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While on vacation, Sukanya receives several e-mail messages from work, each message from one of three associates: Hilary, Jerome, and Lula. Sukanya receives at least one and no more than two messages from each of them. Sukanya receives each message on the day it is sent. No more than one message is sent each day. The messages are received in a manner consistent with the following: The first message is not from Lula. Both the first and last messages are from the same person. Exactly once Sukanya receives a message from Jerome on the day after receiving one from Hilary. Of the first three messages, exactly one is from Jerome. | If Sukanya receives six e-mail messages, the fifth of which is from Lula, which one of the following must be true? | [
"The first message is from Jerome.",
"The second message is from Lula.",
"The third message is from Hilary.",
"The fourth message is from Jerome.",
"The sixth message is from Lula."
] | 3 |
While on vacation, Sukanya receives several e-mail messages from work, each message from one of three associates: Hilary, Jerome, and Lula. Sukanya receives at least one and no more than two messages from each of them. Sukanya receives each message on the day it is sent. No more than one message is sent each day. The messages are received in a manner consistent with the following: The first message is not from Lula. Both the first and last messages are from the same person. Exactly once Sukanya receives a message from Jerome on the day after receiving one from Hilary. Of the first three messages, exactly one is from Jerome. | If Sukanya receives two e-mail messages from Lula, what is the maximum possible number of e-mail messages Sukanya receives after Lula's first message but before Lula's last message? | [
"zero",
"one",
"two",
"three",
"four"
] | 1 |
Mercotek carried out a study to compare the productivity of its night shift with that of its day shift. Every week the company's six crews—F, G, H, R, S, and T—were ranked from first (most productive) to sixth (least productive). There were no ties. For any given week, either G and T were the two night-shift crews or else S and H were—the four other crews were the day-shift crews for that week. The following relationships held for every week of the study: F is more productive than G. R is more productive than S. R is more productive than T. S is more productive than H. G is more productive than T. | Which one of the following could be an accurate ranking of all the crews, in order from first to sixth, for a given week of the study? | [
"F, G, T, R, S, H",
"F, R, G, T, H, S",
"G, R, T, S, H, F",
"R, F, G, S, H, T",
"R, S, H, T, F, G"
] | 3 |
Mercotek carried out a study to compare the productivity of its night shift with that of its day shift. Every week the company's six crews—F, G, H, R, S, and T—were ranked from first (most productive) to sixth (least productive). There were no ties. For any given week, either G and T were the two night-shift crews or else S and H were—the four other crews were the day-shift crews for that week. The following relationships held for every week of the study: F is more productive than G. R is more productive than S. R is more productive than T. S is more productive than H. G is more productive than T. | If F is ranked third for a given week of the study, then which one of the following could also be true of that week? | [
"G ranks second.",
"H ranks fourth.",
"R ranks second.",
"S ranks fourth.",
"T ranks fourth."
] | 1 |
Mercotek carried out a study to compare the productivity of its night shift with that of its day shift. Every week the company's six crews—F, G, H, R, S, and T—were ranked from first (most productive) to sixth (least productive). There were no ties. For any given week, either G and T were the two night-shift crews or else S and H were—the four other crews were the day-shift crews for that week. The following relationships held for every week of the study: F is more productive than G. R is more productive than S. R is more productive than T. S is more productive than H. G is more productive than T. | Which one of the following CANNOT be the crew ranked fifth for any given week of the study? | [
"G",
"H",
"R",
"S",
"T"
] | 2 |
Mercotek carried out a study to compare the productivity of its night shift with that of its day shift. Every week the company's six crews—F, G, H, R, S, and T—were ranked from first (most productive) to sixth (least productive). There were no ties. For any given week, either G and T were the two night-shift crews or else S and H were—the four other crews were the day-shift crews for that week. The following relationships held for every week of the study: F is more productive than G. R is more productive than S. R is more productive than T. S is more productive than H. G is more productive than T. | For any given week of the study, the ranking of all the crews is completely determined if which one of the following is true? | [
"F ranks second that week.",
"G ranks fifth that week.",
"H ranks third that week.",
"R ranks third that week.",
"S ranks third that week."
] | 2 |
Mercotek carried out a study to compare the productivity of its night shift with that of its day shift. Every week the company's six crews—F, G, H, R, S, and T—were ranked from first (most productive) to sixth (least productive). There were no ties. For any given week, either G and T were the two night-shift crews or else S and H were—the four other crews were the day-shift crews for that week. The following relationships held for every week of the study: F is more productive than G. R is more productive than S. R is more productive than T. S is more productive than H. G is more productive than T. | If the night-shift crews rank fifth and sixth for a given week of the study, then which one of the following could also be true of that week? | [
"G ranks fourth.",
"H ranks fifth.",
"R ranks third.",
"S ranks fourth.",
"T ranks fifth."
] | 2 |
Mercotek carried out a study to compare the productivity of its night shift with that of its day shift. Every week the company's six crews—F, G, H, R, S, and T—were ranked from first (most productive) to sixth (least productive). There were no ties. For any given week, either G and T were the two night-shift crews or else S and H were—the four other crews were the day-shift crews for that week. The following relationships held for every week of the study: F is more productive than G. R is more productive than S. R is more productive than T. S is more productive than H. G is more productive than T. | Which one of the following is a complete and accurate list of the crews that CANNOT be ranked third for any given week of the study? | [
"G, H, S",
"R, T",
"F, T",
"G, T",
"T"
] | 4 |
A shuttle van stops exactly four times—once at Fundy, once at Los Altos, once at Mineola, and once at Simcoe—not necessarily in that order. The van starts with exactly four passengers on board—Greg, Jasmine, Rosa, and Vijay—each of whom gets off at a different stop. The following conditions hold: Los Altos is the first or second stop. Rosa is still on board when the van reaches Mineola. Jasmine is on board longer than Vijay. If Jasmine is still on board when the van reaches Fundy, then Greg is still on board when the van reaches Simcoe; otherwise, Greg is not still on board when the van reaches Simcoe. | Which one of the following could be a complete and accurate matching of stops, listed in the order in which the van stops at them, to the passengers who get off at them? | [
"Los Altos: Greg Mineola: Vijay Fundy: Jasmine Simcoe: Rosa",
"Simcoe: Vijay Mineola: Greg Fundy: Rosa Los Altos: Jasmine",
"Los Altos: Jasmine Mineola: Vijay Fundy: Greg Simcoe: Rosa",
"Los Altos: Rosa Mineola: Vijay Fundy: Jasmine Simcoe: Greg",
"Los Altos: Vijay Fundy: Jasmine Mineola: Rosa Simcoe: Greg"
] | 4 |
A shuttle van stops exactly four times—once at Fundy, once at Los Altos, once at Mineola, and once at Simcoe—not necessarily in that order. The van starts with exactly four passengers on board—Greg, Jasmine, Rosa, and Vijay—each of whom gets off at a different stop. The following conditions hold: Los Altos is the first or second stop. Rosa is still on board when the van reaches Mineola. Jasmine is on board longer than Vijay. If Jasmine is still on board when the van reaches Fundy, then Greg is still on board when the van reaches Simcoe; otherwise, Greg is not still on board when the van reaches Simcoe. | If Mineola is the first stop, which one of the following is a complete and accurate list of the passengers who could possibly get off there? | [
"Rosa",
"Greg, Rosa",
"Greg, Vijay",
"Greg, Rosa, Vijay",
"Jasmine, Rosa, Vijay"
] | 3 |
A shuttle van stops exactly four times—once at Fundy, once at Los Altos, once at Mineola, and once at Simcoe—not necessarily in that order. The van starts with exactly four passengers on board—Greg, Jasmine, Rosa, and Vijay—each of whom gets off at a different stop. The following conditions hold: Los Altos is the first or second stop. Rosa is still on board when the van reaches Mineola. Jasmine is on board longer than Vijay. If Jasmine is still on board when the van reaches Fundy, then Greg is still on board when the van reaches Simcoe; otherwise, Greg is not still on board when the van reaches Simcoe. | If Fundy is the first stop, then which one of the following could accurately list the passengers in order from first to last off? | [
"Greg, Vijay, Jasmine, Rosa",
"Rosa, Vijay, Greg, Jasmine",
"Vijay, Greg, Rosa, Jasmine",
"Vijay, Jasmine, Greg, Rosa",
"Vijay, Rosa, Jasmine, Greg"
] | 3 |
A shuttle van stops exactly four times—once at Fundy, once at Los Altos, once at Mineola, and once at Simcoe—not necessarily in that order. The van starts with exactly four passengers on board—Greg, Jasmine, Rosa, and Vijay—each of whom gets off at a different stop. The following conditions hold: Los Altos is the first or second stop. Rosa is still on board when the van reaches Mineola. Jasmine is on board longer than Vijay. If Jasmine is still on board when the van reaches Fundy, then Greg is still on board when the van reaches Simcoe; otherwise, Greg is not still on board when the van reaches Simcoe. | Which one of the following must be true if Greg is still on board both when the van reaches Los Altos and when it reaches Simcoe, not necessarily in that order, assuming he is the second one off the van? | [
"Vijay is on board when the van reaches Simcoe.",
"Vijay is on board when the van reaches Los Altos.",
"Rosa is on board when the van reaches Simcoe.",
"Rosa is on board when the van reaches Fundy.",
"Jasmine is on board when the van reaches Mineola."
] | 2 |
A shuttle van stops exactly four times—once at Fundy, once at Los Altos, once at Mineola, and once at Simcoe—not necessarily in that order. The van starts with exactly four passengers on board—Greg, Jasmine, Rosa, and Vijay—each of whom gets off at a different stop. The following conditions hold: Los Altos is the first or second stop. Rosa is still on board when the van reaches Mineola. Jasmine is on board longer than Vijay. If Jasmine is still on board when the van reaches Fundy, then Greg is still on board when the van reaches Simcoe; otherwise, Greg is not still on board when the van reaches Simcoe. | If Greg is not on board when the van reaches Simcoe, then which one of the following must be false? | [
"Greg is on board when the van reaches Fundy.",
"Jasmine is on board when the van reaches Mineola.",
"Rosa is on board when the van reaches Fundy.",
"Vijay is on board when the van reaches Fundy.",
"Vijay is on board when the van reaches Mineola."
