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Exactly six trade representatives negotiate a treaty: Klosnik, Londi, Manley, Neri, Osata, Poirier. There are exactly six chairs evenly spaced around a circular table. The chairs are numbered 1 through 6, with successively numbered chairs next to each other and chair number 1 next to chair number 6. Each chair is occupied by exactly one of the representatives. The following conditions apply: Poirier sits immediately next to Neri. Londi sits immediately next to Manley, Neri, or both. Klosnik does not sit immediately next to Manley. If Osata sits immediately next to Poirier, Osata does not sit immediately next to Manley. | Which one of the following seating arrangements of the six representatives in chairs 1 through 6 would NOT violate the stated conditions? | [
"Klosnik, Poirier, Neri, Manley, Osata, Londi",
"Klosnik, Londi, Manley, Poirier, Neri, Osata",
"Klosnik, Londi, Manley, Osata, Poirier, Neri",
"Klosnik, Osata, Poirier, Neri, Londi, Manley",
"Klosnik, Neri, Londi, Osata, Manley, Poirier"
] | 1 |
Exactly six trade representatives negotiate a treaty: Klosnik, Londi, Manley, Neri, Osata, Poirier. There are exactly six chairs evenly spaced around a circular table. The chairs are numbered 1 through 6, with successively numbered chairs next to each other and chair number 1 next to chair number 6. Each chair is occupied by exactly one of the representatives. The following conditions apply: Poirier sits immediately next to Neri. Londi sits immediately next to Manley, Neri, or both. Klosnik does not sit immediately next to Manley. If Osata sits immediately next to Poirier, Osata does not sit immediately next to Manley. | If Londi sits immediately next to Poirier, which one of the following is a pair of representatives who must sit immediately next to each other? | [
"Klosnik and Osata",
"Londi and Neri",
"Londi and Osata",
"Manley and Neri",
"Manley and Poirier"
] | 0 |
Exactly six trade representatives negotiate a treaty: Klosnik, Londi, Manley, Neri, Osata, Poirier. There are exactly six chairs evenly spaced around a circular table. The chairs are numbered 1 through 6, with successively numbered chairs next to each other and chair number 1 next to chair number 6. Each chair is occupied by exactly one of the representatives. The following conditions apply: Poirier sits immediately next to Neri. Londi sits immediately next to Manley, Neri, or both. Klosnik does not sit immediately next to Manley. If Osata sits immediately next to Poirier, Osata does not sit immediately next to Manley. | If Klosnik sits directly between Londi and Poirier, then Manley must sit directly between | [
"Londi and Neri",
"Londi and Osata",
"Neri and Osata",
"Neri and Poirier",
"Osata and Poirier"
] | 1 |
Exactly six trade representatives negotiate a treaty: Klosnik, Londi, Manley, Neri, Osata, Poirier. There are exactly six chairs evenly spaced around a circular table. The chairs are numbered 1 through 6, with successively numbered chairs next to each other and chair number 1 next to chair number 6. Each chair is occupied by exactly one of the representatives. The following conditions apply: Poirier sits immediately next to Neri. Londi sits immediately next to Manley, Neri, or both. Klosnik does not sit immediately next to Manley. If Osata sits immediately next to Poirier, Osata does not sit immediately next to Manley. | If Neri sits immediately next to Manley, then Klosnik can sit directly between | [
"Londi and Manley",
"Londi and Poirier",
"Neri and Osata",
"Neri and Poirier",
"Poirier and Osata"
] | 4 |
Exactly six trade representatives negotiate a treaty: Klosnik, Londi, Manley, Neri, Osata, Poirier. There are exactly six chairs evenly spaced around a circular table. The chairs are numbered 1 through 6, with successively numbered chairs next to each other and chair number 1 next to chair number 6. Each chair is occupied by exactly one of the representatives. The following conditions apply: Poirier sits immediately next to Neri. Londi sits immediately next to Manley, Neri, or both. Klosnik does not sit immediately next to Manley. If Osata sits immediately next to Poirier, Osata does not sit immediately next to Manley. | If Londi sits immediately next to Manley, then which one of the following is a complete and accurate list of representatives any one of whom could also sit immediately next to Londi? | [
"Klosnik",
"Klosnik, Neri",
"Neri, Poirier",
"Klosnik, Osata, Poirier",
"Klosnik, Neri, Osata, Poirier"
] | 4 |
Exactly six trade representatives negotiate a treaty: Klosnik, Londi, Manley, Neri, Osata, Poirier. There are exactly six chairs evenly spaced around a circular table. The chairs are numbered 1 through 6, with successively numbered chairs next to each other and chair number 1 next to chair number 6. Each chair is occupied by exactly one of the representatives. The following conditions apply: Poirier sits immediately next to Neri. Londi sits immediately next to Manley, Neri, or both. Klosnik does not sit immediately next to Manley. If Osata sits immediately next to Poirier, Osata does not sit immediately next to Manley. | If Londi sits immediately next to Neri, which one of the following statements must be false? | [
"Klosnik sits immediately next to Osata.",
"Londi sits immediately next to Manley.",
"Osata sits immediately next to Poirier.",
"Neri sits directly between Londi and Poirier.",
"Osata sits directly between Klosnik and Manley."
] | 2 |
Exactly six trade representatives negotiate a treaty: Klosnik, Londi, Manley, Neri, Osata, Poirier. There are exactly six chairs evenly spaced around a circular table. The chairs are numbered 1 through 6, with successively numbered chairs next to each other and chair number 1 next to chair number 6. Each chair is occupied by exactly one of the representatives. The following conditions apply: Poirier sits immediately next to Neri. Londi sits immediately next to Manley, Neri, or both. Klosnik does not sit immediately next to Manley. If Osata sits immediately next to Poirier, Osata does not sit immediately next to Manley. | If Klosnik sits immediately next to Osata, then Londi CANNOT sit directly between | [
"Klosnik and Manley",
"Klosnik and Neri",
"Manley and Neri",
"Manley and Poirier",
"Neri and Osata"
] | 4 |
A small software firm has four offices, numbered 1, 2, 3, and 4. Each of its offices has exactly one computer and exactly one printer. Each of these eight machines was bought in either 1987, 1988, or 1989. The eight machines were bought in a manner consistent with the following conditions: The computer in each office was bought either in an earlier year than or in the same year as the printer in that office. The computer in office 2 and the printer in office 1 were bought in the same year. The computer in office 3 and the printer in office 4 were bought in the same year. The computer in office 2 and the computer in office 3 were bought in different years. The computer in office 1 and the printer in office 3 were bought in 1988. | If the computer in office 3 was bought in an earlier year than the printer in office 3 was, then which one of the following statements could be true? | [
"The computer in office 2 was bought in 1987.",
"The computer in office 2 was bought in 1988.",
"The computer in office 4 was bought in 1988.",
"The printer in office 4 was bought in 1988.",
"The printer in office 4 was bought in 1989."
] | 1 |
A small software firm has four offices, numbered 1, 2, 3, and 4. Each of its offices has exactly one computer and exactly one printer. Each of these eight machines was bought in either 1987, 1988, or 1989. The eight machines were bought in a manner consistent with the following conditions: The computer in each office was bought either in an earlier year than or in the same year as the printer in that office. The computer in office 2 and the printer in office 1 were bought in the same year. The computer in office 3 and the printer in office 4 were bought in the same year. The computer in office 2 and the computer in office 3 were bought in different years. The computer in office 1 and the printer in office 3 were bought in 1988. | Which one of the following statements could be true? | [
"The printer in office 1 was bought in 1987.",
"The computer in office 2 was bought in 1987.",
"The computer in office 3 was bought in 1989.",
"The printer in office 4 was bought in 1988.",
"The printer in office 4 was bought in 1989."
] | 3 |
A small software firm has four offices, numbered 1, 2, 3, and 4. Each of its offices has exactly one computer and exactly one printer. Each of these eight machines was bought in either 1987, 1988, or 1989. The eight machines were bought in a manner consistent with the following conditions: The computer in each office was bought either in an earlier year than or in the same year as the printer in that office. The computer in office 2 and the printer in office 1 were bought in the same year. The computer in office 3 and the printer in office 4 were bought in the same year. The computer in office 2 and the computer in office 3 were bought in different years. The computer in office 1 and the printer in office 3 were bought in 1988. | If as few of the eight machines as possible were bought in 1987, then what is the exact number of machines that were bought in 1987? | [
"0",
"1",
"2",
"3",
"4"
] | 0 |
A small software firm has four offices, numbered 1, 2, 3, and 4. Each of its offices has exactly one computer and exactly one printer. Each of these eight machines was bought in either 1987, 1988, or 1989. The eight machines were bought in a manner consistent with the following conditions: The computer in each office was bought either in an earlier year than or in the same year as the printer in that office. The computer in office 2 and the printer in office 1 were bought in the same year. The computer in office 3 and the printer in office 4 were bought in the same year. The computer in office 2 and the computer in office 3 were bought in different years. The computer in office 1 and the printer in office 3 were bought in 1988. | If the computer in office 4 was bought in 1988, then which one of the following statements must be true? | [
"The printer in office 1 was bought in 1988.",
"The printer in office 1 was bought in 1989.",
"The computer in office 2 was bought in 1988.",
"The computer in office 3 was bought in 1987.",
"The printer in office 4 was bought in 1989."
