spoonful than the T. The U is not in a later spoonful than the X. The Y is in a later spoonful than the W. The U is in the same spoonful as either the Y or the Z, but not both.
|
200609_3-G_4_22
|
[
"Exactly two letters are in the first spoonful.",
"Exactly three letters are in the first spoonful.",
"Exactly three letters are in the second spoonful.",
"Exactly one letter is in the third spoonful.",
"Exactly two letters are in the third spoonful."
] | 0 |
If the T is in the second spoonful, then which one of the following could be true?
|
A clown will select a costume consisting of two pieces and no others: a jacket and overalls. One piece of the costume will be entirely one color, and the other piece will be plaid. Selection is subject to the following restrictions: If the jacket is plaid, then there must be exactly three colors in it. If the overalls are plaid, then there must be exactly two colors in them. The jacket and overalls must have exactly one color in common. Green, red, and violet are the only colors that can be in the jacket. Red, violet, and yellow are the only colors that can be in the overalls.
|
200612_4-G_1_1
|
[
"red red",
"red violet, yellow",
"violet green, violet",
"violet red, violet",
"violet red, violet, yellow"
] | 3 |
Which one of the following could be a complete and accurate list of the colors in the costume? Jacket Overalls
|
A clown will select a costume consisting of two pieces and no others: a jacket and overalls. One piece of the costume will be entirely one color, and the other piece will be plaid. Selection is subject to the following restrictions: If the jacket is plaid, then there must be exactly three colors in it. If the overalls are plaid, then there must be exactly two colors in them. The jacket and overalls must have exactly one color in common. Green, red, and violet are the only colors that can be in the jacket. Red, violet, and yellow are the only colors that can be in the overalls.
|
200612_4-G_1_2
|
[
"At least part of the jacket is green.",
"At least part of the jacket is red.",
"The overalls are red and violet.",
"The overalls are red and yellow.",
"The overalls are violet and yellow."
] | 0 |
If there are exactly two colors in the costume, then which one of the following must be false?
|
A clown will select a costume consisting of two pieces and no others: a jacket and overalls. One piece of the costume will be entirely one color, and the other piece will be plaid. Selection is subject to the following restrictions: If the jacket is plaid, then there must be exactly three colors in it. If the overalls are plaid, then there must be exactly two colors in them. The jacket and overalls must have exactly one color in common. Green, red, and violet are the only colors that can be in the jacket. Red, violet, and yellow are the only colors that can be in the overalls.
|
200612_4-G_1_3
|
[
"The overalls are plaid.",
"No part of the jacket is red.",
"No part of the jacket is violet.",
"At least part of the overalls are yellow.",
"At least part of the overalls are violet."
] | 4 |
If at least part of the jacket is green, then which one of the following could be true?
|
A clown will select a costume consisting of two pieces and no others: a jacket and overalls. One piece of the costume will be entirely one color, and the other piece will be plaid. Selection is subject to the following restrictions: If the jacket is plaid, then there must be exactly three colors in it. If the overalls are plaid, then there must be exactly two colors in them. The jacket and overalls must have exactly one color in common. Green, red, and violet are the only colors that can be in the jacket. Red, violet, and yellow are the only colors that can be in the overalls.
|
200612_4-G_1_4
|
[
"Both green and red are colors used in the costume.",
"Both green and violet are colors used in the costume.",
"Both green and yellow are colors used in the costume.",
"Both red and violet are colors used in the costume.",
"Both violet and yellow are colors used in the costume."
] | 2 |
Which one of the following must be false?
|
A clown will select a costume consisting of two pieces and no others: a jacket and overalls. One piece of the costume will be entirely one color, and the other piece will be plaid. Selection is subject to the following restrictions: If the jacket is plaid, then there must be exactly three colors in it. If the overalls are plaid, then there must be exactly two colors in them. The jacket and overalls must have exactly one color in common. Green, red, and violet are the only colors that can be in the jacket. Red, violet, and yellow are the only colors that can be in the overalls.
