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John receives one grade for each of the following six courses: economics, geology, history, Italian, physics, and Russian. From highest to lowest, the possible grades are A, B, C, D, and E. E is the only failing grade. Two letter grades are consecutive if and only if they are adjacent in the alphabet. John's grades in geology and physics are consecutive. His grades in Italian and Russian are consecutive. He receives a higher grade in economics than in history. He receives a higher grade in geology than in physics. | 199206_2-G_1_5 | [
"John receives both an A and a B.",
"John receives both an A and a C.",
"John receives both a B and a D.",
"John receives both a B and an E.",
"John receives both a D and an E."
] | 2 | Assume that John's grade in physics is higher than his grade in Italian and consecutive with it and that his grades in Russian and physics differ. Which one of the following must be true? |
John receives one grade for each of the following six courses: economics, geology, history, Italian, physics, and Russian. From highest to lowest, the possible grades are A, B, C, D, and E. E is the only failing grade. Two letter grades are consecutive if and only if they are adjacent in the alphabet. John's grades in geology and physics are consecutive. His grades in Italian and Russian are consecutive. He receives a higher grade in economics than in history. He receives a higher grade in geology than in physics. | 199206_2-G_1_6 | [
"He receives a lower grade in Italian than in economics.",
"He receives a lower grade in Italian than in physics.",
"He receives a lower grade in physics than in Italian.",
"He receives a lower grade in Russian than in economics.",
"He receives a lower grade in Russian than in history."
] | 4 | Assume that John receives a lower grade in economics than in physics. He must have failed at least one course if which one of the following is also true? |
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available. | 199206_2-G_2_7 | [
"Two of the shirts that Casey buys are small and two are red.",
"Two of the shirts that Casey buys are medium and two are red.",
"Two of the shirts that Casey buys are large and two are red.",
"Two of the shirts that Casey buys are small, one is yellow, and one is blue.",
"Two of the shirts that Casey buys are medium, one is yellow, and one is blue."
] | 0 | Which one of the following must be false? |
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available. | 199206_2-G_2_8 | [
"Casey buys two blue shirts.",
"Casey buys two red shirts.",
"Casey buys two yellow shirts.",
"Casey buys two small shirts.",
"Casey buys two medium shirts."
] | 1 | If Casey buys a small blue shirt, which one of the following must be false? |
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available. | 199206_2-G_2_9 | [
"Casey buys either a medium red shirt or a small blue shirt.",
"Casey buys either a medium red shirt or a medium blue shirt.",
"Casey buys either a large red shirt or a small blue shirt.",
"Casey buys either a large red shirt or a medium red shirt.",
"Casey buys either a large yellow shirt or a small yellow shirt."
] | 1 | If Casey does not buy a medium yellow shirt, which one of the following must be true? |
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available. | 199206_2-G_2_10 | [
"a medium red shirt",
"a medium yellow shirt",
"a medium blue shirt",
"a large red shirt",
"a large yellow shirt"
] | 1 | If Casey buys exactly one medium shirt and does not buy two shirts of the same color, then she cannot buy which one of the following? |
A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available. | 199206_2-G_2_11 | [
"a red shirt",
"a medium yellow shirt",
"either a large shirt or a small shirt",
"either a medium red shirt or a medium blue shirt",
"either a large yellow shirt or a medium blue shirt"
] | 3 | If neither large red shirts nor small blue shirts are available, which one of the following must Casey buy? |
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X. | 199206_2-G_3_12 | [
"G, H, K W, Y",
"G, J, K W, X",
"G, J, L X, Z",
"H, J, L W, Z",
"H, K, L Y, Z"
] | 1 | Which one of the following is an acceptable selection of fish and plants for the aquarium? Fish Plants |
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X. | 199206_2-G_3_13 | [
"She selects at least one W.",
"She selects at least one X.",
"She selects the J, but no Y's.",
"She selects the K, but no X's.",
"She selects at least one X, but no Y's."
] | 1 | If the hobbyist selects the H, which one of the following must also be true? |
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X. | 199206_2-G_3_14 | [
"G, H, K",
"G, J, K",
"G, K, L",
"H, J, L",
"J, K, L"
] | 2 | If the hobbyist selects both X's and Z's, which one of the following could be the group of fish she selects? |
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X. | 199206_2-G_3_15 | [
"G, K, L",
"H, J, K",
"H, J, L",
"H, K, L",
"J, K, L"
] | 2 | The hobbyist could select any of the following groups of fish for the aquarium EXCEPT |
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X. | 199206_2-G_3_16 | [
"G, H, K",
"H, J, K",
"H, J, L",
"H, K, L",
"J, K, L"
] | 3 | If the hobbyist selects a Y, which one of the following must be the group of fish she selects? |
A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X. | 199206_2-G_3_17 | [
"W and X",
"W and Y",
"W and Z",
"X and Y",
"X and Z"
] | 1 | The hobbyist could select any of the following plant combinations EXCEPT |
A committee ranks five towns—Palmdale, Quietville, Riverdale, Seaside, Tidetown—from first (best) to fifth (worst) on each of three criteria: climate, location, friendliness. For each of the three criteria, none of the five towns receives the same ranking as any other town does. In climate, Tidetown is ranked third, and Seaside fourth. In location, Quietville is ranked second, Riverdale third, Palmdale fourth. In friendliness, Tidetown's ranking is better than Palmdale's, Quietville is ranked fourth and Seaside fifth. Riverdale receives a better ranking in climate than in friendliness. Quietville's three ranking are all different from each other. | 199206_2-G_4_18 | [
"first",
"first, second",
"first, fifth",
"second, fifth",
"first, second, fifth"
] | 1 | Which of the following is a complete and accurate list of the rankings any one of which could be the ranking on climate given to Riverdale? |
A committee ranks five towns—Palmdale, Quietville, Riverdale, Seaside, Tidetown—from first (best) to fifth (worst) on each of three criteria: climate, location, friendliness. For each of the three criteria, none of the five towns receives the same ranking as any other town does. In climate, Tidetown is ranked third, and Seaside fourth. In location, Quietville is ranked second, Riverdale third, Palmdale fourth. In friendliness, Tidetown's ranking is better than Palmdale's, Quietville is ranked fourth and Seaside fifth. Riverdale receives a better ranking in climate than in friendliness. Quietville's three ranking are all different from each other. | 199206_2-G_4_19 | [
"Palmdale",
"Quietville",
"Riverdale",
"Seaside",
"Tidetown"
] | 2 | Which of the following is a town that CANNOT be ranked fifth on any one of the three criteria? |
A committee ranks five towns—Palmdale, Quietville, Riverdale, Seaside, Tidetown—from first (best) to fifth (worst) on each of three criteria: climate, location, friendliness. For each of the three criteria, none of the five towns receives the same ranking as any other town does. In climate, Tidetown is ranked third, and Seaside fourth. In location, Quietville is ranked second, Riverdale third, Palmdale fourth. In friendliness, Tidetown's ranking is better than Palmdale's, Quietville is ranked fourth and Seaside fifth. Riverdale receives a better ranking in climate than in friendliness. Quietville's three ranking are all different from each other. | 199206_2-G_4_20 | [
"Palmdale is ranked first in both climate and friendliness.",
"Quietville is ranked second in both climate and location.",
"Riverdale is ranked first in climate and third in both location and friendliness.",
"Seaside is ranked fifth in friendliness and fourth in both climate and location.",
"Tidetown is ranked third in both climate and friendliness."