] | 1 |
A small software firm has four offices, numbered 1, 2, 3, and 4. Each of its offices has exactly one computer and exactly one printer. Each of these eight machines was bought in either 1987, 1988, or 1989. The eight machines were bought in a manner consistent with the following conditions: The computer in each office was bought either in an earlier year than or in the same year as the printer in that office. The computer in office 2 and the printer in office 1 were bought in the same year. The computer in office 3 and the printer in office 4 were bought in the same year. The computer in office 2 and the computer in office 3 were bought in different years. The computer in office 1 and the printer in office 3 were bought in 1988. | If the computer in office 3 was bought in 1988, then which one of the following statements could be true? | [
"The printer in office 1 was bought in 1988.",
"The computer in office 2 was bought in 1987.",
"The printer in office 2 was bought in 1988.",
"The computer in office 4 was bought in 1987.",
"The printer in office 4 was bought in 1989."
] | 3 |
A small software firm has four offices, numbered 1, 2, 3, and 4. Each of its offices has exactly one computer and exactly one printer. Each of these eight machines was bought in either 1987, 1988, or 1989. The eight machines were bought in a manner consistent with the following conditions: The computer in each office was bought either in an earlier year than or in the same year as the printer in that office. The computer in office 2 and the printer in office 1 were bought in the same year. The computer in office 3 and the printer in office 4 were bought in the same year. The computer in office 2 and the computer in office 3 were bought in different years. The computer in office 1 and the printer in office 3 were bought in 1988. | Suppose that the computer in office 2 and the computer in office 3 had been bought in the same year as each other. If all of the other conditions remained the same, then which one of the following machines could have been bought in 1989? | [
"the printer in office 1",
"the computer in office 2",
"the printer in office 2",
"the computer in office 4",
"the printer in office 4"
] | 2 |
The eight partners of a law firm are Gregg, Hodges, Ivan, James, King, MacNeil, Nader, and Owens. In each of the years 1961 through 1968, exactly one of the partners joined the firm. Hodges joined the firm before Nader. King joined the firm before James. Nader and James joined the firm before Gregg. Nader joined the firm before Owens. James joined the firm before MacNeil. Gregg joined the firm before Ivan. | Which one of the following CANNOT be true? | [
"Hodges joined the law firm in 1961.",
"Hodges joined the law firm in 1963.",
"Gregg joined the law firm in 1964.",
"MacNeil joined the law firm in 1964.",
"Owens joined the law firm in 1964."
] | 2 |
The eight partners of a law firm are Gregg, Hodges, Ivan, James, King, MacNeil, Nader, and Owens. In each of the years 1961 through 1968, exactly one of the partners joined the firm. Hodges joined the firm before Nader. King joined the firm before James. Nader and James joined the firm before Gregg. Nader joined the firm before Owens. James joined the firm before MacNeil. Gregg joined the firm before Ivan. | If James joined the firm in 1962, which one of the following CANNOT be true? | [
"Hodges joined the firm in 1963.",
"MacNeil joined the firm in 1963.",
"Hodges joined the firm in 1964.",
"Nader joined the firm in 1964.",
"Owens joined the firm in 1964."
] | 4 |
The eight partners of a law firm are Gregg, Hodges, Ivan, James, King, MacNeil, Nader, and Owens. In each of the years 1961 through 1968, exactly one of the partners joined the firm. Hodges joined the firm before Nader. King joined the firm before James. Nader and James joined the firm before Gregg. Nader joined the firm before Owens. James joined the firm before MacNeil. Gregg joined the firm before Ivan. | Of the following, which one is the latest year in which James could have joined the firm? | [
"1962",
"1963",
"1964",
"1965",
"1966"
] | 3 |
The eight partners of a law firm are Gregg, Hodges, Ivan, James, King, MacNeil, Nader, and Owens. In each of the years 1961 through 1968, exactly one of the partners joined the firm. Hodges joined the firm before Nader. King joined the firm before James. Nader and James joined the firm before Gregg. Nader joined the firm before Owens. James joined the firm before MacNeil. Gregg joined the firm before Ivan. | If Owens joined the firm in 1965 and MacNeil joined it in 1967, one can determine the years in which exactly how many of the other partners joined the firm? | [
"1",
"2",
"3",
"4",
"5"
] | 1 |
The eight partners of a law firm are Gregg, Hodges, Ivan, James, King, MacNeil, Nader, and Owens. In each of the years 1961 through 1968, exactly one of the partners joined the firm. Hodges joined the firm before Nader. King joined the firm before James. Nader and James joined the firm before Gregg. Nader joined the firm before Owens. James joined the firm before MacNeil. Gregg joined the firm before Ivan. | Assume that Owens joined the law firm before MacNeil. Of the following, which one is the earliest year in which MacNeil could have joined it? | [
"1963",
"1964",
"1965",
"1966",
"1967"
] | 3 |
A railway company has exactly three lines: line 1, line 2, and line 3. The company prints three sets of tickets for January and three sets of tickets for February: one set for each of its lines for each of the two months. The company's tickets are printed in a manner consistent with the following conditions: Each of the six sets of tickets is exactly one of the following colors: green, purple, red, yellow. For each line, the January tickets are a different color than the February tickets. For each month, tickets for different lines are in different colors. Exactly one set of January tickets is red. For line 3, either the January tickets or the February tickets, but not both, are green. The January tickets for line 2 are purple. No February tickets are purple. | If the line 3 tickets for January are red, then which one of the following statements must be true? | [
"The line 1 tickets for January are green.",
"The line 1 tickets for January are yellow.",
"The line 1 tickets for February are red.",
"The line 2 tickets for February are yellow.",
"The line 3 tickets for February are green."
] | 4 |
A railway company has exactly three lines: line 1, line 2, and line 3. The company prints three sets of tickets for January and three sets of tickets for February: one set for each of its lines for each of the two months. The company's tickets are printed in a manner consistent with the following conditions: Each of the six sets of tickets is exactly one of the following colors: green, purple, red, yellow. For each line, the January tickets are a different color than the February tickets. For each month, tickets for different lines are in different colors. Exactly one set of January tickets is red. For line 3, either the January tickets or the February tickets, but not both, are green. The January tickets for line 2 are purple. No February tickets are purple. | If one set of the line 2 tickets is green, then which one of the following statements must be true? | [
"The line 1 tickets for January are red.",
"The line 3 tickets for January are red.",
"The line 1 tickets for February are red.",
"The line 3 tickets for February are green.",
"The line 3 tickets for February are yellow."
] | 0 |
A railway company has exactly three lines: line 1, line 2, and line 3. The company prints three sets of tickets for January and three sets of tickets for February: one set for each of its lines for each of the two months. The company's tickets are printed in a manner consistent with the following conditions: Each of the six sets of tickets is exactly one of the following colors: green, purple, red, yellow. For each line, the January tickets are a different color than the February tickets. For each month, tickets for different lines are in different colors. Exactly one set of January tickets is red. For line 3, either the January tickets or the February tickets, but not both, are green. The January tickets for line 2 are purple. No February tickets are purple. | Which one of the following statements could be true? | [
"No January ticket is green.",
"No February ticket is green.",
"Only line 2 tickets are red.",
"One set of January tickets is green and one set of January tickets is yellow.",
"The line 2 tickets for January are the same color as the line 1 tickets for February."
] | 0 |
A railway company has exactly three lines: line 1, line 2, and line 3. The company prints three sets of tickets for January and three sets of tickets for February: one set for each of its lines for each of the two months. The company's tickets are printed in a manner consistent with the following conditions: Each of the six sets of tickets is exactly one of the following colors: green, purple, red, yellow. For each line, the January tickets are a different color than the February tickets. For each month, tickets for different lines are in different colors. Exactly one set of January tickets is red. For line 3, either the January tickets or the February tickets, but not both, are green. The January tickets for line 2 are purple. No February tickets are purple. | Which one of the following statements could be true? | [
"Both the line 1 tickets for January and the line 2 tickets for February are green.",
"Both the line 1 tickets for January and the line 2 tickets for February are yellow.",
"Both the line 1 tickets for January and the line 3 tickets for February are yellow.",
"The line 1 tickets for January are green, and the line 3 tickets for February are red.",
"The line 3 tickets for January are yellow, and the line 1 tickets for February are red."
] | 1 |
A railway company has exactly three lines: line 1, line 2, and line 3. The company prints three sets of tickets for January and three sets of tickets for February: one set for each of its lines for each of the two months. The company's tickets are printed in a manner consistent with the following conditions: Each of the six sets of tickets is exactly one of the following colors: green, purple, red, yellow. For each line, the January tickets are a different color than the February tickets. For each month, tickets for different lines are in different colors. Exactly one set of January tickets is red. For line 3, either the January tickets or the February tickets, but not both, are green. The January tickets for line 2 are purple. No February tickets are purple. | If the line 3 tickets for February are yellow, then each of the following statements must be true EXCEPT: | [
"One set of January tickets is green.",
"One set of line 1 tickets is red.",
"One set of line 2 tickets is red.",
"The tickets in two of the six sets are red.",
"The tickets in two of the six sets are yellow."
] | 4 |
A railway company has exactly three lines: line 1, line 2, and line 3. The company prints three sets of tickets for January and three sets of tickets for February: one set for each of its lines for each of the two months. The company's tickets are printed in a manner consistent with the following conditions: Each of the six sets of tickets is exactly one of the following colors: green, purple, red, yellow. For each line, the January tickets are a different color than the February tickets. For each month, tickets for different lines are in different colors. Exactly one set of January tickets is red. For line 3, either the January tickets or the February tickets, but not both, are green. The January tickets for line 2 are purple. No February tickets are purple. | Suppose that none of the ticket sets are purple. If all of the other conditions remain the same, then which one of the following statements could be true? | [
"None of the January tickets are green.",
"None of the February tickets are green.",
"None of the line 2 tickets are green.",
"No line 1 or line 2 tickets are yellow.",
"No line 2 or line 3 tickets are red."
