benlipkin/arlsat huggingface dataset:
Seven students—fourth-year students Kim and Lee; third-year students Pat and Robin; and second-year students Sandy, Terry, and Val—and only those seven, are being assigned to rooms of equal size in a dormitory. Each room assigned must have either one, or two, or three students assigned to it, and will accordingly be called either a single, or a double, or a triple. The seven students are assigned to rooms in accordance with the following conditions: No fourth-year student can be assigned to a triple. No second-year student can be assigned to a single. Lee and Robin must not share the same room. Kim and Pat must share the same room.

Question: Which one of the following is a combination of rooms to which the seven students could be assigned?
Options:
two triples and one single
one triple and four singles
three doubles and a single
two doubles and three singles
one double and five singles
Correct option (0-indexed): 2
Seven students—fourth-year students Kim and Lee; third-year students Pat and Robin; and second-year students Sandy, Terry, and Val—and only those seven, are being assigned to rooms of equal size in a dormitory. Each room assigned must have either one, or two, or three students assigned to it, and will accordingly be called either a single, or a double, or a triple. The seven students are assigned to rooms in accordance with the following conditions: No fourth-year student can be assigned to a triple. No second-year student can be assigned to a single. Lee and Robin must not share the same room. Kim and Pat must share the same room.

Question: If the room assigned to Robin is a single, which one of the following could be true?
Options:
There is exactly one double that has a second-year student assigned to it.
Lee is assigned to a single.
Sandy, Pat and one other student are assigned to a triple together.
Exactly three of the rooms assigned to the students are singles.
Exactly two of the rooms assigned to the students are doubles.
Correct option (0-indexed): 1
Seven students—fourth-year students Kim and Lee; third-year students Pat and Robin; and second-year students Sandy, Terry, and Val—and only those seven, are being assigned to rooms of equal size in a dormitory. Each room assigned must have either one, or two, or three students assigned to it, and will accordingly be called either a single, or a double, or a triple. The seven students are assigned to rooms in accordance with the following conditions: No fourth-year student can be assigned to a triple. No second-year student can be assigned to a single. Lee and Robin must not share the same room. Kim and Pat must share the same room.

Question: Which one of the following must be true?
Options:
Lee is assigned to a single.
Pat shares a double with another student.
Robin shares a double with another student.
Two of the second-year students share a double with each other.
Neither of the third-year students is assigned to a single.
Correct option (0-indexed): 1
Seven students—fourth-year students Kim and Lee; third-year students Pat and Robin; and second-year students Sandy, Terry, and Val—and only those seven, are being assigned to rooms of equal size in a dormitory. Each room assigned must have either one, or two, or three students assigned to it, and will accordingly be called either a single, or a double, or a triple. The seven students are assigned to rooms in accordance with the following conditions: No fourth-year student can be assigned to a triple. No second-year student can be assigned to a single. Lee and Robin must not share the same room. Kim and Pat must share the same room.

Question: If Robin is assigned to a triple, which one of the following must be true?
Options:
Lee is assigned to a single.
Two second-year students share a double with each other.
None of the rooms assigned to the students is a single.
Two of the rooms assigned to the students are singles.
Three of the rooms assigned to the students are singles.
Correct option (0-indexed): 2
Seven students—fourth-year students Kim and Lee; third-year students Pat and Robin; and second-year students Sandy, Terry, and Val—and only those seven, are being assigned to rooms of equal size in a dormitory. Each room assigned must have either one, or two, or three students assigned to it, and will accordingly be called either a single, or a double, or a triple. The seven students are assigned to rooms in accordance with the following conditions: No fourth-year student can be assigned to a triple. No second-year student can be assigned to a single. Lee and Robin must not share the same room. Kim and Pat must share the same room.

Question: If Terry and Val are assigned to different doubles from each other, then it must be true of the students' rooms that exactly
Options:
one is a single
two are singles
two are doubles
one is a triple
two are triples
Correct option (0-indexed): 0
Seven students—fourth-year students Kim and Lee; third-year students Pat and Robin; and second-year students Sandy, Terry, and Val—and only those seven, are being assigned to rooms of equal size in a dormitory. Each room assigned must have either one, or two, or three students assigned to it, and will accordingly be called either a single, or a double, or a triple. The seven students are assigned to rooms in accordance with the following conditions: No fourth-year student can be assigned to a triple. No second-year student can be assigned to a single. Lee and Robin must not share the same room. Kim and Pat must share the same room.

Question: Which one of the following could be true?
Options:
The two fourth-year students are assigned to singles.
The two fourth-year students share a double with each other.
Lee shares a room with a second-year student.
Lee shares a room with a third-year student
Pat shares a triple with two other students.
Correct option (0-indexed): 2
A worker will insert colored light bulbs into a billboard equipped with exactly three light sockets, which are labeled lights 1, 2, and 3. The worker has three green bulbs, three purple bulbs, and three yellow bulbs. Selection of bulbs for the sockets is governed by the following conditions: Whenever light 1 is purple, light 2 must be yellow. Whenever light 2 is green, light 1 must be green. Whenever light 3 is either purple or yellow, light 2 must be purple.

