benlipkin/arlsat huggingface dataset:
Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford.

Question: If Rafael votes for promoting only Ganz, Olivos, and Wilford, and if Harrison votes for promoting only Lowry, Olivos, and Stefano, then which one of the following could be the complete roster of associates resulting from this year's review?
Options:
Ganz, Lowry, Wilford
Johnson, Lowry, Stefano
Lowry, Stefano, Turner
Lowry, Stefano, Wilford
Olivos, Turner, Wilford
Correct option (0-indexed): 3
Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford.

Question: If Johnson is to be promoted to associate during next year's review, which one of the following is the smallest number of assistants who must be promoted during this year's review?
Options:
one
two
three
four
five
Correct option (0-indexed): 1
Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford.

Question: Which one of the following must be true after next year's review?
Options:
Lowry is an assistant.
Wilford is a partner.
There are no assistants.
There are at least two assistants.
There are no more than four assistants.
Correct option (0-indexed): 4
Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford.

Question: What is the smallest possible number of associates in the firm immediately after next year's review?
Options:
none
one
two
three
four
Correct option (0-indexed): 1
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P.

Question: If G is played second, which one of the following tapes must be played third?
Options:
the news
H
L
O
S
Correct option (0-indexed): 2
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P.

Question: The news tape can be played in any one of the following time slots EXCEPT the
Options:
second
third
fourth
fifth
sixth
Correct option (0-indexed): 0
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P.

Question: If H and S are to be scheduled as far from each other as possible, then the first, the second, and the third time slots could be filled, respectively, by
Options:
G, H, and L
S, G, and the news
H, G, and L
H, L, and O
L, O, and S
Correct option (0-indexed): 2
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P.

Question: If P is played fifth, L must be played
Options:
first
second
third
fourth
sixth
Correct option (0-indexed): 2
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P.

Question: What is the maximum number of tapes that can separate S from the news?
Options:
1
2
3
4
5
Correct option (0-indexed): 4
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P.

Question: Which one of the following is the latest time slot in which L can be played?
Options:
the third
the fourth
the fifth
the sixth
the seventh
Correct option (0-indexed): 2
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P.

Question: The time slot in which O must be played is completely determined if G is assigned to which one of the following time slots?
Options:
the first
the third
the fourth
the fifth
the sixth
Correct option (0-indexed): 3
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations.

Question: Which one of the following must be a day on which Doctor Yamata lectures?
Options:
Monday
Tuesday
Wednesday
Friday
Saturday
Correct option (0-indexed): 1
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations.

Question: On Wednesday Doctor Yamata could be scheduled to
Options:
conduct research in the morning and operate in the afternoon
lecture in the morning and treat patients in the afternoon
operate in the morning and lecture in the afternoon
operate in the morning and conduct research in the afternoon
treat patients in the morning and treat patients in the afternoon
Correct option (0-indexed): 2
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations.

Question: Which one of the following statements must be true?
Options:
There is one day on which the doctor treats patients both in the morning and in the afternoon.
The doctor conducts research on one of the days on which she lectures.
The doctor conducts research on one of the days on which she treats patients.
The doctor lectures on one of the days on which she treats patients.
The doctor lectures on one of the days on which she operates.
Correct option (0-indexed): 4
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations.

Question: If Doctor Yamata operates on Tuesday, then her schedule for treating patients could be
Options:
Monday morning, Monday afternoon, Friday morning, Friday afternoon
Monday morning, Friday afternoon, Saturday morning, Saturday afternoon
Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon
Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon
Wednesday afternoon, Friday afternoon, Saturday morning, Saturday afternoon
Correct option (0-indexed): 4
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations.

Question: Which one of the following is a pair of days on both of which Doctor Yamata must treat patients?
Options:
Monday and Tuesday
Monday and Saturday
Tuesday and Friday
Tuesday and Saturday
Friday and Saturday
Correct option (0-indexed): 4
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog.