] | 2 |
The Mammoth Corporation has just completed hiring nine new workers: Brandt, Calva, Duvall, Eberle, Fu, Garcia, Haga, Irving, and Jessup. Fu and Irving were hired on the same day as each other, and no one else was hired that day. Calva and Garcia were hired on the same day as each other, and no one else was hired that day. On each of the other days of hiring, exactly one worker was hired. Eberle was hired before Brandt. Haga was hired before Duvall. Duvall was hired after Irving but before Eberle. Garcia was hired after both Jessup and Brandt. Brandt was hired before Jessup. | Who were the last two workers to be hired? | [
"Eberle and Jessup",
"Brandt and Garcia",
"Brandt and Calva",
"Garcia and Calva",
"Jessup and Brandt"
] | 3 |
The Mammoth Corporation has just completed hiring nine new workers: Brandt, Calva, Duvall, Eberle, Fu, Garcia, Haga, Irving, and Jessup. Fu and Irving were hired on the same day as each other, and no one else was hired that day. Calva and Garcia were hired on the same day as each other, and no one else was hired that day. On each of the other days of hiring, exactly one worker was hired. Eberle was hired before Brandt. Haga was hired before Duvall. Duvall was hired after Irving but before Eberle. Garcia was hired after both Jessup and Brandt. Brandt was hired before Jessup. | Who was hired on the fourth day of hiring? | [
"Eberle",
"Brandt",
"Irving",
"Garcia",
"Jessup"
] | 0 |
The Mammoth Corporation has just completed hiring nine new workers: Brandt, Calva, Duvall, Eberle, Fu, Garcia, Haga, Irving, and Jessup. Fu and Irving were hired on the same day as each other, and no one else was hired that day. Calva and Garcia were hired on the same day as each other, and no one else was hired that day. On each of the other days of hiring, exactly one worker was hired. Eberle was hired before Brandt. Haga was hired before Duvall. Duvall was hired after Irving but before Eberle. Garcia was hired after both Jessup and Brandt. Brandt was hired before Jessup. | Exactly how many workers were hired before Jessup? | [
"6",
"5",
"4",
"3",
"2"
] | 0 |
The Mammoth Corporation has just completed hiring nine new workers: Brandt, Calva, Duvall, Eberle, Fu, Garcia, Haga, Irving, and Jessup. Fu and Irving were hired on the same day as each other, and no one else was hired that day. Calva and Garcia were hired on the same day as each other, and no one else was hired that day. On each of the other days of hiring, exactly one worker was hired. Eberle was hired before Brandt. Haga was hired before Duvall. Duvall was hired after Irving but before Eberle. Garcia was hired after both Jessup and Brandt. Brandt was hired before Jessup. | Which one of the following must be true? | [
"Duvall was the first worker to be hired.",
"Haga was the first worker to be hired.",
"Fu and Irving were the first two workers to be hired.",
"Haga and Fu were the first two workers to be hired.",
"Either Haga was the first worker to be hired or Fu and Irving were the first two workers to be hired."
] | 4 |
The Mammoth Corporation has just completed hiring nine new workers: Brandt, Calva, Duvall, Eberle, Fu, Garcia, Haga, Irving, and Jessup. Fu and Irving were hired on the same day as each other, and no one else was hired that day. Calva and Garcia were hired on the same day as each other, and no one else was hired that day. On each of the other days of hiring, exactly one worker was hired. Eberle was hired before Brandt. Haga was hired before Duvall. Duvall was hired after Irving but before Eberle. Garcia was hired after both Jessup and Brandt. Brandt was hired before Jessup. | If Eberle was hired on a Monday, what is the earliest day on which Garcia could have been hired? | [
"Monday",
"Tuesday",
"Wednesday",
"Thursday",
"Friday"
] | 3 |
An apartment building has five floors. Each floor has either one or two apartments. There are exactly eight apartments in the building. The residents of the building are J, K, L, M, N, O, P, and Q, who each live in a different apartment. J lives on a floor with two apartments. K lives on the floor directly above P. The second floor is made up of only one apartment. M and N live on the same floor. O does not live on the same floor as Q. L lives in the only apartment on her floor. Q does not live on the first or second floor. | Which one of the following must be true? | [
"Q lives on the third floor.",
"Q lives on the fifth floor.",
"L does not live on the fourth floor.",
"N does not live on the second floor.",
"J lives on the first floor."
] | 3 |
An apartment building has five floors. Each floor has either one or two apartments. There are exactly eight apartments in the building. The residents of the building are J, K, L, M, N, O, P, and Q, who each live in a different apartment. J lives on a floor with two apartments. K lives on the floor directly above P. The second floor is made up of only one apartment. M and N live on the same floor. O does not live on the same floor as Q. L lives in the only apartment on her floor. Q does not live on the first or second floor. | Which one of the following CANNOT be true? | [
"K lives on the second floor.",
"M lives on the first floor.",
"N lives on the fourth floor.",
"O lives on the third floor.",
"P lives on the fifth floor."
] | 4 |
An apartment building has five floors. Each floor has either one or two apartments. There are exactly eight apartments in the building. The residents of the building are J, K, L, M, N, O, P, and Q, who each live in a different apartment. J lives on a floor with two apartments. K lives on the floor directly above P. The second floor is made up of only one apartment. M and N live on the same floor. O does not live on the same floor as Q. L lives in the only apartment on her floor. Q does not live on the first or second floor. | If J lives on the fourth floor and K lives on the fifth floor, which one of the following can be true? | [
"O lives on the first floor.",
"Q lives on the fourth floor.",
"N lives on the fifth floor.",
"L lives on the fourth floor.",
"P lives on the third floor."
] | 0 |
An apartment building has five floors. Each floor has either one or two apartments. There are exactly eight apartments in the building. The residents of the building are J, K, L, M, N, O, P, and Q, who each live in a different apartment. J lives on a floor with two apartments. K lives on the floor directly above P. The second floor is made up of only one apartment. M and N live on the same floor. O does not live on the same floor as Q. L lives in the only apartment on her floor. Q does not live on the first or second floor. | If O lives on the second floor, which one of the following CANNOT be true? | [
"K lives on the fourth floor.",
"K lives on the fifth floor.",
"L lives on the first floor.",
"L lives on the third floor.",
"L lives on the fourth floor."
] | 4 |
An apartment building has five floors. Each floor has either one or two apartments. There are exactly eight apartments in the building. The residents of the building are J, K, L, M, N, O, P, and Q, who each live in a different apartment. J lives on a floor with two apartments. K lives on the floor directly above P. The second floor is made up of only one apartment. M and N live on the same floor. O does not live on the same floor as Q. L lives in the only apartment on her floor. Q does not live on the first or second floor. | If M lives on the fourth floor, which one of the following must be false? | [
"O lives on the fifth floor.",
"J lives on the first floor.",
"L lives on the second floor.",
"Q lives on the third floor.",
"P lives on the first floor."
] | 2 |
An apartment building has five floors. Each floor has either one or two apartments. There are exactly eight apartments in the building. The residents of the building are J, K, L, M, N, O, P, and Q, who each live in a different apartment. J lives on a floor with two apartments. K lives on the floor directly above P. The second floor is made up of only one apartment. M and N live on the same floor. O does not live on the same floor as Q. L lives in the only apartment on her floor. Q does not live on the first or second floor. | Which one of the following must be true? | [
"If J lives on the fourth floor, then Q does not live on the fifth floor.",
"If O lives on the second floor, then L does not live on the fourth floor.",
"If N lives on the fourth floor, then K does not live on the second floor.",
"If K lives on the third floor, then O does not live on the fifth floor.",
"If P lives on the fourth floor, then M does not live on the third floor."
] | 1 |
An apartment building has five floors. Each floor has either one or two apartments. There are exactly eight apartments in the building. The residents of the building are J, K, L, M, N, O, P, and Q, who each live in a different apartment. J lives on a floor with two apartments. K lives on the floor directly above P. The second floor is made up of only one apartment. M and N live on the same floor. O does not live on the same floor as Q. L lives in the only apartment on her floor. Q does not live on the first or second floor. | If O lives on the fourth floor and P lives on the second floor, which one of the following must be true? | [
"L lives on the first floor.",
"M lives on the third floor.",
"Q lives on the third floor.",
"N lives on the fifth floor.",
"Q lives on the fifth floor."
] | 2 |
Hannah spends 14 days, exclusive of travel time, in a total of six cities. Each city she visits is in one of three countries—X, Y, or Z. Each of the three countries has many cities. Hannah visits at least one city in each of the three countries. She spends at least two days in each city she visits. She spends only whole days in any city. | If Hannah spends exactly eight days in the cities of country X, then which one of the following CANNOT be true? | [
"She visits exactly two cities in country X.",
"She visits exactly two cities in country Y.",
"She visits exactly two cities in country Z.",
"She visits more cities in country Y than in country Z.",
"She visits more cities in country Z than in country Y."
