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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.

If no house faces a house of the same style, then it must be true that house

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.

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:

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.

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?

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.

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:

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.

Which one of the following could be true after exactly two rounds of matches have been played?

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.

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?

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.

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?

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.

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?

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.

Which one of the following is an acceptable schedule of appointments in order from 1 to 7?

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.

If W has appointment 2 and P has appointment 5, then which one of the following must be true?

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.

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?

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.

If P's appointment is immediately before S's appointment, then each of the following could be true EXCEPT:

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.

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?

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.

Which one of the following is a group of three employees who can be assigned together to the Sales Committee?

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.

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

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.

Which one of the following CANNOT be true?

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.

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?

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.

Which one of the following is a group of three employees who can be assigned together to the Quality Committee?

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.

If L is assigned to exactly two committees, which of the following must be true?

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.

Which one of the following CANNOT be true?

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.

Which one of the following statements must be true?

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.

Vladimir must eat which one of the following foods?

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.

If both Vladimir and Wendy eat macaroni on Tuesday, then which one of the following statements could be true?

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.

If Wendy does not eat macaroni on Tuesday, then which one of the following statements could be true?

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.

If Wendy eats poached eggs for breakfast, then which one of the following statements cannot be true?

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.

Which one of the following must be true?

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.

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?

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.

If Owen and Ruth are assigned to the same team as each other, which one of the following must be true?

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.

Any of the following can be true EXCEPT:

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.

If Ruth and Peggy are assigned to the same team as each other, which one of the following must be true?

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.

Any of the following can be true EXCEPT:

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.

If Peggy runs third on the same team to which Jack is assigned, which one of the following must be true?

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.

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?

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.

If G is built at some time after F is built, which one of the following must be true?

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.

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?

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.

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?

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.

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?

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.

Which one of the following must be true?

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.

If salespeople H and I present products on Monday, which one of the following must be true?

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.

If G presents product P on Wednesday, then any of the following could be true EXCEPT:

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.

If products M and P are presented on Monday, which one of the following could be true?

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.

If product O is presented on the same day as product P, which one of the following must be true?

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.

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?

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.

Which one of the following is a possible assignment of rooms for members R, V, and W?

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.

If R is assigned room 104, which one of the following must be assigned either room 103 or else room 105?

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.

What is the greatest number of rooms that could be between the rooms to which F and G are assigned?

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.

Which one of the following CANNOT be assigned room 104?

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.

If no two faculty members of the same rank are assigned adjacent rooms, which one of the following must be true?

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.

If F and G are not assigned rooms that are next to each other, which one of the following CANNOT be assigned room 107?

The coordinator of an exhibition will select at least four and at most six rugs from a group of eight rugs made up of two oval wool rugs, three rectangular wool rugs, one oval silk rug, and two rectangular silk rugs according to the following conditions: At least two oval rugs must be selected. The number of wool rugs selected can be neither less than two nor more than three. If the oval silk rug is selected, at least one rectangular silk rug must be selected.

Which one of the following is an acceptable selection of rugs for the exhibition?

The coordinator of an exhibition will select at least four and at most six rugs from a group of eight rugs made up of two oval wool rugs, three rectangular wool rugs, one oval silk rug, and two rectangular silk rugs according to the following conditions: At least two oval rugs must be selected. The number of wool rugs selected can be neither less than two nor more than three. If the oval silk rug is selected, at least one rectangular silk rug must be selected.

If three wool rugs are selected, then any of the following could be a complete and accurate list of the other rugs selected EXCEPT:

The coordinator of an exhibition will select at least four and at most six rugs from a group of eight rugs made up of two oval wool rugs, three rectangular wool rugs, one oval silk rug, and two rectangular silk rugs according to the following conditions: At least two oval rugs must be selected. The number of wool rugs selected can be neither less than two nor more than three. If the oval silk rug is selected, at least one rectangular silk rug must be selected.

The rugs selected for the exhibition can include any of the following EXCEPT:

The coordinator of an exhibition will select at least four and at most six rugs from a group of eight rugs made up of two oval wool rugs, three rectangular wool rugs, one oval silk rug, and two rectangular silk rugs according to the following conditions: At least two oval rugs must be selected. The number of wool rugs selected can be neither less than two nor more than three. If the oval silk rug is selected, at least one rectangular silk rug must be selected.