] | 2 | Which of the following could be true? |
A committee ranks five towns—Palmdale, Quietville, Riverdale, Seaside, Tidetown—from first (best) to fifth (worst) on each of three criteria: climate, location, friendliness. For each of the three criteria, none of the five towns receives the same ranking as any other town does. In climate, Tidetown is ranked third, and Seaside fourth. In location, Quietville is ranked second, Riverdale third, Palmdale fourth. In friendliness, Tidetown's ranking is better than Palmdale's, Quietville is ranked fourth and Seaside fifth. Riverdale receives a better ranking in climate than in friendliness. Quietville's three ranking are all different from each other. | 199206_2-G_4_21 | [
"Palmdale is ranked second in climate",
"Palmdale is ranked third in friendliness",
"Riverdale is ranked second in friendliness",
"Riverdale is ranked third in friendliness",
"Tidetown is ranked fifth in location"
] | 3 | If Quietville is ranked first in climate, then it must be true that |
A committee ranks five towns—Palmdale, Quietville, Riverdale, Seaside, Tidetown—from first (best) to fifth (worst) on each of three criteria: climate, location, friendliness. For each of the three criteria, none of the five towns receives the same ranking as any other town does. In climate, Tidetown is ranked third, and Seaside fourth. In location, Quietville is ranked second, Riverdale third, Palmdale fourth. In friendliness, Tidetown's ranking is better than Palmdale's, Quietville is ranked fourth and Seaside fifth. Riverdale receives a better ranking in climate than in friendliness. Quietville's three ranking are all different from each other. | 199206_2-G_4_22 | [
"Palmdale is ranked second in friendliness.",
"Quietville is ranked first in climate.",
"Riverdale is ranked first in friendliness.",
"Riverdale is ranked fifth in climate.",
"Tidetown is ranked third in friendliness."
] | 0 | If Palmdale is ranked second in climate, then which one of the following can be true? |
A committee ranks five towns—Palmdale, Quietville, Riverdale, Seaside, Tidetown—from first (best) to fifth (worst) on each of three criteria: climate, location, friendliness. For each of the three criteria, none of the five towns receives the same ranking as any other town does. In climate, Tidetown is ranked third, and Seaside fourth. In location, Quietville is ranked second, Riverdale third, Palmdale fourth. In friendliness, Tidetown's ranking is better than Palmdale's, Quietville is ranked fourth and Seaside fifth. Riverdale receives a better ranking in climate than in friendliness. Quietville's three ranking are all different from each other. | 199206_2-G_4_23 | [
"One",
"Two",
"Three",
"Four",
"Five"
] | 4 | If Tidetown is ranked first in location and Riverdale is ranked second in friendliness, then it is possible to deduce with certainty all three rankings for exactly how many of the towns? |
A committee ranks five towns—Palmdale, Quietville, Riverdale, Seaside, Tidetown—from first (best) to fifth (worst) on each of three criteria: climate, location, friendliness. For each of the three criteria, none of the five towns receives the same ranking as any other town does. In climate, Tidetown is ranked third, and Seaside fourth. In location, Quietville is ranked second, Riverdale third, Palmdale fourth. In friendliness, Tidetown's ranking is better than Palmdale's, Quietville is ranked fourth and Seaside fifth. Riverdale receives a better ranking in climate than in friendliness. Quietville's three ranking are all different from each other. | 199206_2-G_4_24 | [
"Palmdale is ranked first in climate.",
"Quietville is ranked fifth in climate.",
"Riverdale is ranked third in friendliness.",
"Seaside is ranked first in location.",
"Tidetown is ranked second in friendliness."
] | 4 | Which one of the following statements CANNOT be true? |
Petworld has exactly fourteen animals (three gerbils, three hamsters, three lizards, five snakes) that are kept in four separate cages (W, X, Y, Z) according to the following conditions: Each cage contains exactly two, four, or six animals. Any cage containing a gerbil also contains at least one hamster; any cage containing a hamster also contains at least one gerbil. Any cage containing a lizard also contains at least one snake; any cage containing a snake also contains at least one lizard. Neither cage Y nor cage Z contains a gerbil. Neither cage W nor cage X contains a lizard. | 199210_4-G_1_1 | [
"W: one gerbil and one hamster Y: two lizards and two snakes",
"W: one gerbil and two hamsters Y: one lizard and three snakes",
"W: two gerbils and two hamsters Y: one lizard and four snakes",
"W: two gerbils and two hamsters Y: three lizards and one snake",
"W: two gerbils and two lizards Y: two hamsters and two snakes"
] | 0 | Which one of the following could be a complete and accurate list of the animals kept in cages W and Y? |
Petworld has exactly fourteen animals (three gerbils, three hamsters, three lizards, five snakes) that are kept in four separate cages (W, X, Y, Z) according to the following conditions: Each cage contains exactly two, four, or six animals. Any cage containing a gerbil also contains at least one hamster; any cage containing a hamster also contains at least one gerbil. Any cage containing a lizard also contains at least one snake; any cage containing a snake also contains at least one lizard. Neither cage Y nor cage Z contains a gerbil. Neither cage W nor cage X contains a lizard. | 199210_4-G_1_2 | [
"one",
"two",
"three",
"four",
"five"
] | 3 | If there are exactly two hamsters in cage W and the number of gerbils in cage X is equal to the number of snakes in cage Y, then the number of snakes in cage Z must be exactly |
Petworld has exactly fourteen animals (three gerbils, three hamsters, three lizards, five snakes) that are kept in four separate cages (W, X, Y, Z) according to the following conditions: Each cage contains exactly two, four, or six animals. Any cage containing a gerbil also contains at least one hamster; any cage containing a hamster also contains at least one gerbil. Any cage containing a lizard also contains at least one snake; any cage containing a snake also contains at least one lizard. Neither cage Y nor cage Z contains a gerbil. Neither cage W nor cage X contains a lizard. | 199210_4-G_1_3 | [
"Cage Y contains exactly two lizards.",
"Cage Y contains exactly two snakes.",
"Cage Y contains exactly four animals.",
"Cage Z contains exactly three snakes.",
"Cage Z contains exactly two animals."
] | 2 | If cage Z contains exactly twice as many lizards as cage Y, which one of the following can be true? |
Petworld has exactly fourteen animals (three gerbils, three hamsters, three lizards, five snakes) that are kept in four separate cages (W, X, Y, Z) according to the following conditions: Each cage contains exactly two, four, or six animals. Any cage containing a gerbil also contains at least one hamster; any cage containing a hamster also contains at least one gerbil. Any cage containing a lizard also contains at least one snake; any cage containing a snake also contains at least one lizard. Neither cage Y nor cage Z contains a gerbil. Neither cage W nor cage X contains a lizard. | 199210_4-G_1_4 | [
"Cage W contains exactly six animals.",
"Cage X contains exactly six animals.",
"Cage Y contains exactly one snake.",
"Cage Y contains exactly three snakes.",
"Cage Z contains exactly four snakes."