] | 0 |
Hannah spends 14 days, exclusive of travel time, in a total of six cities. Each city she visits is in one of three countries—X, Y, or Z. Each of the three countries has many cities. Hannah visits at least one city in each of the three countries. She spends at least two days in each city she visits. She spends only whole days in any city. | If Hannah visits an equal number of cities in each of the countries, what is the greatest total number of days she can spend visiting cities in country X? | [
"3",
"4",
"5",
"6",
"7"
] | 3 |
Hannah spends 14 days, exclusive of travel time, in a total of six cities. Each city she visits is in one of three countries—X, Y, or Z. Each of the three countries has many cities. Hannah visits at least one city in each of the three countries. She spends at least two days in each city she visits. She spends only whole days in any city. | If Hannah spends three days in the cities of country Y and seven days in the cities of country Z, then which one of the following must be false? | [
"She visits more cities in country X than in country Y.",
"She visits exactly two cities in country X.",
"She visits more cities in country Z than in country X.",
"She visits exactly two cities in country Z.",
"She visits exactly three cities in country Z."
] | 3 |
Hannah spends 14 days, exclusive of travel time, in a total of six cities. Each city she visits is in one of three countries—X, Y, or Z. Each of the three countries has many cities. Hannah visits at least one city in each of the three countries. She spends at least two days in each city she visits. She spends only whole days in any city. | If the city of Nomo is in country X, and if Hannah spends as many days as possible in Nomo and as few days as possible in each of the other cities that she visits, then which one of the following must be true? | [
"Hannah cannot visit any other cities in country X.",
"Hannah can visit four cities in country Y.",
"Hannah can spend six days in Nomo.",
"Hannah cannot spend more than four days in country Z.",
"Hannah can visit, at most, a total of four cities in countries Y and Z."
] | 1 |
Hannah spends 14 days, exclusive of travel time, in a total of six cities. Each city she visits is in one of three countries—X, Y, or Z. Each of the three countries has many cities. Hannah visits at least one city in each of the three countries. She spends at least two days in each city she visits. She spends only whole days in any city. | If Hannah visits a combined total of four cities in countries X and Y, what is the greatest total number of days she can spend visiting cities in country Y? | [
"6",
"7",
"8",
"9",
"10"
] | 2 |
Exactly six dogs—P, Q, R, S, T, and U—are entered in a dog show. The judge of the show awards exactly four ribbons, one for each of first, second, third, and fourth places, to four of the dogs. The information that follows is all that is available about the six dogs: Each dog is either a greyhound or a labrador, but not both. Two of the six dogs are female and four are male. The judge awards ribbons to both female dogs, exactly one of which is a labrador. Exactly one labrador wins a ribbon. Dogs P and R place ahead of dog S, and dog S places ahead of dogs Q and T. Dogs P and R are greyhounds. Dogs S and U are labradors. | Which one of the following is a complete and accurate list of the dogs that can be greyhounds? | [
"P, Q",
"P, R",
"P, Q, R",
"P, R, T",
"P, Q, R, T"
] | 4 |
Exactly six dogs—P, Q, R, S, T, and U—are entered in a dog show. The judge of the show awards exactly four ribbons, one for each of first, second, third, and fourth places, to four of the dogs. The information that follows is all that is available about the six dogs: Each dog is either a greyhound or a labrador, but not both. Two of the six dogs are female and four are male. The judge awards ribbons to both female dogs, exactly one of which is a labrador. Exactly one labrador wins a ribbon. Dogs P and R place ahead of dog S, and dog S places ahead of dogs Q and T. Dogs P and R are greyhounds. Dogs S and U are labradors. | Which one of the following statements CANNOT be true? | [
"A female greyhound wins the second place ribbon.",
"A female labrador wins the second place ribbon.",
"A female labrador wins the third place ribbon.",
"A male greyhound wins the fourth place ribbon.",
"A female greyhound wins the fourth place ribbon."
] | 1 |
Exactly six dogs—P, Q, R, S, T, and U—are entered in a dog show. The judge of the show awards exactly four ribbons, one for each of first, second, third, and fourth places, to four of the dogs. The information that follows is all that is available about the six dogs: Each dog is either a greyhound or a labrador, but not both. Two of the six dogs are female and four are male. The judge awards ribbons to both female dogs, exactly one of which is a labrador. Exactly one labrador wins a ribbon. Dogs P and R place ahead of dog S, and dog S places ahead of dogs Q and T. Dogs P and R are greyhounds. Dogs S and U are labradors. | Which one of the following dogs must be male? | [
"dog P",
"dog R",
"dog S",
"dog T",
"dog U"
] | 4 |
Exactly six dogs—P, Q, R, S, T, and U—are entered in a dog show. The judge of the show awards exactly four ribbons, one for each of first, second, third, and fourth places, to four of the dogs. The information that follows is all that is available about the six dogs: Each dog is either a greyhound or a labrador, but not both. Two of the six dogs are female and four are male. The judge awards ribbons to both female dogs, exactly one of which is a labrador. Exactly one labrador wins a ribbon. Dogs P and R place ahead of dog S, and dog S places ahead of dogs Q and T. Dogs P and R are greyhounds. Dogs S and U are labradors. | Which one of the following statements can be false? | [
"Dog P places ahead of dog R.",
"Dog P places ahead of dog T.",
"Dog R places ahead of dog U.",
"Dog R places ahead of dog T.",
"Dog S places ahead of dog U."
] | 0 |
Exactly six dogs—P, Q, R, S, T, and U—are entered in a dog show. The judge of the show awards exactly four ribbons, one for each of first, second, third, and fourth places, to four of the dogs. The information that follows is all that is available about the six dogs: Each dog is either a greyhound or a labrador, but not both. Two of the six dogs are female and four are male. The judge awards ribbons to both female dogs, exactly one of which is a labrador. Exactly one labrador wins a ribbon. Dogs P and R place ahead of dog S, and dog S places ahead of dogs Q and T. Dogs P and R are greyhounds. Dogs S and U are labradors. | If dog Q is female, which one of the following statements can be false? | [
"Dog P is male.",
"Dog R is male.",
"Dog Q wins the fourth place ribbon.",
"Dog Q is a greyhound.",
"Dog T is a greyhound."
] | 4 |
Exactly six dogs—P, Q, R, S, T, and U—are entered in a dog show. The judge of the show awards exactly four ribbons, one for each of first, second, third, and fourth places, to four of the dogs. The information that follows is all that is available about the six dogs: Each dog is either a greyhound or a labrador, but not both. Two of the six dogs are female and four are male. The judge awards ribbons to both female dogs, exactly one of which is a labrador. Exactly one labrador wins a ribbon. Dogs P and R place ahead of dog S, and dog S places ahead of dogs Q and T. Dogs P and R are greyhounds. Dogs S and U are labradors. | If dog T wins the fourth place ribbon, then which one of the following statements must be true? | [
"Dog P is male.",
"Dog Q is male.",
"Dog T is male.",
"Dog Q is a labrador.",
"Dog T is a labrador."
] | 1 |
Exactly six dogs—P, Q, R, S, T, and U—are entered in a dog show. The judge of the show awards exactly four ribbons, one for each of first, second, third, and fourth places, to four of the dogs. The information that follows is all that is available about the six dogs: Each dog is either a greyhound or a labrador, but not both. Two of the six dogs are female and four are male. The judge awards ribbons to both female dogs, exactly one of which is a labrador. Exactly one labrador wins a ribbon. Dogs P and R place ahead of dog S, and dog S places ahead of dogs Q and T. Dogs P and R are greyhounds. Dogs S and U are labradors. | Which one of the following statements could be true? | [
"Dog P does not win a ribbon.",
"Dog R does not win a ribbon.",
"Dog S does not win a ribbon.",
"Dog T wins a ribbon.",
"Dog U wins a ribbon."
] | 3 |
Three couples—John and Kate, Lewis and Marie, and Nat and Olive have dinner in a restaurant together. Kate, Marie, and Olive are women; the other three are men. Each person orders one and only one of the following kinds of entrees: pork chops, roast beef, swordfish, tilefish, veal cutlet. The six people order in a manner consistent with the following conditions: The two people in each couple do not order the same kind of entree as each other. None of the men orders the same kind of entree as any of the other men. Marie orders swordfish. Neither John nor Nat orders a fish entree. Olive orders roast beef. | Which one of the following is a complete and accurate list of the entrees any one of which Lewis could order? | [
"pork chops, roast beef",
"pork chops, veal cutlet",
"pork chops, swordfish, veal cutlet",
"pork chops, roast beef, tilefish, veal cutlet",
"pork chops, roast beef, swordfish, tilefish, veal cutlet"
] | 3 |
Three couples—John and Kate, Lewis and Marie, and Nat and Olive have dinner in a restaurant together. Kate, Marie, and Olive are women; the other three are men. Each person orders one and only one of the following kinds of entrees: pork chops, roast beef, swordfish, tilefish, veal cutlet. The six people order in a manner consistent with the following conditions: The two people in each couple do not order the same kind of entree as each other. None of the men orders the same kind of entree as any of the other men. Marie orders swordfish. Neither John nor Nat orders a fish entree. Olive orders roast beef. | Which one of the following statements could be true? | [
"John orders the same kind of entree as Marie does.",
"Kate orders the same kind of entree as Nat does.",
"Lewis orders the same kind of entree as Nat does.",
"Marie orders the same kind of entree as Olive does.",
"Nat orders the same kind of entree as Olive does."
