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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.

200912_1-G_4_19

There is exactly one possible order in which the cities are used if which one of the following is true?

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.

200912_1-G_4_20

Which one of the following is a complete and accurate list of the years in which Washington could be used?

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.

200912_1-G_4_21

If Montreal is used in the first year, which one of the following CANNOT be true?

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.

200912_1-G_4_22

Which one of the following could be true?

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.

200912_1-G_4_23

Which one of the following must be false?

A community center will host six arts-and-crafts workshops—Jewelry, Kite-making, Needlepoint, Quilting, Rug-making, and Scrapbooking. The workshops will be given on three consecutive days: Wednesday, Thursday, and Friday. Each workshop will be given once, and exactly two workshops will be given per day, one in the morning and one in the afternoon. The schedule for the workshops is subject to the following constraints: Jewelry must be given in the morning, on the same day as either Kite-making or Quilting. Rug-making must be given in the afternoon, on the same day as either Needlepoint or Scrapbooking. Quilting must be given on an earlier day than both Kite-making and Needlepoint.

201006_2-G_1_1

Which one of the following is an acceptable schedule for the workshops, with each day's workshops listed in the order in which they are to be given?

A community center will host six arts-and-crafts workshops—Jewelry, Kite-making, Needlepoint, Quilting, Rug-making, and Scrapbooking. The workshops will be given on three consecutive days: Wednesday, Thursday, and Friday. Each workshop will be given once, and exactly two workshops will be given per day, one in the morning and one in the afternoon. The schedule for the workshops is subject to the following constraints: Jewelry must be given in the morning, on the same day as either Kite-making or Quilting. Rug-making must be given in the afternoon, on the same day as either Needlepoint or Scrapbooking. Quilting must be given on an earlier day than both Kite-making and Needlepoint.

201006_2-G_1_2

Which one of the following workshops CANNOT be given on Thursday morning?

A community center will host six arts-and-crafts workshops—Jewelry, Kite-making, Needlepoint, Quilting, Rug-making, and Scrapbooking. The workshops will be given on three consecutive days: Wednesday, Thursday, and Friday. Each workshop will be given once, and exactly two workshops will be given per day, one in the morning and one in the afternoon. The schedule for the workshops is subject to the following constraints: Jewelry must be given in the morning, on the same day as either Kite-making or Quilting. Rug-making must be given in the afternoon, on the same day as either Needlepoint or Scrapbooking. Quilting must be given on an earlier day than both Kite-making and Needlepoint.

201006_2-G_1_3

Which one of the following pairs of workshops CANNOT be the ones given on Wednesday morning and Wednesday afternoon, respectively?

A community center will host six arts-and-crafts workshops—Jewelry, Kite-making, Needlepoint, Quilting, Rug-making, and Scrapbooking. The workshops will be given on three consecutive days: Wednesday, Thursday, and Friday. Each workshop will be given once, and exactly two workshops will be given per day, one in the morning and one in the afternoon. The schedule for the workshops is subject to the following constraints: Jewelry must be given in the morning, on the same day as either Kite-making or Quilting. Rug-making must be given in the afternoon, on the same day as either Needlepoint or Scrapbooking. Quilting must be given on an earlier day than both Kite-making and Needlepoint.

201006_2-G_1_4

If Kite-making is given on Friday morning, then which one of the following could be true?

A community center will host six arts-and-crafts workshops—Jewelry, Kite-making, Needlepoint, Quilting, Rug-making, and Scrapbooking. The workshops will be given on three consecutive days: Wednesday, Thursday, and Friday. Each workshop will be given once, and exactly two workshops will be given per day, one in the morning and one in the afternoon. The schedule for the workshops is subject to the following constraints: Jewelry must be given in the morning, on the same day as either Kite-making or Quilting. Rug-making must be given in the afternoon, on the same day as either Needlepoint or Scrapbooking. Quilting must be given on an earlier day than both Kite-making and Needlepoint.

201006_2-G_1_5

If Quilting is given in the morning, then which one of the following workshops CANNOT be given on Thursday?

A community center will host six arts-and-crafts workshops—Jewelry, Kite-making, Needlepoint, Quilting, Rug-making, and Scrapbooking. The workshops will be given on three consecutive days: Wednesday, Thursday, and Friday. Each workshop will be given once, and exactly two workshops will be given per day, one in the morning and one in the afternoon. The schedule for the workshops is subject to the following constraints: Jewelry must be given in the morning, on the same day as either Kite-making or Quilting. Rug-making must be given in the afternoon, on the same day as either Needlepoint or Scrapbooking. Quilting must be given on an earlier day than both Kite-making and Needlepoint.

201006_2-G_1_6

How many of the workshops are there that could be the one given on Wednesday morning?

Exactly six actors—Geyer, Henson, Jhalani, Lin, Mitchell, and Paredes—will appear one after another in the opening credits of a television program. Their contracts contain certain restrictions that affect the order in which they can appear. Given these restrictions, the order in which the actors appear, from first to sixth, must conform to the following: Both Lin and Mitchell appear earlier than Henson. Both Lin and Paredes appear earlier than Jhalani. If Mitchell appears earlier than Paredes, then Henson appears earlier than Geyer. Geyer does not appear last.

201006_2-G_2_7

Which one of the following could be the order, from first to last, in which the actors appear?

Exactly six actors—Geyer, Henson, Jhalani, Lin, Mitchell, and Paredes—will appear one after another in the opening credits of a television program. Their contracts contain certain restrictions that affect the order in which they can appear. Given these restrictions, the order in which the actors appear, from first to sixth, must conform to the following: Both Lin and Mitchell appear earlier than Henson. Both Lin and Paredes appear earlier than Jhalani. If Mitchell appears earlier than Paredes, then Henson appears earlier than Geyer. Geyer does not appear last.

201006_2-G_2_8

Which one of the following CANNOT be true?

Exactly six actors—Geyer, Henson, Jhalani, Lin, Mitchell, and Paredes—will appear one after another in the opening credits of a television program. Their contracts contain certain restrictions that affect the order in which they can appear. Given these restrictions, the order in which the actors appear, from first to sixth, must conform to the following: Both Lin and Mitchell appear earlier than Henson. Both Lin and Paredes appear earlier than Jhalani. If Mitchell appears earlier than Paredes, then Henson appears earlier than Geyer. Geyer does not appear last.

201006_2-G_2_9

Exactly how many of the actors are there any one of whom could appear sixth?

Exactly six actors—Geyer, Henson, Jhalani, Lin, Mitchell, and Paredes—will appear one after another in the opening credits of a television program. Their contracts contain certain restrictions that affect the order in which they can appear. Given these restrictions, the order in which the actors appear, from first to sixth, must conform to the following: Both Lin and Mitchell appear earlier than Henson. Both Lin and Paredes appear earlier than Jhalani. If Mitchell appears earlier than Paredes, then Henson appears earlier than Geyer. Geyer does not appear last.

201006_2-G_2_10

If Jhalani appears earlier than Mitchell, then which one of the following could be the order in which the other four actors appear, from earliest to latest?

