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A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Which one of the following statements must be true?

A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

If light 5 is on, which one of the following could be true?

A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

If light 4 is on, each of the following statements must be true EXCEPT:

A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Suppose that it is no longer part of the specifications that two lights on the north side be on. If all of the other original specifications remain the same, and if exactly one light on the north side is on, which one of the following statements could be false?

Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

What is the maximum possible number of different pairs of chairs in which Frank and Ruby could sit?

Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

Which one of the following statements must be false?

Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

If Thelma sits next to Ivan, and if Frank sits next to Thelma, which one of the following statements could be false?

Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

If Frank does not sit next to any child who sits next to Ivan, which one of the following statements could be true?

Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

If Frank sits east of Ruby, which one of the following pairs of children CANNOT sit next to each other?

The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Each of the following can be true EXCEPT:

The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Which one of the following could be true?

The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Which one of the following could be true?

The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

If X does not respond to ferromycin, then which one of the following must be true?

The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

If any of the organisms responds to two of the antibiotics, then which one of the following is true about such an organism?

The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

If none of the organisms responds to heptocillin, then which one of the following must be true?

The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

If three of the organisms respond to exactly the same set of antibiotics as each other, and if Z does not respond to ferromycin, then each of the following must be true EXCEPT:

A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

Which one of the following is an acceptable selection of flowers for the three corsages? Corsage 1 Corsage 2 Corsage 3

A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

The maximum total number of roses that can be used in the three corsages is

A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

If corsage 1 contains two orchids and one rose, what is the maximum total number of violets that the florist can use in making the three corsages?

A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

If corsage 2 is exactly the same as corsage 3, the nine flowers used in the corsages can include exactly

A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

If two of the corsages contain at least one orchid each, then the flowers in corsage 2 must include at least

A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

If the greatest possible number of violets is used in the three corsages, the florist must use

A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

If corsage 1 contains at least one gardenia and at least one violet, and if corsage 3 contains three different types of flowers, which one of the following could be used to make corsage 2?

From a group of seven people—J, K, L, M, N, P, and Q—exactly four will be selected to attend a diplomat's retirement dinner. Selection must conform to the following conditions: Either J or K must be selected, but J and K cannot both be selected. Either N or P must be selected, but N and P cannot both be selected. N cannot be selected unless L is selected. Q cannot be selected unless K is selected.

Which one of the following could be the four people selected to attend the retirement dinner?

From a group of seven people—J, K, L, M, N, P, and Q—exactly four will be selected to attend a diplomat's retirement dinner. Selection must conform to the following conditions: Either J or K must be selected, but J and K cannot both be selected. Either N or P must be selected, but N and P cannot both be selected. N cannot be selected unless L is selected. Q cannot be selected unless K is selected.

Among the people selected to attend the retirement dinner there must be

From a group of seven people—J, K, L, M, N, P, and Q—exactly four will be selected to attend a diplomat's retirement dinner. Selection must conform to the following conditions: Either J or K must be selected, but J and K cannot both be selected. Either N or P must be selected, but N and P cannot both be selected. N cannot be selected unless L is selected. Q cannot be selected unless K is selected.

Which one of the following is a pair of people who CANNOT both be selected to attend the retirement dinner?

From a group of seven people—J, K, L, M, N, P, and Q—exactly four will be selected to attend a diplomat's retirement dinner. Selection must conform to the following conditions: Either J or K must be selected, but J and K cannot both be selected. Either N or P must be selected, but N and P cannot both be selected. N cannot be selected unless L is selected. Q cannot be selected unless K is selected.

If M is not selected to attend the retirement dinner, the four people selected to attend must include which one of the following pairs of people?

From a group of seven people—J, K, L, M, N, P, and Q—exactly four will be selected to attend a diplomat's retirement dinner. Selection must conform to the following conditions: Either J or K must be selected, but J and K cannot both be selected. Either N or P must be selected, but N and P cannot both be selected. N cannot be selected unless L is selected. Q cannot be selected unless K is selected.

