benlipkin/arlsat huggingface dataset:
A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

Question: If F is selected, any one of the following people could be the chairperson of the committee EXCEPT:
Options:
G
K
P
Q
S
Correct option (0-indexed): 0
A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

Question: If neither F nor K is selected for the committee, which one of the following can be true?
Options:
G is selected.
P is selected.
J is the chairperson.
Q is the chairperson.
S is the chairperson.
Correct option (0-indexed): 2
A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

Question: If the chairperson of the committee is to be a homeowner, which one of the following must be true?
Options:
If G is selected, Q is also selected.
If G is selected, R is also selected.
If J is selected, F is also selected.
If J is selected, Q is also selected.
If J is selected, R is also selected.
Correct option (0-indexed): 0
A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

Question: The committee must include at least one representative from which one of the following pairs?
Options:
F, P
G, J
K, Q
M, P
R, S
Correct option (0-indexed): 2
Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

Question: Which one of the following must be true after the second reassignment of apprentices to projects during the year if that reassignment assigns Nora to project T ?
Options:
Louis is assigned to project S.
Madelyn is assigned to project R.
Madelyn is assigned to project S.
Oliver is assigned to project R.
Oliver is assigned to project S.
Correct option (0-indexed): 4
Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

Question: Which one of the following could be true after only one reassignment during the year?
Options:
Louis is assigned to project T.
Nora is assigned to project R.
Oliver is assigned to project Q.
Louis and Nora each remain assigned to the same projects as before.
Nora and Oliver each remain assigned to the same projects as before.
Correct option (0-indexed): 4
Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

Question: If at some time during the year, Louis is reassigned to project R, which one of the following could have been the assignment of apprentices to the projects immediately before the reassignment?
Options:
Q: Louis; R: Madelyn; S: Oliver; T: Nora
Q: Louis; R: Nora; S: Oliver; T: Madelyn
Q: Nora; R: Madelyn; S: Louis; T: Oliver
Q: Nora; R: Oliver; S: Louis; T: Madelyn
Q: Oliver; R: Nora; S: Louis; T: Madelyn
Correct option (0-indexed): 0
Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

Question: Which one of the following is an acceptable assignment of apprentices to the projects after only one reassignment during the year?
Options:
Q: Louis; R: Madelyn; S: Nora; T: Oliver
Q: Madelyn; R: Louis; S: Nora; T: Oliver
Q: Madelyn; R: Oliver; S: Nora; T: Louis
Q: Nora; R: Louis; S: Oliver; T: Madelyn
Q: Nora; R: Madelyn; S: Oliver; T: Louis
Correct option (0-indexed): 1
Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

Question: If the first reassignment is made according to plan 1, which one of the following must be true?
Options:
Louis is assigned to project T as a result of the second reassignment.
Madelyn is assigned to project Q as a result of the second reassignment.
Madelyn is assigned to project T as a result of the second reassignment.
Oliver is assigned to project S as a result of the second reassignment.
Oliver is assigned to project T as a result of the second reassignment.
Correct option (0-indexed): 0
A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Question: If Janet's lesson is scheduled for the first day, then the lesson for which one of the following students must be scheduled for the sixth day?
Options:
Grace
Henry
Steve
Tom
Una
Correct option (0-indexed): 4
A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Question: For which one of the following students is there an acceptable schedule in which the student's lesson is on the third day and another acceptable schedule in which the student's lesson is on the fifth day?
Options:
Grace
Henry
Steve
Tom
Una
Correct option (0-indexed): 1
A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Question: Which one of the following is a complete and accurate list of the students any one of whom could be the student whose lesson is scheduled for the second day?
Options:
Grace
Tom
Grace, Tom
Henry, Tom
Grace, Henry, Tom
Correct option (0-indexed): 2
A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Question: If Henry's lesson is scheduled for a day either immediately before or immediately after Tom's lesson, then Grace's lesson must be scheduled for the
Options:
first day
second day
third day
fourth day
fifth day
Correct option (0-indexed): 1
A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Question: If Janet's lesson is scheduled for the third day, which one of the following could be true?
Options:
Grace's lesson is scheduled for a later day than Henry's lesson.
Grace's lesson is scheduled for a later day than Una's lesson.
Henry's lesson is scheduled for a later day than Una's lesson.
Tom's lesson is scheduled for a later day than Henry's lesson.
Tom's lesson is scheduled for a later day than Una's lesson.
Correct option (0-indexed): 2
A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Question: Which one of the following is a complete and accurate list of days any one of which could be the day for which Tom's lesson is scheduled?
Options:
first, second, third
second, third, fourth
second, fifth, sixth
first, second, third, fourth
second, third, fourth, sixth
Correct option (0-indexed): 3
Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