] | 3 |
Individual hour-long auditions will be scheduled for each of six saxophonists—Fujimura, Gabrieli, Herman, Jackson, King, and Lauder. The auditions will all take place on the same day. Each audition will begin on the hour, with the first beginning at 1 P.M. and the last at 6 P.M. The schedule of auditions must conform to the following conditions: Jackson auditions earlier than Herman does. Gabrieli auditions earlier than King does. Gabrieli auditions either immediately before or immediately after Lauder does. Exactly one audition separates the auditions of Jackson and Lauder. | Which one of the following is an acceptable schedule for the auditions, listed in order from 1 P.M. through 6 P.M.? | [
"Fujimura, Gabrieli, King, Jackson, Herman, Lauder",
"Fujimura, King, Lauder, Gabrieli, Jackson, Herman",
"Fujimura, Lauder, Gabrieli, King, Jackson, Herman",
"Herman, Jackson, Gabrieli, Lauder, King, Fujimura",
"Jackson, Gabrieli, Lauder, Herman, King, Fujimura"
] | 4 |
Individual hour-long auditions will be scheduled for each of six saxophonists—Fujimura, Gabrieli, Herman, Jackson, King, and Lauder. The auditions will all take place on the same day. Each audition will begin on the hour, with the first beginning at 1 P.M. and the last at 6 P.M. The schedule of auditions must conform to the following conditions: Jackson auditions earlier than Herman does. Gabrieli auditions earlier than King does. Gabrieli auditions either immediately before or immediately after Lauder does. Exactly one audition separates the auditions of Jackson and Lauder. | Which one of the following must be true? | [
"Lauder is scheduled to audition earlier than Herman.",
"Lauder is scheduled to audition earlier than King.",
"Jackson's audition is scheduled to begin at either 1 P.M. or 5 P.M.",
"Fujimura and Jackson are not scheduled to audition in consecutive hours.",
"Gabrieli and King are not scheduled to audition in consecutive hours."
] | 1 |
Individual hour-long auditions will be scheduled for each of six saxophonists—Fujimura, Gabrieli, Herman, Jackson, King, and Lauder. The auditions will all take place on the same day. Each audition will begin on the hour, with the first beginning at 1 P.M. and the last at 6 P.M. The schedule of auditions must conform to the following conditions: Jackson auditions earlier than Herman does. Gabrieli auditions earlier than King does. Gabrieli auditions either immediately before or immediately after Lauder does. Exactly one audition separates the auditions of Jackson and Lauder. | The earliest King's audition could be scheduled to begin is | [
"5 P.M.",
"4 P.M.",
"3 P.M.",
"2 P.M.",
"1 P.M."
] | 2 |
Individual hour-long auditions will be scheduled for each of six saxophonists—Fujimura, Gabrieli, Herman, Jackson, King, and Lauder. The auditions will all take place on the same day. Each audition will begin on the hour, with the first beginning at 1 P.M. and the last at 6 P.M. The schedule of auditions must conform to the following conditions: Jackson auditions earlier than Herman does. Gabrieli auditions earlier than King does. Gabrieli auditions either immediately before or immediately after Lauder does. Exactly one audition separates the auditions of Jackson and Lauder. | The order in which the saxophonists are scheduled to audition is completely determined if which one of the following is true? | [
"Herman's audition is scheduled to begin at 4 P.M.",
"Jackson's audition is scheduled to begin at 1 P.M.",
"Jackson's audition is scheduled to begin at 5 P.M.",
"Lauder's audition is scheduled to begin at 1 P.M.",
"Lauder's audition is scheduled to begin at 2 P.M."
] | 2 |
Individual hour-long auditions will be scheduled for each of six saxophonists—Fujimura, Gabrieli, Herman, Jackson, King, and Lauder. The auditions will all take place on the same day. Each audition will begin on the hour, with the first beginning at 1 P.M. and the last at 6 P.M. The schedule of auditions must conform to the following conditions: Jackson auditions earlier than Herman does. Gabrieli auditions earlier than King does. Gabrieli auditions either immediately before or immediately after Lauder does. Exactly one audition separates the auditions of Jackson and Lauder. | If Fujimura's audition is not scheduled to begin at 1 P.M., which one of the following could be true? | [
"Herman's audition is scheduled to begin at 6 P.M.",
"Gabrieli's audition is scheduled to begin at 5 P.M.",
"Herman's audition is scheduled to begin at 3 P.M.",
"Jackson's audition is scheduled to begin at 2 P.M.",
"Jackson's audition is scheduled to begin at 5 P.M."
] | 0 |
Individual hour-long auditions will be scheduled for each of six saxophonists—Fujimura, Gabrieli, Herman, Jackson, King, and Lauder. The auditions will all take place on the same day. Each audition will begin on the hour, with the first beginning at 1 P.M. and the last at 6 P.M. The schedule of auditions must conform to the following conditions: Jackson auditions earlier than Herman does. Gabrieli auditions earlier than King does. Gabrieli auditions either immediately before or immediately after Lauder does. Exactly one audition separates the auditions of Jackson and Lauder. | Which one of the following must be true? | [
"Gabrieli's audition is scheduled to begin before 5 P.M.",
"Herman's audition is scheduled to begin after 2 P.M.",
"Herman's audition is scheduled to begin before 6 P.M.",
"King's audition is scheduled to begin before 6 P.M.",
"Lauder's audition is scheduled to begin before 5 P.M."
] | 4 |
Four people—Grace, Heather, Josh, and Maria—will help each other move exactly three pieces of furniture—a recliner, a sofa, and a table. Each piece of furniture will be moved by exactly two of the people, and each person will help move at least one of the pieces of furniture, subject to the following constraints: Grace helps move the sofa if, but only if, Heather helps move the recliner. If Josh helps move the table, then Maria helps move the recliner. No piece of furniture is moved by Grace and Josh together. | Which one of the following could be an accurate matching of each piece of furniture to the two people who help each other move it? | [
"recliner: Grace and Maria; sofa: Heather and Josh; table: Grace and Heather",
"recliner: Grace and Maria; sofa: Heather and Maria; table: Grace and Josh",
"recliner: Heather and Josh; sofa: Grace and Heather; table: Josh and Maria",
"recliner: Heather and Josh; sofa: Heather and Maria; table: Grace and Maria",
"recliner: Josh and Maria; sofa: Grace and Heather; table: Grace and Maria"
] | 0 |
Four people—Grace, Heather, Josh, and Maria—will help each other move exactly three pieces of furniture—a recliner, a sofa, and a table. Each piece of furniture will be moved by exactly two of the people, and each person will help move at least one of the pieces of furniture, subject to the following constraints: Grace helps move the sofa if, but only if, Heather helps move the recliner. If Josh helps move the table, then Maria helps move the recliner. No piece of furniture is moved by Grace and Josh together. | If Josh and Maria help each other move the recliner, then which one of the following must be true? | [
"Heather helps move the sofa.",
"Josh helps move the sofa.",
"Maria helps move the sofa.",
"Grace helps move the table.",
"Heather helps move the table."
] | 3 |
Four people—Grace, Heather, Josh, and Maria—will help each other move exactly three pieces of furniture—a recliner, a sofa, and a table. Each piece of furniture will be moved by exactly two of the people, and each person will help move at least one of the pieces of furniture, subject to the following constraints: Grace helps move the sofa if, but only if, Heather helps move the recliner. If Josh helps move the table, then Maria helps move the recliner. No piece of furniture is moved by Grace and Josh together. | If Heather helps move each of the pieces of furniture, then which one of the following could be true? | [
"Grace helps move the recliner.",
"Maria helps move the recliner.",
"Josh helps move the sofa.",
"Maria helps move the sofa.",
"Grace helps move the table."
] | 1 |
Four people—Grace, Heather, Josh, and Maria—will help each other move exactly three pieces of furniture—a recliner, a sofa, and a table. Each piece of furniture will be moved by exactly two of the people, and each person will help move at least one of the pieces of furniture, subject to the following constraints: Grace helps move the sofa if, but only if, Heather helps move the recliner. If Josh helps move the table, then Maria helps move the recliner. No piece of furniture is moved by Grace and Josh together. | Which one of the following could be a pair of people who help each other move both the recliner and the table? | [
"Grace and Josh",
"Grace and Maria",
"Heather and Josh",
"Heather and Maria",
"Josh and Maria"
] | 1 |
Four people—Grace, Heather, Josh, and Maria—will help each other move exactly three pieces of furniture—a recliner, a sofa, and a table. Each piece of furniture will be moved by exactly two of the people, and each person will help move at least one of the pieces of furniture, subject to the following constraints: Grace helps move the sofa if, but only if, Heather helps move the recliner. If Josh helps move the table, then Maria helps move the recliner. No piece of furniture is moved by Grace and Josh together. | If Josh and Maria help each other move the sofa, then which one of the following could be true? | [
"Heather and Josh help each other move the recliner.",
"Heather and Maria help each other move the recliner.",
"Grace and Josh help each other move the table.",
"Grace and Maria help each other move the table.",
"Heather and Maria help each other move the table."
