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A company employee generates a series of five-digit product codes in accordance with the following rules: The codes use the digits 0, 1, 2, 3, and 4, and no others. Each digit occurs exactly once in any code. The second digit has a value exactly twice that of the first digit. The value of the third digit is less than the value of the fifth digit.

If the third digit of an acceptable product code is not 0, which one of the following must be true?

A company employee generates a series of five-digit product codes in accordance with the following rules: The codes use the digits 0, 1, 2, 3, and 4, and no others. Each digit occurs exactly once in any code. The second digit has a value exactly twice that of the first digit. The value of the third digit is less than the value of the fifth digit.

Any of the following pairs could be the third and fourth digits, respectively, of an acceptable product code, EXCEPT:

A company employee generates a series of five-digit product codes in accordance with the following rules: The codes use the digits 0, 1, 2, 3, and 4, and no others. Each digit occurs exactly once in any code. The second digit has a value exactly twice that of the first digit. The value of the third digit is less than the value of the fifth digit.

Which one of the following must be true about any acceptable product code?

Exactly three films—Greed, Harvest, and Limelight—are shown during a film club's festival held on Thursday, Friday, and Saturday. Each film is shown at least once during the festival but never more than once on a given day. On each day at least one film is shown. Films are shown one at a time. The following conditions apply: On Thursday Harvest is shown, and no film is shown after it on that day. On Friday either Greed or Limelight, but not both, is shown, and no film is shown after it on that day. On Saturday either Greed or Harvest, but not both, is shown, and no film is shown after it on that day.

Which one of the following could be a complete and accurate description of the order in which the films are shown at the festival?

Exactly three films—Greed, Harvest, and Limelight—are shown during a film club's festival held on Thursday, Friday, and Saturday. Each film is shown at least once during the festival but never more than once on a given day. On each day at least one film is shown. Films are shown one at a time. The following conditions apply: On Thursday Harvest is shown, and no film is shown after it on that day. On Friday either Greed or Limelight, but not both, is shown, and no film is shown after it on that day. On Saturday either Greed or Harvest, but not both, is shown, and no film is shown after it on that day.

Which one of the following CANNOT be true?

Exactly three films—Greed, Harvest, and Limelight—are shown during a film club's festival held on Thursday, Friday, and Saturday. Each film is shown at least once during the festival but never more than once on a given day. On each day at least one film is shown. Films are shown one at a time. The following conditions apply: On Thursday Harvest is shown, and no film is shown after it on that day. On Friday either Greed or Limelight, but not both, is shown, and no film is shown after it on that day. On Saturday either Greed or Harvest, but not both, is shown, and no film is shown after it on that day.

If Limelight is never shown again during the festival once Greed is shown, then which one of the following is the maximum number of film showings that could occur during the festival?

Exactly three films—Greed, Harvest, and Limelight—are shown during a film club's festival held on Thursday, Friday, and Saturday. Each film is shown at least once during the festival but never more than once on a given day. On each day at least one film is shown. Films are shown one at a time. The following conditions apply: On Thursday Harvest is shown, and no film is shown after it on that day. On Friday either Greed or Limelight, but not both, is shown, and no film is shown after it on that day. On Saturday either Greed or Harvest, but not both, is shown, and no film is shown after it on that day.

If Greed is shown exactly three times, Harvest is shown exactly twice, and Limelight is shown exactly once, then which one of the following must be true?

Exactly three films—Greed, Harvest, and Limelight—are shown during a film club's festival held on Thursday, Friday, and Saturday. Each film is shown at least once during the festival but never more than once on a given day. On each day at least one film is shown. Films are shown one at a time. The following conditions apply: On Thursday Harvest is shown, and no film is shown after it on that day. On Friday either Greed or Limelight, but not both, is shown, and no film is shown after it on that day. On Saturday either Greed or Harvest, but not both, is shown, and no film is shown after it on that day.

If Limelight is shown exactly three times, Harvest is shown exactly twice, and Greed is shown exactly once, then which one of the following is a complete and accurate list of the films that could be the first film shown on Thursday?

A cruise line is scheduling seven week-long voyages for the ship Freedom. Each voyage will occur in exactly one of the first seven weeks of the season: weeks 1 through 7. Each voyage will be to exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad. Each destination will be scheduled for at least one of the weeks. The following conditions apply to Freedom's schedule: Jamaica will not be its destination in week 4. Trinidad will be its destination in week 7. Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages. Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica. No destination will be scheduled for consecutive weeks.

Which one of the following is an acceptable schedule of destinations for Freedom, in order from week 1 through week 7?

A cruise line is scheduling seven week-long voyages for the ship Freedom. Each voyage will occur in exactly one of the first seven weeks of the season: weeks 1 through 7. Each voyage will be to exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad. Each destination will be scheduled for at least one of the weeks. The following conditions apply to Freedom's schedule: Jamaica will not be its destination in week 4. Trinidad will be its destination in week 7. Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages. Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica. No destination will be scheduled for consecutive weeks.

Which one of the following CANNOT be true about Freedom's schedule of voyages?

A cruise line is scheduling seven week-long voyages for the ship Freedom. Each voyage will occur in exactly one of the first seven weeks of the season: weeks 1 through 7. Each voyage will be to exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad. Each destination will be scheduled for at least one of the weeks. The following conditions apply to Freedom's schedule: Jamaica will not be its destination in week 4. Trinidad will be its destination in week 7. Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages. Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica. No destination will be scheduled for consecutive weeks.

If Freedom makes a voyage to Trinidad in week 5, which one of the following could be true?

A cruise line is scheduling seven week-long voyages for the ship Freedom. Each voyage will occur in exactly one of the first seven weeks of the season: weeks 1 through 7. Each voyage will be to exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad. Each destination will be scheduled for at least one of the weeks. The following conditions apply to Freedom's schedule: Jamaica will not be its destination in week 4. Trinidad will be its destination in week 7. Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages. Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica. No destination will be scheduled for consecutive weeks.

If Freedom makes a voyage to Guadeloupe in week 1 and a voyage to Jamaica in week 5, which one of the following must be true?

A cruise line is scheduling seven week-long voyages for the ship Freedom. Each voyage will occur in exactly one of the first seven weeks of the season: weeks 1 through 7. Each voyage will be to exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad. Each destination will be scheduled for at least one of the weeks. The following conditions apply to Freedom's schedule: Jamaica will not be its destination in week 4. Trinidad will be its destination in week 7. Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages. Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica. No destination will be scheduled for consecutive weeks.

If Freedom makes a voyage to Guadeloupe in week 1 and to Trinidad in week 2, which one of the following must be true?

