benlipkin/arlsat huggingface dataset:
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.

Question: If corsage 2 is exactly the same as corsage 3, the nine flowers used in the corsages can include exactly
Options:
two orchids
three gardenias
three roses
five roses
five violets
Correct option (0-indexed): 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. 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.

Question: If two of the corsages contain at least one orchid each, then the flowers in corsage 2 must include at least
Options:
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
Correct option (0-indexed): 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. 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.

Question: If the greatest possible number of violets is used in the three corsages, the florist must use
Options:
exactly one rose and exactly one gardenia
exactly one orchid and exactly four violets
exactly two orchids
exactly two roses
exactly six violets
Correct option (0-indexed): 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.

Question: 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?
Options:
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
Correct option (0-indexed): 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 cannot be selected unless L is selected. Q cannot be selected unless K is selected.

Question: Which one of the following could be the four people selected to attend the retirement dinner?
Options:
J, K, M, P
J, L, N, Q
J, M, N, Q
K, M, P, Q
L, M, N, P
Correct option (0-indexed): 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 cannot be selected unless L is selected. Q cannot be selected unless K is selected.

Question: Among the people selected to attend the retirement dinner there must be
Options:
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
Correct option (0-indexed): 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 cannot be selected unless L is selected. Q cannot be selected unless K is selected.

Question: Which one of the following is a pair of people who CANNOT both be selected to attend the retirement dinner?
Options:
J and N
J and Q
K and L
K and N
N and Q
Correct option (0-indexed): 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 cannot be selected unless L is selected. Q cannot be selected unless K is selected.

Question: 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?
Options:
J and Q
K and L
K and P
L and P
N and Q
Correct option (0-indexed): 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 cannot be selected unless L is selected. Q cannot be selected unless K is selected.

Question: 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?
Options:
one
two
three
four
five
Correct option (0-indexed): 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.

Question: 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?
Options:
J and L
K and M
L and N
L and Q
M and Q
Correct option (0-indexed): 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 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.

Question: 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?
Options:
Rita
Sarah
Tura
Rita, Sarah
Rita, Tura
Correct option (0-indexed): 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.

Question: If Miguel partners Rita in dance 2, which one of the following could be true?
Options:
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.
Correct option (0-indexed): 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.

Question: 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?
Options:
Karl and Rita
Karl and Tura
Luis and Rita
Luis and Tura
Miguel and Tura
Correct option (0-indexed): 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.

Question: 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?
Options:
Karl and Rita
Karl and Tura
Luis and Rita
Luis and Tura
Miguel and Rita
Correct option (0-indexed): 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 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.

Question: If Miguel partners Rita in dance 1, which one of the following must be true?
Options:
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.
Correct option (0-indexed): 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 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.

Question: Which one of the following could be true?
Options:
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.
Correct option (0-indexed): 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 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.

Question: Which one of the following could be true?
Options:
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.
Correct option (0-indexed): 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 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.

Question: 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?
Options:
1, 4
2, 4
4, 5
1, 4, 5
1, 2, 4, 5
Correct option (0-indexed): 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 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.

Question: If each of the six cities contains at least one of the eight institutions, then which one of the following must be true?
Options:
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.
Correct option (0-indexed): 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 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.

Question: In which one of the following cities must there be fewer than three hospitals?
Options:
1
2
4
5
6
Correct option (0-indexed): 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 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.

Question: 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?
Options:
1, 3, 5
1, 4, 5
2, 3, 5
2, 4, 6
4, 5, 6
Correct option (0-indexed): 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 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.

Question: How many different combinations of students could form the level 1 class?
Options:
one
two
three
four
six
Correct option (0-indexed): 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 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.

Question: Which one of the following students could be in the level 2 class but cannot be in the level 3 class?
Options:
Fred
Glen
Jan
Kathy
Nick
Correct option (0-indexed): 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 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.

Question: Which one of the following students could be placed in any one of the three classes?
Options:
Fred
Jan
Kathy
Laura
Mike
Correct option (0-indexed): 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 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.

Question: 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?
Options:
Fred and Kathy
Fred and Mike
Hilary and Jan
Kathy and Laura
Laura and Mike
Correct option (0-indexed): 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 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.

Question: Which one of the following pairs of students cannot be in the same class as Fred?
Options:
Hilary and Nick
Jan and Laura
Kathy and Laura
Jan and Mike
Laura and Mike
Correct option (0-indexed): 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 the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Question: If Lena reviews Seasonings, which one of the following must be true?
Options:
Hilda reviews Retreat.
Jackie reviews Seasonings.
Karl reviews Mystery.
Karl reviews Retreat.
Karl reviews Wolves.
Correct option (0-indexed): 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 the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Question: If Karl does not review Seasonings, which one of the following must be true?
Options:
Lena reviews Mystery.
Lena reviews Retreat.
Lena reviews Seasonings.
Frank and Hilda review Retreat.
Frank and Hilda review Seasonings.
Correct option (0-indexed): 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 the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Question: Which one of the following is a complete and accurate list of the movies each of which could be the movie that Lena reviews?
Options:
Mystery, Retreat
Retreat, Seasonings
Mystery, Seasonings, Wolves
Retreat, Seasonings, Wolves
Mystery, Retreat, Seasonings, Wolves
Correct option (0-indexed): 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 the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Question: Which one of the following can be true?
Options:
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.
Correct option (0-indexed): 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 the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Question: Lena can review any of the following EXCEPT
Options:
Mystery with George
Mystery with Karl
Retreat with Karl
Seasonings with Karl
Wolves with Jackie
Correct option (0-indexed): 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 the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Question: 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?
Options:
Mystery, Retreat
Mystery, Seasonings
Retreat, Seasonings
Mystery, Seasonings, Wolves
Retreat, Seasonings, Wolves
Correct option (0-indexed): 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 the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Question: Which one of the following is an acceptable assignment of reviewers to movies? Mystery Retreat Seasonings Wolves
Options:
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
Correct option (0-indexed): 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 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.

