benlipkin/arlsat huggingface dataset:
The population of a small country is organized into five clans—N, O, P, S, and T. Each year exactly three of the five clans participate in the annual harvest ceremonies. The rules specifying the order of participation of the clans in the ceremonies are as follows: Each clan must participate at least once in any two consecutive years. No clan participates for three consecutive years. Participation takes place in cycles, with each cycle ending when each of the five clans has participated three times. Only then does a new cycle begin. No clan participates more than three times within any cycle.

Question: If, in a particular cycle, N, O, and S participate in the ceremonies in the first year and O, S, and T participate in the third year, then which one of the following could be the clans that participate in the fifth year?
Options:
N, O, P
N, O, S
N, P, S
O, P, S
P, S, T
Correct option (0-indexed): 4
A newly formed company has five employees—F, G, H, K, and L. Each employee holds exactly one of the following positions: president, manager, or technician. Only the president is not supervised. Other employees are each supervised by exactly one employee, who is either the president or a manager. Each supervised employee holds a different position than his or her supervisor. The following conditions apply: There is exactly one president. At least one of the employees whom the president supervises is a manager. Each manager supervises at least one employee. F does not supervise any employee. G supervises exactly two employees.

Question: Which one of the following is an acceptable assignment of employees to the positions? President Manager Technician
Options:
G H, K, L F
G H F, K, L
H F, G K, L
H, K G F, L
K F, G, H, L
Correct option (0-indexed): 1
A newly formed company has five employees—F, G, H, K, and L. Each employee holds exactly one of the following positions: president, manager, or technician. Only the president is not supervised. Other employees are each supervised by exactly one employee, who is either the president or a manager. Each supervised employee holds a different position than his or her supervisor. The following conditions apply: There is exactly one president. At least one of the employees whom the president supervises is a manager. Each manager supervises at least one employee. F does not supervise any employee. G supervises exactly two employees.

Question: Which one of the following must be true?
Options:
There are at most three technicians.
There is exactly one technician.
There are at least two managers.
There are exactly two managers.
There are exactly two employees who supervise no one.
Correct option (0-indexed): 0
A newly formed company has five employees—F, G, H, K, and L. Each employee holds exactly one of the following positions: president, manager, or technician. Only the president is not supervised. Other employees are each supervised by exactly one employee, who is either the president or a manager. Each supervised employee holds a different position than his or her supervisor. The following conditions apply: There is exactly one president. At least one of the employees whom the president supervises is a manager. Each manager supervises at least one employee. F does not supervise any employee. G supervises exactly two employees.

Question: Which one of the following is a pair of employees who could serve as managers together?
Options:
F, H
F, L
G, K
G, L
K, L
Correct option (0-indexed): 4
A newly formed company has five employees—F, G, H, K, and L. Each employee holds exactly one of the following positions: president, manager, or technician. Only the president is not supervised. Other employees are each supervised by exactly one employee, who is either the president or a manager. Each supervised employee holds a different position than his or her supervisor. The following conditions apply: There is exactly one president. At least one of the employees whom the president supervises is a manager. Each manager supervises at least one employee. F does not supervise any employee. G supervises exactly two employees.

Question: Which one of the following could be true?
Options:
There is exactly one technician.
There are exactly two managers.
There are exactly two employees who are not supervised.
There are more managers than technicians.
The president supervises all of the other employees.
Correct option (0-indexed): 1
A newly formed company has five employees—F, G, H, K, and L. Each employee holds exactly one of the following positions: president, manager, or technician. Only the president is not supervised. Other employees are each supervised by exactly one employee, who is either the president or a manager. Each supervised employee holds a different position than his or her supervisor. The following conditions apply: There is exactly one president. At least one of the employees whom the president supervises is a manager. Each manager supervises at least one employee. F does not supervise any employee. G supervises exactly two employees.

Question: If F is supervised by the president, which one of the following must be true?
Options:
G is the president.
H is the president.
L is a technician.
There is exactly one manager.
There are exactly two technicians.
Correct option (0-indexed): 3
A newly formed company has five employees—F, G, H, K, and L. Each employee holds exactly one of the following positions: president, manager, or technician. Only the president is not supervised. Other employees are each supervised by exactly one employee, who is either the president or a manager. Each supervised employee holds a different position than his or her supervisor. The following conditions apply: There is exactly one president. At least one of the employees whom the president supervises is a manager. Each manager supervises at least one employee. F does not supervise any employee. G supervises exactly two employees.

Question: If K supervises exactly two employees, which one of the following must be true?
Options:
F is supervised by K.
G is a manager.
L is supervised.
There are exactly two managers.
There are exactly two technicians.
Correct option (0-indexed): 2
Ron washed a total of seven objects after eating his lunch. Two of the objects were pieces of china: a mug and a plate. Two were pieces of glassware: a water glass and a juice glass. Three were utensils: a fork, a knife, and a spoon. Ron washed the two pieces of china consecutively, the two glasses consecutively, and the three utensils consecutively. He washed the objects as follows: Ron washed each of the objects exactly once. Ron washed the glassware after either the china or the utensils but not after both. He washed the knife before the spoon, and he washed the mug before the plate. He did not wash any two objects at the same time.

