Question: Which one of the following statements must be true?

Answer: If bill 2 is paid on Thursday, bill 3 is paid on Wednesday.

Answer: If bill 4 is paid on Thursday, bill 1 is paid on Wednesday.

Answer: If bill 4 is paid on Thursday, bill 3 is paid on Wednesday.

Answer: If bill 6 is paid on Thursday, bill 3 is also paid on Thursday.

Answer: If bill 6 is paid on Thursday, bill 4 is also paid on Thursday.


Context: Two mannequins—1 and 2—will be dressed for display in outfits chosen from ten articles of clothing. Each article is in exactly one of three colors: navy, red, or yellow. There are three hats—one in each color; three jackets—one in each color; three skirts—one in each color; and one red tie. Each mannequin wears exactly one of the hats, one of the jackets, and one of the skirts. Furthermore, their outfits must meet the following restrictions: Neither mannequin wears all three colors. Each mannequin wears a hat in a different color from the jacket it wears. Mannequin 2 wears the navy skirt. Mannequin 1 wears the tie.

Question: Which one of the following could be complete outfits for the two mannequins?

Answer: mannequin 1: navy hat, red jacket, yellow skirt, red tie mannequin 2: red hat, navy jacket, navy skirt

Answer: mannequin 1: red hat, red jacket, yellow skirt, red tie mannequin 2: yellow hat, navy jacket, navy skirt

Answer: mannequin 1: red hat, yellow jacket, red skirt, red tie mannequin 2: yellow hat, navy jacket, yellow skirt

Answer: mannequin 1: yellow hat, red jacket, yellow skirt, red tie mannequin 2: red hat, navy jacket, navy skirt

Answer: mannequin 1: yellow hat, yellow jacket, red skirt mannequin 2: red hat, navy jacket, navy skirt


Question: Which one of the following could be true of the mannequins' outfits?

Answer: Mannequin 1 wears the navy jacket and the yellow skirt.

Answer: Mannequin 2 wears the red hat and the red jacket.

Answer: Mannequin 1 wears exactly one red article of clothing.

Answer: Mannequin 1 wears exactly three yellow articles of clothing.

Answer: Mannequin 2 wears no red articles of clothing.


Question: If mannequin 1 wears the navy jacket, which one of the following could be true?

Answer: Mannequin 1 wears the yellow hat.

Answer: Mannequin 1 wears the yellow skirt.

Answer: Mannequin 2 wears the red hat.

Answer: Mannequin 2 wears the yellow hat.

Answer: Mannequin 2 wears the yellow jacket.


Question: If all four of the red articles of clothing are included in the two mannequins' outfits, which one of the following must be true?

Answer: Mannequin 1 wears the red hat.

Answer: Mannequin 1 wears the yellow jacket.

Answer: Mannequin 2 wears the navy jacket.

Answer: Mannequin 1 wears no navy articles of clothing.

Answer: Mannequin 2 wears no yellow articles of clothing.


Question: If mannequin 2 wears the red jacket, then mannequin 1 must wear the

Answer: navy hat

Answer: red hat

Answer: yellow hat

Answer: red skirt

Answer: yellow skirt


Question: If all three of the yellow articles of clothing are included in the two mannequins' outfits, which one of the following could be true?

Answer: Mannequin 1 wears the navy jacket.

Answer: Mannequin 1 wears the yellow jacket.

Answer: Mannequin 1 wears the red skirt.

Answer: Mannequin 2 wears the red hat.

Answer: Mannequin 2 wears the red jacket.


Question: If mannequin 1 wears the skirt that is the same color as the jacket that mannequin 2 wears, which one of the following must be true?

Answer: Mannequin 1 wears the yellow hat.

Answer: Mannequin 1 wears the yellow jacket.

Answer: Mannequin 2 wears the navy hat.

Answer: Mannequin 2 wears the red hat.

Answer: Mannequin 2 wears the red jacket.


Context: A college dean will present seven awards for outstanding language research. The awards—one for French, one for German, one for Hebrew, one for Japanese, one for Korean, one for Latin, and one for Swahili—must be presented consecutively, one at a time, in conformity with the following constraints: The German award is not presented first. The Hebrew award is presented at some time before the Korean award is presented. The Latin award is presented at some time before the Japanese award is presented. The French award is presented either immediately before or immediately after the Hebrew award is presented. The Korean award is presented either immediately before or immediately after the Latin award is presented.

Question: Which one of the following must be true?

Answer: The French award is presented at some time before the Japanese award is presented.

Answer: The French award is presented at some time before the Swahili award is presented.

Answer: The German award is presented at some time before the Korean award is presented.

Answer: The German award is presented at some time before the Swahili award is presented.

Answer: The Swahili award is presented at some time before the Hebrew award is presented.


Question: If the Hebrew award is presented fourth, which one of the following must be true?

Answer: The French award is presented fifth.

Answer: The German award is presented third.

Answer: The Japanese award is presented sixth.

Answer: The Korean award is presented fifth.

Answer: The Swahili award is presented first.


Question: If the German award is presented third, which one of the following could be true?

Answer: The French award is presented fourth.

Answer: The Japanese award is presented fifth.

Answer: The Japanese award is presented sixth.

Answer: The Korean award is presented second.

Answer: The Swahili award is presented fifth.


Question: The earliest that the Japanese award could be presented is

Answer: third

Answer: fourth

Answer: fifth

Answer: sixth

Answer: seventh


Question: If the Japanese award is presented at some time before the Swahili award is presented, any of the following could be true EXCEPT:

Answer: The German award is presented immediately before the French award is presented.

Answer: The German award is presented immediately before the Japanese award is presented.

Answer: The Hebrew award is presented immediately before the Latin award is presented.

Answer: The Korean award is presented immediately before the Japanese award is presented.

Answer: The Swahili award is presented immediately before the German award is presented.


Question: The order in which the awards are presented is completely determined if which one of the following is true?

Answer: The French award is presented immediately before the German award is presented, and the Korean award is presented immediately before the Latin award is presented.

Answer: The French award is presented immediately before the Hebrew award is presented, and the Hebrew award is presented immediately before the Korean award is presented.

Answer: The French award is presented immediately before the Latin award is presented, and the Korean award is presented immediately before the Japanese award is presented.

Answer: The German award is presented immediately before the French award is presented, and the Latin award is presented immediately before the Japanese award is presented.

Answer: The German award is presented immediately before the Korean award is presented, and the Hebrew award is presented immediately before the French award is presented.


Context: Exactly six piano classes are given sequentially on Monday: two with more than one student and four with exactly one student. Exactly four females—Gimena, Holly, Iyanna, and Kate—and five males—Leung, Nate, Oscar, Pedro, and Saul—attend these classes. Each student attends exactly one class. The following must obtain: Iyanna and Leung together constitute one class. Pedro and exactly two others together constitute one class. Kate is the first female, but not the first student, to attend a class. Gimena's class is at some time after Iyanna's but at sometime before Pedro's. Oscar's class is at some time after Gimena's.

Question: Which one of the following students could attend the first class?

Answer: Holly

Answer: Leung

Answer: Oscar

Answer: Pedro

Answer: Saul


Question: Which one of the following is a complete and accurate list of classes any one of which could be the class Gimena attends?

Answer: the fourth, the fifth

Answer: the fourth, the sixth

Answer: the second, the fourth, the fifth

Answer: the third, the fifth, the sixth

Answer: the second, the third, the fourth


Question: Which one of the following pairs of students could be in the class with Pedro?

Answer: Gimena and Holly

Answer: Holly and Saul

Answer: Kate and Nate

Answer: Leung and Oscar

Answer: Nate and Saul


Question: If Oscar and Pedro do not attend the same class as each other, then which one of the following could be true?

Answer: Gimena attends the fifth class.

Answer: Holly attends the third class.

Answer: Iyanna attends the fourth class.

Answer: Nate attends the fifth class.

Answer: Saul attends the second class.