Question: Which one of the following could be a sentence in the word game?
Options:
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
Correct option (0-indexed): 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 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.

Question: The last letter of the alphabet that the first word of a sentence in the word game can begin with is
Options:
t
w
x
y
z
Correct option (0-indexed): 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 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.

Question: If the first word in a sentence is "blender" and the third word is "slender", then the second word can be
Options:
bender
gender
lender
sender
tender
Correct option (0-indexed): 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 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.

Question: If the first word in a sentence consists of nine letters, then the minimum number of letters that the fourth word can contain is
Options:
four
five
six
seven
eight
Correct option (0-indexed): 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 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.

Question: 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?
Options:
second
third
fourth, fifth
second, third, fourth
third, fourth, fifth
Correct option (0-indexed): 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 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.

Question: 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
Options:
four
five
six
seven
eight
Correct option (0-indexed): 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 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.

Question: Which one of the following is an acceptable selection of concertos that the soloist could play on the first through the sixth Sunday?
Options:
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
Correct option (0-indexed): 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 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.

Question: 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?
Options:
J
K
O
Y
Z
Correct option (0-indexed): 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 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.

Question: 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?
Options:
H
K
N
P
X
Correct option (0-indexed): 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 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.

Question: If O is selected for the first Sunday, which one of the following is a concerto that must also be selected?
Options:
J
K
M
N
X
Correct option (0-indexed): 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 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.

Question: Which one of the following is a concerto that must be selected?
Options:
J
K
O
Y
Z
Correct option (0-indexed): 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 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.

Question: Which one of the following is a concerto that CANNOT be selected together with N?
Options:
M
O
P
X
Z
Correct option (0-indexed): 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, 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.

Question: Which one of the following is an acceptable assignment of the counselors to the activities?
Options:
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, Nathan; Volleyball: Fran, Lewis, Olga
Swimming: Henry, Nathan; Tennis: Fran, Kathy, Lewis; Volleyball: George, Joan, Olga
Correct option (0-indexed): 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, 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.

Question: Which one of the following is a pair of counselors who could be two of three counselors assigned to supervise swimming?
Options:
George and Nathan
George and Olga
Joan and Kathy
Joan and Nathan
Joan and Olga
Correct option (0-indexed): 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, 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.

Question: Which one of the following is a pair of counselors who could together be assigned to supervise tennis?
Options:
Fran and Kathy
George and Nathan
Henry and Lewis
Joan and Nathan
Joan and Olga
Correct option (0-indexed): 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, 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.

Question: If George and Kathy are two of three counselors assigned to supervise swimming, which one of the following could be true of the assignment?
Options:
Fran supervises swimming.
Henry supervises tennis.
Joan supervises volleyball.
Lewis supervises volleyball.
Nathan supervises tennis.
Correct option (0-indexed): 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, 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.

Question: If Fran and Lewis are two of three counselors assigned to supervise swimming, which one of the following must be true of the assignment?
Options:
George supervises volleyball.
Henry supervises volleyball.
Joan supervises tennis.
Kathy supervises swimming.
Nathan supervises tennis.
Correct option (0-indexed): 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, 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.

Question: If Joan is assigned to supervise the same activity as Olga, which one of the following CANNOT be true of the assignment?
Options:
Fran supervises swimming.
George supervises swimming.
Kathy supervises volleyball.
Lewis supervises volleyball.
Nathan supervises tennis.
Correct option (0-indexed): 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 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.

Question: Which one of the following CANNOT be a Monday-to-Friday work schedule?
Options:
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
Correct option (0-indexed): 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 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.

Question: 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?
Options:
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
Correct option (0-indexed): 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 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.

Question: If both Fuentes and Jackson work during a week, which one of the following statements CANNOT be true?
Options:
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.
Correct option (0-indexed): 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 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.

Question: If Fuentes works two days during the week and Jackson works on Thursday, which one of the following statements could be true?
Options:
Fuentes works on Tuesday.
Graber works on Tuesday.
Howell works on Tuesday.
Graber works on Wednesday.
Howell works on Wednesday.
Correct option (0-indexed): 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 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.

Question: If Graber does not work during the week, which one of the following statements must be true?
Options:
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.
Correct option (0-indexed): 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 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.

Question: Which one of the following is an acceptable selection of representatives for the committee?
Options:
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
Correct option (0-indexed): 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 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.

Question: Which one of the following lists three representatives who could be selected together for the committee?
Options:
F, G, J
F, G, M
F, J, M
G, J, K
G, J, M
Correct option (0-indexed): 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 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.

Question: If M is the chairperson of the committee, which one of the following is among the people who must also be on the committee?
Options:
F
G
K
P
R
Correct option (0-indexed): 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 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.

Question: If F is the chairperson of the committee, which one of the following is among the people who must also be on the committee?
Options:
G
K
P
R
S
Correct option (0-indexed): 1