If only one silk rug is selected for the exhibition, then the other rugs selected must be a group made up of

The coordinator of an exhibition will select at least four and at most six rugs from a group of eight rugs made up of two oval wool rugs, three rectangular wool rugs, one oval silk rug, and two rectangular silk rugs according to the following conditions: At least two oval rugs must be selected. The number of wool rugs selected can be neither less than two nor more than three. If the oval silk rug is selected, at least one rectangular silk rug must be selected.

If exactly four rugs are selected, then the rugs selected could be

The coordinator of an exhibition will select at least four and at most six rugs from a group of eight rugs made up of two oval wool rugs, three rectangular wool rugs, one oval silk rug, and two rectangular silk rugs according to the following conditions: At least two oval rugs must be selected. The number of wool rugs selected can be neither less than two nor more than three. If the oval silk rug is selected, at least one rectangular silk rug must be selected.

If all three silk rugs are selected, then each of the following could be a complete and accurate list of the other rugs selected EXCEPT:

The coordinator of an exhibition will select at least four and at most six rugs from a group of eight rugs made up of two oval wool rugs, three rectangular wool rugs, one oval silk rug, and two rectangular silk rugs according to the following conditions: At least two oval rugs must be selected. The number of wool rugs selected can be neither less than two nor more than three. If the oval silk rug is selected, at least one rectangular silk rug must be selected.

If exactly six rugs are selected, they must include

During a period of six consecutive days—day 1 through day 6—each of exactly six factories—F, G, H, J, Q, and R—will be inspected. During this period, each of the factories will be inspected exactly once, one factory per day. The schedule for the inspections must conform to the following conditions: F is inspected on either day 1 or day 6. J is inspected on an earlier day than Q is inspected. Q is inspected on the day immediately before R is inspected. If G is inspected on day 3, Q is inspected on day 5.

Which one of the following could be a list of the factories in the order of their scheduled inspections, from day 1 thought day 6?

During a period of six consecutive days—day 1 through day 6—each of exactly six factories—F, G, H, J, Q, and R—will be inspected. During this period, each of the factories will be inspected exactly once, one factory per day. The schedule for the inspections must conform to the following conditions: F is inspected on either day 1 or day 6. J is inspected on an earlier day than Q is inspected. Q is inspected on the day immediately before R is inspected. If G is inspected on day 3, Q is inspected on day 5.

Which one of the following must be false?

During a period of six consecutive days—day 1 through day 6—each of exactly six factories—F, G, H, J, Q, and R—will be inspected. During this period, each of the factories will be inspected exactly once, one factory per day. The schedule for the inspections must conform to the following conditions: F is inspected on either day 1 or day 6. J is inspected on an earlier day than Q is inspected. Q is inspected on the day immediately before R is inspected. If G is inspected on day 3, Q is inspected on day 5.

The inspection of which one of the following CANNOT be scheduled for day 5 ?

During a period of six consecutive days—day 1 through day 6—each of exactly six factories—F, G, H, J, Q, and R—will be inspected. During this period, each of the factories will be inspected exactly once, one factory per day. The schedule for the inspections must conform to the following conditions: F is inspected on either day 1 or day 6. J is inspected on an earlier day than Q is inspected. Q is inspected on the day immediately before R is inspected. If G is inspected on day 3, Q is inspected on day 5.

The inspection scheduled for day 3 and day 5, respectively, could be those of

During a period of six consecutive days—day 1 through day 6—each of exactly six factories—F, G, H, J, Q, and R—will be inspected. During this period, each of the factories will be inspected exactly once, one factory per day. The schedule for the inspections must conform to the following conditions: F is inspected on either day 1 or day 6. J is inspected on an earlier day than Q is inspected. Q is inspected on the day immediately before R is inspected. If G is inspected on day 3, Q is inspected on day 5.

If the inspection of R is scheduled for the day immediately before the inspection of F, which one of the following must be true about the schedule?