Question: Which one of the following could be an accurate list of the colors of light bulbs selected for lights 1, 2, and 3, respectively?
Options:
green, green, yellow
purple, green, green
purple, purple, green
yellow, purple, green
yellow, yellow, yellow
Correct option (0-indexed): 3
A worker will insert colored light bulbs into a billboard equipped with exactly three light sockets, which are labeled lights 1, 2, and 3. The worker has three green bulbs, three purple bulbs, and three yellow bulbs. Selection of bulbs for the sockets is governed by the following conditions: Whenever light 1 is purple, light 2 must be yellow. Whenever light 2 is green, light 1 must be green. Whenever light 3 is either purple or yellow, light 2 must be purple.

Question: If light 1 is yellow, then any of the following can be true, EXCEPT:
Options:
Light 2 is green.
Light 2 is purple.
Light 3 is green.
Light 3 is purple.
Light 3 is yellow.
Correct option (0-indexed): 0
A worker will insert colored light bulbs into a billboard equipped with exactly three light sockets, which are labeled lights 1, 2, and 3. The worker has three green bulbs, three purple bulbs, and three yellow bulbs. Selection of bulbs for the sockets is governed by the following conditions: Whenever light 1 is purple, light 2 must be yellow. Whenever light 2 is green, light 1 must be green. Whenever light 3 is either purple or yellow, light 2 must be purple.

Question: There is exactly one possible color sequence of the three lights if which one of the following is true?
Options:
Light 1 is purple.
Light 2 is purple.
Light 2 is yellow.
Light 3 is purple.
Light 3 is yellow.
Correct option (0-indexed): 0
A worker will insert colored light bulbs into a billboard equipped with exactly three light sockets, which are labeled lights 1, 2, and 3. The worker has three green bulbs, three purple bulbs, and three yellow bulbs. Selection of bulbs for the sockets is governed by the following conditions: Whenever light 1 is purple, light 2 must be yellow. Whenever light 2 is green, light 1 must be green. Whenever light 3 is either purple or yellow, light 2 must be purple.

Question: If no green bulbs are selected, there are exactly how many possible different color sequences of the three lights?
Options:
one
two
three
four
five
Correct option (0-indexed): 1
A worker will insert colored light bulbs into a billboard equipped with exactly three light sockets, which are labeled lights 1, 2, and 3. The worker has three green bulbs, three purple bulbs, and three yellow bulbs. Selection of bulbs for the sockets is governed by the following conditions: Whenever light 1 is purple, light 2 must be yellow. Whenever light 2 is green, light 1 must be green. Whenever light 3 is either purple or yellow, light 2 must be purple.

Question: If no two lights are assigned light bulbs that are the same color as each other, then which one of the following could be true?
Options:
Light 1 is green, and light 2 is purple.
Light 1 is green, and light 2 is yellow.
Light 1 is purple, and light 3 is yellow.
Light 1 is yellow, and light 2 is green.
Light 1 is yellow, and light 3 is purple.
Correct option (0-indexed): 0
An attorney is scheduling interviews with witnesses for a given week, Monday through Saturday. Two full consecutive days of the week must be reserved for interviewing hostile witnesses. In addition, nonhostile witnesses Q, R, U, X, Y, and Z will each be interviewed exactly once for a full morning or afternoon. The only witnesses who will be interviewed simultaneously with each other are Q and R. The following conditions apply: X must be interviewed on Thursday morning. Q must be interviewed at some time before X. U must be interviewed at some time before R. Z must be interviewed at some time after X and at some time after Y.

Question: Which one of the following is a sequence, from first to last, in which the nonhostile witnesses could be interviewed?
Options:
Q with R, U, X, Y, Z
Q, U, R, X with Y, Z
U, X, Q, with R, X, Z
U, Y, Q with R, X, Z
X, Q with U, Z, R, Y
Correct option (0-indexed): 3
An attorney is scheduling interviews with witnesses for a given week, Monday through Saturday. Two full consecutive days of the week must be reserved for interviewing hostile witnesses. In addition, nonhostile witnesses Q, R, U, X, Y, and Z will each be interviewed exactly once for a full morning or afternoon. The only witnesses who will be interviewed simultaneously with each other are Q and R. The following conditions apply: X must be interviewed on Thursday morning. Q must be interviewed at some time before X. U must be interviewed at some time before R. Z must be interviewed at some time after X and at some time after Y.

Question: Which one of the following is acceptable as a complete schedule of witnesses for Tuesday morning, Tuesday afternoon, and Wednesday morning, respectively?
Options:
Q, R, none
R, none, Y
U, none, X
U, Y, none
Y, Z, none
Correct option (0-indexed): 3
An attorney is scheduling interviews with witnesses for a given week, Monday through Saturday. Two full consecutive days of the week must be reserved for interviewing hostile witnesses. In addition, nonhostile witnesses Q, R, U, X, Y, and Z will each be interviewed exactly once for a full morning or afternoon. The only witnesses who will be interviewed simultaneously with each other are Q and R. The following conditions apply: X must be interviewed on Thursday morning. Q must be interviewed at some time before X. U must be interviewed at some time before R. Z must be interviewed at some time after X and at some time after Y.

Question: If Y is interviewed at some time after X, which one of the following must be a day reserved for interviewing hostile witnesses?
Options:
Monday
Tuesday
Wednesday
Friday
Saturday
Correct option (0-indexed): 1
An attorney is scheduling interviews with witnesses for a given week, Monday through Saturday. Two full consecutive days of the week must be reserved for interviewing hostile witnesses. In addition, nonhostile witnesses Q, R, U, X, Y, and Z will each be interviewed exactly once for a full morning or afternoon. The only witnesses who will be interviewed simultaneously with each other are Q and R. The following conditions apply: X must be interviewed on Thursday morning. Q must be interviewed at some time before X. U must be interviewed at some time before R. Z must be interviewed at some time after X and at some time after Y.