Question: If F is in group 1, which one of the following could be true?
Options:
G and K are in group 3.
G and R are in group 3.
J and S are in group 2.
K and R are in group 1.
Q and S are in group 2.
Correct option (0-indexed): 4
Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

Question: If F and S are in group 3, which one of the following must be true?
Options:
G is in group 2.
H is in group 3.
K is in group 1.
Q is in group 2.
R is in group 1.
Correct option (0-indexed): 0
Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

Question: If G and K are in group 3, which one of the following must be true?
Options:
H is in group 3.
J is in group 1.
R is in group 2.
S is in group 3.
T is in group 1.
Correct option (0-indexed): 4
Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

Question: If Q is in group 1 and S is in group 3, which one of the following CANNOT be true?
Options:
G is in group 2.
T is in group 1.
There is exactly one child in group 1.
There is exactly one child in group 2.
There is exactly one child in group 3.
Correct option (0-indexed): 3
Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

Question: If G is the only child in group 1, which one of the following must be true?
Options:
F is in group 3.
K is in group 3.
Q is in group 2.
R is in group 1.
S is in group 2.
Correct option (0-indexed): 1
Lara, Mendel, and Nastassia each buy at least one kind of food from a street vendor who sells only fruit cups, hot dogs, pretzels, and shish kebabs. They make their selections in accordance with the following restrictions: None of the three buys more than one portion of each kind of food. If any of the three buys a hot dog, that person does not also buy a shish kebab. At least one of the three buys a hot dog, and at least one buys a pretzel. Mendel buys a shish kebab. Nastassia buys a fruit cup. Neither Lara nor Nastassia buys a pretzel. Mendel does not buy any kind of food that Nastassia buys.

Question: Which one of the following statements must be true?
Options:
Lara buys a hot dog.
Lara buys a shish kebab.
Mendel buys a hot dog.
Mendel buys a pretzel.
Nastassia buys a hot dog.
Correct option (0-indexed): 3
Lara, Mendel, and Nastassia each buy at least one kind of food from a street vendor who sells only fruit cups, hot dogs, pretzels, and shish kebabs. They make their selections in accordance with the following restrictions: None of the three buys more than one portion of each kind of food. If any of the three buys a hot dog, that person does not also buy a shish kebab. At least one of the three buys a hot dog, and at least one buys a pretzel. Mendel buys a shish kebab. Nastassia buys a fruit cup. Neither Lara nor Nastassia buys a pretzel. Mendel does not buy any kind of food that Nastassia buys.

Question: If the vendor charges $1 for each portion of food, what is the minimum amount the three people could spend?
Options:
$3
$4
$5
$6
$7
Correct option (0-indexed): 1
Lara, Mendel, and Nastassia each buy at least one kind of food from a street vendor who sells only fruit cups, hot dogs, pretzels, and shish kebabs. They make their selections in accordance with the following restrictions: None of the three buys more than one portion of each kind of food. If any of the three buys a hot dog, that person does not also buy a shish kebab. At least one of the three buys a hot dog, and at least one buys a pretzel. Mendel buys a shish kebab. Nastassia buys a fruit cup. Neither Lara nor Nastassia buys a pretzel. Mendel does not buy any kind of food that Nastassia buys.