] | 1 |
Three couples—John and Kate, Lewis and Marie, and Nat and Olive have dinner in a restaurant together. Kate, Marie, and Olive are women; the other three are men. Each person orders one and only one of the following kinds of entrees: pork chops, roast beef, swordfish, tilefish, veal cutlet. The six people order in a manner consistent with the following conditions: The two people in each couple do not order the same kind of entree as each other. None of the men orders the same kind of entree as any of the other men. Marie orders swordfish. Neither John nor Nat orders a fish entree. Olive orders roast beef. | Which one of the following statements must be true? | [
"One of the men orders pork chops or veal cutlet.",
"One of the men orders swordfish or veal cutlet.",
"Two of the women order tilefish.",
"None of the men orders a fish entree.",
"Exactly one of the women orders a fish entree."
] | 0 |
Three couples—John and Kate, Lewis and Marie, and Nat and Olive have dinner in a restaurant together. Kate, Marie, and Olive are women; the other three are men. Each person orders one and only one of the following kinds of entrees: pork chops, roast beef, swordfish, tilefish, veal cutlet. The six people order in a manner consistent with the following conditions: The two people in each couple do not order the same kind of entree as each other. None of the men orders the same kind of entree as any of the other men. Marie orders swordfish. Neither John nor Nat orders a fish entree. Olive orders roast beef. | If John orders veal cutlet, then which one of the following statements must be true? | [
"Kate orders roast beef.",
"Kate orders swordfish.",
"Lewis orders tilefish.",
"Lewis orders veal cutlet.",
"Nat orders pork chops."
] | 4 |
Three couples—John and Kate, Lewis and Marie, and Nat and Olive have dinner in a restaurant together. Kate, Marie, and Olive are women; the other three are men. Each person orders one and only one of the following kinds of entrees: pork chops, roast beef, swordfish, tilefish, veal cutlet. The six people order in a manner consistent with the following conditions: The two people in each couple do not order the same kind of entree as each other. None of the men orders the same kind of entree as any of the other men. Marie orders swordfish. Neither John nor Nat orders a fish entree. Olive orders roast beef. | If none of the six people orders pork chops, then which one of the following statements must be true? | [
"John orders veal cutlet.",
"Kate orders tilefish.",
"Lewis orders tilefish.",
"One of the men orders swordfish.",
"One of the women orders tilefish."
] | 2 |
Three couples—John and Kate, Lewis and Marie, and Nat and Olive have dinner in a restaurant together. Kate, Marie, and Olive are women; the other three are men. Each person orders one and only one of the following kinds of entrees: pork chops, roast beef, swordfish, tilefish, veal cutlet. The six people order in a manner consistent with the following conditions: The two people in each couple do not order the same kind of entree as each other. None of the men orders the same kind of entree as any of the other men. Marie orders swordfish. Neither John nor Nat orders a fish entree. Olive orders roast beef. | If Lewis orders pork chops, then which one of the following is a complete and accurate list of the entrees any one of which John could order? | [
"roast beef",
"veal cutlet",
"roast beef, veal cutlet",
"roast beef, swordfish",
"pork chops, roast beef, swordfish"
] | 0 |
Three couples—John and Kate, Lewis and Marie, and Nat and Olive have dinner in a restaurant together. Kate, Marie, and Olive are women; the other three are men. Each person orders one and only one of the following kinds of entrees: pork chops, roast beef, swordfish, tilefish, veal cutlet. The six people order in a manner consistent with the following conditions: The two people in each couple do not order the same kind of entree as each other. None of the men orders the same kind of entree as any of the other men. Marie orders swordfish. Neither John nor Nat orders a fish entree. Olive orders roast beef. | Suppose that the people in each couple both order the same kind of entree as each other rather than order different kinds of entrees. If all other conditions remain the same, and no two women order the same kind of entree, then which one of the following statements could be true? | [
"John orders roast beef.",
"John orders swordfish.",
"Kate orders roast beef.",
"Two of the people order pork chops.",
"Two of the people order tilefish."
] | 3 |
There are exactly seven houses on a street. Each house is occupied by exactly one of seven families: the Kahns, Lowes, Muirs, Newmans, Owens, Piatts, Rutans. All the houses are on the same side of the street, which runs from west to east. The Rutans do not live in the first or the last house on the street. The Kahns live in the fourth house from the west end of the street. The Muirs live next to the Kahns. The Piatts live east of both the Kahns and the Muirs but west of the Lowes. | Which one of the following families could live in the house that is the farthest east? | [
"the Kahns",
"the Muirs",
"the Newmans",
"the Piatts",
"the Rutans"
] | 2 |
There are exactly seven houses on a street. Each house is occupied by exactly one of seven families: the Kahns, Lowes, Muirs, Newmans, Owens, Piatts, Rutans. All the houses are on the same side of the street, which runs from west to east. The Rutans do not live in the first or the last house on the street. The Kahns live in the fourth house from the west end of the street. The Muirs live next to the Kahns. The Piatts live east of both the Kahns and the Muirs but west of the Lowes. | Which one of the following families CANNOT live next to the Kahns? | [
"the Lowes",
"the Newmans",
"the Owens",
"the Piatts",
"the Rutans"
] | 0 |
There are exactly seven houses on a street. Each house is occupied by exactly one of seven families: the Kahns, Lowes, Muirs, Newmans, Owens, Piatts, Rutans. All the houses are on the same side of the street, which runs from west to east. The Rutans do not live in the first or the last house on the street. The Kahns live in the fourth house from the west end of the street. The Muirs live next to the Kahns. The Piatts live east of both the Kahns and the Muirs but west of the Lowes. | If the Muirs live west of the Kahns, then the Rutans CANNOT live next to both | [
"the Kahns and the Piatts",
"the Lowes and the Piatts",
"the Muirs and the Piatts",
"the Muirs and the Owens",
"the Muirs and the Newmans"
] | 2 |
There are exactly seven houses on a street. Each house is occupied by exactly one of seven families: the Kahns, Lowes, Muirs, Newmans, Owens, Piatts, Rutans. All the houses are on the same side of the street, which runs from west to east. The Rutans do not live in the first or the last house on the street. The Kahns live in the fourth house from the west end of the street. The Muirs live next to the Kahns. The Piatts live east of both the Kahns and the Muirs but west of the Lowes. | If the Newmans live immediately west of the Kahns, which one of the following statements must be false? | [
"The Owens live next to the Newmans.",
"The Owens live next to the Rutans.",
"The Piatts live next to the Lowes.",
"The Piatts live next to the Muirs.",
"The Rutans live next to the Newmans."
] | 0 |
There are exactly seven houses on a street. Each house is occupied by exactly one of seven families: the Kahns, Lowes, Muirs, Newmans, Owens, Piatts, Rutans. All the houses are on the same side of the street, which runs from west to east. The Rutans do not live in the first or the last house on the street. The Kahns live in the fourth house from the west end of the street. The Muirs live next to the Kahns. The Piatts live east of both the Kahns and the Muirs but west of the Lowes. | If the Owens live east of the Muirs, which one of the following statements must be true? | [
"The Kahns live east of the Muirs.",
"The Kahns live west of the Rutans.",
"The Owens live west of the Lowes.",
"The Owens live east of the Piatts.",
"The Owens live west of the Piatts."
] | 0 |
There are exactly seven houses on a street. Each house is occupied by exactly one of seven families: the Kahns, Lowes, Muirs, Newmans, Owens, Piatts, Rutans. All the houses are on the same side of the street, which runs from west to east. The Rutans do not live in the first or the last house on the street. The Kahns live in the fourth house from the west end of the street. The Muirs live next to the Kahns. The Piatts live east of both the Kahns and the Muirs but west of the Lowes. | If the Owens live east of the Kahns, which one of the following pairs of families must live next to each other? | [
"the Kahns and the Piatts",
"the Lowes and the Owens",
"the Muirs and the Newmans",
"the Newmans and the Rutans",
"the Owens and the Piatts"
] | 3 |
At an automobile exhibition, cars are displayed on each floor of a three-floor building. On each floor the cars are either all family cars or all sports cars, either all new or all used, and either all production models or all research models. The following conditions apply to this exhibition: If the exhibition includes both family cars and sports cars, then each family car is displayed on a lower numbered floor than any sports car. The exhibition includes no used research models. The exhibition includes no research models that are sports cars. There are new cars on floor 1. There are used cars on floor 3. | If there are sports cars on exactly two floors, then which one of the following statements could be true? | [
"There are research models on floor 1.",
"There are sports cars on floor 1.",
"There are family cars on floor 2.",
"There are research models on floor 2.",
"There are family cars on floor 3."
] | 0 |
At an automobile exhibition, cars are displayed on each floor of a three-floor building. On each floor the cars are either all family cars or all sports cars, either all new or all used, and either all production models or all research models. The following conditions apply to this exhibition: If the exhibition includes both family cars and sports cars, then each family car is displayed on a lower numbered floor than any sports car. The exhibition includes no used research models. The exhibition includes no research models that are sports cars. There are new cars on floor 1. There are used cars on floor 3. | Which one of the following statements could be true? | [
"The exhibition includes new research model sports cars.",
"The exhibition includes used research model family cars.",
"The exhibition includes used research model sports cars.",
"There are research models on exactly one floor.",
"There are research models on all three floors."
] | 3 |
At an automobile exhibition, cars are displayed on each floor of a three-floor building. On each floor the cars are either all family cars or all sports cars, either all new or all used, and either all production models or all research models. The following conditions apply to this exhibition: If the exhibition includes both family cars and sports cars, then each family car is displayed on a lower numbered floor than any sports car. The exhibition includes no used research models. The exhibition includes no research models that are sports cars. There are new cars on floor 1. There are used cars on floor 3. | Which one of the following statements must be true? | [
"There are production models on floor 1.",
"There are research models on floor 1.",
"There are production models on floor 2.",
"There are production models on floor 3.",
"There are research models on floor 3."