] | 4 |
A town has exactly two public parks—Graystone Park and Landing Park—which are to be planted with North American trees. There are exactly four varieties of trees available—maples, oaks, sycamores, and tamaracks. The planting of the trees must be in accord with the following: Each of the parks is planted with exactly three of the varieties. At least one of the parks is planted with both maples and sycamores. Any park that is planted with oaks will also be planted with tamaracks. Graystone Park is planted with maples. | Which one of the following could be a complete and accurate list of the varieties of trees planted in each of the parks? | [
"Graystone Park: maples, oaks, sycamores Landing Park: maples, oaks, sycamores",
"Graystone Park: maples, oaks, tamaracks Landing Park: maples, oaks, tamaracks",
"Graystone Park: maples, sycamores, tamaracks Landing Park: maples, oaks, sycamores",
"Graystone Park: maples, sycamores, tamaracks Landing Park: maples, oaks, tamaracks",
"Graystone Park: oaks, sycamores, tamaracks Landing Park: maples, sycamores, tamaracks"
] | 3 |
A town has exactly two public parks—Graystone Park and Landing Park—which are to be planted with North American trees. There are exactly four varieties of trees available—maples, oaks, sycamores, and tamaracks. The planting of the trees must be in accord with the following: Each of the parks is planted with exactly three of the varieties. At least one of the parks is planted with both maples and sycamores. Any park that is planted with oaks will also be planted with tamaracks. Graystone Park is planted with maples. | Which one of the following must be true? | [
"Graystone Park is planted with sycamores.",
"Landing Park is planted with maples.",
"Landing Park is planted with tamaracks.",
"The number of the parks planted with maples is equal to the number of the parks planted with sycamores.",
"The number of the parks planted with maples is greater than the number of the parks planted with sycamores."
] | 2 |
A town has exactly two public parks—Graystone Park and Landing Park—which are to be planted with North American trees. There are exactly four varieties of trees available—maples, oaks, sycamores, and tamaracks. The planting of the trees must be in accord with the following: Each of the parks is planted with exactly three of the varieties. At least one of the parks is planted with both maples and sycamores. Any park that is planted with oaks will also be planted with tamaracks. Graystone Park is planted with maples. | If both parks are planted with sycamores, which one of the following could be true? | [
"The number of the parks planted with maples is equal to the number of the parks planted with oaks.",
"The number of the parks planted with maples is greater than the number of the parks planted with sycamores.",
"The number of the parks planted with oaks is equal to the number of the parks planted with sycamores.",
"Graystone Park is planted with both maples and oaks.",
"Landing Park is planted with both maples and oaks."
] | 0 |
A town has exactly two public parks—Graystone Park and Landing Park—which are to be planted with North American trees. There are exactly four varieties of trees available—maples, oaks, sycamores, and tamaracks. The planting of the trees must be in accord with the following: Each of the parks is planted with exactly three of the varieties. At least one of the parks is planted with both maples and sycamores. Any park that is planted with oaks will also be planted with tamaracks. Graystone Park is planted with maples. | Which one of the following must be false? | [
"Both parks are planted with oaks.",
"Both parks are planted with sycamores.",
"Both parks are planted with tamaracks.",
"Exactly one of the parks is planted with maples.",
"Exactly one of the parks is planted with sycamores."
] | 0 |
A town has exactly two public parks—Graystone Park and Landing Park—which are to be planted with North American trees. There are exactly four varieties of trees available—maples, oaks, sycamores, and tamaracks. The planting of the trees must be in accord with the following: Each of the parks is planted with exactly three of the varieties. At least one of the parks is planted with both maples and sycamores. Any park that is planted with oaks will also be planted with tamaracks. Graystone Park is planted with maples. | Which one of the following could be true? | [
"The number of the parks planted with oaks is equal to the number of the parks planted with tamaracks.",
"The number of the parks planted with oaks is greater than the number of the parks planted with sycamores.",
"Exactly one of the parks is planted with tamaracks.",
"Neither park is planted with tamaracks.",
"Both parks contain exactly the same three varieties of trees as each other."
] | 4 |
Five executives—Quinn, Rodriguez, Sasada, Taylor, and Vandercar—are being scheduled to make site visits to three of their company's manufacturing plants—Farmington, Homestead, and Morningside. Each site will be visited by at least one of the executives and each executive will visit just one site. Each of the three site visits will take place on a different day. The schedule of site visits must conform to the following requirements: The Farmington visit must take place before the Homestead visit. The Farmington visit will include only one of the executives. The site visit that includes Quinn must take place before any site visit that includes either Rodriguez or Taylor. The site visit that includes Sasada cannot take place after any site visit that includes Vandercar. | Which one of the following could be the executives included in each of the site visits, with the sites listed in the order in which they are visited? | [
"Farmington: Quinn Homestead: Rodriguez, Sasada Morningside: Taylor, Vandercar",
"Farmington: Quinn Homestead: Rodriguez, Vandercar Morningside: Sasada, Taylor",
"Farmington: Rodriguez Morningside: Quinn, Taylor Homestead: Sasada, Vandercar",
"Homestead: Sasada Farmington: Quinn Morningside: Rodriguez, Taylor, Vandercar",
"Morningside: Quinn Farmington: Rodriguez, Sasada Homestead: Taylor, Vandercar"
] | 0 |
Five executives—Quinn, Rodriguez, Sasada, Taylor, and Vandercar—are being scheduled to make site visits to three of their company's manufacturing plants—Farmington, Homestead, and Morningside. Each site will be visited by at least one of the executives and each executive will visit just one site. Each of the three site visits will take place on a different day. The schedule of site visits must conform to the following requirements: The Farmington visit must take place before the Homestead visit. The Farmington visit will include only one of the executives. The site visit that includes Quinn must take place before any site visit that includes either Rodriguez or Taylor. The site visit that includes Sasada cannot take place after any site visit that includes Vandercar. | If the second of the three site visits includes both Rodriguez and Taylor, which one of the following must be true? | [
"The Farmington visit includes Quinn.",
"The Homestead visit includes Vandercar.",
"The Morningside visit includes Sasada.",
"The second of the three site visits includes Sasada.",
"The second of the three site visits includes exactly three of the executives."
] | 0 |
Five executives—Quinn, Rodriguez, Sasada, Taylor, and Vandercar—are being scheduled to make site visits to three of their company's manufacturing plants—Farmington, Homestead, and Morningside. Each site will be visited by at least one of the executives and each executive will visit just one site. Each of the three site visits will take place on a different day. The schedule of site visits must conform to the following requirements: The Farmington visit must take place before the Homestead visit. The Farmington visit will include only one of the executives. The site visit that includes Quinn must take place before any site visit that includes either Rodriguez or Taylor. The site visit that includes Sasada cannot take place after any site visit that includes Vandercar. | If one of the site visits includes both Quinn and Sasada, which one of the following could be true? | [
"The Farmington visit is the first of the three site visits.",
"The Homestead visit is the second of the three site visits.",
"One of the site visits includes only Vandercar.",
"The second of the three site visits includes Sasada.",
"The second of the three site visits includes exactly two of the executives."
] | 2 |
Five executives—Quinn, Rodriguez, Sasada, Taylor, and Vandercar—are being scheduled to make site visits to three of their company's manufacturing plants—Farmington, Homestead, and Morningside. Each site will be visited by at least one of the executives and each executive will visit just one site. Each of the three site visits will take place on a different day. The schedule of site visits must conform to the following requirements: The Farmington visit must take place before the Homestead visit. The Farmington visit will include only one of the executives. The site visit that includes Quinn must take place before any site visit that includes either Rodriguez or Taylor. The site visit that includes Sasada cannot take place after any site visit that includes Vandercar. | The executives who visit Homestead CANNOT be | [
"Quinn and Vandercar only",
"Rodriguez and Taylor only",
"Sasada and Taylor only",
"Quinn, Sasada, and Vandercar",
"Rodriguez, Sasada, and Taylor"
] | 3 |
Five executives—Quinn, Rodriguez, Sasada, Taylor, and Vandercar—are being scheduled to make site visits to three of their company's manufacturing plants—Farmington, Homestead, and Morningside. Each site will be visited by at least one of the executives and each executive will visit just one site. Each of the three site visits will take place on a different day. The schedule of site visits must conform to the following requirements: The Farmington visit must take place before the Homestead visit. The Farmington visit will include only one of the executives. The site visit that includes Quinn must take place before any site visit that includes either Rodriguez or Taylor. The site visit that includes Sasada cannot take place after any site visit that includes Vandercar. | If the Morningside visit includes both Quinn and Vandercar, which one of the following could be true? | [
"One of the site visits includes both Rodriguez and Sasada.",
"The second of the three site visits includes exactly three of the executives.",
"The last of the three site visits includes exactly three of the executives.",
"The Homestead visit takes place earlier than the Morningside visit.",
"The Morningside visit takes place earlier than the Farmington visit."
] | 4 |
Five executives—Quinn, Rodriguez, Sasada, Taylor, and Vandercar—are being scheduled to make site visits to three of their company's manufacturing plants—Farmington, Homestead, and Morningside. Each site will be visited by at least one of the executives and each executive will visit just one site. Each of the three site visits will take place on a different day. The schedule of site visits must conform to the following requirements: The Farmington visit must take place before the Homestead visit. The Farmington visit will include only one of the executives. The site visit that includes Quinn must take place before any site visit that includes either Rodriguez or Taylor. The site visit that includes Sasada cannot take place after any site visit that includes Vandercar. | Which one of the following must be true? | [
"The Farmington visit takes place earlier than the Morningside visit.",
"The site visit that includes Vandercar takes place earlier than the site visit that includes Rodriguez.",
"One of the first two site visits includes Sasada.",
"The second of the three site visits includes at least two of the executives.",
"At least one of the first two site visits includes only one of the executives."
] | 4 |
Five executives—Quinn, Rodriguez, Sasada, Taylor, and Vandercar—are being scheduled to make site visits to three of their company's manufacturing plants—Farmington, Homestead, and Morningside. Each site will be visited by at least one of the executives and each executive will visit just one site. Each of the three site visits will take place on a different day. The schedule of site visits must conform to the following requirements: The Farmington visit must take place before the Homestead visit. The Farmington visit will include only one of the executives. The site visit that includes Quinn must take place before any site visit that includes either Rodriguez or Taylor. The site visit that includes Sasada cannot take place after any site visit that includes Vandercar. | If the Farmington visit includes Sasada, which one of the following must be true? | [
"One of the site visits includes exactly three of the executives.",
"The last of the three site visits includes Rodriguez.",
"The Homestead visit includes Quinn.",
"The Morningside visit includes Taylor.",
"The site visit that includes Vandercar also includes Quinn."
