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In a certain recipe contest, each contestant submits two recipes, one for an appetizer and one for a main dish. Together the two recipes must include exactly seven flavorings—fenugreek, ginger, lemongrass, nutmeg, paprika, saffron, and turmeric—with no flavoring included in more than one of the two recipes. Each contestant's recipes must satisfy the following conditions: The appetizer recipe includes at most three of the flavorings. Fenugreek is not included in the same recipe as nutmeg. Saffron is not included in the same recipe as turmeric. Ginger is included in the same recipe as nutmeg.

Which one of the following could be a complete and accurate list of the flavorings included in one contestant's main-dish recipe?

In a certain recipe contest, each contestant submits two recipes, one for an appetizer and one for a main dish. Together the two recipes must include exactly seven flavorings—fenugreek, ginger, lemongrass, nutmeg, paprika, saffron, and turmeric—with no flavoring included in more than one of the two recipes. Each contestant's recipes must satisfy the following conditions: The appetizer recipe includes at most three of the flavorings. Fenugreek is not included in the same recipe as nutmeg. Saffron is not included in the same recipe as turmeric. Ginger is included in the same recipe as nutmeg.

If a contestant's appetizer recipe does not include fenugreek, then the contestant's appetizer recipe must include

In a certain recipe contest, each contestant submits two recipes, one for an appetizer and one for a main dish. Together the two recipes must include exactly seven flavorings—fenugreek, ginger, lemongrass, nutmeg, paprika, saffron, and turmeric—with no flavoring included in more than one of the two recipes. Each contestant's recipes must satisfy the following conditions: The appetizer recipe includes at most three of the flavorings. Fenugreek is not included in the same recipe as nutmeg. Saffron is not included in the same recipe as turmeric. Ginger is included in the same recipe as nutmeg.

Which one of the following could be a list of all of the flavorings included in one contestant's appetizer recipe?

In a certain recipe contest, each contestant submits two recipes, one for an appetizer and one for a main dish. Together the two recipes must include exactly seven flavorings—fenugreek, ginger, lemongrass, nutmeg, paprika, saffron, and turmeric—with no flavoring included in more than one of the two recipes. Each contestant's recipes must satisfy the following conditions: The appetizer recipe includes at most three of the flavorings. Fenugreek is not included in the same recipe as nutmeg. Saffron is not included in the same recipe as turmeric. Ginger is included in the same recipe as nutmeg.

If a contestant includes lemongrass in the same recipe as paprika, which one of the following is a flavoring that must be included in the contestant's main-dish recipe?

In a certain recipe contest, each contestant submits two recipes, one for an appetizer and one for a main dish. Together the two recipes must include exactly seven flavorings—fenugreek, ginger, lemongrass, nutmeg, paprika, saffron, and turmeric—with no flavoring included in more than one of the two recipes. Each contestant's recipes must satisfy the following conditions: The appetizer recipe includes at most three of the flavorings. Fenugreek is not included in the same recipe as nutmeg. Saffron is not included in the same recipe as turmeric. Ginger is included in the same recipe as nutmeg.

If the condition that requires ginger to be included in the same recipe as nutmeg is suspended but all of the other original conditions remain in effect, then which one of the following could be a list of all of the flavorings included in one contestant's main-dish recipe?

Seven singers—Jamie, Ken, Lalitha, Maya, Norton, Olive, and Patrick—will be scheduled to perform in the finals of a singing competition. During the evening of the competition, each singer, performing alone, will give exactly one performance. The schedule for the evening must conform to the following requirements: Jamie performs immediately after Ken. Patrick performs at some time after Maya. Lalitha performs third only if Norton performs fifth. If Patrick does not perform second, he performs fifth.

Which one of the following is an acceptable schedule for the evening's performers, from first through seventh?

Seven singers—Jamie, Ken, Lalitha, Maya, Norton, Olive, and Patrick—will be scheduled to perform in the finals of a singing competition. During the evening of the competition, each singer, performing alone, will give exactly one performance. The schedule for the evening must conform to the following requirements: Jamie performs immediately after Ken. Patrick performs at some time after Maya. Lalitha performs third only if Norton performs fifth. If Patrick does not perform second, he performs fifth.

If Lalitha is scheduled for the third performance, which one of the following must be scheduled for the sixth performance?

Seven singers—Jamie, Ken, Lalitha, Maya, Norton, Olive, and Patrick—will be scheduled to perform in the finals of a singing competition. During the evening of the competition, each singer, performing alone, will give exactly one performance. The schedule for the evening must conform to the following requirements: Jamie performs immediately after Ken. Patrick performs at some time after Maya. Lalitha performs third only if Norton performs fifth. If Patrick does not perform second, he performs fifth.

If Norton is scheduled for the fifth performance, which one of the following could be true?

Seven singers—Jamie, Ken, Lalitha, Maya, Norton, Olive, and Patrick—will be scheduled to perform in the finals of a singing competition. During the evening of the competition, each singer, performing alone, will give exactly one performance. The schedule for the evening must conform to the following requirements: Jamie performs immediately after Ken. Patrick performs at some time after Maya. Lalitha performs third only if Norton performs fifth. If Patrick does not perform second, he performs fifth.

If Maya is scheduled for the second performance, which one of the following could be true?

Seven singers—Jamie, Ken, Lalitha, Maya, Norton, Olive, and Patrick—will be scheduled to perform in the finals of a singing competition. During the evening of the competition, each singer, performing alone, will give exactly one performance. The schedule for the evening must conform to the following requirements: Jamie performs immediately after Ken. Patrick performs at some time after Maya. Lalitha performs third only if Norton performs fifth. If Patrick does not perform second, he performs fifth.

If Jamie's performance is scheduled to be immediately before Lalitha's performance, Jamie's performance CANNOT be scheduled to be

At a small press, six textbooks, three introductory—F, G, and H—and three advanced—X, Y, and Z—will each be evaluated once by the editor, Juarez, and once by the publisher, Rosenberg, during six consecutive weeks—week 1 through week 6. Each evaluator evaluates exactly one textbook per week. No textbook will be evaluated by Juarez and Rosenberg during the same week. The following additional constraints apply: Rosenberg cannot evaluate any introductory textbook until Juarez has evaluated that textbook. Juarez cannot evaluate any advanced textbook until Rosenberg has evaluated that textbook. Rosenberg cannot evaluate any two introductory textbooks consecutively. Juarez must evaluate X during week 4.

Which one of the following is an acceptable evaluation schedule, with the textbooks listed in order of evaluation from week 1 through week 6?

At a small press, six textbooks, three introductory—F, G, and H—and three advanced—X, Y, and Z—will each be evaluated once by the editor, Juarez, and once by the publisher, Rosenberg, during six consecutive weeks—week 1 through week 6. Each evaluator evaluates exactly one textbook per week. No textbook will be evaluated by Juarez and Rosenberg during the same week. The following additional constraints apply: Rosenberg cannot evaluate any introductory textbook until Juarez has evaluated that textbook. Juarez cannot evaluate any advanced textbook until Rosenberg has evaluated that textbook. Rosenberg cannot evaluate any two introductory textbooks consecutively. Juarez must evaluate X during week 4.

If Juarez evaluates H during week 3 and Rosenberg evaluates G during week 6, which one of the following must be true?

