benlipkin/arlsat huggingface dataset:
Four lions—F, G, H, J—and two tigers—K and M—will be assigned to exactly six stalls, one animal per stall. The stalls are arranged as follows: First Row: 1 2 3 Second Row: 4 5 6 The only stalls that face each other are stalls 1 and 4, stalls 2 and 5, and stalls 3 and 6. The following conditions apply: The tigers' stalls cannot face each other. A lion must be assigned to stall 1. H must be assigned to stall 6. J must be assigned to a stall numbered one higher than K's stall. K cannot be assigned to the stall that faces H's stall.

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

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

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

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

Question: Which one of the following must be true?
Options:
A tiger is assigned to stall 2.
A tiger is assigned to stall 4.
A tiger is assigned to stall 5.
A lion is assigned to stall 3.
A lion is assigned to stall 4.
Correct option (0-indexed): 1
On an undeveloped street, a developer will simultaneously build four houses on one side, numbered consecutively 1, 3, 5, and 7, and fos on the opposite side, numbered consecutively 2, 4, 6, and 8. Houses 2, 4, 6, and 8 will face houses 1, 3, 5, and 7, respectively. Each house will be exactly one of three styles—ranch, split-level, or Tudor—according to the following conditions: Adjacent houses are of different styles. No split-level house faces another split-level house. Every ranch house has at least one Tudor house adjacent to it. House 3 is a ranch house. House 6 is a split-level house.

Question: Any of the following could be a Tudor house EXCEPT house
Options:
1
2
4
7
8
Correct option (0-indexed): 3
On an undeveloped street, a developer will simultaneously build four houses on one side, numbered consecutively 1, 3, 5, and 7, and fos on the opposite side, numbered consecutively 2, 4, 6, and 8. Houses 2, 4, 6, and 8 will face houses 1, 3, 5, and 7, respectively. Each house will be exactly one of three styles—ranch, split-level, or Tudor—according to the following conditions: Adjacent houses are of different styles. No split-level house faces another split-level house. Every ranch house has at least one Tudor house adjacent to it. House 3 is a ranch house. House 6 is a split-level house.

Question: If there is one ranch house directly opposite another ranch house, which one of the following could be true?
Options:
House 8 is a ranch house.
House 7 is a split-level house.
House 4 is a Tudor house.
House 2 is a split-level house.
House 1 is a ranch house.
Correct option (0-indexed): 1
On an undeveloped street, a developer will simultaneously build four houses on one side, numbered consecutively 1, 3, 5, and 7, and fos on the opposite side, numbered consecutively 2, 4, 6, and 8. Houses 2, 4, 6, and 8 will face houses 1, 3, 5, and 7, respectively. Each house will be exactly one of three styles—ranch, split-level, or Tudor—according to the following conditions: Adjacent houses are of different styles. No split-level house faces another split-level house. Every ranch house has at least one Tudor house adjacent to it. House 3 is a ranch house. House 6 is a split-level house.

Question: If house 4 is a Tudor house, then it could be true that house
Options:
1 is a Tudor house
2 is a Tudor house
5 is a ranch house
7 is a Tudor house
8 is a ranch house
Correct option (0-indexed): 0
On an undeveloped street, a developer will simultaneously build four houses on one side, numbered consecutively 1, 3, 5, and 7, and fos on the opposite side, numbered consecutively 2, 4, 6, and 8. Houses 2, 4, 6, and 8 will face houses 1, 3, 5, and 7, respectively. Each house will be exactly one of three styles—ranch, split-level, or Tudor—according to the following conditions: Adjacent houses are of different styles. No split-level house faces another split-level house. Every ranch house has at least one Tudor house adjacent to it. House 3 is a ranch house. House 6 is a split-level house.

Question: On the street, there could be exactly
Options:
one ranch house
one Tudor house
two Tudor houses
four ranch houses
five ranch houses
Correct option (0-indexed): 0
On an undeveloped street, a developer will simultaneously build four houses on one side, numbered consecutively 1, 3, 5, and 7, and fos on the opposite side, numbered consecutively 2, 4, 6, and 8. Houses 2, 4, 6, and 8 will face houses 1, 3, 5, and 7, respectively. Each house will be exactly one of three styles—ranch, split-level, or Tudor—according to the following conditions: Adjacent houses are of different styles. No split-level house faces another split-level house. Every ranch house has at least one Tudor house adjacent to it. House 3 is a ranch house. House 6 is a split-level house.

Question: If no house faces a house of the same style, then it must be true that house
Options:
1 is a split-level house
1 is a Tudor house
2 is a ranch house
2 is a split-level house
4 is a Tudor house
Correct option (0-indexed): 4
On an undeveloped street, a developer will simultaneously build four houses on one side, numbered consecutively 1, 3, 5, and 7, and fos on the opposite side, numbered consecutively 2, 4, 6, and 8. Houses 2, 4, 6, and 8 will face houses 1, 3, 5, and 7, respectively. Each house will be exactly one of three styles—ranch, split-level, or Tudor—according to the following conditions: Adjacent houses are of different styles. No split-level house faces another split-level house. Every ranch house has at least one Tudor house adjacent to it. House 3 is a ranch house. House 6 is a split-level house.