A cruise line is scheduling seven week-long voyages for the ship Freedom. Each voyage will occur in exactly one of the first seven weeks of the season: weeks 1 through 7. Each voyage will be to exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad. Each destination will be scheduled for at least one of the weeks. The following conditions apply to Freedom's schedule: Jamaica will not be its destination in week 4. Trinidad will be its destination in week 7. Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages. Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica. No destination will be scheduled for consecutive weeks.

If Freedom makes a voyage to Martinique in week 3, which one of the following could be an accurate list of Freedom's destinations in week 4 and week 5, respectively?

A cruise line is scheduling seven week-long voyages for the ship Freedom. Each voyage will occur in exactly one of the first seven weeks of the season: weeks 1 through 7. Each voyage will be to exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad. Each destination will be scheduled for at least one of the weeks. The following conditions apply to Freedom's schedule: Jamaica will not be its destination in week 4. Trinidad will be its destination in week 7. Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages. Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica. No destination will be scheduled for consecutive weeks.

Which one of the following must be true about Freedom's schedule of voyages?

There are exactly three recycling centers in Rivertown: Center 1, Center 2, and Center 3. Exactly five kinds of material are recycled at these recycling centers: glass, newsprint, plastic, tin, and wood. Each recycling center recycles at least two but no more than three of these kinds of material. The following conditions must hold: Any recycling center that recycles wood also recycles newsprint. Every kind of material that Center 2 recycles is also recycled at Center 1. Only one of the recycling centers recycles plastic, and that recycling center does not recycle glass.

Which one of the following could be an accurate account of all the kinds of material recycled at each recycling center in Rivertown?

There are exactly three recycling centers in Rivertown: Center 1, Center 2, and Center 3. Exactly five kinds of material are recycled at these recycling centers: glass, newsprint, plastic, tin, and wood. Each recycling center recycles at least two but no more than three of these kinds of material. The following conditions must hold: Any recycling center that recycles wood also recycles newsprint. Every kind of material that Center 2 recycles is also recycled at Center 1. Only one of the recycling centers recycles plastic, and that recycling center does not recycle glass.

Which one of the following is a complete and accurate list of the recycling centers in Rivertown any one of which could recycle plastic?

There are exactly three recycling centers in Rivertown: Center 1, Center 2, and Center 3. Exactly five kinds of material are recycled at these recycling centers: glass, newsprint, plastic, tin, and wood. Each recycling center recycles at least two but no more than three of these kinds of material. The following conditions must hold: Any recycling center that recycles wood also recycles newsprint. Every kind of material that Center 2 recycles is also recycled at Center 1. Only one of the recycling centers recycles plastic, and that recycling center does not recycle glass.

If Center 2 recycles three kinds of material, then which one of the following kinds of material must Center 3 recycle?

There are exactly three recycling centers in Rivertown: Center 1, Center 2, and Center 3. Exactly five kinds of material are recycled at these recycling centers: glass, newsprint, plastic, tin, and wood. Each recycling center recycles at least two but no more than three of these kinds of material. The following conditions must hold: Any recycling center that recycles wood also recycles newsprint. Every kind of material that Center 2 recycles is also recycled at Center 1. Only one of the recycling centers recycles plastic, and that recycling center does not recycle glass.

If each recycling center in Rivertown recycles exactly three kinds of material, then which one of the following could be true?

There are exactly three recycling centers in Rivertown: Center 1, Center 2, and Center 3. Exactly five kinds of material are recycled at these recycling centers: glass, newsprint, plastic, tin, and wood. Each recycling center recycles at least two but no more than three of these kinds of material. The following conditions must hold: Any recycling center that recycles wood also recycles newsprint. Every kind of material that Center 2 recycles is also recycled at Center 1. Only one of the recycling centers recycles plastic, and that recycling center does not recycle glass.

If Center 3 recycles glass, then which one of the following kinds of material must Center 2 recycle?

There are exactly three recycling centers in Rivertown: Center 1, Center 2, and Center 3. Exactly five kinds of material are recycled at these recycling centers: glass, newsprint, plastic, tin, and wood. Each recycling center recycles at least two but no more than three of these kinds of material. The following conditions must hold: Any recycling center that recycles wood also recycles newsprint. Every kind of material that Center 2 recycles is also recycled at Center 1. Only one of the recycling centers recycles plastic, and that recycling center does not recycle glass.

If Center 1 is the only recycling center that recycles wood, then which one of the following could be a complete and accurate list of the kinds of material that one of the recycling centers recycles?

Workers at a water treatment plant open eight valves—G, H, I, K, L, N, O, and P—to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions: Both K and P are opened before H. O is opened before L but after H. L is opened after G. N is opened before H. I is opened after K.

Which one of the following could be the order, from first to last, in which the valves are opened?

Workers at a water treatment plant open eight valves—G, H, I, K, L, N, O, and P—to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions: Both K and P are opened before H. O is opened before L but after H. L is opened after G. N is opened before H. I is opened after K.

Each of the following could be the fifth valve opened EXCEPT:

Workers at a water treatment plant open eight valves—G, H, I, K, L, N, O, and P—to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions: Both K and P are opened before H. O is opened before L but after H. L is opened after G. N is opened before H. I is opened after K.

If I is the second valve opened, then each of the following could be true EXCEPT:

Workers at a water treatment plant open eight valves—G, H, I, K, L, N, O, and P—to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions: Both K and P are opened before H. O is opened before L but after H. L is opened after G. N is opened before H. I is opened after K.

If L is the seventh valve opened, then each of the following could be the second valve opened EXCEPT:

Workers at a water treatment plant open eight valves—G, H, I, K, L, N, O, and P—to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions: Both K and P are opened before H. O is opened before L but after H. L is opened after G. N is opened before H. I is opened after K.

Which one of the following must be true?

Workers at a water treatment plant open eight valves—G, H, I, K, L, N, O, and P—to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions: Both K and P are opened before H. O is opened before L but after H. L is opened after G. N is opened before H. I is opened after K.

If K is the fourth valve opened, then which one of the following could be true?

Workers at a water treatment plant open eight valves—G, H, I, K, L, N, O, and P—to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions: Both K and P are opened before H. O is opened before L but after H. L is opened after G. N is opened before H. I is opened after K.

If G is the first valve opened and I is the third valve opened, then each of the following must be true EXCEPT:

On a field trip to the Museum of Natural History, each of six children—Juana, Kyle, Lucita, Salim, Thanh, and Veronica—is accompanied by one of three adults—Ms. Margoles, Mr. O'Connell, and Ms. Podorski. Each adult accompanies exactly two of the children, consistent with the following conditions: If Ms. Margoles accompanies Juana, then Ms. Podorski accompanies Lucita. If Kyle is not accompanied by Ms. Margoles, then Veronica is accompanied by Mr. O'Connell. Either Ms. Margoles or Mr. O'Connell accompanies Thanh. Juana is not accompanied by the same adult as Kyle; nor is Lucita accompanied by the same adult as Salim; nor is Thanh accompanied by the same adult as Veronica.