During a period of six consecutive days—day 1 through day 6—each of exactly six factories—F, G, H, J, Q, and R—will be inspected. During this period, each of the factories will be inspected exactly once, one factory per day. The schedule for the inspections must conform to the following conditions: F is inspected on either day 1 or day 6. J is inspected on an earlier day than Q is inspected. Q is inspected on the day immediately before R is inspected. If G is inspected on day 3, Q is inspected on day 5.

If the inspection of G and of H are scheduled, not necessarily in that order, for days as far apart as possible, which one of the following is a complete and accurate list of the factories any one of which could be scheduled for inspection for day 1?

During a period of six consecutive days—day 1 through day 6—each of exactly six factories—F, G, H, J, Q, and R—will be inspected. During this period, each of the factories will be inspected exactly once, one factory per day. The schedule for the inspections must conform to the following conditions: F is inspected on either day 1 or day 6. J is inspected on an earlier day than Q is inspected. Q is inspected on the day immediately before R is inspected. If G is inspected on day 3, Q is inspected on day 5.

If the inspection of G is scheduled for the day immediately before the inspection of Q, which one of the following could be true?

In a theater company, four two-day workshops—Lighting, Production, Rehearsals, and Staging—are conducted over the course of five days, Monday through Friday. The workshops are conducted in a manner consistent with the following constraints: The two days on which a given workshop is in session are consecutive. On each of the five days, at least one, but no more than two, of the workshops are in session. The workshops on Production and Rehearsals begin no earlier than the day immediately following the second day of the workshop on Lighting.

Which one of the following could be true?

In a theater company, four two-day workshops—Lighting, Production, Rehearsals, and Staging—are conducted over the course of five days, Monday through Friday. The workshops are conducted in a manner consistent with the following constraints: The two days on which a given workshop is in session are consecutive. On each of the five days, at least one, but no more than two, of the workshops are in session. The workshops on Production and Rehearsals begin no earlier than the day immediately following the second day of the workshop on Lighting.

Which one of the following could be true?

In a theater company, four two-day workshops—Lighting, Production, Rehearsals, and Staging—are conducted over the course of five days, Monday through Friday. The workshops are conducted in a manner consistent with the following constraints: The two days on which a given workshop is in session are consecutive. On each of the five days, at least one, but no more than two, of the workshops are in session. The workshops on Production and Rehearsals begin no earlier than the day immediately following the second day of the workshop on Lighting.

If the workshop on Production is in session on Wednesday, which one of the following must be true?

In a theater company, four two-day workshops—Lighting, Production, Rehearsals, and Staging—are conducted over the course of five days, Monday through Friday. The workshops are conducted in a manner consistent with the following constraints: The two days on which a given workshop is in session are consecutive. On each of the five days, at least one, but no more than two, of the workshops are in session. The workshops on Production and Rehearsals begin no earlier than the day immediately following the second day of the workshop on Lighting.

If the workshop on production is the only workshop in session on Friday, which one of the following must be false?

In a theater company, four two-day workshops—Lighting, Production, Rehearsals, and Staging—are conducted over the course of five days, Monday through Friday. The workshops are conducted in a manner consistent with the following constraints: The two days on which a given workshop is in session are consecutive. On each of the five days, at least one, but no more than two, of the workshops are in session. The workshops on Production and Rehearsals begin no earlier than the day immediately following the second day of the workshop on Lighting.

If the workshop on Lighting is the only workshop in session on Monday, which one of the following could be true?

Each of two boats, boat 1 and boat 2, will be assigned exactly four people. Exactly eight people, three adults—F, G, and H—and five children—V, W, X, Y, and Z—must be assigned to the boats according to the following conditions: Each boat is assigned at least one adult. If F is assigned to boat 2, G is assigned to boat 2. If V is assigned to boat 1, W is assigned to boat 2. X and Z are assigned to different boats.

Which one of the following is an acceptable assignment of people to boat I ?

Each of two boats, boat 1 and boat 2, will be assigned exactly four people. Exactly eight people, three adults—F, G, and H—and five children—V, W, X, Y, and Z—must be assigned to the boats according to the following conditions: Each boat is assigned at least one adult. If F is assigned to boat 2, G is assigned to boat 2. If V is assigned to boat 1, W is assigned to boat 2. X and Z are assigned to different boats.