Question: If the vendor charges $1 for each portion of food, what is the greatest amount the three people could spend?
Options:
$5
$6
$7
$8
$9
Correct option (0-indexed): 1
Lara, Mendel, and Nastassia each buy at least one kind of food from a street vendor who sells only fruit cups, hot dogs, pretzels, and shish kebabs. They make their selections in accordance with the following restrictions: None of the three buys more than one portion of each kind of food. If any of the three buys a hot dog, that person does not also buy a shish kebab. At least one of the three buys a hot dog, and at least one buys a pretzel. Mendel buys a shish kebab. Nastassia buys a fruit cup. Neither Lara nor Nastassia buys a pretzel. Mendel does not buy any kind of food that Nastassia buys.

Question: If Lara and Mendel buy exactly two kinds of food each, which one of the following statements must be true.
Options:
Lara buys a fruit cup.
Lara buys a hot dog.
Mendel buys a fruit cup.
There is exactly one kind of food that Lara and Mendel both buy.
There is exactly one kind of food that Lara and Nastassia both buy.
Correct option (0-indexed): 0
Lara, Mendel, and Nastassia each buy at least one kind of food from a street vendor who sells only fruit cups, hot dogs, pretzels, and shish kebabs. They make their selections in accordance with the following restrictions: None of the three buys more than one portion of each kind of food. If any of the three buys a hot dog, that person does not also buy a shish kebab. At least one of the three buys a hot dog, and at least one buys a pretzel. Mendel buys a shish kebab. Nastassia buys a fruit cup. Neither Lara nor Nastassia buys a pretzel. Mendel does not buy any kind of food that Nastassia buys.

Question: If Lara buys a shish kebab, which one of the following statements must be true?
Options:
Lara buys a fruit cup.
Mendel buys a fruit cup.
Nastassia buys a hot dog.
Nastassia buys exactly one kind of food.
Exactly one person buys a fruit cup.
Correct option (0-indexed): 2
Lara, Mendel, and Nastassia each buy at least one kind of food from a street vendor who sells only fruit cups, hot dogs, pretzels, and shish kebabs. They make their selections in accordance with the following restrictions: None of the three buys more than one portion of each kind of food. If any of the three buys a hot dog, that person does not also buy a shish kebab. At least one of the three buys a hot dog, and at least one buys a pretzel. Mendel buys a shish kebab. Nastassia buys a fruit cup. Neither Lara nor Nastassia buys a pretzel. Mendel does not buy any kind of food that Nastassia buys.

Question: Assume that the condition is removed that prevents a customer who buys a hot dog from buying a shish kebab but all other conditions remain the same. If the vendor charges $1 for each portion of food, what is the maximum amount the three people could spend?
Options:
$5
$6
$7
$8
$9
Correct option (0-indexed): 2
A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply: The product of an experiment cannot be used in further experiments. Mixing the contents of 1 and 2 produces a red chemical. Mixing the contents of 2 and 3 produces an orange chemical. Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical. Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical.

Question: If the student performs exactly one experiment, which one of the following could be the colors of the chemicals in the resulting three nonempty flasks?
Options:
blue, blue, green
blue, orange, orange
blue, orange, red
green, green, red
green, orange, orange
Correct option (0-indexed): 3
A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply: The product of an experiment cannot be used in further experiments. Mixing the contents of 1 and 2 produces a red chemical. Mixing the contents of 2 and 3 produces an orange chemical. Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical. Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical.

Question: If the student performs exactly two experiments, which one of the following could be the colors of the chemicals in the resulting two nonempty flasks?
Options:
blue, blue
blue, orange
blue, red
green, red
orange, orange
Correct option (0-indexed): 2
A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply: The product of an experiment cannot be used in further experiments. Mixing the contents of 1 and 2 produces a red chemical. Mixing the contents of 2 and 3 produces an orange chemical. Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical. Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical.

Question: If the student performs exactly one experiment and none of the resulting three nonempty flasks contains a red chemical, which one of the following could be the colors of the chemicals in the three flasks?
Options:
blue, blue, green
blue, green, green
blue, green, orange
blue, orange, orange
green, green, orange
Correct option (0-indexed): 1
A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply: The product of an experiment cannot be used in further experiments. Mixing the contents of 1 and 2 produces a red chemical. Mixing the contents of 2 and 3 produces an orange chemical. Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical. Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical.