Which one of the following could be an accurate matching of the adults to the children they accompany?

On a field trip to the Museum of Natural History, each of six children—Juana, Kyle, Lucita, Salim, Thanh, and Veronica—is accompanied by one of three adults—Ms. Margoles, Mr. O'Connell, and Ms. Podorski. Each adult accompanies exactly two of the children, consistent with the following conditions: If Ms. Margoles accompanies Juana, then Ms. Podorski accompanies Lucita. If Kyle is not accompanied by Ms. Margoles, then Veronica is accompanied by Mr. O'Connell. Either Ms. Margoles or Mr. O'Connell accompanies Thanh. Juana is not accompanied by the same adult as Kyle; nor is Lucita accompanied by the same adult as Salim; nor is Thanh accompanied by the same adult as Veronica.

If Ms. Margoles accompanies Lucita and Thanh, then which one of the following must be true?

On a field trip to the Museum of Natural History, each of six children—Juana, Kyle, Lucita, Salim, Thanh, and Veronica—is accompanied by one of three adults—Ms. Margoles, Mr. O'Connell, and Ms. Podorski. Each adult accompanies exactly two of the children, consistent with the following conditions: If Ms. Margoles accompanies Juana, then Ms. Podorski accompanies Lucita. If Kyle is not accompanied by Ms. Margoles, then Veronica is accompanied by Mr. O'Connell. Either Ms. Margoles or Mr. O'Connell accompanies Thanh. Juana is not accompanied by the same adult as Kyle; nor is Lucita accompanied by the same adult as Salim; nor is Thanh accompanied by the same adult as Veronica.

If Ms. Podorski accompanies Juana and Veronica, then Ms. Margoles could accompany which one of the following pairs of children?

On a field trip to the Museum of Natural History, each of six children—Juana, Kyle, Lucita, Salim, Thanh, and Veronica—is accompanied by one of three adults—Ms. Margoles, Mr. O'Connell, and Ms. Podorski. Each adult accompanies exactly two of the children, consistent with the following conditions: If Ms. Margoles accompanies Juana, then Ms. Podorski accompanies Lucita. If Kyle is not accompanied by Ms. Margoles, then Veronica is accompanied by Mr. O'Connell. Either Ms. Margoles or Mr. O'Connell accompanies Thanh. Juana is not accompanied by the same adult as Kyle; nor is Lucita accompanied by the same adult as Salim; nor is Thanh accompanied by the same adult as Veronica.

Ms. Podorski CANNOT accompany which one of the following pairs of children?

On a field trip to the Museum of Natural History, each of six children—Juana, Kyle, Lucita, Salim, Thanh, and Veronica—is accompanied by one of three adults—Ms. Margoles, Mr. O'Connell, and Ms. Podorski. Each adult accompanies exactly two of the children, consistent with the following conditions: If Ms. Margoles accompanies Juana, then Ms. Podorski accompanies Lucita. If Kyle is not accompanied by Ms. Margoles, then Veronica is accompanied by Mr. O'Connell. Either Ms. Margoles or Mr. O'Connell accompanies Thanh. Juana is not accompanied by the same adult as Kyle; nor is Lucita accompanied by the same adult as Salim; nor is Thanh accompanied by the same adult as Veronica.

Mr. O'Connell CANNOT accompany which one of the following pairs of children?

Three short seminars—Goals, Objections, and Persuasion—and three long seminars—Humor, Negotiating, and Telemarketing—will be scheduled for a three-day sales training conference. On each day, two of the seminars will be given consecutively. Each seminar will be given exactly once. The schedule must conform to the following conditions: Exactly one short seminar and exactly one long seminar will be given each day. Telemarketing will not be given until both Goals and Objections have been given. Negotiating will not be given until Persuasion has been given.

Which one of the following could be an accurate schedule for the sales training conference?

Three short seminars—Goals, Objections, and Persuasion—and three long seminars—Humor, Negotiating, and Telemarketing—will be scheduled for a three-day sales training conference. On each day, two of the seminars will be given consecutively. Each seminar will be given exactly once. The schedule must conform to the following conditions: Exactly one short seminar and exactly one long seminar will be given each day. Telemarketing will not be given until both Goals and Objections have been given. Negotiating will not be given until Persuasion has been given.

If Goals is given on the first day of the sales training conference, then which one of the following could be true?

Three short seminars—Goals, Objections, and Persuasion—and three long seminars—Humor, Negotiating, and Telemarketing—will be scheduled for a three-day sales training conference. On each day, two of the seminars will be given consecutively. Each seminar will be given exactly once. The schedule must conform to the following conditions: Exactly one short seminar and exactly one long seminar will be given each day. Telemarketing will not be given until both Goals and Objections have been given. Negotiating will not be given until Persuasion has been given.

If Negotiating is given at some time before Objections, then which one of the following must be true?

Three short seminars—Goals, Objections, and Persuasion—and three long seminars—Humor, Negotiating, and Telemarketing—will be scheduled for a three-day sales training conference. On each day, two of the seminars will be given consecutively. Each seminar will be given exactly once. The schedule must conform to the following conditions: Exactly one short seminar and exactly one long seminar will be given each day. Telemarketing will not be given until both Goals and Objections have been given. Negotiating will not be given until Persuasion has been given.

Which one of the following CANNOT be the second seminar given on the second day of the sales training conference?

Three short seminars—Goals, Objections, and Persuasion—and three long seminars—Humor, Negotiating, and Telemarketing—will be scheduled for a three-day sales training conference. On each day, two of the seminars will be given consecutively. Each seminar will be given exactly once. The schedule must conform to the following conditions: Exactly one short seminar and exactly one long seminar will be given each day. Telemarketing will not be given until both Goals and Objections have been given. Negotiating will not be given until Persuasion has been given.

If Humor is given on the second day of the sales training conference, then which one of the following could be true?

A bread truck makes exactly one bread delivery to each of six restaurants in succession—Figueroa's, Ginsberg's, Harris's, Kanzaki's, Leacock's, and Malpighi's—though not necessarily in that order. The following conditions must apply: Ginsberg's delivery is earlier than Kanzaki's but later than Figueroa's. Harris's delivery is earlier than Ginsberg's. If Figueroa's delivery is earlier than Malpighi's, then Leacock's delivery is earlier than Harris's. Either Malpighi's delivery is earlier than Harris's or it is later than Kanzaki's, but not both.