Question: If R is interviewed at some time after Y, which one of the following must be a day reserved for interviewing hostile witnesses?
Options:
Monday
Tuesday
Wednesday
Thursday
Friday
Correct option (0-indexed): 4
An attorney is scheduling interviews with witnesses for a given week, Monday through Saturday. Two full consecutive days of the week must be reserved for interviewing hostile witnesses. In addition, nonhostile witnesses Q, R, U, X, Y, and Z will each be interviewed exactly once for a full morning or afternoon. The only witnesses who will be interviewed simultaneously with each other are Q and R. The following conditions apply: X must be interviewed on Thursday morning. Q must be interviewed at some time before X. U must be interviewed at some time before R. Z must be interviewed at some time after X and at some time after Y.

Question: If on Wednesday afternoon and on Monday the attorney conducts no interviews, which one of the following must be true?
Options:
Q is interviewed on the same day as U.
R is interviewed on the same day as Y.
Y is interviewed at some time before U.
Y is interviewed at some time before Wednesday.
Z is interviewed at some time before Friday.
Correct option (0-indexed): 4
An attorney is scheduling interviews with witnesses for a given week, Monday through Saturday. Two full consecutive days of the week must be reserved for interviewing hostile witnesses. In addition, nonhostile witnesses Q, R, U, X, Y, and Z will each be interviewed exactly once for a full morning or afternoon. The only witnesses who will be interviewed simultaneously with each other are Q and R. The following conditions apply: X must be interviewed on Thursday morning. Q must be interviewed at some time before X. U must be interviewed at some time before R. Z must be interviewed at some time after X and at some time after Y.

Question: If Z is interviewed on Saturday morning, which one of the following can be true?
Options:
Wednesday is a day reserved for interviewing hostile witnesses.
Friday is a day reserved for interviewing hostile witnesses.
R is interviewed on Thursday.
U is interviewed on Tuesday.
Y is interviewed at some time before Thursday.
Correct option (0-indexed): 0
During a four-week period, each of seven previously unadvertised products—G, H, J, K, L, M, and O—will be advertised. A different pair of these products will be advertised each week. Exactly one of the products will be a member of two of these four pairs. The following constraints must be observed: J is not advertised during a given week unless H is advertised during the immediately preceding week. The product that is advertised during two of the weeks is advertised during week 4 but is not advertised during week 3. G is not advertised during a given week unless either J or else O is also advertised that week. K is advertised during one of the first two weeks. O is one of the products advertised during week 3.

Question: Which one of the following could be the schedule of advertisements?
Options:
week 1: G, J; week 2: K, L; week 3: O, M; week 4: H, L
week l: H, K; week 2: J, G; week 3: O, L; week 4: M, K
week 1: H, K; week 2: J, M; week 3: O, L; week 4: G, M
week 1: H, L; week 2: J, M; week 3: O, G; week 4: K, L
week 1: K, M; week 2: H, J; week 3: O, G; week 4: L, M
Correct option (0-indexed): 1
During a four-week period, each of seven previously unadvertised products—G, H, J, K, L, M, and O—will be advertised. A different pair of these products will be advertised each week. Exactly one of the products will be a member of two of these four pairs. The following constraints must be observed: J is not advertised during a given week unless H is advertised during the immediately preceding week. The product that is advertised during two of the weeks is advertised during week 4 but is not advertised during week 3. G is not advertised during a given week unless either J or else O is also advertised that week. K is advertised during one of the first two weeks. O is one of the products advertised during week 3.

Question: Which one of the following is a pair of products that CANNOT be advertised during the same week as each other?
Options:
H and K
H and M
J and O
K and L
L and M
Correct option (0-indexed): 2
During a four-week period, each of seven previously unadvertised products—G, H, J, K, L, M, and O—will be advertised. A different pair of these products will be advertised each week. Exactly one of the products will be a member of two of these four pairs. The following constraints must be observed: J is not advertised during a given week unless H is advertised during the immediately preceding week. The product that is advertised during two of the weeks is advertised during week 4 but is not advertised during week 3. G is not advertised during a given week unless either J or else O is also advertised that week. K is advertised during one of the first two weeks. O is one of the products advertised during week 3.

Question: Which one of the following must be advertised during week 2?
Options:
G
J
K
L
M
Correct option (0-indexed): 1
During a four-week period, each of seven previously unadvertised products—G, H, J, K, L, M, and O—will be advertised. A different pair of these products will be advertised each week. Exactly one of the products will be a member of two of these four pairs. The following constraints must be observed: J is not advertised during a given week unless H is advertised during the immediately preceding week. The product that is advertised during two of the weeks is advertised during week 4 but is not advertised during week 3. G is not advertised during a given week unless either J or else O is also advertised that week. K is advertised during one of the first two weeks. O is one of the products advertised during week 3.

