context stringlengths 339 932 | question stringlengths 18 356 | answers listlengths 5 5 | label int64 0 4 |
|---|---|---|---|
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... | Which one of the following statements must be true? | [
"If light 2 is on, then light 6 is off.",
"If light 3 is on, then light 2 is on.",
"If light 4 is on, then light 3 is off.",
"If light 5 is off, then light 4 is on.",
"If light 6 is off, then light 1 is on."
] | 3 |
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... | If light 5 is on, which one of the following could be true? | [
"Light 1 is off and light 6 is off.",
"Light 1 is on and light 7 is on.",
"Light 2 is off and light 4 is on.",
"Light 2 is off and light 6 is off.",
"Light 6 is on and light 7 is on."
] | 0 |
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... | If light 4 is on, each of the following statements must be true EXCEPT: | [
"Light 1 is on.",
"Light 2 is on.",
"Light 5 is off.",
"Light 6 is on.",
"Light 7 is off."
] | 1 |
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... | 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? | [
"Light 1 is off.",
"Light 2 is on.",
"Light 3 is off.",
"Light 4 is on.",
"Light 5 is on."
] | 4 |
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 on... | What is the maximum possible number of different pairs of chairs in which Frank and Ruby could sit? | [
"one",
"two",
"three",
"four",
"five"
] | 2 |
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 on... | Which one of the following statements must be false? | [
"Both Harry and Joel sit east of Frank.",
"Both Harry and Ruby sit east of Frank.",
"Both Harry and Joel sit west of Frank.",
"Both Harry and Ruby sit west of Frank.",
"Both Joel and Ruby sit east of Frank."
] | 2 |
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 on... | If Thelma sits next to Ivan, and if Frank sits next to Thelma, which one of the following statements could be false? | [
"Both Frank and Ivan sit east of Ruby.",
"Both Frank and Ruby sit west of Thelma.",
"Both Frank and Sylvia sit east of Ruby.",
"Both Frank and Thelma sit west of Sylvia.",
"Both Frank and Ruby sit west of Joel."
] | 4 |
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 on... | If Frank does not sit next to any child who sits next to Ivan, which one of the following statements could be true? | [
"Harry sits west of Frank.",
"Joel sits west of Ivan.",
"Ruby sits west of Frank.",
"Thelma sits west of Frank.",
"Thelma sits west of Ruby."
] | 1 |
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 on... | If Frank sits east of Ruby, which one of the following pairs of children CANNOT sit next to each other? | [
"Frank and Thelma",
"Harry and Ruby",
"Harry and Sylvia",
"Ivan and Ruby",
"Joel and Ruby"
] | 3 |
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 ferromyc... | Each of the following can be true EXCEPT: | [
"W responds to heptocillin.",
"X responds to ganocyclene.",
"X responds to heptocillin.",
"Y responds to heptocillin.",
"Z responds to ganocyclene."
] | 3 |
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 ferromyc... | Which one of the following could be true? | [
"W, X, and Z all respond to ferromycin.",
"W, X, and Z all respond to ganocyclene.",
"W and exactly one other organism respond to ganocyclene.",
"W responds to more of the antibiotics than X does.",
"More of the organisms respond to ferromycin than to ganocyclene."
] | 1 |
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 ferromyc... | Which one of the following could be true? | [
"Exactly one of the organisms responds to ferromycin.",
"All four of the organisms respond to heptocillin.",
"At least one of the organisms responds both to ferromycin and to heptocillin.",
"At least one of the organisms responds neither to ganocyclene nor to heptocillin.",
"At least one of the organisms re... | 4 |
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 ferromyc... | If X does not respond to ferromycin, then which one of the following must be true? | [
"W responds to ganocyclene.",
"X responds to ganocyclene.",
"X responds to heptocillin.",
"Z responds to ferromycin.",
"Z responds to heptocillin."
] | 3 |
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 ferromyc... | If any of the organisms responds to two of the antibiotics, then which one of the following is true about such an organism? | [
"It must respond to ferromycin.",
"It must respond to ganocyclene.",
"It must respond to heptocillin.",
"It cannot respond to ferromycin.",
"It cannot respond to ganocyclene."