If P is not selected to attend the retirement dinner, then exactly how many different groups of four are there each of which would be an acceptable selection?

From a group of seven people—J, K, L, M, N, P, and Q—exactly four will be selected to attend a diplomat's retirement dinner. Selection must conform to the following conditions: Either J or K must be selected, but J and K cannot both be selected. Either N or P must be selected, but N and P cannot both be selected. N cannot be selected unless L is selected. Q cannot be selected unless K is selected.

There is only one acceptable group of four that can be selected to attend the retirement dinner if which one of the following pairs of people is selected?

Three boys—Karl, Luis, and Miguel—and three girls—Rita, Sarah, and Tura—are giving a dance recital. Three dances—1, 2, and 3—are to be performed. Each dance involves three pairs of children, a boy and a girl partnering each other in each pair, according to the following conditions: Karl partners Sarah in either dance 1 or dance 2. Whoever partners Rita in dance 2 must partner Sarah in dance 3. No two children can partner each other in more than one dance.

If Sarah partners Luis in dance 3, which one of the following is a complete and accurate list of the girls any one of whom could partner Miguel in dance 1?

Three boys—Karl, Luis, and Miguel—and three girls—Rita, Sarah, and Tura—are giving a dance recital. Three dances—1, 2, and 3—are to be performed. Each dance involves three pairs of children, a boy and a girl partnering each other in each pair, according to the following conditions: Karl partners Sarah in either dance 1 or dance 2. Whoever partners Rita in dance 2 must partner Sarah in dance 3. No two children can partner each other in more than one dance.

If Miguel partners Rita in dance 2, which one of the following could be true?

Three boys—Karl, Luis, and Miguel—and three girls—Rita, Sarah, and Tura—are giving a dance recital. Three dances—1, 2, and 3—are to be performed. Each dance involves three pairs of children, a boy and a girl partnering each other in each pair, according to the following conditions: Karl partners Sarah in either dance 1 or dance 2. Whoever partners Rita in dance 2 must partner Sarah in dance 3. No two children can partner each other in more than one dance.

If Miguel partners Sarah in dance 1, which one of the following is a pair of children who must partner each other in dance 3?

Three boys—Karl, Luis, and Miguel—and three girls—Rita, Sarah, and Tura—are giving a dance recital. Three dances—1, 2, and 3—are to be performed. Each dance involves three pairs of children, a boy and a girl partnering each other in each pair, according to the following conditions: Karl partners Sarah in either dance 1 or dance 2. Whoever partners Rita in dance 2 must partner Sarah in dance 3. No two children can partner each other in more than one dance.

If Luis partners Sarah in dance 2, which one of the following is a pair of children who must partner each other in dance 1?

Three boys—Karl, Luis, and Miguel—and three girls—Rita, Sarah, and Tura—are giving a dance recital. Three dances—1, 2, and 3—are to be performed. Each dance involves three pairs of children, a boy and a girl partnering each other in each pair, according to the following conditions: Karl partners Sarah in either dance 1 or dance 2. Whoever partners Rita in dance 2 must partner Sarah in dance 3. No two children can partner each other in more than one dance.

If Miguel partners Rita in dance 1, which one of the following must be true?

Six cities are located within the numbered areas as follows: Within the six-city area there are exactly four hospitals, two jails, and two universities. These eight institutions are located as follows: No institution is in more than one of the cities. None of the cities contains more than one jail, and none contains more than one university. None of the cities contains both a jail and a university. Each jail is located in a city that contains at least one hospital. The universities are located in two cities that do not share a common boundary. City 3 contains a university, and city 6 contains a jail.

Which one of the following could be true?

Six cities are located within the numbered areas as follows: Within the six-city area there are exactly four hospitals, two jails, and two universities. These eight institutions are located as follows: No institution is in more than one of the cities. None of the cities contains more than one jail, and none contains more than one university. None of the cities contains both a jail and a university. Each jail is located in a city that contains at least one hospital. The universities are located in two cities that do not share a common boundary. City 3 contains a university, and city 6 contains a jail.

Which one of the following could be true?