] | 1 |
On a particular Saturday, a student will perform six activities—grocery shopping, hedge trimming, jogging, kitchen cleaning, laundry, and motorbike servicing. Each activity will be performed once, one at a time. The order in which the activities are performed is subject to the following conditions: Grocery shopping has to be immediately after hedge trimming. Kitchen cleaning has to be earlier than grocery shopping. Motorbike servicing has to be earlier than laundry. Motorbike servicing has to be either immediately before or immediately after jogging. | Which one of the following could be the order, from first to last, of the student's activities? | [
"jogging, kitchen cleaning, hedge trimming, grocery shopping, motorbike servicing, laundry",
"jogging, motorbike servicing, laundry, hedge trimming, grocery shopping, kitchen cleaning",
"kitchen cleaning, hedge trimming, grocery shopping, laundry, motorbike servicing, jogging",
"kitchen cleaning, jogging, motorbike servicing, laundry, hedge trimming, grocery shopping",
"motorbike servicing, jogging, laundry, hedge trimming, kitchen cleaning, grocery shopping"
] | 3 |
On a particular Saturday, a student will perform six activities—grocery shopping, hedge trimming, jogging, kitchen cleaning, laundry, and motorbike servicing. Each activity will be performed once, one at a time. The order in which the activities are performed is subject to the following conditions: Grocery shopping has to be immediately after hedge trimming. Kitchen cleaning has to be earlier than grocery shopping. Motorbike servicing has to be earlier than laundry. Motorbike servicing has to be either immediately before or immediately after jogging. | Which one of the following activities CANNOT be third? | [
"grocery shopping",
"hedge trimming",
"jogging",
"kitchen cleaning",
"motorbike servicing"
] | 1 |
On a particular Saturday, a student will perform six activities—grocery shopping, hedge trimming, jogging, kitchen cleaning, laundry, and motorbike servicing. Each activity will be performed once, one at a time. The order in which the activities are performed is subject to the following conditions: Grocery shopping has to be immediately after hedge trimming. Kitchen cleaning has to be earlier than grocery shopping. Motorbike servicing has to be earlier than laundry. Motorbike servicing has to be either immediately before or immediately after jogging. | Which one of the following CANNOT be true? | [
"Hedge trimming is fourth.",
"Jogging is fourth.",
"Kitchen cleaning is second.",
"Laundry is third.",
"Motorbike servicing is second."
] | 2 |
On a particular Saturday, a student will perform six activities—grocery shopping, hedge trimming, jogging, kitchen cleaning, laundry, and motorbike servicing. Each activity will be performed once, one at a time. The order in which the activities are performed is subject to the following conditions: Grocery shopping has to be immediately after hedge trimming. Kitchen cleaning has to be earlier than grocery shopping. Motorbike servicing has to be earlier than laundry. Motorbike servicing has to be either immediately before or immediately after jogging. | Which one of the following activities CANNOT be fifth? | [
"grocery shopping",
"hedge trimming",
"jogging",
"laundry",
"motorbike servicing"
] | 3 |
On a particular Saturday, a student will perform six activities—grocery shopping, hedge trimming, jogging, kitchen cleaning, laundry, and motorbike servicing. Each activity will be performed once, one at a time. The order in which the activities are performed is subject to the following conditions: Grocery shopping has to be immediately after hedge trimming. Kitchen cleaning has to be earlier than grocery shopping. Motorbike servicing has to be earlier than laundry. Motorbike servicing has to be either immediately before or immediately after jogging. | Which one of the following, if substituted for the condition that motorbike servicing has to be earlier than laundry, would have the same effect in determining the order of the student's activities? | [
"Laundry has to be one of the last three activities.",
"Laundry has to be either immediately before or immediately after jogging.",
"Jogging has to be earlier than laundry.",
"Laundry has to be earlier than hedge trimming.",
"Laundry has to be earlier than jogging."
] | 2 |
Each of exactly three actors—Gombrich, Otto, and Raines—auditions for parts on exactly two of the following days of a particular week: Wednesday, Thursday, Friday, and Saturday. On each of these days at least one of the actors auditions for parts. The order of that week's auditions must meet the following conditions: The first day on which Otto auditions is some day before the first day on which Raines auditions. There is at least one day on which both Gombrich and Raines audition. At least one of the actors auditions on both Thursday and Saturday. | Which one of the following could be an accurate matching of the actors to the days on which they audition? | [
"Gombrich: Thursday, Friday Otto: Wednesday, Saturday Raines: Friday, Saturday",
"Gombrich: Thursday, Saturday Otto: Wednesday, Friday Raines: Friday, Saturday",
"Gombrich: Friday, Saturday Otto: Thursday, Saturday Raines: Wednesday, Friday",
"Gombrich: Wednesday, Thursday Otto: Wednesday, Saturday Raines: Thursday, Saturday",
"Gombrich: Wednesday, Friday Otto: Wednesday, Thursday Raines: Thursday, Saturday"
] | 1 |
Each of exactly three actors—Gombrich, Otto, and Raines—auditions for parts on exactly two of the following days of a particular week: Wednesday, Thursday, Friday, and Saturday. On each of these days at least one of the actors auditions for parts. The order of that week's auditions must meet the following conditions: The first day on which Otto auditions is some day before the first day on which Raines auditions. There is at least one day on which both Gombrich and Raines audition. At least one of the actors auditions on both Thursday and Saturday. | If Otto auditions on both Thursday and Saturday, then Gombrich could audition on both | [
"Wednesday and Thursday",
"Wednesday and Friday",
"Thursday and Friday",
"Thursday and Saturday",
"Friday and Saturday"
] | 1 |
Each of exactly three actors—Gombrich, Otto, and Raines—auditions for parts on exactly two of the following days of a particular week: Wednesday, Thursday, Friday, and Saturday. On each of these days at least one of the actors auditions for parts. The order of that week's auditions must meet the following conditions: The first day on which Otto auditions is some day before the first day on which Raines auditions. There is at least one day on which both Gombrich and Raines audition. At least one of the actors auditions on both Thursday and Saturday. | Which one of the following CANNOT be true of the week's auditions? | [
"Gombrich's last audition is on Thursday.",
"Gombrich's last audition is on Friday.",
"Otto's last audition is on Saturday.",
"Raines's last audition is on Friday.",
"Raines's last audition is on Thursday."
] | 4 |
Each of exactly three actors—Gombrich, Otto, and Raines—auditions for parts on exactly two of the following days of a particular week: Wednesday, Thursday, Friday, and Saturday. On each of these days at least one of the actors auditions for parts. The order of that week's auditions must meet the following conditions: The first day on which Otto auditions is some day before the first day on which Raines auditions. There is at least one day on which both Gombrich and Raines audition. At least one of the actors auditions on both Thursday and Saturday. | Which one of the following pairs of days CANNOT be the two days on which Otto auditions? | [
"Wednesday and Thursday",
"Wednesday and Friday",
"Wednesday and Saturday",
"Thursday and Friday",
"Thursday and Saturday"
] | 3 |
Each of exactly three actors—Gombrich, Otto, and Raines—auditions for parts on exactly two of the following days of a particular week: Wednesday, Thursday, Friday, and Saturday. On each of these days at least one of the actors auditions for parts. The order of that week's auditions must meet the following conditions: The first day on which Otto auditions is some day before the first day on which Raines auditions. There is at least one day on which both Gombrich and Raines audition. At least one of the actors auditions on both Thursday and Saturday. | Which one of the following could be true? | [
"All three actors audition on Wednesday.",
"All three actors audition on Friday.",
"All three actors audition on Saturday.",
"Otto auditions on Friday and on Saturday.",
"Raines auditions on Wednesday and on Friday."
] | 2 |
Each of exactly three actors—Gombrich, Otto, and Raines—auditions for parts on exactly two of the following days of a particular week: Wednesday, Thursday, Friday, and Saturday. On each of these days at least one of the actors auditions for parts. The order of that week's auditions must meet the following conditions: The first day on which Otto auditions is some day before the first day on which Raines auditions. There is at least one day on which both Gombrich and Raines audition. At least one of the actors auditions on both Thursday and Saturday. | If Gombrich auditions on both Wednesday and Saturday, then which one of the following could be true? | [
"Otto auditions on both Wednesday and Thursday.",
"Otto auditions on both Wednesday and Friday.",
"Otto auditions on both Wednesday and Saturday.",
"Raines auditions on both Wednesday and Saturday.",
"Raines auditions on both Thursday and Friday."