Question: If the condition requiring house 6 to be a split-level house is suspended but all other original conditions remain the same, then any of the following could be an accurate list of the styles of houses 2, 4, 6, and 8, respectively, EXCEPT:
Options:
ranch, split-level, ranch, Tudor
split-level, ranch, Tudor, split-level
split-level, Tudor, ranch, split-level
Tudor, ranch, Tudor, split-level
Tudor, split-level, ranch, Tudor
Correct option (0-indexed): 0
Within a tennis league each of five teams occupies one of five positions, numbered 1 through 5 in order of rank, with number 1 as the highest position. The teams are initially in the order R, J, S, M, L, with R in position 1. Teams change positions only when a lower-positioned team defeats a higher-positioned team. The rules are as follows: Matches are played alternately in odd-position rounds and in even-position rounds. In an odd-position round, teams in positions 3 and 5 play against teams positioned immediately above them. In an even-position round, teams in positions 2 and 4 play against teams positioned immediately above them. When a lower-positioned team defeats a higher-positioned team, the two teams switch positions after the round is completed.

Question: Which one of the following could be the order of teams, from position 1 through position 5 respectively, after exactly one round of even-position matches if no odd-position round has yet been played?
Options:
J, R, M, L, S
J, R, S, L, M
R, J, M, L, S
R, J, M, S, L
R, S, J, L, M
Correct option (0-indexed): 3
Within a tennis league each of five teams occupies one of five positions, numbered 1 through 5 in order of rank, with number 1 as the highest position. The teams are initially in the order R, J, S, M, L, with R in position 1. Teams change positions only when a lower-positioned team defeats a higher-positioned team. The rules are as follows: Matches are played alternately in odd-position rounds and in even-position rounds. In an odd-position round, teams in positions 3 and 5 play against teams positioned immediately above them. In an even-position round, teams in positions 2 and 4 play against teams positioned immediately above them. When a lower-positioned team defeats a higher-positioned team, the two teams switch positions after the round is completed.

Question: If exactly two rounds of matches have been played, beginning with an odd-position round, and if the lower-positioned teams have won every match in those two rounds, then each of the following must be true EXCEPT:
Options:
L is one position higher than J.
R is one position higher than L.
S is one position higher than R.
J is in position 4.
M is in position 3.
Correct option (0-indexed): 4
Within a tennis league each of five teams occupies one of five positions, numbered 1 through 5 in order of rank, with number 1 as the highest position. The teams are initially in the order R, J, S, M, L, with R in position 1. Teams change positions only when a lower-positioned team defeats a higher-positioned team. The rules are as follows: Matches are played alternately in odd-position rounds and in even-position rounds. In an odd-position round, teams in positions 3 and 5 play against teams positioned immediately above them. In an even-position round, teams in positions 2 and 4 play against teams positioned immediately above them. When a lower-positioned team defeats a higher-positioned team, the two teams switch positions after the round is completed.

Question: Which one of the following could be true after exactly two rounds of matches have been played?
Options:
J has won two matches.
L has lost two matches.
R has won two matches.
L's only match was played against J.
M played against S in two matches.
Correct option (0-indexed): 0
Within a tennis league each of five teams occupies one of five positions, numbered 1 through 5 in order of rank, with number 1 as the highest position. The teams are initially in the order R, J, S, M, L, with R in position 1. Teams change positions only when a lower-positioned team defeats a higher-positioned team. The rules are as follows: Matches are played alternately in odd-position rounds and in even-position rounds. In an odd-position round, teams in positions 3 and 5 play against teams positioned immediately above them. In an even-position round, teams in positions 2 and 4 play against teams positioned immediately above them. When a lower-positioned team defeats a higher-positioned team, the two teams switch positions after the round is completed.

Question: If after exactly three rounds of matches M is in position 4, and J and L have won all of their matches, then which one of the following can be true?
Options:
J is in position 2.
J is in position 3.
L is in position 2.
R is in position 1.
S is in position 3.
Correct option (0-indexed): 2
Within a tennis league each of five teams occupies one of five positions, numbered 1 through 5 in order of rank, with number 1 as the highest position. The teams are initially in the order R, J, S, M, L, with R in position 1. Teams change positions only when a lower-positioned team defeats a higher-positioned team. The rules are as follows: Matches are played alternately in odd-position rounds and in even-position rounds. In an odd-position round, teams in positions 3 and 5 play against teams positioned immediately above them. In an even-position round, teams in positions 2 and 4 play against teams positioned immediately above them. When a lower-positioned team defeats a higher-positioned team, the two teams switch positions after the round is completed.