Six cities are located within the numbered areas as follows: Within the six-city area there are exactly four hospitals, two jails, and two universities. These eight institutions are located as follows: No institution is in more than one of the cities. None of the cities contains more than one jail, and none contains more than one university. None of the cities contains both a jail and a university. Each jail is located in a city that contains at least one hospital. The universities are located in two cities that do not share a common boundary. City 3 contains a university, and city 6 contains a jail.

Which one of the following is a complete and accurate list of the cities any one of which could contain the jail that is not in city 6?

Six cities are located within the numbered areas as follows: Within the six-city area there are exactly four hospitals, two jails, and two universities. These eight institutions are located as follows: No institution is in more than one of the cities. None of the cities contains more than one jail, and none contains more than one university. None of the cities contains both a jail and a university. Each jail is located in a city that contains at least one hospital. The universities are located in two cities that do not share a common boundary. City 3 contains a university, and city 6 contains a jail.

If each of the six cities contains at least one of the eight institutions, then which one of the following must be true?

Six cities are located within the numbered areas as follows: Within the six-city area there are exactly four hospitals, two jails, and two universities. These eight institutions are located as follows: No institution is in more than one of the cities. None of the cities contains more than one jail, and none contains more than one university. None of the cities contains both a jail and a university. Each jail is located in a city that contains at least one hospital. The universities are located in two cities that do not share a common boundary. City 3 contains a university, and city 6 contains a jail.

In which one of the following cities must there be fewer than three hospitals?

Six cities are located within the numbered areas as follows: Within the six-city area there are exactly four hospitals, two jails, and two universities. These eight institutions are located as follows: No institution is in more than one of the cities. None of the cities contains more than one jail, and none contains more than one university. None of the cities contains both a jail and a university. Each jail is located in a city that contains at least one hospital. The universities are located in two cities that do not share a common boundary. City 3 contains a university, and city 6 contains a jail.

If one of the cities contains exactly two hospitals and exactly one university, then which one of the following lists three cities that might, among them, contain no hospital?

On the basis of an examination, nine students—Fred, Glen, Hilary, Ida, Jan, Kathy, Laura, Mike, and Nick—are each placed in one of three classes. The three highest scorers are placed in the level 1 class; the three lowest scorers are placed in the level 3 class. The remaining three are placed in the level 2 class. Each class has exactly three students. Ida scores higher than Glen. Glen scores higher than both Jan and Kathy. Jan scores higher than Mike. Mike scores higher than Hilary. Hilary scores higher than Nick. Kathy scores higher than both Fred and Laura.

How many different combinations of students could form the level 1 class?

On the basis of an examination, nine students—Fred, Glen, Hilary, Ida, Jan, Kathy, Laura, Mike, and Nick—are each placed in one of three classes. The three highest scorers are placed in the level 1 class; the three lowest scorers are placed in the level 3 class. The remaining three are placed in the level 2 class. Each class has exactly three students. Ida scores higher than Glen. Glen scores higher than both Jan and Kathy. Jan scores higher than Mike. Mike scores higher than Hilary. Hilary scores higher than Nick. Kathy scores higher than both Fred and Laura.

Which one of the following students could be in the level 2 class but cannot be in the level 3 class?

On the basis of an examination, nine students—Fred, Glen, Hilary, Ida, Jan, Kathy, Laura, Mike, and Nick—are each placed in one of three classes. The three highest scorers are placed in the level 1 class; the three lowest scorers are placed in the level 3 class. The remaining three are placed in the level 2 class. Each class has exactly three students. Ida scores higher than Glen. Glen scores higher than both Jan and Kathy. Jan scores higher than Mike. Mike scores higher than Hilary. Hilary scores higher than Nick. Kathy scores higher than both Fred and Laura.

Which one of the following students could be placed in any one of the three classes?