Exactly six actors—Geyer, Henson, Jhalani, Lin, Mitchell, and Paredes—will appear one after another in the opening credits of a television program. Their contracts contain certain restrictions that affect the order in which they can appear. Given these restrictions, the order in which the actors appear, from first to sixth, must conform to the following: Both Lin and Mitchell appear earlier than Henson. Both Lin and Paredes appear earlier than Jhalani. If Mitchell appears earlier than Paredes, then Henson appears earlier than Geyer. Geyer does not appear last.

201006_2-G_2_11

If Lin appears immediately before Geyer, then which one of the following must be true?

Exactly six actors—Geyer, Henson, Jhalani, Lin, Mitchell, and Paredes—will appear one after another in the opening credits of a television program. Their contracts contain certain restrictions that affect the order in which they can appear. Given these restrictions, the order in which the actors appear, from first to sixth, must conform to the following: Both Lin and Mitchell appear earlier than Henson. Both Lin and Paredes appear earlier than Jhalani. If Mitchell appears earlier than Paredes, then Henson appears earlier than Geyer. Geyer does not appear last.

201006_2-G_2_12

If Mitchell appears first, then which one of the following must be true?

Over the course of one day, a landscaper will use a truck to haul exactly seven loads—three loads of mulch and four loads of stone. The truck's cargo bed will be cleaned in between carrying any two loads of different materials. To meet the landscaper's needs as efficiently as possible, the following constraints apply: The cargo bed cannot be cleaned more than three times. The fifth load must be mulch.

201006_2-G_3_13

Which one of the following is a pair of loads that can both be mulch?

Over the course of one day, a landscaper will use a truck to haul exactly seven loads—three loads of mulch and four loads of stone. The truck's cargo bed will be cleaned in between carrying any two loads of different materials. To meet the landscaper's needs as efficiently as possible, the following constraints apply: The cargo bed cannot be cleaned more than three times. The fifth load must be mulch.

201006_2-G_3_14

Which one of the following must be true?

Over the course of one day, a landscaper will use a truck to haul exactly seven loads—three loads of mulch and four loads of stone. The truck's cargo bed will be cleaned in between carrying any two loads of different materials. To meet the landscaper's needs as efficiently as possible, the following constraints apply: The cargo bed cannot be cleaned more than three times. The fifth load must be mulch.

201006_2-G_3_15

If the third load is mulch, which one of the following must be true?

Over the course of one day, a landscaper will use a truck to haul exactly seven loads—three loads of mulch and four loads of stone. The truck's cargo bed will be cleaned in between carrying any two loads of different materials. To meet the landscaper's needs as efficiently as possible, the following constraints apply: The cargo bed cannot be cleaned more than three times. The fifth load must be mulch.

201006_2-G_3_16

If the cargo bed is cleaned exactly twice, which one of the following must be true?

Over the course of one day, a landscaper will use a truck to haul exactly seven loads—three loads of mulch and four loads of stone. The truck's cargo bed will be cleaned in between carrying any two loads of different materials. To meet the landscaper's needs as efficiently as possible, the following constraints apply: The cargo bed cannot be cleaned more than three times. The fifth load must be mulch.

201006_2-G_3_17

If no more than two loads of the same material are hauled consecutively, then which one of the following could be true?

A travel magazine has hired six interns—Farber, Gombarick, Hall, Jackson, Kanze, and Lha—to assist in covering three stories—Romania, Spain, and Tuscany. Each intern will be trained either as a photographer's assistant or as a writer's assistant. Each story is assigned a team of two interns—one photographer's assistant and one writer's assistant—in accordance with the following conditions: Gombarick and Lha will be trained in the same field. Farber and Kanze will be trained in different fields. Hall will be trained as a photographer's assistant. Jackson is assigned to Tuscany. Kanze is not assigned to Spain.

201006_2-G_4_18

Which one of the following could be an acceptable assignment of photographer's assistants to stories?

A travel magazine has hired six interns—Farber, Gombarick, Hall, Jackson, Kanze, and Lha—to assist in covering three stories—Romania, Spain, and Tuscany. Each intern will be trained either as a photographer's assistant or as a writer's assistant. Each story is assigned a team of two interns—one photographer's assistant and one writer's assistant—in accordance with the following conditions: Gombarick and Lha will be trained in the same field. Farber and Kanze will be trained in different fields. Hall will be trained as a photographer's assistant. Jackson is assigned to Tuscany. Kanze is not assigned to Spain.

201006_2-G_4_19

If Farber is assigned to Romania, then which one of the following must be true?

A travel magazine has hired six interns—Farber, Gombarick, Hall, Jackson, Kanze, and Lha—to assist in covering three stories—Romania, Spain, and Tuscany. Each intern will be trained either as a photographer's assistant or as a writer's assistant. Each story is assigned a team of two interns—one photographer's assistant and one writer's assistant—in accordance with the following conditions: Gombarick and Lha will be trained in the same field. Farber and Kanze will be trained in different fields. Hall will be trained as a photographer's assistant. Jackson is assigned to Tuscany. Kanze is not assigned to Spain.

201006_2-G_4_20

If Farber and Hall are assigned to the same story as each other, then which one of the following could be true?

A travel magazine has hired six interns—Farber, Gombarick, Hall, Jackson, Kanze, and Lha—to assist in covering three stories—Romania, Spain, and Tuscany. Each intern will be trained either as a photographer's assistant or as a writer's assistant. Each story is assigned a team of two interns—one photographer's assistant and one writer's assistant—in accordance with the following conditions: Gombarick and Lha will be trained in the same field. Farber and Kanze will be trained in different fields. Hall will be trained as a photographer's assistant. Jackson is assigned to Tuscany. Kanze is not assigned to Spain.

201006_2-G_4_21

If Farber is a writer's assistant, then which one of the following pairs could be the team of interns assigned to Romania?

A travel magazine has hired six interns—Farber, Gombarick, Hall, Jackson, Kanze, and Lha—to assist in covering three stories—Romania, Spain, and Tuscany. Each intern will be trained either as a photographer's assistant or as a writer's assistant. Each story is assigned a team of two interns—one photographer's assistant and one writer's assistant—in accordance with the following conditions: Gombarick and Lha will be trained in the same field. Farber and Kanze will be trained in different fields. Hall will be trained as a photographer's assistant. Jackson is assigned to Tuscany. Kanze is not assigned to Spain.

201006_2-G_4_22

If Gombarick and Kanze are assigned to the same story as each other, then which one of the following could be true?

A travel magazine has hired six interns—Farber, Gombarick, Hall, Jackson, Kanze, and Lha—to assist in covering three stories—Romania, Spain, and Tuscany. Each intern will be trained either as a photographer's assistant or as a writer's assistant. Each story is assigned a team of two interns—one photographer's assistant and one writer's assistant—in accordance with the following conditions: Gombarick and Lha will be trained in the same field. Farber and Kanze will be trained in different fields. Hall will be trained as a photographer's assistant. Jackson is assigned to Tuscany. Kanze is not assigned to Spain.

201006_2-G_4_23

Which one of the following interns CANNOT be assigned to Tuscany?