Question: If after exactly three rounds M has won three matches and the rankings of the other four teams relative to each other remain the same, then which one of the following must be in position 3?
Options:
J
L
M
R
S
Correct option (0-indexed): 0
Within a tennis league each of five teams occupies one of five positions, numbered 1 through 5 in order of rank, with number 1 as the highest position. The teams are initially in the order R, J, S, M, L, with R in position 1. Teams change positions only when a lower-positioned team defeats a higher-positioned team. The rules are as follows: Matches are played alternately in odd-position rounds and in even-position rounds. In an odd-position round, teams in positions 3 and 5 play against teams positioned immediately above them. In an even-position round, teams in positions 2 and 4 play against teams positioned immediately above them. When a lower-positioned team defeats a higher-positioned team, the two teams switch positions after the round is completed.

Question: If after exactly three rounds the teams, in order from first to fifth position, are R, J, L, S, and M, then which one of the following could be the order, from first to fifth position, of the teams after the second round?
Options:
J, R, M, S, L
J, L, S, M, R
R, J, S, L, M
R, L, M, S, J
R, M, L, S, J
Correct option (0-indexed): 2
On Wednesday a physician will have exactly one appointment with seven patients—P, Q, R, S, T, U, W—one patient per appointment. The schedule of appointments, chronologically numbered 1 through 7, must meet the following conditions: Q's appointment is at some time before W's appointment. U's appointment is at some time before P's appointment. Either R or T has appointment 3. S's appointment is either the appointment immediately before or the appointment immediately after R's appointment.

Question: Which one of the following is an acceptable schedule of appointments in order from 1 to 7?
Options:
Q, S, R, P, W, U, T
Q, U, W, S, R, T, P
S, Q, R, T, W, U, P
T, U, R, S, W, P, Q
U, Q, T, P, R, S, W
Correct option (0-indexed): 4
On Wednesday a physician will have exactly one appointment with seven patients—P, Q, R, S, T, U, W—one patient per appointment. The schedule of appointments, chronologically numbered 1 through 7, must meet the following conditions: Q's appointment is at some time before W's appointment. U's appointment is at some time before P's appointment. Either R or T has appointment 3. S's appointment is either the appointment immediately before or the appointment immediately after R's appointment.

Question: If W has appointment 2 and P has appointment 5, then which one of the following must be true?
Options:
R has appointment 6.
S has appointment 4.
S has appointment 7.
U has appointment 1.
U has appointment 4.
Correct option (0-indexed): 4
On Wednesday a physician will have exactly one appointment with seven patients—P, Q, R, S, T, U, W—one patient per appointment. The schedule of appointments, chronologically numbered 1 through 7, must meet the following conditions: Q's appointment is at some time before W's appointment. U's appointment is at some time before P's appointment. Either R or T has appointment 3. S's appointment is either the appointment immediately before or the appointment immediately after R's appointment.

Question: If U's appointment is immediately after T's appointment and immediately before R's appointment, then which one of the following must be true?
Options:
Q's appointment is at some time before P's appointment.
S's appointment is at some time before P's appointment.
S's appointment is immediately before Q's appointment.
W's appointment is immediately before P's appointment.
W's appointment is at some time before S's appointment.
Correct option (0-indexed): 1
On Wednesday a physician will have exactly one appointment with seven patients—P, Q, R, S, T, U, W—one patient per appointment. The schedule of appointments, chronologically numbered 1 through 7, must meet the following conditions: Q's appointment is at some time before W's appointment. U's appointment is at some time before P's appointment. Either R or T has appointment 3. S's appointment is either the appointment immediately before or the appointment immediately after R's appointment.

Question: If P's appointment is immediately before S's appointment, then each of the following could be true EXCEPT:
Options:
R's appointment is immediately before W's appointment.
T's appointment is immediately before Q's appointment.
U's appointment is immediately before P's appointment.
U's appointment is immediately before Q's appointment.
W's appointment is immediately before T's appointment.
Correct option (0-indexed): 1
On Wednesday a physician will have exactly one appointment with seven patients—P, Q, R, S, T, U, W—one patient per appointment. The schedule of appointments, chronologically numbered 1 through 7, must meet the following conditions: Q's appointment is at some time before W's appointment. U's appointment is at some time before P's appointment. Either R or T has appointment 3. S's appointment is either the appointment immediately before or the appointment immediately after R's appointment.