Which one of the following accurately represents an order in which the deliveries could occur, from first to last?

A bread truck makes exactly one bread delivery to each of six restaurants in succession—Figueroa's, Ginsberg's, Harris's, Kanzaki's, Leacock's, and Malpighi's—though not necessarily in that order. The following conditions must apply: Ginsberg's delivery is earlier than Kanzaki's but later than Figueroa's. Harris's delivery is earlier than Ginsberg's. If Figueroa's delivery is earlier than Malpighi's, then Leacock's delivery is earlier than Harris's. Either Malpighi's delivery is earlier than Harris's or it is later than Kanzaki's, but not both.

If Figueroa's delivery is fourth, then which one of the following must be true?

A bread truck makes exactly one bread delivery to each of six restaurants in succession—Figueroa's, Ginsberg's, Harris's, Kanzaki's, Leacock's, and Malpighi's—though not necessarily in that order. The following conditions must apply: Ginsberg's delivery is earlier than Kanzaki's but later than Figueroa's. Harris's delivery is earlier than Ginsberg's. If Figueroa's delivery is earlier than Malpighi's, then Leacock's delivery is earlier than Harris's. Either Malpighi's delivery is earlier than Harris's or it is later than Kanzaki's, but not both.

If Malpighi's delivery is first and Leacock's delivery is third, then which one of the following must be true?

A bread truck makes exactly one bread delivery to each of six restaurants in succession—Figueroa's, Ginsberg's, Harris's, Kanzaki's, Leacock's, and Malpighi's—though not necessarily in that order. The following conditions must apply: Ginsberg's delivery is earlier than Kanzaki's but later than Figueroa's. Harris's delivery is earlier than Ginsberg's. If Figueroa's delivery is earlier than Malpighi's, then Leacock's delivery is earlier than Harris's. Either Malpighi's delivery is earlier than Harris's or it is later than Kanzaki's, but not both.

Which one of the following must be true?

A bread truck makes exactly one bread delivery to each of six restaurants in succession—Figueroa's, Ginsberg's, Harris's, Kanzaki's, Leacock's, and Malpighi's—though not necessarily in that order. The following conditions must apply: Ginsberg's delivery is earlier than Kanzaki's but later than Figueroa's. Harris's delivery is earlier than Ginsberg's. If Figueroa's delivery is earlier than Malpighi's, then Leacock's delivery is earlier than Harris's. Either Malpighi's delivery is earlier than Harris's or it is later than Kanzaki's, but not both.

If Kanzaki's delivery is earlier than Leacock's, then which one of the following could be true?

A bread truck makes exactly one bread delivery to each of six restaurants in succession—Figueroa's, Ginsberg's, Harris's, Kanzaki's, Leacock's, and Malpighi's—though not necessarily in that order. The following conditions must apply: Ginsberg's delivery is earlier than Kanzaki's but later than Figueroa's. Harris's delivery is earlier than Ginsberg's. If Figueroa's delivery is earlier than Malpighi's, then Leacock's delivery is earlier than Harris's. Either Malpighi's delivery is earlier than Harris's or it is later than Kanzaki's, but not both.

Which one of the following must be false?

Five performers—Traugott, West, Xavier, Young, and Zinser—are recruited by three talent agencies—Fame Agency, Premier Agency, and Star Agency. Each performer signs with exactly one of the agencies and each agency signs at least one of the performers. The performers' signing with the agencies is in accord with the following: Xavier signs with Fame Agency. Xavier and Young do not sign with the same agency as each other. Zinser signs with the same agency as Young. If Traugott signs with Star Agency, West also signs with Star Agency.

Which one of the following could be a complete and accurate list of the performers who sign with each agency?

Five performers—Traugott, West, Xavier, Young, and Zinser—are recruited by three talent agencies—Fame Agency, Premier Agency, and Star Agency. Each performer signs with exactly one of the agencies and each agency signs at least one of the performers. The performers' signing with the agencies is in accord with the following: Xavier signs with Fame Agency. Xavier and Young do not sign with the same agency as each other. Zinser signs with the same agency as Young. If Traugott signs with Star Agency, West also signs with Star Agency.

Which one of the following could be true?

Five performers—Traugott, West, Xavier, Young, and Zinser—are recruited by three talent agencies—Fame Agency, Premier Agency, and Star Agency. Each performer signs with exactly one of the agencies and each agency signs at least one of the performers. The performers' signing with the agencies is in accord with the following: Xavier signs with Fame Agency. Xavier and Young do not sign with the same agency as each other. Zinser signs with the same agency as Young. If Traugott signs with Star Agency, West also signs with Star Agency.

Which one of the following must be true?

Five performers—Traugott, West, Xavier, Young, and Zinser—are recruited by three talent agencies—Fame Agency, Premier Agency, and Star Agency. Each performer signs with exactly one of the agencies and each agency signs at least one of the performers. The performers' signing with the agencies is in accord with the following: Xavier signs with Fame Agency. Xavier and Young do not sign with the same agency as each other. Zinser signs with the same agency as Young. If Traugott signs with Star Agency, West also signs with Star Agency.

The agency with which each of the performers signs is completely determined if which one of the following is true?

Five performers—Traugott, West, Xavier, Young, and Zinser—are recruited by three talent agencies—Fame Agency, Premier Agency, and Star Agency. Each performer signs with exactly one of the agencies and each agency signs at least one of the performers. The performers' signing with the agencies is in accord with the following: Xavier signs with Fame Agency. Xavier and Young do not sign with the same agency as each other. Zinser signs with the same agency as Young. If Traugott signs with Star Agency, West also signs with Star Agency.

If Zinser signs with Star Agency, which one of the following must be false?

A competition is being held to select a design for Yancy College's new student union building. Each of six architects—Green, Jackson, Liu, Mertz, Peete, and Valdez—has submitted exactly one design. There are exactly six designs, and they are presented one at a time to the panel of judges, each design being presented exactly once, consistent with the following conditions: Mertz's design is presented at some time before Liu's and after Peete's. Green's design is presented either at some time before Jackson's or at some time after Liu's, but not both. Valdez's design is presented either at some time before Green's or at some time after Peete's, but not both.

Which one of the following could be the order in which the designs are presented, from first to last?

A competition is being held to select a design for Yancy College's new student union building. Each of six architects—Green, Jackson, Liu, Mertz, Peete, and Valdez—has submitted exactly one design. There are exactly six designs, and they are presented one at a time to the panel of judges, each design being presented exactly once, consistent with the following conditions: Mertz's design is presented at some time before Liu's and after Peete's. Green's design is presented either at some time before Jackson's or at some time after Liu's, but not both. Valdez's design is presented either at some time before Green's or at some time after Peete's, but not both.

