benlipkin/arlsat huggingface dataset:
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.

Question: Which one of the following seating arrangements of the six representatives in chairs 1 through 6 would NOT violate the stated conditions?
Options:
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
Correct option (0-indexed): 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.

Question: 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?
Options:
Klosnik and Osata
Londi and Neri
Londi and Osata
Manley and Neri
Manley and Poirier
Correct option (0-indexed): 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.

Question: If Klosnik sits directly between Londi and Poirier, then Manley must sit directly between
Options:
Londi and Neri
Londi and Osata
Neri and Osata
Neri and Poirier
Osata and Poirier
Correct option (0-indexed): 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.

Question: If Neri sits immediately next to Manley, then Klosnik can sit directly between
Options:
Londi and Manley
Londi and Poirier
Neri and Osata
Neri and Poirier
Poirier and Osata
Correct option (0-indexed): 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.

Question: 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?
Options:
Klosnik
Klosnik, Neri
Neri, Poirier
Klosnik, Osata, Poirier
Klosnik, Neri, Osata, Poirier
Correct option (0-indexed): 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.

Question: If Londi sits immediately next to Neri, which one of the following statements must be false?
Options:
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.
Correct option (0-indexed): 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.

Question: If Klosnik sits immediately next to Osata, then Londi CANNOT sit directly between
Options:
Klosnik and Manley
Klosnik and Neri
Manley and Neri
Manley and Poirier
Neri and Osata
Correct option (0-indexed): 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.

Question: 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?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following statements could be true?
Options:
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.
Correct option (0-indexed): 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.

Question: 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?
Options:
0
1
2
3
4
Correct option (0-indexed): 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.

Question: If the computer in office 4 was bought in 1988, then which one of the following statements must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If the computer in office 3 was bought in 1988, then which one of the following statements could be true?
Options:
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.
Correct option (0-indexed): 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.

Question: 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?
Options:
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
Correct option (0-indexed): 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.

Question: Which one of the following CANNOT be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If James joined the firm in 1962, which one of the following CANNOT be true?
Options:
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.
Correct option (0-indexed): 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.

Question: Of the following, which one is the latest year in which James could have joined the firm?
Options:
1962
1963
1964
1965
1966
Correct option (0-indexed): 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.

Question: 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?
Options:
1
2
3
4
5
Correct option (0-indexed): 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.

Question: 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?
Options:
1963
1964
1965
1966
1967
Correct option (0-indexed): 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.

Question: If the line 3 tickets for January are red, then which one of the following statements must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If one set of the line 2 tickets is green, then which one of the following statements must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following statements could be true?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following statements could be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If the line 3 tickets for February are yellow, then each of the following statements must be true EXCEPT:
Options:
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.
Correct option (0-indexed): 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.

Question: 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?
Options:
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.
Correct option (0-indexed): 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.

Question: Who were the last two workers to be hired?
Options:
Eberle and Jessup
Brandt and Garcia
Brandt and Calva
Garcia and Calva
Jessup and Brandt
Correct option (0-indexed): 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.

Question: Who was hired on the fourth day of hiring?
Options:
Eberle
Brandt
Irving
Garcia
Jessup
Correct option (0-indexed): 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.

Question: Exactly how many workers were hired before Jessup?
Options:
6
5
4
3
2
Correct option (0-indexed): 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.

Question: Which one of the following must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If Eberle was hired on a Monday, what is the earliest day on which Garcia could have been hired?
Options:
Monday
Tuesday
Wednesday
Thursday
Friday
Correct option (0-indexed): 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.

Question: Which one of the following must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following CANNOT be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If J lives on the fourth floor and K lives on the fifth floor, which one of the following can be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If O lives on the second floor, which one of the following CANNOT be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If M lives on the fourth floor, which one of the following must be false?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If O lives on the fourth floor and P lives on the second floor, which one of the following must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If Hannah spends exactly eight days in the cities of country X, then which one of the following CANNOT be true?
Options:
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.
Correct option (0-indexed): 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.

Question: 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?
Options:
3
4
5
6
7
Correct option (0-indexed): 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.

Question: 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?
Options:
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.
Correct option (0-indexed): 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.

Question: 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?
Options:
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.
Correct option (0-indexed): 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.

Question: 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?
Options:
6
7
8
9
10
Correct option (0-indexed): 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.

Question: Which one of the following is a complete and accurate list of the dogs that can be greyhounds?
Options:
P, Q
P, R
P, Q, R
P, R, T
P, Q, R, T
Correct option (0-indexed): 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.

Question: Which one of the following statements CANNOT be true?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following dogs must be male?
Options:
dog P
dog R
dog S
dog T
dog U
Correct option (0-indexed): 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.

Question: Which one of the following statements can be false?
Options:
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.
Correct option (0-indexed): 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.

Question: If dog Q is female, which one of the following statements can be false?
Options:
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.
Correct option (0-indexed): 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.

Question: If dog T wins the fourth place ribbon, then which one of the following statements must be true?
Options:
Dog P is male.
Dog Q is male.
Dog T is male.
Dog Q is a labrador.
Dog T is a labrador.
Correct option (0-indexed): 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.

Question: Which one of the following statements could be true?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following is a complete and accurate list of the entrees any one of which Lewis could order?
Options:
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
Correct option (0-indexed): 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.

Question: Which one of the following statements could be true?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following statements must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If John orders veal cutlet, then which one of the following statements must be true?
Options:
Kate orders roast beef.
Kate orders swordfish.
Lewis orders tilefish.
Lewis orders veal cutlet.
Nat orders pork chops.
Correct option (0-indexed): 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.

Question: If none of the six people orders pork chops, then which one of the following statements must be true?
Options:
John orders veal cutlet.
Kate orders tilefish.
Lewis orders tilefish.
One of the men orders swordfish.
One of the women orders tilefish.
Correct option (0-indexed): 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.

Question: 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?
Options:
roast beef
veal cutlet
roast beef, veal cutlet
roast beef, swordfish
pork chops, roast beef, swordfish
Correct option (0-indexed): 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.

Question: 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?
Options:
John orders roast beef.
John orders swordfish.
Kate orders roast beef.
Two of the people order pork chops.
Two of the people order tilefish.
Correct option (0-indexed): 3