] | 1 |
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 ferromyc... | If none of the organisms responds to heptocillin, then which one of the following must be true? | [
"W responds to ferromycin.",
"X responds to ferromycin.",
"Z responds to ferromycin.",
"Exactly three of the organisms respond to ganocyclene.",
"Exactly four of the organisms respond to ganocyclene."
] | 4 |
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 ferromyc... | 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: | [
"W responds to ferromycin.",
"X responds to ganocyclene.",
"Z responds to ganocyclene.",
"W responds to exactly the same set of antibiotics as Y.",
"X responds to exactly the same set of antibiotics as Y."
] | 2 |
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. Th... | Which one of the following is an acceptable selection of flowers for the three corsages? Corsage 1 Corsage 2 Corsage 3 | [
"2 gardenias 1 orchid 1 gardenia 1 rose 1 rose 1 orchid 1 violet 1 violet",
"2 orchids 2 orchids 2 gardenias 1 rose 1 rose 1 rose",
"2 orchids 3 roses 1 gardenia 1 rose 2 violets",
"1 gardenia 1 gardenia 1 gardenia 1 orchid 1 rose 1 rose 1 rose 1 violet 1 violet",
"1 orchid 3 violets 3 gardenias 2 roses"
] | 2 |
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. Th... | The maximum total number of roses that can be used in the three corsages is | [
"three",
"four",
"five",
"six",
"seven"
] | 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. Th... | 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? | [
"one",
"two",
"three",
"four",
"five"
] | 1 |
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. Th... | If corsage 2 is exactly the same as corsage 3, the nine flowers used in the corsages can include exactly | [
"two orchids",
"three gardenias",
"three roses",
"five roses",
"five violets"
] | 0 |
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. Th... | If two of the corsages contain at least one orchid each, then the flowers in corsage 2 must include at least | [
"one gardenia and one orchid",
"one gardenia and one rose",
"one orchid and one rose",
"one orchid and one violet",
"one rose and one violet"
] | 2 |
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. Th... | If the greatest possible number of violets is used in the three corsages, the florist must use | [
"exactly one rose and exactly one gardenia",
"exactly one orchid and exactly four violets",
"exactly two orchids",
"exactly two roses",
"exactly six violets"
] | 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. Th... | 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? | [
"one rose, one orchid, and one gardenia",
"one rose and two orchids",
"one rose and two violets",
"two roses and one gardenia",
"two roses and one violet"
] | 0 |
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 can... | Which one of the following could be the four people selected to attend the retirement dinner? | [
"J, K, M, P",
"J, L, N, Q",
"J, M, N, Q",
"K, M, P, Q",
"L, M, N, P"
] | 3 |
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 can... | Among the people selected to attend the retirement dinner there must be | [
"K or Q or both",
"L or M or both",
"N or M or both",
"N or Q or both",
"P or Q or both"
] | 1 |
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 can... | Which one of the following is a pair of people who CANNOT both be selected to attend the retirement dinner? | [
"J and N",
"J and Q",
"K and L",
"K and N",
"N and Q"
] | 1 |
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 can... | 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? | [
"J and Q",
"K and L",
"K and P",
"L and P",
"N and Q"
] | 1 |
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 can... | 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? | [
"one",
"two",
"three",
"four",
"five"
] | 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 can... | 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? | [
"J and L",
"K and M",
"L and N",
"L and Q",
"M and Q"
] | 4 |
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... | 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? | [
"Rita",
"Sarah",
"Tura",
"Rita, Sarah",
"Rita, Tura"
] | 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... | If Miguel partners Rita in dance 2, which one of the following could be true? | [
"Karl partners Tura in dance 1.",
"Luis partners Sarah in dance 2.",
"Luis partners Sarah in dance 3.",
"Miguel partners Sarah in dance 1.",
"Miguel partners Tura in dance 3."