] | 3 |
At an automobile exhibition, cars are displayed on each floor of a three-floor building. On each floor the cars are either all family cars or all sports cars, either all new or all used, and either all production models or all research models. The following conditions apply to this exhibition: If the exhibition includes both family cars and sports cars, then each family car is displayed on a lower numbered floor than any sports car. The exhibition includes no used research models. The exhibition includes no research models that are sports cars. There are new cars on floor 1. There are used cars on floor 3. | If there are research models on exactly two floors, then which one of the following statements can be false? | [
"There are family cars on floor 1.",
"There are research models on floor 1.",
"There are new cars on floor 2.",
"There are research models on floor 2.",
"There are family cars on floor 3."
] | 4 |
At an automobile exhibition, cars are displayed on each floor of a three-floor building. On each floor the cars are either all family cars or all sports cars, either all new or all used, and either all production models or all research models. The following conditions apply to this exhibition: If the exhibition includes both family cars and sports cars, then each family car is displayed on a lower numbered floor than any sports car. The exhibition includes no used research models. The exhibition includes no research models that are sports cars. There are new cars on floor 1. There are used cars on floor 3. | If all the new cars in the exhibition are research models, then which one of the following statements must be true? | [
"All the family cars in the exhibition are new.",
"All the family cars in the exhibition are research models.",
"All the family cars in the exhibition are used.",
"All the new cars in the exhibition are family cars.",
"All the production models in the exhibition are family cars."
] | 3 |
At an automobile exhibition, cars are displayed on each floor of a three-floor building. On each floor the cars are either all family cars or all sports cars, either all new or all used, and either all production models or all research models. The following conditions apply to this exhibition: If the exhibition includes both family cars and sports cars, then each family car is displayed on a lower numbered floor than any sports car. The exhibition includes no used research models. The exhibition includes no research models that are sports cars. There are new cars on floor 1. There are used cars on floor 3. | If all the production models in the exhibition are used, then which one of the following statements must be true? | [
"There are family cars on floor 1.",
"There are new cars on floor 2.",
"There are research models on floor 2.",
"There are family cars on floor 3.",
"There are sports cars on floor 3."
] | 0 |
Planes 1, 2, 3, and 4—and no others—are available to fly in an air show. Pilots Anna, Bob, and Cindy are all aboard planes that are flying in the show and they are the only qualified pilots in the show. Copilots Dave, Ed, and Fran are all aboard planes that are flying in the show and they are the only qualified copilots in the show. No plane flies in the show without a qualified pilot aboard. No one but qualified pilots and qualified copilots flies in the show. Anna will only fly in either plane 1 or plane 4. Dave will only fly in either plane 2 or plane 3. | If Anna flies in plane 4 and Dave flies in plane 2, which one of the following must be true? | [
"Cindy flies in either plane 1 or plane 3.",
"If Cindy flies in plane 3, Bob flies in plane 2.",
"Bob and one other person fly in plane l.",
"If Bob is aboard plane 4, Cindy flies in plane 3.",
"If Cindy is in plane 2, Bob flies in plane 3."
] | 1 |
Planes 1, 2, 3, and 4—and no others—are available to fly in an air show. Pilots Anna, Bob, and Cindy are all aboard planes that are flying in the show and they are the only qualified pilots in the show. Copilots Dave, Ed, and Fran are all aboard planes that are flying in the show and they are the only qualified copilots in the show. No plane flies in the show without a qualified pilot aboard. No one but qualified pilots and qualified copilots flies in the show. Anna will only fly in either plane 1 or plane 4. Dave will only fly in either plane 2 or plane 3. | If Bob and Anna fly on the same plane, which one of the following must be true? | [
"Cindy flies with Dave and Ed.",
"Cindy flies with Ed.",
"Dave flies with Cindy.",
"Dave flies with Cindy, Ed, and Fran.",
"Fran flies with Ed."
] | 2 |
Planes 1, 2, 3, and 4—and no others—are available to fly in an air show. Pilots Anna, Bob, and Cindy are all aboard planes that are flying in the show and they are the only qualified pilots in the show. Copilots Dave, Ed, and Fran are all aboard planes that are flying in the show and they are the only qualified copilots in the show. No plane flies in the show without a qualified pilot aboard. No one but qualified pilots and qualified copilots flies in the show. Anna will only fly in either plane 1 or plane 4. Dave will only fly in either plane 2 or plane 3. | If Cindy and Fran are the only people in one of the planes, which one of the following must be true? | [
"Bob flies with Anna.",
"Dave flies with Ed.",
"Dave and Ed fly with Bob.",
"Dave flies with Bob.",
"Ed flies with Anna."
] | 3 |
Planes 1, 2, 3, and 4—and no others—are available to fly in an air show. Pilots Anna, Bob, and Cindy are all aboard planes that are flying in the show and they are the only qualified pilots in the show. Copilots Dave, Ed, and Fran are all aboard planes that are flying in the show and they are the only qualified copilots in the show. No plane flies in the show without a qualified pilot aboard. No one but qualified pilots and qualified copilots flies in the show. Anna will only fly in either plane 1 or plane 4. Dave will only fly in either plane 2 or plane 3. | If plane 1 is used, its crew could consist of | [
"Anna, Bob, Cindy, Fran",
"Anna, Bob, Ed, Fran",
"Bob, Cindy, Ed, Fran",
"Bob, Cindy, Dave, Ed",
"Bob, Dave, Ed, Fran"
] | 1 |
Planes 1, 2, 3, and 4—and no others—are available to fly in an air show. Pilots Anna, Bob, and Cindy are all aboard planes that are flying in the show and they are the only qualified pilots in the show. Copilots Dave, Ed, and Fran are all aboard planes that are flying in the show and they are the only qualified copilots in the show. No plane flies in the show without a qualified pilot aboard. No one but qualified pilots and qualified copilots flies in the show. Anna will only fly in either plane 1 or plane 4. Dave will only fly in either plane 2 or plane 3. | If as many of the pilots and copilots as possible fly in plane 4, that group will consist of | [
"exactly two people",
"exactly three people",
"exactly four people",
"exactly five people",
"three pilots and two copilots"
] | 2 |
A law firm has exactly nine partners: Fox, Glassen, Hae, Inman, Jacoby, Kohn, Lopez, Malloy, and Nassar. Kohn's salary is greater than both Inman's and Lopez's. Lopez's salary is greater than Nassar's. Inman's salary is greater than Fox's. Fox's salary is greater than Malloy's. Malloy's salary is greater than Glassen's. Glassen's salary is greater than Jacoby's. Jacoby's salary is greater than Hae's. | Which one of the following partners cannot have the third highest salary? | [
"Fox",
"Inman",
"Lopez",
"Malloy",
"Nassar"
] | 3 |
A law firm has exactly nine partners: Fox, Glassen, Hae, Inman, Jacoby, Kohn, Lopez, Malloy, and Nassar. Kohn's salary is greater than both Inman's and Lopez's. Lopez's salary is greater than Nassar's. Inman's salary is greater than Fox's. Fox's salary is greater than Malloy's. Malloy's salary is greater than Glassen's. Glassen's salary is greater than Jacoby's. Jacoby's salary is greater than Hae's. | If Malloy and Nassar earn the same salary, at least how many of the partners must have lower salaries than Lopez? | [
"3",
"4",
"5",
"6",
"7"
] | 2 |
A law firm has exactly nine partners: Fox, Glassen, Hae, Inman, Jacoby, Kohn, Lopez, Malloy, and Nassar. Kohn's salary is greater than both Inman's and Lopez's. Lopez's salary is greater than Nassar's. Inman's salary is greater than Fox's. Fox's salary is greater than Malloy's. Malloy's salary is greater than Glassen's. Glassen's salary is greater than Jacoby's. Jacoby's salary is greater than Hae's. | The salary rankings of each of the nine partners could be completely determined if which one of the following statements were true? | [
"Lopez's salary is greater than Fox's.",
"Lopez's salary is greater than Inman's.",
"Nassar's salary is greater than Fox's.",
"Nassar's salary is greater than Inman's.",
"Nassar's salary is greater than Malloy's."
] | 3 |
A law firm has exactly nine partners: Fox, Glassen, Hae, Inman, Jacoby, Kohn, Lopez, Malloy, and Nassar. Kohn's salary is greater than both Inman's and Lopez's. Lopez's salary is greater than Nassar's. Inman's salary is greater than Fox's. Fox's salary is greater than Malloy's. Malloy's salary is greater than Glassen's. Glassen's salary is greater than Jacoby's. Jacoby's salary is greater than Hae's. | If Nassar's salary is the same as that of one other partner of the firm, which one of the following must be false? | [
"Inman's salary is less than Lopez's.",
"Jacoby's salary is less than Lopez's.",
"Lopez's salary is less than Fox's.",
"Lopez's salary is less than Hae's.",
"Nassar's salary is less than Glassen's."