Exactly six workers—Faith, Gus, Hannah, Juan, Kenneth, and Lisa—will travel to a business convention in two cars—car 1 and car 2. Each car must carry at least two of the workers, one of whom will be assigned to drive. For the entire trip, the workers will comply with an assignment that also meets the following constraints: Either Faith or Gus must drive the car in which Hannah travels. Either Faith or Kenneth must drive the car in which Juan travels. Gus must travel in the same car as Lisa.

201010_3-G_1_1

Which one of the following is a possible assignment of the workers to the cars?

Exactly six workers—Faith, Gus, Hannah, Juan, Kenneth, and Lisa—will travel to a business convention in two cars—car 1 and car 2. Each car must carry at least two of the workers, one of whom will be assigned to drive. For the entire trip, the workers will comply with an assignment that also meets the following constraints: Either Faith or Gus must drive the car in which Hannah travels. Either Faith or Kenneth must drive the car in which Juan travels. Gus must travel in the same car as Lisa.

201010_3-G_1_2

The two workers who drive the cars CANNOT be

Exactly six workers—Faith, Gus, Hannah, Juan, Kenneth, and Lisa—will travel to a business convention in two cars—car 1 and car 2. Each car must carry at least two of the workers, one of whom will be assigned to drive. For the entire trip, the workers will comply with an assignment that also meets the following constraints: Either Faith or Gus must drive the car in which Hannah travels. Either Faith or Kenneth must drive the car in which Juan travels. Gus must travel in the same car as Lisa.

201010_3-G_1_3

If Lisa drives one of the cars, then which one of the following could be true?

Exactly six workers—Faith, Gus, Hannah, Juan, Kenneth, and Lisa—will travel to a business convention in two cars—car 1 and car 2. Each car must carry at least two of the workers, one of whom will be assigned to drive. For the entire trip, the workers will comply with an assignment that also meets the following constraints: Either Faith or Gus must drive the car in which Hannah travels. Either Faith or Kenneth must drive the car in which Juan travels. Gus must travel in the same car as Lisa.

201010_3-G_1_4

If Faith travels with two other workers in car 1, and if Faith is not the driver, then the person in car 1 other than Faith and the driver must be

Exactly six workers—Faith, Gus, Hannah, Juan, Kenneth, and Lisa—will travel to a business convention in two cars—car 1 and car 2. Each car must carry at least two of the workers, one of whom will be assigned to drive. For the entire trip, the workers will comply with an assignment that also meets the following constraints: Either Faith or Gus must drive the car in which Hannah travels. Either Faith or Kenneth must drive the car in which Juan travels. Gus must travel in the same car as Lisa.

201010_3-G_1_5

Which one of the following CANNOT be true?

An archaeologist has six ancient artifacts—a figurine, a headdress, a jar, a necklace, a plaque, and a tureen—no two of which are the same age. She will order them from first (oldest) to sixth (most recent). The following has already been determined: The figurine is older than both the jar and the headdress. The necklace and the jar are both older than the tureen. Either the plaque is older than both the headdress and the necklace, or both the headdress and the necklace are older than the plaque.

201010_3-G_2_6

Which one of the following could be the artifacts in the order of their age, from first to sixth?

An archaeologist has six ancient artifacts—a figurine, a headdress, a jar, a necklace, a plaque, and a tureen—no two of which are the same age. She will order them from first (oldest) to sixth (most recent). The following has already been determined: The figurine is older than both the jar and the headdress. The necklace and the jar are both older than the tureen. Either the plaque is older than both the headdress and the necklace, or both the headdress and the necklace are older than the plaque.

201010_3-G_2_7

Exactly how many of the artifacts are there any one of which could be first?

An archaeologist has six ancient artifacts—a figurine, a headdress, a jar, a necklace, a plaque, and a tureen—no two of which are the same age. She will order them from first (oldest) to sixth (most recent). The following has already been determined: The figurine is older than both the jar and the headdress. The necklace and the jar are both older than the tureen. Either the plaque is older than both the headdress and the necklace, or both the headdress and the necklace are older than the plaque.

201010_3-G_2_8

Which one of the following artifacts CANNOT be fourth?

An archaeologist has six ancient artifacts—a figurine, a headdress, a jar, a necklace, a plaque, and a tureen—no two of which are the same age. She will order them from first (oldest) to sixth (most recent). The following has already been determined: The figurine is older than both the jar and the headdress. The necklace and the jar are both older than the tureen. Either the plaque is older than both the headdress and the necklace, or both the headdress and the necklace are older than the plaque.

201010_3-G_2_9

If the figurine is third, which one of the following must be second?

An archaeologist has six ancient artifacts—a figurine, a headdress, a jar, a necklace, a plaque, and a tureen—no two of which are the same age. She will order them from first (oldest) to sixth (most recent). The following has already been determined: The figurine is older than both the jar and the headdress. The necklace and the jar are both older than the tureen. Either the plaque is older than both the headdress and the necklace, or both the headdress and the necklace are older than the plaque.

201010_3-G_2_10

If the plaque is first, then exactly how many artifacts are there any one of which could be second?

An archaeologist has six ancient artifacts—a figurine, a headdress, a jar, a necklace, a plaque, and a tureen—no two of which are the same age. She will order them from first (oldest) to sixth (most recent). The following has already been determined: The figurine is older than both the jar and the headdress. The necklace and the jar are both older than the tureen. Either the plaque is older than both the headdress and the necklace, or both the headdress and the necklace are older than the plaque.

201010_3-G_2_11

Which one of the following, if substituted for the information that the necklace and the jar are both older than the tureen, would have the same effect in determining the order of the artifacts?

The coach of a women's track team must determine which four of five runners—Quinn, Ramirez, Smith, Terrell, and Uzoma—will run in the four races of an upcoming track meet. Each of the four runners chosen will run in exactly one of the four races—the first, second, third, or fourth. The coach's selection is bound by the following constraints: If Quinn runs in the track meet, then Terrell runs in the race immediately after the race in which Quinn runs. Smith does not run in either the second race or the fourth race. If Uzoma does not run in the track meet, then Ramirez runs in the second race. If Ramirez runs in the second race, then Uzoma does not run in the track meet.

201010_3-G_3_12

Which one of the following could be the order in which the runners run, from first to fourth?

The coach of a women's track team must determine which four of five runners—Quinn, Ramirez, Smith, Terrell, and Uzoma—will run in the four races of an upcoming track meet. Each of the four runners chosen will run in exactly one of the four races—the first, second, third, or fourth. The coach's selection is bound by the following constraints: If Quinn runs in the track meet, then Terrell runs in the race immediately after the race in which Quinn runs. Smith does not run in either the second race or the fourth race. If Uzoma does not run in the track meet, then Ramirez runs in the second race. If Ramirez runs in the second race, then Uzoma does not run in the track meet.

201010_3-G_3_13

Which one of the following runners must the coach select to run in the track meet?

The coach of a women's track team must determine which four of five runners—Quinn, Ramirez, Smith, Terrell, and Uzoma—will run in the four races of an upcoming track meet. Each of the four runners chosen will run in exactly one of the four races—the first, second, third, or fourth. The coach's selection is bound by the following constraints: If Quinn runs in the track meet, then Terrell runs in the race immediately after the race in which Quinn runs. Smith does not run in either the second race or the fourth race. If Uzoma does not run in the track meet, then Ramirez runs in the second race. If Ramirez runs in the second race, then Uzoma does not run in the track meet.