Question: Which one of the following statements CANNOT be true?
Options:
Ron washed the fork first.
Ron washed the fork second.
Ron washed the mug first.
Ron washed the plate second.
Ron washed the plate third.
Correct option (0-indexed): 4
Ron washed a total of seven objects after eating his lunch. Two of the objects were pieces of china: a mug and a plate. Two were pieces of glassware: a water glass and a juice glass. Three were utensils: a fork, a knife, and a spoon. Ron washed the two pieces of china consecutively, the two glasses consecutively, and the three utensils consecutively. He washed the objects as follows: Ron washed each of the objects exactly once. Ron washed the glassware after either the china or the utensils but not after both. He washed the knife before the spoon, and he washed the mug before the plate. He did not wash any two objects at the same time.

Question: Which one of the following statements can be true?
Options:
Ron washed the knife second.
Ron washed the knife seventh.
Ron washed the mug second.
Ron washed the mug third.
Ron washed the mug fourth.
Correct option (0-indexed): 0
Ron washed a total of seven objects after eating his lunch. Two of the objects were pieces of china: a mug and a plate. Two were pieces of glassware: a water glass and a juice glass. Three were utensils: a fork, a knife, and a spoon. Ron washed the two pieces of china consecutively, the two glasses consecutively, and the three utensils consecutively. He washed the objects as follows: Ron washed each of the objects exactly once. Ron washed the glassware after either the china or the utensils but not after both. He washed the knife before the spoon, and he washed the mug before the plate. He did not wash any two objects at the same time.

Question: Which one of the following CANNOT be an accurate list of the objects Ron washed second, third, and fourth, respectively?
Options:
fork, spoon, water glass
knife, fork, juice glass
knife, spoon, juice glass
knife, spoon, water glass
plate, water glass, juice glass
Correct option (0-indexed): 1
Ron washed a total of seven objects after eating his lunch. Two of the objects were pieces of china: a mug and a plate. Two were pieces of glassware: a water glass and a juice glass. Three were utensils: a fork, a knife, and a spoon. Ron washed the two pieces of china consecutively, the two glasses consecutively, and the three utensils consecutively. He washed the objects as follows: Ron washed each of the objects exactly once. Ron washed the glassware after either the china or the utensils but not after both. He washed the knife before the spoon, and he washed the mug before the plate. He did not wash any two objects at the same time.

Question: It is NOT possible that Ron washed the knife
Options:
first
second
third
fifth
sixth
Correct option (0-indexed): 2
Ron washed a total of seven objects after eating his lunch. Two of the objects were pieces of china: a mug and a plate. Two were pieces of glassware: a water glass and a juice glass. Three were utensils: a fork, a knife, and a spoon. Ron washed the two pieces of china consecutively, the two glasses consecutively, and the three utensils consecutively. He washed the objects as follows: Ron washed each of the objects exactly once. Ron washed the glassware after either the china or the utensils but not after both. He washed the knife before the spoon, and he washed the mug before the plate. He did not wash any two objects at the same time.

Question: If Ron washed the spoon immediately before the fork, then which one of the following statements can be true?
Options:
He washed the knife second.
He washed the knife third.
He washed the plate third.
He washed the plate sixth.
He washed the plate seventh.
Correct option (0-indexed): 4
Ron washed a total of seven objects after eating his lunch. Two of the objects were pieces of china: a mug and a plate. Two were pieces of glassware: a water glass and a juice glass. Three were utensils: a fork, a knife, and a spoon. Ron washed the two pieces of china consecutively, the two glasses consecutively, and the three utensils consecutively. He washed the objects as follows: Ron washed each of the objects exactly once. Ron washed the glassware after either the china or the utensils but not after both. He washed the knife before the spoon, and he washed the mug before the plate. He did not wash any two objects at the same time.

Question: If Ron washed a glass and the knife consecutively, but not necessarily in that order, then which one of the following statements must be false?
Options:
He washed the fork before the plate.
He washed the fork before the spoon.
He washed the juice glass before the knife.
He washed the plate before the water glass.
He washed the spoon before the fork.
Correct option (0-indexed): 0
A breeder has ten birds: Kind Male Female Goldfinches H J, K Lovebirds M N Parakeets Q, R, S T, W The breeder exhibits pairs of birds consisting of one male and one female of the same kind. At most two pairs can be exhibited at a time; the remaining birds must be distributed between two cages. The breeder is constrained by the following conditions: Neither cage can contain more than four birds. Any two birds that are both of the same sex and of the same kind as each other cannot be caged together. Whenever either J or W is exhibited, S cannot be exhibited.