] | 3 | If the number of animals in cage W is equal to the number of animals in cage Z, then which one of the following can be true? |
Petworld has exactly fourteen animals (three gerbils, three hamsters, three lizards, five snakes) that are kept in four separate cages (W, X, Y, Z) according to the following conditions: Each cage contains exactly two, four, or six animals. Any cage containing a gerbil also contains at least one hamster; any cage containing a hamster also contains at least one gerbil. Any cage containing a lizard also contains at least one snake; any cage containing a snake also contains at least one lizard. Neither cage Y nor cage Z contains a gerbil. Neither cage W nor cage X contains a lizard. | 199210_4-G_1_5 | [
"Cage W contains two gerbils.",
"Cage X contains four animals.",
"Cage Z contains two snakes.",
"The number of snakes in cage Y is equal to the number of lizards in cage Y.",
"The number of snakes in cage Z is equal to the number of lizards in cage Z."
] | 4 | If cage Y contains six animals, which one of the following must be true? |
Petworld has exactly fourteen animals (three gerbils, three hamsters, three lizards, five snakes) that are kept in four separate cages (W, X, Y, Z) according to the following conditions: Each cage contains exactly two, four, or six animals. Any cage containing a gerbil also contains at least one hamster; any cage containing a hamster also contains at least one gerbil. Any cage containing a lizard also contains at least one snake; any cage containing a snake also contains at least one lizard. Neither cage Y nor cage Z contains a gerbil. Neither cage W nor cage X contains a lizard. | 199210_4-G_1_6 | [
"one",
"two",
"three",
"four",
"five"
] | 3 | At most, how many snakes can occupy cage Y at any one time? |
A soft drink manufacturer surveyed consumer preferences for exactly seven proposed names for its new soda: Jazz, Kola, Luck, Mist, Nipi, Oboy, and Ping. The manufacturer ranked the seven names according to the number of votes they received. The name that received the most votes was ranked first. Every name received a different number of votes. Some of the survey results are as follows: Jazz received more votes than Oboy. Oboy received more votes than Kola. Kola received more votes than Mist. Nipi did not receive the fewest votes. Ping received fewer votes than Luck but more votes than Nipi and more votes than Oboy. | 199210_4-G_2_7 | [
"Jazz, Luck, Ping, Nipi, Kola, Oboy, Mist",
"Jazz, Luck, Ping, Oboy, Kola, Mist, Nipi",
"Luck, Ping, Jazz, Nipi, Oboy, Kola, Mist",
"Luck, Ping, Nipi, Oboy, Jazz, Kola, Mist",
"Ping, Luck, Jazz, Oboy, Nipi, Kola, Mist"
] | 2 | Which one of the following could be an accurate list of the seven names in rank order from first through seventh? |
A soft drink manufacturer surveyed consumer preferences for exactly seven proposed names for its new soda: Jazz, Kola, Luck, Mist, Nipi, Oboy, and Ping. The manufacturer ranked the seven names according to the number of votes they received. The name that received the most votes was ranked first. Every name received a different number of votes. Some of the survey results are as follows: Jazz received more votes than Oboy. Oboy received more votes than Kola. Kola received more votes than Mist. Nipi did not receive the fewest votes. Ping received fewer votes than Luck but more votes than Nipi and more votes than Oboy. | 199210_4-G_2_8 | [
"Jazz received more votes than Nipi.",
"Kola received more votes than Nipi.",
"Luck received more votes than Jazz.",
"Nipi received more votes than Oboy.",
"Ping received more votes than Kola."
] | 4 | Which one of the following statements must be true? |
A soft drink manufacturer surveyed consumer preferences for exactly seven proposed names for its new soda: Jazz, Kola, Luck, Mist, Nipi, Oboy, and Ping. The manufacturer ranked the seven names according to the number of votes they received. The name that received the most votes was ranked first. Every name received a different number of votes. Some of the survey results are as follows: Jazz received more votes than Oboy. Oboy received more votes than Kola. Kola received more votes than Mist. Nipi did not receive the fewest votes. Ping received fewer votes than Luck but more votes than Nipi and more votes than Oboy. | 199210_4-G_2_9 | [
"Jazz received more votes than Luck.",
"Jazz received more votes than Ping.",
"Nipi received more votes than Oboy.",
"Nipi received more votes than Mist.",
"Oboy received more votes than Nipi."
] | 2 | If the ranks of Ping, Oboy, and Kola were consecutive, then which one of the following statements would have to be false? |
A soft drink manufacturer surveyed consumer preferences for exactly seven proposed names for its new soda: Jazz, Kola, Luck, Mist, Nipi, Oboy, and Ping. The manufacturer ranked the seven names according to the number of votes they received. The name that received the most votes was ranked first. Every name received a different number of votes. Some of the survey results are as follows: Jazz received more votes than Oboy. Oboy received more votes than Kola. Kola received more votes than Mist. Nipi did not receive the fewest votes. Ping received fewer votes than Luck but more votes than Nipi and more votes than Oboy. | 199210_4-G_2_10 | [
"one",
"two",
"three",
"four",
"five"
] | 0 | What is the total number of the soft drink names whose exact ranks can be deduced from the partial survey results? |
A soft drink manufacturer surveyed consumer preferences for exactly seven proposed names for its new soda: Jazz, Kola, Luck, Mist, Nipi, Oboy, and Ping. The manufacturer ranked the seven names according to the number of votes they received. The name that received the most votes was ranked first. Every name received a different number of votes. Some of the survey results are as follows: Jazz received more votes than Oboy. Oboy received more votes than Kola. Kola received more votes than Mist. Nipi did not receive the fewest votes. Ping received fewer votes than Luck but more votes than Nipi and more votes than Oboy. | 199210_4-G_2_11 | [
"three",
"four",
"five",
"six",
"seven"
] | 1 | What is the maximum possible number of the soft drink names any one of which could be among the three most popular? |
A soft drink manufacturer surveyed consumer preferences for exactly seven proposed names for its new soda: Jazz, Kola, Luck, Mist, Nipi, Oboy, and Ping. The manufacturer ranked the seven names according to the number of votes they received. The name that received the most votes was ranked first. Every name received a different number of votes. Some of the survey results are as follows: Jazz received more votes than Oboy. Oboy received more votes than Kola. Kola received more votes than Mist. Nipi did not receive the fewest votes. Ping received fewer votes than Luck but more votes than Nipi and more votes than Oboy. | 199210_4-G_2_12 | [
"two",
"three",
"four",
"five",
"six"
] | 1 | If Ping received more votes than Jazz, then what is the maximum possible number of names whose ranks can be determined? |
Eight benches—J, K, L, T, U, X, Y, and Z are arranged along the perimeter of a park as shown below: The following is true: J, K, and L are green; T and U are red; X, Y, and Z are pink. The green benches stand next to one another along the park's perimeter. The pink benches stand next to one another along the park's perimeter. No green bench stands next to a pink bench. The bench on the southeast corner is T. J stands at the center of the park's north side. If T stands next to X, then T does not also stand next to L. | 199210_4-G_3_13 | [
"Z",
"Y",
"X",
"T",
"L"
] | 4 | Which one of the following benches could be on the northeast corner of the park? |
Eight benches—J, K, L, T, U, X, Y, and Z are arranged along the perimeter of a park as shown below: The following is true: J, K, and L are green; T and U are red; X, Y, and Z are pink. The green benches stand next to one another along the park's perimeter. The pink benches stand next to one another along the park's perimeter. No green bench stands next to a pink bench. The bench on the southeast corner is T. J stands at the center of the park's north side. If T stands next to X, then T does not also stand next to L. | 199210_4-G_3_14 | [
"The bench on the northwest corner is pink.",
"The bench on the northeast corner is green.",
"The bench on the southwest corner is pink.",
"The middle bench on the east side of the park is green.",
"The middle bench on the west side of the park is pink."