Question: If T's appointment is immediately after P's appointment and immediately before W's appointment, then which one of the following must be true?
Options:
W's appointment is at some time before R's appointment.
U's appointment is at some time before R's appointment.
S's appointment is at some time before U's appointment.
R's appointment is at some time before P's appointment.
Q's appointment is at some time before S's appointment.
Correct option (0-indexed): 3
Exactly six employees—officers F, G, and H, and supervisors K, L, and M—must be assigned to exactly three committees—Policy, Quality, and Sales—with exactly three employees per committee. Committee assignments must conform to the following conditions: Each committee must have at least one officer assigned to it. Each employee must be assigned to at least one committee. All three officers must be assigned to the Policy Committee. G cannot be assigned to the same committee as L. K must be assigned to the Sales Committee.

Question: Which one of the following is a group of three employees who can be assigned together to the Sales Committee?
Options:
F, G, and H
F, G, and M
G, K, and L
H, K, and L
K, L, and M
Correct option (0-indexed): 3
Exactly six employees—officers F, G, and H, and supervisors K, L, and M—must be assigned to exactly three committees—Policy, Quality, and Sales—with exactly three employees per committee. Committee assignments must conform to the following conditions: Each committee must have at least one officer assigned to it. Each employee must be assigned to at least one committee. All three officers must be assigned to the Policy Committee. G cannot be assigned to the same committee as L. K must be assigned to the Sales Committee.

Question: If H is assigned to exactly one committee, and if no committee has both F and M assigned to it, then it must be true that
Options:
G and M are both assigned to the Quality Committee
K and L are both assigned to the Sales Committee
K is assigned to exactly two committees
L is assigned to exactly two committees
M is assigned to exactly two committees
Correct option (0-indexed): 2
Exactly six employees—officers F, G, and H, and supervisors K, L, and M—must be assigned to exactly three committees—Policy, Quality, and Sales—with exactly three employees per committee. Committee assignments must conform to the following conditions: Each committee must have at least one officer assigned to it. Each employee must be assigned to at least one committee. All three officers must be assigned to the Policy Committee. G cannot be assigned to the same committee as L. K must be assigned to the Sales Committee.

Question: Which one of the following CANNOT be true?
Options:
F is assigned to exactly one committee.
G is assigned to exactly three committees.
H is assigned to exactly three committees.
K is assigned to exactly one committee.
L is assigned to exactly two committees.
Correct option (0-indexed): 1
Exactly six employees—officers F, G, and H, and supervisors K, L, and M—must be assigned to exactly three committees—Policy, Quality, and Sales—with exactly three employees per committee. Committee assignments must conform to the following conditions: Each committee must have at least one officer assigned to it. Each employee must be assigned to at least one committee. All three officers must be assigned to the Policy Committee. G cannot be assigned to the same committee as L. K must be assigned to the Sales Committee.

Question: If F is assigned to exactly three committees, and G is assigned to exactly two committees, then which one of the following must be true?
Options:
G is assigned to the Quality Committee.
G is assigned to the Sales Committee.
K is assigned to the Quality Committee.
L is assigned to the Sales Committee.
M is assigned to the Quality Committee.
Correct option (0-indexed): 4
Exactly six employees—officers F, G, and H, and supervisors K, L, and M—must be assigned to exactly three committees—Policy, Quality, and Sales—with exactly three employees per committee. Committee assignments must conform to the following conditions: Each committee must have at least one officer assigned to it. Each employee must be assigned to at least one committee. All three officers must be assigned to the Policy Committee. G cannot be assigned to the same committee as L. K must be assigned to the Sales Committee.

Question: Which one of the following is a group of three employees who can be assigned together to the Quality Committee?
Options:
F, G, and H
F, G, and K
G, H, and K
G, K, and L
H, L, and M
Correct option (0-indexed): 4
Exactly six employees—officers F, G, and H, and supervisors K, L, and M—must be assigned to exactly three committees—Policy, Quality, and Sales—with exactly three employees per committee. Committee assignments must conform to the following conditions: Each committee must have at least one officer assigned to it. Each employee must be assigned to at least one committee. All three officers must be assigned to the Policy Committee. G cannot be assigned to the same committee as L. K must be assigned to the Sales Committee.

Question: If L is assigned to exactly two committees, which of the following must be true?
Options:
F is assigned to the Sales Committee.
G is assigned to the Sales Committee.
H is assigned to the Quality Committee.
K is assigned to the Quality Committee.
M is assigned to the Quality Committee.
Correct option (0-indexed): 4
Exactly six employees—officers F, G, and H, and supervisors K, L, and M—must be assigned to exactly three committees—Policy, Quality, and Sales—with exactly three employees per committee. Committee assignments must conform to the following conditions: Each committee must have at least one officer assigned to it. Each employee must be assigned to at least one committee. All three officers must be assigned to the Policy Committee. G cannot be assigned to the same committee as L. K must be assigned to the Sales Committee.