At a small press, six textbooks, three introductory—F, G, and H—and three advanced—X, Y, and Z—will each be evaluated once by the editor, Juarez, and once by the publisher, Rosenberg, during six consecutive weeks—week 1 through week 6. Each evaluator evaluates exactly one textbook per week. No textbook will be evaluated by Juarez and Rosenberg during the same week. The following additional constraints apply: Rosenberg cannot evaluate any introductory textbook until Juarez has evaluated that textbook. Juarez cannot evaluate any advanced textbook until Rosenberg has evaluated that textbook. Rosenberg cannot evaluate any two introductory textbooks consecutively. Juarez must evaluate X during week 4.

If Juarez evaluates Z during week 2, then Rosenberg must evaluate which one of the following textbooks during week 5?

At a small press, six textbooks, three introductory—F, G, and H—and three advanced—X, Y, and Z—will each be evaluated once by the editor, Juarez, and once by the publisher, Rosenberg, during six consecutive weeks—week 1 through week 6. Each evaluator evaluates exactly one textbook per week. No textbook will be evaluated by Juarez and Rosenberg during the same week. The following additional constraints apply: Rosenberg cannot evaluate any introductory textbook until Juarez has evaluated that textbook. Juarez cannot evaluate any advanced textbook until Rosenberg has evaluated that textbook. Rosenberg cannot evaluate any two introductory textbooks consecutively. Juarez must evaluate X during week 4.

Which one of the following must be true?

At a small press, six textbooks, three introductory—F, G, and H—and three advanced—X, Y, and Z—will each be evaluated once by the editor, Juarez, and once by the publisher, Rosenberg, during six consecutive weeks—week 1 through week 6. Each evaluator evaluates exactly one textbook per week. No textbook will be evaluated by Juarez and Rosenberg during the same week. The following additional constraints apply: Rosenberg cannot evaluate any introductory textbook until Juarez has evaluated that textbook. Juarez cannot evaluate any advanced textbook until Rosenberg has evaluated that textbook. Rosenberg cannot evaluate any two introductory textbooks consecutively. Juarez must evaluate X during week 4.

If Rosenberg evaluates X during week 1 and F during week 2, which one of the following could be true?

At a small press, six textbooks, three introductory—F, G, and H—and three advanced—X, Y, and Z—will each be evaluated once by the editor, Juarez, and once by the publisher, Rosenberg, during six consecutive weeks—week 1 through week 6. Each evaluator evaluates exactly one textbook per week. No textbook will be evaluated by Juarez and Rosenberg during the same week. The following additional constraints apply: Rosenberg cannot evaluate any introductory textbook until Juarez has evaluated that textbook. Juarez cannot evaluate any advanced textbook until Rosenberg has evaluated that textbook. Rosenberg cannot evaluate any two introductory textbooks consecutively. Juarez must evaluate X during week 4.

Which one of the following is a complete and accurate list of those weeks during which Juarez must evaluate an introductory textbook?

At a small press, six textbooks, three introductory—F, G, and H—and three advanced—X, Y, and Z—will each be evaluated once by the editor, Juarez, and once by the publisher, Rosenberg, during six consecutive weeks—week 1 through week 6. Each evaluator evaluates exactly one textbook per week. No textbook will be evaluated by Juarez and Rosenberg during the same week. The following additional constraints apply: Rosenberg cannot evaluate any introductory textbook until Juarez has evaluated that textbook. Juarez cannot evaluate any advanced textbook until Rosenberg has evaluated that textbook. Rosenberg cannot evaluate any two introductory textbooks consecutively. Juarez must evaluate X during week 4.

Which one of the following could be true?

Nine different treatments are available for a certain illness: three antibiotics—F, G, and H—three dietary regimens—M, N, and O—and three physical therapies—U, V, and W. For each case of the illness, a doctor will prescribe exactly five of the treatments, in accordance with the following conditions: If two of the antibiotics are prescribed, the remaining antibiotic cannot be prescribed. There must be exactly one dietary regimen prescribed. If O is not prescribed, F cannot be prescribed. If W is prescribed, F cannot be prescribed. G cannot be prescribed if both N and U are prescribed. V cannot be prescribed unless both H and M are prescribed.

Which one of the following could be the five treatments prescribed for a given case?

Nine different treatments are available for a certain illness: three antibiotics—F, G, and H—three dietary regimens—M, N, and O—and three physical therapies—U, V, and W. For each case of the illness, a doctor will prescribe exactly five of the treatments, in accordance with the following conditions: If two of the antibiotics are prescribed, the remaining antibiotic cannot be prescribed. There must be exactly one dietary regimen prescribed. If O is not prescribed, F cannot be prescribed. If W is prescribed, F cannot be prescribed. G cannot be prescribed if both N and U are prescribed. V cannot be prescribed unless both H and M are prescribed.

Which one of the following could be the antibiotics and physical therapies prescribed for a given case?

Nine different treatments are available for a certain illness: three antibiotics—F, G, and H—three dietary regimens—M, N, and O—and three physical therapies—U, V, and W. For each case of the illness, a doctor will prescribe exactly five of the treatments, in accordance with the following conditions: If two of the antibiotics are prescribed, the remaining antibiotic cannot be prescribed. There must be exactly one dietary regimen prescribed. If O is not prescribed, F cannot be prescribed. If W is prescribed, F cannot be prescribed. G cannot be prescribed if both N and U are prescribed. V cannot be prescribed unless both H and M are prescribed.

If O is prescribed for a given case, which one of the following is a pair of treatments both of which must also be prescribed for that case?

Nine different treatments are available for a certain illness: three antibiotics—F, G, and H—three dietary regimens—M, N, and O—and three physical therapies—U, V, and W. For each case of the illness, a doctor will prescribe exactly five of the treatments, in accordance with the following conditions: If two of the antibiotics are prescribed, the remaining antibiotic cannot be prescribed. There must be exactly one dietary regimen prescribed. If O is not prescribed, F cannot be prescribed. If W is prescribed, F cannot be prescribed. G cannot be prescribed if both N and U are prescribed. V cannot be prescribed unless both H and M are prescribed.

If G is prescribed for a given case, which one of the following is a pair of treatments both of which could also be prescribed for that case?

Nine different treatments are available for a certain illness: three antibiotics—F, G, and H—three dietary regimens—M, N, and O—and three physical therapies—U, V, and W. For each case of the illness, a doctor will prescribe exactly five of the treatments, in accordance with the following conditions: If two of the antibiotics are prescribed, the remaining antibiotic cannot be prescribed. There must be exactly one dietary regimen prescribed. If O is not prescribed, F cannot be prescribed. If W is prescribed, F cannot be prescribed. G cannot be prescribed if both N and U are prescribed. V cannot be prescribed unless both H and M are prescribed.

Which one of the following is a list of three treatments that could be prescribed together for a given case?

Nine different treatments are available for a certain illness: three antibiotics—F, G, and H—three dietary regimens—M, N, and O—and three physical therapies—U, V, and W. For each case of the illness, a doctor will prescribe exactly five of the treatments, in accordance with the following conditions: If two of the antibiotics are prescribed, the remaining antibiotic cannot be prescribed. There must be exactly one dietary regimen prescribed. If O is not prescribed, F cannot be prescribed. If W is prescribed, F cannot be prescribed. G cannot be prescribed if both N and U are prescribed. V cannot be prescribed unless both H and M are prescribed.