] | 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... | 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? | [
"Karl and Rita",
"Karl and Tura",
"Luis and Rita",
"Luis and Tura",
"Miguel and Tura"
] | 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... | 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? | [
"Karl and Rita",
"Karl and Tura",
"Luis and Rita",
"Luis and Tura",
"Miguel and Rita"
] | 2 |
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... | If Miguel partners Rita in dance 1, which one of the following must be true? | [
"Karl partners Rita in dance 2.",
"Karl partners Sarah in dance 3.",
"Karl partners Tura in dance 1.",
"Luis partners Rita in dance 2.",
"Luis partners Tura in dance 3."
] | 3 |
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 mo... | Which one of the following could be true? | [
"City 5 contains a university.",
"City 6 contains a university.",
"City 2 contains a jail.",
"City 3 contains a jail.",
"City 3 contains a hospital."
] | 4 |
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 mo... | Which one of the following could be true? | [
"City 1 contains exactly one hospital.",
"City 1 contains exactly one university.",
"City 2 contains exactly one jail.",
"City 5 contains exactly one university.",
"City 6 contains exactly one university."
] | 0 |
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 mo... | 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? | [
"1, 4",
"2, 4",
"4, 5",
"1, 4, 5",
"1, 2, 4, 5"
] | 3 |
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 mo... | If each of the six cities contains at least one of the eight institutions, then which one of the following must be true? | [
"There is a jail in city 1.",
"There is a hospital in city 2.",
"There is a hospital in city 3.",
"There is a hospital in city 4.",
"There is a jail in city 4."
] | 3 |
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 mo... | In which one of the following cities must there be fewer than three hospitals? | [
"1",
"2",
"4",
"5",
"6"
] | 1 |
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 mo... | 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? | [
"1, 3, 5",
"1, 4, 5",
"2, 3, 5",
"2, 4, 6",
"4, 5, 6"
] | 0 |
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... | How many different combinations of students could form the level 1 class? | [
"one",
"two",
"three",
"four",
"six"
] | 1 |
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... | Which one of the following students could be in the level 2 class but cannot be in the level 3 class? | [
"Fred",
"Glen",
"Jan",
"Kathy",
"Nick"
] | 2 |
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... | Which one of the following students could be placed in any one of the three classes? | [
"Fred",
"Jan",
"Kathy",
"Laura",
"Mike"
] | 2 |
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... | 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? | [
"Fred and Kathy",
"Fred and Mike",
"Hilary and Jan",
"Kathy and Laura",
"Laura and Mike"
] | 2 |
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... | Which one of the following pairs of students cannot be in the same class as Fred? | [
"Hilary and Nick",
"Jan and Laura",
"Kathy and Laura",
"Jan and Mike",
"Laura and Mike"
] | 4 |
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... | If Lena reviews Seasonings, which one of the following must be true? | [
"Hilda reviews Retreat.",
"Jackie reviews Seasonings.",
"Karl reviews Mystery.",
"Karl reviews Retreat.",
"Karl reviews Wolves."
] | 0 |
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... | If Karl does not review Seasonings, which one of the following must be true? | [
"Lena reviews Mystery.",
"Lena reviews Retreat.",
"Lena reviews Seasonings.",
"Frank and Hilda review Retreat.",
"Frank and Hilda review Seasonings."
] | 4 |
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... | Which one of the following is a complete and accurate list of the movies each of which could be the movie that Lena reviews? | [
"Mystery, Retreat",
"Retreat, Seasonings",
"Mystery, Seasonings, Wolves",
"Retreat, Seasonings, Wolves",
"Mystery, Retreat, Seasonings, Wolves"
] | 4 |
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... | Which one of the following can be true? | [
"Frank and George review Mystery.",
"Frank and Lena review Wolves.",
"George and Jackie review Mystery.",
"Karl reviews Wolves and Lena reviews Mystery.",
"Lena reviews Retreat and Frank reviews Seasonings."