Question: Which one of the following CANNOT be the product that is advertised during two of the weeks?
Options:
G
H
K
L
M
Correct option (0-indexed): 0
During a four-week period, each of seven previously unadvertised products—G, H, J, K, L, M, and O—will be advertised. A different pair of these products will be advertised each week. Exactly one of the products will be a member of two of these four pairs. The following constraints must be observed: J is not advertised during a given week unless H is advertised during the immediately preceding week. The product that is advertised during two of the weeks is advertised during week 4 but is not advertised during week 3. G is not advertised during a given week unless either J or else O is also advertised that week. K is advertised during one of the first two weeks. O is one of the products advertised during week 3.

Question: If L is the product that is advertised during two of the weeks, which one of the following is a product that must be advertised during one of the weeks in which L is advertised?
Options:
G
H
J
K
M
Correct option (0-indexed): 4
During a four-week period, each of seven previously unadvertised products—G, H, J, K, L, M, and O—will be advertised. A different pair of these products will be advertised each week. Exactly one of the products will be a member of two of these four pairs. The following constraints must be observed: J is not advertised during a given week unless H is advertised during the immediately preceding week. The product that is advertised during two of the weeks is advertised during week 4 but is not advertised during week 3. G is not advertised during a given week unless either J or else O is also advertised that week. K is advertised during one of the first two weeks. O is one of the products advertised during week 3.

Question: Which one of the following is a product that could be advertised in any of the four weeks?
Options:
H
J
K
L
O
Correct option (0-indexed): 3
During a four-week period, each of seven previously unadvertised products—G, H, J, K, L, M, and O—will be advertised. A different pair of these products will be advertised each week. Exactly one of the products will be a member of two of these four pairs. The following constraints must be observed: J is not advertised during a given week unless H is advertised during the immediately preceding week. The product that is advertised during two of the weeks is advertised during week 4 but is not advertised during week 3. G is not advertised during a given week unless either J or else O is also advertised that week. K is advertised during one of the first two weeks. O is one of the products advertised during week 3.

Question: Which one of the following is a pair of products that could be advertised during the same week as each other?
Options:
G and H
H and J
H and O
K and O
M and O
Correct option (0-indexed): 4
An upholsterer will do seven jobs—N, O, P, S, T, U, and X—during a given week on Monday through Friday. Each job is done on exactly one of the days, and no two jobs are done concurrently. Each job takes either one half day or an entire day. The following conditions apply: N is done on the same day as S. X is done on Wednesday, and T is done on Friday. S is done earlier than the day on which P is done. U and X are the only jobs that must take an entire day each.

Question: Which one of the following is an acceptable schedule for the seven jobs? Mon. Tues. Wed. Thurs. Fri.
Options:
N, S P X O, U T
O N, S X P U
P U X N, S O, T
S N, P X U O, T
U N, S X O P, T
Correct option (0-indexed): 4
An upholsterer will do seven jobs—N, O, P, S, T, U, and X—during a given week on Monday through Friday. Each job is done on exactly one of the days, and no two jobs are done concurrently. Each job takes either one half day or an entire day. The following conditions apply: N is done on the same day as S. X is done on Wednesday, and T is done on Friday. S is done earlier than the day on which P is done. U and X are the only jobs that must take an entire day each.

Question: Which one of the following is a complete and accurate list of those jobs each of which CANNOT be done on Tuesday?
Options:
P, U
T, X
N, P, S
N, S, X
T, U, X
Correct option (0-indexed): 1
An upholsterer will do seven jobs—N, O, P, S, T, U, and X—during a given week on Monday through Friday. Each job is done on exactly one of the days, and no two jobs are done concurrently. Each job takes either one half day or an entire day. The following conditions apply: N is done on the same day as S. X is done on Wednesday, and T is done on Friday. S is done earlier than the day on which P is done. U and X are the only jobs that must take an entire day each.

Question: If O is done on Thursday, N could be done on
Options:
Monday, but on no other day
Thursday, but on no other day
Monday or else on Tuesday, but on no other day
Tuesday or else on Wednesday, but on no other day
Wednesday or else on Thursday, but on no other day
Correct option (0-indexed): 2
An upholsterer will do seven jobs—N, O, P, S, T, U, and X—during a given week on Monday through Friday. Each job is done on exactly one of the days, and no two jobs are done concurrently. Each job takes either one half day or an entire day. The following conditions apply: N is done on the same day as S. X is done on Wednesday, and T is done on Friday. S is done earlier than the day on which P is done. U and X are the only jobs that must take an entire day each.

Question: Which one of the following must be true if the upholsterer does two jobs on Thursday and two jobs on Friday?
Options:
N is done on Monday.
O is done on Tuesday.
P is done on Friday.
O is done on the same day as P.
O is done on the same day as T.
Correct option (0-indexed): 2
An upholsterer will do seven jobs—N, O, P, S, T, U, and X—during a given week on Monday through Friday. Each job is done on exactly one of the days, and no two jobs are done concurrently. Each job takes either one half day or an entire day. The following conditions apply: N is done on the same day as S. X is done on Wednesday, and T is done on Friday. S is done earlier than the day on which P is done. U and X are the only jobs that must take an entire day each.

Question: If P is not done on Friday, which one of the following must be true?
Options:
N is done on Monday or else on Thursday.
O is done on Wednesday or else on Thursday.
S is done on Monday or else on Thursday.
P is done on the same day as O.
O is done on the same day as either P or T.
Correct option (0-indexed): 4
An upholsterer will do seven jobs—N, O, P, S, T, U, and X—during a given week on Monday through Friday. Each job is done on exactly one of the days, and no two jobs are done concurrently. Each job takes either one half day or an entire day. The following conditions apply: N is done on the same day as S. X is done on Wednesday, and T is done on Friday. S is done earlier than the day on which P is done. U and X are the only jobs that must take an entire day each.