Which one of the following treatments CANNOT be prescribed for any case?

The members of two committees, a planting committee and a trails committee, are to be selected from among seven volunteers—F, G, H, J, K, L, and M. The following conditions govern the composition of the committees: Each committee must have at least three members. F cannot be on the same committee as K. If K is on a committee, J must also be on that committee. M must be on at least one of the committees. The two committees must have at least one member in common.

Which one of the following represents an acceptable selection of volunteers for the committees?

The members of two committees, a planting committee and a trails committee, are to be selected from among seven volunteers—F, G, H, J, K, L, and M. The following conditions govern the composition of the committees: Each committee must have at least three members. F cannot be on the same committee as K. If K is on a committee, J must also be on that committee. M must be on at least one of the committees. The two committees must have at least one member in common.

If the planting committee consists of F, H, L, and M, and if the trails committee consists of G, H, and J, then K could replace which one of the following committee members on a committee without violating any of the conditions governing the composition of the committees?

The members of two committees, a planting committee and a trails committee, are to be selected from among seven volunteers—F, G, H, J, K, L, and M. The following conditions govern the composition of the committees: Each committee must have at least three members. F cannot be on the same committee as K. If K is on a committee, J must also be on that committee. M must be on at least one of the committees. The two committees must have at least one member in common.

If the only members of the planting committee are G, H, and L and if the two committees are to have as many members in common as the conditions allow, then which one of the following must be true?

The members of two committees, a planting committee and a trails committee, are to be selected from among seven volunteers—F, G, H, J, K, L, and M. The following conditions govern the composition of the committees: Each committee must have at least three members. F cannot be on the same committee as K. If K is on a committee, J must also be on that committee. M must be on at least one of the committees. The two committees must have at least one member in common.

If K is on both committees and L is also on both committees and if the planting committee has exactly three members, then which one of the following must be true?

The members of two committees, a planting committee and a trails committee, are to be selected from among seven volunteers—F, G, H, J, K, L, and M. The following conditions govern the composition of the committees: Each committee must have at least three members. F cannot be on the same committee as K. If K is on a committee, J must also be on that committee. M must be on at least one of the committees. The two committees must have at least one member in common.

The largest number of members that the planting committee and the trails committee could have in common is

Exactly six tourists—Harry, Irene, Klaus, Laura, Michael, Norma—are to be assigned to four guides: Valois, Xerxes, Yossarian, Zalamea. Each tourist is assigned to exactly one guide, with at least one tourist assigned to each guide. Valois speaks only French. Xerxes speaks only Turkish and Spanish. Yossarian speaks only French and Turkish. Zalamea speaks only Spanish and Russian. Each tourist speaks exactly one of the languages spoken by his or her guide and speaks no other language. The following rules govern the assignment of the tourists to the guides: At least Harry and Irene are assigned to Yossarian. At least Laura is assigned to Zalamea. If Klaus is assigned to Xerxes, then Michael speaks French.

Each of the following could be true EXCEPT:

Exactly six tourists—Harry, Irene, Klaus, Laura, Michael, Norma—are to be assigned to four guides: Valois, Xerxes, Yossarian, Zalamea. Each tourist is assigned to exactly one guide, with at least one tourist assigned to each guide. Valois speaks only French. Xerxes speaks only Turkish and Spanish. Yossarian speaks only French and Turkish. Zalamea speaks only Spanish and Russian. Each tourist speaks exactly one of the languages spoken by his or her guide and speaks no other language. The following rules govern the assignment of the tourists to the guides: At least Harry and Irene are assigned to Yossarian. At least Laura is assigned to Zalamea. If Klaus is assigned to Xerxes, then Michael speaks French.

Which one of the following must be true?

Exactly six tourists—Harry, Irene, Klaus, Laura, Michael, Norma—are to be assigned to four guides: Valois, Xerxes, Yossarian, Zalamea. Each tourist is assigned to exactly one guide, with at least one tourist assigned to each guide. Valois speaks only French. Xerxes speaks only Turkish and Spanish. Yossarian speaks only French and Turkish. Zalamea speaks only Spanish and Russian. Each tourist speaks exactly one of the languages spoken by his or her guide and speaks no other language. The following rules govern the assignment of the tourists to the guides: At least Harry and Irene are assigned to Yossarian. At least Laura is assigned to Zalamea. If Klaus is assigned to Xerxes, then Michael speaks French.

Each of the following could be true of the assignment of tourists to guides EXCEPT:

Exactly six tourists—Harry, Irene, Klaus, Laura, Michael, Norma—are to be assigned to four guides: Valois, Xerxes, Yossarian, Zalamea. Each tourist is assigned to exactly one guide, with at least one tourist assigned to each guide. Valois speaks only French. Xerxes speaks only Turkish and Spanish. Yossarian speaks only French and Turkish. Zalamea speaks only Spanish and Russian. Each tourist speaks exactly one of the languages spoken by his or her guide and speaks no other language. The following rules govern the assignment of the tourists to the guides: At least Harry and Irene are assigned to Yossarian. At least Laura is assigned to Zalamea. If Klaus is assigned to Xerxes, then Michael speaks French.

If Klaus and Laura speak the same language as each other, then which one of the following must be true?

Exactly six tourists—Harry, Irene, Klaus, Laura, Michael, Norma—are to be assigned to four guides: Valois, Xerxes, Yossarian, Zalamea. Each tourist is assigned to exactly one guide, with at least one tourist assigned to each guide. Valois speaks only French. Xerxes speaks only Turkish and Spanish. Yossarian speaks only French and Turkish. Zalamea speaks only Spanish and Russian. Each tourist speaks exactly one of the languages spoken by his or her guide and speaks no other language. The following rules govern the assignment of the tourists to the guides: At least Harry and Irene are assigned to Yossarian. At least Laura is assigned to Zalamea. If Klaus is assigned to Xerxes, then Michael speaks French.

If Laura and Norma speak the same language as each other, then the maximum number of the tourists who could speak Turkish is

Exactly six tourists—Harry, Irene, Klaus, Laura, Michael, Norma—are to be assigned to four guides: Valois, Xerxes, Yossarian, Zalamea. Each tourist is assigned to exactly one guide, with at least one tourist assigned to each guide. Valois speaks only French. Xerxes speaks only Turkish and Spanish. Yossarian speaks only French and Turkish. Zalamea speaks only Spanish and Russian. Each tourist speaks exactly one of the languages spoken by his or her guide and speaks no other language. The following rules govern the assignment of the tourists to the guides: At least Harry and Irene are assigned to Yossarian. At least Laura is assigned to Zalamea. If Klaus is assigned to Xerxes, then Michael speaks French.

If exactly two tourists are assigned to Xerxes, then which one of the following could be true?

Exactly six tourists—Harry, Irene, Klaus, Laura, Michael, Norma—are to be assigned to four guides: Valois, Xerxes, Yossarian, Zalamea. Each tourist is assigned to exactly one guide, with at least one tourist assigned to each guide. Valois speaks only French. Xerxes speaks only Turkish and Spanish. Yossarian speaks only French and Turkish. Zalamea speaks only Spanish and Russian. Each tourist speaks exactly one of the languages spoken by his or her guide and speaks no other language. The following rules govern the assignment of the tourists to the guides: At least Harry and Irene are assigned to Yossarian. At least Laura is assigned to Zalamea. If Klaus is assigned to Xerxes, then Michael speaks French.