Question: Suppose the condition that Oscar attends a class after Gimena is replaced with the condition that Oscar attends a class before Gimena and after Kate. If all the other conditions remain the same, then which class must Holly attend?

Answer: the second

Answer: the third

Answer: the fourth

Answer: the fifth

Answer: the sixth


Context: This morning, a bakery makes exactly one delivery, consisting of exactly six loaves of bread. Each of the loaves is exactly one of three kinds: oatmeal, rye, or wheat, and each is either sliced or unsliced. The loaves that the bakery delivers this morning must be consistent with the following: There are at least two kinds of loaves. There are no more than three rye loaves. There is no unsliced wheat loaf. There is at least one unsliced oatmeal loaf. If two or more of the loaves are unsliced, then at least one of the unsliced loaves is rye.

Question: Which one of the following could be a complete and accurate list of the loaves that the bakery delivers?

Answer: six unsliced oatmeal loaves

Answer: five unsliced oatmeal loaves, one sliced rye loaf

Answer: five unsliced oatmeal loaves, one unsliced wheat loaf

Answer: four unsliced oatmeal loaves, two unsliced rye loaves

Answer: four unsliced oatmeal loaves, two sliced wheat loaves


Question: Each of the following could be a complete and accurate list of the unsliced loaves that the bakery delivers EXCEPT:

Answer: three oatmeal loaves

Answer: three oatmeal loaves, one rye loaf

Answer: two oatmeal loaves, two rye loaves

Answer: two oatmeal loaves, three rye loaves

Answer: one oatmeal loaf, one rye loaf


Question: Which one of the following statements CANNOT be true?

Answer: The only unsliced loaves are oatmeal loaves.

Answer: The only sliced loaves are rye loaves.

Answer: The only unsliced loaves are rye loaves.

Answer: The number of sliced loaves is exactly one greater than the number of sliced oatmeal loaves.

Answer: The number of unsliced loaves is exactly one greater than the number of unsliced oatmeal loaves.


Question: Which one of the following statements must be true?

Answer: At least one of the loaves is rye.

Answer: At least one of the loaves is wheat.

Answer: At least one of the loaves is sliced.

Answer: No more than four oatmeal loaves are sliced.

Answer: No more than four wheat loaves are sliced.


Question: If the bakery delivers exactly four wheat loaves, then the bakery could also deliver

Answer: one sliced rye loaf and one unsliced rye loaf

Answer: one sliced oatmeal loaf and one unsliced oatmeal loaf

Answer: two unsliced rye loaves

Answer: two unsliced oatmeal loaves

Answer: two sliced oatmeal loaves


Context: The six messages on an answering machine were each left by one of Fleure, Greta, Hildy, Liam, Pasquale, or Theodore, consistent with the following: At most one person left more than one message. No person left more than three messages. If the first message is Hildy's, the last is Pasquale's. If Greta left any message, Fleure and Pasquale did also. If Fleure left any message, Pasquale and Theodore did also, all of Pasquale's preceding any of Theodore's. If Pasquale left any message, Hildy and Liam did also, all of Hildy's preceding any of Liam's.

Question: Which one of the following could be a complete and accurate list of the messages left on the answering machine, from first to last?

Answer: Fleure's, Pasquale's, Theodore's, Hildy's, Pasquale's, Liam's

Answer: Greta's, Pasquale's, Theodore's, Theodore's, Hildy's, Liam's

Answer: Hildy's, Hildy's, Hildy's, Liam's, Pasquale's, Theodore's

Answer: Pasquale's, Hildy's, Fleure's, Liam's, Theodore's, Theodore's

Answer: Pasquale's, Hildy's, Theodore's, Hildy's, Liam's, Liam's


Question: The first and last messages on the answering machine could be the first and second messages left by which one of the following?

Answer: Fleure

Answer: Hildy

Answer: Liam

Answer: Pasquale

Answer: Theodore


Question: If Greta left the fifth message, then which one of the following messages CANNOT have been left by Theodore?

Answer: the first message

Answer: the second message

Answer: the third message

Answer: the fourth message

Answer: the sixth message


Question: Each of the following must be true EXCEPT:

Answer: Liam left at least one message.

Answer: Theodore left at least one message.

Answer: Hildy left at least one message.

Answer: Exactly one person left at least two messages.

Answer: At least four people left messages.


Question: If the only message Pasquale left is the fifth message, then which one of the following could be true?

Answer: Hildy left the first message.

Answer: Theodore left exactly two messages.

Answer: Liam left exactly two messages.

Answer: Liam left the second message.

Answer: Fleure left the third and fourth messages.


Context: Exactly five cars—Frank's, Marquitta's, Orlando's, Taishah's, and Vinquetta's—are washed, each exactly once. The cars are washed one at a time, with each receiving exactly one kind of wash: regular, super, or premium. The following conditions must apply: The first car washed does not receive a super wash, though at least one car does. Exactly one car receives a premium wash. The second and third cars washed receive the same kind of wash as each other. Neither Orlando's nor Taishah's is washed before Vinquetta's. Marquitta's is washed before Frank's, but after Orlando's. Marquitta's and the car washed immediately before Marquitta's receive regular washes.

Question: Which one of the following could be an accurate list of the cars in the order in which they are washed, matched with type of wash received?

Answer: Orlando's: premium; Vinquetta's: regular; Taishah's: regular; Marquitta's: regular; Frank's: super

Answer: Vinquetta's: premium; Orlando's: regular; Taishah's: regular; Marquitta's: regular; Frank's: super

Answer: Vinquetta's: regular; Marquitta's: regular; Taishah's: regular; Orlando's: super; Frank's: super

Answer: Vinquetta's: super; Orlando's: regular; Marquitta's: regular; Frank's: regular; Taishah's: super

Answer: Vinquetta's: premium; Orlando's: regular; Marquitta's: regular; Frank's: regular; Taishah's: regular


Question: If Vinquetta's car does not receive a premium wash, which one of the following must be true?

Answer: Orlando's and Vinquetta's cars receive the same kind of wash as each other.

Answer: Marquitta's and Taishah's cars receive the same kind of wash as each other.

Answer: The fourth car washed receives a premium wash.

Answer: Orlando's car is washed third.

Answer: Marquitta's car is washed fourth.


Question: If the last two cars washed receive the same kind of wash as each other, then which one of the following could be true?

Answer: Orlando's car is washed third.

Answer: Taishah's car is washed fifth.

Answer: Taishah's car is washed before Marquitta's car.

Answer: Vinquetta's car receives a regular wash.

Answer: Exactly one car receives a super wash.


Question: Which one of the following must be true?

Answer: Vinquetta's car receives a premium wash.

Answer: Exactly two cars receive a super wash.

Answer: The fifth car washed receives a super wash.

Answer: The fourth car washed receives a super wash.

Answer: The second car washed receives a regular wash.


Question: Which one of the following is a complete and accurate list of the cars that must receive a regular wash?

Answer: Frank's, Marquitta's

Answer: Marquitta's, Orlando's

Answer: Marquitta's, Orlando's, Taishah's

Answer: Marquitta's, Taishah's

Answer: Marquitta's, Vinquetta's


Question: Suppose that in addition to the original five cars Jabrohn's car is also washed. If all the other conditions hold as given, which one of the following CANNOT be true?

Answer: Orlando's car receives a premium wash.

Answer: Vinquetta's car receives a super wash.

Answer: Four cars receive a regular wash.

Answer: Only the second and third cars washed receive a regular wash.

Answer: Jabrohn's car is washed after Frank's car.


Context: Exactly seven toy-truck models—F, G, H, J, K, M, and S—are assembled on seven assembly lines, exactly one model to a line. The seven lines are arranged side by side and numbered consecutively 1 through 7. Assignment of models to lines must meet the following conditions: F is assembled on a lower-numbered line than J. M is assembled on the line numbered one lower than the line on which G is assembled. H is assembled on line 1 or else line 7. S is assembled on line 4.

Question: Which one of the following is an acceptable assignment of toy-truck models to lines, on order from line 1 through line 7?