Question: Which one of the following CANNOT be true?
Options:
F and G are each assigned to exactly one committee.
F and H are each assigned to exactly one committee.
G and H are each assigned to exactly one committee.
F and M are both assigned to the Sales Committee.
G and K are both assigned to the Quality Committee.
Correct option (0-indexed): 1
On Tuesday Vladimir and Wendy each eat exactly four separate meals: breakfast, lunch, dinner, and a snack. The following is all that is known about what they eat during that day: At no meal does Vladimir eat the same kind of food as Wendy. Neither of them eats the same kind of food more than once during the day. For breakfast, each eats exactly one of the following: hot cakes, poached eggs, or omelet. For lunch, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For dinner, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For a snack, each eats exactly one of the following: fish or omelet. Wendy eats an omelet for lunch.

Question: Which one of the following statements must be true?
Options:
Vladimir eats fish for lunch.
Vladimir eats fish for dinner.
Vladimir eats fish for his snack.
Wendy eats fish for dinner.
Wendy eats fish for her snack.
Correct option (0-indexed): 4
On Tuesday Vladimir and Wendy each eat exactly four separate meals: breakfast, lunch, dinner, and a snack. The following is all that is known about what they eat during that day: At no meal does Vladimir eat the same kind of food as Wendy. Neither of them eats the same kind of food more than once during the day. For breakfast, each eats exactly one of the following: hot cakes, poached eggs, or omelet. For lunch, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For dinner, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For a snack, each eats exactly one of the following: fish or omelet. Wendy eats an omelet for lunch.

Question: Vladimir must eat which one of the following foods?
Options:
fish
hot cakes
macaroni
omelet
poached eggs
Correct option (0-indexed): 3
On Tuesday Vladimir and Wendy each eat exactly four separate meals: breakfast, lunch, dinner, and a snack. The following is all that is known about what they eat during that day: At no meal does Vladimir eat the same kind of food as Wendy. Neither of them eats the same kind of food more than once during the day. For breakfast, each eats exactly one of the following: hot cakes, poached eggs, or omelet. For lunch, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For dinner, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For a snack, each eats exactly one of the following: fish or omelet. Wendy eats an omelet for lunch.

Question: If both Vladimir and Wendy eat macaroni on Tuesday, then which one of the following statements could be true?
Options:
Vladimir eats fish for lunch.
Vladimir eats hot cakes for lunch.
Vladimir eats macaroni for dinner.
Wendy eats hot cakes for breakfast.
Wendy eats hot cakes for dinner.
Correct option (0-indexed): 3
On Tuesday Vladimir and Wendy each eat exactly four separate meals: breakfast, lunch, dinner, and a snack. The following is all that is known about what they eat during that day: At no meal does Vladimir eat the same kind of food as Wendy. Neither of them eats the same kind of food more than once during the day. For breakfast, each eats exactly one of the following: hot cakes, poached eggs, or omelet. For lunch, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For dinner, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For a snack, each eats exactly one of the following: fish or omelet. Wendy eats an omelet for lunch.

Question: If Wendy does not eat macaroni on Tuesday, then which one of the following statements could be true?
Options:
Vladimir eats poached eggs for breakfast.
Vladimir eats fish for lunch.
Vladimir eats hot cakes for lunch.
Wendy eats hot cakes for breakfast.
Wendy eats fish for dinner.
Correct option (0-indexed): 1
On Tuesday Vladimir and Wendy each eat exactly four separate meals: breakfast, lunch, dinner, and a snack. The following is all that is known about what they eat during that day: At no meal does Vladimir eat the same kind of food as Wendy. Neither of them eats the same kind of food more than once during the day. For breakfast, each eats exactly one of the following: hot cakes, poached eggs, or omelet. For lunch, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For dinner, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For a snack, each eats exactly one of the following: fish or omelet. Wendy eats an omelet for lunch.

Question: If Wendy eats poached eggs for breakfast, then which one of the following statements cannot be true?
Options:
Vladimir eats fish for lunch.
Vladimir eats hot cakes for lunch.
Vladimir eats macaroni for dinner.
Wendy eats hot cakes for dinner.
Wendy eats macaroni for dinner.
Correct option (0-indexed): 1
Eight people—Jack, Karen, Laura, Mark, Nick, Owen, Peggy, and Ruth—will be placed on two four-person teams—X and Y—for a relay race that is run in four successive legs: first, second, third, and fourth. The teams race concurrently. Each team member runs exactly one of the legs, one team member per leg, according to the following conditions: Jack is on the same team as Karen. Karen is not on the same team as Nick. Ruth runs an earlier leg of the race than Peggy runs, whether or not they are on the same team as each other. Mark and Nick are both on team Y. Neither Jack nor Mark runs third. Karen and Laura both run second. Owen runs fourth.