Question: If O is done on Monday, which one of the following must be true?
Options:
N is done on Tuesday.
P is done on Thursday.
P is done on Friday.
S is done on Thursday.
U is done on Friday.
Correct option (0-indexed): 2
Seven persons—G, H, I, K, L, M, and P—are going rock-climbing together. One person will be the organizer and not a member of any team. The remaining six will form three climbing teams, each consisting of two persons. No person can be on more than one team. The following conditions also apply: M and P cannot be on the same team as each other. If K is on a team, M must also be on that team. If G is on a team, either H or I must also be on that team. If H is on a team, K must be the organizer.

Question: Which one of the following can be a list of the members of the three teams?
Options:
Team 1: G, H; Team 2: I, L; Team 3: M, P
Team 1: G, H; Team 2: L, P; Team 3: K, M
Team 1: G, I; Team 2: H, M; Team 3: L, P
Team 1: G, P; Team 2: I, L; Team 3: K, M
Team 1: H, M; Team 2: I, L; Team 3: K, P
Correct option (0-indexed): 2
Seven persons—G, H, I, K, L, M, and P—are going rock-climbing together. One person will be the organizer and not a member of any team. The remaining six will form three climbing teams, each consisting of two persons. No person can be on more than one team. The following conditions also apply: M and P cannot be on the same team as each other. If K is on a team, M must also be on that team. If G is on a team, either H or I must also be on that team. If H is on a team, K must be the organizer.

Question: Each of the following is a pair of persons who can constitute a team EXCEPT:
Options:
H, I
H, M
I, M
I, P
L, P
Correct option (0-indexed): 0
Seven persons—G, H, I, K, L, M, and P—are going rock-climbing together. One person will be the organizer and not a member of any team. The remaining six will form three climbing teams, each consisting of two persons. No person can be on more than one team. The following conditions also apply: M and P cannot be on the same team as each other. If K is on a team, M must also be on that team. If G is on a team, either H or I must also be on that team. If H is on a team, K must be the organizer.

Question: Which one of the following can be the organizer, who is not on any team?
Options:
G
H
I
L
P
Correct option (0-indexed): 1
Seven persons—G, H, I, K, L, M, and P—are going rock-climbing together. One person will be the organizer and not a member of any team. The remaining six will form three climbing teams, each consisting of two persons. No person can be on more than one team. The following conditions also apply: M and P cannot be on the same team as each other. If K is on a team, M must also be on that team. If G is on a team, either H or I must also be on that team. If H is on a team, K must be the organizer.

Question: If G and I form a team and if H is a member of a team, then H must be on the same team as either
Options:
K or L
K or P
L or M
L or P
M or P
Correct option (0-indexed): 4
Seven persons—G, H, I, K, L, M, and P—are going rock-climbing together. One person will be the organizer and not a member of any team. The remaining six will form three climbing teams, each consisting of two persons. No person can be on more than one team. The following conditions also apply: M and P cannot be on the same team as each other. If K is on a team, M must also be on that team. If G is on a team, either H or I must also be on that team. If H is on a team, K must be the organizer.

Question: If L and M are on different teams, which one of the following must be true?
Options:
H is the organizer.
K is the organizer.
G is on the same team as H.
I is on the same team as M.
L is on the same team as P.
Correct option (0-indexed): 4
Seven persons—G, H, I, K, L, M, and P—are going rock-climbing together. One person will be the organizer and not a member of any team. The remaining six will form three climbing teams, each consisting of two persons. No person can be on more than one team. The following conditions also apply: M and P cannot be on the same team as each other. If K is on a team, M must also be on that team. If G is on a team, either H or I must also be on that team. If H is on a team, K must be the organizer.

Question: Which one of the following lists three persons each of whom must be on a team and no two of whom can be on the same team as each other?
Options:
G, L, M
G, M, P
H, I, L
I, L, P
L, M, P
Correct option (0-indexed): 1
Seven persons—G, H, I, K, L, M, and P—are going rock-climbing together. One person will be the organizer and not a member of any team. The remaining six will form three climbing teams, each consisting of two persons. No person can be on more than one team. The following conditions also apply: M and P cannot be on the same team as each other. If K is on a team, M must also be on that team. If G is on a team, either H or I must also be on that team. If H is on a team, K must be the organizer.

Question: There are how many different persons any one of whom could be paired with M to form a team?
Options:
one
two
three
four
five
Correct option (0-indexed): 3
A train makes five trips around a loop through five stations—P, Q, R, S, and T, in that order—stopping at exactly three of the stations on each trip. The train must conform to the following conditions: The train stops at any given station on exactly three trips, but not on three consecutive trips. The train stops at any given station at least once in any two consecutive trips.

Question: Which one of the following could be the list of stations at which the train stops on the first two trips?
Options:
first trip: P, Q, S; second trip: P, Q, R
first trip: P, Q, T; second trip: Q, R, T
first trip: Q, R, S; second trip: P, Q, S
first trip: Q, S, T; second trip: P, R, S
first trip: R, S, T; second trip: P, R, T
Correct option (0-indexed): 3
A train makes five trips around a loop through five stations—P, Q, R, S, and T, in that order—stopping at exactly three of the stations on each trip. The train must conform to the following conditions: The train stops at any given station on exactly three trips, but not on three consecutive trips. The train stops at any given station at least once in any two consecutive trips.