Question: Which one of the following is a possible assignment of the birds? First Cage Second Cage Exhibition
Options:
H, M, N J, K, S Q, R, T, W
K, M, Q N, R, W H, J, S, T
K, Q, S R, T, W H, J, M, N
H, J, M, R K, N, S, W Q, T
H, J, M, R, W K, N, S Q, T, W
Correct option (0-indexed): 3
A breeder has ten birds: Kind Male Female Goldfinches H J, K Lovebirds M N Parakeets Q, R, S T, W The breeder exhibits pairs of birds consisting of one male and one female of the same kind. At most two pairs can be exhibited at a time; the remaining birds must be distributed between two cages. The breeder is constrained by the following conditions: Neither cage can contain more than four birds. Any two birds that are both of the same sex and of the same kind as each other cannot be caged together. Whenever either J or W is exhibited, S cannot be exhibited.

Question: Which one of the following lists two pairs of birds that the breeder can exhibit at the same time?
Options:
H and J; M and N
H and J; S and T
H and K; M and N
H and K; R and W
M and N; S and W
Correct option (0-indexed): 3
A breeder has ten birds: Kind Male Female Goldfinches H J, K Lovebirds M N Parakeets Q, R, S T, W The breeder exhibits pairs of birds consisting of one male and one female of the same kind. At most two pairs can be exhibited at a time; the remaining birds must be distributed between two cages. The breeder is constrained by the following conditions: Neither cage can contain more than four birds. Any two birds that are both of the same sex and of the same kind as each other cannot be caged together. Whenever either J or W is exhibited, S cannot be exhibited.

Question: If Q and R are among the birds that are assigned to the cages, then it must be true that
Options:
H is exhibited
K is exhibited
N is exhibited
J is assigned to one of the cages
T is assigned to one of the cages
Correct option (0-indexed): 3
A breeder has ten birds: Kind Male Female Goldfinches H J, K Lovebirds M N Parakeets Q, R, S T, W The breeder exhibits pairs of birds consisting of one male and one female of the same kind. At most two pairs can be exhibited at a time; the remaining birds must be distributed between two cages. The breeder is constrained by the following conditions: Neither cage can contain more than four birds. Any two birds that are both of the same sex and of the same kind as each other cannot be caged together. Whenever either J or W is exhibited, S cannot be exhibited.

Question: If Q and T are among the birds assigned to the cages, which one of the following is a pair of birds that must be exhibited?
Options:
H and J
H and K
M and N
R and W
S and W
Correct option (0-indexed): 3
A breeder has ten birds: Kind Male Female Goldfinches H J, K Lovebirds M N Parakeets Q, R, S T, W The breeder exhibits pairs of birds consisting of one male and one female of the same kind. At most two pairs can be exhibited at a time; the remaining birds must be distributed between two cages. The breeder is constrained by the following conditions: Neither cage can contain more than four birds. Any two birds that are both of the same sex and of the same kind as each other cannot be caged together. Whenever either J or W is exhibited, S cannot be exhibited.

Question: Which one of the following CANNOT be true?
Options:
One pair of parakeets are the only birds exhibited together.
One pair of goldfinches and one pair of lovebirds are exhibited together.
One pair of goldfinches and one pair of parakeets are exhibited together.
One pair of lovebirds and one pair of parakeets are exhibited together.
Two pairs of parakeets are exhibited together.
Correct option (0-indexed): 1
A breeder has ten birds: Kind Male Female Goldfinches H J, K Lovebirds M N Parakeets Q, R, S T, W The breeder exhibits pairs of birds consisting of one male and one female of the same kind. At most two pairs can be exhibited at a time; the remaining birds must be distributed between two cages. The breeder is constrained by the following conditions: Neither cage can contain more than four birds. Any two birds that are both of the same sex and of the same kind as each other cannot be caged together. Whenever either J or W is exhibited, S cannot be exhibited.

Question: If S is one of the birds exhibited, it must be true that
Options:
H is exhibited
M is exhibited
K is assigned to a cage
N is assigned to a cage
R is assigned to a cage
Correct option (0-indexed): 4
During each of the fall, winter, spring, and summer seasons of one year, Nikki and Otto each participate in exactly one of the following five sports: hockey, kayaking, mountaineering, running, and volleyball. Each child participates in exactly four different sports during the year. In the fall, each child participates in mountaineering, running, or volleyball. In the winter, each child participates in hockey or volleyball. In the spring, each child participates in kayaking, mountaineering, running, or volleyball. In the summer, each child participates in kayaking, mountaineering, or volleyball. Nikki and Otto do not participate in the same sport during the same season. Otto's summer sport is volleyball.

Question: Which one of the following statements must be true?
Options:
Nikki's fall sport is running.
Nikki's winter sport is volleyball.
Nikki's spring sport is mountaineering.
Otto's fall sport is mountaineering.
Otto's spring sport is kayaking.
Correct option (0-indexed): 1
During each of the fall, winter, spring, and summer seasons of one year, Nikki and Otto each participate in exactly one of the following five sports: hockey, kayaking, mountaineering, running, and volleyball. Each child participates in exactly four different sports during the year. In the fall, each child participates in mountaineering, running, or volleyball. In the winter, each child participates in hockey or volleyball. In the spring, each child participates in kayaking, mountaineering, running, or volleyball. In the summer, each child participates in kayaking, mountaineering, or volleyball. Nikki and Otto do not participate in the same sport during the same season. Otto's summer sport is volleyball.