Mertz's design CANNOT be presented

A competition is being held to select a design for Yancy College's new student union building. Each of six architects—Green, Jackson, Liu, Mertz, Peete, and Valdez—has submitted exactly one design. There are exactly six designs, and they are presented one at a time to the panel of judges, each design being presented exactly once, consistent with the following conditions: Mertz's design is presented at some time before Liu's and after Peete's. Green's design is presented either at some time before Jackson's or at some time after Liu's, but not both. Valdez's design is presented either at some time before Green's or at some time after Peete's, but not both.

If Liu's design is presented sixth, then which one of the following must be true?

A competition is being held to select a design for Yancy College's new student union building. Each of six architects—Green, Jackson, Liu, Mertz, Peete, and Valdez—has submitted exactly one design. There are exactly six designs, and they are presented one at a time to the panel of judges, each design being presented exactly once, consistent with the following conditions: Mertz's design is presented at some time before Liu's and after Peete's. Green's design is presented either at some time before Jackson's or at some time after Liu's, but not both. Valdez's design is presented either at some time before Green's or at some time after Peete's, but not both.

If Jackson's design is presented at some time before Mertz's, then each of the following could be true EXCEPT:

A competition is being held to select a design for Yancy College's new student union building. Each of six architects—Green, Jackson, Liu, Mertz, Peete, and Valdez—has submitted exactly one design. There are exactly six designs, and they are presented one at a time to the panel of judges, each design being presented exactly once, consistent with the following conditions: Mertz's design is presented at some time before Liu's and after Peete's. Green's design is presented either at some time before Jackson's or at some time after Liu's, but not both. Valdez's design is presented either at some time before Green's or at some time after Peete's, but not both.

Which one of the following designs CANNOT be the design presented first?

A competition is being held to select a design for Yancy College's new student union building. Each of six architects—Green, Jackson, Liu, Mertz, Peete, and Valdez—has submitted exactly one design. There are exactly six designs, and they are presented one at a time to the panel of judges, each design being presented exactly once, consistent with the following conditions: Mertz's design is presented at some time before Liu's and after Peete's. Green's design is presented either at some time before Jackson's or at some time after Liu's, but not both. Valdez's design is presented either at some time before Green's or at some time after Peete's, but not both.

Which one of the following could be an accurate partial list of the architects, each matched with his or her design's place in the order in which the designs are presented?

Detectives investigating a citywide increase in burglaries questioned exactly seven suspects—S, T, V, W, X, Y, and Z—each on a different one of seven consecutive days. Each suspect was questioned exactly once. Any suspect who confessed did so while being questioned. The investigation conformed to the following: T was questioned on day three. The suspect questioned on day four did not confess. S was questioned after W was questioned. Both X and V were questioned after Z was questioned. No suspects confessed after W was questioned. Exactly two suspects confessed after T was questioned.

Which one of the following could be true?

Detectives investigating a citywide increase in burglaries questioned exactly seven suspects—S, T, V, W, X, Y, and Z—each on a different one of seven consecutive days. Each suspect was questioned exactly once. Any suspect who confessed did so while being questioned. The investigation conformed to the following: T was questioned on day three. The suspect questioned on day four did not confess. S was questioned after W was questioned. Both X and V were questioned after Z was questioned. No suspects confessed after W was questioned. Exactly two suspects confessed after T was questioned.

If Z was the second suspect to confess, then each of the following statements could be true EXCEPT:

Detectives investigating a citywide increase in burglaries questioned exactly seven suspects—S, T, V, W, X, Y, and Z—each on a different one of seven consecutive days. Each suspect was questioned exactly once. Any suspect who confessed did so while being questioned. The investigation conformed to the following: T was questioned on day three. The suspect questioned on day four did not confess. S was questioned after W was questioned. Both X and V were questioned after Z was questioned. No suspects confessed after W was questioned. Exactly two suspects confessed after T was questioned.

If Y was questioned after V but before X, then which one of the following could be true?

Detectives investigating a citywide increase in burglaries questioned exactly seven suspects—S, T, V, W, X, Y, and Z—each on a different one of seven consecutive days. Each suspect was questioned exactly once. Any suspect who confessed did so while being questioned. The investigation conformed to the following: T was questioned on day three. The suspect questioned on day four did not confess. S was questioned after W was questioned. Both X and V were questioned after Z was questioned. No suspects confessed after W was questioned. Exactly two suspects confessed after T was questioned.

Which one of the following suspects must have been questioned before T was questioned?

Detectives investigating a citywide increase in burglaries questioned exactly seven suspects—S, T, V, W, X, Y, and Z—each on a different one of seven consecutive days. Each suspect was questioned exactly once. Any suspect who confessed did so while being questioned. The investigation conformed to the following: T was questioned on day three. The suspect questioned on day four did not confess. S was questioned after W was questioned. Both X and V were questioned after Z was questioned. No suspects confessed after W was questioned. Exactly two suspects confessed after T was questioned.

If X and Y both confessed, then each of the following could be true EXCEPT:

Detectives investigating a citywide increase in burglaries questioned exactly seven suspects—S, T, V, W, X, Y, and Z—each on a different one of seven consecutive days. Each suspect was questioned exactly once. Any suspect who confessed did so while being questioned. The investigation conformed to the following: T was questioned on day three. The suspect questioned on day four did not confess. S was questioned after W was questioned. Both X and V were questioned after Z was questioned. No suspects confessed after W was questioned. Exactly two suspects confessed after T was questioned.

If neither X nor V confessed, then which one of the following must be true?

The three highest-placing teams in a high school debate tournament are the teams from Fairview, Gillom, and Hilltop high schools. Each team has exactly two members. The individuals on these three teams are Mei, Navarro, O'Rourke, Pavlovich, Sethna, and Tsudama. The following is the case: Sethna is on the team from Gillom High. Tsudama is on the second-place team. Mei and Pavlovich are not on the same team. Pavlovich's team places higher than Navarro's team. The team from Gillom High places higher than the team from Hilltop High.

Which one of the following could be an accurate list of the members of each of the three highest-placing teams?

The three highest-placing teams in a high school debate tournament are the teams from Fairview, Gillom, and Hilltop high schools. Each team has exactly two members. The individuals on these three teams are Mei, Navarro, O'Rourke, Pavlovich, Sethna, and Tsudama. The following is the case: Sethna is on the team from Gillom High. Tsudama is on the second-place team. Mei and Pavlovich are not on the same team. Pavlovich's team places higher than Navarro's team. The team from Gillom High places higher than the team from Hilltop High.

If Pavlovich is on the team from Hilltop High, then which one of the following could be true?