] | 4 |
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... | Lena can review any of the following EXCEPT | [
"Mystery with George",
"Mystery with Karl",
"Retreat with Karl",
"Seasonings with Karl",
"Wolves with Jackie"
] | 1 |
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... | 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? | [
"Mystery, Retreat",
"Mystery, Seasonings",
"Retreat, Seasonings",
"Mystery, Seasonings, Wolves",
"Retreat, Seasonings, Wolves"
] | 2 |
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... | Which one of the following is an acceptable assignment of reviewers to movies? Mystery Retreat Seasonings Wolves | [
"George Frank, Hilda Jackie, Lena Karl",
"George Frank, Hilda Karl, Lena Jackie",
"George Karl, Lena Jackie Frank, Hilda",
"George, Karl Frank, Hilda Lena Jackie",
"Jackie George, Lena Frank, Hilda Karl"
] | 1 |
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... | Which one of the following could be a sentence in the word game? | [
"bzeak bleak leak peak pea",
"crbek creek reek seek sxeek",
"dteam gleam glean lean mean",
"feed freed reed seed seeg",
"food fool fools fopls opls"
] | 1 |
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... | The last letter of the alphabet that the first word of a sentence in the word game can begin with is | [
"t",
"w",
"x",
"y",
"z"
] | 3 |
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... | If the first word in a sentence is "blender" and the third word is "slender", then the second word can be | [
"bender",
"gender",
"lender",
"sender",
"tender"
] | 2 |
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... | If the first word in a sentence consists of nine letters, then the minimum number of letters that the fourth word can contain is | [
"four",
"five",
"six",
"seven",
"eight"
] | 3 |
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... | 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? | [
"second",
"third",
"fourth, fifth",
"second, third, fourth",
"third, fourth, fifth"
] | 4 |
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... | 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 | [
"four",
"five",
"six",
"seven",
"eight"
] | 2 |
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 cond... | Which one of the following is an acceptable selection of concertos that the soloist could play on the first through the sixth Sunday? | [
"H Z M N Y K",
"K J Y O Z N",
"K Y P J Z M",
"P Y J H X O",
"X N K O J Z"
] | 1 |
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 cond... | 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? | [
"J",
"K",
"O",
"Y",
"Z"
] | 2 |
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 cond... | 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? | [
"H",
"K",
"N",
"P",
"X"
] | 4 |
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 cond... | If O is selected for the first Sunday, which one of the following is a concerto that must also be selected? | [
"J",
"K",
"M",
"N",
"X"
] | 1 |
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 cond... | Which one of the following is a concerto that must be selected? | [
"J",
"K",
"O",
"Y",
"Z"
] | 3 |
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 cond... | Which one of the following is a concerto that CANNOT be selected together with N? | [
"M",
"O",
"P",
"X",
"Z"
] | 0 |
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... | Which one of the following is an acceptable assignment of the counselors to the activities? | [
"Swimming: Fran, George, Henry; Tennis: Joan, Lewis; Volleyball: Kathy, Nathan, Olga",
"Swimming: George, Henry, Olga; Tennis: Fran, Joan, Lewis; Volleyball: Kathy, Nathan",
"Swimming: Henry; Tennis: Fran, George, Joan, Lewis; Volleyball: Kathy, Nathan, Olga",
"Swimming: Henry, Joan, Kathy; Tennis: George, Na... | 0 |
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... | Which one of the following is a pair of counselors who could be two of three counselors assigned to supervise swimming? | [
"George and Nathan",
"George and Olga",
"Joan and Kathy",
"Joan and Nathan",
"Joan and Olga"
] | 4 |
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... | Which one of the following is a pair of counselors who could together be assigned to supervise tennis? | [
"Fran and Kathy",
"George and Nathan",
"Henry and Lewis",
"Joan and Nathan",
"Joan and Olga"
] | 1 |
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... | If George and Kathy are two of three counselors assigned to supervise swimming, which one of the following could be true of the assignment? | [
"Fran supervises swimming.",
"Henry supervises tennis.",
"Joan supervises volleyball.",
"Lewis supervises volleyball.",
"Nathan supervises tennis."
] | 3 |
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... | If Fran and Lewis are two of three counselors assigned to supervise swimming, which one of the following must be true of the assignment? | [
"George supervises volleyball.",
"Henry supervises volleyball.",
"Joan supervises tennis.",
"Kathy supervises swimming.",
"Nathan supervises tennis."