Question: It CANNOT be true that both Nikki and Otto participate during the year in which one of the following sports?
Options:
hockey
kayaking
mountaineering
running
volleyball
Correct option (0-indexed): 0
During each of the fall, winter, spring, and summer seasons of one year, Nikki and Otto each participate in exactly one of the following five sports: hockey, kayaking, mountaineering, running, and volleyball. Each child participates in exactly four different sports during the year. In the fall, each child participates in mountaineering, running, or volleyball. In the winter, each child participates in hockey or volleyball. In the spring, each child participates in kayaking, mountaineering, running, or volleyball. In the summer, each child participates in kayaking, mountaineering, or volleyball. Nikki and Otto do not participate in the same sport during the same season. Otto's summer sport is volleyball.

Question: If Nikki's fall sport is running, then which one of the following statements must be true?
Options:
Nikki's spring sport is kayaking.
Nikki's summer sport is mountaineering.
Otto's fall sport is mountaineering.
Otto's spring sport is kayaking.
Otto's spring sport is running.
Correct option (0-indexed): 2
During each of the fall, winter, spring, and summer seasons of one year, Nikki and Otto each participate in exactly one of the following five sports: hockey, kayaking, mountaineering, running, and volleyball. Each child participates in exactly four different sports during the year. In the fall, each child participates in mountaineering, running, or volleyball. In the winter, each child participates in hockey or volleyball. In the spring, each child participates in kayaking, mountaineering, running, or volleyball. In the summer, each child participates in kayaking, mountaineering, or volleyball. Nikki and Otto do not participate in the same sport during the same season. Otto's summer sport is volleyball.

Question: Which one of the following statements could be true?
Options:
Nikki's fall sport is neither mountaineering nor running.
Nikki's spring sport is neither mountaineering nor running.
Nikki's summer sport is neither kayaking nor mountaineering.
Otto's fall sport is neither mountaineering nor running.
Otto's spring sport is neither kayaking, nor mountaineering, nor running.
Correct option (0-indexed): 1
During each of the fall, winter, spring, and summer seasons of one year, Nikki and Otto each participate in exactly one of the following five sports: hockey, kayaking, mountaineering, running, and volleyball. Each child participates in exactly four different sports during the year. In the fall, each child participates in mountaineering, running, or volleyball. In the winter, each child participates in hockey or volleyball. In the spring, each child participates in kayaking, mountaineering, running, or volleyball. In the summer, each child participates in kayaking, mountaineering, or volleyball. Nikki and Otto do not participate in the same sport during the same season. Otto's summer sport is volleyball.

Question: If Otto does not run during the year, then which one of the following statements must be false?
Options:
Nikki's fall sport is running.
Nikki's spring sport is running.
Nikki's summer sport is kayaking.
Otto's fall sport is mountaineering.
Otto's spring sport is kayaking.
Correct option (0-indexed): 1
During each of the fall, winter, spring, and summer seasons of one year, Nikki and Otto each participate in exactly one of the following five sports: hockey, kayaking, mountaineering, running, and volleyball. Each child participates in exactly four different sports during the year. In the fall, each child participates in mountaineering, running, or volleyball. In the winter, each child participates in hockey or volleyball. In the spring, each child participates in kayaking, mountaineering, running, or volleyball. In the summer, each child participates in kayaking, mountaineering, or volleyball. Nikki and Otto do not participate in the same sport during the same season. Otto's summer sport is volleyball.

Question: Which one of the following statements could be true?
Options:
Nikki's fall sport is mountaineering and Otto's spring sport is running.
Nikki's spring sport is running and her summer sport is mountaineering.
Nikki's spring sport is mountaineering and Otto's fall sport is mountaineering.
Nikki's spring sport is running and Otto's fall sport is mountaineering.
Nikki's summer sport is mountaineering and Otto's spring sport is mountaineering.
Correct option (0-indexed): 2
A professor will listen to exactly one speech from each of six students—H, J, K, R, S, and T. The six speeches will be delivered one at a time, consecutively, according to the following conditions: The speeches delivered by H, J, and K, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. The speeches delivered by R, S, and T, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. H's speech must be earlier than S's speech. J's speech can be neither first nor sixth. T's speech can be neither immediately before nor immediately after J's speech.

Question: Which one of the following could be the order, from first to last, in which the students deliver their speeches?
Options:
H, J, R, S, T, K
H, R, T, K, S, J
K, J, T, H, S, R
R, J, K, T, H, S
T, R, J, S, K, H
Correct option (0-indexed): 3
A professor will listen to exactly one speech from each of six students—H, J, K, R, S, and T. The six speeches will be delivered one at a time, consecutively, according to the following conditions: The speeches delivered by H, J, and K, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. The speeches delivered by R, S, and T, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. H's speech must be earlier than S's speech. J's speech can be neither first nor sixth. T's speech can be neither immediately before nor immediately after J's speech.