|
200612_4-G_1_5
|
[
"entirely red or else red and violet plaid",
"entirely yellow or else violet and yellow plaid",
"entirely violet or else red and violet plaid",
"entirely red or else entirely yellow",
"entirely red or else entirely violet"
] | 4 |
If there are exactly three colors in the costume, the overalls must be
|
Six hotel suites—F, G, H, J, K, L—are ranked from most expensive (first) to least expensive (sixth). There are no ties. The ranking must be consistent with the following conditions: H is more expensive than L. If G is more expensive than H, then neither K nor L is more expensive than J. If H is more expensive than G, then neither J nor L is more expensive than K. F is more expensive than G, or else F is more expensive than H, but not both.
|
200612_4-G_2_6
|
[
"G, F, H, L, J, K",
"H, K, F, J, G, L",
"J, H, F, K, G, L",
"J, K, G, H, L, F",
"K, J, L, H, F, G"
] | 1 |
Which one of the following could be the ranking of the suites, from most expensive to least expensive?
|
Six hotel suites—F, G, H, J, K, L—are ranked from most expensive (first) to least expensive (sixth). There are no ties. The ranking must be consistent with the following conditions: H is more expensive than L. If G is more expensive than H, then neither K nor L is more expensive than J. If H is more expensive than G, then neither J nor L is more expensive than K. F is more expensive than G, or else F is more expensive than H, but not both.
|
200612_4-G_2_7
|
[
"H is more expensive than F.",
"H is more expensive than G.",
"K is more expensive than F.",
"K is more expensive than J.",
"L is more expensive than F."
] | 2 |
If G is the second most expensive suite, then which one of the following could be true?
|
Six hotel suites—F, G, H, J, K, L—are ranked from most expensive (first) to least expensive (sixth). There are no ties. The ranking must be consistent with the following conditions: H is more expensive than L. If G is more expensive than H, then neither K nor L is more expensive than J. If H is more expensive than G, then neither J nor L is more expensive than K. F is more expensive than G, or else F is more expensive than H, but not both.
|
200612_4-G_2_8
|
[
"F",
"G",
"H",
"J",
"K"
] | 0 |
Which one of the following CANNOT be the most expensive suite?
|
Six hotel suites—F, G, H, J, K, L—are ranked from most expensive (first) to least expensive (sixth). There are no ties. The ranking must be consistent with the following conditions: H is more expensive than L. If G is more expensive than H, then neither K nor L is more expensive than J. If H is more expensive than G, then neither J nor L is more expensive than K. F is more expensive than G, or else F is more expensive than H, but not both.
|
200612_4-G_2_9
|
[
"F is more expensive than H.",
"F is more expensive than K.",
"G is more expensive than H.",
"G is more expensive than J.",
"G is more expensive than L."
] | 3 |
If L is more expensive than F, then which one of the following could be true?
|
Six hotel suites—F, G, H, J, K, L—are ranked from most expensive (first) to least expensive (sixth). There are no ties. The ranking must be consistent with the following conditions: H is more expensive than L. If G is more expensive than H, then neither K nor L is more expensive than J. If H is more expensive than G, then neither J nor L is more expensive than K. F is more expensive than G, or else F is more expensive than H, but not both.
|
200612_4-G_2_10
|
[
"F is more expensive than H.",
"G is more expensive than F.",
"G is more expensive than H.",
"J is more expensive than L.",
"L is more expensive than K."
] | 3 |
If H is more expensive than J and less expensive than K, then which one of the following could be true?
|
A locally known guitarist's demo CD contains exactly seven different songs—S, T, V, W, X, Y, and Z. Each song occupies exactly one of the CD's seven tracks. Some of the songs are rock classics; the others are new compositions. The following conditions must hold: S occupies the fourth track of the CD. Both W and Y precede S on the CD. T precedes W on the CD. A rock classic occupies the sixth track of the CD. Each rock classic is immediately preceded on the CD by a new composition. Z is a rock classic.
|
200612_4-G_3_11
|
[
"T, W, V, S, Y, X, Z",
"V, Y, T, S, W, Z, X",
"X, Y, W, S, T, Z, S",
"Y, T, W, S, X, Z, V",
"Z, T, X, W, V, Y, S"
] | 3 |
Which one of the following could be the order of the songs on the CD, from the first track through the seventh?