] | 1 |
Each of seven toy dinosaurs—an iguanadon, a lambeosaur, a plateosaur, a stegosaur, a tyrannosaur, an ultrasaur, and a velociraptor—is completely colored either green, mauve, red, or yellow. A display is to consist entirely of exactly five of these toys. The display must meet the following specifications: Exactly two mauve toys are included. The stegosaur is red and is included. The iguanadon is included only if it is green. The plateosaur is included only if it is yellow. The velociraptor is included only if the ultrasaur is not. If both the lambeosaur and the ultrasaur are included, at least one of them is not mauve. | Which one of the following could be the toys included in the display? | [
"the lambeosaur, the plateosaur, the stegosaur, the ultrasaur, the velociraptor",
"the lambeosaur, the plateosaur, the stegosaur, the tyrannosaur, the ultrasaur",
"the iguanadon, the lambeosaur, the plateosaur, the stegosaur, the ultrasaur",
"the iguanadon, the lambeosaur, the plateosaur, the tyrannosaur, the velociraptor",
"the iguanadon, the lambeosaur, the stegosaur, the ultrasaur, the velociraptor"
] | 1 |
Each of seven toy dinosaurs—an iguanadon, a lambeosaur, a plateosaur, a stegosaur, a tyrannosaur, an ultrasaur, and a velociraptor—is completely colored either green, mauve, red, or yellow. A display is to consist entirely of exactly five of these toys. The display must meet the following specifications: Exactly two mauve toys are included. The stegosaur is red and is included. The iguanadon is included only if it is green. The plateosaur is included only if it is yellow. The velociraptor is included only if the ultrasaur is not. If both the lambeosaur and the ultrasaur are included, at least one of them is not mauve. | If the tyrannosaur is not included in the display, then the display must contain each of the following EXCEPT: | [
"a green iguanadon",
"a mauve velociraptor",
"a mauve lambeosaur",
"a mauve ultrasaur",
"a yellow plateosaur"
] | 3 |
Each of seven toy dinosaurs—an iguanadon, a lambeosaur, a plateosaur, a stegosaur, a tyrannosaur, an ultrasaur, and a velociraptor—is completely colored either green, mauve, red, or yellow. A display is to consist entirely of exactly five of these toys. The display must meet the following specifications: Exactly two mauve toys are included. The stegosaur is red and is included. The iguanadon is included only if it is green. The plateosaur is included only if it is yellow. The velociraptor is included only if the ultrasaur is not. If both the lambeosaur and the ultrasaur are included, at least one of them is not mauve. | Which one of the following is a pair of toys that could be included in the display together? | [
"a green lambeosaur and a mauve velociraptor",
"a green lambeosaur and a yellow tyrannosaur",
"a green lambeosaur and a yellow ultrasaur",
"a yellow tyrannosaur and a green ultrasaur",
"a yellow tyrannosaur and a red velociraptor"
] | 0 |
Each of seven toy dinosaurs—an iguanadon, a lambeosaur, a plateosaur, a stegosaur, a tyrannosaur, an ultrasaur, and a velociraptor—is completely colored either green, mauve, red, or yellow. A display is to consist entirely of exactly five of these toys. The display must meet the following specifications: Exactly two mauve toys are included. The stegosaur is red and is included. The iguanadon is included only if it is green. The plateosaur is included only if it is yellow. The velociraptor is included only if the ultrasaur is not. If both the lambeosaur and the ultrasaur are included, at least one of them is not mauve. | If the display includes a yellow tyrannosaur, then which one of the following must be true? | [
"The iguanadon is included in the display.",
"The plateosaur is not included in the display.",
"The display includes two yellow toy dinosaurs.",
"The display contains a green lambeosaur.",
"The display contains a mauve velociraptor."
] | 4 |
Each of seven toy dinosaurs—an iguanadon, a lambeosaur, a plateosaur, a stegosaur, a tyrannosaur, an ultrasaur, and a velociraptor—is completely colored either green, mauve, red, or yellow. A display is to consist entirely of exactly five of these toys. The display must meet the following specifications: Exactly two mauve toys are included. The stegosaur is red and is included. The iguanadon is included only if it is green. The plateosaur is included only if it is yellow. The velociraptor is included only if the ultrasaur is not. If both the lambeosaur and the ultrasaur are included, at least one of them is not mauve. | If both the iguanadon and the ultrasaur are included in the display, then the display must contain which one of the following? | [
"a mauve tyrannosaur",
"a mauve ultrasaur",
"a yellow lambeosaur",
"a yellow plateosaur",
"a yellow ultrasaur"
] | 0 |
Each of seven toy dinosaurs—an iguanadon, a lambeosaur, a plateosaur, a stegosaur, a tyrannosaur, an ultrasaur, and a velociraptor—is completely colored either green, mauve, red, or yellow. A display is to consist entirely of exactly five of these toys. The display must meet the following specifications: Exactly two mauve toys are included. The stegosaur is red and is included. The iguanadon is included only if it is green. The plateosaur is included only if it is yellow. The velociraptor is included only if the ultrasaur is not. If both the lambeosaur and the ultrasaur are included, at least one of them is not mauve. | If the display includes two green toys, then which one of the following could be true? | [
"There is exactly one yellow toy included in the display.",
"The tyrannosaur is included in the display and it is green.",
"Neither the lambeosaur nor the velociraptor is included in the display.",
"Neither the tyrannosaur nor the velociraptor is included in the display.",
"Neither the ultrasaur nor the velociraptor is included in the display."
] | 1 |
A charitable foundation awards grants in exactly four areas—medical services, theater arts, wildlife preservation, and youth services—each grant being in one of these areas. One or more grants are awarded in each of the four quarters of a calendar year. Additionally, over the course of a calendar year, the following must obtain: Grants are awarded in all four areas. No more than six grants are awarded. No grants in the same area are awarded in the same quarter or in consecutive quarters. Exactly two medical services grants are awarded. A wildlife preservation grant is awarded in the second quarter. | Which one of the following is a possible allocation of grants in a particular calendar year? | [
"first quarter: theater arts second quarter: wildlife preservation third quarter: medical services, youth services fourth quarter: theater arts",
"first quarter: wildlife preservation second quarter: medical services third quarter: theater arts fourth quarter: medical services, youth services",
"first quarter: youth services second quarter: wildlife preservation, medical services third quarter: theater arts fourth quarter: medical services, youth services",
"first quarter: medical services, theater arts second quarter: theater arts, wildlife preservation third quarter: youth services fourth quarter: medical services",
"first quarter: medical services, theater arts second quarter: wildlife preservation, youth services third quarter: theater arts fourth quarter: medical services, youth services"
] | 2 |
A charitable foundation awards grants in exactly four areas—medical services, theater arts, wildlife preservation, and youth services—each grant being in one of these areas. One or more grants are awarded in each of the four quarters of a calendar year. Additionally, over the course of a calendar year, the following must obtain: Grants are awarded in all four areas. No more than six grants are awarded. No grants in the same area are awarded in the same quarter or in consecutive quarters. Exactly two medical services grants are awarded. A wildlife preservation grant is awarded in the second quarter. | Which one of the following CANNOT be true in a particular calendar year? | [
"In each of the two quarters in which a medical services grant is awarded, no other grant is awarded.",
"Exactly two theater arts grants are awarded, one in the second quarter and one in the fourth quarter.",
"Exactly two youth services grants are awarded, one in the first quarter and one in the third quarter.",
"Two wildlife preservation grants and two youth services grants are awarded.",
"Three grants are awarded in the fourth quarter."
] | 3 |
A charitable foundation awards grants in exactly four areas—medical services, theater arts, wildlife preservation, and youth services—each grant being in one of these areas. One or more grants are awarded in each of the four quarters of a calendar year. Additionally, over the course of a calendar year, the following must obtain: Grants are awarded in all four areas. No more than six grants are awarded. No grants in the same area are awarded in the same quarter or in consecutive quarters. Exactly two medical services grants are awarded. A wildlife preservation grant is awarded in the second quarter. | If a wildlife preservation grant and a youth services grant are awarded in the same quarter of a particular calendar year, then any of the following could be true that year EXCEPT: | [
"A medical services grant is awarded in the second quarter.",
"A theater arts grant is awarded in the first quarter.",
"A theater arts grant is awarded in the second quarter.",
"A wildlife preservation grant is awarded in the fourth quarter.",
"A youth services grant is awarded in the third quarter."
] | 4 |
A charitable foundation awards grants in exactly four areas—medical services, theater arts, wildlife preservation, and youth services—each grant being in one of these areas. One or more grants are awarded in each of the four quarters of a calendar year. Additionally, over the course of a calendar year, the following must obtain: Grants are awarded in all four areas. No more than six grants are awarded. No grants in the same area are awarded in the same quarter or in consecutive quarters. Exactly two medical services grants are awarded. A wildlife preservation grant is awarded in the second quarter. | If exactly two grants are awarded in just one of the four quarters of a particular calendar year, then which one of the following could be true that year? | [
"Two youth services grants are awarded.",
"Neither a medical services grant nor a youth services grant is awarded in the first quarter.",
"A wildlife preservation grant is awarded in the fourth quarter.",
"Both a youth services grant and a theater arts grant are awarded in the first quarter.",
"A youth services grant is awarded in the first quarter and a theater arts grant is awarded in the second quarter."
] | 1 |
A charitable foundation awards grants in exactly four areas—medical services, theater arts, wildlife preservation, and youth services—each grant being in one of these areas. One or more grants are awarded in each of the four quarters of a calendar year. Additionally, over the course of a calendar year, the following must obtain: Grants are awarded in all four areas. No more than six grants are awarded. No grants in the same area are awarded in the same quarter or in consecutive quarters. Exactly two medical services grants are awarded. A wildlife preservation grant is awarded in the second quarter. | Which one of the following CANNOT be true in a particular calendar year? | [
"Three grants are awarded in a quarter, none of which is a medical services grant.",
"Exactly two grants are awarded in the first quarter and exactly two in the third quarter.",
"Exactly two grants are awarded in the first quarter and exactly two in the fourth quarter.",
"Theater arts grants are awarded in the first and fourth quarters, and no other grants are awarded in those two quarters.",
"Wildlife preservation grants are awarded in the second and fourth quarters, and no other grants are awarded in those two quarters."
] | 3 |
A charitable foundation awards grants in exactly four areas—medical services, theater arts, wildlife preservation, and youth services—each grant being in one of these areas. One or more grants are awarded in each of the four quarters of a calendar year. Additionally, over the course of a calendar year, the following must obtain: Grants are awarded in all four areas. No more than six grants are awarded. No grants in the same area are awarded in the same quarter or in consecutive quarters. Exactly two medical services grants are awarded. A wildlife preservation grant is awarded in the second quarter. | It is fully determined which grants are awarded for each quarter of a particular calendar year if which one of the following is true that year? | [
"Two theater arts grants are awarded.",
"Two youth services grants are awarded.",
"Three grants are awarded in the first quarter.",
"Three grants are awarded in the second quarter.",
"Three grants are awarded in the third quarter."