If Harry, Irene, Michael, and Norma all speak the same language as each other, then which one of the following could be true?

Each of six people—Kim, Lina, Maricella, Oliver, Paulo, and Shigeru—plays exactly one of two sports—golf, and tennis. If a sport is played by more than one of the six people, then the people who play that sport are ranked in order of ability from highest to lowest, with no ties. The following conditions must apply: Oliver plays tennis. Lina plays golf. There is no golf player ranked higher than Lina. If Maricella plays golf, then Paulo and Shigeru play golf, Paulo ranking lower than Maricella but higher than Shigeru. If Maricella plays tennis, then Shigeru plays tennis, Shigeru ranking lower than Oliver but higher than Maricella. If Paulo plays tennis, then Kim plays tennis, Oliver ranking lower than Kim but higher than Paulo.

Which one of the following could be true?

Each of six people—Kim, Lina, Maricella, Oliver, Paulo, and Shigeru—plays exactly one of two sports—golf, and tennis. If a sport is played by more than one of the six people, then the people who play that sport are ranked in order of ability from highest to lowest, with no ties. The following conditions must apply: Oliver plays tennis. Lina plays golf. There is no golf player ranked higher than Lina. If Maricella plays golf, then Paulo and Shigeru play golf, Paulo ranking lower than Maricella but higher than Shigeru. If Maricella plays tennis, then Shigeru plays tennis, Shigeru ranking lower than Oliver but higher than Maricella. If Paulo plays tennis, then Kim plays tennis, Oliver ranking lower than Kim but higher than Paulo.

Each of the following could be the lowest-ranking tennis player EXCEPT:

Each of six people—Kim, Lina, Maricella, Oliver, Paulo, and Shigeru—plays exactly one of two sports—golf, and tennis. If a sport is played by more than one of the six people, then the people who play that sport are ranked in order of ability from highest to lowest, with no ties. The following conditions must apply: Oliver plays tennis. Lina plays golf. There is no golf player ranked higher than Lina. If Maricella plays golf, then Paulo and Shigeru play golf, Paulo ranking lower than Maricella but higher than Shigeru. If Maricella plays tennis, then Shigeru plays tennis, Shigeru ranking lower than Oliver but higher than Maricella. If Paulo plays tennis, then Kim plays tennis, Oliver ranking lower than Kim but higher than Paulo.

Which one of the following could be a complete and accurate list of the people who play tennis, listed in order of rank from highest to lowest?

Each of six people—Kim, Lina, Maricella, Oliver, Paulo, and Shigeru—plays exactly one of two sports—golf, and tennis. If a sport is played by more than one of the six people, then the people who play that sport are ranked in order of ability from highest to lowest, with no ties. The following conditions must apply: Oliver plays tennis. Lina plays golf. There is no golf player ranked higher than Lina. If Maricella plays golf, then Paulo and Shigeru play golf, Paulo ranking lower than Maricella but higher than Shigeru. If Maricella plays tennis, then Shigeru plays tennis, Shigeru ranking lower than Oliver but higher than Maricella. If Paulo plays tennis, then Kim plays tennis, Oliver ranking lower than Kim but higher than Paulo.

If Shigeru plays golf, then each of the following are pairs of people who must play the same sport as each other EXCEPT:

Each of six people—Kim, Lina, Maricella, Oliver, Paulo, and Shigeru—plays exactly one of two sports—golf, and tennis. If a sport is played by more than one of the six people, then the people who play that sport are ranked in order of ability from highest to lowest, with no ties. The following conditions must apply: Oliver plays tennis. Lina plays golf. There is no golf player ranked higher than Lina. If Maricella plays golf, then Paulo and Shigeru play golf, Paulo ranking lower than Maricella but higher than Shigeru. If Maricella plays tennis, then Shigeru plays tennis, Shigeru ranking lower than Oliver but higher than Maricella. If Paulo plays tennis, then Kim plays tennis, Oliver ranking lower than Kim but higher than Paulo.

If Oliver is the highest-ranking tennis player, which one of the following must be true?

Each of six people—Kim, Lina, Maricella, Oliver, Paulo, and Shigeru—plays exactly one of two sports—golf, and tennis. If a sport is played by more than one of the six people, then the people who play that sport are ranked in order of ability from highest to lowest, with no ties. The following conditions must apply: Oliver plays tennis. Lina plays golf. There is no golf player ranked higher than Lina. If Maricella plays golf, then Paulo and Shigeru play golf, Paulo ranking lower than Maricella but higher than Shigeru. If Maricella plays tennis, then Shigeru plays tennis, Shigeru ranking lower than Oliver but higher than Maricella. If Paulo plays tennis, then Kim plays tennis, Oliver ranking lower than Kim but higher than Paulo.

Suppose that the condition is added that Shigeru and Paulo do not play the same sport as each other. If all the other conditions remain in effect, then each of the following could be true EXCEPT:

A disc jockey will play a sequence consisting of exactly seven different songs: three ballads—F, G, and H—and four dance tunes—R, S, V, and X. The following conditions must be met: No dance tune can be played immediately after another dance tune. H must be played earlier in the sequence than V. V and S must be separated from each other by exactly one song. S must be played immediately before or immediately after F. F must be played immediately after R, unless G is played earlier than R.

Which one of the following could be the order of the songs in the sequence?

A disc jockey will play a sequence consisting of exactly seven different songs: three ballads—F, G, and H—and four dance tunes—R, S, V, and X. The following conditions must be met: No dance tune can be played immediately after another dance tune. H must be played earlier in the sequence than V. V and S must be separated from each other by exactly one song. S must be played immediately before or immediately after F. F must be played immediately after R, unless G is played earlier than R.

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

A disc jockey will play a sequence consisting of exactly seven different songs: three ballads—F, G, and H—and four dance tunes—R, S, V, and X. The following conditions must be met: No dance tune can be played immediately after another dance tune. H must be played earlier in the sequence than V. V and S must be separated from each other by exactly one song. S must be played immediately before or immediately after F. F must be played immediately after R, unless G is played earlier than R.

Which one of the following could be the fourth song in the sequence?

A disc jockey will play a sequence consisting of exactly seven different songs: three ballads—F, G, and H—and four dance tunes—R, S, V, and X. The following conditions must be met: No dance tune can be played immediately after another dance tune. H must be played earlier in the sequence than V. V and S must be separated from each other by exactly one song. S must be played immediately before or immediately after F. F must be played immediately after R, unless G is played earlier than R.

Which one of the following could be the first song in the sequence?

A disc jockey will play a sequence consisting of exactly seven different songs: three ballads—F, G, and H—and four dance tunes—R, S, V, and X. The following conditions must be met: No dance tune can be played immediately after another dance tune. H must be played earlier in the sequence than V. V and S must be separated from each other by exactly one song. S must be played immediately before or immediately after F. F must be played immediately after R, unless G is played earlier than R.

If the third song in the sequence is S, which one of the following must be the sixth song?

A disc jockey will play a sequence consisting of exactly seven different songs: three ballads—F, G, and H—and four dance tunes—R, S, V, and X. The following conditions must be met: No dance tune can be played immediately after another dance tune. H must be played earlier in the sequence than V. V and S must be separated from each other by exactly one song. S must be played immediately before or immediately after F. F must be played immediately after R, unless G is played earlier than R.