Question: If the student performs exactly one experiment and exactly one of the resulting three nonempty flasks contains a blue chemical, which one of the following must be the colors of the chemicals in the other two flasks?
Options:
both green
both orange
both red
one green and one red
one orange and one red
Correct option (0-indexed): 0
A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply: The product of an experiment cannot be used in further experiments. Mixing the contents of 1 and 2 produces a red chemical. Mixing the contents of 2 and 3 produces an orange chemical. Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical. Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical.

Question: If the student will perform exactly two experiments and after the first experiment exactly one of the resulting three nonempty flasks contains an orange chemical, then in the second experiment the student could mix together the contents of flasks
Options:
1 and 2
1 and 3
1 and 4
2 and 3
3 and 4
Correct option (0-indexed): 4
A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply: The product of an experiment cannot be used in further experiments. Mixing the contents of 1 and 2 produces a red chemical. Mixing the contents of 2 and 3 produces an orange chemical. Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical. Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical.

Question: If the student performs exactly one experiment and none of the resulting three nonempty flasks contains an orange chemical, then the student must have mixed the contents of
Options:
flask 1 with flask 2
flask 1 with flask 4
flask 2 with flask 4
flask 2 with one of the other flasks
flask 4 with one of the other flasks
Correct option (0-indexed): 4
A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply: The product of an experiment cannot be used in further experiments. Mixing the contents of 1 and 2 produces a red chemical. Mixing the contents of 2 and 3 produces an orange chemical. Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical. Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical.

Question: If the student performs exactly two experiments and exactly one of the resulting two nonempty flasks contains an orange chemical, then it must be true that the contents of the other nonempty flask is
Options:
obtained by mixing flasks 1 and 2
obtained by mixing flasks 2 and 4
blue
green
red
Correct option (0-indexed): 3
Exactly eight consumers—F, G, H, J, K, L, M, and N—will be interviewed by market researchers. The eight will be divided into exactly two 4-person groups—group 1 and group 2—before interviews begin. Each person is assigned to exactly one of the two groups according to the following conditions: F must be in the same group as J. G must be in a different group from M. If H is in group 1, then L must be in group 1. If N is in group 2, then G must be in group 1.

Question: Group 1 could consist of
Options:
F, G, H, and J
F, H, L, and M
F, J, K, and L
G, H, L, and N
G, K, M, and N
Correct option (0-indexed): 3
Exactly eight consumers—F, G, H, J, K, L, M, and N—will be interviewed by market researchers. The eight will be divided into exactly two 4-person groups—group 1 and group 2—before interviews begin. Each person is assigned to exactly one of the two groups according to the following conditions: F must be in the same group as J. G must be in a different group from M. If H is in group 1, then L must be in group 1. If N is in group 2, then G must be in group 1.

Question: If K is in the same group as N, which one of the following must be true?
Options:
G is in group 1.
H is in group 2.
J is in group 1.
K is in group 2.
M is in group 1.
Correct option (0-indexed): 1
Exactly eight consumers—F, G, H, J, K, L, M, and N—will be interviewed by market researchers. The eight will be divided into exactly two 4-person groups—group 1 and group 2—before interviews begin. Each person is assigned to exactly one of the two groups according to the following conditions: F must be in the same group as J. G must be in a different group from M. If H is in group 1, then L must be in group 1. If N is in group 2, then G must be in group 1.

Question: If F is in the same group as H, which one of the following must be true?
Options:
G is in group 2.
J is in group 1.
K is in group 1.
L is in group 2.
M is in group 2.
Correct option (0-indexed): 2
Exactly eight consumers—F, G, H, J, K, L, M, and N—will be interviewed by market researchers. The eight will be divided into exactly two 4-person groups—group 1 and group 2—before interviews begin. Each person is assigned to exactly one of the two groups according to the following conditions: F must be in the same group as J. G must be in a different group from M. If H is in group 1, then L must be in group 1. If N is in group 2, then G must be in group 1.