201010_3-G_3_14

The question of which runners will be chosen to run in the track meet and in what races they will run can be completely resolved if which one of the following is true?

The coach of a women's track team must determine which four of five runners—Quinn, Ramirez, Smith, Terrell, and Uzoma—will run in the four races of an upcoming track meet. Each of the four runners chosen will run in exactly one of the four races—the first, second, third, or fourth. The coach's selection is bound by the following constraints: If Quinn runs in the track meet, then Terrell runs in the race immediately after the race in which Quinn runs. Smith does not run in either the second race or the fourth race. If Uzoma does not run in the track meet, then Ramirez runs in the second race. If Ramirez runs in the second race, then Uzoma does not run in the track meet.

201010_3-G_3_15

Which one of the following CANNOT be true?

The coach of a women's track team must determine which four of five runners—Quinn, Ramirez, Smith, Terrell, and Uzoma—will run in the four races of an upcoming track meet. Each of the four runners chosen will run in exactly one of the four races—the first, second, third, or fourth. The coach's selection is bound by the following constraints: If Quinn runs in the track meet, then Terrell runs in the race immediately after the race in which Quinn runs. Smith does not run in either the second race or the fourth race. If Uzoma does not run in the track meet, then Ramirez runs in the second race. If Ramirez runs in the second race, then Uzoma does not run in the track meet.

201010_3-G_3_16

If Uzoma runs in the first race, then which one of the following must be true?

The coach of a women's track team must determine which four of five runners—Quinn, Ramirez, Smith, Terrell, and Uzoma—will run in the four races of an upcoming track meet. Each of the four runners chosen will run in exactly one of the four races—the first, second, third, or fourth. The coach's selection is bound by the following constraints: If Quinn runs in the track meet, then Terrell runs in the race immediately after the race in which Quinn runs. Smith does not run in either the second race or the fourth race. If Uzoma does not run in the track meet, then Ramirez runs in the second race. If Ramirez runs in the second race, then Uzoma does not run in the track meet.

201010_3-G_3_17

If both Quinn and Smith run in the track meet, then how many of the runners are there any one of whom could be the one who runs in the first race?

From the 1st through the 7th of next month, seven nurses—Farnham, Griseldi, Heany, Juarez, Khan, Lightfoot, and Moreau—will each conduct one information session at a community center. Each nurse's session will fall on a different day. The nurses' schedule is governed by the following constraints: At least two of the other nurses' sessions must fall in between Heany's session and Moreau's session. Griseldi's session must be on the day before Khan's. Juarez's session must be on a later day than Moreau's. Farnham's session must be on an earlier day than Khan's but on a later day than Lightfoot's. Lightfoot cannot conduct the session on the 2nd.

201010_3-G_4_18

Which one of the following could be the order of the nurses' sessions, from first to last?

From the 1st through the 7th of next month, seven nurses—Farnham, Griseldi, Heany, Juarez, Khan, Lightfoot, and Moreau—will each conduct one information session at a community center. Each nurse's session will fall on a different day. The nurses' schedule is governed by the following constraints: At least two of the other nurses' sessions must fall in between Heany's session and Moreau's session. Griseldi's session must be on the day before Khan's. Juarez's session must be on a later day than Moreau's. Farnham's session must be on an earlier day than Khan's but on a later day than Lightfoot's. Lightfoot cannot conduct the session on the 2nd.

201010_3-G_4_19

Juarez's session CANNOT be on which one of the following days?

From the 1st through the 7th of next month, seven nurses—Farnham, Griseldi, Heany, Juarez, Khan, Lightfoot, and Moreau—will each conduct one information session at a community center. Each nurse's session will fall on a different day. The nurses' schedule is governed by the following constraints: At least two of the other nurses' sessions must fall in between Heany's session and Moreau's session. Griseldi's session must be on the day before Khan's. Juarez's session must be on a later day than Moreau's. Farnham's session must be on an earlier day than Khan's but on a later day than Lightfoot's. Lightfoot cannot conduct the session on the 2nd.

201010_3-G_4_20

If Juarez's session is on the 3rd, then which one of the following could be true?

From the 1st through the 7th of next month, seven nurses—Farnham, Griseldi, Heany, Juarez, Khan, Lightfoot, and Moreau—will each conduct one information session at a community center. Each nurse's session will fall on a different day. The nurses' schedule is governed by the following constraints: At least two of the other nurses' sessions must fall in between Heany's session and Moreau's session. Griseldi's session must be on the day before Khan's. Juarez's session must be on a later day than Moreau's. Farnham's session must be on an earlier day than Khan's but on a later day than Lightfoot's. Lightfoot cannot conduct the session on the 2nd.

201010_3-G_4_21

If Khan's session is on an earlier day than Moreau's, which one of the following could conduct the session on the 3rd?

From the 1st through the 7th of next month, seven nurses—Farnham, Griseldi, Heany, Juarez, Khan, Lightfoot, and Moreau—will each conduct one information session at a community center. Each nurse's session will fall on a different day. The nurses' schedule is governed by the following constraints: At least two of the other nurses' sessions must fall in between Heany's session and Moreau's session. Griseldi's session must be on the day before Khan's. Juarez's session must be on a later day than Moreau's. Farnham's session must be on an earlier day than Khan's but on a later day than Lightfoot's. Lightfoot cannot conduct the session on the 2nd.

201010_3-G_4_22

If Griseldi's session is on the 5th, then which one of the following must be true?

From the 1st through the 7th of next month, seven nurses—Farnham, Griseldi, Heany, Juarez, Khan, Lightfoot, and Moreau—will each conduct one information session at a community center. Each nurse's session will fall on a different day. The nurses' schedule is governed by the following constraints: At least two of the other nurses' sessions must fall in between Heany's session and Moreau's session. Griseldi's session must be on the day before Khan's. Juarez's session must be on a later day than Moreau's. Farnham's session must be on an earlier day than Khan's but on a later day than Lightfoot's. Lightfoot cannot conduct the session on the 2nd.

201010_3-G_4_23

Lightfoot's session could be on which one of the following days?

A motel operator is scheduling appointments to start up services at a new motel. Appointments for six services—gas, landscaping, power, satellite, telephone, and water—will be scheduled, one appointment per day for the next six days. The schedule for the appointments is subject to the following conditions: The water appointment must be scheduled for an earlier day than the landscaping appointment. The power appointment must be scheduled for an earlier day than both the gas and satellite appointments. The appointments scheduled for the second and third days cannot be for either gas, satellite, or telephone. The telephone appointment cannot be scheduled for the sixth day.

201012_3-G_1_1

Which one of the following is an acceptable schedule of appointments, listed in order from earliest to latest?

A motel operator is scheduling appointments to start up services at a new motel. Appointments for six services—gas, landscaping, power, satellite, telephone, and water—will be scheduled, one appointment per day for the next six days. The schedule for the appointments is subject to the following conditions: The water appointment must be scheduled for an earlier day than the landscaping appointment. The power appointment must be scheduled for an earlier day than both the gas and satellite appointments. The appointments scheduled for the second and third days cannot be for either gas, satellite, or telephone. The telephone appointment cannot be scheduled for the sixth day.