On the basis of an examination, nine students—Fred, Glen, Hilary, Ida, Jan, Kathy, Laura, Mike, and Nick—are each placed in one of three classes. The three highest scorers are placed in the level 1 class; the three lowest scorers are placed in the level 3 class. The remaining three are placed in the level 2 class. Each class has exactly three students. Ida scores higher than Glen. Glen scores higher than both Jan and Kathy. Jan scores higher than Mike. Mike scores higher than Hilary. Hilary scores higher than Nick. Kathy scores higher than both Fred and Laura.

The composition of each class can be completely determined if which one of the following pairs of students is known to be in the level 2 class?

On the basis of an examination, nine students—Fred, Glen, Hilary, Ida, Jan, Kathy, Laura, Mike, and Nick—are each placed in one of three classes. The three highest scorers are placed in the level 1 class; the three lowest scorers are placed in the level 3 class. The remaining three are placed in the level 2 class. Each class has exactly three students. Ida scores higher than Glen. Glen scores higher than both Jan and Kathy. Jan scores higher than Mike. Mike scores higher than Hilary. Hilary scores higher than Nick. Kathy scores higher than both Fred and Laura.

Which one of the following pairs of students cannot be in the same class as Fred?

Six reviewers—Frank, George, Hilda, Jackie, Karl, and Lena—will review four movies—Mystery, Retreat, Seasonings, and Wolves—according to the following conditions: Each reviewer reviews exactly one movie, and each movie is reviewed by at least one of the six reviewers. Hilda reviews the same movie as Frank. Lena reviews the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

If Lena reviews Seasonings, which one of the following must be true?

Six reviewers—Frank, George, Hilda, Jackie, Karl, and Lena—will review four movies—Mystery, Retreat, Seasonings, and Wolves—according to the following conditions: Each reviewer reviews exactly one movie, and each movie is reviewed by at least one of the six reviewers. Hilda reviews the same movie as Frank. Lena reviews the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

If Karl does not review Seasonings, which one of the following must be true?

Six reviewers—Frank, George, Hilda, Jackie, Karl, and Lena—will review four movies—Mystery, Retreat, Seasonings, and Wolves—according to the following conditions: Each reviewer reviews exactly one movie, and each movie is reviewed by at least one of the six reviewers. Hilda reviews the same movie as Frank. Lena reviews the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Which one of the following is a complete and accurate list of the movies each of which could be the movie that Lena reviews?

Six reviewers—Frank, George, Hilda, Jackie, Karl, and Lena—will review four movies—Mystery, Retreat, Seasonings, and Wolves—according to the following conditions: Each reviewer reviews exactly one movie, and each movie is reviewed by at least one of the six reviewers. Hilda reviews the same movie as Frank. Lena reviews the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Which one of the following can be true?

Six reviewers—Frank, George, Hilda, Jackie, Karl, and Lena—will review four movies—Mystery, Retreat, Seasonings, and Wolves—according to the following conditions: Each reviewer reviews exactly one movie, and each movie is reviewed by at least one of the six reviewers. Hilda reviews the same movie as Frank. Lena reviews the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Lena can review any of the following EXCEPT

Six reviewers—Frank, George, Hilda, Jackie, Karl, and Lena—will review four movies—Mystery, Retreat, Seasonings, and Wolves—according to the following conditions: Each reviewer reviews exactly one movie, and each movie is reviewed by at least one of the six reviewers. Hilda reviews the same movie as Frank. Lena reviews the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

If Karl reviews the same movie as exactly one other reviewer, which one of the following is a complete and accurate list of the movies any one of which could be the movie that these two reviewers review?

Six reviewers—Frank, George, Hilda, Jackie, Karl, and Lena—will review four movies—Mystery, Retreat, Seasonings, and Wolves—according to the following conditions: Each reviewer reviews exactly one movie, and each movie is reviewed by at least one of the six reviewers. Hilda reviews the same movie as Frank. Lena reviews the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Which one of the following is an acceptable assignment of reviewers to movies? Mystery Retreat Seasonings Wolves

In a game, "words" (real or nonsensical) consist of any combination of at least four letters of the English alphabet. Any "sentence" consists of exactly five words and satisfies the following conditions: The five words are written from left to right on a single line in alphabetical order. The sentence is started by any word, and each successive word is formed by applying exactly one of three operations to the word immediately to its left: delete one letter; add one letter; replace one letter with another letter. At most three of the five words begin with the same letter as one another. Except for the leftmost word, each word is formed by a different operation from that which formed the word immediately to its left.