The three highest-placing teams in a high school debate tournament are the teams from Fairview, Gillom, and Hilltop high schools. Each team has exactly two members. The individuals on these three teams are Mei, Navarro, O'Rourke, Pavlovich, Sethna, and Tsudama. The following is the case: Sethna is on the team from Gillom High. Tsudama is on the second-place team. Mei and Pavlovich are not on the same team. Pavlovich's team places higher than Navarro's team. The team from Gillom High places higher than the team from Hilltop High.

If O'Rourke is on the second-place team, then which one of the following could be true?

The three highest-placing teams in a high school debate tournament are the teams from Fairview, Gillom, and Hilltop high schools. Each team has exactly two members. The individuals on these three teams are Mei, Navarro, O'Rourke, Pavlovich, Sethna, and Tsudama. The following is the case: Sethna is on the team from Gillom High. Tsudama is on the second-place team. Mei and Pavlovich are not on the same team. Pavlovich's team places higher than Navarro's team. The team from Gillom High places higher than the team from Hilltop High.

If Pavlovich and Tsudama are teammates, then for how many of the individuals can it be exactly determined where his or her team places?

The three highest-placing teams in a high school debate tournament are the teams from Fairview, Gillom, and Hilltop high schools. Each team has exactly two members. The individuals on these three teams are Mei, Navarro, O'Rourke, Pavlovich, Sethna, and Tsudama. The following is the case: Sethna is on the team from Gillom High. Tsudama is on the second-place team. Mei and Pavlovich are not on the same team. Pavlovich's team places higher than Navarro's team. The team from Gillom High places higher than the team from Hilltop High.

If Mei is on a team that places higher than the Hilltop team, then which one of the following could be true?

The three highest-placing teams in a high school debate tournament are the teams from Fairview, Gillom, and Hilltop high schools. Each team has exactly two members. The individuals on these three teams are Mei, Navarro, O'Rourke, Pavlovich, Sethna, and Tsudama. The following is the case: Sethna is on the team from Gillom High. Tsudama is on the second-place team. Mei and Pavlovich are not on the same team. Pavlovich's team places higher than Navarro's team. The team from Gillom High places higher than the team from Hilltop High.

Sethna's teammate could be any one of the following EXCEPT:

A dance is being choreographed for six dancers: three men—Felipe, Grant, and Hassan—and three women—Jaclyn, Keiko, and Lorena. At no time during the dance will anyone other than the dancers be on stage. Who is on stage and who is off stage at any particular time in the dance is determined by the following constraints: If Jaclyn is on stage, Lorena is off stage. If Lorena is off stage, Jaclyn is on stage. If Felipe is off stage, Jaclyn is also off stage. If any of the women are on stage, Grant is also on stage.

Which one of the following is a list of all of the dancers who could be on stage at a particular time?

A dance is being choreographed for six dancers: three men—Felipe, Grant, and Hassan—and three women—Jaclyn, Keiko, and Lorena. At no time during the dance will anyone other than the dancers be on stage. Who is on stage and who is off stage at any particular time in the dance is determined by the following constraints: If Jaclyn is on stage, Lorena is off stage. If Lorena is off stage, Jaclyn is on stage. If Felipe is off stage, Jaclyn is also off stage. If any of the women are on stage, Grant is also on stage.

Which one of the following CANNOT be true at any time during the dance?

A dance is being choreographed for six dancers: three men—Felipe, Grant, and Hassan—and three women—Jaclyn, Keiko, and Lorena. At no time during the dance will anyone other than the dancers be on stage. Who is on stage and who is off stage at any particular time in the dance is determined by the following constraints: If Jaclyn is on stage, Lorena is off stage. If Lorena is off stage, Jaclyn is on stage. If Felipe is off stage, Jaclyn is also off stage. If any of the women are on stage, Grant is also on stage.

Which one of the following is a complete and accurate list of the dancers any one of whom could be off stage when Jaclyn is on stage?

A dance is being choreographed for six dancers: three men—Felipe, Grant, and Hassan—and three women—Jaclyn, Keiko, and Lorena. At no time during the dance will anyone other than the dancers be on stage. Who is on stage and who is off stage at any particular time in the dance is determined by the following constraints: If Jaclyn is on stage, Lorena is off stage. If Lorena is off stage, Jaclyn is on stage. If Felipe is off stage, Jaclyn is also off stage. If any of the women are on stage, Grant is also on stage.

If there are more women than men on stage, then exactly how many dancers must be on stage?

A dance is being choreographed for six dancers: three men—Felipe, Grant, and Hassan—and three women—Jaclyn, Keiko, and Lorena. At no time during the dance will anyone other than the dancers be on stage. Who is on stage and who is off stage at any particular time in the dance is determined by the following constraints: If Jaclyn is on stage, Lorena is off stage. If Lorena is off stage, Jaclyn is on stage. If Felipe is off stage, Jaclyn is also off stage. If any of the women are on stage, Grant is also on stage.

What is the minimum number of dancers that must be on stage at any given time?

A critic has prepared a review of exactly six music CDs—Headstrong, In Flight, Nice, Quasi, Reunion, and Sounds Good. Each CD received a rating of either one, two, three, or four stars, with each CD receiving exactly one rating. Although the ratings were meant to be kept secret until the review was published, the following facts have been leaked to the public: For each of the ratings, at least one but no more than two of the CDs received that rating. Headstrong received exactly one more star than Nice did. Either Headstrong or Reunion received the same number of stars as In Flight did. At most one CD received more stars than Quasi did.

Which one of the following could be an accurate matching of ratings to the CDs that received those ratings?

A critic has prepared a review of exactly six music CDs—Headstrong, In Flight, Nice, Quasi, Reunion, and Sounds Good. Each CD received a rating of either one, two, three, or four stars, with each CD receiving exactly one rating. Although the ratings were meant to be kept secret until the review was published, the following facts have been leaked to the public: For each of the ratings, at least one but no more than two of the CDs received that rating. Headstrong received exactly one more star than Nice did. Either Headstrong or Reunion received the same number of stars as In Flight did. At most one CD received more stars than Quasi did.

If Headstrong is the only CD that received a rating of two stars, then which one of the following must be true?

A critic has prepared a review of exactly six music CDs—Headstrong, In Flight, Nice, Quasi, Reunion, and Sounds Good. Each CD received a rating of either one, two, three, or four stars, with each CD receiving exactly one rating. Although the ratings were meant to be kept secret until the review was published, the following facts have been leaked to the public: For each of the ratings, at least one but no more than two of the CDs received that rating. Headstrong received exactly one more star than Nice did. Either Headstrong or Reunion received the same number of stars as In Flight did. At most one CD received more stars than Quasi did.

If Reunion received the same rating as Sounds Good, then which one of the following must be true?