Question: If T delivers the third speech, which one of the following must be true?
Options:
H delivers the first speech.
J delivers the fifth speech.
K delivers the fourth speech.
R delivers the sixth speech.
S delivers the fourth speech.
Correct option (0-indexed): 1
A professor will listen to exactly one speech from each of six students—H, J, K, R, S, and T. The six speeches will be delivered one at a time, consecutively, according to the following conditions: The speeches delivered by H, J, and K, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. The speeches delivered by R, S, and T, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. H's speech must be earlier than S's speech. J's speech can be neither first nor sixth. T's speech can be neither immediately before nor immediately after J's speech.

Question: If S delivers the third speech and T delivers the fourth speech, then which one of the following must be true?
Options:
H delivers the second speech.
J delivers the fifth speech.
K delivers the fifth speech.
K delivers the first speech.
R delivers the first speech.
Correct option (0-indexed): 2
A professor will listen to exactly one speech from each of six students—H, J, K, R, S, and T. The six speeches will be delivered one at a time, consecutively, according to the following conditions: The speeches delivered by H, J, and K, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. The speeches delivered by R, S, and T, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. H's speech must be earlier than S's speech. J's speech can be neither first nor sixth. T's speech can be neither immediately before nor immediately after J's speech.

Question: If K delivers the first speech and H delivers the fifth speech, which one of the following must be true?
Options:
R delivers the third speech.
T delivers the fourth speech.
J's speech is immediately before H's speech.
K's speech is immediately before T's speech.
R's speech is immediately before J's speech.
Correct option (0-indexed): 0
A professor will listen to exactly one speech from each of six students—H, J, K, R, S, and T. The six speeches will be delivered one at a time, consecutively, according to the following conditions: The speeches delivered by H, J, and K, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. The speeches delivered by R, S, and T, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. H's speech must be earlier than S's speech. J's speech can be neither first nor sixth. T's speech can be neither immediately before nor immediately after J's speech.

Question: If R's speech is immediately after S's speech and immediately before K's speech, then which one of the following could be true?
Options:
H's speech is immediately before S's speech.
H's speech is immediately before T's speech.
K's speech is immediately before J's speech.
K's speech is immediately before T's speech.
T's speech is immediately before S's speech.
Correct option (0-indexed): 3
A professor will listen to exactly one speech from each of six students—H, J, K, R, S, and T. The six speeches will be delivered one at a time, consecutively, according to the following conditions: The speeches delivered by H, J, and K, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. The speeches delivered by R, S, and T, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. H's speech must be earlier than S's speech. J's speech can be neither first nor sixth. T's speech can be neither immediately before nor immediately after J's speech.

Question: If K delivers the third speech, any of the following could be the student who makes the fourth speech EXCEPT
Options:
H
J
R
S
T
Correct option (0-indexed): 0
The country of Zendu contains exactly four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Zendu. Part of R intersects T; part of S also intersects T; R does not intersect S. Area U is completely within R and also completely within T. At noon exactly four planes J, K, L, M—are over Zendu, in a manner consistent with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas.

Question: Which one of the following could be a complete listing of the planes located in the four areas at noon, with each plane listed in every area in which it is located?
Options:
R: J, L; S: J, M; T: L; U: L
R: J, L; S: K; T: M; U: none
R: K; S: J; T: L; U: M
R: K, M; S: J, L; T: J; U: none
R: M; S: J, K; T: J, L; U: none
Correct option (0-indexed): 3
The country of Zendu contains exactly four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Zendu. Part of R intersects T; part of S also intersects T; R does not intersect S. Area U is completely within R and also completely within T. At noon exactly four planes J, K, L, M—are over Zendu, in a manner consistent with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas.

Question: If at noon K is within exactly two of the four areas, then which one of the following CANNOT be true at that time?
Options:
J is within area T.
K is within area R.
K is within area T.
L is within area R.
L is within area T.
Correct option (0-indexed): 0
The country of Zendu contains exactly four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Zendu. Part of R intersects T; part of S also intersects T; R does not intersect S. Area U is completely within R and also completely within T. At noon exactly four planes J, K, L, M—are over Zendu, in a manner consistent with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas.

Question: Which one of the following is a complete and accurate list of those planes any one of which could be within area T at noon?
Options:
M
J, L
J, L, M
K, L, M
J, K, L, M
Correct option (0-indexed): 4
The country of Zendu contains exactly four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Zendu. Part of R intersects T; part of S also intersects T; R does not intersect S. Area U is completely within R and also completely within T. At noon exactly four planes J, K, L, M—are over Zendu, in a manner consistent with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas.