Answer: F, J, K, S, H, M, G

Answer: F, K, J, S, M, G, H

Answer: F, M, K, S, G, J, H

Answer: H, K, S, M, G, F, J

Answer: H, M, G, S, J, F, K


Question: It must be true that the lowest-numbered line on which

Answer: F can be assembled is line 2

Answer: G can be assembled is line 3

Answer: J can be assembled is line 2

Answer: K can be assembled is line 3

Answer: M can be assembled is line 2


Question: If K is assembled on line 5, which one of the following is a pair of models that could be assembled, not necessarily in the order given, on lines whose numbers are consecutive to each other?

Answer: G, H

Answer: G, J

Answer: H, J

Answer: J, M

Answer: M, S


Question: There can be at most how many lines between the line on which F is assembled and the line on which J is assembled?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


Question: If K is assembled on line 2, which one of the following must be true?

Answer: F is assembled on a lower-numbered line than S.

Answer: H is assembled on a lower-numbered line than G.

Answer: J is assembled on a lower-numbered line than H.

Answer: M is assembled on a lower-numbered line than J.

Answer: S is assembled on a lower-numbered line than J.


Question: If G is assembled on the line numbered one less than the line on which F is assembled, then which one of the following must be true?

Answer: F is assembled on line 3.

Answer: G is assembled on line 5.

Answer: H is assembled on line 1.

Answer: K is assembled on line 5.

Answer: M is assembled on line 6.


Question: If M is assembled on line 1, which one of the following could be true?

Answer: F is assembled on a line numbered one lower than the line on which H is assembled.

Answer: F is assembled on a line numbered one lower than the line on which K is assembled.

Answer: G is assembled on a line numbered one lower than the line on which J is assembled.

Answer: G is assembled on a line numbered one lower than the line on which K is assembled.

Answer: K is assembled on a line numbered one lower than the line on which G is assembled.


Context: At a water carnival, each of the eight lifeguards—J, K, L, M, P, Q, R, and S—will participate in two events, a boat race and a rescue exercise. For each of these events the eight lifeguards are grouped into four two-person teams, subject to the following rules: If two lifeguards are teammates in the boat race, they cannot also be teammates in the rescue exercise. L and Q are teammates in the boat race. K and L are teammates in the rescue exercise. R and S are not teammates in either event.

Question: Which one of the following could be a list of the four teams participating in the boat race?

Answer: J and L; K and S; M and Q; P and R

Answer: J and M; K and P; L and Q; R and S

Answer: J and M; K and R; L and S; P and Q

Answer: J and M; K and S; L and Q; P and R

Answer: J and P; K and L; M and R; Q and S


Question: Which one of the following is a pair of lifeguards who cannot be teammates in the rescue exercise but who could be teammates in the boat race?

Answer: J and P

Answer: K and R

Answer: L and S

Answer: P and M

Answer: P and Q


Question: If M and P are teammates in the boat race and J and R are teammates in the rescue exercise, which one of the following is a pair that must be teammates in the boat race?

Answer: J and K

Answer: J and S

Answer: K and L

Answer: K and S

Answer: Q and R


Question: If P and K are teammates in the boat race and P and Q are teammates in the rescue exercise, then each of the following lists a pair of lifeguards who must be teammates in one of the two events EXCEPT:

Answer: J and M

Answer: J and R

Answer: J and S

Answer: M and R

Answer: M and S


Question: If J and P are teammates in the boat race, then M could be the teammate of

Answer: K in the boat race and S in the rescue exercise

Answer: L in the boat race and S in the rescue exercise

Answer: R in the boat race and L in the rescue exercise

Answer: S in the boat race and K in the rescue exercise

Answer: S in the boat race and P in the rescue exercise


Context: A critic ranks exactly seven restaurants—Lautrec, Medici, Pastilla, Robusto, Scheherazade's, Tantoko, and Vistula—from highest (best) to lowest (worst). The ranking must meet the following conditions: Pastilla ranks higher than Lautrec but lower than Robusto. Medici ranks higher than Vistula but lower than Tantoko. If Scheherazade's ranks higher than Pastilla, Medici ranks higher than Scheherazade's. If Medici ranks higher than Scheherazade's, Scheherazade's ranks higher than Pastilla. There are no ties.

Question: Which one of the following could be an accurate ranking of the restaurants, from highest to lowest?

Answer: Tantoko, Medici, Scheherazade's, Pastilla, Vistula, Robusto, Lautrec

Answer: Robusto, Pastilla, Tantoko, Medici, Scheherazade's, Vistula, Lautrec

Answer: Tantoko, Medici, Scheherazade's, Robusto, Vistula, Pastilla, Lautrec

Answer: Tantoko, Robusto, Medici, Vistula, Pastilla, Scheherazade's, Lautrec

Answer: Robusto, Pastilla, Scheherazade's, Medici, Vistula, Tantoko, Lautrec


Question: If Pastilla ranks second highest, then which one of the following is a complete and accurate list of restaurants any one of which could be ranked fourth highest?

Answer: Lautrec

Answer: Lautrec, Vistula

Answer: Scheherazade's, Lautrec

Answer: Scheherazade's, Lautrec, Medici

Answer: Scheherazade's, Lautrec, Tantoko


Question: Which one of the following is the lowest ranking that Medici could have?

Answer: second highest

Answer: third highest

Answer: fourth highest

Answer: fifth highest

Answer: sixth highest


Question: If Medici ranks lower than Lautrec, then which one of the following must be true?

Answer: Lautrec ranks higher than Tantoko.

Answer: Scheherazade's ranks higher than Vistula.

Answer: Pastilla ranks higher than Tantoko.

Answer: Tantoko ranks higher than Scheherazade's.

Answer: Tantoko ranks higher than Pastilla.


Question: If Vistula ranks higher than Robusto, then which one of the following restaurants could be ranked fifth highest?

Answer: Tantoko

Answer: Medici

Answer: Scheherazade's

Answer: Vistula

Answer: Pastilla


Question: Which one of the following CANNOT be true?

Answer: Pastilla ranks second highest.

Answer: Vistula ranks third highest.

Answer: Lautrec ranks third highest.

Answer: Robusto ranks fifth highest.

Answer: Scheherazade's ranks sixth highest.


Question: If Tantoko is ranked third highest, then which one of the following CANNOT be true?

Answer: Lautrec ranked fourth highest.

Answer: Pastilla is ranked fifth highest.

Answer: Medici is ranked fifth highest.

Answer: Scheherazade's is ranked fifth highest.

Answer: Medici is ranked sixth highest.


Context: Each of exactly three parks—Jessup, Island, and Hilltop—has at least one attraction. Each attraction is exactly one of five different types: fountain, garden, museum, playground, or theater. Among the three parks at least one of each type of attraction is included. No two attractions of the same type are included in any park. The following conditions must apply: Each of exactly two parks has a garden. Jessup has a museum but not a theater. Island has exactly one attraction. No park has both a playground and a fountain. Each park that has a theater also has a garden. Each park that has a museum also has a playground.

Question: Which one of the following could be a complete and accurate matching of each park to its attractions?

Answer: Jessup: garden, museum; Island: playground; Hilltop: garden, theater

Answer: Jessup: museum, theater; Island: garden; Hilltop: fountain, garden, playground, theater

Answer: Jessup: garden, museum, playground; Island: theater; Hilltop: garden, museum, playground

Answer: Jessup: garden, museum, playground; Island: fountain; Hilltop: garden, theater

Answer: Jessup: museum, playground; Island: fountain, garden; Hilltop: garden, theater


Question: Which one of the following CANNOT be true?

Answer: Neither Island nor Hilltop has a museum.

Answer: Neither Island nor Hilltop has a playground.

Answer: Neither Jessup nor Hilltop has a fountain.

Answer: Neither Jessup nor Island has a garden.

Answer: Neither Jessup nor Island has a theater.


Question: If each of exactly two of the parks has a fountain, then which one of the following could be true?

Answer: Island does not have a fountain.

Answer: Jessup does not have a garden.

Answer: Jessup has exactly two attractions.