Question: If the two moderates did not vote the same way as each other, then which one of the following could be true?
Options:
No conservative and exactly two liberals voted for Datalog.
Exactly one conservative and exactly one liberal voted for Datalog.
Exactly one conservative and all three liberals voted for Datalog.
Exactly two conservatives and exactly one liberal voted for Datalog.
Exactly two conservatives and exactly two liberals voted for Datalog.
Correct option (0-indexed): 1
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog.

Question: Which one of the following must be true?
Options:
At least one conservative voted for Datalog.
At least one liberal voted against Datalog.
At least one liberal voted for Datalog.
At least one moderate voted against Datalog.
At least one moderate voted for Datalog.
Correct option (0-indexed): 2
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog.

Question: If the three liberals all voted the same way as each other, which one of the following must be true?
Options:
Both moderates voted for Datalog.
Both moderates voted against Datalog.
One conservative voted for Datalog and one conservative voted against Datalog.
One moderate voted for Datalog and one moderate voted against Datalog.
All three liberals voted for Datalog.
Correct option (0-indexed): 4
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog.

Question: If exactly two judges voted against Datalog, then which one of the following must be true?
Options:
Both moderates voted for Datalog.
Exactly one conservative voted for Datalog.
No conservative voted for Datalog.
Exactly two liberals voted for Datalog.
Exactly three liberals voted for Datalog.
Correct option (0-indexed): 0
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog.

Question: Each of the following could be a complete and accurate list of those judges who voted for Datalog EXCEPT
Options:
two liberals
one conservative, one liberal
two moderates, three liberals
one conservative, two moderates, two liberals
one conservative, two moderates, three liberals
Correct option (0-indexed): 4
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog.

Question: If the two conservatives voted the same way as each other, but the liberals did not all vote the same way as each other, then each of the following must be true EXCEPT:
Options:
Both conservatives voted against Datalog.
Both moderates voted for Datalog.
At least one liberal voted against Datalog.
Exactly two liberals voted for Datalog.
Exactly five of the judges voted against Datalog.
Correct option (0-indexed): 1
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned.

Question: Which one of the following is a possible assignment of runners to lanes by the charity they represent?
Options:
F G H K J
G H J K F
G K F J H
H J G K F
J H F K G
Correct option (0-indexed): 4
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned.

Question: The lane to which Patricia is assigned must be a lane that is
Options:
next to the lane to which Larry is assigned
next to the lane to which Ned is assigned
separated by exactly one lane from the lane to which Ned is assigned
separated by exactly one lane from the lane to which Olivia is assigned
separated by exactly one lane from the lane to which Sonja is assigned
Correct option (0-indexed): 3
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned.

Question: If Olivia is assigned to lane 2, which one of the following assignments must be made? Charity Lane
Options:
F 1
G 5
H 1
H 3
J 5
Correct option (0-indexed): 1
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned.

Question: Which one of the following, is a complete and accurate list of runners each of whom could be the runner representing F?
Options:
Larry, Ned
Patricia, Sonja
Larry, Ned, Olivia
Larry, Ned, Sonja
Ned, Patricia, Sonja
Correct option (0-indexed): 3
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned.

Question: If Ned is the runner representing J, then it must be true that
Options:
the runner representing G is assigned to lane 1
the runner representing H is assigned to lane 2
Larry is the runner representing K
Olivia is the runner representing F
Patricia is the runner representing H
Correct option (0-indexed): 1
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned.

Question: If Larry represents J, which one of the following could be the assignment of runners to lanes?
Options:
Larry Olivia Ned Patricia Sonja
Larry Ned Olivia Sonja Patricia
Larry Sonja Patricia Ned Olivia
Ned Olivia Larry Patricia Sonja
Ned Sonja Olivia Patricia Larry
Correct option (0-indexed): 0
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled.

Question: Which one of the following is a pair of students whose sessions can both be scheduled for Tuesday, not necessarily in the order given?
Options:
H and U
H and Z
K and O
O and U
U and Z
Correct option (0-indexed): 3
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled.