] | 0 | Each of the following statements must be true EXCEPT: |
Eight benches—J, K, L, T, U, X, Y, and Z are arranged along the perimeter of a park as shown below: The following is true: J, K, and L are green; T and U are red; X, Y, and Z are pink. The green benches stand next to one another along the park's perimeter. The pink benches stand next to one another along the park's perimeter. No green bench stands next to a pink bench. The bench on the southeast corner is T. J stands at the center of the park's north side. If T stands next to X, then T does not also stand next to L. | 199210_4-G_3_15 | [
"K",
"L",
"T",
"U",
"X"
] | 3 | Which one of the following benches must be next to J? |
Eight benches—J, K, L, T, U, X, Y, and Z are arranged along the perimeter of a park as shown below: The following is true: J, K, and L are green; T and U are red; X, Y, and Z are pink. The green benches stand next to one another along the park's perimeter. The pink benches stand next to one another along the park's perimeter. No green bench stands next to a pink bench. The bench on the southeast corner is T. J stands at the center of the park's north side. If T stands next to X, then T does not also stand next to L. | 199210_4-G_3_16 | [
"K",
"T",
"X",
"Y",
"Z"
] | 0 | For which one of the following benches are there two and no more than two locations either one of which could be the location the bench occupies? |
Eight benches—J, K, L, T, U, X, Y, and Z are arranged along the perimeter of a park as shown below: The following is true: J, K, and L are green; T and U are red; X, Y, and Z are pink. The green benches stand next to one another along the park's perimeter. The pink benches stand next to one another along the park's perimeter. No green bench stands next to a pink bench. The bench on the southeast corner is T. J stands at the center of the park's north side. If T stands next to X, then T does not also stand next to L. | 199210_4-G_3_17 | [
"J is directly west of K.",
"K is directly east of U.",
"U is directly north of X.",
"X is directly south of J.",
"Z is directly south of J."
] | 3 | If Z is directly north of Y, which one of the following statements must be true? |
Eight benches—J, K, L, T, U, X, Y, and Z are arranged along the perimeter of a park as shown below: The following is true: J, K, and L are green; T and U are red; X, Y, and Z are pink. The green benches stand next to one another along the park's perimeter. The pink benches stand next to one another along the park's perimeter. No green bench stands next to a pink bench. The bench on the southeast corner is T. J stands at the center of the park's north side. If T stands next to X, then T does not also stand next to L. | 199210_4-G_3_18 | [
"K and X",
"K and Z",
"L and U",
"L and X",
"L and Z"
] | 1 | If Y is in the middle of the west side of the park, then the two benches in which one of the following pairs CANNOT be two of the corner benches? |
Eight benches—J, K, L, T, U, X, Y, and Z are arranged along the perimeter of a park as shown below: The following is true: J, K, and L are green; T and U are red; X, Y, and Z are pink. The green benches stand next to one another along the park's perimeter. The pink benches stand next to one another along the park's perimeter. No green bench stands next to a pink bench. The bench on the southeast corner is T. J stands at the center of the park's north side. If T stands next to X, then T does not also stand next to L. | 199210_4-G_3_19 | [
"J and L",
"K and T",
"T and X",
"U and Y",
"X and Z"
] | 2 | If Y is farther south than L and farther north than T, then the benches in each of the following pairs must be next to each other EXCEPT |
A lake contains exactly five islands—J, K, L, M, O—which are unconnected by bridges. Contractors will build a network of bridges that satisfies the following specifications: Each bridge directly connects exactly two islands with each other, and no two bridges intersect. No more than one bridge directly connects any two islands. No island has more than three bridges that directly connect it with other islands. J, K, and L are each directly connected by bridge with one or both of M and O. J is directly connected by bridge with exactly two islands. K is directly connected by bridge with exactly one island. A bridge directly connects J with O, and a bridge directly connects M with O. | 199210_4-G_4_20 | [
"J, K",
"J, M",
"J, O",
"J, M, O",
"J, K, M, O"
] | 3 | Which one of the following is a complete and accurate list of the islands any one of which could be directly connected by bridge with L ? |
A lake contains exactly five islands—J, K, L, M, O—which are unconnected by bridges. Contractors will build a network of bridges that satisfies the following specifications: Each bridge directly connects exactly two islands with each other, and no two bridges intersect. No more than one bridge directly connects any two islands. No island has more than three bridges that directly connect it with other islands. J, K, and L are each directly connected by bridge with one or both of M and O. J is directly connected by bridge with exactly two islands. K is directly connected by bridge with exactly one island. A bridge directly connects J with O, and a bridge directly connects M with O. | 199210_4-G_4_21 | [
"J is directly connected by bridge both with L and with M.",
"K is directly connected by bridge both with M and with O.",
"L is directly connected by bridge both with J and with M.",
"M is directly connected by bridge with J, with K, and with L.",
"O is directly connected by bridge with K, with L, and with M."
] | 2 | Which one of the following could be true about the completed network of bridges? |
A lake contains exactly five islands—J, K, L, M, O—which are unconnected by bridges. Contractors will build a network of bridges that satisfies the following specifications: Each bridge directly connects exactly two islands with each other, and no two bridges intersect. No more than one bridge directly connects any two islands. No island has more than three bridges that directly connect it with other islands. J, K, and L are each directly connected by bridge with one or both of M and O. J is directly connected by bridge with exactly two islands. K is directly connected by bridge with exactly one island. A bridge directly connects J with O, and a bridge directly connects M with O. | 199210_4-G_4_22 | [
"No bridge directly connects L with M.",
"A bridge directly connects J with L.",
"A bridge directly connects L with O.",
"There are exactly three bridges directly connecting L with other islands.",
"There are exactly two bridges directly connecting O with other islands."
] | 1 | If a bridge directly connects K with O, then which one of the following could be true? |
A lake contains exactly five islands—J, K, L, M, O—which are unconnected by bridges. Contractors will build a network of bridges that satisfies the following specifications: Each bridge directly connects exactly two islands with each other, and no two bridges intersect. No more than one bridge directly connects any two islands. No island has more than three bridges that directly connect it with other islands. J, K, and L are each directly connected by bridge with one or both of M and O. J is directly connected by bridge with exactly two islands. K is directly connected by bridge with exactly one island. A bridge directly connects J with O, and a bridge directly connects M with O. | 199210_4-G_4_23 | [
"A bridge directly connects J with M.",
"A bridge directly connects K with M.",
"A bridge directly connects K with O.",
"There are exactly two bridges directly connecting L with other islands.",
"There are exactly two bridges directly connecting M with other islands."