Answer: Hilltop has exactly three attractions.

Answer: Hilltop has exactly four attractions.


Question: If Jessup has exactly three attractions, then it is possible to determine the exact set of attractions featured by which of the parks?

Answer: Island only

Answer: Jessup only

Answer: Island and Hilltop only

Answer: Island and Jessup only

Answer: Jessup, Island, and Hilltop


Question: If the attraction included in Island is of the same type as an attraction included in Jessup, then which one of the following must be true?

Answer: Hilltop has a playground.

Answer: Island has a museum.

Answer: Island has a fountain.

Answer: Island has a garden.

Answer: Jessup has a garden.


Question: Which one of the following could be true?

Answer: Both Hilltop and Island have a garden.

Answer: Both Hilltop and Island have a playground.

Answer: Both Hilltop and Island have a theater.

Answer: Both Island and Jessup have a fountain.

Answer: Both Island and Jessup have a garden.


Question: If Hilltop has exactly three attractions, then each of the following could be true EXCEPT:

Answer: Hilltop has a museum.

Answer: Hilltop has a playground.

Answer: Island does not have a fountain.

Answer: Island has a garden.

Answer: Jessup has a garden.


Context: Each year for the next three years, Dynamic Motors will assemble four new automobile models—the Volante, the Whisper, the Xavier, and the Ziggurat—in exactly five of its factories—F, G, H, I, and K. Each factory will assemble exactly one model in each year. Because of contractual obligations Dynamic will assemble all four models each year according to the following constraints: No model is manufactured in the same factory in consecutive years. Neither Volantes nor Whispers are assembled in any factory in which Xaviers were assembled the previous year. Neither Volantes nor Xaviers are assembled in any factory in which Ziggurats were assembled the previous year. In any year, only one factory assembles Zigurats.

Question: Which one of the following could be the assembly schedule for factories F and G for the first two years?

Answer: year 1: Volantes in F, Ziggurats in G year 2: Xaviers in F, Whispers in G

Answer: year 1: Whispers in F, Xaviers in G year 2: Whispers in F, Ziggurats in G

Answer: year 1: Xaviers in F, Volantes in G year 2: Ziggurats in F, Ziggurats in G

Answer: year 1: Xaviers in F, Xaviers in G year 2: Whispers in F, Ziggurats in G

Answer: year 1: Ziggurats in F, Whispers in G year 2: Volantes in F, Volantes in G


Question: If in the first year Volantes and Whispers are assembled in F and G, respectively, the models that are assembled in the second year in F and G, respectively, could be

Answer: Volantes and Whispers

Answer: Whispers and Volantes

Answer: Whispers and Ziggurats

Answer: Ziggurats and Whispers

Answer: Ziggurats and Ziggurats


Question: Which one of the following must be true?

Answer: Xaviers are assembled in exactly two of the factories in the first year.

Answer: Xaviers are assembled in exactly one of the factories in the second year.

Answer: Xaviers are assembled in exactly two of the factories in the second year.

Answer: Xaviers are assembled in exactly one of the factories in the third year.

Answer: Xaviers are assembled in exactly two of the factories in the third year.


Question: If in the second year Ziggurats are assembled in F, which one of the following must be true?

Answer: Volantes are assembled in exactly one of the factories in the third year.

Answer: Whispers are assembled in exactly one of the factories in the third year.

Answer: Volantes are assembled in F in the first year.

Answer: Whispers are assembled in F in the first year.

Answer: Xaviers are assembled in F in the first year.


Question: If in the second year Volantes and Whispers are assembled in F and G, respectively, the models that are assembled in the first year in F and G, respectively, could be

Answer: Whispers and Volantes

Answer: Whispers and Xaviers

Answer: Xaviers and Volantes

Answer: Xaviers and Ziggurats

Answer: Ziggurats and Volantes


Context: Each of seven television programs—H, J, L, P, Q, S, V—is assigned a different rank: from first through seventh (from most popular to least popular). The ranking is consistent with the following conditions: J and L are each less popular than H. J is more popular than Q. S and V are each less popular than L. P and S are each less popular than Q. S is not seventh.

Question: Which one of the following could be the order of the programs, from most popular to least popular?

Answer: J, H, L, Q, V, S, P

Answer: H, L, Q, J, S, P, V

Answer: H, J, Q, L, S, V, P

Answer: H, J, V, L, Q, S, P

Answer: H, L, V, J, Q, P, S


Question: If J is more popular than L, and S is more popular than P, then which one of the following must be true of the ranking?

Answer: J is second.

Answer: J is third.

Answer: L is third.

Answer: Q is third.

Answer: P is seventh.


Question: Which one of the following programs CANNOT be ranked third?

Answer: L

Answer: J

Answer: Q

Answer: V

Answer: P


Question: If V is more popular than Q and J is less popular than L, then which one of the following could be true of the ranking?

Answer: P is more popular than S.

Answer: S is more popular than V.

Answer: P is more popular than L.

Answer: J is more popular than V.

Answer: Q is more popular than V.


Question: If Q is more popular than L, then each of the following must be true of the ranking EXCEPT:

Answer: H is first.

Answer: L is fourth.

Answer: V is not fourth.

Answer: J is not third.

Answer: Q is third.


Context: Bird-watchers explore a forest to see which of the following six kinds of birds—grosbeak, harrier, jay, martin, shrike, wren—it contains. The findings are consistent with the following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are.

Question: Which one of the following could be a complete and accurate list of the birds NOT in the forest?

Answer: jays, shrikes

Answer: harriers, grosbeaks

Answer: grosbeaks, jays, martins

Answer: grosbeaks, martins, shrikes, wrens

Answer: martins, shrikes


Question: If both martins and harriers are in the forest, then which one of the following must be true?

Answer: Shrikes are the only other birds in the forest.

Answer: Jays are the only other birds in the forest.

Answer: The forest contains neither jays nor shrikes.

Answer: There are at least two other kinds of birds in the forest.

Answer: There are at most two other kinds of birds in the forest.


Question: If jays are not in the forest, then which one of the following must be false?

Answer: Martins are in the forest.

Answer: Harriers are in the forest.

Answer: Neither martins nor harriers are in the forest.

Answer: Neither martins nor shrikes are in the forest.

Answer: Harriers and shrikes are the only birds in the forest.


Question: Which one of the following is the maximum number of the six kinds of birds the forest could contain?

Answer: two

Answer: three

Answer: four

Answer: five

Answer: six


Question: Which one of the following pairs of birds CANNOT be among those birds contained in the forest?

Answer: jays, wrens

Answer: jays, shrikes

Answer: shrikes, wrens

Answer: jays, martins

Answer: shrikes, martins


Question: If grosbeaks are in the forest, then which one of the following must be true?

Answer: Shrikes are in the forest.

Answer: Wrens are in the forest.

Answer: The forest contains both wrens and shrikes.

Answer: At most two kinds of birds are in the forest.

Answer: At least three kinds of birds are in the forest.


Question: Suppose the condition is added that if shrikes are in the forest, then harriers are not. If all other conditions remain in effect, then which one of the following could be true?

Answer: The forest contains both jays and shrikes.

Answer: The forest contains both wrens and shrikes.

Answer: The forest contains both martins and shrikes.

Answer: Jays are not in the forest, whereas martins are.

Answer: Only two of the six kinds of birds are not in the forest.


Context: From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three—F, G, and H—are rubies; three—J, K, and M—are sapphires; and four—W, X, Y, and Z—are topazes. The selection of stones must meet the following restrictions: At least two of the topazes are selected. If exactly two of the sapphires are selected, exactly one of the rubies is selected. If W is selected, neither H nor Z is selected. If M is selected, W is also selected.

Question: Which one of the following could be the selection of stones?

Answer: F, G, H, M, X, Y

Answer: F, G, J, K, M, W

Answer: F, G, J, K, W, X

Answer: G, H, J, X, Y, Z

Answer: G, H, K, W, X, Z


Question: Which one of the following most be true?

Answer: G is selected.

Answer: J is selected.