A critic has prepared a review of exactly six music CDs—Headstrong, In Flight, Nice, Quasi, Reunion, and Sounds Good. Each CD received a rating of either one, two, three, or four stars, with each CD receiving exactly one rating. Although the ratings were meant to be kept secret until the review was published, the following facts have been leaked to the public: For each of the ratings, at least one but no more than two of the CDs received that rating. Headstrong received exactly one more star than Nice did. Either Headstrong or Reunion received the same number of stars as In Flight did. At most one CD received more stars than Quasi did.

If Nice and Reunion each received a rating of one star, then which one of the following could be true?

A critic has prepared a review of exactly six music CDs—Headstrong, In Flight, Nice, Quasi, Reunion, and Sounds Good. Each CD received a rating of either one, two, three, or four stars, with each CD receiving exactly one rating. Although the ratings were meant to be kept secret until the review was published, the following facts have been leaked to the public: For each of the ratings, at least one but no more than two of the CDs received that rating. Headstrong received exactly one more star than Nice did. Either Headstrong or Reunion received the same number of stars as In Flight did. At most one CD received more stars than Quasi did.

Which one of the following CANNOT be true?

A critic has prepared a review of exactly six music CDs—Headstrong, In Flight, Nice, Quasi, Reunion, and Sounds Good. Each CD received a rating of either one, two, three, or four stars, with each CD receiving exactly one rating. Although the ratings were meant to be kept secret until the review was published, the following facts have been leaked to the public: For each of the ratings, at least one but no more than two of the CDs received that rating. Headstrong received exactly one more star than Nice did. Either Headstrong or Reunion received the same number of stars as In Flight did. At most one CD received more stars than Quasi did.

If Reunion is the only CD that received a rating of one star, then which one of the following could be true?

A critic has prepared a review of exactly six music CDs—Headstrong, In Flight, Nice, Quasi, Reunion, and Sounds Good. Each CD received a rating of either one, two, three, or four stars, with each CD receiving exactly one rating. Although the ratings were meant to be kept secret until the review was published, the following facts have been leaked to the public: For each of the ratings, at least one but no more than two of the CDs received that rating. Headstrong received exactly one more star than Nice did. Either Headstrong or Reunion received the same number of stars as In Flight did. At most one CD received more stars than Quasi did.

Which one of the following CANNOT have received a rating of four stars?

A cake has exactly six layers—lemon, marzipan, orange, raspberry, strawberry, and vanilla. There is exactly one bottom layer (the first layer), and each succeeding layer (from second through sixth) completely covers the layer beneath it. The following conditions must apply: The raspberry layer is neither immediately above nor immediately below the strawberry layer. The marzipan layer is immediately above the lemon layer. The orange layer is above the marzipan layer but below the strawberry layer.

Which one of the following could be an accurate list of the layers of the cake, from bottom to top?

A cake has exactly six layers—lemon, marzipan, orange, raspberry, strawberry, and vanilla. There is exactly one bottom layer (the first layer), and each succeeding layer (from second through sixth) completely covers the layer beneath it. The following conditions must apply: The raspberry layer is neither immediately above nor immediately below the strawberry layer. The marzipan layer is immediately above the lemon layer. The orange layer is above the marzipan layer but below the strawberry layer.

If the strawberry layer is not immediately above the orange layer, then which one of the following could be true?

A cake has exactly six layers—lemon, marzipan, orange, raspberry, strawberry, and vanilla. There is exactly one bottom layer (the first layer), and each succeeding layer (from second through sixth) completely covers the layer beneath it. The following conditions must apply: The raspberry layer is neither immediately above nor immediately below the strawberry layer. The marzipan layer is immediately above the lemon layer. The orange layer is above the marzipan layer but below the strawberry layer.

If the strawberry layer is not the top layer, then which one of the following is a complete and accurate list of the layers that could be the vanilla layer?

A cake has exactly six layers—lemon, marzipan, orange, raspberry, strawberry, and vanilla. There is exactly one bottom layer (the first layer), and each succeeding layer (from second through sixth) completely covers the layer beneath it. The following conditions must apply: The raspberry layer is neither immediately above nor immediately below the strawberry layer. The marzipan layer is immediately above the lemon layer. The orange layer is above the marzipan layer but below the strawberry layer.

If the lemon layer is third, then which one of the following could be true?

A cake has exactly six layers—lemon, marzipan, orange, raspberry, strawberry, and vanilla. There is exactly one bottom layer (the first layer), and each succeeding layer (from second through sixth) completely covers the layer beneath it. The following conditions must apply: The raspberry layer is neither immediately above nor immediately below the strawberry layer. The marzipan layer is immediately above the lemon layer. The orange layer is above the marzipan layer but below the strawberry layer.

Which one of the following could be an accurate list of the two lowest layers of the cake, listed in order from the bottom up?

A panel reviews six contract bids—H, J, K, R, S, and T. No two bids have the same cost. Exactly one of the bids is accepted. The following conditions must hold: The accepted bid is either K or R and is either the second or the third lowest in cost. H is lower in cost than each of J and K. If J is the fourth lowest in cost, then J is lower in cost than each of S and T. If J is not the fourth lowest in cost, then J is higher in cost than each of S and T. Either R or S is the fifth lowest in cost.

Which one of the following could be an accurate list of the bids in order from lowest to highest in cost?

A panel reviews six contract bids—H, J, K, R, S, and T. No two bids have the same cost. Exactly one of the bids is accepted. The following conditions must hold: The accepted bid is either K or R and is either the second or the third lowest in cost. H is lower in cost than each of J and K. If J is the fourth lowest in cost, then J is lower in cost than each of S and T. If J is not the fourth lowest in cost, then J is higher in cost than each of S and T. Either R or S is the fifth lowest in cost.

Which one of the following bids CANNOT be the fourth lowest in cost?

A panel reviews six contract bids—H, J, K, R, S, and T. No two bids have the same cost. Exactly one of the bids is accepted. The following conditions must hold: The accepted bid is either K or R and is either the second or the third lowest in cost. H is lower in cost than each of J and K. If J is the fourth lowest in cost, then J is lower in cost than each of S and T. If J is not the fourth lowest in cost, then J is higher in cost than each of S and T. Either R or S is the fifth lowest in cost.

Which one of the following bids CANNOT be the second lowest in cost?

A panel reviews six contract bids—H, J, K, R, S, and T. No two bids have the same cost. Exactly one of the bids is accepted. The following conditions must hold: The accepted bid is either K or R and is either the second or the third lowest in cost. H is lower in cost than each of J and K. If J is the fourth lowest in cost, then J is lower in cost than each of S and T. If J is not the fourth lowest in cost, then J is higher in cost than each of S and T. Either R or S is the fifth lowest in cost.