] | 2 |
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... | If Joan is assigned to supervise the same activity as Olga, which one of the following CANNOT be true of the assignment? | [
"Fran supervises swimming.",
"George supervises swimming.",
"Kathy supervises volleyball.",
"Lewis supervises volleyball.",
"Nathan supervises tennis."
] | 1 |
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 ... | Which one of the following CANNOT be a Monday-to-Friday work schedule? | [
"Fuentes, Iman, Fuentes, Jackson, Iman",
"Fuentes, Jackson, Howell, Graber, Fuentes",
"Graber, Fuentes, Graber, Fuentes, Jackson",
"Graber, Howell, Graber, Fuentes, Jackson",
"Howell, Graber, Iman, Graber, Iman"
] | 1 |
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 ... | 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? | [
"Howell, Graber, Howell, Graber, Iman",
"Howell, Howell, Graber, Fuentes, Iman",
"Iman, Fuentes, Jackson, Iman, Iman",
"Fuentes, Howell, Graber, Fuentes, Jackson",
"Jackson, Howell, Graber, Iman, Fuentes"
] | 3 |
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 ... | If both Fuentes and Jackson work during a week, which one of the following statements CANNOT be true? | [
"Fuentes works on Monday and Wednesday.",
"Jackson works on Monday and Wednesday.",
"Fuentes works on Tuesday and Thursday.",
"Jackson works on Tuesday and Thursday.",
"Jackson works on Wednesday and Friday."
] | 1 |
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 ... | If Fuentes works two days during the week and Jackson works on Thursday, which one of the following statements could be true? | [
"Fuentes works on Tuesday.",
"Graber works on Tuesday.",
"Howell works on Tuesday.",
"Graber works on Wednesday.",
"Howell works on Wednesday."
] | 1 |
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 ... | If Graber does not work during the week, which one of the following statements must be true? | [
"Fuentes works exactly one day during the week.",
"Fuentes works exactly two days during the week.",
"Iman works exactly one day during the week.",
"Iman works exactly two days during the week.",
"Jackson works exactly one day during the week."
] | 3 |
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 re... | Which one of the following is an acceptable selection of representatives for the committee? | [
"F, G, Q, R, S",
"F, J, K, P, Q",
"F, P, Q, R, S",
"J, K, M, Q, S",
"J, M, P, Q, S"
] | 3 |
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 re... | Which one of the following lists three representatives who could be selected together for the committee? | [
"F, G, J",
"F, G, M",
"F, J, M",
"G, J, K",
"G, J, M"
] | 2 |
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 re... | If M is the chairperson of the committee, which one of the following is among the people who must also be on the committee? | [
"F",
"G",
"K",
"P",
"R"
] | 4 |
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 re... | If F is the chairperson of the committee, which one of the following is among the people who must also be on the committee? | [
"G",
"K",
"P",
"R",
"S"
] | 1 |
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 re... | If F is selected, any one of the following people could be the chairperson of the committee EXCEPT: | [
"G",
"K",
"P",
"Q",
"S"
] | 0 |
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 re... | If neither F nor K is selected for the committee, which one of the following can be true? | [
"G is selected.",
"P is selected.",
"J is the chairperson.",
"Q is the chairperson.",
"S is the chairperson."
] | 2 |
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 re... | If the chairperson of the committee is to be a homeowner, which one of the following must be true? | [
"If G is selected, Q is also selected.",
"If G is selected, R is also selected.",
"If J is selected, F is also selected.",
"If J is selected, Q is also selected.",
"If J is selected, R is also selected."
] | 0 |
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 re... | The committee must include at least one representative from which one of the following pairs? | [
"F, P",
"G, J",
"K, Q",
"M, P",
"R, S"
] | 2 |
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... | 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 ? | [
"Louis is assigned to project S.",
"Madelyn is assigned to project R.",
"Madelyn is assigned to project S.",
"Oliver is assigned to project R.",
"Oliver is assigned to project S."