] | 4 |
Historical records show that over the course of five consecutive years—601, 602, 603, 604, and 605—a certain emperor began construction of six monuments: F, G, H, L, M, and S. A historian is trying to determine the years in which the individual monuments were begun. The following facts have been established: L was begun in a later year than G, but in an earlier year than F. H was begun no earlier than 604. M was begun earlier than 604. Two of the monuments were begun in 601, and no other monument was begun in the same year as any of the other monuments. | Which one of the following could be an accurate matching of monuments to the years in which they were begun? | [
"601: G; 602: L, S; 603: M; 604: H; 605: F",
"601: G, M; 602: L; 603: H; 604: S; 605: F",
"601: G, M; 602: S; 603: F; 604: L; 605: H",
"601: G, S; 602: L; 603: F; 604: M; 605: H",
"601: G, S; 602: L; 603: M; 604: H; 605: F"
] | 4 |
Historical records show that over the course of five consecutive years—601, 602, 603, 604, and 605—a certain emperor began construction of six monuments: F, G, H, L, M, and S. A historian is trying to determine the years in which the individual monuments were begun. The following facts have been established: L was begun in a later year than G, but in an earlier year than F. H was begun no earlier than 604. M was begun earlier than 604. Two of the monuments were begun in 601, and no other monument was begun in the same year as any of the other monuments. | What is the latest year in which L could have been begun? | [
"601",
"602",
"603",
"604",
"605"
] | 2 |
Historical records show that over the course of five consecutive years—601, 602, 603, 604, and 605—a certain emperor began construction of six monuments: F, G, H, L, M, and S. A historian is trying to determine the years in which the individual monuments were begun. The following facts have been established: L was begun in a later year than G, but in an earlier year than F. H was begun no earlier than 604. M was begun earlier than 604. Two of the monuments were begun in 601, and no other monument was begun in the same year as any of the other monuments. | The years in which each of the monuments were begun can be completely determined if which one of the following is discovered to be true? | [
"F was begun in 603.",
"G was begun in 602.",
"H was begun in 605.",
"M was begun in 602.",
"S was begun in 604."
] | 4 |
Historical records show that over the course of five consecutive years—601, 602, 603, 604, and 605—a certain emperor began construction of six monuments: F, G, H, L, M, and S. A historian is trying to determine the years in which the individual monuments were begun. The following facts have been established: L was begun in a later year than G, but in an earlier year than F. H was begun no earlier than 604. M was begun earlier than 604. Two of the monuments were begun in 601, and no other monument was begun in the same year as any of the other monuments. | Which one of the following must be true? | [
"F was begun in a later year than M.",
"F was begun in a later year than S.",
"H was begun in a later year than F.",
"H was begun in a later year than S.",
"M was begun in a later year than G."
] | 0 |
Historical records show that over the course of five consecutive years—601, 602, 603, 604, and 605—a certain emperor began construction of six monuments: F, G, H, L, M, and S. A historian is trying to determine the years in which the individual monuments were begun. The following facts have been established: L was begun in a later year than G, but in an earlier year than F. H was begun no earlier than 604. M was begun earlier than 604. Two of the monuments were begun in 601, and no other monument was begun in the same year as any of the other monuments. | L must be the monument that was begun in 602 if which one of the following is true? | [
"F was begun in 605.",
"G was begun in 601.",
"H was begun in 604.",
"M was begun in 601.",
"S was begun in 603."
] | 4 |
Historical records show that over the course of five consecutive years—601, 602, 603, 604, and 605—a certain emperor began construction of six monuments: F, G, H, L, M, and S. A historian is trying to determine the years in which the individual monuments were begun. The following facts have been established: L was begun in a later year than G, but in an earlier year than F. H was begun no earlier than 604. M was begun earlier than 604. Two of the monuments were begun in 601, and no other monument was begun in the same year as any of the other monuments. | If M was begun in a later year than L, then which one of the following could be true? | [
"F was begun in 603.",
"G was begun in 602.",
"H was begun in 605.",
"L was begun in 603.",
"S was begun in 604."
] | 2 |
A company organizing on-site day care consults with a group of parents composed exclusively of volunteers from among the seven employees—Felicia, Leah, Masatomo, Rochelle, Salman, Terry, and Veena—who have become parents this year. The composition of the volunteer group must be consistent with the following: If Rochelle volunteers, then so does Masatomo. If Masatomo volunteers, then so does Terry. If Salman does not volunteer, then Veena volunteers. If Rochelle does not volunteer, then Leah volunteers. If Terry volunteers, then neither Felicia nor Veena volunteers. | Which one of the following could be a complete and accurate list of the volunteers? | [
"Felicia, Salman",
"Masatomo, Rochelle",
"Leah, Salman, Terry",
"Salman, Rochelle, Veena",
"Leah, Salman, Terry, Veena"
] | 2 |
A company organizing on-site day care consults with a group of parents composed exclusively of volunteers from among the seven employees—Felicia, Leah, Masatomo, Rochelle, Salman, Terry, and Veena—who have become parents this year. The composition of the volunteer group must be consistent with the following: If Rochelle volunteers, then so does Masatomo. If Masatomo volunteers, then so does Terry. If Salman does not volunteer, then Veena volunteers. If Rochelle does not volunteer, then Leah volunteers. If Terry volunteers, then neither Felicia nor Veena volunteers. | If Veena volunteers, then which one of the following could be true? | [
"Felicia and Rochelle also volunteer.",
"Felicia and Salman also volunteer.",
"Leah and Masatomo also volunteer.",
"Leah and Terry also volunteer.",
"Salman and Terry also volunteer."
] | 1 |
A company organizing on-site day care consults with a group of parents composed exclusively of volunteers from among the seven employees—Felicia, Leah, Masatomo, Rochelle, Salman, Terry, and Veena—who have become parents this year. The composition of the volunteer group must be consistent with the following: If Rochelle volunteers, then so does Masatomo. If Masatomo volunteers, then so does Terry. If Salman does not volunteer, then Veena volunteers. If Rochelle does not volunteer, then Leah volunteers. If Terry volunteers, then neither Felicia nor Veena volunteers. | If Terry does not volunteer, then which one of the following CANNOT be true? | [
"Felicia volunteers.",
"Leah volunteers.",
"Rochelle volunteers.",
"Salman volunteers.",
"Veena volunteers."
] | 2 |
A company organizing on-site day care consults with a group of parents composed exclusively of volunteers from among the seven employees—Felicia, Leah, Masatomo, Rochelle, Salman, Terry, and Veena—who have become parents this year. The composition of the volunteer group must be consistent with the following: If Rochelle volunteers, then so does Masatomo. If Masatomo volunteers, then so does Terry. If Salman does not volunteer, then Veena volunteers. If Rochelle does not volunteer, then Leah volunteers. If Terry volunteers, then neither Felicia nor Veena volunteers. | If Masatomo volunteers, then which one of the following could be true? | [
"Felicia volunteers.",
"Leah volunteers.",
"Veena volunteers.",
"Salman does not volunteer.",
"Terry does not volunteer."
] | 1 |
A company organizing on-site day care consults with a group of parents composed exclusively of volunteers from among the seven employees—Felicia, Leah, Masatomo, Rochelle, Salman, Terry, and Veena—who have become parents this year. The composition of the volunteer group must be consistent with the following: If Rochelle volunteers, then so does Masatomo. If Masatomo volunteers, then so does Terry. If Salman does not volunteer, then Veena volunteers. If Rochelle does not volunteer, then Leah volunteers. If Terry volunteers, then neither Felicia nor Veena volunteers. | If Felicia volunteers, then which one of the following must be true? | [
"Leah volunteers.",
"Salman volunteers.",
"Veena does not volunteer.",
"Exactly three of the employees volunteer.",
"Exactly four of the employees volunteer."
] | 0 |
A company organizing on-site day care consults with a group of parents composed exclusively of volunteers from among the seven employees—Felicia, Leah, Masatomo, Rochelle, Salman, Terry, and Veena—who have become parents this year. The composition of the volunteer group must be consistent with the following: If Rochelle volunteers, then so does Masatomo. If Masatomo volunteers, then so does Terry. If Salman does not volunteer, then Veena volunteers. If Rochelle does not volunteer, then Leah volunteers. If Terry volunteers, then neither Felicia nor Veena volunteers. | Which one of the following pairs of employees is such that at least one member of the pair volunteers? | [
"Felicia and Terry",
"Leah and Masatomo",
"Leah and Veena",
"Rochelle and Salman",
"Salman and Terry"
] | 1 |
Flyhigh Airlines owns exactly two planes: P and Q. Getaway Airlines owns exactly three planes: R, S, T. On Sunday, each plane makes exactly one flight, according to the following conditions: Only one plane departs at a time. Each plane makes either a domestic or an international flight, but not both. Plane P makes an international flight. Planes Q and R make domestic flights. All international flights depart before any domestic flight. Any Getaway domestic flight departs before Flyhigh's domestic flight. | Which one of the following could be the order, from first to last, in which the five planes depart? | [
"P, Q, R, S, T",
"P, Q, T, S, R",
"P, S, T, Q, R",
"P, S, T, R, Q",
"T, S, R, P, Q"
] | 3 |
Flyhigh Airlines owns exactly two planes: P and Q. Getaway Airlines owns exactly three planes: R, S, T. On Sunday, each plane makes exactly one flight, according to the following conditions: Only one plane departs at a time. Each plane makes either a domestic or an international flight, but not both. Plane P makes an international flight. Planes Q and R make domestic flights. All international flights depart before any domestic flight. Any Getaway domestic flight departs before Flyhigh's domestic flight. | The plane that departs second could be any one of exactly how many of the planes? | [
"one",
"two",
"three",
"four",
"five"
] | 3 |
Flyhigh Airlines owns exactly two planes: P and Q. Getaway Airlines owns exactly three planes: R, S, T. On Sunday, each plane makes exactly one flight, according to the following conditions: Only one plane departs at a time. Each plane makes either a domestic or an international flight, but not both. Plane P makes an international flight. Planes Q and R make domestic flights. All international flights depart before any domestic flight. Any Getaway domestic flight departs before Flyhigh's domestic flight. | If plane S departs sometime before plane P, then which one of the following must be false? | [
"Plane S departs first.",
"Plane S departs third.",
"Plane T departs second.",
"Plane T departs third.",
"Plane T departs fourth."
] | 1 |
Flyhigh Airlines owns exactly two planes: P and Q. Getaway Airlines owns exactly three planes: R, S, T. On Sunday, each plane makes exactly one flight, according to the following conditions: Only one plane departs at a time. Each plane makes either a domestic or an international flight, but not both. Plane P makes an international flight. Planes Q and R make domestic flights. All international flights depart before any domestic flight. Any Getaway domestic flight departs before Flyhigh's domestic flight. | Which one of the following must be true? | [
"Plane P departs first.",
"Plane Q departs last.",
"Plane R departs second.",
"Plane S departs first.",
"Plane T departs fourth."