] | 1 | If a bridge directly connects L with M and a bridge directly connects L with O, then which one of the following must be true? |
A lake contains exactly five islands—J, K, L, M, O—which are unconnected by bridges. Contractors will build a network of bridges that satisfies the following specifications: Each bridge directly connects exactly two islands with each other, and no two bridges intersect. No more than one bridge directly connects any two islands. No island has more than three bridges that directly connect it with other islands. J, K, and L are each directly connected by bridge with one or both of M and O. J is directly connected by bridge with exactly two islands. K is directly connected by bridge with exactly one island. A bridge directly connects J with O, and a bridge directly connects M with O. | 199210_4-G_4_24 | [
"J with L",
"J with M",
"K with O",
"L with M",
"L with O"
] | 0 | If no island that is directly connected by bridge with M is also directly connected by bridge with O, then there must be a bridge directly connecting |
Each of five students—Hubert, Lori, Paul, Regina, and Sharon—will visit exactly one of three cities—Montreal, Toronto, or Vancouver—for the month of March, according to the following conditions: Sharon visits a different city than Paul. Hubert visits the same city as Regina. Lori visits Montreal or else Toronto. If Paul visits Vancouver, Hubert visits Vancouver with him. Each student visits one of the cities with at least one of the other four students. | 199212_1-G_1_1 | [
"Hubert, Lori, and Paul visit Toronto, and Regina and Sharon visit Vancouver.",
"Hubert, Lori, Paul, and Regina visit Montreal, and Sharon visits Vancouver.",
"Hubert, Paul, and Regina visit Toronto, and Lori and Sharon visit Montreal.",
"Hubert, Regina, and Sharon visit Montreal, and Lori and Paul visit Vancouver.",
"Lori, Paul, and Sharon visit Montreal, and Hubert and Regina visit Toronto."
] | 2 | Which one of the following could be true for March? |
Each of five students—Hubert, Lori, Paul, Regina, and Sharon—will visit exactly one of three cities—Montreal, Toronto, or Vancouver—for the month of March, according to the following conditions: Sharon visits a different city than Paul. Hubert visits the same city as Regina. Lori visits Montreal or else Toronto. If Paul visits Vancouver, Hubert visits Vancouver with him. Each student visits one of the cities with at least one of the other four students. | 199212_1-G_1_2 | [
"Hubert visits the same city as Paul.",
"Lori visits the same city as Regina.",
"Paul visits the same city as Regina.",
"Paul visits Toronto.",
"Paul visits Vancouver."
] | 3 | If Hubert and Sharon visit a city together, which one of the following could be true in March? |
Each of five students—Hubert, Lori, Paul, Regina, and Sharon—will visit exactly one of three cities—Montreal, Toronto, or Vancouver—for the month of March, according to the following conditions: Sharon visits a different city than Paul. Hubert visits the same city as Regina. Lori visits Montreal or else Toronto. If Paul visits Vancouver, Hubert visits Vancouver with him. Each student visits one of the cities with at least one of the other four students. | 199212_1-G_1_3 | [
"Hubert visits Montreal.",
"Lori visits Montreal.",
"Paul visits Toronto.",
"Lori visits the same city as Paul.",
"Lori visits the same city as Regina."
] | 3 | If Sharon visits Vancouver, which one of the following must be true for March? |
Each of five students—Hubert, Lori, Paul, Regina, and Sharon—will visit exactly one of three cities—Montreal, Toronto, or Vancouver—for the month of March, according to the following conditions: Sharon visits a different city than Paul. Hubert visits the same city as Regina. Lori visits Montreal or else Toronto. If Paul visits Vancouver, Hubert visits Vancouver with him. Each student visits one of the cities with at least one of the other four students. | 199212_1-G_1_4 | [
"Sharon must visit Montreal if Paul visits Vancouver.",
"Regina must visit Vancouver if Paul visits Vancouver.",
"Regina visits a city with exactly two of the other four students.",
"Lori visits a city with exactly one of the other four students.",
"Lori visits a city with Paul or else with Sharon."
] | 0 | Which one of the following could be false in March? |
Each of five students—Hubert, Lori, Paul, Regina, and Sharon—will visit exactly one of three cities—Montreal, Toronto, or Vancouver—for the month of March, according to the following conditions: Sharon visits a different city than Paul. Hubert visits the same city as Regina. Lori visits Montreal or else Toronto. If Paul visits Vancouver, Hubert visits Vancouver with him. Each student visits one of the cities with at least one of the other four students. | 199212_1-G_1_5 | [
"Lori visits Toronto.",
"Lori visits Vancouver.",
"Paul visits Toronto.",
"Paul visits Vancouver.",
"Sharon visits Vancouver."
] | 2 | If Regina visits Toronto, which one of the following could be true in March? |
Each of five students—Hubert, Lori, Paul, Regina, and Sharon—will visit exactly one of three cities—Montreal, Toronto, or Vancouver—for the month of March, according to the following conditions: Sharon visits a different city than Paul. Hubert visits the same city as Regina. Lori visits Montreal or else Toronto. If Paul visits Vancouver, Hubert visits Vancouver with him. Each student visits one of the cities with at least one of the other four students. | 199212_1-G_1_6 | [
"If any of the students visits Montreal, Lori visits Montreal.",
"If any of the students visits Montreal, exactly two of them do.",
"If any of the students visits Toronto, exactly three of them do.",
"If any of the students visits Vancouver, Paul visits Vancouver.",
"If any of the students visits Vancouver, exactly three of them do."
] | 4 | Which one of the following must be true for March? |
A college offers one course in each of three subjects—mathematics, nutrition, and oceanography—in the fall and again in the spring. Students' book orders for these course offerings are kept in six folders, numbered 1 through 6, from which labels identifying the folders' contents are missing. The following is known: Each folder contains only the orders for one of the six course offerings. Folder 1 contains orders for the same subject as folder 2 does. The orders in folder 3 are for a different subject than are the orders in folder 4. The fall mathematics orders are in folder 1 or else folder 4. The spring oceanography orders are in folder 1 or else folder 4. The spring nutrition orders are not in folder 5. | 199212_1-G_2_7 | [
"fall mathematics, spring mathematics, fall oceanography, fall nutrition, spring nutrition, spring oceanography",
"fall oceanography, spring nutrition, fall nutrition, fall mathematics, spring mathematics, spring oceanography",
"spring mathematics, fall mathematics, spring nutrition, fall oceanography, fall nutrition, spring oceanography",
"spring oceanography, fall oceanography, fall nutrition, fall mathematics, spring mathematics, spring nutrition",
"spring oceanography, fall oceanography, spring mathematics, fall mathematics, fall nutrition, spring nutrition"
] | 3 | Which one of the following could be the list of the contents of the folders, in order from folder 1 to folder 6 ? |
A college offers one course in each of three subjects—mathematics, nutrition, and oceanography—in the fall and again in the spring. Students' book orders for these course offerings are kept in six folders, numbered 1 through 6, from which labels identifying the folders' contents are missing. The following is known: Each folder contains only the orders for one of the six course offerings. Folder 1 contains orders for the same subject as folder 2 does. The orders in folder 3 are for a different subject than are the orders in folder 4. The fall mathematics orders are in folder 1 or else folder 4. The spring oceanography orders are in folder 1 or else folder 4. The spring nutrition orders are not in folder 5. | 199212_1-G_2_8 | [
"The spring mathematics orders are in folder 3.",
"The fall nutrition orders are in folder 3.",
"The spring oceanography orders are in folder 1.",
"The spring nutrition orders are in folder 6.",
"The fall oceanography orders are in folder 5."