] | 3 |
A law firm has exactly nine partners: Fox, Glassen, Hae, Inman, Jacoby, Kohn, Lopez, Malloy, and Nassar. Kohn's salary is greater than both Inman's and Lopez's. Lopez's salary is greater than Nassar's. Inman's salary is greater than Fox's. Fox's salary is greater than Malloy's. Malloy's salary is greater than Glassen's. Glassen's salary is greater than Jacoby's. Jacoby's salary is greater than Hae's. | What is the minimum number of different salaries earned by the nine partners of the firm? | [
"5",
"6",
"7",
"8",
"9"
] | 2 |
A law firm has exactly nine partners: Fox, Glassen, Hae, Inman, Jacoby, Kohn, Lopez, Malloy, and Nassar. Kohn's salary is greater than both Inman's and Lopez's. Lopez's salary is greater than Nassar's. Inman's salary is greater than Fox's. Fox's salary is greater than Malloy's. Malloy's salary is greater than Glassen's. Glassen's salary is greater than Jacoby's. Jacoby's salary is greater than Hae's. | Assume that the partners of the firm are ranked according to their salaries, from first (highest) to ninth (lowest), and that no two salaries are the same. Which one of the following is a complete and accurate list of Glassen's possible ranks? | [
"fifth",
"fifth, sixth",
"fifth, seventh",
"fifth, sixth, seventh",
"fifth, sixth, seventh, eighth"
] | 3 |
Each of five illnesses—J, K, L, M, and N—is characterized by at least one of the following three symptoms: fever, headache, and sneezing. None of the illnesses has any symptom that is not one of these three. Illness J is characterized by headache and sneezing. Illnesses J and K have no symptoms in common. Illnesses J and L have at least one symptom in common. Illness L has a greater number of symptoms than illness K. Illnesses L and N have no symptoms in common. Illness M has more symptoms than illness J. | Which one of the following statements must be false? | [
"Illness J has exactly two symptoms.",
"Illness K has exactly one symptom.",
"Illness L has exactly two symptoms.",
"Illness M has exactly three symptoms.",
"Illness N has exactly two symptoms."
] | 4 |
Each of five illnesses—J, K, L, M, and N—is characterized by at least one of the following three symptoms: fever, headache, and sneezing. None of the illnesses has any symptom that is not one of these three. Illness J is characterized by headache and sneezing. Illnesses J and K have no symptoms in common. Illnesses J and L have at least one symptom in common. Illness L has a greater number of symptoms than illness K. Illnesses L and N have no symptoms in common. Illness M has more symptoms than illness J. | In which one of the following pairs could the first member of the pair be characterized by exactly the same number and types of symptoms as the second member of the pair? | [
"J and N",
"K and L",
"K and N",
"L and M",
"M and N"
] | 2 |
Each of five illnesses—J, K, L, M, and N—is characterized by at least one of the following three symptoms: fever, headache, and sneezing. None of the illnesses has any symptom that is not one of these three. Illness J is characterized by headache and sneezing. Illnesses J and K have no symptoms in common. Illnesses J and L have at least one symptom in common. Illness L has a greater number of symptoms than illness K. Illnesses L and N have no symptoms in common. Illness M has more symptoms than illness J. | If illness L is characterized by a combination of symptoms different from any of the other illnesses, then which one of the following statements must be true? | [
"Fever is a symptom of illness L.",
"Sneezing is a symptom of illness L.",
"Headache is a symptom of illness L.",
"Illnesses K and N are characterized by exactly the same symptoms.",
"Illnesses M and N are characterized by exactly the same symptoms."
] | 0 |
Each of five illnesses—J, K, L, M, and N—is characterized by at least one of the following three symptoms: fever, headache, and sneezing. None of the illnesses has any symptom that is not one of these three. Illness J is characterized by headache and sneezing. Illnesses J and K have no symptoms in common. Illnesses J and L have at least one symptom in common. Illness L has a greater number of symptoms than illness K. Illnesses L and N have no symptoms in common. Illness M has more symptoms than illness J. | The illnesses in which one of the following pairs must have exactly one symptom in common? | [
"J and L",
"J and M",
"J and N",
"K and L",
"M and N"
] | 4 |
Each of five illnesses—J, K, L, M, and N—is characterized by at least one of the following three symptoms: fever, headache, and sneezing. None of the illnesses has any symptom that is not one of these three. Illness J is characterized by headache and sneezing. Illnesses J and K have no symptoms in common. Illnesses J and L have at least one symptom in common. Illness L has a greater number of symptoms than illness K. Illnesses L and N have no symptoms in common. Illness M has more symptoms than illness J. | If Walter has exactly two of the three symptoms, then he cannot have all of the symptoms of | [
"both illness J and illness L",
"both illness J and illness N",
"both illness K and illness L",
"both illness K and illness N",
"both illness L and illness N"
] | 4 |
A street cleaning crew works only Monday to Friday, and only during the day. It takes the crew an entire morning or an entire afternoon to clean a street. During one week the crew cleaned exactly eight streets—First, Second, Third, Fourth, Fifth, Sixth, Seventh, and Eighth streets. The following is known about the crew's schedule for the week: The crew cleaned no street on Friday morning. The crew cleaned no street on Wednesday afternoon. It cleaned Fourth Street on Tuesday morning. It cleaned Seventh Street on Thursday morning. It cleaned Fourth Street before Sixth Street and after Eighth Street. It cleaned Second, Fifth, and Eighth streets on afternoons. | If the crew cleaned Second Street earlier in the week than Seventh Street, then it must have cleaned which one of the following streets on Tuesday afternoon? | [
"First Street",
"Second Street",
"Third Street",
"Fifth Street",
"Eighth Street"
] | 1 |
A street cleaning crew works only Monday to Friday, and only during the day. It takes the crew an entire morning or an entire afternoon to clean a street. During one week the crew cleaned exactly eight streets—First, Second, Third, Fourth, Fifth, Sixth, Seventh, and Eighth streets. The following is known about the crew's schedule for the week: The crew cleaned no street on Friday morning. The crew cleaned no street on Wednesday afternoon. It cleaned Fourth Street on Tuesday morning. It cleaned Seventh Street on Thursday morning. It cleaned Fourth Street before Sixth Street and after Eighth Street. It cleaned Second, Fifth, and Eighth streets on afternoons. | If the crew cleaned Sixth Street on a morning and cleaned Second Street before Seventh Street, then what is the maximum number of streets whose cleaning times cannot be determined? | [
"1",
"2",
"3",
"4",
"5"
] | 2 |
A street cleaning crew works only Monday to Friday, and only during the day. It takes the crew an entire morning or an entire afternoon to clean a street. During one week the crew cleaned exactly eight streets—First, Second, Third, Fourth, Fifth, Sixth, Seventh, and Eighth streets. The following is known about the crew's schedule for the week: The crew cleaned no street on Friday morning. The crew cleaned no street on Wednesday afternoon. It cleaned Fourth Street on Tuesday morning. It cleaned Seventh Street on Thursday morning. It cleaned Fourth Street before Sixth Street and after Eighth Street. It cleaned Second, Fifth, and Eighth streets on afternoons. | What is the maximum possible number of streets any one of which could be the one the crew cleaned on Friday afternoon? | [
"1",
"2",
"3",
"4",
"5"
] | 4 |
A street cleaning crew works only Monday to Friday, and only during the day. It takes the crew an entire morning or an entire afternoon to clean a street. During one week the crew cleaned exactly eight streets—First, Second, Third, Fourth, Fifth, Sixth, Seventh, and Eighth streets. The following is known about the crew's schedule for the week: The crew cleaned no street on Friday morning. The crew cleaned no street on Wednesday afternoon. It cleaned Fourth Street on Tuesday morning. It cleaned Seventh Street on Thursday morning. It cleaned Fourth Street before Sixth Street and after Eighth Street. It cleaned Second, Fifth, and Eighth streets on afternoons. | If the crew cleaned First Street earlier in the week than Third Street, then which one of the following statements must be false? | [
"The crew cleaned First Street on Tuesday afternoon.",
"The crew cleaned Second Street on Thursday afternoon.",
"The crew cleaned Third Street on Wednesday morning.",
"The crew cleaned Fifth Street on Thursday afternoon.",
"The crew cleaned Sixth Street on Friday afternoon."
] | 0 |
A street cleaning crew works only Monday to Friday, and only during the day. It takes the crew an entire morning or an entire afternoon to clean a street. During one week the crew cleaned exactly eight streets—First, Second, Third, Fourth, Fifth, Sixth, Seventh, and Eighth streets. The following is known about the crew's schedule for the week: The crew cleaned no street on Friday morning. The crew cleaned no street on Wednesday afternoon. It cleaned Fourth Street on Tuesday morning. It cleaned Seventh Street on Thursday morning. It cleaned Fourth Street before Sixth Street and after Eighth Street. It cleaned Second, Fifth, and Eighth streets on afternoons. | If the crew cleaned Fifth, Sixth, and Seventh streets in numerical order, then what is the maximum number of different schedules any one of which the crew could have had for the entire week? | [
"1",
"2",
"3",
"4",
"5"
] | 3 |
A street cleaning crew works only Monday to Friday, and only during the day. It takes the crew an entire morning or an entire afternoon to clean a street. During one week the crew cleaned exactly eight streets—First, Second, Third, Fourth, Fifth, Sixth, Seventh, and Eighth streets. The following is known about the crew's schedule for the week: The crew cleaned no street on Friday morning. The crew cleaned no street on Wednesday afternoon. It cleaned Fourth Street on Tuesday morning. It cleaned Seventh Street on Thursday morning. It cleaned Fourth Street before Sixth Street and after Eighth Street. It cleaned Second, Fifth, and Eighth streets on afternoons. | Suppose the crew had cleaned Fourth Street on Tuesday afternoon instead of on Tuesday morning, but all other conditions remained the same. Which one of the following statements could be false? | [
"The crew cleaned First Street before Second Street.",
"The crew cleaned Second Street before Fifth Street.",
"The crew cleaned Third Street before Second Street.",
"The crew cleaned Sixth Street before Fifth Street.",
"The crew cleaned Seventh Street before Second Street."