Question: Which one of the following must be true?
Options:
If Jack and Owen are assigned to the same team as each other, Jack runs first.
If Jack and Peggy are assigned to the same team as each other, Jack runs fourth.
If Jack and Ruth are assigned to the same team as each other, Ruth runs third.
If Mark and Owen are assigned to the same team as each other, Mark runs fourth.
If Mark and Ruth are assigned to the same team as each other, Ruth runs third.
Correct option (0-indexed): 0
Eight people—Jack, Karen, Laura, Mark, Nick, Owen, Peggy, and Ruth—will be placed on two four-person teams—X and Y—for a relay race that is run in four successive legs: first, second, third, and fourth. The teams race concurrently. Each team member runs exactly one of the legs, one team member per leg, according to the following conditions: Jack is on the same team as Karen. Karen is not on the same team as Nick. Ruth runs an earlier leg of the race than Peggy runs, whether or not they are on the same team as each other. Mark and Nick are both on team Y. Neither Jack nor Mark runs third. Karen and Laura both run second. Owen runs fourth.

Question: If Ruth is assigned to team X, which one of the following is a complete and accurate list of the legs that she could run?
Options:
first
second
first, second
first, third
second, third
Correct option (0-indexed): 3
Eight people—Jack, Karen, Laura, Mark, Nick, Owen, Peggy, and Ruth—will be placed on two four-person teams—X and Y—for a relay race that is run in four successive legs: first, second, third, and fourth. The teams race concurrently. Each team member runs exactly one of the legs, one team member per leg, according to the following conditions: Jack is on the same team as Karen. Karen is not on the same team as Nick. Ruth runs an earlier leg of the race than Peggy runs, whether or not they are on the same team as each other. Mark and Nick are both on team Y. Neither Jack nor Mark runs third. Karen and Laura both run second. Owen runs fourth.

Question: If Owen and Ruth are assigned to the same team as each other, which one of the following must be true?
Options:
Mark runs fourth.
Nick runs first.
Nick runs fourth.
Peggy runs first.
Peggy runs fourth.
Correct option (0-indexed): 4
Eight people—Jack, Karen, Laura, Mark, Nick, Owen, Peggy, and Ruth—will be placed on two four-person teams—X and Y—for a relay race that is run in four successive legs: first, second, third, and fourth. The teams race concurrently. Each team member runs exactly one of the legs, one team member per leg, according to the following conditions: Jack is on the same team as Karen. Karen is not on the same team as Nick. Ruth runs an earlier leg of the race than Peggy runs, whether or not they are on the same team as each other. Mark and Nick are both on team Y. Neither Jack nor Mark runs third. Karen and Laura both run second. Owen runs fourth.

Question: Any of the following can be true EXCEPT:
Options:
Jack runs first.
Mark runs fourth.
Nick runs first.
Nick and Peggy both run third.
Owen and Peggy both run fourth.
Correct option (0-indexed): 2
Eight people—Jack, Karen, Laura, Mark, Nick, Owen, Peggy, and Ruth—will be placed on two four-person teams—X and Y—for a relay race that is run in four successive legs: first, second, third, and fourth. The teams race concurrently. Each team member runs exactly one of the legs, one team member per leg, according to the following conditions: Jack is on the same team as Karen. Karen is not on the same team as Nick. Ruth runs an earlier leg of the race than Peggy runs, whether or not they are on the same team as each other. Mark and Nick are both on team Y. Neither Jack nor Mark runs third. Karen and Laura both run second. Owen runs fourth.

Question: If Ruth and Peggy are assigned to the same team as each other, which one of the following must be true?
Options:
Jack runs first.
Mark runs fourth.
Nick runs third.
Peggy runs third.
Ruth runs first.
Correct option (0-indexed): 2
Eight people—Jack, Karen, Laura, Mark, Nick, Owen, Peggy, and Ruth—will be placed on two four-person teams—X and Y—for a relay race that is run in four successive legs: first, second, third, and fourth. The teams race concurrently. Each team member runs exactly one of the legs, one team member per leg, according to the following conditions: Jack is on the same team as Karen. Karen is not on the same team as Nick. Ruth runs an earlier leg of the race than Peggy runs, whether or not they are on the same team as each other. Mark and Nick are both on team Y. Neither Jack nor Mark runs third. Karen and Laura both run second. Owen runs fourth.

Question: Any of the following can be true EXCEPT:
Options:
Jack runs fourth.
Nick runs fourth.
Peggy runs fourth.
Ruth runs first.
Ruth runs third.
Correct option (0-indexed): 1
Eight people—Jack, Karen, Laura, Mark, Nick, Owen, Peggy, and Ruth—will be placed on two four-person teams—X and Y—for a relay race that is run in four successive legs: first, second, third, and fourth. The teams race concurrently. Each team member runs exactly one of the legs, one team member per leg, according to the following conditions: Jack is on the same team as Karen. Karen is not on the same team as Nick. Ruth runs an earlier leg of the race than Peggy runs, whether or not they are on the same team as each other. Mark and Nick are both on team Y. Neither Jack nor Mark runs third. Karen and Laura both run second. Owen runs fourth.