Question: If L and M are in group 2, then a person who could be assigned either to group 1 or, alternatively, to group 2 is
Options:
F
G
H
J
K
Correct option (0-indexed): 4
Exactly eight consumers—F, G, H, J, K, L, M, and N—will be interviewed by market researchers. The eight will be divided into exactly two 4-person groups—group 1 and group 2—before interviews begin. Each person is assigned to exactly one of the two groups according to the following conditions: F must be in the same group as J. G must be in a different group from M. If H is in group 1, then L must be in group 1. If N is in group 2, then G must be in group 1.

Question: Each of the following is a pair of people who could be in group 1 together EXCEPT
Options:
F and G
F and H
F and L
H and G
H and N
Correct option (0-indexed): 1
Exactly eight consumers—F, G, H, J, K, L, M, and N—will be interviewed by market researchers. The eight will be divided into exactly two 4-person groups—group 1 and group 2—before interviews begin. Each person is assigned to exactly one of the two groups according to the following conditions: F must be in the same group as J. G must be in a different group from M. If H is in group 1, then L must be in group 1. If N is in group 2, then G must be in group 1.

Question: If L is in group 2, then each of the following is a pair of people who could be in group 1 together EXCEPT
Options:
F and M
G and N
J and N
K and M
M and N
Correct option (0-indexed): 3
Five people—Harry, Iris, Kate, Nancy, and Victor—are to be scheduled as contestants on a television show, one contestant per day, for five consecutive days from Monday through Friday. The following restrictions governing the scheduling of contestants must be observed: Nancy is not scheduled for Monday. If Harry is scheduled for Monday, Nancy is scheduled for Friday. If Nancy is scheduled for Tuesday, Iris is scheduled for Monday. Kate is scheduled for the next day after the day for which Victor is scheduled.

Question: Victor can be scheduled for any day EXCEPT
Options:
Monday
Tuesday
Wednesday
Thursday
Friday
Correct option (0-indexed): 4
Five people—Harry, Iris, Kate, Nancy, and Victor—are to be scheduled as contestants on a television show, one contestant per day, for five consecutive days from Monday through Friday. The following restrictions governing the scheduling of contestants must be observed: Nancy is not scheduled for Monday. If Harry is scheduled for Monday, Nancy is scheduled for Friday. If Nancy is scheduled for Tuesday, Iris is scheduled for Monday. Kate is scheduled for the next day after the day for which Victor is scheduled.

Question: If Iris is scheduled for the next day after Harry, which one of the following lists all those days any one of which could be the day for which Harry is scheduled?
Options:
Monday, Tuesday
Monday, Wednesday
Monday, Thursday
Monday, Tuesday, Wednesday
Monday, Wednesday, Thursday
Correct option (0-indexed): 4
Five people—Harry, Iris, Kate, Nancy, and Victor—are to be scheduled as contestants on a television show, one contestant per day, for five consecutive days from Monday through Friday. The following restrictions governing the scheduling of contestants must be observed: Nancy is not scheduled for Monday. If Harry is scheduled for Monday, Nancy is scheduled for Friday. If Nancy is scheduled for Tuesday, Iris is scheduled for Monday. Kate is scheduled for the next day after the day for which Victor is scheduled.

Question: If Kate is scheduled for Wednesday, which one of the following could be true?
Options:
Iris is scheduled for Friday.
Nancy is scheduled for Tuesday.
Nancy is scheduled for an earlier day than the day for which Harry is scheduled.
Nancy is scheduled for an earlier day than the day for which Iris is scheduled.
Nancy is scheduled for an earlier day than the day for which Kate is scheduled.
Correct option (0-indexed): 2
Five people—Harry, Iris, Kate, Nancy, and Victor—are to be scheduled as contestants on a television show, one contestant per day, for five consecutive days from Monday through Friday. The following restrictions governing the scheduling of contestants must be observed: Nancy is not scheduled for Monday. If Harry is scheduled for Monday, Nancy is scheduled for Friday. If Nancy is scheduled for Tuesday, Iris is scheduled for Monday. Kate is scheduled for the next day after the day for which Victor is scheduled.