] | 1 |
J, K, L, M, N, and O are square ski chalets of the same size, which are positioned in two straight rows as shown below: J K L row 1: ■ ■ ■ row 2: ■ ■ ■ M N O J is directly opposite M; K is directly opposite N; and L is directly opposite O. After a snowstorm, residents shovel a single continuous path that connects all of the chalets and meets the following conditions: The path is composed of five straight segments, each of which directly connects exactly two of the chalets. Each chalet is directly connected by a segment of the path to another chalet. No chalet is directly connected by segments of the path to more than two other chalets. No segment of the path crosses any other segment. One segment of the path directly connects chalets J and N, and another segment directly connects chalets K and L. | Which one of the following statements could be true? | [
"One segment of the path directly connects chalets M and K.",
"One segment of the path directly connects chalets M and L.",
"One segment of the path directly connects chalets M and O.",
"One segment of the path directly connects chalets J and K and another segment directly connects chalets K and M.",
"One segment of the path directly connects chalets O and L and another segment directly connects chalets O and N."
] | 4 |
J, K, L, M, N, and O are square ski chalets of the same size, which are positioned in two straight rows as shown below: J K L row 1: ■ ■ ■ row 2: ■ ■ ■ M N O J is directly opposite M; K is directly opposite N; and L is directly opposite O. After a snowstorm, residents shovel a single continuous path that connects all of the chalets and meets the following conditions: The path is composed of five straight segments, each of which directly connects exactly two of the chalets. Each chalet is directly connected by a segment of the path to another chalet. No chalet is directly connected by segments of the path to more than two other chalets. No segment of the path crosses any other segment. One segment of the path directly connects chalets J and N, and another segment directly connects chalets K and L. | If one segment of the path directly connects chalets K and N, then the two chalets in which one of the following pairs must be directly connected to each other by a segment? | [
"J and K",
"K and O",
"L and O",
"M and N",
"N and O"
] | 2 |
J, K, L, M, N, and O are square ski chalets of the same size, which are positioned in two straight rows as shown below: J K L row 1: ■ ■ ■ row 2: ■ ■ ■ M N O J is directly opposite M; K is directly opposite N; and L is directly opposite O. After a snowstorm, residents shovel a single continuous path that connects all of the chalets and meets the following conditions: The path is composed of five straight segments, each of which directly connects exactly two of the chalets. Each chalet is directly connected by a segment of the path to another chalet. No chalet is directly connected by segments of the path to more than two other chalets. No segment of the path crosses any other segment. One segment of the path directly connects chalets J and N, and another segment directly connects chalets K and L. | If a segment of the path directly connects chalets J and K, then the two chalets in which one of the following pairs must be directly connected to each other by a segment? | [
"J and M",
"K and N",
"K and O",
"L and O",
"N and O"
] | 3 |
J, K, L, M, N, and O are square ski chalets of the same size, which are positioned in two straight rows as shown below: J K L row 1: ■ ■ ■ row 2: ■ ■ ■ M N O J is directly opposite M; K is directly opposite N; and L is directly opposite O. After a snowstorm, residents shovel a single continuous path that connects all of the chalets and meets the following conditions: The path is composed of five straight segments, each of which directly connects exactly two of the chalets. Each chalet is directly connected by a segment of the path to another chalet. No chalet is directly connected by segments of the path to more than two other chalets. No segment of the path crosses any other segment. One segment of the path directly connects chalets J and N, and another segment directly connects chalets K and L. | If one segment of the path directly connects chalets K and O, then which one of the following statements could be true? | [
"Chalet J is directly connected to chalet M.",
"Chalet K is directly connected to chalet N.",
"Chalet L is directly connected to chalet O.",
"Chalet L is directly connected to exactly two chalets.",
"Chalet O is directly connected to exactly one chalet."
] | 0 |
J, K, L, M, N, and O are square ski chalets of the same size, which are positioned in two straight rows as shown below: J K L row 1: ■ ■ ■ row 2: ■ ■ ■ M N O J is directly opposite M; K is directly opposite N; and L is directly opposite O. After a snowstorm, residents shovel a single continuous path that connects all of the chalets and meets the following conditions: The path is composed of five straight segments, each of which directly connects exactly two of the chalets. Each chalet is directly connected by a segment of the path to another chalet. No chalet is directly connected by segments of the path to more than two other chalets. No segment of the path crosses any other segment. One segment of the path directly connects chalets J and N, and another segment directly connects chalets K and L. | Which one of the following statements, if true, guarantees that one segment of the path directly connects chalets M and N? | [
"One segment of the path directly connects chalets K and J.",
"One segment of the path directly connects chalets N and O.",
"One segment of the path directly connects chalet K and a chalet in row 2.",
"One segment of the path directly connects chalet L and a chalet in row 2.",
"One segment of the path directly connects chalet O and a chalet in row 1."
] | 0 |
J, K, L, M, N, and O are square ski chalets of the same size, which are positioned in two straight rows as shown below: J K L row 1: ■ ■ ■ row 2: ■ ■ ■ M N O J is directly opposite M; K is directly opposite N; and L is directly opposite O. After a snowstorm, residents shovel a single continuous path that connects all of the chalets and meets the following conditions: The path is composed of five straight segments, each of which directly connects exactly two of the chalets. Each chalet is directly connected by a segment of the path to another chalet. No chalet is directly connected by segments of the path to more than two other chalets. No segment of the path crosses any other segment. One segment of the path directly connects chalets J and N, and another segment directly connects chalets K and L. | Which one of the following chalets cannot be directly connected by segments of the path to exactly two other chalets? | [
"K",
"L",
"M",
"N",
"O"
] | 2 |
J, K, L, M, N, and O are square ski chalets of the same size, which are positioned in two straight rows as shown below: J K L row 1: ■ ■ ■ row 2: ■ ■ ■ M N O J is directly opposite M; K is directly opposite N; and L is directly opposite O. After a snowstorm, residents shovel a single continuous path that connects all of the chalets and meets the following conditions: The path is composed of five straight segments, each of which directly connects exactly two of the chalets. Each chalet is directly connected by a segment of the path to another chalet. No chalet is directly connected by segments of the path to more than two other chalets. No segment of the path crosses any other segment. One segment of the path directly connects chalets J and N, and another segment directly connects chalets K and L. | If no segment of the path directly connects any chalet in row 1 with the chalet in row 2 that is directly opposite it, then each of the following statements must be true EXCEPT: | [
"A segment of the path directly connects chalets M and N.",
"A segment of the path directly connects chalets N and O.",
"Chalet L is directly connected to exactly one other chalet.",
"Chalet N is directly connected to exactly two other chalets.",
"Chalet O is directly connected to exactly two other chalets."
] | 1 |
John receives one grade for each of the following six courses: economics, geology, history, Italian, physics, and Russian. From highest to lowest, the possible grades are A, B, C, D, and E. E is the only failing grade. Two letter grades are consecutive if and only if they are adjacent in the alphabet. John's grades in geology and physics are consecutive. His grades in Italian and Russian are consecutive. He receives a higher grade in economics than in history. He receives a higher grade in geology than in physics. | If John receives the same grade in economics and Italian, and if he fails Russian, which one of the following must be true? | [
"John's geology grade is a B.",
"John's history grade is a D.",
"John's history grade is an E.",
"John's physics grade is a B.",
"John's physics grade is a C."
] | 2 |
John receives one grade for each of the following six courses: economics, geology, history, Italian, physics, and Russian. From highest to lowest, the possible grades are A, B, C, D, and E. E is the only failing grade. Two letter grades are consecutive if and only if they are adjacent in the alphabet. John's grades in geology and physics are consecutive. His grades in Italian and Russian are consecutive. He receives a higher grade in economics than in history. He receives a higher grade in geology than in physics. | If John passes all his courses and receives a higher grade in geology than in either language, which one of the following must be true? | [
"He receives exactly one A.",
"He receives exactly one B.",
"He receives exactly two Bs.",
"He receives at least one B and at least one C.",
"He receives at least one C and at least one D."
] | 3 |
John receives one grade for each of the following six courses: economics, geology, history, Italian, physics, and Russian. From highest to lowest, the possible grades are A, B, C, D, and E. E is the only failing grade. Two letter grades are consecutive if and only if they are adjacent in the alphabet. John's grades in geology and physics are consecutive. His grades in Italian and Russian are consecutive. He receives a higher grade in economics than in history. He receives a higher grade in geology than in physics. | If John receives a higher grade in physics than in economics and receives a higher grade in economics than in either language, which one of the following allows all six of his grades to be determined? | [
"His grade in history is D.",
"His grade in Italian is D.",
"His grades in history and Italian are identical.",
"His grades in history and Russian are identical.",
"His grade in history is higher than his grade in Russian."
] | 4 |
John receives one grade for each of the following six courses: economics, geology, history, Italian, physics, and Russian. From highest to lowest, the possible grades are A, B, C, D, and E. E is the only failing grade. Two letter grades are consecutive if and only if they are adjacent in the alphabet. John's grades in geology and physics are consecutive. His grades in Italian and Russian are consecutive. He receives a higher grade in economics than in history. He receives a higher grade in geology than in physics. | If John receives a higher grade in physics than in economics and receives a higher grade in history than in Italian, exactly how many of his grades can be determined? | [
"2",
"3",
"4",
"5",
"6"
] | 4 |
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