Answer: X is selected.

Answer: Of at least one of the three types of stones, exactly one stone is selected.

Answer: Of at least one of the three types of stones, exactly three stones are selected.


Question: If Z is selected, which one of the following could be true?

Answer: All three of the sapphires are selected.

Answer: Both J and M are selected.

Answer: Both K and M are selected.

Answer: None of the rubies is selected.

Answer: None of the sapphires is selected.


Question: If exactly two rubies are selected, which one of the following must be true?

Answer: H is selected.

Answer: J is selected.

Answer: Z is selected.

Answer: Exactly one sapphire is selected.

Answer: Exactly two topazes are selected.


Question: Which one of the following must be true?

Answer: The selection of stones includes at least one ruby.

Answer: The selection of stones includes at most two rubies.

Answer: The selection of stones includes either F or Z, or both.

Answer: The selection of stones includes either X or Y, or both.

Answer: The selection of stones includes either X or Z, or both.


Question: If J and M are the only sapphires selected, which one of the following could be true?

Answer: F and G are both selected.

Answer: F and X are both selected.

Answer: G and H are both selected.

Answer: G and K are both selected.

Answer: Y and Z are both selected.


Context: There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions: No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street. Red lights decorate store 4. Yellow lights decorate store 5.

Question: Which one of the following could be an accurate list of the colors of the lights that decorate stores 2, 4, 6, 8, and 10, respectively?

Answer: green, red, green, red, green

Answer: green, red, green, yellow, red

Answer: green, red, yellow, red, green

Answer: yellow, green, red, green, red

Answer: yellow, red, green, red, yellow


Question: If green lights decorate store 7, then each of the following statements could be false EXCEPT:

Answer: Green lights decorate store 2.

Answer: Green lights decorate store 10.

Answer: Red lights decorate store 8.

Answer: Red lights decorate store 9.

Answer: Yellow lights decorate store 2.


Question: Which one of the following statements must be true?

Answer: Green lights decorate store 10.

Answer: Red lights decorate store 1.

Answer: Red lights decorate store 8.

Answer: Yellow lights decorate store 8.

Answer: Yellow lights decorate store 10.


Question: If green lights decorate five stores on the street, then which one of the following statements must be true?

Answer: Green lights decorate store 9.

Answer: Red lights decorate store 2.

Answer: Red lights decorate store 7.

Answer: Red lights decorate store 10.

Answer: Yellow lights decorate store 8.


Question: Suppose that yellow lights decorate exactly two stores, not just one, on the south side of the street and decorate exactly one store on the north side. If all of the other conditions remain the same, then which one of the following statements must be true?

Answer: Green lights decorate store 1.

Answer: Red lights decorate store 7.

Answer: Red lights decorate store 10.

Answer: Yellow lights decorate store 2.

Answer: Yellow lights decorate store 8.


Context: Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively 1 through 9 from one end of the store to the other. Each aisle is stocked by exactly one clerk and no clerk stocks more than two aisles. Stocking assignments must meet the following conditions: Olga stocks exactly one aisle. Kurt stocks aisle 2. Manny does not stock aisle 1. Jill does not stock consecutive aisles. Kurt stocks the only aisle between the two aisles Manny stocks. Exactly one of Larisa's aisles is an end aisle. Olga's aisle is numbered higher than either of Kurt's aisles, and lower than at least one of Larisa's.

Question: Which one of the following clerks could stock two consecutive aisles?

Answer: Jill

Answer: Kurt

Answer: Larisa

Answer: Manny

Answer: Olga


Question: Which one of the following is a pair of clerks, neither of whom could stock aisle 5?

Answer: Jill and Manny

Answer: Kurt and Olga

Answer: Larisa and Manny

Answer: Kurt and Manny

Answer: Larisa and Olga


Question: Which one of the following is a complete and accurate list of clerks, any one of whom could stock aisle 3?

Answer: Jill, Kurt, Larisa

Answer: Jill, Larisa, Manny

Answer: Jill, Larisa, Olga

Answer: Jill, Kurt, Larisa, Manny

Answer: Jill, Kurt, Larisa, Olga


Question: Which one of the following is a complete and accurate list of aisles, any one of which could be one of the aisles Manny stocks?

Answer: 1, 3, 4, 5

Answer: 3, 5, 7, 9

Answer: 3, 4, 5, 6

Answer: 3, 4, 5, 6, 7

Answer: 3, 5, 7


Question: If Larisa's aisles are separated by the maximum number of aisles that could separate her aisles, which one of the following could be true?

Answer: Jill stocks aisle 6.

Answer: Manny stocks aisle 7.

Answer: Both of Jill's aisles are numbered lower than Olga's.

Answer: Jill stocks only even-numbered aisles.

Answer: Only one clerk stocks a higher numbered aisle than Olga does.


Question: If Jill stocks aisle 3, then which one of the following CANNOT be true?

Answer: Jill stocks aisle 9.

Answer: Kurt stocks aisle 6.

Answer: Larisa stocks aisle 4.

Answer: Manny stocks aisle 4.

Answer: Olga stocks aisle 6.


Question: Suppose that, rather than just one, Larisa stocks both end aisles; all other conditions remaining in effect, which one of the following CANNOT be true?

Answer: Jill stocks aisle 3.

Answer: Olga stocks aisle 6.

Answer: Olga stocks the only aisle between the two aisles that Jill stocks.

Answer: Kurt stocks only even-numbered aisles.

Answer: One of Larisa's aisles is immediately next to Olga's.


Context: A five-week adult education course consists of exactly five lectures with a different lecture given each week. No lecture is given more than once. Each lecture is delivered by a different speaker. The following conditions are true about the speakers and their lectures: Each speaker lectures on a philosopher in whom he or she specializes. No two speakers lecture on the same philosopher. The first week's speaker specializes in Kant, Locke, and Mill, and no other philosophers. The second week's speaker specializes in Kant, Locke, Mill, and Nietzsche, and no other philosophers. The third week's and fourth week's speakers each specialize in Mill and Nietzsche, and no other philosophers. The fifth week's speaker specializes in Nietzsche, Ockham, and Plato, and no other philosophers.

Question: Which one of the following statements could be true?

Answer: The first speaker lectures on Mill.

Answer: The second speaker lectures on Mill.

Answer: The second speaker lectures on Nietzsche.

Answer: The fifth speaker lectures on Nietzsche.

Answer: The fifth speaker lectures on Ockham.


Question: What is the maximum possible number of different schedules for the five lectures in which those philosophers who are discussed are discussed in alphabetical order?

Answer: 2

Answer: 3

Answer: 4

Answer: 5

Answer: 6


Question: Which one of the following, if known, would allow one to determine the entire lecture schedule and identify for each week the philosopher who is lectured on that week?

Answer: the weeks that Kant, Locke, and Mill are lectured on

Answer: the weeks that Kant, Mill, and Nietzsche are lectured on

Answer: the weeks that Kant, Mill, and Ockham are lectured on

Answer: the weeks that Mill, Nietzsche, and Ockham are lectured on

Answer: the weeks that Mill, Nietzsche, and Plato are lectured on


Question: Assume that, of the six philosophers, Kant and Nietzsche are the only German philosophers, and Locke, Mill, and Ockham are the only British philosophers. Each of the following statements could be true EXCEPT:

Answer: The first and fourth speakers lecture on British philosophers.

Answer: The first and fourth speakers lecture on German philosophers.

Answer: The second and third speakers lecture on British philosophers.

Answer: The third and fourth speakers lecture on German philosophers.

Answer: The fourth and fifth speakers lecture on British philosophers.


Question: Suppose the third speaker were a specialist not only in Mill and Nietzsche, but also in Sartre. If all of the other conditions remained the same, then each of the following could be true EXCEPT:

Answer: Mill is lectured on in the first lecture and Nietzsche in the fourth.

Answer: Mill is lectured on in the second lecture and Nietzsche in the third.

Answer: Mill is lectured on in the second lecture and Nietzsche in the fourth.