If the seventh song in the sequence is R, which one of the following could be the fifth song?

Eight physics students—four majors: Frank, Gwen, Henry, and Joan; and four nonmajors: Victor, Wanda, Xavier, and Yvette—are being assigned to four laboratory benches, numbered 1 through 4. Each student is assigned to exactly one bench, and exactly two students are assigned to each bench. Assignments of students to benches must conform to the following conditions: Exactly one major is assigned to each bench. Frank and Joan are assigned to consecutively numbered benches, with Frank assigned to the lower-numbered bench. Frank is assigned to the same bench as Victor. Gwen is not assigned to the same bench as Wanda.

Which one of the following could be the assignment of students to benches?

Eight physics students—four majors: Frank, Gwen, Henry, and Joan; and four nonmajors: Victor, Wanda, Xavier, and Yvette—are being assigned to four laboratory benches, numbered 1 through 4. Each student is assigned to exactly one bench, and exactly two students are assigned to each bench. Assignments of students to benches must conform to the following conditions: Exactly one major is assigned to each bench. Frank and Joan are assigned to consecutively numbered benches, with Frank assigned to the lower-numbered bench. Frank is assigned to the same bench as Victor. Gwen is not assigned to the same bench as Wanda.

If Victor is assigned to bench 2 and Wanda is assigned to bench 4, which one of the following must be true?

Eight physics students—four majors: Frank, Gwen, Henry, and Joan; and four nonmajors: Victor, Wanda, Xavier, and Yvette—are being assigned to four laboratory benches, numbered 1 through 4. Each student is assigned to exactly one bench, and exactly two students are assigned to each bench. Assignments of students to benches must conform to the following conditions: Exactly one major is assigned to each bench. Frank and Joan are assigned to consecutively numbered benches, with Frank assigned to the lower-numbered bench. Frank is assigned to the same bench as Victor. Gwen is not assigned to the same bench as Wanda.

If Gwen and Henry are not assigned to consecutively numbered benches, which one of the following must be true?

Eight physics students—four majors: Frank, Gwen, Henry, and Joan; and four nonmajors: Victor, Wanda, Xavier, and Yvette—are being assigned to four laboratory benches, numbered 1 through 4. Each student is assigned to exactly one bench, and exactly two students are assigned to each bench. Assignments of students to benches must conform to the following conditions: Exactly one major is assigned to each bench. Frank and Joan are assigned to consecutively numbered benches, with Frank assigned to the lower-numbered bench. Frank is assigned to the same bench as Victor. Gwen is not assigned to the same bench as Wanda.

If Henry and Yvette are both assigned to bench 1, which one of the following could be true?

Eight physics students—four majors: Frank, Gwen, Henry, and Joan; and four nonmajors: Victor, Wanda, Xavier, and Yvette—are being assigned to four laboratory benches, numbered 1 through 4. Each student is assigned to exactly one bench, and exactly two students are assigned to each bench. Assignments of students to benches must conform to the following conditions: Exactly one major is assigned to each bench. Frank and Joan are assigned to consecutively numbered benches, with Frank assigned to the lower-numbered bench. Frank is assigned to the same bench as Victor. Gwen is not assigned to the same bench as Wanda.

If Gwen is assigned to bench 4 and Xavier is assigned to bench 3, then any one of the following could be true EXCEPT:

Eight physics students—four majors: Frank, Gwen, Henry, and Joan; and four nonmajors: Victor, Wanda, Xavier, and Yvette—are being assigned to four laboratory benches, numbered 1 through 4. Each student is assigned to exactly one bench, and exactly two students are assigned to each bench. Assignments of students to benches must conform to the following conditions: Exactly one major is assigned to each bench. Frank and Joan are assigned to consecutively numbered benches, with Frank assigned to the lower-numbered bench. Frank is assigned to the same bench as Victor. Gwen is not assigned to the same bench as Wanda.

If Wanda is assigned to a lower-numbered bench than is Joan, then Henry must be assigned to a

Eight physics students—four majors: Frank, Gwen, Henry, and Joan; and four nonmajors: Victor, Wanda, Xavier, and Yvette—are being assigned to four laboratory benches, numbered 1 through 4. Each student is assigned to exactly one bench, and exactly two students are assigned to each bench. Assignments of students to benches must conform to the following conditions: Exactly one major is assigned to each bench. Frank and Joan are assigned to consecutively numbered benches, with Frank assigned to the lower-numbered bench. Frank is assigned to the same bench as Victor. Gwen is not assigned to the same bench as Wanda.

Which one of the following could be the assignments for bench 2 and bench 4?

A messenger will deliver exactly seven packages—L, M, N, O, P, S, and T—one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions: P is delivered either first or seventh. The messenger delivers N at some time after delivering L. The messenger delivers T at some time after delivering M. The messenger delivers exactly one package between delivering L and delivering O, whether or not L is delivered before O. The messenger delivers exactly one package between delivering M and delivering P, whether or not M is delivered before P.

Which one of the following is an order in which the messenger could make the deliveries, from first to seventh?

A messenger will deliver exactly seven packages—L, M, N, O, P, S, and T—one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions: P is delivered either first or seventh. The messenger delivers N at some time after delivering L. The messenger delivers T at some time after delivering M. The messenger delivers exactly one package between delivering L and delivering O, whether or not L is delivered before O. The messenger delivers exactly one package between delivering M and delivering P, whether or not M is delivered before P.

Which one of the following could be true?

A messenger will deliver exactly seven packages—L, M, N, O, P, S, and T—one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions: P is delivered either first or seventh. The messenger delivers N at some time after delivering L. The messenger delivers T at some time after delivering M. The messenger delivers exactly one package between delivering L and delivering O, whether or not L is delivered before O. The messenger delivers exactly one package between delivering M and delivering P, whether or not M is delivered before P.

If N is delivered fourth, which one of the following could be true?

A messenger will deliver exactly seven packages—L, M, N, O, P, S, and T—one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions: P is delivered either first or seventh. The messenger delivers N at some time after delivering L. The messenger delivers T at some time after delivering M. The messenger delivers exactly one package between delivering L and delivering O, whether or not L is delivered before O. The messenger delivers exactly one package between delivering M and delivering P, whether or not M is delivered before P.

If T is delivered fourth, the seventh package delivered must be

A messenger will deliver exactly seven packages—L, M, N, O, P, S, and T—one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions: P is delivered either first or seventh. The messenger delivers N at some time after delivering L. The messenger delivers T at some time after delivering M. The messenger delivers exactly one package between delivering L and delivering O, whether or not L is delivered before O. The messenger delivers exactly one package between delivering M and delivering P, whether or not M is delivered before P.

If the messenger delivers M at some time after delivering O, the fifth package delivered could be any one of the following EXCEPT:

Each of exactly five persons—Nguyen, Olson, Pike, Tyner, and Valdez—participates in exactly one of three activities: going to a movie, going to a soccer game, or going to a restaurant. The following conditions must apply. Nguyen and Olson do not participate in the same activity as each other, nor does either one of them participate in the same activity as Pike. Exactly two persons go to a soccer game. Tyner and Pike do not participate in the same activity as each other. If Nguyen or Valdez goes to a movie, they both go to a movie.

Which one of the following could be an accurate list of the activities participated in by Nguyen, Olson, Pike, Tyner, and Valdez, respectively?