201012_3-G_1_2

If neither the gas nor the satellite nor the telephone appointment is scheduled for the fourth day, which one of the following must be true?

A motel operator is scheduling appointments to start up services at a new motel. Appointments for six services—gas, landscaping, power, satellite, telephone, and water—will be scheduled, one appointment per day for the next six days. The schedule for the appointments is subject to the following conditions: The water appointment must be scheduled for an earlier day than the landscaping appointment. The power appointment must be scheduled for an earlier day than both the gas and satellite appointments. The appointments scheduled for the second and third days cannot be for either gas, satellite, or telephone. The telephone appointment cannot be scheduled for the sixth day.

201012_3-G_1_3

Which one of the following must be true?

A motel operator is scheduling appointments to start up services at a new motel. Appointments for six services—gas, landscaping, power, satellite, telephone, and water—will be scheduled, one appointment per day for the next six days. The schedule for the appointments is subject to the following conditions: The water appointment must be scheduled for an earlier day than the landscaping appointment. The power appointment must be scheduled for an earlier day than both the gas and satellite appointments. The appointments scheduled for the second and third days cannot be for either gas, satellite, or telephone. The telephone appointment cannot be scheduled for the sixth day.

201012_3-G_1_4

Which one of the following CANNOT be the appointments scheduled for the fourth, fifth, and sixth days, listed in that order?

A motel operator is scheduling appointments to start up services at a new motel. Appointments for six services—gas, landscaping, power, satellite, telephone, and water—will be scheduled, one appointment per day for the next six days. The schedule for the appointments is subject to the following conditions: The water appointment must be scheduled for an earlier day than the landscaping appointment. The power appointment must be scheduled for an earlier day than both the gas and satellite appointments. The appointments scheduled for the second and third days cannot be for either gas, satellite, or telephone. The telephone appointment cannot be scheduled for the sixth day.

201012_3-G_1_5

If neither the gas appointment nor the satellite appointment is scheduled for the sixth day, which one of the following must be true?

A motel operator is scheduling appointments to start up services at a new motel. Appointments for six services—gas, landscaping, power, satellite, telephone, and water—will be scheduled, one appointment per day for the next six days. The schedule for the appointments is subject to the following conditions: The water appointment must be scheduled for an earlier day than the landscaping appointment. The power appointment must be scheduled for an earlier day than both the gas and satellite appointments. The appointments scheduled for the second and third days cannot be for either gas, satellite, or telephone. The telephone appointment cannot be scheduled for the sixth day.

201012_3-G_1_6

Which one of the following, if substituted for the condition that the telephone appointment cannot be scheduled for the sixth day, would have the same effect in determining the order of the appointments?

An artisan has been hired to create three stained glass windows. The artisan will use exactly five colors of glass: green, orange, purple, rose, and yellow. Each color of glass will be used at least once, and each window will contain at least two different colors of glass. The windows must also conform to the following conditions: Exactly one of the windows contains both green glass and purple glass. Exactly two of the windows contain rose glass. If a window contains yellow glass, then that window contains neither green glass nor orange glass. If a window does not contain purple glass, then that window contains orange glass.

201012_3-G_2_7

Which one of the following could be the color combinations of the glass in the three windows?

An artisan has been hired to create three stained glass windows. The artisan will use exactly five colors of glass: green, orange, purple, rose, and yellow. Each color of glass will be used at least once, and each window will contain at least two different colors of glass. The windows must also conform to the following conditions: Exactly one of the windows contains both green glass and purple glass. Exactly two of the windows contain rose glass. If a window contains yellow glass, then that window contains neither green glass nor orange glass. If a window does not contain purple glass, then that window contains orange glass.

201012_3-G_2_8

Which one of the following CANNOT be the complete color combination of the glass in one of the windows?

An artisan has been hired to create three stained glass windows. The artisan will use exactly five colors of glass: green, orange, purple, rose, and yellow. Each color of glass will be used at least once, and each window will contain at least two different colors of glass. The windows must also conform to the following conditions: Exactly one of the windows contains both green glass and purple glass. Exactly two of the windows contain rose glass. If a window contains yellow glass, then that window contains neither green glass nor orange glass. If a window does not contain purple glass, then that window contains orange glass.

201012_3-G_2_9

If two of the windows are made with exactly two colors of glass each, then the complete color combination of the glass in one of those windows could be

An artisan has been hired to create three stained glass windows. The artisan will use exactly five colors of glass: green, orange, purple, rose, and yellow. Each color of glass will be used at least once, and each window will contain at least two different colors of glass. The windows must also conform to the following conditions: Exactly one of the windows contains both green glass and purple glass. Exactly two of the windows contain rose glass. If a window contains yellow glass, then that window contains neither green glass nor orange glass. If a window does not contain purple glass, then that window contains orange glass.

201012_3-G_2_10

If the complete color combination of the glass in one of the windows is purple, rose, and orange, then the complete color combination of the glass in one of the other windows could be

An artisan has been hired to create three stained glass windows. The artisan will use exactly five colors of glass: green, orange, purple, rose, and yellow. Each color of glass will be used at least once, and each window will contain at least two different colors of glass. The windows must also conform to the following conditions: Exactly one of the windows contains both green glass and purple glass. Exactly two of the windows contain rose glass. If a window contains yellow glass, then that window contains neither green glass nor orange glass. If a window does not contain purple glass, then that window contains orange glass.

201012_3-G_2_11

If orange glass is used in more of the windows than green glass, then the complete color combination of the glass in one of the windows could be

An artisan has been hired to create three stained glass windows. The artisan will use exactly five colors of glass: green, orange, purple, rose, and yellow. Each color of glass will be used at least once, and each window will contain at least two different colors of glass. The windows must also conform to the following conditions: Exactly one of the windows contains both green glass and purple glass. Exactly two of the windows contain rose glass. If a window contains yellow glass, then that window contains neither green glass nor orange glass. If a window does not contain purple glass, then that window contains orange glass.

201012_3-G_2_12

Which one of the following could be used in all three windows?

An artisan has been hired to create three stained glass windows. The artisan will use exactly five colors of glass: green, orange, purple, rose, and yellow. Each color of glass will be used at least once, and each window will contain at least two different colors of glass. The windows must also conform to the following conditions: Exactly one of the windows contains both green glass and purple glass. Exactly two of the windows contain rose glass. If a window contains yellow glass, then that window contains neither green glass nor orange glass. If a window does not contain purple glass, then that window contains orange glass.

201012_3-G_2_13

If none of the windows contains both rose glass and orange glass, then the complete color combination of the glass in one of the windows must be

A conference on management skills consists of exactly five talks, which are held successively in the following order: Feedback, Goal Sharing, Handling People, Information Overload, and Leadership. Exactly four employees of SoftCorp—Quigley, Rivera, Spivey, and Tran—each attend exactly two of the talks. No talk is attended by more than two of the employees, who attend the talks in accordance with the following conditions: Quigley attends neither Feedback nor Handling People. Rivera attends neither Goal Sharing nor Handling People. Spivey does not attend either of the talks that Tran attends. Quigley attends the first talk Tran attends. Spivey attends the first talk Rivera attends.