Question: If on the first and third trips the train is to stop at Q, R, and S, and at R, S, and T, respectively, which one of the following is the list of stations at which it must stop on the second trip?
Options:
P, Q, R
P, Q, T
P, S, T
Q, R, T
Q, S, T
Correct option (0-indexed): 1
A train makes five trips around a loop through five stations—P, Q, R, S, and T, in that order—stopping at exactly three of the stations on each trip. The train must conform to the following conditions: The train stops at any given station on exactly three trips, but not on three consecutive trips. The train stops at any given station at least once in any two consecutive trips.

Question: The train CANNOT stop at both P and Q on both the
Options:
first and third trips
first and fourth trips
second and fourth trips
second and fifth trips
fourth and fifth trips
Correct option (0-indexed): 4
A train makes five trips around a loop through five stations—P, Q, R, S, and T, in that order—stopping at exactly three of the stations on each trip. The train must conform to the following conditions: The train stops at any given station on exactly three trips, but not on three consecutive trips. The train stops at any given station at least once in any two consecutive trips.

Question: If the train is to stop at Q, R, and T on the first trip and at Q, R, and S on the fourth trip, then it could be true that the train
Options:
stops at Q on the second trip
stops at R on the fifth trip
stops at T on the second trip
does not stop at P on the third trip
does not stop at T on the fifth trip
Correct option (0-indexed): 0
A train makes five trips around a loop through five stations—P, Q, R, S, and T, in that order—stopping at exactly three of the stations on each trip. The train must conform to the following conditions: The train stops at any given station on exactly three trips, but not on three consecutive trips. The train stops at any given station at least once in any two consecutive trips.

Question: Suppose that the train's scheduler mistakenly scheduled the train to make the following stops on the first three trips: Q, R, and S on the first trip; P, Q, and S on the second trip; and R, S, and T on the third trip. Which one of the following is a substitution that results in a schedule for those three trips under which the train violates no condition?
Options:
on the first trip, P for Q
on the second trip, R for S
on the second trip, T for S
on the third trip, P for R
on the third trip, P for S
Correct option (0-indexed): 2
On a certain morning, each of six speakers—Feinberg, Guzman, Harrison, Jansen, Kim, and Mackey—will lecture for exactly one hour. Each lecture will take place in either the library or the studio, with exactly one speaker at a time lecturing in each of these two rooms. The lectures must be given in a manner consistent with the following conditions: Exactly three of the lectures are given in each room, the first beginning at precisely 8 A.M. , the second at precisely 9 A.M., and the third at precisely 10 A.M. Feinberg's lecture cannot begin earlier than Guzman's. Neither Jansen's lecture nor Mackey's lecture begins at the same time as Feinberg's. Harrison's lecture begins earlier than Feinberg's. Jansen and Mackey, not necessarily in that order, lecture in the studio.

Question: Which one of the following must be true?
Options:
Either Jansen or else Mackey lectures in the studio beginning at 8 A.M.
Either Harrison or else Mackey lectures in the studio beginning at 9 A.M.
Either Guzman or else Harrison lectures in the library beginning at 8 A.M.
Either Feinberg or else Guzman lectures in the library beginning at 9 A.M.
Either Feinberg or else Guzman lectures in the library beginning at 10 A.M.
Correct option (0-indexed): 0
On a certain morning, each of six speakers—Feinberg, Guzman, Harrison, Jansen, Kim, and Mackey—will lecture for exactly one hour. Each lecture will take place in either the library or the studio, with exactly one speaker at a time lecturing in each of these two rooms. The lectures must be given in a manner consistent with the following conditions: Exactly three of the lectures are given in each room, the first beginning at precisely 8 A.M. , the second at precisely 9 A.M., and the third at precisely 10 A.M. Feinberg's lecture cannot begin earlier than Guzman's. Neither Jansen's lecture nor Mackey's lecture begins at the same time as Feinberg's. Harrison's lecture begins earlier than Feinberg's. Jansen and Mackey, not necessarily in that order, lecture in the studio.

Question: If both Kim's lecture and Mackey's lecture begin at 9 A.M. , which one of the following could be true?
Options:
Guzman's lecture begins at 8 A.M.
Harrison's lecture begins at 10 A.M.
Jansen's lecture begins at 10 A.M.
Guzman lectures in the library.
Harrison lectures in the studio.
Correct option (0-indexed): 3
On a certain morning, each of six speakers—Feinberg, Guzman, Harrison, Jansen, Kim, and Mackey—will lecture for exactly one hour. Each lecture will take place in either the library or the studio, with exactly one speaker at a time lecturing in each of these two rooms. The lectures must be given in a manner consistent with the following conditions: Exactly three of the lectures are given in each room, the first beginning at precisely 8 A.M. , the second at precisely 9 A.M., and the third at precisely 10 A.M. Feinberg's lecture cannot begin earlier than Guzman's. Neither Jansen's lecture nor Mackey's lecture begins at the same time as Feinberg's. Harrison's lecture begins earlier than Feinberg's. Jansen and Mackey, not necessarily in that order, lecture in the studio.