Which one of the following could be a sentence in the word game?

In a game, "words" (real or nonsensical) consist of any combination of at least four letters of the English alphabet. Any "sentence" consists of exactly five words and satisfies the following conditions: The five words are written from left to right on a single line in alphabetical order. The sentence is started by any word, and each successive word is formed by applying exactly one of three operations to the word immediately to its left: delete one letter; add one letter; replace one letter with another letter. At most three of the five words begin with the same letter as one another. Except for the leftmost word, each word is formed by a different operation from that which formed the word immediately to its left.

The last letter of the alphabet that the first word of a sentence in the word game can begin with is

In a game, "words" (real or nonsensical) consist of any combination of at least four letters of the English alphabet. Any "sentence" consists of exactly five words and satisfies the following conditions: The five words are written from left to right on a single line in alphabetical order. The sentence is started by any word, and each successive word is formed by applying exactly one of three operations to the word immediately to its left: delete one letter; add one letter; replace one letter with another letter. At most three of the five words begin with the same letter as one another. Except for the leftmost word, each word is formed by a different operation from that which formed the word immediately to its left.

If the first word in a sentence is "blender" and the third word is "slender", then the second word can be

In a game, "words" (real or nonsensical) consist of any combination of at least four letters of the English alphabet. Any "sentence" consists of exactly five words and satisfies the following conditions: The five words are written from left to right on a single line in alphabetical order. The sentence is started by any word, and each successive word is formed by applying exactly one of three operations to the word immediately to its left: delete one letter; add one letter; replace one letter with another letter. At most three of the five words begin with the same letter as one another. Except for the leftmost word, each word is formed by a different operation from that which formed the word immediately to its left.

If the first word in a sentence consists of nine letters, then the minimum number of letters that the fourth word can contain is

In a game, "words" (real or nonsensical) consist of any combination of at least four letters of the English alphabet. Any "sentence" consists of exactly five words and satisfies the following conditions: The five words are written from left to right on a single line in alphabetical order. The sentence is started by any word, and each successive word is formed by applying exactly one of three operations to the word immediately to its left: delete one letter; add one letter; replace one letter with another letter. At most three of the five words begin with the same letter as one another. Except for the leftmost word, each word is formed by a different operation from that which formed the word immediately to its left.

If "clean" is the first word in a sentence and "learn" is another word in the sentence, then which one of the following is a complete and accurate list of the positions each of which could be the position in which "learn" occurs in the sentence?

In a game, "words" (real or nonsensical) consist of any combination of at least four letters of the English alphabet. Any "sentence" consists of exactly five words and satisfies the following conditions: The five words are written from left to right on a single line in alphabetical order. The sentence is started by any word, and each successive word is formed by applying exactly one of three operations to the word immediately to its left: delete one letter; add one letter; replace one letter with another letter. At most three of the five words begin with the same letter as one another. Except for the leftmost word, each word is formed by a different operation from that which formed the word immediately to its left.

If the first word in a sentence consists of four letters, then the maximum number of letters that the fifth word in this sentence could contain is

A soloist will play six different guitar concertos, exactly one each Sunday for six consecutive weeks. Two concertos will be selected from among three concertos by Giuliani—H, J, and K; two from among four concertos by Rodrigo—M, N, O, and P; and two from among three concertos by Vivaldi—X, Y, and Z. The following conditions apply without exception: If N is selected, then J is also selected. If M is selected, then neither J nor O can be selected. If X is selected, then neither Z nor P can be selected. If both J and O are selected, then J is played at some time before O. X cannot be played on the fifth Sunday unless one of Rodrigo's concertos is played on the first Sunday.

Which one of the following is an acceptable selection of concertos that the soloist could play on the first through the sixth Sunday?