If F is assigned to boat 2, which one of the following is a pair of people who could be assigned to the same boat as each other?

Each of two boats, boat 1 and boat 2, will be assigned exactly four people. Exactly eight people, three adults—F, G, and H—and five children—V, W, X, Y, and Z—must be assigned to the boats according to the following conditions: Each boat is assigned at least one adult. If F is assigned to boat 2, G is assigned to boat 2. If V is assigned to boat 1, W is assigned to boat 2. X and Z are assigned to different boats.

If exactly three children are assigned to boat 1, which one of the following is a pair of people who could both be assigned to boat 2?

Each of two boats, boat 1 and boat 2, will be assigned exactly four people. Exactly eight people, three adults—F, G, and H—and five children—V, W, X, Y, and Z—must be assigned to the boats according to the following conditions: Each boat is assigned at least one adult. If F is assigned to boat 2, G is assigned to boat 2. If V is assigned to boat 1, W is assigned to boat 2. X and Z are assigned to different boats.

If G is assigned to boat 1, which one of the following must be true?

Each of two boats, boat 1 and boat 2, will be assigned exactly four people. Exactly eight people, three adults—F, G, and H—and five children—V, W, X, Y, and Z—must be assigned to the boats according to the following conditions: Each boat is assigned at least one adult. If F is assigned to boat 2, G is assigned to boat 2. If V is assigned to boat 1, W is assigned to boat 2. X and Z are assigned to different boats.

If V and W are assigned to the same boat as each other, which one of the following is a pair of people who must also be assigned to the same boat as each other?

Each of two boats, boat 1 and boat 2, will be assigned exactly four people. Exactly eight people, three adults—F, G, and H—and five children—V, W, X, Y, and Z—must be assigned to the boats according to the following conditions: Each boat is assigned at least one adult. If F is assigned to boat 2, G is assigned to boat 2. If V is assigned to boat 1, W is assigned to boat 2. X and Z are assigned to different boats.

If H is assigned to a different boat than Y, which one of the following must be assigned to boat 1?

Each of two boats, boat 1 and boat 2, will be assigned exactly four people. Exactly eight people, three adults—F, G, and H—and five children—V, W, X, Y, and Z—must be assigned to the boats according to the following conditions: Each boat is assigned at least one adult. If F is assigned to boat 2, G is assigned to boat 2. If V is assigned to boat 1, W is assigned to boat 2. X and Z are assigned to different boats.

If exactly one adult is assigned to boat 1, which one of the following must be true?

Each of nine students—Faith, Gregory, Harlan, Jennifer, Kenji, Lisa, Marcus, Nari, and Paul—will be assigned to exactly one of three panels: Oceans, Recycling, and Wetlands. Exactly three of the students will be assigned to each panel. The assignment of students to panels must meet the following conditions: Faith is assigned to the same panel as Gregory. Kenji is assigned to the same panel as Marcus. Faith is not assigned to the same panel as Paul. Gregory is not assigned to the same panel as Harlan. Jennifer is not assigned to the same panel as Kenji. Harlan is not assigned to the Oceans panel if Paul is not assigned to the Oceans panel.

Which one of the following is an acceptable assignment of students to the panels?

Each of nine students—Faith, Gregory, Harlan, Jennifer, Kenji, Lisa, Marcus, Nari, and Paul—will be assigned to exactly one of three panels: Oceans, Recycling, and Wetlands. Exactly three of the students will be assigned to each panel. The assignment of students to panels must meet the following conditions: Faith is assigned to the same panel as Gregory. Kenji is assigned to the same panel as Marcus. Faith is not assigned to the same panel as Paul. Gregory is not assigned to the same panel as Harlan. Jennifer is not assigned to the same panel as Kenji. Harlan is not assigned to the Oceans panel if Paul is not assigned to the Oceans panel.

If Marcus and Paul are both assigned to the Wetlands panel, which one of the following must be true?