Question: If Harrison's lecture begins at 9 A.M. , which one of the following must be true?
Options:
Feinberg lectures in the library.
Guzman lectures in the studio.
Harrison lectures in the library.
Kim lectures in the studio.
Mackey lectures in the library.
Correct option (0-indexed): 2
On a certain morning, each of six speakers—Feinberg, Guzman, Harrison, Jansen, Kim, and Mackey—will lecture for exactly one hour. Each lecture will take place in either the library or the studio, with exactly one speaker at a time lecturing in each of these two rooms. The lectures must be given in a manner consistent with the following conditions: Exactly three of the lectures are given in each room, the first beginning at precisely 8 A.M. , the second at precisely 9 A.M., and the third at precisely 10 A.M. Feinberg's lecture cannot begin earlier than Guzman's. Neither Jansen's lecture nor Mackey's lecture begins at the same time as Feinberg's. Harrison's lecture begins earlier than Feinberg's. Jansen and Mackey, not necessarily in that order, lecture in the studio.

Question: Each of the following is a pair of speakers whose lectures could begin at the same time as each other EXCEPT:
Options:
Feinberg and Guzman
Feinberg and Kim
Guzman and Jansen
Guzman and Kim
Guzman and Mackey
Correct option (0-indexed): 3
On a certain morning, each of six speakers—Feinberg, Guzman, Harrison, Jansen, Kim, and Mackey—will lecture for exactly one hour. Each lecture will take place in either the library or the studio, with exactly one speaker at a time lecturing in each of these two rooms. The lectures must be given in a manner consistent with the following conditions: Exactly three of the lectures are given in each room, the first beginning at precisely 8 A.M. , the second at precisely 9 A.M., and the third at precisely 10 A.M. Feinberg's lecture cannot begin earlier than Guzman's. Neither Jansen's lecture nor Mackey's lecture begins at the same time as Feinberg's. Harrison's lecture begins earlier than Feinberg's. Jansen and Mackey, not necessarily in that order, lecture in the studio.

Question: If Feinberg lectures in the library beginning at 9 A.M., which one of the following could be true?
Options:
Guzman lectures in the studio beginning at 10 A.M.
Harrison lectures in the studio beginning at 8 A.M.
Jansen lectures in the studio beginning at 10 A.M.
Kim lectures in the studio beginning at 9 A.M.
Mackey lectures in the studio beginning at 9 A.M.
Correct option (0-indexed): 2
On a certain morning, each of six speakers—Feinberg, Guzman, Harrison, Jansen, Kim, and Mackey—will lecture for exactly one hour. Each lecture will take place in either the library or the studio, with exactly one speaker at a time lecturing in each of these two rooms. The lectures must be given in a manner consistent with the following conditions: Exactly three of the lectures are given in each room, the first beginning at precisely 8 A.M. , the second at precisely 9 A.M., and the third at precisely 10 A.M. Feinberg's lecture cannot begin earlier than Guzman's. Neither Jansen's lecture nor Mackey's lecture begins at the same time as Feinberg's. Harrison's lecture begins earlier than Feinberg's. Jansen and Mackey, not necessarily in that order, lecture in the studio.

Question: Which one of the following could be a list of the speakers who give their lectures in the studio, in the order in which they give their lectures, from first to third, respectively?
Options:
Feinberg, Jansen, Mackey
Guzman, Kim, Mackey
Harrison, Jansen, Kim
Jansen, Mackey, Harrison
Mackey, Feinberg, Jansen
Correct option (0-indexed): 4
At a benefit dinner, a community theater's seven sponsors—K, L, M, P, Q, V, and Z—will be seated at three tables—1, 2, and 3. Of the sponsors, only K, L, and M will receive honors, and only M, P, and Q will give a speech. The sponsors' seating assignments must conform to the following conditions: Each table has at least two sponsors seated at it, and each sponsor is seated at exactly one table. Any sponsor receiving honors is seated at table 1 or table 2. L is seated at the same table as V.

Question: Which one of the following is an acceptable assignment of sponsors to tables?
Options:
Table 1: K, P; Table 2: M, Q; Table 3: L, V, Z
Table 1: K, Q, Z; Table 2: L, V; Table 3: M, P
Table 1: L, P; Table 2: K, M; Table 3: Q, V, Z
Table 1: L, Q, V; Table 2: K, M; Table 3: P, Z
Table 1: L, V, Z; Table 2: K, M, P; Table 3: Q
Correct option (0-indexed): 3
At a benefit dinner, a community theater's seven sponsors—K, L, M, P, Q, V, and Z—will be seated at three tables—1, 2, and 3. Of the sponsors, only K, L, and M will receive honors, and only M, P, and Q will give a speech. The sponsors' seating assignments must conform to the following conditions: Each table has at least two sponsors seated at it, and each sponsor is seated at exactly one table. Any sponsor receiving honors is seated at table 1 or table 2. L is seated at the same table as V.

Question: Which one of the following is a list of all and only those sponsors any one of whom could be among the sponsors assigned to table 3?
Options:
P, Q
Q, Z
P, Q, Z
Q, V, Z
P, Q, V, Z
Correct option (0-indexed): 2
At a benefit dinner, a community theater's seven sponsors—K, L, M, P, Q, V, and Z—will be seated at three tables—1, 2, and 3. Of the sponsors, only K, L, and M will receive honors, and only M, P, and Q will give a speech. The sponsors' seating assignments must conform to the following conditions: Each table has at least two sponsors seated at it, and each sponsor is seated at exactly one table. Any sponsor receiving honors is seated at table 1 or table 2. L is seated at the same table as V.