A soloist will play six different guitar concertos, exactly one each Sunday for six consecutive weeks. Two concertos will be selected from among three concertos by Giuliani—H, J, and K; two from among four concertos by Rodrigo—M, N, O, and P; and two from among three concertos by Vivaldi—X, Y, and Z. The following conditions apply without exception: If N is selected, then J is also selected. If M is selected, then neither J nor O can be selected. If X is selected, then neither Z nor P can be selected. If both J and O are selected, then J is played at some time before O. X cannot be played on the fifth Sunday unless one of Rodrigo's concertos is played on the first Sunday.

If the six concertos to be played are J, K, N, O, Y, and Z and if N is to be played on the first Sunday, then which one of the following concertos CANNOT be played on the second Sunday?

A soloist will play six different guitar concertos, exactly one each Sunday for six consecutive weeks. Two concertos will be selected from among three concertos by Giuliani—H, J, and K; two from among four concertos by Rodrigo—M, N, O, and P; and two from among three concertos by Vivaldi—X, Y, and Z. The following conditions apply without exception: If N is selected, then J is also selected. If M is selected, then neither J nor O can be selected. If X is selected, then neither Z nor P can be selected. If both J and O are selected, then J is played at some time before O. X cannot be played on the fifth Sunday unless one of Rodrigo's concertos is played on the first Sunday.

If J, O, and Y are the first three concertos to be played, not necessarily in the order given, which one of the following is a concerto that CANNOT be played on the fifth Sunday?

A soloist will play six different guitar concertos, exactly one each Sunday for six consecutive weeks. Two concertos will be selected from among three concertos by Giuliani—H, J, and K; two from among four concertos by Rodrigo—M, N, O, and P; and two from among three concertos by Vivaldi—X, Y, and Z. The following conditions apply without exception: If N is selected, then J is also selected. If M is selected, then neither J nor O can be selected. If X is selected, then neither Z nor P can be selected. If both J and O are selected, then J is played at some time before O. X cannot be played on the fifth Sunday unless one of Rodrigo's concertos is played on the first Sunday.

If O is selected for the first Sunday, which one of the following is a concerto that must also be selected?

A soloist will play six different guitar concertos, exactly one each Sunday for six consecutive weeks. Two concertos will be selected from among three concertos by Giuliani—H, J, and K; two from among four concertos by Rodrigo—M, N, O, and P; and two from among three concertos by Vivaldi—X, Y, and Z. The following conditions apply without exception: If N is selected, then J is also selected. If M is selected, then neither J nor O can be selected. If X is selected, then neither Z nor P can be selected. If both J and O are selected, then J is played at some time before O. X cannot be played on the fifth Sunday unless one of Rodrigo's concertos is played on the first Sunday.

Which one of the following is a concerto that must be selected?

A soloist will play six different guitar concertos, exactly one each Sunday for six consecutive weeks. Two concertos will be selected from among three concertos by Giuliani—H, J, and K; two from among four concertos by Rodrigo—M, N, O, and P; and two from among three concertos by Vivaldi—X, Y, and Z. The following conditions apply without exception: If N is selected, then J is also selected. If M is selected, then neither J nor O can be selected. If X is selected, then neither Z nor P can be selected. If both J and O are selected, then J is played at some time before O. X cannot be played on the fifth Sunday unless one of Rodrigo's concertos is played on the first Sunday.

Which one of the following is a concerto that CANNOT be selected together with N?

Eight camp counselors—Fran, George, Henry, Joan, Kathy, Lewis, Nathan, and Olga—must each be assigned to supervise exactly one of three activities—swimming, tennis, and volleyball. The assignment of counselors must conform to the following conditions: Each activity is supervised by at least two, but not more than three, of the eight counselors. Henry supervises swimming. Neither Kathy nor Olga supervises tennis. Neither Kathy nor Nathan supervises the same activity as Joan. If George supervises swimming, both Nathan and Olga supervise volleyball.

Which one of the following is an acceptable assignment of the counselors to the activities?