Each of exactly five persons—Nguyen, Olson, Pike, Tyner, and Valdez—participates in exactly one of three activities: going to a movie, going to a soccer game, or going to a restaurant. The following conditions must apply. Nguyen and Olson do not participate in the same activity as each other, nor does either one of them participate in the same activity as Pike. Exactly two persons go to a soccer game. Tyner and Pike do not participate in the same activity as each other. If Nguyen or Valdez goes to a movie, they both go to a movie.

If Valdez goes to a soccer game, then each of the following could be true EXCEPT:

Each of exactly five persons—Nguyen, Olson, Pike, Tyner, and Valdez—participates in exactly one of three activities: going to a movie, going to a soccer game, or going to a restaurant. The following conditions must apply. Nguyen and Olson do not participate in the same activity as each other, nor does either one of them participate in the same activity as Pike. Exactly two persons go to a soccer game. Tyner and Pike do not participate in the same activity as each other. If Nguyen or Valdez goes to a movie, they both go to a movie.

Which one of the following is a pair of persons who could go to a movie together?

Each of exactly five persons—Nguyen, Olson, Pike, Tyner, and Valdez—participates in exactly one of three activities: going to a movie, going to a soccer game, or going to a restaurant. The following conditions must apply. Nguyen and Olson do not participate in the same activity as each other, nor does either one of them participate in the same activity as Pike. Exactly two persons go to a soccer game. Tyner and Pike do not participate in the same activity as each other. If Nguyen or Valdez goes to a movie, they both go to a movie.

Each of the following statements must be false EXCEPT:

Each of exactly five persons—Nguyen, Olson, Pike, Tyner, and Valdez—participates in exactly one of three activities: going to a movie, going to a soccer game, or going to a restaurant. The following conditions must apply. Nguyen and Olson do not participate in the same activity as each other, nor does either one of them participate in the same activity as Pike. Exactly two persons go to a soccer game. Tyner and Pike do not participate in the same activity as each other. If Nguyen or Valdez goes to a movie, they both go to a movie.

If Nguyen goes to a soccer game, then which one of the following is a complete and accurate list of the persons any one of whom could go to a movie?

Each of exactly five persons—Nguyen, Olson, Pike, Tyner, and Valdez—participates in exactly one of three activities: going to a movie, going to a soccer game, or going to a restaurant. The following conditions must apply. Nguyen and Olson do not participate in the same activity as each other, nor does either one of them participate in the same activity as Pike. Exactly two persons go to a soccer game. Tyner and Pike do not participate in the same activity as each other. If Nguyen or Valdez goes to a movie, they both go to a movie.

If the condition that exactly two persons go to a soccer game is changed to require that exactly three persons go to a soccer game, but all other conditions remain the same, then which one of the following persons must participate in an activity other than going to a soccer game?

In each of two years exactly two of four lawmakers—Feld, Gibson, Hsu, and Ivins—and exactly two of three scientists—Vega, Young, and Zapora—will serve as members of a four-person panel. In each year, one of the members will be chairperson. The chairperson in the first year cannot serve on the panel in the second year. The chairperson in the second year must have served on the panel in the first year. Service on the panel must obey the following conditions: Gibson and Vega do not serve on the panel in the same year as each other. Hsu and Young do not serve on the panel in the same year as each other. Each year, either Ivins or Vega, but not both, serves on the panel.

Which one of the following could be the list of the people who serve on the panel in the first year?

In each of two years exactly two of four lawmakers—Feld, Gibson, Hsu, and Ivins—and exactly two of three scientists—Vega, Young, and Zapora—will serve as members of a four-person panel. In each year, one of the members will be chairperson. The chairperson in the first year cannot serve on the panel in the second year. The chairperson in the second year must have served on the panel in the first year. Service on the panel must obey the following conditions: Gibson and Vega do not serve on the panel in the same year as each other. Hsu and Young do not serve on the panel in the same year as each other. Each year, either Ivins or Vega, but not both, serves on the panel.

If Vega is the chairperson in the first year, which one of the following is a pair of people who must serve on the panel in the second year?

In each of two years exactly two of four lawmakers—Feld, Gibson, Hsu, and Ivins—and exactly two of three scientists—Vega, Young, and Zapora—will serve as members of a four-person panel. In each year, one of the members will be chairperson. The chairperson in the first year cannot serve on the panel in the second year. The chairperson in the second year must have served on the panel in the first year. Service on the panel must obey the following conditions: Gibson and Vega do not serve on the panel in the same year as each other. Hsu and Young do not serve on the panel in the same year as each other. Each year, either Ivins or Vega, but not both, serves on the panel.

If Hsu is the chairperson in the first year, which one of the following could be the chairperson in the second year?

In each of two years exactly two of four lawmakers—Feld, Gibson, Hsu, and Ivins—and exactly two of three scientists—Vega, Young, and Zapora—will serve as members of a four-person panel. In each year, one of the members will be chairperson. The chairperson in the first year cannot serve on the panel in the second year. The chairperson in the second year must have served on the panel in the first year. Service on the panel must obey the following conditions: Gibson and Vega do not serve on the panel in the same year as each other. Hsu and Young do not serve on the panel in the same year as each other. Each year, either Ivins or Vega, but not both, serves on the panel.

IF Feld serves on the panel in a given year, any one of the following could serve on the panel that year EXCEPT:

In each of two years exactly two of four lawmakers—Feld, Gibson, Hsu, and Ivins—and exactly two of three scientists—Vega, Young, and Zapora—will serve as members of a four-person panel. In each year, one of the members will be chairperson. The chairperson in the first year cannot serve on the panel in the second year. The chairperson in the second year must have served on the panel in the first year. Service on the panel must obey the following conditions: Gibson and Vega do not serve on the panel in the same year as each other. Hsu and Young do not serve on the panel in the same year as each other. Each year, either Ivins or Vega, but not both, serves on the panel.

If Ivins is the chairperson in the first year, which one of the following could be the chairperson in the second year?

In each of two years exactly two of four lawmakers—Feld, Gibson, Hsu, and Ivins—and exactly two of three scientists—Vega, Young, and Zapora—will serve as members of a four-person panel. In each year, one of the members will be chairperson. The chairperson in the first year cannot serve on the panel in the second year. The chairperson in the second year must have served on the panel in the first year. Service on the panel must obey the following conditions: Gibson and Vega do not serve on the panel in the same year as each other. Hsu and Young do not serve on the panel in the same year as each other. Each year, either Ivins or Vega, but not both, serves on the panel.

Which one of the following must be true?

During a period of seven consecutive days—from day 1 through day 7—seven investors—Fennelly, Gupta, Hall, Jones, Knight, Lopez, and Moss—will each view a building site exactly once. Each day exactly one investor will view the site. The investors must view the site in accordance with the following conditions: Fennelly views the site on day 3 or else day 5. Lopez views the site on neither day 4 nor day 6. If Jones views the site on day 1, Hall views the site on day 2. If Knight views the site on day 4, Lopez views the site on day 5. Gupta views the site on the day after the day on which Hall views the site.

Which one of the following could be the order in which the investors view the site, from day 1 through day 7?