Question: If K's session is scheduled for Tuesday, then which one of the following is the earliest day for which Z's session can be scheduled?
Options:
Monday
Tuesday
Wednesday
Thursday
Friday
Correct option (0-indexed): 1
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled.

Question: Which one of the following must be true?
Options:
If U's session is scheduled for Monday, H's session is scheduled for Tuesday.
If U's session is scheduled for Tuesday, O's session is scheduled for Wednesday.
If U's session is scheduled for Wednesday, Z's session is scheduled for Tuesday.
If U's session is scheduled for Thursday, Z's session is scheduled for Friday.
If U's session is scheduled for Friday, Z's session is scheduled for Thursday.
Correct option (0-indexed): 3
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled.

Question: Scheduling Z's session for which one of the following days determines the day for which U's session must be scheduled?
Options:
Monday
Tuesday
Wednesday
Thursday
Friday
Correct option (0-indexed): 3
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled.

Question: If H's session is scheduled as the next session after U's session, which one of the following could be true about H's session and U's session?
Options:
U's session is scheduled for Monday, and H's session is scheduled for Tuesday.
U's session is scheduled for Thursday, and H's session is scheduled for Friday.
They are both scheduled for Tuesday.
They are both scheduled for Thursday.
They are both scheduled for Friday.
Correct option (0-indexed): 0
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Question: Which one of the following could be a complete and accurate list of lights that are on together?
Options:
1, 3, 5, 7
2, 4, 6, 8
2, 3, 5, 6, 8
3, 4, 6, 7, 8
1, 2, 4, 5, 6, 8
Correct option (0-indexed): 2
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Question: Which one of the following lights must be on?
Options:
light 2
light 3
light 4
light 5
light 6
Correct option (0-indexed): 1
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Question: If light 1 is off, which one of the following is a light that must also be off?
Options:
light 3
light 4
light 5
light 6
light 7
Correct option (0-indexed): 1
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Question: Which one of the following statements must be true?
Options:
If light 2 is on, then light 6 is off.
If light 3 is on, then light 2 is on.
If light 4 is on, then light 3 is off.
If light 5 is off, then light 4 is on.
If light 6 is off, then light 1 is on.
Correct option (0-indexed): 3
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Question: If light 5 is on, which one of the following could be true?
Options:
Light 1 is off and light 6 is off.
Light 1 is on and light 7 is on.
Light 2 is off and light 4 is on.
Light 2 is off and light 6 is off.
Light 6 is on and light 7 is on.
Correct option (0-indexed): 0
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Question: If light 4 is on, each of the following statements must be true EXCEPT:
Options:
Light 1 is on.
Light 2 is on.
Light 5 is off.
Light 6 is on.
Light 7 is off.
Correct option (0-indexed): 1
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Question: Suppose that it is no longer part of the specifications that two lights on the north side be on. If all of the other original specifications remain the same, and if exactly one light on the north side is on, which one of the following statements could be false?
Options:
Light 1 is off.
Light 2 is on.
Light 3 is off.
Light 4 is on.
Light 5 is on.
Correct option (0-indexed): 4
Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

Question: What is the maximum possible number of different pairs of chairs in which Frank and Ruby could sit?
Options:
one
two
three
four
five
Correct option (0-indexed): 2
Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

Question: Which one of the following statements must be false?
Options:
Both Harry and Joel sit east of Frank.
Both Harry and Ruby sit east of Frank.
Both Harry and Joel sit west of Frank.
Both Harry and Ruby sit west of Frank.
Both Joel and Ruby sit east of Frank.
Correct option (0-indexed): 2
Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

Question: If Thelma sits next to Ivan, and if Frank sits next to Thelma, which one of the following statements could be false?
Options:
Both Frank and Ivan sit east of Ruby.
Both Frank and Ruby sit west of Thelma.
Both Frank and Sylvia sit east of Ruby.
Both Frank and Thelma sit west of Sylvia.
Both Frank and Ruby sit west of Joel.
Correct option (0-indexed): 4
Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