Eight camp counselors—Fran, George, Henry, Joan, Kathy, Lewis, Nathan, and Olga—must each be assigned to supervise exactly one of three activities—swimming, tennis, and volleyball. The assignment of counselors must conform to the following conditions: Each activity is supervised by at least two, but not more than three, of the eight counselors. Henry supervises swimming. Neither Kathy nor Olga supervises tennis. Neither Kathy nor Nathan supervises the same activity as Joan. If George supervises swimming, both Nathan and Olga supervise volleyball.

Which one of the following is a pair of counselors who could be two of three counselors assigned to supervise swimming?

Eight camp counselors—Fran, George, Henry, Joan, Kathy, Lewis, Nathan, and Olga—must each be assigned to supervise exactly one of three activities—swimming, tennis, and volleyball. The assignment of counselors must conform to the following conditions: Each activity is supervised by at least two, but not more than three, of the eight counselors. Henry supervises swimming. Neither Kathy nor Olga supervises tennis. Neither Kathy nor Nathan supervises the same activity as Joan. If George supervises swimming, both Nathan and Olga supervise volleyball.

Which one of the following is a pair of counselors who could together be assigned to supervise tennis?

Eight camp counselors—Fran, George, Henry, Joan, Kathy, Lewis, Nathan, and Olga—must each be assigned to supervise exactly one of three activities—swimming, tennis, and volleyball. The assignment of counselors must conform to the following conditions: Each activity is supervised by at least two, but not more than three, of the eight counselors. Henry supervises swimming. Neither Kathy nor Olga supervises tennis. Neither Kathy nor Nathan supervises the same activity as Joan. If George supervises swimming, both Nathan and Olga supervise volleyball.

If George and Kathy are two of three counselors assigned to supervise swimming, which one of the following could be true of the assignment?

Eight camp counselors—Fran, George, Henry, Joan, Kathy, Lewis, Nathan, and Olga—must each be assigned to supervise exactly one of three activities—swimming, tennis, and volleyball. The assignment of counselors must conform to the following conditions: Each activity is supervised by at least two, but not more than three, of the eight counselors. Henry supervises swimming. Neither Kathy nor Olga supervises tennis. Neither Kathy nor Nathan supervises the same activity as Joan. If George supervises swimming, both Nathan and Olga supervise volleyball.

If Fran and Lewis are two of three counselors assigned to supervise swimming, which one of the following must be true of the assignment?

Eight camp counselors—Fran, George, Henry, Joan, Kathy, Lewis, Nathan, and Olga—must each be assigned to supervise exactly one of three activities—swimming, tennis, and volleyball. The assignment of counselors must conform to the following conditions: Each activity is supervised by at least two, but not more than three, of the eight counselors. Henry supervises swimming. Neither Kathy nor Olga supervises tennis. Neither Kathy nor Nathan supervises the same activity as Joan. If George supervises swimming, both Nathan and Olga supervise volleyball.

If Joan is assigned to supervise the same activity as Olga, which one of the following CANNOT be true of the assignment?

A fire chief is determining the work schedules of five firefighters: Fuentes, Graber, Howell, Iman, and Jackson. The schedule must meet the following conditions: Except for Saturday and Sunday, when none of them works, exactly one of the firefighters works each day. None of the firefighters can work more than two days per week. No firefighter works on two consecutive days. Fuentes never works later in the week than Jackson. If Howell works, then Graber must work on the following day.

Which one of the following CANNOT be a Monday-to-Friday work schedule?

A fire chief is determining the work schedules of five firefighters: Fuentes, Graber, Howell, Iman, and Jackson. The schedule must meet the following conditions: Except for Saturday and Sunday, when none of them works, exactly one of the firefighters works each day. None of the firefighters can work more than two days per week. No firefighter works on two consecutive days. Fuentes never works later in the week than Jackson. If Howell works, then Graber must work on the following day.

If each firefighter is required to have at least two consecutive days off during the Monday-to-Friday workweek, which one of the following could be a possible work schedule?