] | 4 |
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... | Which one of the following could be true after only one reassignment during the year? | [
"Louis is assigned to project T.",
"Nora is assigned to project R.",
"Oliver is assigned to project Q.",
"Louis and Nora each remain assigned to the same projects as before.",
"Nora and Oliver each remain assigned to the same projects as before."
] | 4 |
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... | 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? | [
"Q: Louis; R: Madelyn; S: Oliver; T: Nora",
"Q: Louis; R: Nora; S: Oliver; T: Madelyn",
"Q: Nora; R: Madelyn; S: Louis; T: Oliver",
"Q: Nora; R: Oliver; S: Louis; T: Madelyn",
"Q: Oliver; R: Nora; S: Louis; T: Madelyn"
] | 0 |
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... | Which one of the following is an acceptable assignment of apprentices to the projects after only one reassignment during the year? | [
"Q: Louis; R: Madelyn; S: Nora; T: Oliver",
"Q: Madelyn; R: Louis; S: Nora; T: Oliver",
"Q: Madelyn; R: Oliver; S: Nora; T: Louis",
"Q: Nora; R: Louis; S: Oliver; T: Madelyn",
"Q: Nora; R: Madelyn; S: Oliver; T: Louis"
] | 1 |
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... | If the first reassignment is made according to plan 1, which one of the following must be true? | [
"Louis is assigned to project T as a result of the second reassignment.",
"Madelyn is assigned to project Q as a result of the second reassignment.",
"Madelyn is assigned to project T as a result of the second reassignment.",
"Oliver is assigned to project S as a result of the second reassignment.",
"Oliver... | 0 |
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 tha... | 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? | [
"Grace",
"Henry",
"Steve",
"Tom",
"Una"
] | 4 |
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 tha... | 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? | [
"Grace",
"Henry",
"Steve",
"Tom",
"Una"
] | 1 |
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 tha... | 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? | [
"Grace",
"Tom",
"Grace, Tom",
"Henry, Tom",
"Grace, Henry, Tom"
] | 2 |
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 tha... | 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 | [
"first day",
"second day",
"third day",
"fourth day",
"fifth day"
] | 1 |
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 tha... | If Janet's lesson is scheduled for the third day, which one of the following could be true? | [
"Grace's lesson is scheduled for a later day than Henry's lesson.",
"Grace's lesson is scheduled for a later day than Una's lesson.",
"Henry's lesson is scheduled for a later day than Una's lesson.",
"Tom's lesson is scheduled for a later day than Henry's lesson.",
"Tom's lesson is scheduled for a later day... | 2 |
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 tha... | 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? | [
"first, second, third",
"second, third, fourth",
"second, fifth, sixth",
"first, second, third, fourth",
"second, third, fourth, sixth"
] | 3 |
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... | If F is in group 1, which one of the following could be true? | [
"G and K are in group 3.",
"G and R are in group 3.",
"J and S are in group 2.",
"K and R are in group 1.",
"Q and S are in group 2."
] | 4 |
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... | If F and S are in group 3, which one of the following must be true? | [
"G is in group 2.",
"H is in group 3.",
"K is in group 1.",
"Q is in group 2.",
"R is in group 1."
] | 0 |
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... | If G and K are in group 3, which one of the following must be true? | [
"H is in group 3.",
"J is in group 1.",
"R is in group 2.",
"S is in group 3.",
"T is in group 1."
] | 4 |
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... | If Q is in group 1 and S is in group 3, which one of the following CANNOT be true? | [
"G is in group 2.",
"T is in group 1.",
"There is exactly one child in group 1.",
"There is exactly one child in group 2.",
"There is exactly one child in group 3."
] | 3 |
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... | If G is the only child in group 1, which one of the following must be true? | [
"F is in group 3.",
"K is in group 3.",
"Q is in group 2.",
"R is in group 1.",
"S is in group 2."
] | 1 |
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... | Which one of the following statements must be true? | [
"Lara buys a hot dog.",
"Lara buys a shish kebab.",
"Mendel buys a hot dog.",
"Mendel buys a pretzel.",
"Nastassia buys a hot dog."
] | 3 |
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