201012_3-G_3_14

Which one of the following could be a complete and accurate matching of the talks to the SoftCorp employees who attend them?

A conference on management skills consists of exactly five talks, which are held successively in the following order: Feedback, Goal Sharing, Handling People, Information Overload, and Leadership. Exactly four employees of SoftCorp—Quigley, Rivera, Spivey, and Tran—each attend exactly two of the talks. No talk is attended by more than two of the employees, who attend the talks in accordance with the following conditions: Quigley attends neither Feedback nor Handling People. Rivera attends neither Goal Sharing nor Handling People. Spivey does not attend either of the talks that Tran attends. Quigley attends the first talk Tran attends. Spivey attends the first talk Rivera attends.

201012_3-G_3_15

If none of the SoftCorp employees attends Handling People, then which one of the following must be true?

A conference on management skills consists of exactly five talks, which are held successively in the following order: Feedback, Goal Sharing, Handling People, Information Overload, and Leadership. Exactly four employees of SoftCorp—Quigley, Rivera, Spivey, and Tran—each attend exactly two of the talks. No talk is attended by more than two of the employees, who attend the talks in accordance with the following conditions: Quigley attends neither Feedback nor Handling People. Rivera attends neither Goal Sharing nor Handling People. Spivey does not attend either of the talks that Tran attends. Quigley attends the first talk Tran attends. Spivey attends the first talk Rivera attends.

201012_3-G_3_16

Which one of the following is a complete and accurate list of the talks any one of which Rivera and Spivey could attend together?

A conference on management skills consists of exactly five talks, which are held successively in the following order: Feedback, Goal Sharing, Handling People, Information Overload, and Leadership. Exactly four employees of SoftCorp—Quigley, Rivera, Spivey, and Tran—each attend exactly two of the talks. No talk is attended by more than two of the employees, who attend the talks in accordance with the following conditions: Quigley attends neither Feedback nor Handling People. Rivera attends neither Goal Sharing nor Handling People. Spivey does not attend either of the talks that Tran attends. Quigley attends the first talk Tran attends. Spivey attends the first talk Rivera attends.

201012_3-G_3_17

If Quigley is the only SoftCorp employee to attend Leadership, then which one of the following could be false?

A conference on management skills consists of exactly five talks, which are held successively in the following order: Feedback, Goal Sharing, Handling People, Information Overload, and Leadership. Exactly four employees of SoftCorp—Quigley, Rivera, Spivey, and Tran—each attend exactly two of the talks. No talk is attended by more than two of the employees, who attend the talks in accordance with the following conditions: Quigley attends neither Feedback nor Handling People. Rivera attends neither Goal Sharing nor Handling People. Spivey does not attend either of the talks that Tran attends. Quigley attends the first talk Tran attends. Spivey attends the first talk Rivera attends.

201012_3-G_3_18

If Rivera is the only SoftCorp employee to attend Information Overload, then which one of the following could be false?

Exactly six witnesses will testify in a trial: Mangione, Ramirez, Sanderson, Tannenbaum, Ujemori, and Wong. The witnesses will testify one by one, and each only once. The order in which the witnesses testify is subject to the following constraints: Sanderson must testify immediately before either Tannenbaum or Ujemori. Ujemori must testify earlier than both Ramirez and Wong. Either Tannenbaum or Wong must testify immediately before Mangione.

201012_3-G_4_19

Which one of the following lists the witnesses in an order in which they could testify?

Exactly six witnesses will testify in a trial: Mangione, Ramirez, Sanderson, Tannenbaum, Ujemori, and Wong. The witnesses will testify one by one, and each only once. The order in which the witnesses testify is subject to the following constraints: Sanderson must testify immediately before either Tannenbaum or Ujemori. Ujemori must testify earlier than both Ramirez and Wong. Either Tannenbaum or Wong must testify immediately before Mangione.

201012_3-G_4_20

If Tannenbaum testifies first, then which one of the following could be true?

Exactly six witnesses will testify in a trial: Mangione, Ramirez, Sanderson, Tannenbaum, Ujemori, and Wong. The witnesses will testify one by one, and each only once. The order in which the witnesses testify is subject to the following constraints: Sanderson must testify immediately before either Tannenbaum or Ujemori. Ujemori must testify earlier than both Ramirez and Wong. Either Tannenbaum or Wong must testify immediately before Mangione.

201012_3-G_4_21

If Sanderson testifies fifth, then Ujemori must testify

Exactly six witnesses will testify in a trial: Mangione, Ramirez, Sanderson, Tannenbaum, Ujemori, and Wong. The witnesses will testify one by one, and each only once. The order in which the witnesses testify is subject to the following constraints: Sanderson must testify immediately before either Tannenbaum or Ujemori. Ujemori must testify earlier than both Ramirez and Wong. Either Tannenbaum or Wong must testify immediately before Mangione.

201012_3-G_4_22

Which one of the following pairs of witnesses CANNOT testify third and fourth, respectively?

Exactly six witnesses will testify in a trial: Mangione, Ramirez, Sanderson, Tannenbaum, Ujemori, and Wong. The witnesses will testify one by one, and each only once. The order in which the witnesses testify is subject to the following constraints: Sanderson must testify immediately before either Tannenbaum or Ujemori. Ujemori must testify earlier than both Ramirez and Wong. Either Tannenbaum or Wong must testify immediately before Mangione.

201012_3-G_4_23

Which one of the following pairs of witnesses CANNOT testify first and second, respectively?

A movie studio is scheduling the release of six films—Fiesta, Glaciers, Hurricanes, Jets, Kangaroos, and Lovebird. No two of these films can be released on the same date. The release schedule is governed by the following conditions: Fiesta must be released earlier than both Jets and Lovebird. Kangaroos must be released earlier than Jets, and Jets must be released earlier than Hurricanes. Lovebird must be released earlier than Glaciers.

201312_2-G_1_1

Which one of the following CANNOT be true?

A movie studio is scheduling the release of six films—Fiesta, Glaciers, Hurricanes, Jets, Kangaroos, and Lovebird. No two of these films can be released on the same date. The release schedule is governed by the following conditions: Fiesta must be released earlier than both Jets and Lovebird. Kangaroos must be released earlier than Jets, and Jets must be released earlier than Hurricanes. Lovebird must be released earlier than Glaciers.

201312_2-G_1_2

Which one of the following must be true?

A movie studio is scheduling the release of six films—Fiesta, Glaciers, Hurricanes, Jets, Kangaroos, and Lovebird. No two of these films can be released on the same date. The release schedule is governed by the following conditions: Fiesta must be released earlier than both Jets and Lovebird. Kangaroos must be released earlier than Jets, and Jets must be released earlier than Hurricanes. Lovebird must be released earlier than Glaciers.

201312_2-G_1_3

If Glaciers is released earlier than Hurricanes, then each of the following could be true EXCEPT:

A movie studio is scheduling the release of six films—Fiesta, Glaciers, Hurricanes, Jets, Kangaroos, and Lovebird. No two of these films can be released on the same date. The release schedule is governed by the following conditions: Fiesta must be released earlier than both Jets and Lovebird. Kangaroos must be released earlier than Jets, and Jets must be released earlier than Hurricanes. Lovebird must be released earlier than Glaciers.