A fire chief is determining the work schedules of five firefighters: Fuentes, Graber, Howell, Iman, and Jackson. The schedule must meet the following conditions: Except for Saturday and Sunday, when none of them works, exactly one of the firefighters works each day. None of the firefighters can work more than two days per week. No firefighter works on two consecutive days. Fuentes never works later in the week than Jackson. If Howell works, then Graber must work on the following day.

If both Fuentes and Jackson work during a week, which one of the following statements CANNOT be true?

A fire chief is determining the work schedules of five firefighters: Fuentes, Graber, Howell, Iman, and Jackson. The schedule must meet the following conditions: Except for Saturday and Sunday, when none of them works, exactly one of the firefighters works each day. None of the firefighters can work more than two days per week. No firefighter works on two consecutive days. Fuentes never works later in the week than Jackson. If Howell works, then Graber must work on the following day.

If Fuentes works two days during the week and Jackson works on Thursday, which one of the following statements could be true?

A fire chief is determining the work schedules of five firefighters: Fuentes, Graber, Howell, Iman, and Jackson. The schedule must meet the following conditions: Except for Saturday and Sunday, when none of them works, exactly one of the firefighters works each day. None of the firefighters can work more than two days per week. No firefighter works on two consecutive days. Fuentes never works later in the week than Jackson. If Howell works, then Graber must work on the following day.

If Graber does not work during the week, which one of the following statements must be true?

A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

Which one of the following is an acceptable selection of representatives for the committee?

A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

Which one of the following lists three representatives who could be selected together for the committee?

A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

If M is the chairperson of the committee, which one of the following is among the people who must also be on the committee?

A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

If F is the chairperson of the committee, which one of the following is among the people who must also be on the committee?

A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

If F is selected, any one of the following people could be the chairperson of the committee EXCEPT:

A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

If neither F nor K is selected for the committee, which one of the following can be true?

A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

If the chairperson of the committee is to be a homeowner, which one of the following must be true?

A housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

The committee must include at least one representative from which one of the following pairs?

Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

Which one of the following must be true after the second reassignment of apprentices to projects during the year if that reassignment assigns Nora to project T ?

Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

Which one of the following could be true after only one reassignment during the year?

Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

If at some time during the year, Louis is reassigned to project R, which one of the following could have been the assignment of apprentices to the projects immediately before the reassignment?

Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

Which one of the following is an acceptable assignment of apprentices to the projects after only one reassignment during the year?

Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

If the first reassignment is made according to plan 1, which one of the following must be true?

A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

If Janet's lesson is scheduled for the first day, then the lesson for which one of the following students must be scheduled for the sixth day?

A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

For which one of the following students is there an acceptable schedule in which the student's lesson is on the third day and another acceptable schedule in which the student's lesson is on the fifth day?

A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Which one of the following is a complete and accurate list of the students any one of whom could be the student whose lesson is scheduled for the second day?

A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

If Henry's lesson is scheduled for a day either immediately before or immediately after Tom's lesson, then Grace's lesson must be scheduled for the

A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

If Janet's lesson is scheduled for the third day, which one of the following could be true?

A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Which one of the following is a complete and accurate list of days any one of which could be the day for which Tom's lesson is scheduled?

Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

If F is in group 1, which one of the following could be true?

Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

If F and S are in group 3, which one of the following must be true?

Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

If G and K are in group 3, which one of the following must be true?

Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

If Q is in group 1 and S is in group 3, which one of the following CANNOT be true?

Five children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

If G is the only child in group 1, which one of the following must be true?

Lara, Mendel, and Nastassia each buy at least one kind of food from a street vendor who sells only fruit cups, hot dogs, pretzels, and shish kebabs. They make their selections in accordance with the following restrictions: None of the three buys more than one portion of each kind of food. If any of the three buys a hot dog, that person does not also buy a shish kebab. At least one of the three buys a hot dog, and at least one buys a pretzel. Mendel buys a shish kebab. Nastassia buys a fruit cup. Neither Lara nor Nastassia buys a pretzel. Mendel does not buy any kind of food that Nastassia buys.

Which one of the following statements must be true?