Question: If K is assigned to a different table than M, which one of the following must be true of the seating assignment?
Options:
K is seated at the same table as L.
L is seated at the same table as Q.
M is seated at the same table as V.
Exactly two sponsors are seated at table 1.
Exactly two sponsors are seated at table 3.
Correct option (0-indexed): 4
At a benefit dinner, a community theater's seven sponsors—K, L, M, P, Q, V, and Z—will be seated at three tables—1, 2, and 3. Of the sponsors, only K, L, and M will receive honors, and only M, P, and Q will give a speech. The sponsors' seating assignments must conform to the following conditions: Each table has at least two sponsors seated at it, and each sponsor is seated at exactly one table. Any sponsor receiving honors is seated at table 1 or table 2. L is seated at the same table as V.

Question: If Q is assigned to table 1 along with two other sponsors, which one of the following could be true of the seating assignment?
Options:
K is seated at the same table as L.
K is seated at the same table as Q.
M is seated at the same table as V.
M is seated at the same table as Z.
P Is seated at the same table as Q.
Correct option (0-indexed): 1
At a benefit dinner, a community theater's seven sponsors—K, L, M, P, Q, V, and Z—will be seated at three tables—1, 2, and 3. Of the sponsors, only K, L, and M will receive honors, and only M, P, and Q will give a speech. The sponsors' seating assignments must conform to the following conditions: Each table has at least two sponsors seated at it, and each sponsor is seated at exactly one table. Any sponsor receiving honors is seated at table 1 or table 2. L is seated at the same table as V.

Question: If the sponsors assigned to table 3 include exactly one of the sponsors who will give a speech, then the sponsors assigned to table 1 could include any of the following EXCEPT:
Options:
K
M
P
Q
Z
Correct option (0-indexed): 4
At a benefit dinner, a community theater's seven sponsors—K, L, M, P, Q, V, and Z—will be seated at three tables—1, 2, and 3. Of the sponsors, only K, L, and M will receive honors, and only M, P, and Q will give a speech. The sponsors' seating assignments must conform to the following conditions: Each table has at least two sponsors seated at it, and each sponsor is seated at exactly one table. Any sponsor receiving honors is seated at table 1 or table 2. L is seated at the same table as V.

Question: If three sponsors, exactly two of whom are receiving honors, are assigned to table 2, which one of the following could be the list of sponsors assigned to table 1?
Options:
K, M
K, Z
P, V
P, Z
Q, Z
Correct option (0-indexed): 1
At a benefit dinner, a community theater's seven sponsors—K, L, M, P, Q, V, and Z—will be seated at three tables—1, 2, and 3. Of the sponsors, only K, L, and M will receive honors, and only M, P, and Q will give a speech. The sponsors' seating assignments must conform to the following conditions: Each table has at least two sponsors seated at it, and each sponsor is seated at exactly one table. Any sponsor receiving honors is seated at table 1 or table 2. L is seated at the same table as V.

Question: Which one of the following conditions, if added to the existing conditions, results in a set of conditions to which no seating assignment for the sponsors can conform?
Options:
At most two sponsors are seated at table 1.
Any sponsor giving a speech is seated at table 1 or else table 2.
Any sponsor giving a speech is seated at table 2 or else table 3.
Exactly three of the sponsors are seated at table 1.
Any table at which both L and V are seated also has a third sponsor seated at it.
Correct option (0-indexed): 1
Exactly four medical training sessions—M, O, R, and S—will be scheduled for four consecutive days—day 1 through day 4—one session each day. Six professionals—three nurses and three psychologists—will teach the sessions. The nurses are Fine, Johnson, and Leopold; the psychologists are Tyler, Vitale, and Wong. Each session will be taught by exactly one nurse and exactly one psychologist. The schedule must conform to the following conditions: Each professional teaches at least once. Day 3 is a day on which Leopold teaches. Neither Fine nor Leopold teaches with Tyler. Johnson teaches session S only. Session M is taught on the day after the day on which session S is taught.

Question: If session R is the only session for which Leopold is scheduled, which one of the following is a pair of professionals who could be scheduled for day 2 together?
Options:
Fine and Tyler
Fine and Wong
Johnson and Tyler
Johnson and Wong
Leopold and Wong
Correct option (0-indexed): 1
Exactly four medical training sessions—M, O, R, and S—will be scheduled for four consecutive days—day 1 through day 4—one session each day. Six professionals—three nurses and three psychologists—will teach the sessions. The nurses are Fine, Johnson, and Leopold; the psychologists are Tyler, Vitale, and Wong. Each session will be taught by exactly one nurse and exactly one psychologist. The schedule must conform to the following conditions: Each professional teaches at least once. Day 3 is a day on which Leopold teaches. Neither Fine nor Leopold teaches with Tyler. Johnson teaches session S only. Session M is taught on the day after the day on which session S is taught.

Question: Which one of the following must be false?
Options:
Session O is scheduled for day 1.
Session S is scheduled for day 3.
Leopold is scheduled for day 1.
Vitale is scheduled for day 4.
Wong is scheduled for day 1.
Correct option (0-indexed): 1