Each of nine students—Faith, Gregory, Harlan, Jennifer, Kenji, Lisa, Marcus, Nari, and Paul—will be assigned to exactly one of three panels: Oceans, Recycling, and Wetlands. Exactly three of the students will be assigned to each panel. The assignment of students to panels must meet the following conditions: Faith is assigned to the same panel as Gregory. Kenji is assigned to the same panel as Marcus. Faith is not assigned to the same panel as Paul. Gregory is not assigned to the same panel as Harlan. Jennifer is not assigned to the same panel as Kenji. Harlan is not assigned to the Oceans panel if Paul is not assigned to the Oceans panel.

Which one of the following is a pair of students who could be assigned to the same panel as each other?

Each of nine students—Faith, Gregory, Harlan, Jennifer, Kenji, Lisa, Marcus, Nari, and Paul—will be assigned to exactly one of three panels: Oceans, Recycling, and Wetlands. Exactly three of the students will be assigned to each panel. The assignment of students to panels must meet the following conditions: Faith is assigned to the same panel as Gregory. Kenji is assigned to the same panel as Marcus. Faith is not assigned to the same panel as Paul. Gregory is not assigned to the same panel as Harlan. Jennifer is not assigned to the same panel as Kenji. Harlan is not assigned to the Oceans panel if Paul is not assigned to the Oceans panel.

If Kenji and Paul are both assigned to the Recycling panel, which one of the following could be true?

Each of nine students—Faith, Gregory, Harlan, Jennifer, Kenji, Lisa, Marcus, Nari, and Paul—will be assigned to exactly one of three panels: Oceans, Recycling, and Wetlands. Exactly three of the students will be assigned to each panel. The assignment of students to panels must meet the following conditions: Faith is assigned to the same panel as Gregory. Kenji is assigned to the same panel as Marcus. Faith is not assigned to the same panel as Paul. Gregory is not assigned to the same panel as Harlan. Jennifer is not assigned to the same panel as Kenji. Harlan is not assigned to the Oceans panel if Paul is not assigned to the Oceans panel.

Each of the following is a pair of students who could be assigned to the same panel as each other EXCEPT:

Each of seven travelers—Norris, Oribe, Paulsen, Rosen, Semonelli, Tan, and Underwood—will be assigned to exactly one of nine airplane seats. The seats are numbered from 1 through 9 and arranged in rows as follows: Front row: 1 2 3 Middle row: 4 5 6 Last row: 7 8 9 Only seats in the same row as each other are immediately beside each other. Seat assignments must meet the following conditions: Oribe's seat is in the last row. Paulsen's seat is immediately beside Rosen's seat and also immediately beside an unassigned seat. Rosen's seat is in the row immediately behind the row in which Norris' seat is located. Neither Semonelli nor Underwood is seated immediately beside Norris.

Which one of the following is a pair of travelers who could be assigned to seats 2 and 8, respectively?

Each of seven travelers—Norris, Oribe, Paulsen, Rosen, Semonelli, Tan, and Underwood—will be assigned to exactly one of nine airplane seats. The seats are numbered from 1 through 9 and arranged in rows as follows: Front row: 1 2 3 Middle row: 4 5 6 Last row: 7 8 9 Only seats in the same row as each other are immediately beside each other. Seat assignments must meet the following conditions: Oribe's seat is in the last row. Paulsen's seat is immediately beside Rosen's seat and also immediately beside an unassigned seat. Rosen's seat is in the row immediately behind the row in which Norris' seat is located. Neither Semonelli nor Underwood is seated immediately beside Norris.

If Semonelli and Underwood are not assigned to seats in the same row as each other, which one of the following must be false?

Each of seven travelers—Norris, Oribe, Paulsen, Rosen, Semonelli, Tan, and Underwood—will be assigned to exactly one of nine airplane seats. The seats are numbered from 1 through 9 and arranged in rows as follows: Front row: 1 2 3 Middle row: 4 5 6 Last row: 7 8 9 Only seats in the same row as each other are immediately beside each other. Seat assignments must meet the following conditions: Oribe's seat is in the last row. Paulsen's seat is immediately beside Rosen's seat and also immediately beside an unassigned seat. Rosen's seat is in the row immediately behind the row in which Norris' seat is located. Neither Semonelli nor Underwood is seated immediately beside Norris.

If Semonelli is assigned to a seat in the same row as Underwood, which one of the following travelers could be assigned to a seat immediately beside one of the unassigned seats?