] | 1 |
Flyhigh Airlines owns exactly two planes: P and Q. Getaway Airlines owns exactly three planes: R, S, T. On Sunday, each plane makes exactly one flight, according to the following conditions: Only one plane departs at a time. Each plane makes either a domestic or an international flight, but not both. Plane P makes an international flight. Planes Q and R make domestic flights. All international flights depart before any domestic flight. Any Getaway domestic flight departs before Flyhigh's domestic flight. | If plane S departs third, then each of the following can be true EXCEPT: | [
"Plane R departs sometime before plane S and sometime before plane T.",
"Plane S departs sometime before plane Q and sometime before plane T.",
"Plane S departs sometime before plane R and sometime before plane T.",
"Plane T departs sometime before plane P and sometime before plane S.",
"Plane T departs sometime before plane R and sometime before plane S."
] | 2 |
A student is choosing courses to take during a summer school session. Each summer school student must take at least three courses from among the following seven: history, linguistics, music, physics, statistics, theater, and writing. The summer school schedule restricts the courses a student can take in the following ways: If history is taken, then neither statistics nor music can be taken. If music is taken, then neither physics nor theater can be taken. If writing is taken, then neither physics nor statistics can be taken. | The student could take which one of the following groups of courses during the summer school session? | [
"history, linguistics, and statistics",
"history, music, and physics",
"history, physics, and theater",
"linguistics, physics, theater, and writing",
"music, theater, and writing"
] | 2 |
A student is choosing courses to take during a summer school session. Each summer school student must take at least three courses from among the following seven: history, linguistics, music, physics, statistics, theater, and writing. The summer school schedule restricts the courses a student can take in the following ways: If history is taken, then neither statistics nor music can be taken. If music is taken, then neither physics nor theater can be taken. If writing is taken, then neither physics nor statistics can be taken. | What is the maximum number of courses the student could take during the summer school session? | [
"seven",
"six",
"five",
"four",
"three"
] | 3 |
A student is choosing courses to take during a summer school session. Each summer school student must take at least three courses from among the following seven: history, linguistics, music, physics, statistics, theater, and writing. The summer school schedule restricts the courses a student can take in the following ways: If history is taken, then neither statistics nor music can be taken. If music is taken, then neither physics nor theater can be taken. If writing is taken, then neither physics nor statistics can be taken. | If the student takes neither physics nor writing, then it could be true that the student also takes neither | [
"history nor linguistics",
"history nor music",
"history nor statistics",
"linguistics nor music",
"statistics nor theater"
] | 1 |
A student is choosing courses to take during a summer school session. Each summer school student must take at least three courses from among the following seven: history, linguistics, music, physics, statistics, theater, and writing. The summer school schedule restricts the courses a student can take in the following ways: If history is taken, then neither statistics nor music can be taken. If music is taken, then neither physics nor theater can be taken. If writing is taken, then neither physics nor statistics can be taken. | If the student takes music, then which one of the following must the student also take? | [
"writing",
"theater",
"statistics",
"physics",
"linguistics"
] | 4 |
A student is choosing courses to take during a summer school session. Each summer school student must take at least three courses from among the following seven: history, linguistics, music, physics, statistics, theater, and writing. The summer school schedule restricts the courses a student can take in the following ways: If history is taken, then neither statistics nor music can be taken. If music is taken, then neither physics nor theater can be taken. If writing is taken, then neither physics nor statistics can be taken. | The student must take one or the other or both of | [
"history or statistics",
"linguistics or theater",
"linguistics or writing",
"music or physics",
"theater or writing"
] | 1 |
A student is choosing courses to take during a summer school session. Each summer school student must take at least three courses from among the following seven: history, linguistics, music, physics, statistics, theater, and writing. The summer school schedule restricts the courses a student can take in the following ways: If history is taken, then neither statistics nor music can be taken. If music is taken, then neither physics nor theater can be taken. If writing is taken, then neither physics nor statistics can be taken. | Which one of the following, if substituted for the restriction that if music is taken, then neither physics nor theater can be taken, would have the same effect in determining which courses the student can take? | [
"If music is taken, then either statistics or writing must also be taken.",
"The only courses that are eligible to be taken together with music are linguistics, statistics, and writing.",
"The only courses that are eligible to be taken together with physics are history and linguistics.",
"The only courses that are eligible to be taken together with theater are history, linguistics, and writing.",
"If both physics and theater are taken, then music cannot be taken."
] | 1 |
A law firm has seven departments—family law, health law, injury law, labor law, probate, securities, and tax law. The firm is to occupy a building with three floors—the bottom floor, the middle floor, and the top floor. Each floor can accommodate up to four departments, and no department is to be on more than one floor. Assignment of departments to floors is subject to the following constraints: Probate must be on the same floor as tax law. Health law must be on the floor immediately above injury law. Labor law must occupy an entire floor by itself. | Which one of the following could be the assignment of departments to floors? | [
"top floor: labor law middle floor: injury law, probate, tax law bottom floor: family law, health law, securities",
"top floor: family law, health law, probate middle floor: injury law, securities, tax law bottom floor: labor law",
"top floor: health law, probate, tax law middle floor: family law, injury law, securities bottom floor: labor law",
"top floor: health law, probate, tax law middle floor: injury law, securities bottom floor: family law, labor law",
"top floor: family law, health law, probate, tax law middle floor: labor law bottom floor: injury law, securities"
] | 2 |
A law firm has seven departments—family law, health law, injury law, labor law, probate, securities, and tax law. The firm is to occupy a building with three floors—the bottom floor, the middle floor, and the top floor. Each floor can accommodate up to four departments, and no department is to be on more than one floor. Assignment of departments to floors is subject to the following constraints: Probate must be on the same floor as tax law. Health law must be on the floor immediately above injury law. Labor law must occupy an entire floor by itself. | If injury law and probate are both assigned to the middle floor, which one of the following could be true? | [
"Family law is assigned to the middle floor.",
"Health law is assigned to the middle floor.",
"Labor law is assigned to the top floor.",
"Securities is assigned to the bottom floor.",
"Tax law is assigned to the top floor."
] | 0 |
A law firm has seven departments—family law, health law, injury law, labor law, probate, securities, and tax law. The firm is to occupy a building with three floors—the bottom floor, the middle floor, and the top floor. Each floor can accommodate up to four departments, and no department is to be on more than one floor. Assignment of departments to floors is subject to the following constraints: Probate must be on the same floor as tax law. Health law must be on the floor immediately above injury law. Labor law must occupy an entire floor by itself. | Which one of the following CANNOT be the assignment for any of the floors? | [
"family law, health law, probate, and tax law",
"family law, injury law, probate, and tax law",
"family law, probate, securities, and tax law",
"health law, probate, securities, and tax law",
"injury law, probate, securities, and tax law"
] | 2 |
A law firm has seven departments—family law, health law, injury law, labor law, probate, securities, and tax law. The firm is to occupy a building with three floors—the bottom floor, the middle floor, and the top floor. Each floor can accommodate up to four departments, and no department is to be on more than one floor. Assignment of departments to floors is subject to the following constraints: Probate must be on the same floor as tax law. Health law must be on the floor immediately above injury law. Labor law must occupy an entire floor by itself. | If family law is assigned to the same floor as securities, which one of the following could be true? | [
"Exactly one department is assigned to the middle floor.",
"Exactly four departments are assigned to the middle floor.",
"Exactly two departments are assigned to the bottom floor.",
"Exactly three departments are assigned to the bottom floor.",
"Exactly four departments are assigned to the bottom floor."
] | 3 |
A law firm has seven departments—family law, health law, injury law, labor law, probate, securities, and tax law. The firm is to occupy a building with three floors—the bottom floor, the middle floor, and the top floor. Each floor can accommodate up to four departments, and no department is to be on more than one floor. Assignment of departments to floors is subject to the following constraints: Probate must be on the same floor as tax law. Health law must be on the floor immediately above injury law. Labor law must occupy an entire floor by itself. | If probate is assigned to the middle floor along with exactly two other departments, then which one of the following must be true? | [
"Family law is assigned to the floor immediately above health law.",
"Family law is assigned to the floor immediately below labor law.",
"Family law is assigned to the same floor as securities.",
"Probate is assigned to the same floor as health law.",
"Probate is assigned to the same floor as injury law."
] | 2 |
A museum curator is arranging seven photographs—Fence, Gardenias, Hibiscus, Irises, Katydid, Lotus, and Magnolia—on a gallery wall in accordance with the photographer's requirements. The photographs are to be hung along the wall in a row, in seven positions sequentially numbered from first to seventh. The photographer's requirements are as follows: Gardenias must be immediately before Katydid. Hibiscus must be somewhere before Katydid but cannot be the first photograph. Irises and Lotus must be next to one another. Magnolia must be one of the first three photographs. Fence must be either first or seventh. | Which one of the following could be the positions, from first to seventh, in which the photographs are hung? | [
"Fence, Hibiscus, Gardenias, Magnolia, Katydid, Irises, Lotus",
"Hibiscus, Magnolia, Gardenias, Katydid, Irises, Lotus, Fence",
"Irises, Lotus, Magnolia, Hibiscus, Gardenias, Katydid, Fence",
"Lotus, Magnolia, Irises, Hibiscus, Gardenias, Katydid, Fence",
"Magnolia, Fence, Hibiscus, Gardenias, Katydid, Lotus, Irises"
] | 2 |
A museum curator is arranging seven photographs—Fence, Gardenias, Hibiscus, Irises, Katydid, Lotus, and Magnolia—on a gallery wall in accordance with the photographer's requirements. The photographs are to be hung along the wall in a row, in seven positions sequentially numbered from first to seventh. The photographer's requirements are as follows: Gardenias must be immediately before Katydid. Hibiscus must be somewhere before Katydid but cannot be the first photograph. Irises and Lotus must be next to one another. Magnolia must be one of the first three photographs. Fence must be either first or seventh. | If Irises is immediately before Gardenias, which one of the following could be true? | [
"Gardenias is fourth.",
"Hibiscus is fourth.",
"Irises is third.",
"Lotus is second.",
"Magnolia is third."