Answer: Mill is lectured on in the fourth lecture and Nietzsche in the fifth.

Answer: Nietzsche is lectured on in the second lecture and Mill in the fourth.


Context: Exactly seven different trains—Quigley, Rockville, Sunnydale, Tilbury, Victoria, Wooster, and York—arrive at Middlebrook Station on Saturday. The following conditions govern their arrivals: The trains arrive one at a time. Either the York or the Wooster arrives fourth. The Sunnydale arrives at some time after the Wooster but at some time before the York. Both the Tilbury and the Victoria arrive at some time after the Rockville. The Tilbury does not arrive next after the Victoria; nor does the Victoria arrive next after the Tilbury.

Question: Which one of the following could be the order in which the trains arrive, from first to last?

Answer: Rockville, Tilbury, Victoria, Wooster, Sunnydale, York, Quigley

Answer: Rockville, Wooster, Quigley, York, Tilbury, Sunnydale, Victoria

Answer: Rockville, Tilbury, Quigley, Wooster, Sunnydale, York, Victoria

Answer: Quigley, Rockville, Wooster, Sunnydale, Victoria, York, Tilbury

Answer: Tilbury, Rockville, Quigley, Wooster, Sunnydale, York, Victoria


Question: If the Wooster arrives at some time before the Rockville, then exactly how many different orders are there in which the seven trains could arrive?

Answer: four

Answer: five

Answer: six

Answer: seven

Answer: eight


Question: Which one of the following must be true?

Answer: The first train to arrive is the Rockville.

Answer: The Quigley arrives at some time before the Sunnydale.

Answer: The Rockville arrives at some time before the Wooster.

Answer: The Victoria arrives at some time before the York.

Answer: The Wooster arrives at some time before the York.


Question: Which one of the following could be true?

Answer: The Sunnydale is the next train to arrive after the Quigley.

Answer: The Rockville is the next train to arrive after the Sunnydale.

Answer: The Rockville is the next train to arrive after the Tilbury.

Answer: The Quigley is the next train to arrive after the Sunnydale.

Answer: The Quigley is the next train to arrive after the Wooster.


Question: If exactly one of the trains arrives after the Wooster but before the York, then which one of the following could be true?

Answer: The sixth train to arrive is the Sunnydale.

Answer: The sixth train to arrive is the Tilbury.

Answer: The third train to arrive is the Rockville.

Answer: The second train to arrive is the Sunnydale.

Answer: The first train to arrive is the Rockville.


Question: If the Quigley arrives at some time before the Rockville, then the Wooster must arrive

Answer: second

Answer: third

Answer: fourth

Answer: fifth

Answer: sixth


Context: Each of exactly six doctors—Juarez, Kudrow, Longtree, Nance, Onawa, and Palermo—is at exactly one of two clinics: Souderton or Randsborough. The following conditions must be satisfied: Kudrow is at Randsborough if Juarez is at Souderton. Onawa is at Souderton if Juarez is at Randsborough. If Longtree is at Souderton, then both Nance and Palermo are at Randsborough. If Nance is at Randsborough, then so is Onawa. If Palermo is at Randsborough, then both Kudrow and Onawa are at Souderton.

Question: Which one of the following could be a complete and accurate list of the doctors that are at Souderton?

Answer: Juarez, Kudrow, Onawa

Answer: Juarez, Nance, Onawa, Palermo

Answer: Kudrow, Longtree, Onawa

Answer: Nance, Onawa

Answer: Nance, Palermo


Question: If Palermo is at Randsborough, then which one of the following must be true?

Answer: Juarez is at Randsborough.

Answer: Kudrow is at Randsborough.

Answer: Longtree is at Souderton.

Answer: Nance is at Randsborough.

Answer: Onawa is at Randsborough.


Question: What is the minimum number of doctors that could be at Souderton?

Answer: zero

Answer: one

Answer: two

Answer: three

Answer: four


Question: If Nance and Onawa are at different clinics, which one of the following must be true?

Answer: Juarez is at Souderton.

Answer: Kudrow is at Souderton.

Answer: Palermo is at Randsborough.

Answer: Four doctors are at Souderton.

Answer: Four doctors are at Randsborough.


Question: Which one of the following CANNOT be a pair of the doctors at Randsborough?

Answer: Juarez and Kudrow

Answer: Juarez and Palermo

Answer: Kudrow and Onawa

Answer: Nance and Onawa

Answer: Nance and Palermo


Question: If Kudrow is at Souderton, then which one of the following must be true?

Answer: Juarez is at Souderton.

Answer: Nance is at Souderton.

Answer: Onawa is at Randsborough.

Answer: Palermo is at Souderton.

Answer: Palermo is at Randsborough.


Context: From among eight candidates, four astronauts will be selected for a space flight. Four of the candidates—F, J, K, and L—are experienced astronauts and four—M, N, P, and T—are inexperienced astronauts. F, M, P, and T are geologists whereas J, K, L, and N are radiobiologists. The astronauts must be selected according to the following conditions: Exactly two experienced astronauts and two inexperienced astronauts are selected. Exactly two geologists and two radiobiologists are selected. Either P or L or both are selected.

Question: Which one of the following is an acceptable selection of astronauts for the space flight?

Answer: F, J, N, and T

Answer: F, L, M, and P

Answer: F, M, N, and P

Answer: J, L, M, and T

Answer: K, L, N, and T


Question: If F and P are selected for the space flight, the other two astronauts selected must be

Answer: a radiobiologist who is an experienced astronaut and a radiobiologist who is an inexperienced astronaut

Answer: a radiobiologist who is an experienced astronaut and a geologist who is an inexperienced astronaut

Answer: a radiobiologist and a geologist, both of whom are experienced astronauts

Answer: two radiobiologists, both of whom are experienced astronauts

Answer: two radiobiologists, both of whom are inexperienced astronauts


Question: If F and J are selected for the space flight, which one of the following must also be selected?

Answer: K

Answer: L

Answer: M

Answer: N

Answer: T


Question: If M and T are selected for the space flight, which one of the following could be, but need not be, selected for the flight?

Answer: F

Answer: J

Answer: L

Answer: N

Answer: P


Question: If N is selected for the space flight, which one of the following must also be selected?

Answer: F

Answer: J

Answer: L

Answer: M

Answer: T


Context: A showroom contains exactly six new cars—T, V, W, X, Y, and Z—each equipped with at least one of the following three options: power windows, leather interior, and sunroof. No car has any other options. The following conditions must apply: V has power windows and a sunroof. W has power windows and a leather interior. W and Y have no options in common. X has more options than W. V and Z have exactly one option in common. T has fewer options than Z.

Question: For exactly how many of the six cars is it possible to determine exactly which options each one has?

Answer: two

Answer: three

Answer: four

Answer: five

Answer: six


Question: Which one of the following must be false?

Answer: Exactly five of the six cars have leather interiors.

Answer: Exactly five of the six cars have sunroofs.

Answer: Exactly four of the six cars have leather interiors.

Answer: Exactly four of the six cars have power windows.

Answer: Exactly four of the six cars have sunroofs.


Question: If all the cars that have leather interiors also have power windows, which one of the following must be false?

Answer: T has power windows.

Answer: T has a sunroof.

Answer: V has power windows.

Answer: Z has power windows.

Answer: Z has a sunroof.


Question: If Z has no options in common with T but has at least one option in common with every other car, then which one of the following must be false?

Answer: T has power windows.

Answer: Z has a sunroof.

Answer: Exactly four of the six cars have power windows.

Answer: Exactly four of the six cars have leather interiors.

Answer: Exactly four of the six cars have sunroofs.


Question: Suppose that no two cars have exactly the same options as one another. In that case, each of the following could be true EXCEPT:

Answer: Exactly three of the six cars have power windows.

Answer: Exactly four of the six cars have power windows.

Answer: Exactly three of the six cars have sunroofs.

Answer: Exactly four of the six cars have sunroofs.

Answer: Exactly four of the six cars have leather interiors.