Question: Which one of the following statements CANNOT be true at noon about the planes?
Options:
K is within area T.
K is within area U.
L is within area R.
M is within area R.
M is within area U.
Correct option (0-indexed): 4
The country of Zendu contains exactly four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Zendu. Part of R intersects T; part of S also intersects T; R does not intersect S. Area U is completely within R and also completely within T. At noon exactly four planes J, K, L, M—are over Zendu, in a manner consistent with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas.

Question: It CANNOT be true that at noon there is at least one plane that is within both area
Options:
R and area T
R and area U
S and area T
S and area U
T and area U
Correct option (0-indexed): 3
The country of Zendu contains exactly four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Zendu. Part of R intersects T; part of S also intersects T; R does not intersect S. Area U is completely within R and also completely within T. At noon exactly four planes J, K, L, M—are over Zendu, in a manner consistent with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas.

Question: If at noon M is within area T, then which one of the following statements CANNOT be true at that time?
Options:
J is within area T.
L is within area R.
L is within area S.
K is within exactly two areas.
L is within exactly two areas.
Correct option (0-indexed): 4
The country of Zendu contains exactly four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Zendu. Part of R intersects T; part of S also intersects T; R does not intersect S. Area U is completely within R and also completely within T. At noon exactly four planes J, K, L, M—are over Zendu, in a manner consistent with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas.

Question: If at noon plane L is within exactly three of the areas, which one of the following could be true at that time?
Options:
J is within exactly two of the areas.
J is within exactly three of the areas.
K is within area S.
M is within area R.
M is within area T.
Correct option (0-indexed): 0
Four people—Fritz, Gina, Helen, and Jerry—have formed a car pool to commute to work together six days a week from Monday through Saturday. Each day exactly one of the people drives. The schedule of the car pool's drivers for any given week must meet the following conditions: Each person drives on at least one day. No person drives on two consecutive days. Fritz does not drive on Monday. Jerry drives on Wednesday or Saturday or both, and he may also drive on other days. If Gina drives on Monday, then Jerry does not drive on Saturday.

Question: Which one of the following could be the schedule of drivers for one week, for the days Monday through Saturday, respectively?
Options:
Gina, Fritz, Jerry, Helen, Gina, Gina
Gina, Fritz, Jerry, Helen, Fritz, Jerry
Helen, Fritz, Gina, Jerry, Helen, Fritz
Helen, Gina, Jerry, Fritz, Helen, Fritz
Helen, Gina, Jerry, Helen, Jerry, Gina
Correct option (0-indexed): 3
Four people—Fritz, Gina, Helen, and Jerry—have formed a car pool to commute to work together six days a week from Monday through Saturday. Each day exactly one of the people drives. The schedule of the car pool's drivers for any given week must meet the following conditions: Each person drives on at least one day. No person drives on two consecutive days. Fritz does not drive on Monday. Jerry drives on Wednesday or Saturday or both, and he may also drive on other days. If Gina drives on Monday, then Jerry does not drive on Saturday.

Question: Which one of the following could be true of one week's schedule of drivers?
Options:
Fritz drives on both Wednesday and Saturday.
Gina drives on both Monday and Wednesday.
Jerry drives on both Tuesday and Friday.
Gina drives on Monday and Jerry drives on Thursday.
Jerry drives on Wednesday and Gina drives on Saturday.
Correct option (0-indexed): 4
Four people—Fritz, Gina, Helen, and Jerry—have formed a car pool to commute to work together six days a week from Monday through Saturday. Each day exactly one of the people drives. The schedule of the car pool's drivers for any given week must meet the following conditions: Each person drives on at least one day. No person drives on two consecutive days. Fritz does not drive on Monday. Jerry drives on Wednesday or Saturday or both, and he may also drive on other days. If Gina drives on Monday, then Jerry does not drive on Saturday.

Question: If during one week Jerry drives on Wednesday and Saturday only, which one of the following must be true of that week?
Options:
Fritz drives on Tuesday.
Gina drives on Friday.
Helen drives on Monday.
Fritz drives on exactly two days.
Helen drives on exactly two days.
Correct option (0-indexed): 2
Four people—Fritz, Gina, Helen, and Jerry—have formed a car pool to commute to work together six days a week from Monday through Saturday. Each day exactly one of the people drives. The schedule of the car pool's drivers for any given week must meet the following conditions: Each person drives on at least one day. No person drives on two consecutive days. Fritz does not drive on Monday. Jerry drives on Wednesday or Saturday or both, and he may also drive on other days. If Gina drives on Monday, then Jerry does not drive on Saturday.

Question: If during one week Gina drives on Monday and Saturday only, which one of the following must be true of that week?
Options:
One other person besides Gina drives on exactly two days.
The person who drives on Wednesday does not drive on Friday.
Helen drives on a day immediately before a day on which Fritz drives.
Either Fritz or Helen drives on Friday.
Either Helen or Jerry drives on Tuesday.
Correct option (0-indexed): 0
Four people—Fritz, Gina, Helen, and Jerry—have formed a car pool to commute to work together six days a week from Monday through Saturday. Each day exactly one of the people drives. The schedule of the car pool's drivers for any given week must meet the following conditions: Each person drives on at least one day. No person drives on two consecutive days. Fritz does not drive on Monday. Jerry drives on Wednesday or Saturday or both, and he may also drive on other days. If Gina drives on Monday, then Jerry does not drive on Saturday.