Question: If Frank does not sit next to any child who sits next to Ivan, which one of the following statements could be true?
Options:
Harry sits west of Frank.
Joel sits west of Ivan.
Ruby sits west of Frank.
Thelma sits west of Frank.
Thelma sits west of Ruby.
Correct option (0-indexed): 1
Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

Question: If Frank sits east of Ruby, which one of the following pairs of children CANNOT sit next to each other?
Options:
Frank and Thelma
Harry and Ruby
Harry and Sylvia
Ivan and Ruby
Joel and Ruby
Correct option (0-indexed): 3
The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Question: Each of the following can be true EXCEPT:
Options:
W responds to heptocillin.
X responds to ganocyclene.
X responds to heptocillin.
Y responds to heptocillin.
Z responds to ganocyclene.
Correct option (0-indexed): 3
The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Question: Which one of the following could be true?
Options:
W, X, and Z all respond to ferromycin.
W, X, and Z all respond to ganocyclene.
W and exactly one other organism respond to ganocyclene.
W responds to more of the antibiotics than X does.
More of the organisms respond to ferromycin than to ganocyclene.
Correct option (0-indexed): 1
The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Question: Which one of the following could be true?
Options:
Exactly one of the organisms responds to ferromycin.
All four of the organisms respond to heptocillin.
At least one of the organisms responds both to ferromycin and to heptocillin.
At least one of the organisms responds neither to ganocyclene nor to heptocillin.
At least one of the organisms responds to ganocyclene but does not respond to ferromycin.
Correct option (0-indexed): 4
The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Question: If X does not respond to ferromycin, then which one of the following must be true?
Options:
W responds to ganocyclene.
X responds to ganocyclene.
X responds to heptocillin.
Z responds to ferromycin.
Z responds to heptocillin.
Correct option (0-indexed): 3
The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Question: If any of the organisms responds to two of the antibiotics, then which one of the following is true about such an organism?
Options:
It must respond to ferromycin.
It must respond to ganocyclene.
It must respond to heptocillin.
It cannot respond to ferromycin.
It cannot respond to ganocyclene.
Correct option (0-indexed): 1
The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Question: If none of the organisms responds to heptocillin, then which one of the following must be true?
Options:
W responds to ferromycin.
X responds to ferromycin.
Z responds to ferromycin.
Exactly three of the organisms respond to ganocyclene.
Exactly four of the organisms respond to ganocyclene.
Correct option (0-indexed): 4
The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Question: If three of the organisms respond to exactly the same set of antibiotics as each other, and if Z does not respond to ferromycin, then each of the following must be true EXCEPT:
Options:
W responds to ferromycin.
X responds to ganocyclene.
Z responds to ganocyclene.
W responds to exactly the same set of antibiotics as Y.
X responds to exactly the same set of antibiotics as Y.
Correct option (0-indexed): 2
A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

Question: Which one of the following is an acceptable selection of flowers for the three corsages? Corsage 1 Corsage 2 Corsage 3
Options:
2 gardenias 1 orchid 1 gardenia 1 rose 1 rose 1 orchid 1 violet 1 violet
2 orchids 2 orchids 2 gardenias 1 rose 1 rose 1 rose
2 orchids 3 roses 1 gardenia 1 rose 2 violets
1 gardenia 1 gardenia 1 gardenia 1 orchid 1 rose 1 rose 1 rose 1 violet 1 violet
1 orchid 3 violets 3 gardenias 2 roses
Correct option (0-indexed): 2
A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

Question: The maximum total number of roses that can be used in the three corsages is
Options:
three
four
five
six
seven
Correct option (0-indexed): 3
A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

Question: If corsage 1 contains two orchids and one rose, what is the maximum total number of violets that the florist can use in making the three corsages?
Options:
one
two
three
four
five
Correct option (0-indexed): 1