] | 0 | Which one of the following statements must be false? |
A college offers one course in each of three subjects—mathematics, nutrition, and oceanography—in the fall and again in the spring. Students' book orders for these course offerings are kept in six folders, numbered 1 through 6, from which labels identifying the folders' contents are missing. The following is known: Each folder contains only the orders for one of the six course offerings. Folder 1 contains orders for the same subject as folder 2 does. The orders in folder 3 are for a different subject than are the orders in folder 4. The fall mathematics orders are in folder 1 or else folder 4. The spring oceanography orders are in folder 1 or else folder 4. The spring nutrition orders are not in folder 5. | 199212_1-G_2_9 | [
"The spring mathematics orders are in folder 4.",
"The spring mathematics orders are in folder 6.",
"The fall nutrition orders are in folder 1.",
"The spring nutrition orders are in neither folder 3 nor folder 6.",
"Neither the spring nor the fall nutrition orders are in folder 3."
] | 1 | If the fall oceanography orders are in folder 2, then which one of the following statements could be true? |
A college offers one course in each of three subjects—mathematics, nutrition, and oceanography—in the fall and again in the spring. Students' book orders for these course offerings are kept in six folders, numbered 1 through 6, from which labels identifying the folders' contents are missing. The following is known: Each folder contains only the orders for one of the six course offerings. Folder 1 contains orders for the same subject as folder 2 does. The orders in folder 3 are for a different subject than are the orders in folder 4. The fall mathematics orders are in folder 1 or else folder 4. The spring oceanography orders are in folder 1 or else folder 4. The spring nutrition orders are not in folder 5. | 199212_1-G_2_10 | [
"The spring mathematics orders are in folder 1.",
"The fall oceanography orders are in folder 1.",
"The fall nutrition orders are in folder 4, and the fall oceanography orders are in folder 6.",
"The fall oceanography orders are in folder 2, and the spring oceanography orders are in folder 1.",
"The spring oceanography orders are in folder 1, and neither the spring nor the fall nutrition orders are in folder 3."
] | 3 | Which one of the following statements could be true? |
A college offers one course in each of three subjects—mathematics, nutrition, and oceanography—in the fall and again in the spring. Students' book orders for these course offerings are kept in six folders, numbered 1 through 6, from which labels identifying the folders' contents are missing. The following is known: Each folder contains only the orders for one of the six course offerings. Folder 1 contains orders for the same subject as folder 2 does. The orders in folder 3 are for a different subject than are the orders in folder 4. The fall mathematics orders are in folder 1 or else folder 4. The spring oceanography orders are in folder 1 or else folder 4. The spring nutrition orders are not in folder 5. | 199212_1-G_2_11 | [
"one",
"two",
"three",
"four",
"five"
] | 1 | If the fall oceanography orders are in folder 2, then for exactly how many of the remaining five folders can it be deduced which course offering's orders are in that folder? |
A college offers one course in each of three subjects—mathematics, nutrition, and oceanography—in the fall and again in the spring. Students' book orders for these course offerings are kept in six folders, numbered 1 through 6, from which labels identifying the folders' contents are missing. The following is known: Each folder contains only the orders for one of the six course offerings. Folder 1 contains orders for the same subject as folder 2 does. The orders in folder 3 are for a different subject than are the orders in folder 4. The fall mathematics orders are in folder 1 or else folder 4. The spring oceanography orders are in folder 1 or else folder 4. The spring nutrition orders are not in folder 5. | 199212_1-G_2_12 | [
"3 and 5",
"4 and 5",
"3 and 6",
"4 and 6",
"5 and 6"
] | 4 | Which one of the following lists a pair of folders that must together contain orders for two different subjects? |
A college offers one course in each of three subjects—mathematics, nutrition, and oceanography—in the fall and again in the spring. Students' book orders for these course offerings are kept in six folders, numbered 1 through 6, from which labels identifying the folders' contents are missing. The following is known: Each folder contains only the orders for one of the six course offerings. Folder 1 contains orders for the same subject as folder 2 does. The orders in folder 3 are for a different subject than are the orders in folder 4. The fall mathematics orders are in folder 1 or else folder 4. The spring oceanography orders are in folder 1 or else folder 4. The spring nutrition orders are not in folder 5. | 199212_1-G_2_13 | [
"The fall mathematics and spring oceanography orders are in folders with consecutive numbers.",
"Folder 5 contains the orders for a spring course in a subject other than mathematics.",
"Folder 6 contains the orders for a subject other than nutrition.",
"The mathematics orders are in folders 1 and 4.",
"The orders for the fall courses are in folders 1, 3, and 6."
] | 2 | Which one of the following could be true? |
Greenburg has exactly five subway lines: Ll, L2, L3, L4, and L5. Along each of the lines, trains run in both directions, stopping at every station. Ll runs in a loop connecting exactly seven stations, their order being Rincon-Tonka-French-Semplain-Urstine-Quetzal-Park-Rincon in one direction of travel, and the reverse in the other direction. L2 connects Tonka with Semplain, and with no other station. L3 connects Rincon with Urstine, and with no other station. L4 runs from Quetzal through exactly one other station, Greene, to Rincon. L5 connects Quetzal with Tonka, and with no other station. | 199212_1-G_3_14 | [
"two",
"three",
"four",
"five",
"six"
] | 2 | How many different stations are there that a traveler starting at Rincon could reach by using the subway lines without making any intermediate stops? |
Greenburg has exactly five subway lines: Ll, L2, L3, L4, and L5. Along each of the lines, trains run in both directions, stopping at every station. Ll runs in a loop connecting exactly seven stations, their order being Rincon-Tonka-French-Semplain-Urstine-Quetzal-Park-Rincon in one direction of travel, and the reverse in the other direction. L2 connects Tonka with Semplain, and with no other station. L3 connects Rincon with Urstine, and with no other station. L4 runs from Quetzal through exactly one other station, Greene, to Rincon. L5 connects Quetzal with Tonka, and with no other station. | 199212_1-G_3_15 | [
"French",
"Park",
"Quetzal",
"Rincon",
"Tonka"
] | 2 | In order to go from Greene to Semplain taking the fewest possible subway lines and making the fewest possible stops, a traveler must make a stop at |
Greenburg has exactly five subway lines: Ll, L2, L3, L4, and L5. Along each of the lines, trains run in both directions, stopping at every station. Ll runs in a loop connecting exactly seven stations, their order being Rincon-Tonka-French-Semplain-Urstine-Quetzal-Park-Rincon in one direction of travel, and the reverse in the other direction. L2 connects Tonka with Semplain, and with no other station. L3 connects Rincon with Urstine, and with no other station. L4 runs from Quetzal through exactly one other station, Greene, to Rincon. L5 connects Quetzal with Tonka, and with no other station. | 199212_1-G_3_16 | [
"Quetzal, Tonka",
"Semplain, French",
"Semplain, Park",