Question: Which one of the following CANNOT be true of one week's schedule of drivers?
Options:
Fritz drives on Tuesday and Gina drives on Friday.
Gina drives on Monday and Jerry drives on Tuesday.
Gina drives on Monday and Jerry drives on Friday.
Helen drives on Monday and Jerry drives on Tuesday.
Helen drives on Tuesday and Jerry drives on Friday.
Correct option (0-indexed): 1
Four people—Fritz, Gina, Helen, and Jerry—have formed a car pool to commute to work together six days a week from Monday through Saturday. Each day exactly one of the people drives. The schedule of the car pool's drivers for any given week must meet the following conditions: Each person drives on at least one day. No person drives on two consecutive days. Fritz does not drive on Monday. Jerry drives on Wednesday or Saturday or both, and he may also drive on other days. If Gina drives on Monday, then Jerry does not drive on Saturday.

Question: If during one week Fritz drives exactly twice but he drives on neither Tuesday nor Wednesday, which one of the following could be true of that week?
Options:
One person drives exactly three times during the week.
Three people drive exactly one time each during the week.
Jerry drives on no day that is immediately before a day on which Fritz drives.
Gina drives on Wednesday.
Jerry drives on Friday.
Correct option (0-indexed): 4
Five experienced plumbers—Frank, Gene, Jill, Kathy, and Mark—and four inexperienced plumbers—Roberta, Sally, Tim, and Vernon—must decide which of them will be assigned to four work teams of exactly two plumbers each. Assignments must meet the following restrictions: Each plumber is assigned to at most one team. At least one plumber on each team must be experienced. Neither Mark nor Roberta nor Vernon can be assigned to a team with Frank. If Tim is assigned to a team, either Gene or Kathy must be assigned to that team. Jill cannot be assigned to a team with Roberta.

Question: Which one of the following is an inexperienced plumber who can be assigned to a team with Frank?
Options:
Kathy
Roberta
Sally
Tim
Vernon
Correct option (0-indexed): 2
Five experienced plumbers—Frank, Gene, Jill, Kathy, and Mark—and four inexperienced plumbers—Roberta, Sally, Tim, and Vernon—must decide which of them will be assigned to four work teams of exactly two plumbers each. Assignments must meet the following restrictions: Each plumber is assigned to at most one team. At least one plumber on each team must be experienced. Neither Mark nor Roberta nor Vernon can be assigned to a team with Frank. If Tim is assigned to a team, either Gene or Kathy must be assigned to that team. Jill cannot be assigned to a team with Roberta.

Question: Which one of the following is a pair of plumbers who can be assigned together to a team?
Options:
Frank and Roberta
Frank and Vernon
Jill and Mark
Roberta and Tim
Sally and Vernon
Correct option (0-indexed): 2
Five experienced plumbers—Frank, Gene, Jill, Kathy, and Mark—and four inexperienced plumbers—Roberta, Sally, Tim, and Vernon—must decide which of them will be assigned to four work teams of exactly two plumbers each. Assignments must meet the following restrictions: Each plumber is assigned to at most one team. At least one plumber on each team must be experienced. Neither Mark nor Roberta nor Vernon can be assigned to a team with Frank. If Tim is assigned to a team, either Gene or Kathy must be assigned to that team. Jill cannot be assigned to a team with Roberta.

Question: If Tim is assigned to a team, and if Sally is assigned to a team with a plumber who could have been assigned to a team with Tim, then the only plumber with whom Frank could be assigned to a team is
Options:
Gene
Jill
Mark
Roberta
Vernon
Correct option (0-indexed): 1
Five experienced plumbers—Frank, Gene, Jill, Kathy, and Mark—and four inexperienced plumbers—Roberta, Sally, Tim, and Vernon—must decide which of them will be assigned to four work teams of exactly two plumbers each. Assignments must meet the following restrictions: Each plumber is assigned to at most one team. At least one plumber on each team must be experienced. Neither Mark nor Roberta nor Vernon can be assigned to a team with Frank. If Tim is assigned to a team, either Gene or Kathy must be assigned to that team. Jill cannot be assigned to a team with Roberta.

Question: If Gene is not assigned to a team, then Jill must be assigned to a team with
Options:
Vernon
Tim
Mark
Kathy
Frank
Correct option (0-indexed): 0
Five experienced plumbers—Frank, Gene, Jill, Kathy, and Mark—and four inexperienced plumbers—Roberta, Sally, Tim, and Vernon—must decide which of them will be assigned to four work teams of exactly two plumbers each. Assignments must meet the following restrictions: Each plumber is assigned to at most one team. At least one plumber on each team must be experienced. Neither Mark nor Roberta nor Vernon can be assigned to a team with Frank. If Tim is assigned to a team, either Gene or Kathy must be assigned to that team. Jill cannot be assigned to a team with Roberta.