201312_2-G_1_4

If Lovebird is released earlier than Kangaroos, which one of the following could be true?

A movie studio is scheduling the release of six films—Fiesta, Glaciers, Hurricanes, Jets, Kangaroos, and Lovebird. No two of these films can be released on the same date. The release schedule is governed by the following conditions: Fiesta must be released earlier than both Jets and Lovebird. Kangaroos must be released earlier than Jets, and Jets must be released earlier than Hurricanes. Lovebird must be released earlier than Glaciers.

201312_2-G_1_5

Which one of the following, if substituted for the condition that Fiesta must be released earlier than both Jets and Lovebird, would have the same effect on the order in which the films are released?

The applications of seven job candidates—Farrell, Grant, Hong, Inman, Kent, Lopez, and Madsen—will be evaluated by four human resource officers—Rao, Smith, Tipton, and Ullman. Each application will be evaluated by exactly one officer, and each officer will evaluate at least one application, subject to the following constraints: Grant's application must be evaluated by Ullman. Farrell's application must be evaluated by the same officer who evaluates Lopez's application. Neither Hong's application nor Madsen's application can be evaluated by the same officer who evaluates Inman's application. The officer who evaluates Kent's application cannot evaluate any other applications. Smith must evaluate more of the applications than Tipton does.

201312_2-G_2_6

Which one of the following could be the assignment of applications to officers?

The applications of seven job candidates—Farrell, Grant, Hong, Inman, Kent, Lopez, and Madsen—will be evaluated by four human resource officers—Rao, Smith, Tipton, and Ullman. Each application will be evaluated by exactly one officer, and each officer will evaluate at least one application, subject to the following constraints: Grant's application must be evaluated by Ullman. Farrell's application must be evaluated by the same officer who evaluates Lopez's application. Neither Hong's application nor Madsen's application can be evaluated by the same officer who evaluates Inman's application. The officer who evaluates Kent's application cannot evaluate any other applications. Smith must evaluate more of the applications than Tipton does.

201312_2-G_2_7

If Hong's application is evaluated by Rao, which one of the following could be true?

The applications of seven job candidates—Farrell, Grant, Hong, Inman, Kent, Lopez, and Madsen—will be evaluated by four human resource officers—Rao, Smith, Tipton, and Ullman. Each application will be evaluated by exactly one officer, and each officer will evaluate at least one application, subject to the following constraints: Grant's application must be evaluated by Ullman. Farrell's application must be evaluated by the same officer who evaluates Lopez's application. Neither Hong's application nor Madsen's application can be evaluated by the same officer who evaluates Inman's application. The officer who evaluates Kent's application cannot evaluate any other applications. Smith must evaluate more of the applications than Tipton does.

201312_2-G_2_8

If exactly two of the applications are evaluated by Tipton, then each of the following must be true EXCEPT:

The applications of seven job candidates—Farrell, Grant, Hong, Inman, Kent, Lopez, and Madsen—will be evaluated by four human resource officers—Rao, Smith, Tipton, and Ullman. Each application will be evaluated by exactly one officer, and each officer will evaluate at least one application, subject to the following constraints: Grant's application must be evaluated by Ullman. Farrell's application must be evaluated by the same officer who evaluates Lopez's application. Neither Hong's application nor Madsen's application can be evaluated by the same officer who evaluates Inman's application. The officer who evaluates Kent's application cannot evaluate any other applications. Smith must evaluate more of the applications than Tipton does.

201312_2-G_2_9

If the officer who evaluates Madsens application does not evaluate any other application, which one of the following must be true?

The applications of seven job candidates—Farrell, Grant, Hong, Inman, Kent, Lopez, and Madsen—will be evaluated by four human resource officers—Rao, Smith, Tipton, and Ullman. Each application will be evaluated by exactly one officer, and each officer will evaluate at least one application, subject to the following constraints: Grant's application must be evaluated by Ullman. Farrell's application must be evaluated by the same officer who evaluates Lopez's application. Neither Hong's application nor Madsen's application can be evaluated by the same officer who evaluates Inman's application. The officer who evaluates Kent's application cannot evaluate any other applications. Smith must evaluate more of the applications than Tipton does.

201312_2-G_2_10

If Farrells application is evaluated by the same officer who evaluates Inmans application, then any of the following could be true EXCEPT:

The applications of seven job candidates—Farrell, Grant, Hong, Inman, Kent, Lopez, and Madsen—will be evaluated by four human resource officers—Rao, Smith, Tipton, and Ullman. Each application will be evaluated by exactly one officer, and each officer will evaluate at least one application, subject to the following constraints: Grant's application must be evaluated by Ullman. Farrell's application must be evaluated by the same officer who evaluates Lopez's application. Neither Hong's application nor Madsen's application can be evaluated by the same officer who evaluates Inman's application. The officer who evaluates Kent's application cannot evaluate any other applications. Smith must evaluate more of the applications than Tipton does.

201312_2-G_2_11

If Farrells application is evaluated by Rao, then for how many of the other applications is the identity of the officer who evaluates it fully determined?

A six-week literature course is being planned in which six books—F, K, N, O, R, and T—will be discussed. The books will be discussed one at a time, one book per week. In addition, written summaries will be required for one or more of the books. The order in which the books are discussed and the selection of books to be summarized is subject to the following conditions: No two books that are summarized are discussed in consecutive weeks. If N is not summarized, then both R and T are summarized. N is discussed earlier than T, and T is discussed earlier than O. F is discussed earlier than O, and O is discussed earlier than both K and R.

201312_2-G_3_12

Which one of the following could be the plan for the course, showing the order, from first to last, in which the books are discussed and the choice of books to be summarized?

A six-week literature course is being planned in which six books—F, K, N, O, R, and T—will be discussed. The books will be discussed one at a time, one book per week. In addition, written summaries will be required for one or more of the books. The order in which the books are discussed and the selection of books to be summarized is subject to the following conditions: No two books that are summarized are discussed in consecutive weeks. If N is not summarized, then both R and T are summarized. N is discussed earlier than T, and T is discussed earlier than O. F is discussed earlier than O, and O is discussed earlier than both K and R.

201312_2-G_3_13

If N is the second book discussed and it is not summarized, which one of the following could be true?

A six-week literature course is being planned in which six books—F, K, N, O, R, and T—will be discussed. The books will be discussed one at a time, one book per week. In addition, written summaries will be required for one or more of the books. The order in which the books are discussed and the selection of books to be summarized is subject to the following conditions: No two books that are summarized are discussed in consecutive weeks. If N is not summarized, then both R and T are summarized. N is discussed earlier than T, and T is discussed earlier than O. F is discussed earlier than O, and O is discussed earlier than both K and R.

201312_2-G_3_14

If O is summarized, which one of the following CANNOT be true?