Question: If Peggy runs third on the same team to which Jack is assigned, which one of the following must be true?
Options:
Jack runs the first leg on the team to which he is assigned.
Ruth runs the first leg on the team to which she is assigned.
Owen runs on the same team as Jack.
Owen runs on the same team as Mark.
Ruth runs on the same team as Mark.
Correct option (0-indexed): 1
A contractor is scheduling construction of seven decks—F, G, H, J, K, L, and M—during a seven-week period: week 1 through week 7. Because of customers' requirements, exactly one deck must be built each week according to the following conditions: G must be built at some time before K is built. L must be built either immediately before or immediately after M is built. F must be built during week 5. J must be built during week 2 or week 6.

Question: Which one of the following is an acceptable construction schedule for the decks, in order from the deck built in week 1 to that built in week 7?
Options:
G, K, H, M, F, J, L
H, G, L, M, F, K, J
H, J, G, F, M, L, K
H, M, L, G, F, J, K
K, J, H, G, F, M, L
Correct option (0-indexed): 3
A contractor is scheduling construction of seven decks—F, G, H, J, K, L, and M—during a seven-week period: week 1 through week 7. Because of customers' requirements, exactly one deck must be built each week according to the following conditions: G must be built at some time before K is built. L must be built either immediately before or immediately after M is built. F must be built during week 5. J must be built during week 2 or week 6.

Question: If G is built at some time after F is built, which one of the following must be true?
Options:
G is built during week 7.
H is built during week 1.
J is built during week 6.
L is built during week 3.
M is built during week 1.
Correct option (0-indexed): 1
A contractor is scheduling construction of seven decks—F, G, H, J, K, L, and M—during a seven-week period: week 1 through week 7. Because of customers' requirements, exactly one deck must be built each week according to the following conditions: G must be built at some time before K is built. L must be built either immediately before or immediately after M is built. F must be built during week 5. J must be built during week 2 or week 6.

Question: Which one of the following is a complete and accurate list of the weeks any one of which could be the week in which K is built?
Options:
2, 3, 6
2, 3, 7
2, 5, 6, 7
1, 2, 3, 6, 7
2, 3, 4, 6, 7
Correct option (0-indexed): 4
A contractor is scheduling construction of seven decks—F, G, H, J, K, L, and M—during a seven-week period: week 1 through week 7. Because of customers' requirements, exactly one deck must be built each week according to the following conditions: G must be built at some time before K is built. L must be built either immediately before or immediately after M is built. F must be built during week 5. J must be built during week 2 or week 6.

Question: Which one of the following is a complete and accurate list of decks any one of which could be the deck built in week 3?
Options:
K, L, M
F, G, H, K
F, H, K, M
G, H, K, L, M
H, J, K, L, M
Correct option (0-indexed): 3
A contractor is scheduling construction of seven decks—F, G, H, J, K, L, and M—during a seven-week period: week 1 through week 7. Because of customers' requirements, exactly one deck must be built each week according to the following conditions: G must be built at some time before K is built. L must be built either immediately before or immediately after M is built. F must be built during week 5. J must be built during week 2 or week 6.

Question: If G is built during week 4, then there are exactly how many acceptable orders any one of which could be the order in which the seven decks are built?
Options:
one
two
three
four
five
Correct option (0-indexed): 3
Each of five salespeople—F, G, H, I, and J—will present a different one of a company's products—L, M, N, O, and P—at a convention running from Monday through Wednesday. Exactly two products will be presented on Monday, exactly one on Tuesday, and exactly two on Wednesday. The scheduling of presentations is governed by the following conditions: F cannot present a product on the same day as H. Either I or else J must present product N on Tuesday. G must present a product on the day that product O is presented, whether or not G is the salesperson who presents product O.

Question: Which one of the following must be true?
Options:
If F presents a product on Monday, then G presents product O.
If I presents a product on Tuesday, then J presents a product on Monday.
If J presents a product on Tuesday, then G presents a product on Monday.
If both F and J present products on Monday, then H presents product O.
If both H and I present products on Wednesday, then product O is presented on Monday.
Correct option (0-indexed): 4
Each of five salespeople—F, G, H, I, and J—will present a different one of a company's products—L, M, N, O, and P—at a convention running from Monday through Wednesday. Exactly two products will be presented on Monday, exactly one on Tuesday, and exactly two on Wednesday. The scheduling of presentations is governed by the following conditions: F cannot present a product on the same day as H. Either I or else J must present product N on Tuesday. G must present a product on the day that product O is presented, whether or not G is the salesperson who presents product O.

