benlipkin/arlsat huggingface dataset:
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.

Question: Which one of the following families could live in the house that is the farthest east?
Options:
the Kahns
the Muirs
the Newmans
the Piatts
the Rutans
Correct option (0-indexed): 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.

Question: Which one of the following families CANNOT live next to the Kahns?
Options:
the Lowes
the Newmans
the Owens
the Piatts
the Rutans
Correct option (0-indexed): 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.

Question: If the Muirs live west of the Kahns, then the Rutans CANNOT live next to both
Options:
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
Correct option (0-indexed): 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.

Question: If the Newmans live immediately west of the Kahns, which one of the following statements must be false?
Options:
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.
Correct option (0-indexed): 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.

Question: If the Owens live east of the Muirs, which one of the following statements must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If the Owens live east of the Kahns, which one of the following pairs of families must live next to each other?
Options:
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
Correct option (0-indexed): 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.

Question: If there are sports cars on exactly two floors, then which one of the following statements could be true?
Options:
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.
Correct option (0-indexed): 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.

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

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

Question: If there are research models on exactly two floors, then which one of the following statements can be false?
Options:
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.
Correct option (0-indexed): 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.

Question: If all the new cars in the exhibition are research models, then which one of the following statements must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If all the production models in the exhibition are used, then which one of the following statements must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If Anna flies in plane 4 and Dave flies in plane 2, which one of the following must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If Bob and Anna fly on the same plane, which one of the following must be true?
Options:
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.
Correct option (0-indexed): 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.

Question: If Cindy and Fran are the only people in one of the planes, which one of the following must be true?
Options:
Bob flies with Anna.
Dave flies with Ed.
Dave and Ed fly with Bob.
Dave flies with Bob.
Ed flies with Anna.
Correct option (0-indexed): 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.

Question: If plane 1 is used, its crew could consist of
Options:
Anna, Bob, Cindy, Fran
Anna, Bob, Ed, Fran
Bob, Cindy, Ed, Fran
Bob, Cindy, Dave, Ed
Bob, Dave, Ed, Fran
Correct option (0-indexed): 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.

Question: If as many of the pilots and copilots as possible fly in plane 4, that group will consist of
Options:
exactly two people
exactly three people
exactly four people
exactly five people
three pilots and two copilots
Correct option (0-indexed): 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.

Question: Which one of the following partners cannot have the third highest salary?
Options:
Fox
Inman
Lopez
Malloy
Nassar
Correct option (0-indexed): 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.

Question: If Malloy and Nassar earn the same salary, at least how many of the partners must have lower salaries than Lopez?
Options:
3
4
5
6
7
Correct option (0-indexed): 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.

Question: The salary rankings of each of the nine partners could be completely determined if which one of the following statements were true?
Options:
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.
Correct option (0-indexed): 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.

Question: If Nassar's salary is the same as that of one other partner of the firm, which one of the following must be false?
Options:
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.
Correct option (0-indexed): 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.

Question: What is the minimum number of different salaries earned by the nine partners of the firm?
Options:
5
6
7
8
9
Correct option (0-indexed): 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.

Question: 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?
Options:
fifth
fifth, sixth
fifth, seventh
fifth, sixth, seventh
fifth, sixth, seventh, eighth
Correct option (0-indexed): 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.

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

Question: 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?
Options:
J and N
K and L
K and N
L and M
M and N
Correct option (0-indexed): 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.

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

Question: The illnesses in which one of the following pairs must have exactly one symptom in common?
Options:
J and L
J and M
J and N
K and L
M and N
Correct option (0-indexed): 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.

Question: If Walter has exactly two of the three symptoms, then he cannot have all of the symptoms of
Options:
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
Correct option (0-indexed): 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.

Question: 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?
Options:
First Street
Second Street
Third Street
Fifth Street
Eighth Street
Correct option (0-indexed): 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.

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

Question: What is the maximum possible number of streets any one of which could be the one the crew cleaned on Friday afternoon?
Options:
1
2
3
4
5
Correct option (0-indexed): 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.

Question: If the crew cleaned First Street earlier in the week than Third Street, then which one of the following statements must be false?
Options:
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.
Correct option (0-indexed): 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.