During a period of seven consecutive days—from day 1 through day 7—seven investors—Fennelly, Gupta, Hall, Jones, Knight, Lopez, and Moss—will each view a building site exactly once. Each day exactly one investor will view the site. The investors must view the site in accordance with the following conditions: Fennelly views the site on day 3 or else day 5. Lopez views the site on neither day 4 nor day 6. If Jones views the site on day 1, Hall views the site on day 2. If Knight views the site on day 4, Lopez views the site on day 5. Gupta views the site on the day after the day on which Hall views the site.

If Jones views the site on day 1, which one of the following investors must view the site on day 4?

During a period of seven consecutive days—from day 1 through day 7—seven investors—Fennelly, Gupta, Hall, Jones, Knight, Lopez, and Moss—will each view a building site exactly once. Each day exactly one investor will view the site. The investors must view the site in accordance with the following conditions: Fennelly views the site on day 3 or else day 5. Lopez views the site on neither day 4 nor day 6. If Jones views the site on day 1, Hall views the site on day 2. If Knight views the site on day 4, Lopez views the site on day 5. Gupta views the site on the day after the day on which Hall views the site.

If Knight views the site on day 4 and Moss views the site on some day after the day on which Jones views the site, which one of the following must be true?

During a period of seven consecutive days—from day 1 through day 7—seven investors—Fennelly, Gupta, Hall, Jones, Knight, Lopez, and Moss—will each view a building site exactly once. Each day exactly one investor will view the site. The investors must view the site in accordance with the following conditions: Fennelly views the site on day 3 or else day 5. Lopez views the site on neither day 4 nor day 6. If Jones views the site on day 1, Hall views the site on day 2. If Knight views the site on day 4, Lopez views the site on day 5. Gupta views the site on the day after the day on which Hall views the site.

If Hall views the site on day 2, which one of the following is a complete and accurate list of investors any one of whom could be the investor who views the site on day 4?

During a period of seven consecutive days—from day 1 through day 7—seven investors—Fennelly, Gupta, Hall, Jones, Knight, Lopez, and Moss—will each view a building site exactly once. Each day exactly one investor will view the site. The investors must view the site in accordance with the following conditions: Fennelly views the site on day 3 or else day 5. Lopez views the site on neither day 4 nor day 6. If Jones views the site on day 1, Hall views the site on day 2. If Knight views the site on day 4, Lopez views the site on day 5. Gupta views the site on the day after the day on which Hall views the site.

If Hall views the site on the day after the day Knight views the site and if Fennelly views the site on the day after the day Lopez views the site, then Jones must view the site on day

During a period of seven consecutive days—from day 1 through day 7—seven investors—Fennelly, Gupta, Hall, Jones, Knight, Lopez, and Moss—will each view a building site exactly once. Each day exactly one investor will view the site. The investors must view the site in accordance with the following conditions: Fennelly views the site on day 3 or else day 5. Lopez views the site on neither day 4 nor day 6. If Jones views the site on day 1, Hall views the site on day 2. If Knight views the site on day 4, Lopez views the site on day 5. Gupta views the site on the day after the day on which Hall views the site.

If the day on which Gupta views the site and the day on which Lopez views the site both come at some time before the day on which Fennelly views the site, which one of the following is an investor who could view the site on day 3?

A zoo's reptile house has a straight row of exactly five consecutive habitats—numbered 1 through 5 from left to right—for housing exactly seven reptiles—four snakes and three lizards. Five of the reptiles are female and two are male. The reptiles must be housed as follows: No habitat houses more than two reptiles. No habitat houses both a snake and a lizard. No female snake is housed in a habitat that is immediately next to a habitat housing a male lizard.

Which one of the following could be a complete and accurate matching of habitats to reptiles?

A zoo's reptile house has a straight row of exactly five consecutive habitats—numbered 1 through 5 from left to right—for housing exactly seven reptiles—four snakes and three lizards. Five of the reptiles are female and two are male. The reptiles must be housed as follows: No habitat houses more than two reptiles. No habitat houses both a snake and a lizard. No female snake is housed in a habitat that is immediately next to a habitat housing a male lizard.

If habitat 2 contains at least one female snake and habitat 4 contains two male lizards, then which one of the following could be true?

A zoo's reptile house has a straight row of exactly five consecutive habitats—numbered 1 through 5 from left to right—for housing exactly seven reptiles—four snakes and three lizards. Five of the reptiles are female and two are male. The reptiles must be housed as follows: No habitat houses more than two reptiles. No habitat houses both a snake and a lizard. No female snake is housed in a habitat that is immediately next to a habitat housing a male lizard.

Which one of the following must be true?

A zoo's reptile house has a straight row of exactly five consecutive habitats—numbered 1 through 5 from left to right—for housing exactly seven reptiles—four snakes and three lizards. Five of the reptiles are female and two are male. The reptiles must be housed as follows: No habitat houses more than two reptiles. No habitat houses both a snake and a lizard. No female snake is housed in a habitat that is immediately next to a habitat housing a male lizard.

Which one of the following CANNOT be the complete housing arrangement for habitats 1 and 2?

A zoo's reptile house has a straight row of exactly five consecutive habitats—numbered 1 through 5 from left to right—for housing exactly seven reptiles—four snakes and three lizards. Five of the reptiles are female and two are male. The reptiles must be housed as follows: No habitat houses more than two reptiles. No habitat houses both a snake and a lizard. No female snake is housed in a habitat that is immediately next to a habitat housing a male lizard.

If habitat 3 is empty, and no snake is housed in a habitat that is immediately next to a habitat containing a snake, then which one of the following could be false?

A zoo's reptile house has a straight row of exactly five consecutive habitats—numbered 1 through 5 from left to right—for housing exactly seven reptiles—four snakes and three lizards. Five of the reptiles are female and two are male. The reptiles must be housed as follows: No habitat houses more than two reptiles. No habitat houses both a snake and a lizard. No female snake is housed in a habitat that is immediately next to a habitat housing a male lizard.

If all snakes are female and each of the lizards has a habitat to itself, then which one of the following habitats CANNOT contain any snakes?

Exactly seven film buffs—Ginnie, Ian, Lianna, Marcos, Reveka, Viktor, and Yow—attend a showing of classic films. Three films are shown, one directed by Fellini, one by Hitchcock, and one by Kurosawa. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions must apply: Exactly twice as many of the film buffs see the Hitchcock film as see the Fellini film. Ginnie and Reveka do not see the same film as each other. Ian and Marcos do not see the same film as each other. Viktor and Yow see the same film as each other. Lianna sees the Hitchcock film. Ginnie sees either the Fellini film or the Kurosawa film.

Which one of the following could be an accurate matching of film buffs to films?

Exactly seven film buffs—Ginnie, Ian, Lianna, Marcos, Reveka, Viktor, and Yow—attend a showing of classic films. Three films are shown, one directed by Fellini, one by Hitchcock, and one by Kurosawa. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions must apply: Exactly twice as many of the film buffs see the Hitchcock film as see the Fellini film. Ginnie and Reveka do not see the same film as each other. Ian and Marcos do not see the same film as each other. Viktor and Yow see the same film as each other. Lianna sees the Hitchcock film. Ginnie sees either the Fellini film or the Kurosawa film.

Each of the following must be false EXCEPT:

Exactly seven film buffs—Ginnie, Ian, Lianna, Marcos, Reveka, Viktor, and Yow—attend a showing of classic films. Three films are shown, one directed by Fellini, one by Hitchcock, and one by Kurosawa. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions must apply: Exactly twice as many of the film buffs see the Hitchcock film as see the Fellini film. Ginnie and Reveka do not see the same film as each other. Ian and Marcos do not see the same film as each other. Viktor and Yow see the same film as each other. Lianna sees the Hitchcock film. Ginnie sees either the Fellini film or the Kurosawa film.