Question: If salespeople H and I present products on Monday, which one of the following must be true?
Options:
F presents product M.
G presents product L.
I presents product N.
Product O is presented on Wednesday.
Product P is presented on Wednesday.
Correct option (0-indexed): 3
Each of five salespeople—F, G, H, I, and J—will present a different one of a company's products—L, M, N, O, and P—at a convention running from Monday through Wednesday. Exactly two products will be presented on Monday, exactly one on Tuesday, and exactly two on Wednesday. The scheduling of presentations is governed by the following conditions: F cannot present a product on the same day as H. Either I or else J must present product N on Tuesday. G must present a product on the day that product O is presented, whether or not G is the salesperson who presents product O.

Question: If G presents product P on Wednesday, then any of the following could be true EXCEPT:
Options:
H presents product O.
I presents product N.
I presents product O.
F makes a presentation on Monday.
F makes a presentation on Wednesday.
Correct option (0-indexed): 2
Each of five salespeople—F, G, H, I, and J—will present a different one of a company's products—L, M, N, O, and P—at a convention running from Monday through Wednesday. Exactly two products will be presented on Monday, exactly one on Tuesday, and exactly two on Wednesday. The scheduling of presentations is governed by the following conditions: F cannot present a product on the same day as H. Either I or else J must present product N on Tuesday. G must present a product on the day that product O is presented, whether or not G is the salesperson who presents product O.

Question: If products M and P are presented on Monday, which one of the following could be true?
Options:
G presents product P.
I presents product O.
J presents product L.
F presents a product on Monday.
G presents a product on Monday.
Correct option (0-indexed): 3
Each of five salespeople—F, G, H, I, and J—will present a different one of a company's products—L, M, N, O, and P—at a convention running from Monday through Wednesday. Exactly two products will be presented on Monday, exactly one on Tuesday, and exactly two on Wednesday. The scheduling of presentations is governed by the following conditions: F cannot present a product on the same day as H. Either I or else J must present product N on Tuesday. G must present a product on the day that product O is presented, whether or not G is the salesperson who presents product O.

Question: If product O is presented on the same day as product P, which one of the following must be true?
Options:
F presents product O or else product P.
F presents neither product O nor product P.
H presents product O or else product P.
I presents product O or else product P.
J presents neither product O nor product P.
Correct option (0-indexed): 4
The seven members of an academic department are each to be assigned a different room as an office. The department members are professors F and G, lecturers Q, R, and S, and instructors V and W. The available rooms are seven consecutive rooms along one side of a straight hallway numbered sequentially 101 through 107. The assignment must conform to the following conditions: Neither instructor is assigned a room next to a professor's room. Neither professor is assigned room 101 and neither professor is assigned room 107. G is not assigned a room next to R's room. W is not assigned a room next to V's room unless R is also assigned a room next to V's room.

Question: If F and G are assigned rooms that have exactly one room between them, which one of the following is the list of department members each of whom could be assigned to the intervening room?
Options:
Q, R
Q, S
Q, V
R, W
S, V
Correct option (0-indexed): 1
The seven members of an academic department are each to be assigned a different room as an office. The department members are professors F and G, lecturers Q, R, and S, and instructors V and W. The available rooms are seven consecutive rooms along one side of a straight hallway numbered sequentially 101 through 107. The assignment must conform to the following conditions: Neither instructor is assigned a room next to a professor's room. Neither professor is assigned room 101 and neither professor is assigned room 107. G is not assigned a room next to R's room. W is not assigned a room next to V's room unless R is also assigned a room next to V's room.

Question: Which one of the following is a possible assignment of rooms for members R, V, and W?
Options:
101: V; 102: W; 103: R
101: V; 102: W, 104: R
101: V; 103: W; 104: R
103: W; 104: V; 106: R
105: R; 106: W; 107: V
Correct option (0-indexed): 2
The seven members of an academic department are each to be assigned a different room as an office. The department members are professors F and G, lecturers Q, R, and S, and instructors V and W. The available rooms are seven consecutive rooms along one side of a straight hallway numbered sequentially 101 through 107. The assignment must conform to the following conditions: Neither instructor is assigned a room next to a professor's room. Neither professor is assigned room 101 and neither professor is assigned room 107. G is not assigned a room next to R's room. W is not assigned a room next to V's room unless R is also assigned a room next to V's room.

Question: If R is assigned room 104, which one of the following must be assigned either room 103 or else room 105?
Options:
F
G
Q
V
W
Correct option (0-indexed): 0
The seven members of an academic department are each to be assigned a different room as an office. The department members are professors F and G, lecturers Q, R, and S, and instructors V and W. The available rooms are seven consecutive rooms along one side of a straight hallway numbered sequentially 101 through 107. The assignment must conform to the following conditions: Neither instructor is assigned a room next to a professor's room. Neither professor is assigned room 101 and neither professor is assigned room 107. G is not assigned a room next to R's room. W is not assigned a room next to V's room unless R is also assigned a room next to V's room.

Question: What is the greatest number of rooms that could be between the rooms to which F and G are assigned?
Options:
one
two
three
four
five
Correct option (0-indexed): 0