Question: If Kate is scheduled for Friday, which one of the following must be true?
Options:
Harry is scheduled for Tuesday.
Harry is scheduled for Wednesday.
Iris is scheduled for Monday.
Iris is scheduled for Wednesday.
Nancy is scheduled for Wednesday.
Correct option (0-indexed): 2
Five people—Harry, Iris, Kate, Nancy, and Victor—are to be scheduled as contestants on a television show, one contestant per day, for five consecutive days from Monday through Friday. The following restrictions governing the scheduling of contestants must be observed: Nancy is not scheduled for Monday. If Harry is scheduled for Monday, Nancy is scheduled for Friday. If Nancy is scheduled for Tuesday, Iris is scheduled for Monday. Kate is scheduled for the next day after the day for which Victor is scheduled.

Question: If Iris is scheduled for Wednesday, which one of the following must be true?
Options:
Harry is scheduled for an earlier day than the day for which Nancy is scheduled.
Harry is scheduled for an earlier day than the day for which Kate is scheduled.
Kate is scheduled for an earlier day than the day for which Harry is scheduled.
Nancy is scheduled for an earlier day than the day for which Kate is scheduled.
Nancy is scheduled for an earlier day than the day for which Iris is scheduled.
Correct option (0-indexed): 2
An art teacher will schedule exactly six of eight lectures—fresco, history, lithography, naturalism, oils, pastels, sculpture, and watercolors—for three days—1, 2, and 3. There will be exactly two lectures each day—morning and afternoon. Scheduling is governed by the following conditions: Day 2 is the only day for which oils can be scheduled. Neither sculpture nor watercolors can be scheduled for the afternoon. Neither oils nor pastels can be scheduled for the same day as lithography. If pastels is scheduled for day 1 or day 2, then the lectures scheduled for the day immediately following pastels must be fresco and history, not necessarily in that order.

Question: Which one of the following is an acceptable schedule of lectures for days 1, 2, and 3, respectively?
Options:
Morning: lithography, history, sculpture Afternoon: pastels, fresco, naturalism
Morning: naturalism, oils, fresco Afternoon: lithography, pastels, history
Morning: oils, history, naturalism Afternoon: pastels, fresco, lithography
Morning: sculpture, lithography, naturalism Afternoon: watercolors, fresco, pastels
Morning: sculpture, pastels, fresco Afternoon: lithography, history, naturalism
Correct option (0-indexed): 1
An art teacher will schedule exactly six of eight lectures—fresco, history, lithography, naturalism, oils, pastels, sculpture, and watercolors—for three days—1, 2, and 3. There will be exactly two lectures each day—morning and afternoon. Scheduling is governed by the following conditions: Day 2 is the only day for which oils can be scheduled. Neither sculpture nor watercolors can be scheduled for the afternoon. Neither oils nor pastels can be scheduled for the same day as lithography. If pastels is scheduled for day 1 or day 2, then the lectures scheduled for the day immediately following pastels must be fresco and history, not necessarily in that order.

Question: If lithography and fresco are scheduled for the afternoons of day 2 and day 3, respectively, which one of the following is a lecture that could be scheduled for the afternoon of day 1?
Options:
history
oils
pastels
sculpture
watercolors
Correct option (0-indexed): 0
An art teacher will schedule exactly six of eight lectures—fresco, history, lithography, naturalism, oils, pastels, sculpture, and watercolors—for three days—1, 2, and 3. There will be exactly two lectures each day—morning and afternoon. Scheduling is governed by the following conditions: Day 2 is the only day for which oils can be scheduled. Neither sculpture nor watercolors can be scheduled for the afternoon. Neither oils nor pastels can be scheduled for the same day as lithography. If pastels is scheduled for day 1 or day 2, then the lectures scheduled for the day immediately following pastels must be fresco and history, not necessarily in that order.