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

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

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

Question: 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?
Options:
J and K
K and O
L and O
M and N
N and O
Correct option (0-indexed): 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.

Question: 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?
Options:
J and M
K and N
K and O
L and O
N and O
Correct option (0-indexed): 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.

Question: If one segment of the path directly connects chalets K and O, then which one of the following statements could be true?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following statements, if true, guarantees that one segment of the path directly connects chalets M and N?
Options:
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.
Correct option (0-indexed): 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.

Question: Which one of the following chalets cannot be directly connected by segments of the path to exactly two other chalets?
Options:
K
L
M
N
O
Correct option (0-indexed): 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.

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

Question: If John receives the same grade in economics and Italian, and if he fails Russian, which one of the following must be true?
Options:
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.
Correct option (0-indexed): 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.

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

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

Question: 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?
Options:
2
3
4
5
6
Correct option (0-indexed): 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.

Question: Assume that John's grade in physics is higher than his grade in Italian and consecutive with it and that his grades in Russian and physics differ. Which one of the following must be true?
Options:
John receives both an A and a B.
John receives both an A and a C.
John receives both a B and a D.
John receives both a B and an E.
John receives both a D and an E.
Correct option (0-indexed): 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.

Question: Assume that John receives a lower grade in economics than in physics. He must have failed at least one course if which one of the following is also true?
Options:
He receives a lower grade in Italian than in economics.
He receives a lower grade in Italian than in physics.
He receives a lower grade in physics than in Italian.
He receives a lower grade in Russian than in economics.
He receives a lower grade in Russian than in history.
Correct option (0-indexed): 4
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available.

Question: Which one of the following must be false?
Options:
Two of the shirts that Casey buys are small and two are red.
Two of the shirts that Casey buys are medium and two are red.
Two of the shirts that Casey buys are large and two are red.
Two of the shirts that Casey buys are small, one is yellow, and one is blue.
Two of the shirts that Casey buys are medium, one is yellow, and one is blue.
Correct option (0-indexed): 0
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available.

Question: If Casey buys a small blue shirt, which one of the following must be false?
Options:
Casey buys two blue shirts.
Casey buys two red shirts.
Casey buys two yellow shirts.
Casey buys two small shirts.
Casey buys two medium shirts.
Correct option (0-indexed): 1
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available.

Question: If Casey does not buy a medium yellow shirt, which one of the following must be true?
Options:
Casey buys either a medium red shirt or a small blue shirt.
Casey buys either a medium red shirt or a medium blue shirt.
Casey buys either a large red shirt or a small blue shirt.
Casey buys either a large red shirt or a medium red shirt.
Casey buys either a large yellow shirt or a small yellow shirt.
Correct option (0-indexed): 1
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available.

Question: If Casey buys exactly one medium shirt and does not buy two shirts of the same color, then she cannot buy which one of the following?
Options:
a medium red shirt
a medium yellow shirt
a medium blue shirt
a large red shirt
a large yellow shirt
Correct option (0-indexed): 1
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available.

Question: If neither large red shirts nor small blue shirts are available, which one of the following must Casey buy?
Options:
a red shirt
a medium yellow shirt
either a large shirt or a small shirt
either a medium red shirt or a medium blue shirt
either a large yellow shirt or a medium blue shirt
Correct option (0-indexed): 3
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X.

Question: Which one of the following is an acceptable selection of fish and plants for the aquarium? Fish Plants
Options:
G, H, K W, Y
G, J, K W, X
G, J, L X, Z
H, J, L W, Z
H, K, L Y, Z
Correct option (0-indexed): 1
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X.

Question: If the hobbyist selects the H, which one of the following must also be true?
Options:
She selects at least one W.
She selects at least one X.
She selects the J, but no Y's.
She selects the K, but no X's.
She selects at least one X, but no Y's.
Correct option (0-indexed): 1
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X.

Question: If the hobbyist selects both X's and Z's, which one of the following could be the group of fish she selects?
Options:
G, H, K
G, J, K
G, K, L
H, J, L
J, K, L
Correct option (0-indexed): 2
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X.

Question: The hobbyist could select any of the following groups of fish for the aquarium EXCEPT
Options:
G, K, L
H, J, K
H, J, L
H, K, L
J, K, L
Correct option (0-indexed): 2