"Quetzal, Park, Greene",
"Semplain, French, Tonka"
] | 0 | If L3 is not running and a traveler goes by subway from Urstine to Rincon making the fewest possible stops, which one of the following lists all of the intermediate stations in sequence along one of the routes that the traveler could take? |
Greenburg has exactly five subway lines: Ll, L2, L3, L4, and L5. Along each of the lines, trains run in both directions, stopping at every station. Ll runs in a loop connecting exactly seven stations, their order being Rincon-Tonka-French-Semplain-Urstine-Quetzal-Park-Rincon in one direction of travel, and the reverse in the other direction. L2 connects Tonka with Semplain, and with no other station. L3 connects Rincon with Urstine, and with no other station. L4 runs from Quetzal through exactly one other station, Greene, to Rincon. L5 connects Quetzal with Tonka, and with no other station. | 199212_1-G_3_17 | [
"zero",
"one",
"two",
"three",
"four"
] | 2 | In order to go by subway from French to Greene, the minimum number of intermediate stops a traveler must make is |
Greenburg has exactly five subway lines: Ll, L2, L3, L4, and L5. Along each of the lines, trains run in both directions, stopping at every station. Ll runs in a loop connecting exactly seven stations, their order being Rincon-Tonka-French-Semplain-Urstine-Quetzal-Park-Rincon in one direction of travel, and the reverse in the other direction. L2 connects Tonka with Semplain, and with no other station. L3 connects Rincon with Urstine, and with no other station. L4 runs from Quetzal through exactly one other station, Greene, to Rincon. L5 connects Quetzal with Tonka, and with no other station. | 199212_1-G_3_18 | [
"French or Tonka",
"Greene or Urstine",
"Quetzal or Tonka",
"Quetzal or Urstine or both",
"Rincon or Tonka or both"
] | 4 | If the tracks that directly connect Urstine and Quetzal are blocked in both directions, a traveler going from Semplain to Park and making the fewest possible intermediate stops must pass through |
Greenburg has exactly five subway lines: Ll, L2, L3, L4, and L5. Along each of the lines, trains run in both directions, stopping at every station. Ll runs in a loop connecting exactly seven stations, their order being Rincon-Tonka-French-Semplain-Urstine-Quetzal-Park-Rincon in one direction of travel, and the reverse in the other direction. L2 connects Tonka with Semplain, and with no other station. L3 connects Rincon with Urstine, and with no other station. L4 runs from Quetzal through exactly one other station, Greene, to Rincon. L5 connects Quetzal with Tonka, and with no other station. | 199212_1-G_3_19 | [
"French, Greene, and Park",
"French, Greene, and Quetzal",
"French, Greene, and Rincon",
"Park, Tonka, and Urstine",
"Park, Semplain, and Tonka"
] | 0 | If a sixth subway line is to be constructed so that all of the stations would have two or more lines reaching them, the stations connected by the new subway line must include at least |
Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford. | 199212_1-G_4_20 | [
"Partner: Harrison, Olivos, Rafael. Associate: Ganz, Johnson, Lowry. Assistance: Stefano, Turner, Wilford",
"Partner: Harrison, Rafael. Associate: Lowry, Olivos, Stefano. Assistance: Ganz, Johnson, Turner, Wilford",
"Partner: Harrison, Olivos, Rafael, Stefano. Associate: Ganz, Lowry, Turner, Wilford. Assistance: Johnson",
"Partner: Harrison, Olivos, Rafael. Assistance: Ganz, Johnson, Lowry, Stefano, Turner, Wilford",
"Partner: Harrison, Olivos, Rafael. Associate: Ganz, Lowry Stefano, Turner. Assistance: Johnson, Wilford"
] | 4 | Which one of the following could be the distribution of staff resulting from this year's review? |
Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford. | 199212_1-G_4_21 | [
"Ganz, Lowry, Wilford",
"Johnson, Lowry, Stefano",
"Lowry, Stefano, Turner",
"Lowry, Stefano, Wilford",
"Olivos, Turner, Wilford"
] | 3 | If Rafael votes for promoting only Ganz, Olivos, and Wilford, and if Harrison votes for promoting only Lowry, Olivos, and Stefano, then which one of the following could be the complete roster of associates resulting from this year's review? |
Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford. | 199212_1-G_4_22 | [
"one",
"two",
"three",
"four",
"five"
] | 1 | If Johnson is to be promoted to associate during next year's review, which one of the following is the smallest number of assistants who must be promoted during this year's review? |
Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford. | 199212_1-G_4_23 | [
"Lowry is an assistant.",
"Wilford is a partner.",
"There are no assistants.",
"There are at least two assistants.",
"There are no more than four assistants."
] | 4 | Which one of the following must be true after next year's review? |
Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford. | 199212_1-G_4_24 | [
"none",
"one",
"two",
"three",
"four"
] | 1 | What is the smallest possible number of associates in the firm immediately after next year's review? |
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P. | 199302_2-G_1_1 | [
"the news",
"H",
"L",
"O",
"S"
] | 2 | If G is played second, which one of the following tapes must be played third? |
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P. | 199302_2-G_1_2 | [
"second",
"third",
"fourth",
"fifth",
"sixth"
] | 0 | The news tape can be played in any one of the following time slots EXCEPT the |
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P. | 199302_2-G_1_3 | [
"G, H, and L",
"S, G, and the news",
"H, G, and L",
"H, L, and O",
"L, O, and S"
] | 2 | If H and S are to be scheduled as far from each other as possible, then the first, the second, and the third time slots could be filled, respectively, by |
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P. | 199302_2-G_1_4 | [
"first",
"second",
"third",
"fourth",
"sixth"
] | 2 | If P is played fifth, L must be played |
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P. | 199302_2-G_1_5 | [
"1",
"2",
"3",
"4",
"5"
] | 4 | What is the maximum number of tapes that can separate S from the news? |
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P. | 199302_2-G_1_6 | [
"the third",
"the fourth",
"the fifth",
"the sixth",
"the seventh"
] | 2 | Which one of the following is the latest time slot in which L can be played? |
Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P. | 199302_2-G_1_7 | [
"the first",
"the third",
"the fourth",
"the fifth",
"the sixth"
] | 3 | The time slot in which O must be played is completely determined if G is assigned to which one of the following time slots? |
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations. | 199302_2-G_2_8 | [
"Monday",
"Tuesday",
"Wednesday",
"Friday",
"Saturday"
] | 1 | Which one of the following must be a day on which Doctor Yamata lectures? |
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations. | 199302_2-G_2_9 | [
"conduct research in the morning and operate in the afternoon",
"lecture in the morning and treat patients in the afternoon",
"operate in the morning and lecture in the afternoon",
"operate in the morning and conduct research in the afternoon",
"treat patients in the morning and treat patients in the afternoon"
] | 2 | On Wednesday Doctor Yamata could be scheduled to |
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations. | 199302_2-G_2_10 | [
"There is one day on which the doctor treats patients both in the morning and in the afternoon.",
"The doctor conducts research on one of the days on which she lectures.",
"The doctor conducts research on one of the days on which she treats patients.",
"The doctor lectures on one of the days on which she treats patients.",
"The doctor lectures on one of the days on which she operates."