|
A locally known guitarist's demo CD contains exactly seven different songs—S, T, V, W, X, Y, and Z. Each song occupies exactly one of the CD's seven tracks. Some of the songs are rock classics; the others are new compositions. The following conditions must hold: S occupies the fourth track of the CD. Both W and Y precede S on the CD. T precedes W on the CD. A rock classic occupies the sixth track of the CD. Each rock classic is immediately preceded on the CD by a new composition. Z is a rock classic.
|
200612_4-G_3_12
|
[
"S and V",
"S and W",
"T and Z",
"T and Y",
"V and Z"
] | 4 |
Which one of the following is a pair of songs that must occupy consecutive tracks on the CD?
|
A locally known guitarist's demo CD contains exactly seven different songs—S, T, V, W, X, Y, and Z. Each song occupies exactly one of the CD's seven tracks. Some of the songs are rock classics; the others are new compositions. The following conditions must hold: S occupies the fourth track of the CD. Both W and Y precede S on the CD. T precedes W on the CD. A rock classic occupies the sixth track of the CD. Each rock classic is immediately preceded on the CD by a new composition. Z is a rock classic.
|
200612_4-G_3_13
|
[
"S",
"T",
"W",
"X",
"Y"
] | 3 |
Which one of the following songs must be a new composition?
|
A locally known guitarist's demo CD contains exactly seven different songs—S, T, V, W, X, Y, and Z. Each song occupies exactly one of the CD's seven tracks. Some of the songs are rock classics; the others are new compositions. The following conditions must hold: S occupies the fourth track of the CD. Both W and Y precede S on the CD. T precedes W on the CD. A rock classic occupies the sixth track of the CD. Each rock classic is immediately preceded on the CD by a new composition. Z is a rock classic.
|
200612_4-G_3_14
|
[
"S is a rock classic.",
"V is a rock classic.",
"Y is a rock classic.",
"T is a new composition.",
"W is a new composition."
] | 3 |
If W precedes Y on the CD, then which one of the following must be true?
|
A locally known guitarist's demo CD contains exactly seven different songs—S, T, V, W, X, Y, and Z. Each song occupies exactly one of the CD's seven tracks. Some of the songs are rock classics; the others are new compositions. The following conditions must hold: S occupies the fourth track of the CD. Both W and Y precede S on the CD. T precedes W on the CD. A rock classic occupies the sixth track of the CD. Each rock classic is immediately preceded on the CD by a new composition. Z is a rock classic.
|
200612_4-G_3_15
|
[
"V occupies the seventh track of the CD.",
"X occupies the fifth track of the CD.",
"Y occupies the third track of the CD.",
"T is a rock classic.",
"W is a rock classic."
] | 4 |
If there are exactly two songs on the CD that both precede V and are preceded by Y, then which one of the following could be true?
|
A courier delivers exactly eight parcels—G, H, J, K, L, M, N, and O. No two parcels are delivered at the same time, nor is any parcel delivered more than once. The following conditions must apply: L is delivered later than H. K is delivered earlier than O. H is delivered earlier than M. O is delivered later than G. M is delivered earlier than G. Both N and J are delivered earlier than M.
|
200612_4-G_4_16
|
[
"N, H, K, M, J, G, O, L",
"H, N, J, K, G, O, L, M",
"J, H, N, M, K, O, G, L",
"N, J, H, L, M, K, G, O",
"K, N, J, M, G, H, O, L"
] | 3 |
Which one of the following could be the order of deliveries from first to last?
|
A courier delivers exactly eight parcels—G, H, J, K, L, M, N, and O. No two parcels are delivered at the same time, nor is any parcel delivered more than once. The following conditions must apply: L is delivered later than H. K is delivered earlier than O. H is delivered earlier than M. O is delivered later than G. M is delivered earlier than G. Both N and J are delivered earlier than M.
|
200612_4-G_4_17
|
[
"At least one parcel is delivered earlier than K is delivered.",
"At least two parcels are delivered later than G is delivered.",
"At least four parcels are delivered later than H is delivered.",
"At least four parcels are delivered later than J is delivered.",
"At least four parcels are delivered earlier than M is delivered."