Question: If all of the inexperienced plumbers are assigned to teams, and neither Roberta nor Tim nor Vernon is assigned to a team with Gene, then Sally must be assigned to a team with either
Options:
Frank or else Gene
Frank or else Mark
Gene or else Mark
Jill or else Kathy
Jill or else Mark
Correct option (0-indexed): 0
Eight new students—R, S, T, V, W, X, Y, Z—are being divided among exactly three classes—class 1, class 2, and class 3. Classes 1 and 2 will gain three new students each; class 3 will gain two new students. The following restrictions apply: R must be added to class 1. S must be added to class 3. Neither S nor W can be added to the same class as Y. V cannot be added to the same class as Z. If T is added to class 1, Z must also be added to class 1.

Question: Which one of the following is an acceptable assignment of students to the three classes?
Options:
R, T, Y V, W, X S, Z
R, T, Z S, V, Y W, X
R, W, X V, Y, Z S, T
R, X, Z T, V, Y S, W
R, X, Z V, W, Y S, T
Correct option (0-indexed): 3
Eight new students—R, S, T, V, W, X, Y, Z—are being divided among exactly three classes—class 1, class 2, and class 3. Classes 1 and 2 will gain three new students each; class 3 will gain two new students. The following restrictions apply: R must be added to class 1. S must be added to class 3. Neither S nor W can be added to the same class as Y. V cannot be added to the same class as Z. If T is added to class 1, Z must also be added to class 1.

Question: Which one of the following is a complete and accurate list of classes any one of which could be the class to which V is added?
Options:
class 1
class 3
class 1, class 3
class 2, class 3
class 1, class 2, class 3
Correct option (0-indexed): 4
Eight new students—R, S, T, V, W, X, Y, Z—are being divided among exactly three classes—class 1, class 2, and class 3. Classes 1 and 2 will gain three new students each; class 3 will gain two new students. The following restrictions apply: R must be added to class 1. S must be added to class 3. Neither S nor W can be added to the same class as Y. V cannot be added to the same class as Z. If T is added to class 1, Z must also be added to class 1.

Question: If X is added to class 1, which one of the following is a student who must be added to class 2?
Options:
T
V
W
Y
Z
Correct option (0-indexed): 0
Eight new students—R, S, T, V, W, X, Y, Z—are being divided among exactly three classes—class 1, class 2, and class 3. Classes 1 and 2 will gain three new students each; class 3 will gain two new students. The following restrictions apply: R must be added to class 1. S must be added to class 3. Neither S nor W can be added to the same class as Y. V cannot be added to the same class as Z. If T is added to class 1, Z must also be added to class 1.

Question: If X is added to class 3, each of the following is a pair of students who can be added to class 1 EXCEPT
Options:
Y and Z
W and Z
V and Y
V and W
T and Z
Correct option (0-indexed): 4
Eight new students—R, S, T, V, W, X, Y, Z—are being divided among exactly three classes—class 1, class 2, and class 3. Classes 1 and 2 will gain three new students each; class 3 will gain two new students. The following restrictions apply: R must be added to class 1. S must be added to class 3. Neither S nor W can be added to the same class as Y. V cannot be added to the same class as Z. If T is added to class 1, Z must also be added to class 1.

Question: If T is added to class 3, which one of the following is a student who must be added to class 2?
Options:
V
W
X
Y
Z
Correct option (0-indexed): 2
Eight new students—R, S, T, V, W, X, Y, Z—are being divided among exactly three classes—class 1, class 2, and class 3. Classes 1 and 2 will gain three new students each; class 3 will gain two new students. The following restrictions apply: R must be added to class 1. S must be added to class 3. Neither S nor W can be added to the same class as Y. V cannot be added to the same class as Z. If T is added to class 1, Z must also be added to class 1.

Question: Which one of the following must be true?
Options:
If T and X are added to class 2, V is added to class 3.
If V and W are added to class 1, T is added to class 3.
If V and W are added to class 1, Z is added to class 3.
If V and X are added to class 1, W is added to class 3.
If Y and Z are added to class 2, X is added to class 2.
Correct option (0-indexed): 3
Four lions—F, G, H, J—and two tigers—K and M—will be assigned to exactly six stalls, one animal per stall. The stalls are arranged as follows: First Row: 1 2 3 Second Row: 4 5 6 The only stalls that face each other are stalls 1 and 4, stalls 2 and 5, and stalls 3 and 6. The following conditions apply: The tigers' stalls cannot face each other. A lion must be assigned to stall 1. H must be assigned to stall 6. J must be assigned to a stall numbered one higher than K's stall. K cannot be assigned to the stall that faces H's stall.

Question: Which one of the following must be true?
Options:
F is assigned to an even-numbered stall.
F is assigned to stall 1.
J is assigned to stall 2 or else stall 3.
J is assigned to stall 3 or else stall 4.
K is assigned to stall 2 or else stall 4.
Correct option (0-indexed): 4