Question: If exactly four of the six cars have leather interiors, and exactly four of the six cars have power windows, then each of the following must be true EXCEPT:

Answer: T and V have no options in common.

Answer: T and Y have no options in common.

Answer: T and Z have exactly one option in common.

Answer: W and Z have exactly one option in common.

Answer: Y and Z have no options in common.


Question: Suppose that the condition requiring that X has more options than W is replaced by a new condition requiring that X and W have exactly two options in common. If all of the other original conditions remain in effect, which one of the following must be false?

Answer: T and X have no options in common.

Answer: V and X have exactly one option in common.

Answer: V and X have exactly two options in common.

Answer: X and Z have no options in common.

Answer: X and Z have exactly two options in common.


Context: Quentin, Robert, Shiro, Tony, and Umeko are the only members of the Kim family who attend an opera. Each of them sits in a separate seat in either row G or row H, and each sits in a seat numbered 1, 2, or 3. Consecutively numbered seats within each row are adjacent. Each member of the Kim family sits in a seat adjacent to, and in the same row as, at least one other member of the family. Tony and Umeko sit in row H. Shiro and Umeko sit in lower numbered seats than does Tony. Robert sits in the same row as Quentin or Shiro or both. Robert sits in a seat numbered 2.

Question: Which one of the following statements could be true?

Answer: Seat G3 is empty.

Answer: Seat H2 is empty.

Answer: Shiro sits in a seat numbered 3.

Answer: Tony sits in a seat numbered 1.

Answer: Umeko sits in a seat numbered 3.


Question: Which one of the following statements could be true?

Answer: Robert sits in row H.

Answer: Shiro sits in row H.

Answer: Quentin sits in the same row as, and in a seat adjacent to, Shiro.

Answer: Robert sits in the same row as, and in a seat adjacent to, Tony.

Answer: Robert sits in the same row as, and in a seat adjacent to, Umeko.


Question: If Tony sits in a seat numbered 2, then which one of the following statements could be false?

Answer: Quentin sits in a seat numbered 3.

Answer: Umeko sits in a seat numbered 1.

Answer: Quentin sits in the same row as, and in a seat adjacent to, Robert.

Answer: Robert sits in the same row as, and in a seat adjacent to, Shiro.

Answer: Tony sits in the same row as, and in a seat adjacent to, Umeko.


Question: Considering only the six seats in which members of the Kim family could sit, which one of the following is a complete and accurate list of those seats any one of which could be empty?

Answer: G1, G3

Answer: G3, H1

Answer: H1, H3

Answer: G1, G3, H1

Answer: G1, G3, H1, H3


Question: Which one of the following is a complete and accurate list of those members of the Kim family any one of whom could sit in seat H2?

Answer: Quentin

Answer: Shiro, Umeko

Answer: Robert, Shiro, Umeko

Answer: Tony, Shiro, Umeko

Answer: Quentin, Shiro, Tony, Umeko


Context: Exactly seven professors—Madison, Nilsson, Orozco, Paton, Robinson, Sarkis, and Togo—were hired in the years 1989 through 1995. Each professor has one or more specialities, and any two professors hired in the same year or in consecutive years do not have a specialty in common. The professors were hired according to the following conditions: Madison was hired in 1993, Robinson in 1991. There is at least one specialty that Madison, Orozco, and Togo have in common. Nilsson shares a specialty with Robinson. Paton and Sarkis were each hired at least one year before Madison and at least one year after Nilsson. Orozco, who shares a specialty with Sarkis, was hired in 1990.

Question: Which one of the following is a complete and accurate list of the professors who could have been hired in the years 1989 through 1991?

Answer: Nilsson, Orozco, Robinson

Answer: Orozco, Robinson, Sarkis

Answer: Nilsson, Orozco, Paton, Robinson

Answer: Nilsson, Orozco, Paton, Sarkis

Answer: Orozco, Paton, Robinson, Sarkis


Question: If exactly one professor was hired in 1991, then which one of the following could be true?

Answer: Madison and Paton share a specialty.

Answer: Robinson and Sarkis share a specialty.

Answer: Paton was hired exactly one year after Orozco.

Answer: Exactly one professor was hired in 1994.

Answer: Exactly two professors were hired in 1993.


Question: Which one of the following must be false?

Answer: Nilsson was hired in 1989.

Answer: Paton was hired in 1990.

Answer: Paton was hired in 1991.

Answer: Sarkis was hired in 1992.

Answer: Togo was hired in 1994.


Question: Which one of the following must be true?

Answer: Orozco was hired before Paton.

Answer: Paton was hired before Sarkis.

Answer: Sarkis was hired before Robinson.

Answer: Robinson was hired before Sarkis.

Answer: Madison was hired before Sarkis.


Question: If exactly two professors were hired in 1992, then which one of the following could be true?

Answer: Orozco, Paton, and Togo share a specialty.

Answer: Madison, Paton, and Togo share a specialty.

Answer: Exactly two professors were hired in 1991.

Answer: Exactly two professors were hired in 1993.

Answer: Paton was hired in 1991.


Question: If Paton and Madison have a specialty in common, then which one of the following must be true?

Answer: Nilsson does not share a specialty with Paton.

Answer: Exactly one professor was hired in 1990.

Answer: Exactly one professor was hired in 1991.

Answer: Exactly two professors were hired in each of two years.

Answer: Paton was hired at least one year before Sarkis.


Context: A fruit stand carries at least one kind of the following kinds of fruit: figs, kiwis, oranges, pears, tangerines, and watermelons. The stand does not carry any other kind of fruit. The selection of fruits the stand carries is consistent with the following conditions: If the stand carries kiwis, then it does not carry pears. If the stand does not carry tangerines, then it carries kiwis. If the stand carries oranges, then it carries both pears and watermelons. If the stand carries watermelons, then it carries figs or tangerines or both.

Question: Which one of the following could be a complete and accurate list of the kinds of fruit the stand carries?

Answer: oranges, pears

Answer: pears, tangerines

Answer: oranges, pears, watermelons

Answer: oranges, tangerines, watermelons

Answer: kiwis, oranges, pears, watermelons


Question: Which one of the following could be the only kind of fruit the stand carries?

Answer: figs

Answer: oranges

Answer: pears

Answer: tangerines

Answer: watermelons


Question: Which one of the following CANNOT be a complete and accurate list of the kinds of fruit the stand carries?

Answer: kiwis, tangerines

Answer: tangerines, watermelons

Answer: figs, kiwis, watermelons

Answer: oranges, pears, tangerines, watermelons

Answer: figs, kiwis, oranges, pears, watermelons


Question: If the stand carries no watermelons, then which one of the following must be true?

Answer: The stand carries kiwis.

Answer: The stand carries at least two kinds of fruit.

Answer: The stand carries at most three kinds of fruit.

Answer: The stand carries neither oranges nor pears.

Answer: The stand carries neither oranges nor kiwis.


Question: If the stand carries watermelons, then which one of the following must be false?

Answer: The stand does not carry figs.

Answer: The stand does not carry tangerines.

Answer: The stand does not carry pears.

Answer: The stand carries pears but not oranges.

Answer: The stand carries pears but not tangerines.


Question: If the condition that if the fruit stand does not carry tangerines then it does carry kiwis is suspended, and all other conditions remain in effect, then which one of the following CANNOT be a complete and accurate list of the kinds of fruit the stand carries?

Answer: pears

Answer: figs, pears

Answer: oranges, pears, watermelons

Answer: figs, pears, watermelons

Answer: figs, oranges, pears, watermelons


Context: A radio talk show host airs five telephone calls sequentially. The calls, one from each of Felicia, Gwen, Henry, Isaac, and Mel, are each either live or taped (but not both). Two calls are from Vancouver, two are from Seattle, and one is from Kelowna. The following conditions must apply: Isaac's and Mel's calls are the first two calls aired, but not necessarily in that order. The third call aired, from Kelowna, is taped. Both Seattle calls are live. Both Gwen's and Felicia's calls air after Henry's. Neither Mel nor Felicia calls from Seattle.