Question: If lithography and history are scheduled for the mornings of day 2 and day 3, respectively, which one of the following lectures could be scheduled for the morning of day 1?
Options:
fresco
naturalism
oils
pastels
sculpture
Correct option (0-indexed): 4
An art teacher will schedule exactly six of eight lectures—fresco, history, lithography, naturalism, oils, pastels, sculpture, and watercolors—for three days—1, 2, and 3. There will be exactly two lectures each day—morning and afternoon. Scheduling is governed by the following conditions: Day 2 is the only day for which oils can be scheduled. Neither sculpture nor watercolors can be scheduled for the afternoon. Neither oils nor pastels can be scheduled for the same day as lithography. If pastels is scheduled for day 1 or day 2, then the lectures scheduled for the day immediately following pastels must be fresco and history, not necessarily in that order.

Question: If oils and lithography are scheduled for the mornings of day 2 and day 3, respectively, which one of the following CANNOT be scheduled for any day?
Options:
fresco
history
naturalism
pastels
sculpture
Correct option (0-indexed): 3
An art teacher will schedule exactly six of eight lectures—fresco, history, lithography, naturalism, oils, pastels, sculpture, and watercolors—for three days—1, 2, and 3. There will be exactly two lectures each day—morning and afternoon. Scheduling is governed by the following conditions: Day 2 is the only day for which oils can be scheduled. Neither sculpture nor watercolors can be scheduled for the afternoon. Neither oils nor pastels can be scheduled for the same day as lithography. If pastels is scheduled for day 1 or day 2, then the lectures scheduled for the day immediately following pastels must be fresco and history, not necessarily in that order.

Question: If neither fresco nor naturalism is scheduled for any day, which one of the following must be scheduled for day 1?
Options:
history
lithography
oils
pastels
sculpture
Correct option (0-indexed): 1
An art teacher will schedule exactly six of eight lectures—fresco, history, lithography, naturalism, oils, pastels, sculpture, and watercolors—for three days—1, 2, and 3. There will be exactly two lectures each day—morning and afternoon. Scheduling is governed by the following conditions: Day 2 is the only day for which oils can be scheduled. Neither sculpture nor watercolors can be scheduled for the afternoon. Neither oils nor pastels can be scheduled for the same day as lithography. If pastels is scheduled for day 1 or day 2, then the lectures scheduled for the day immediately following pastels must be fresco and history, not necessarily in that order.

Question: If the lectures scheduled for the mornings are fresco, history, and lithography, not necessarily in that order, which one of the following could be true?
Options:
Lithography is scheduled for day 3.
Naturalism is scheduled for day 2.
Fresco is scheduled for the same day as naturalism.
History is scheduled for the same day as naturalism.
History is scheduled for the same day as oils.
Correct option (0-indexed): 4
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 the clans participating in the first year of a given cycle are N, O, and P, which one of the following could be the clans participating in the second year of that cycle?
Options:
N, O, S
N, O, T
N, P, S
O, P, T
O, S, T
Correct option (0-indexed): 4
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: Which one of the following can be true about the clans' participation in the ceremonies?
Options:
N participates in the first, second, and third years.
N participates in the second, third, and fourth years.
Both O and S participate in the first and third years.
Both N and S participate in the first, third, and fifth years.
Both S and T participate in the second, third, and fifth years.
Correct option (0-indexed): 2
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: Any cycle for the clans' participation in the ceremonies must be completed at the end of exactly how many years?
Options:
five
six
seven
eight
nine
Correct option (0-indexed): 0
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: Which one of the following must be true about the three clans that participate in the ceremonies in the first year?
Options:
At most two of them participate together in the third year.
At least two of them participate together in the second year.
All three of them participate together in the fourth year.
All three of them participate together in the fifth year.
None of them participates in the third year.
Correct option (0-indexed): 0
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, which one of the following must be true?
Options:
N participates in the second and third years.
O participates in the third and fourth years.
N and O both participate in the third year.
P and T both participate in the fifth year.
S and T both participate in the fifth year.
Correct option (0-indexed): 3
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 T participate in the first year and if O and P participate in the fourth year, any of the following could be a clan that participates in the third year EXCEPT
Options:
N
O
P
S
T
Correct option (0-indexed): 2