Each of seven travelers—Norris, Oribe, Paulsen, Rosen, Semonelli, Tan, and Underwood—will be assigned to exactly one of nine airplane seats. The seats are numbered from 1 through 9 and arranged in rows as follows: Front row: 1 2 3 Middle row: 4 5 6 Last row: 7 8 9 Only seats in the same row as each other are immediately beside each other. Seat assignments must meet the following conditions: Oribe's seat is in the last row. Paulsen's seat is immediately beside Rosen's seat and also immediately beside an unassigned seat. Rosen's seat is in the row immediately behind the row in which Norris' seat is located. Neither Semonelli nor Underwood is seated immediately beside Norris.

If the seat to which Tan is assigned is immediately beside a seat assigned to another traveler and also immediately beside one of the unassigned seats, which one of the following must be true?

Each of seven travelers—Norris, Oribe, Paulsen, Rosen, Semonelli, Tan, and Underwood—will be assigned to exactly one of nine airplane seats. The seats are numbered from 1 through 9 and arranged in rows as follows: Front row: 1 2 3 Middle row: 4 5 6 Last row: 7 8 9 Only seats in the same row as each other are immediately beside each other. Seat assignments must meet the following conditions: Oribe's seat is in the last row. Paulsen's seat is immediately beside Rosen's seat and also immediately beside an unassigned seat. Rosen's seat is in the row immediately behind the row in which Norris' seat is located. Neither Semonelli nor Underwood is seated immediately beside Norris.

If Oribe is assigned to a seat immediately beside one of the unassigned seats, which one of the following must be true?

A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions: If both G and S are reduced, W is also reduced. If N is reduced, neither R nor S is reduced. If P is reduced, L is not reduced. Of the three areas L, M, and R, exactly two are reduced.

Which one of the following could be a complete and accurate list of the areas of expenditure reduced by the committee?

A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions: If both G and S are reduced, W is also reduced. If N is reduced, neither R nor S is reduced. If P is reduced, L is not reduced. Of the three areas L, M, and R, exactly two are reduced.

If W is reduced, which one of the following could be a complete and accurate list of the four other areas of expenditure to be reduced?

A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions: If both G and S are reduced, W is also reduced. If N is reduced, neither R nor S is reduced. If P is reduced, L is not reduced. Of the three areas L, M, and R, exactly two are reduced.

If P is reduced, which one of the following is a pair of areas of expenditure both of which must be reduced?

A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions: If both G and S are reduced, W is also reduced. If N is reduced, neither R nor S is reduced. If P is reduced, L is not reduced. Of the three areas L, M, and R, exactly two are reduced.

If both L and S are reduced, which one of the following could be a pair of areas of expenditure both of which are reduced?

A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions: If both G and S are reduced, W is also reduced. If N is reduced, neither R nor S is reduced. If P is reduced, L is not reduced. Of the three areas L, M, and R, exactly two are reduced.

If R is not reduced, which one of the following must be true?

A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions: If both G and S are reduced, W is also reduced. If N is reduced, neither R nor S is reduced. If P is reduced, L is not reduced. Of the three areas L, M, and R, exactly two are reduced.

If both M and R are reduced, which one of the following is a pair of areas neither of which could be reduced?

A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions: If both G and S are reduced, W is also reduced. If N is reduced, neither R nor S is reduced. If P is reduced, L is not reduced. Of the three areas L, M, and R, exactly two are reduced.

Which one of the following areas must be reduced?

A jeweler makes a single strand of beads by threading onto a string in a single direction from a clasp a series of solid-colored beads. Each bead is either green, orange, purple, red, or yellow. The resulting strand satisfies the following specifications: If a purple bead is adjacent to a yellow bead, any bead that immediately follows and any bead that immediately precedes that pair must be red. Any pair of beads adjacent to each other that are the same color as each other must be green. No orange bead can be adjacent to any red bead. Any portion of the strand containing eight consecutive beads must include at least one bead of each color.

If the strand has exactly eight beads, which one of the following is an acceptable order, starting from the clasp, for the eight beads?