Which one of the following could be a complete and accurate list of the film buffs who do NOT see the Hitchcock film?

Exactly seven film buffs—Ginnie, Ian, Lianna, Marcos, Reveka, Viktor, and Yow—attend a showing of classic films. Three films are shown, one directed by Fellini, one by Hitchcock, and one by Kurosawa. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions must apply: Exactly twice as many of the film buffs see the Hitchcock film as see the Fellini film. Ginnie and Reveka do not see the same film as each other. Ian and Marcos do not see the same film as each other. Viktor and Yow see the same film as each other. Lianna sees the Hitchcock film. Ginnie sees either the Fellini film or the Kurosawa film.

If exactly one film buff sees the Kurosawa film, then which one of the following must be true?

Exactly seven film buffs—Ginnie, Ian, Lianna, Marcos, Reveka, Viktor, and Yow—attend a showing of classic films. Three films are shown, one directed by Fellini, one by Hitchcock, and one by Kurosawa. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions must apply: Exactly twice as many of the film buffs see the Hitchcock film as see the Fellini film. Ginnie and Reveka do not see the same film as each other. Ian and Marcos do not see the same film as each other. Viktor and Yow see the same film as each other. Lianna sees the Hitchcock film. Ginnie sees either the Fellini film or the Kurosawa film.

Which one of the following must be true?

Exactly seven film buffs—Ginnie, Ian, Lianna, Marcos, Reveka, Viktor, and Yow—attend a showing of classic films. Three films are shown, one directed by Fellini, one by Hitchcock, and one by Kurosawa. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions must apply: Exactly twice as many of the film buffs see the Hitchcock film as see the Fellini film. Ginnie and Reveka do not see the same film as each other. Ian and Marcos do not see the same film as each other. Viktor and Yow see the same film as each other. Lianna sees the Hitchcock film. Ginnie sees either the Fellini film or the Kurosawa film.

If Viktor sees the same film as Ginnie does, then which one of the following could be true?

Exactly seven film buffs—Ginnie, Ian, Lianna, Marcos, Reveka, Viktor, and Yow—attend a showing of classic films. Three films are shown, one directed by Fellini, one by Hitchcock, and one by Kurosawa. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions must apply: Exactly twice as many of the film buffs see the Hitchcock film as see the Fellini film. Ginnie and Reveka do not see the same film as each other. Ian and Marcos do not see the same film as each other. Viktor and Yow see the same film as each other. Lianna sees the Hitchcock film. Ginnie sees either the Fellini film or the Kurosawa film.

Each of the following could be complete and accurate list of the film buffs who see the Fellini film EXCEPT:

Six cars are to be arranged in a straight line, and will be numbered 1 through 6, in order, from the front of the line to the back of the line. Each car is exactly one color: two are green, two are orange, and two are purple. The arrangement of cars is restricted as follows: No car can be the same color as any car next to it in line. Either car 5 or car 6 must be purple. Car 1 cannot be orange. Car 4 cannot be green.

The cars in which one of the following pairs CANNOT be the same color as each other?

Six cars are to be arranged in a straight line, and will be numbered 1 through 6, in order, from the front of the line to the back of the line. Each car is exactly one color: two are green, two are orange, and two are purple. The arrangement of cars is restricted as follows: No car can be the same color as any car next to it in line. Either car 5 or car 6 must be purple. Car 1 cannot be orange. Car 4 cannot be green.

If car 2 is the same color as car 4, then which one of the following statements must be true?

Six cars are to be arranged in a straight line, and will be numbered 1 through 6, in order, from the front of the line to the back of the line. Each car is exactly one color: two are green, two are orange, and two are purple. The arrangement of cars is restricted as follows: No car can be the same color as any car next to it in line. Either car 5 or car 6 must be purple. Car 1 cannot be orange. Car 4 cannot be green.

If car 4 is purple, which one of the following must be true?

Six cars are to be arranged in a straight line, and will be numbered 1 through 6, in order, from the front of the line to the back of the line. Each car is exactly one color: two are green, two are orange, and two are purple. The arrangement of cars is restricted as follows: No car can be the same color as any car next to it in line. Either car 5 or car 6 must be purple. Car 1 cannot be orange. Car 4 cannot be green.

Which one of the following statements must be false?

Six cars are to be arranged in a straight line, and will be numbered 1 through 6, in order, from the front of the line to the back of the line. Each car is exactly one color: two are green, two are orange, and two are purple. The arrangement of cars is restricted as follows: No car can be the same color as any car next to it in line. Either car 5 or car 6 must be purple. Car 1 cannot be orange. Car 4 cannot be green.

If one of the two orange cars is replaced by a third green car, and if the arrangement of cars in line must conform to the same restrictions as before, then which one of the following is a complete and accurate list of the cars each of which must be green?

Exactly eight boats—Jewel, Kashmir, Neptune, Ojibwa, Pacific, Spain, Tornado, and Valhalla—arrived at a dock. No boat arrived at the same time as any other boat. The boats arrived in an order consistent with the following conditions: Tornado arrived before Spain but after Jewel. Neptune arrived before Tornado. Kashmir arrived after Jewel but before Spain. Spain arrived before Ojibwa.

If Neptune arrived after Kashmir, which one of the following must be false?

Exactly eight boats—Jewel, Kashmir, Neptune, Ojibwa, Pacific, Spain, Tornado, and Valhalla—arrived at a dock. No boat arrived at the same time as any other boat. The boats arrived in an order consistent with the following conditions: Tornado arrived before Spain but after Jewel. Neptune arrived before Tornado. Kashmir arrived after Jewel but before Spain. Spain arrived before Ojibwa.

Which one of the following must be true?

Exactly eight boats—Jewel, Kashmir, Neptune, Ojibwa, Pacific, Spain, Tornado, and Valhalla—arrived at a dock. No boat arrived at the same time as any other boat. The boats arrived in an order consistent with the following conditions: Tornado arrived before Spain but after Jewel. Neptune arrived before Tornado. Kashmir arrived after Jewel but before Spain. Spain arrived before Ojibwa.

Of the eight boats, what is the maximum number that could have arrived before Jewel?

Exactly eight boats—Jewel, Kashmir, Neptune, Ojibwa, Pacific, Spain, Tornado, and Valhalla—arrived at a dock. No boat arrived at the same time as any other boat. The boats arrived in an order consistent with the following conditions: Tornado arrived before Spain but after Jewel. Neptune arrived before Tornado. Kashmir arrived after Jewel but before Spain. Spain arrived before Ojibwa.

Of the eight boats, if Valhalla was the second to arrive, then which one of the following CANNOT be true?

Exactly eight boats—Jewel, Kashmir, Neptune, Ojibwa, Pacific, Spain, Tornado, and Valhalla—arrived at a dock. No boat arrived at the same time as any other boat. The boats arrived in an order consistent with the following conditions: Tornado arrived before Spain but after Jewel. Neptune arrived before Tornado. Kashmir arrived after Jewel but before Spain. Spain arrived before Ojibwa.

If Valhalla arrived before Neptune but after Pacific, which one of the following could be true?