] | 4 | Which one of the following statements must be true? |
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations. | 199302_2-G_2_11 | [
"Monday morning, Monday afternoon, Friday morning, Friday afternoon",
"Monday morning, Friday afternoon, Saturday morning, Saturday afternoon",
"Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon",
"Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon",
"Wednesday afternoon, Friday afternoon, Saturday morning, Saturday afternoon"
] | 4 | If Doctor Yamata operates on Tuesday, then her schedule for treating patients could be |
Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations. | 199302_2-G_2_12 | [
"Monday and Tuesday",
"Monday and Saturday",
"Tuesday and Friday",
"Tuesday and Saturday",
"Friday and Saturday"
] | 4 | Which one of the following is a pair of days on both of which Doctor Yamata must treat patients? |
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog. | 199302_2-G_3_13 | [
"No conservative and exactly two liberals voted for Datalog.",
"Exactly one conservative and exactly one liberal voted for Datalog.",
"Exactly one conservative and all three liberals voted for Datalog.",
"Exactly two conservatives and exactly one liberal voted for Datalog.",
"Exactly two conservatives and exactly two liberals voted for Datalog."
] | 1 | If the two moderates did not vote the same way as each other, then which one of the following could be true? |
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog. | 199302_2-G_3_14 | [
"At least one conservative voted for Datalog.",
"At least one liberal voted against Datalog.",
"At least one liberal voted for Datalog.",
"At least one moderate voted against Datalog.",
"At least one moderate voted for Datalog."
] | 2 | Which one of the following must be true? |
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog. | 199302_2-G_3_15 | [
"Both moderates voted for Datalog.",
"Both moderates voted against Datalog.",
"One conservative voted for Datalog and one conservative voted against Datalog.",
"One moderate voted for Datalog and one moderate voted against Datalog.",
"All three liberals voted for Datalog."
] | 4 | If the three liberals all voted the same way as each other, which one of the following must be true? |
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog. | 199302_2-G_3_16 | [
"Both moderates voted for Datalog.",
"Exactly one conservative voted for Datalog.",
"No conservative voted for Datalog.",
"Exactly two liberals voted for Datalog.",
"Exactly three liberals voted for Datalog."
] | 0 | If exactly two judges voted against Datalog, then which one of the following must be true? |
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog. | 199302_2-G_3_17 | [
"two liberals",
"one conservative, one liberal",
"two moderates, three liberals",
"one conservative, two moderates, two liberals",
"one conservative, two moderates, three liberals"
] | 4 | Each of the following could be a complete and accurate list of those judges who voted for Datalog EXCEPT |
Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog. | 199302_2-G_3_18 | [
"Both conservatives voted against Datalog.",
"Both moderates voted for Datalog.",
"At least one liberal voted against Datalog.",
"Exactly two liberals voted for Datalog.",
"Exactly five of the judges voted against Datalog."
] | 1 | If the two conservatives voted the same way as each other, but the liberals did not all vote the same way as each other, then each of the following must be true EXCEPT: |
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned. | 199302_2-G_4_19 | [
"F G H K J",
"G H J K F",
"G K F J H",
"H J G K F",
"J H F K G"
] | 4 | Which one of the following is a possible assignment of runners to lanes by the charity they represent? |
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned. | 199302_2-G_4_20 | [
"next to the lane to which Larry is assigned",
"next to the lane to which Ned is assigned",
"separated by exactly one lane from the lane to which Ned is assigned",
"separated by exactly one lane from the lane to which Olivia is assigned",
"separated by exactly one lane from the lane to which Sonja is assigned"
] | 3 | The lane to which Patricia is assigned must be a lane that is |
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned. | 199302_2-G_4_21 | [
"F 1",
"G 5",
"H 1",
"H 3",
"J 5"
] | 1 | If Olivia is assigned to lane 2, which one of the following assignments must be made? Charity Lane |
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned. | 199302_2-G_4_22 | [
"Larry, Ned",
"Patricia, Sonja",
"Larry, Ned, Olivia",
"Larry, Ned, Sonja",
"Ned, Patricia, Sonja"
] | 3 | Which one of the following, is a complete and accurate list of runners each of whom could be the runner representing F? |
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned. | 199302_2-G_4_23 | [
"the runner representing G is assigned to lane 1",
"the runner representing H is assigned to lane 2",
"Larry is the runner representing K",
"Olivia is the runner representing F",
"Patricia is the runner representing H"
] | 1 | If Ned is the runner representing J, then it must be true that |
An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned. | 199302_2-G_4_24 | [
"Larry Olivia Ned Patricia Sonja",
"Larry Ned Olivia Sonja Patricia",
"Larry Sonja Patricia Ned Olivia",
"Ned Olivia Larry Patricia Sonja",
"Ned Sonja Olivia Patricia Larry"
] | 0 | If Larry represents J, which one of the following could be the assignment of runners to lanes? |
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled. | 199306_2-G_1_1 | [
"H and U",
"H and Z",
"K and O",
"O and U",
"U and Z"
] | 3 | Which one of the following is a pair of students whose sessions can both be scheduled for Tuesday, not necessarily in the order given? |
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled. | 199306_2-G_1_2 | [
"Monday",
"Tuesday",
"Wednesday",
"Thursday",
"Friday"
] | 1 | If K's session is scheduled for Tuesday, then which one of the following is the earliest day for which Z's session can be scheduled? |
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled. | 199306_2-G_1_3 | [
"If U's session is scheduled for Monday, H's session is scheduled for Tuesday.",
"If U's session is scheduled for Tuesday, O's session is scheduled for Wednesday.",
"If U's session is scheduled for Wednesday, Z's session is scheduled for Tuesday.",
"If U's session is scheduled for Thursday, Z's session is scheduled for Friday.",
"If U's session is scheduled for Friday, Z's session is scheduled for Thursday."
] | 3 | Which one of the following must be true? |
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled. | 199306_2-G_1_4 | [
"Monday",
"Tuesday",
"Wednesday",
"Thursday",
"Friday"
] | 3 | Scheduling Z's session for which one of the following days determines the day for which U's session must be scheduled? |
A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled. | 199306_2-G_1_5 | [
"U's session is scheduled for Monday, and H's session is scheduled for Tuesday.",
"U's session is scheduled for Thursday, and H's session is scheduled for Friday.",
"They are both scheduled for Tuesday.",
"They are both scheduled for Thursday.",
"They are both scheduled for Friday."
] | 0 | If H's session is scheduled as the next session after U's session, which one of the following could be true about H's session and U's session? |
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on. | 199306_2-G_2_6 | [
"1, 3, 5, 7",
"2, 4, 6, 8",
"2, 3, 5, 6, 8",
"3, 4, 6, 7, 8",
"1, 2, 4, 5, 6, 8"
] | 2 | Which one of the following could be a complete and accurate list of lights that are on together? |
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on. | 199306_2-G_2_7 | [
"light 2",
"light 3",
"light 4",
"light 5",
"light 6"
] | 1 | Which one of the following lights must be on? |
A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on. | 199306_2-G_2_8 | [
"light 3",
"light 4",
"light 5",
"light 6",
"light 7"
] | 1 | If light 1 is off, which one of the following is a light that must also be off? |