] | 2 |
Which one of the following must be true?
|
A courier delivers exactly eight parcels—G, H, J, K, L, M, N, and O. No two parcels are delivered at the same time, nor is any parcel delivered more than once. The following conditions must apply: L is delivered later than H. K is delivered earlier than O. H is delivered earlier than M. O is delivered later than G. M is delivered earlier than G. Both N and J are delivered earlier than M.
|
200612_4-G_4_18
|
[
"G is the fifth parcel delivered.",
"O is the seventh parcel delivered.",
"J is delivered later than H.",
"K is delivered later than N.",
"G is delivered later than L."
] | 3 |
If M is the fourth parcel delivered, then which one of the following must be true?
|
A courier delivers exactly eight parcels—G, H, J, K, L, M, N, and O. No two parcels are delivered at the same time, nor is any parcel delivered more than once. The following conditions must apply: L is delivered later than H. K is delivered earlier than O. H is delivered earlier than M. O is delivered later than G. M is delivered earlier than G. Both N and J are delivered earlier than M.
|
200612_4-G_4_19
|
[
"K is the fifth parcel delivered.",
"L is the sixth parcel delivered.",
"M is the sixth parcel delivered.",
"G is the seventh parcel delivered.",
"O is the seventh parcel delivered."
] | 0 |
If H is the fourth parcel delivered, then each of the following could be true EXCEPT:
|
A courier delivers exactly eight parcels—G, H, J, K, L, M, N, and O. No two parcels are delivered at the same time, nor is any parcel delivered more than once. The following conditions must apply: L is delivered later than H. K is delivered earlier than O. H is delivered earlier than M. O is delivered later than G. M is delivered earlier than G. Both N and J are delivered earlier than M.
|
200612_4-G_4_20
|
[
"H is delivered later than K.",
"J is delivered later than G.",
"L is delivered later than O.",
"M is delivered later than L.",
"N is delivered later than H."
] | 1 |
Each of the following could be true EXCEPT:
|
A courier delivers exactly eight parcels—G, H, J, K, L, M, N, and O. No two parcels are delivered at the same time, nor is any parcel delivered more than once. The following conditions must apply: L is delivered later than H. K is delivered earlier than O. H is delivered earlier than M. O is delivered later than G. M is delivered earlier than G. Both N and J are delivered earlier than M.
|
200612_4-G_4_21
|
[
"G is the fifth parcel delivered.",
"M is the fifth parcel delivered.",
"H is the fourth parcel delivered.",
"L is the fourth parcel delivered.",
"J is the third parcel delivered."
] | 2 |
If K is the seventh parcel delivered, then each of the following could be true EXCEPT:
|
A courier delivers exactly eight parcels—G, H, J, K, L, M, N, and O. No two parcels are delivered at the same time, nor is any parcel delivered more than once. The following conditions must apply: L is delivered later than H. K is delivered earlier than O. H is delivered earlier than M. O is delivered later than G. M is delivered earlier than G. Both N and J are delivered earlier than M.
|
200612_4-G_4_22
|
[
"N is the second parcel delivered.",
"L is the third parcel delivered.",
"H is the fourth parcel delivered.",
"K is the fifth parcel delivered.",
"M is the sixth parcel delivered."
] | 2 |
If L is delivered earlier than K, then which one of the following must be false?
|
A company employee generates a series of five-digit product codes in accordance with the following rules: The codes use the digits 0, 1, 2, 3, and 4, and no others. Each digit occurs exactly once in any code. The second digit has a value exactly twice that of the first digit. The value of the third digit is less than the value of the fifth digit.
|
200706_1-G_1_1
|
[
"first digit is 2",
"second digit is 0",
"third digit is 3",
"fourth digit is 4",
"fourth digit is 0"
] | 0 |
If the last digit of an acceptable product code is 1, it must be true that the
|
A company employee generates a series of five-digit product codes in accordance with the following rules: The codes use the digits 0, 1, 2, 3, and 4, and no others. Each digit occurs exactly once in any code. The second digit has a value exactly twice that of the first digit. The value of the third digit is less than the value of the fifth digit.
|
200706_1-G_1_2
|
[
"The digit 1 appears in some position before the digit 2.",
"The digit 1 appears in some position before the digit 3.",
"The digit 2 appears in some position before the digit 3.",
"The digit 3 appears in some position before the digit 0.",
"The digit 4 appears in some position before the digit 3."
] | 2 |
Which one of the following must be true about any acceptable product code?
|
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