A six-week literature course is being planned in which six books—F, K, N, O, R, and T—will be discussed. The books will be discussed one at a time, one book per week. In addition, written summaries will be required for one or more of the books. The order in which the books are discussed and the selection of books to be summarized is subject to the following conditions: No two books that are summarized are discussed in consecutive weeks. If N is not summarized, then both R and T are summarized. N is discussed earlier than T, and T is discussed earlier than O. F is discussed earlier than O, and O is discussed earlier than both K and R.

201312_2-G_3_15

If neither of the last two books discussed is summarized, which one of the following could be true?

A six-week literature course is being planned in which six books—F, K, N, O, R, and T—will be discussed. The books will be discussed one at a time, one book per week. In addition, written summaries will be required for one or more of the books. The order in which the books are discussed and the selection of books to be summarized is subject to the following conditions: No two books that are summarized are discussed in consecutive weeks. If N is not summarized, then both R and T are summarized. N is discussed earlier than T, and T is discussed earlier than O. F is discussed earlier than O, and O is discussed earlier than both K and R.

201312_2-G_3_16

Which one of the following, if substituted for the condition that F is discussed earlier than O, and O is discussed earlier than both K and R, would have the same effect in determining the plan for the literature course?

A museum curator is arranging seven paintings—a Morisot, a Pissarro, a Renoir, a Sisley, a Turner, a Vuillard, and a Whistler. The paintings will be arranged in a horizontal row of seven positions, with the first position being closest to the entrance and the seventh being furthest from the entrance. The arrangement is subject to the following constraints: The Turner must be closer to the entrance than the Whistler is. The Renoir must be closer to the entrance than the Morisot is, with exactly one other painting between them. The Pissarro and the Sisley must be next to each other. If the Vuillard is not in the third position, it must be in the fourth position.

201312_2-G_4_17

Which one of the following could be the arrangement of the paintings, listed in order from the first position to the seventh?

A museum curator is arranging seven paintings—a Morisot, a Pissarro, a Renoir, a Sisley, a Turner, a Vuillard, and a Whistler. The paintings will be arranged in a horizontal row of seven positions, with the first position being closest to the entrance and the seventh being furthest from the entrance. The arrangement is subject to the following constraints: The Turner must be closer to the entrance than the Whistler is. The Renoir must be closer to the entrance than the Morisot is, with exactly one other painting between them. The Pissarro and the Sisley must be next to each other. If the Vuillard is not in the third position, it must be in the fourth position.

201312_2-G_4_18

If the Sisley is in the seventh position, which one of the following could be the position that the Turner is in?

A museum curator is arranging seven paintings—a Morisot, a Pissarro, a Renoir, a Sisley, a Turner, a Vuillard, and a Whistler. The paintings will be arranged in a horizontal row of seven positions, with the first position being closest to the entrance and the seventh being furthest from the entrance. The arrangement is subject to the following constraints: The Turner must be closer to the entrance than the Whistler is. The Renoir must be closer to the entrance than the Morisot is, with exactly one other painting between them. The Pissarro and the Sisley must be next to each other. If the Vuillard is not in the third position, it must be in the fourth position.

201312_2-G_4_19

If the Pissarro is in the fifth position, which one of the following must be true?

A museum curator is arranging seven paintings—a Morisot, a Pissarro, a Renoir, a Sisley, a Turner, a Vuillard, and a Whistler. The paintings will be arranged in a horizontal row of seven positions, with the first position being closest to the entrance and the seventh being furthest from the entrance. The arrangement is subject to the following constraints: The Turner must be closer to the entrance than the Whistler is. The Renoir must be closer to the entrance than the Morisot is, with exactly one other painting between them. The Pissarro and the Sisley must be next to each other. If the Vuillard is not in the third position, it must be in the fourth position.

201312_2-G_4_20

Any one of the following could be in the third position EXCEPT:

A museum curator is arranging seven paintings—a Morisot, a Pissarro, a Renoir, a Sisley, a Turner, a Vuillard, and a Whistler. The paintings will be arranged in a horizontal row of seven positions, with the first position being closest to the entrance and the seventh being furthest from the entrance. The arrangement is subject to the following constraints: The Turner must be closer to the entrance than the Whistler is. The Renoir must be closer to the entrance than the Morisot is, with exactly one other painting between them. The Pissarro and the Sisley must be next to each other. If the Vuillard is not in the third position, it must be in the fourth position.

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If the Renoir and the Morisot are both between the Turner and the Whistler, which one of the following could be true?

A museum curator is arranging seven paintings—a Morisot, a Pissarro, a Renoir, a Sisley, a Turner, a Vuillard, and a Whistler. The paintings will be arranged in a horizontal row of seven positions, with the first position being closest to the entrance and the seventh being furthest from the entrance. The arrangement is subject to the following constraints: The Turner must be closer to the entrance than the Whistler is. The Renoir must be closer to the entrance than the Morisot is, with exactly one other painting between them. The Pissarro and the Sisley must be next to each other. If the Vuillard is not in the third position, it must be in the fourth position.

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If there is exactly one painting between the Turner and the Whistler, which one of the following must be true?

A museum curator is arranging seven paintings—a Morisot, a Pissarro, a Renoir, a Sisley, a Turner, a Vuillard, and a Whistler. The paintings will be arranged in a horizontal row of seven positions, with the first position being closest to the entrance and the seventh being furthest from the entrance. The arrangement is subject to the following constraints: The Turner must be closer to the entrance than the Whistler is. The Renoir must be closer to the entrance than the Morisot is, with exactly one other painting between them. The Pissarro and the Sisley must be next to each other. If the Vuillard is not in the third position, it must be in the fourth position.

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If the Turner is next to the Vuillard, which one of the following is a pair of paintings in which the one mentioned first must be closer to the entrance than the one mentioned second?

A radio station airs hourly news updates every morning. Each update consists of exactly five reports—two of general interest: international and national; and three of local interest: sports, traffic, and weather. Each update must be structured as follows: There are exactly two segments, the first segment containing three reports and the second segment containing two. Within each segment, reports are ordered by length, from longest to shortest. Each segment contains at least one report of local interest. The national report is always the longest of the five reports. The sports report is always the shortest of the five reports. The international report is always longer than the weather report.

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Which one of the following could be an accurate matching of reports to their segments, with the reports listed in order from earliest to latest?

A radio station airs hourly news updates every morning. Each update consists of exactly five reports—two of general interest: international and national; and three of local interest: sports, traffic, and weather. Each update must be structured as follows: There are exactly two segments, the first segment containing three reports and the second segment containing two. Within each segment, reports are ordered by length, from longest to shortest. Each segment contains at least one report of local interest. The national report is always the longest of the five reports. The sports report is always the shortest of the five reports. The international report is always longer than the weather report.

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If the traffic report is the last report in the first segment, then which one of the following must be true?

A radio station airs hourly news updates every morning. Each update consists of exactly five reports—two of general interest: international and national; and three of local interest: sports, traffic, and weather. Each update must be structured as follows: There are exactly two segments, the first segment containing three reports and the second segment containing two. Within each segment, reports are ordered by length, from longest to shortest. Each segment contains at least one report of local interest. The national report is always the longest of the five reports. The sports report is always the shortest of the five reports. The international report is always longer than the weather report.

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If the national report is the first report in the second segment, then exactly how many of the reports are there any one of which could be the first report in the first segment?