A jeweler makes a single strand of beads by threading onto a string in a single direction from a clasp a series of solid-colored beads. Each bead is either green, orange, purple, red, or yellow. The resulting strand satisfies the following specifications: If a purple bead is adjacent to a yellow bead, any bead that immediately follows and any bead that immediately precedes that pair must be red. Any pair of beads adjacent to each other that are the same color as each other must be green. No orange bead can be adjacent to any red bead. Any portion of the strand containing eight consecutive beads must include at least one bead of each color.

If an orange bead is the fourth bead from the clasp, which one of the following is a pair that could be the second and third beads, respectively?

A jeweler makes a single strand of beads by threading onto a string in a single direction from a clasp a series of solid-colored beads. Each bead is either green, orange, purple, red, or yellow. The resulting strand satisfies the following specifications: If a purple bead is adjacent to a yellow bead, any bead that immediately follows and any bead that immediately precedes that pair must be red. Any pair of beads adjacent to each other that are the same color as each other must be green. No orange bead can be adjacent to any red bead. Any portion of the strand containing eight consecutive beads must include at least one bead of each color.

If on an eight-bead strand the second, third, and fourth beads from the clasp are red, green, and yellow, respectively, and the sixth and seventh beads are purple and red, respectively, then which one of the following must be true?

A jeweler makes a single strand of beads by threading onto a string in a single direction from a clasp a series of solid-colored beads. Each bead is either green, orange, purple, red, or yellow. The resulting strand satisfies the following specifications: If a purple bead is adjacent to a yellow bead, any bead that immediately follows and any bead that immediately precedes that pair must be red. Any pair of beads adjacent to each other that are the same color as each other must be green. No orange bead can be adjacent to any red bead. Any portion of the strand containing eight consecutive beads must include at least one bead of each color.

If on a six-bead strand the first and second beads from the clasp are purple and yellow, respectively, then the fifth and sixth beads CANNOT be

A jeweler makes a single strand of beads by threading onto a string in a single direction from a clasp a series of solid-colored beads. Each bead is either green, orange, purple, red, or yellow. The resulting strand satisfies the following specifications: If a purple bead is adjacent to a yellow bead, any bead that immediately follows and any bead that immediately precedes that pair must be red. Any pair of beads adjacent to each other that are the same color as each other must be green. No orange bead can be adjacent to any red bead. Any portion of the strand containing eight consecutive beads must include at least one bead of each color.

If on a nine-bead strand the first and fourth beads from the clasp are purple, and the second and fifth beads are yellow, which one of the following could be true?

A jeweler makes a single strand of beads by threading onto a string in a single direction from a clasp a series of solid-colored beads. Each bead is either green, orange, purple, red, or yellow. The resulting strand satisfies the following specifications: If a purple bead is adjacent to a yellow bead, any bead that immediately follows and any bead that immediately precedes that pair must be red. Any pair of beads adjacent to each other that are the same color as each other must be green. No orange bead can be adjacent to any red bead. Any portion of the strand containing eight consecutive beads must include at least one bead of each color.

If on an eight-bead strand the first, second, third, and fourth beads from the clasp are red, yellow, green, and red, respectively, then the fifth and sixth beads CANNOT be

At an evening concert, a total of six songs—O, P, T, X, Y, and Z—will be performed by three vocalists—George, Helen, and Leslie. The songs will be sung consecutively as solos, and each will be performed exactly once. The following constraints govern the composition of the concert program: Y must be performed earlier than T and earlier than O. P must be performed earlier than Z and later than O. George can perform only X, Y, and Z. Helen can perform only T, P, and X. Leslie can perform only O, P, and X. The vocalist who performs first must be different from the vocalist who performs last.

Which one of the following is an acceptable schedule for the performance of the songs, in order from the first to last song performed?

At an evening concert, a total of six songs—O, P, T, X, Y, and Z—will be performed by three vocalists—George, Helen, and Leslie. The songs will be sung consecutively as solos, and each will be performed exactly once. The following constraints govern the composition of the concert program: Y must be performed earlier than T and earlier than O. P must be performed earlier than Z and later than O. George can perform only X, Y, and Z. Helen can perform only T, P, and X. Leslie can perform only O, P, and X. The vocalist who performs first must be different from the vocalist who performs last.

Which one of the following must be true about the program?