] | 4 |
A museum curator is arranging seven photographs—Fence, Gardenias, Hibiscus, Irises, Katydid, Lotus, and Magnolia—on a gallery wall in accordance with the photographer's requirements. The photographs are to be hung along the wall in a row, in seven positions sequentially numbered from first to seventh. The photographer's requirements are as follows: Gardenias must be immediately before Katydid. Hibiscus must be somewhere before Katydid but cannot be the first photograph. Irises and Lotus must be next to one another. Magnolia must be one of the first three photographs. Fence must be either first or seventh. | Where each photograph is hung is fully determined if which one of the following is true? | [
"Gardenias is fourth.",
"Hibiscus is second.",
"Irises is second.",
"Lotus is first.",
"Magnolia is third."
] | 3 |
A museum curator is arranging seven photographs—Fence, Gardenias, Hibiscus, Irises, Katydid, Lotus, and Magnolia—on a gallery wall in accordance with the photographer's requirements. The photographs are to be hung along the wall in a row, in seven positions sequentially numbered from first to seventh. The photographer's requirements are as follows: Gardenias must be immediately before Katydid. Hibiscus must be somewhere before Katydid but cannot be the first photograph. Irises and Lotus must be next to one another. Magnolia must be one of the first three photographs. Fence must be either first or seventh. | If Magnolia is second, which one of the following CANNOT be true? | [
"Hibiscus is third.",
"Hibiscus is fourth.",
"Hibiscus is fifth.",
"Gardenias is fourth.",
"Gardenias is sixth."
] | 1 |
A museum curator is arranging seven photographs—Fence, Gardenias, Hibiscus, Irises, Katydid, Lotus, and Magnolia—on a gallery wall in accordance with the photographer's requirements. The photographs are to be hung along the wall in a row, in seven positions sequentially numbered from first to seventh. The photographer's requirements are as follows: Gardenias must be immediately before Katydid. Hibiscus must be somewhere before Katydid but cannot be the first photograph. Irises and Lotus must be next to one another. Magnolia must be one of the first three photographs. Fence must be either first or seventh. | Which one of the following, if substituted for the condition that Hibiscus must be hung somewhere before Katydid but cannot be the first photograph, would have the same effect in determining the arrangement of the photographs? | [
"If Fence is seventh, Hibiscus is second.",
"Gardenias is somewhere after Hibiscus, and either Fence or Magnolia is first.",
"Hibiscus must be somewhere between the first and sixth photographs.",
"Unless Hibiscus is second, it must be somewhere between Magnolia and Gardenias.",
"Katydid is somewhere after Hibiscus, which must be somewhere after Fence."
] | 3 |
Alicia will take exactly four courses this semester. She must choose from the following seven courses—Geography, Japanese, Macroeconomics, Psychology, Russian, Statistics (which is offered twice, once each on Tuesdays at 9 A.M. and 3 P.M.), and World History. No one is allowed to take any course more than once per semester. Because of university requirements and time conflicts, the following restrictions apply to Alicia's choices: She must take Japanese if she does not take Russian. She cannot take Japanese if she takes Macroeconomics. She cannot take World History if she takes Statistics at 9 A.M. She must take Statistics at 9 A.M. if she takes Psychology. She must take either Geography or World History but cannot take both. | Which one of the following could be the list of the four courses Alicia takes? | [
"Geography, Japanese, Psychology, Russian",
"Geography, Macroeconomics, Psychology, Statistics",
"Geography, Japanese, Macroeconomics, Russian",
"Geography, Psychology, Russian, Statistics",
"Macroeconomics, Psychology, Russian, Statistics"
] | 3 |
Alicia will take exactly four courses this semester. She must choose from the following seven courses—Geography, Japanese, Macroeconomics, Psychology, Russian, Statistics (which is offered twice, once each on Tuesdays at 9 A.M. and 3 P.M.), and World History. No one is allowed to take any course more than once per semester. Because of university requirements and time conflicts, the following restrictions apply to Alicia's choices: She must take Japanese if she does not take Russian. She cannot take Japanese if she takes Macroeconomics. She cannot take World History if she takes Statistics at 9 A.M. She must take Statistics at 9 A.M. if she takes Psychology. She must take either Geography or World History but cannot take both. | Which one of the following could be an accurate list of three of the courses Alicia takes? | [
"Geography, Statistics, World History",
"Japanese, Macroeconomics, Statistics",
"Japanese, Psychology, World History",
"Psychology, Russian, World History",
"Russian, Statistics, World History"
] | 4 |
Alicia will take exactly four courses this semester. She must choose from the following seven courses—Geography, Japanese, Macroeconomics, Psychology, Russian, Statistics (which is offered twice, once each on Tuesdays at 9 A.M. and 3 P.M.), and World History. No one is allowed to take any course more than once per semester. Because of university requirements and time conflicts, the following restrictions apply to Alicia's choices: She must take Japanese if she does not take Russian. She cannot take Japanese if she takes Macroeconomics. She cannot take World History if she takes Statistics at 9 A.M. She must take Statistics at 9 A.M. if she takes Psychology. She must take either Geography or World History but cannot take both. | Which courses Alicia takes is fully determined if she takes Russian and which one of the following? | [
"World History",
"Statistics",
"Psychology",
"Macroeconomics",
"Japanese"
] | 2 |
Alicia will take exactly four courses this semester. She must choose from the following seven courses—Geography, Japanese, Macroeconomics, Psychology, Russian, Statistics (which is offered twice, once each on Tuesdays at 9 A.M. and 3 P.M.), and World History. No one is allowed to take any course more than once per semester. Because of university requirements and time conflicts, the following restrictions apply to Alicia's choices: She must take Japanese if she does not take Russian. She cannot take Japanese if she takes Macroeconomics. She cannot take World History if she takes Statistics at 9 A.M. She must take Statistics at 9 A.M. if she takes Psychology. She must take either Geography or World History but cannot take both. | Alicia could take Statistics at either of the available times if she takes which one of the following pairs of courses? | [
"Geography and Japanese",
"Geography and Psychology",
"Japanese and World History",
"Psychology and Russian",
"Russian and World History"
] | 0 |
Alicia will take exactly four courses this semester. She must choose from the following seven courses—Geography, Japanese, Macroeconomics, Psychology, Russian, Statistics (which is offered twice, once each on Tuesdays at 9 A.M. and 3 P.M.), and World History. No one is allowed to take any course more than once per semester. Because of university requirements and time conflicts, the following restrictions apply to Alicia's choices: She must take Japanese if she does not take Russian. She cannot take Japanese if she takes Macroeconomics. She cannot take World History if she takes Statistics at 9 A.M. She must take Statistics at 9 A.M. if she takes Psychology. She must take either Geography or World History but cannot take both. | If Alicia takes Statistics at 3 P.M. and Geography, then which one of the following courses must she also take? | [
"Japanese",
"Macroeconomics",
"Psychology",
"Russian",
"World History"
] | 3 |
Alicia will take exactly four courses this semester. She must choose from the following seven courses—Geography, Japanese, Macroeconomics, Psychology, Russian, Statistics (which is offered twice, once each on Tuesdays at 9 A.M. and 3 P.M.), and World History. No one is allowed to take any course more than once per semester. Because of university requirements and time conflicts, the following restrictions apply to Alicia's choices: She must take Japanese if she does not take Russian. She cannot take Japanese if she takes Macroeconomics. She cannot take World History if she takes Statistics at 9 A.M. She must take Statistics at 9 A.M. if she takes Psychology. She must take either Geography or World History but cannot take both. | Suppose that Alicia must take Statistics if she takes Psychology, but rather than being restricted to taking Statistics at 9 A.M. she can take it at either 9 A.M. or at 3 P.M. If all the other restrictions remain the same, then which one of the following could be the list of the four courses Alicia takes? | [
"Psychology, Russian, Statistics, World History",
"Macroeconomics, Psychology, Statistics, World History",
"Macroeconomics, Psychology, Russian, World History",
"Geography, Psychology, Russian, World History",
"Geography, Macroeconomics, Russian, World History"
] | 0 |
An organization will hold its first six annual meetings in exactly six cities—Los Angeles, Montreal, New York, Toronto, Vancouver, and Washington—using each city only once. The following conditions govern the order in which the cities are used: Los Angeles must be used in some year after the year in which Toronto is used. Vancouver must be used either immediately before or immediately after Washington. The meeting in Toronto must be separated from the meeting in Montreal by meetings in exactly two other cities. The meeting in Vancouver must be separated from the meeting in Los Angeles by meetings in exactly two other cities. | Which one of the following lists the cities in an order in which they could be used for the meetings, from the first year through the sixth? | [
"Toronto, Vancouver, Washington, Montreal, Los Angeles, New York",
"Vancouver, Washington, Montreal, Los Angeles, New York, Toronto",
"Vancouver, Washington, Toronto, New York, Los Angeles, Montreal",
"Washington, Montreal, Vancouver, New York, Toronto, Los Angeles",
"Washington, Vancouver, New York, Toronto, Los Angeles, Montreal"
] | 0 |
An organization will hold its first six annual meetings in exactly six cities—Los Angeles, Montreal, New York, Toronto, Vancouver, and Washington—using each city only once. The following conditions govern the order in which the cities are used: Los Angeles must be used in some year after the year in which Toronto is used. Vancouver must be used either immediately before or immediately after Washington. The meeting in Toronto must be separated from the meeting in Montreal by meetings in exactly two other cities. The meeting in Vancouver must be separated from the meeting in Los Angeles by meetings in exactly two other cities. | Which one of the following must be true? | [
"Toronto is used in the first year.",
"Montreal is used in the fourth year.",
"Toronto is used at some time before Montreal is used.",
"New York is used either immediately before or immediately after Vancouver.",
"The meeting in New York is separated from the meeting in Washington by meetings in exactly two other cities."
] | 4 |