If R is the accepted bid, then which one of the following must be true?

A panel reviews six contract bids—H, J, K, R, S, and T. No two bids have the same cost. Exactly one of the bids is accepted. The following conditions must hold: The accepted bid is either K or R and is either the second or the third lowest in cost. H is lower in cost than each of J and K. If J is the fourth lowest in cost, then J is lower in cost than each of S and T. If J is not the fourth lowest in cost, then J is higher in cost than each of S and T. Either R or S is the fifth lowest in cost.

Which one of the following must be true?

A panel reviews six contract bids—H, J, K, R, S, and T. No two bids have the same cost. Exactly one of the bids is accepted. The following conditions must hold: The accepted bid is either K or R and is either the second or the third lowest in cost. H is lower in cost than each of J and K. If J is the fourth lowest in cost, then J is lower in cost than each of S and T. If J is not the fourth lowest in cost, then J is higher in cost than each of S and T. Either R or S is the fifth lowest in cost.

If R is the lowest in cost, then which one of the following could be false?

There are exactly six law students—Gambini, Little, Mitchum, Richardson, Saito, and Veracruz—in a trial advocacy class. The class is divided into three trial teams—team 1, team 2, and team 3—of exactly two students each. Each student is on exactly one of the teams. Each student prepares exactly one of either the opening argument or the final argument for his or her team. The teams must be formed according to the following specifications: Mitchum is on the same team as either Gambini or Veracruz. Little prepares an opening argument. Either Gambini or Richardson, but not both, prepares a final argument.

Which one of the following could be the composition of each team and the argument each student prepares?

There are exactly six law students—Gambini, Little, Mitchum, Richardson, Saito, and Veracruz—in a trial advocacy class. The class is divided into three trial teams—team 1, team 2, and team 3—of exactly two students each. Each student is on exactly one of the teams. Each student prepares exactly one of either the opening argument or the final argument for his or her team. The teams must be formed according to the following specifications: Mitchum is on the same team as either Gambini or Veracruz. Little prepares an opening argument. Either Gambini or Richardson, but not both, prepares a final argument.

If Gambini is on the same team as Mitchum, and if Gambini prepares the final argument for that team, then which one of the following could be true?

There are exactly six law students—Gambini, Little, Mitchum, Richardson, Saito, and Veracruz—in a trial advocacy class. The class is divided into three trial teams—team 1, team 2, and team 3—of exactly two students each. Each student is on exactly one of the teams. Each student prepares exactly one of either the opening argument or the final argument for his or her team. The teams must be formed according to the following specifications: Mitchum is on the same team as either Gambini or Veracruz. Little prepares an opening argument. Either Gambini or Richardson, but not both, prepares a final argument.

Which one of the following could be true?

There are exactly six law students—Gambini, Little, Mitchum, Richardson, Saito, and Veracruz—in a trial advocacy class. The class is divided into three trial teams—team 1, team 2, and team 3—of exactly two students each. Each student is on exactly one of the teams. Each student prepares exactly one of either the opening argument or the final argument for his or her team. The teams must be formed according to the following specifications: Mitchum is on the same team as either Gambini or Veracruz. Little prepares an opening argument. Either Gambini or Richardson, but not both, prepares a final argument.

If Richardson is on the same team as Veracruz, then for exactly how many of the students can it be determined which of the arguments he or she prepares?

There are exactly six law students—Gambini, Little, Mitchum, Richardson, Saito, and Veracruz—in a trial advocacy class. The class is divided into three trial teams—team 1, team 2, and team 3—of exactly two students each. Each student is on exactly one of the teams. Each student prepares exactly one of either the opening argument or the final argument for his or her team. The teams must be formed according to the following specifications: Mitchum is on the same team as either Gambini or Veracruz. Little prepares an opening argument. Either Gambini or Richardson, but not both, prepares a final argument.

If Little is on the same team as Richardson, then which one of the following must be true?

There are exactly six law students—Gambini, Little, Mitchum, Richardson, Saito, and Veracruz—in a trial advocacy class. The class is divided into three trial teams—team 1, team 2, and team 3—of exactly two students each. Each student is on exactly one of the teams. Each student prepares exactly one of either the opening argument or the final argument for his or her team. The teams must be formed according to the following specifications: Mitchum is on the same team as either Gambini or Veracruz. Little prepares an opening argument. Either Gambini or Richardson, but not both, prepares a final argument.

If Saito prepares an opening argument, then which one of the following pairs of students could be on the same team as each other?

While on vacation, Sukanya receives several e-mail messages from work, each message from one of three associates: Hilary, Jerome, and Lula. Sukanya receives at least one and no more than two messages from each of them. Sukanya receives each message on the day it is sent. No more than one message is sent each day. The messages are received in a manner consistent with the following: The first message is not from Lula. Both the first and last messages are from the same person. Exactly once Sukanya receives a message from Jerome on the day after receiving one from Hilary. Of the first three messages, exactly one is from Jerome.

Which one of the following could be an accurate list of the e-mail messages Sukanya receives, identified by the person each message is from and listed in the order she receives them?

While on vacation, Sukanya receives several e-mail messages from work, each message from one of three associates: Hilary, Jerome, and Lula. Sukanya receives at least one and no more than two messages from each of them. Sukanya receives each message on the day it is sent. No more than one message is sent each day. The messages are received in a manner consistent with the following: The first message is not from Lula. Both the first and last messages are from the same person. Exactly once Sukanya receives a message from Jerome on the day after receiving one from Hilary. Of the first three messages, exactly one is from Jerome.

What is the maximum possible number of e-mail messages Sukanya receives after Jerome's first message but before Hilary's first message?

While on vacation, Sukanya receives several e-mail messages from work, each message from one of three associates: Hilary, Jerome, and Lula. Sukanya receives at least one and no more than two messages from each of them. Sukanya receives each message on the day it is sent. No more than one message is sent each day. The messages are received in a manner consistent with the following: The first message is not from Lula. Both the first and last messages are from the same person. Exactly once Sukanya receives a message from Jerome on the day after receiving one from Hilary. Of the first three messages, exactly one is from Jerome.

If Sukanya receives exactly four e-mail messages, then which one of the following must be true?

While on vacation, Sukanya receives several e-mail messages from work, each message from one of three associates: Hilary, Jerome, and Lula. Sukanya receives at least one and no more than two messages from each of them. Sukanya receives each message on the day it is sent. No more than one message is sent each day. The messages are received in a manner consistent with the following: The first message is not from Lula. Both the first and last messages are from the same person. Exactly once Sukanya receives a message from Jerome on the day after receiving one from Hilary. Of the first three messages, exactly one is from Jerome.

Which one of the following e-mail messages CANNOT be from Lula?