Question: Which one of the following could be an accurate list of the calls, listed in the order in which they are aired?

Answer: Isaac's, Henry's, Felicia's, Mel's, Gwen's

Answer: Isaac's, Mel's, Gwen's, Henry's, Felicia's

Answer: Mel's, Gwen's, Henry's, Isaac's, Felicia's

Answer: Mel's, Isaac's, Gwen's, Henry's, Felicia's

Answer: Mel's, Isaac's, Henry's, Felicia's, Gwen's


Question: Which one of the following could be true?

Answer: Felicia's call airs fifth.

Answer: Gwen's call airs first.

Answer: Henry's call airs second.

Answer: Isaac's call airs third.

Answer: Mel's call airs fifth.


Question: If the first call aired is from Seattle, then which one of the following could be true?

Answer: Felicia's call is the next call aired after Isaac's.

Answer: Henry's call is the next call aired after Felicia's.

Answer: Henry's call is the next call aired after Mel's.

Answer: Henry's call is the next call aired after Isaac's.

Answer: Isaac's call is the next call aired after Mel's.


Question: If a taped call airs first, then which one of the following CANNOT be true?

Answer: Felicia's call airs fourth.

Answer: Gwen's call airs fifth.

Answer: A taped call airs second.

Answer: A taped call airs third.

Answer: A taped call airs fourth.


Question: Which one of the following must be true?

Answer: Gwen's call is live.

Answer: Henry's call is live.

Answer: Mel's call is live.

Answer: Felicia's call is taped.

Answer: Isaac's call is taped.


Question: If no two live calls are aired consecutively and no two taped calls are aired consecutively, then in exactly how many distinct orders could the calls from the five people be aired?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


Question: If a taped call airs second, then which one of the following CANNOT be true?

Answer: The first call aired is from Seattle.

Answer: The first call aired is from Vancouver.

Answer: The fourth call aired is from Seattle.

Answer: The fifth call aired is from Seattle.

Answer: The fifth call aired is from Vancouver.


Context: Gutierrez, Hoffman, Imamura, Kelly, Lapas, and Moore ride a bus together. Each sits facing forward in a different one of the six seats on the left side of the bus. The seats are in consecutive rows that are numbered 1, 2, and 3 from front to back. Each row has exactly two seats: a window seat and an aisle seat. The following conditions must apply: Hoffman occupies the aisle seat immediately behind Gutierrez's aisle seat. If Moore occupies an aisle seat, Hoffman sits in the same row as Lapas. If Gutierrez sits in the same row as Kelly, Moore occupies the seat immediately and directly behind Imamura's seat. If Kelly occupies a window seat, Moore sits in row 3. If Kelly sits in row 3, Imamura sits in row 1.

Question: Which one of the following could be true?

Answer: Imamura sits in row 2, whereas Kelly sits in row 3.

Answer: Gutierrez sits in the same row as Kelly, immediately and directly behind Moore.

Answer: Gutierrez occupies a window seat in the same row as Lapas.

Answer: Moore occupies an aisle seat in the same row as Lapas.

Answer: Kelly and Moore both sit in row 3.


Question: If Lapas and Kelly each occupy a window seat, then which one of the following could be true?

Answer: Moore occupies the aisle seat in row 3.

Answer: Imamura occupies the window seat in row 3.

Answer: Gutierrez sits in the same row as Kelly.

Answer: Gutierrez sits in the same row as Moore.

Answer: Moore sits in the same row as Lapas.


Question: If Moore sits in row 1, then which one of the following must be true?

Answer: Hoffman sits in row 2.

Answer: Imamura sits in row 2.

Answer: Imamura sits in row 3.

Answer: Kelly sits in row 1.

Answer: Lapas sits in row 3.


Question: If Kelly occupies the aisle seat in row 3, then each of the following must be true EXCEPT:

Answer: Gutierrez sits in the same row as Imamura.

Answer: Hoffman sits in the same row as Lapas.

Answer: Lapas occupies a window seat.

Answer: Moore occupies a window seat.

Answer: Gutierrez sits in row 1.


Question: If neither Gutierrez nor Imamura sits in row 1, then which one of the following could be true?

Answer: Hoffman sits in row 2.

Answer: Kelly sits in row 2.

Answer: Moore sits in row 2.

Answer: Imamura occupies an aisle seat.

Answer: Moore occupies an aisle seat.


Context: An airline has four flights from New York to Sarasota—flights 1, 2, 3, and 4. On each flight there is exactly one pilot and exactly one co-pilot. The pilots are Fazio, Germond, Kyle, and Lopez; the co-pilots are Reich, Simon, Taylor, and Umlas. Each pilot and co-pilot is assigned to exactly one flight. The flights take off in numerical order. Fazio's flight takes off before Germond's, and at least one other flight takes off between their flights. Kyle is assigned to flight 2. Lopez is assigned to the same flight as Umlas.

Question: Which one of the following pilot and co-pilot teams could be assigned to flight 1?

Answer: Fazio and Reich

Answer: Fazio and Umlas

Answer: Germond and Reich

Answer: Germond and Umlas

Answer: Lopez and Taylor


Question: If Reich's flight is later than Umlas's, which one of the following statements cannot be true?

Answer: Fazio's flight is earlier than Simon's.

Answer: Kyle's flight is earlier than Reich's.

Answer: Kyle's flight is earlier than Taylor's.

Answer: Simon's flight is earlier than Reich's.

Answer: Taylor's flight is earlier than Kyle's.


Question: If Lopez's flight is earlier than Germond's, which one of the following statements could be false?

Answer: Fazio's flight is earlier than Umlas's.

Answer: Germond is assigned to flight 4.

Answer: Either Reich's or Taylor's flight is earlier than Umlas's.

Answer: Simon's flight is earlier than Umlas's.

Answer: Umlas is assigned to flight 3.


Question: What is the maximum possible number of different pilot and co-pilot teams, any one of which could be assigned to flight 4?

Answer: 2

Answer: 3

Answer: 4

Answer: 5

Answer: 6


Question: If Simon's flight is later than Lopez's, then which one of the following statements could be false?

Answer: Germond's flight is later than Reich's.

Answer: Germond's flight is later than Taylor's.

Answer: Lopez's flight is later than Taylor's.

Answer: Taylor's flight is later than Reich's.

Answer: Umlas's flight is later than Reich's.


Context: A school has exactly four dormitories that are to be fully occupied—Richards, Tuscarora, Veblen, and Wisteria—each consisting entirely of a North wing and a South wing. The following rules govern assignment of students to dormitory wings: Each wing is assigned only male students or only female students. Exactly three wings have males assigned to them. Richards North and Tuscarora North are assigned females. If a dormitory has males assigned to one of its wings, then its other wing is assigned females. If males are assigned to Veblen South, then Wisteria North is assigned males.

Question: If females are assigned to Veblen South and Veblen North, then which one of the following could be two other wings that are also assigned females?

Answer: Richards North and Tuscarora South

Answer: Richards South and Wisteria South

Answer: Richards South and Tuscarora North

Answer: Tuscarora North and Wisteria South

Answer: Tuscarora South and Wisteria South


Question: It CANNOT be true that females are assigned to both

Answer: Richards South and Wisteria South

Answer: Richards South and Tuscarora South

Answer: Richards South and Veblen North

Answer: Tuscarora South and Wisteria South

Answer: Veblen North and Wisteria South


Question: If Wisteria North is assigned females, then females must also be assigned to which one of the following?

Answer: Richards South

Answer: Wisteria South

Answer: Tuscarora South

Answer: Veblen South

Answer: Veblen North


Question: If males are assigned to Veblen South, which one of the following is a complete and accurate list of the wings that CANNOT be assigned males?

Answer: Richards North, Tuscarora North

Answer: Richards North, Tuscarora North, Veblen North

Answer: Richards North, Tuscarora North, Wisteria South

Answer: Richards North, Tuscarora North, Veblen North, Wisteria South

Answer: Richards North, Richards South, Tuscarora North, Veblen North, Wisteria South


Question: If Tuscarora South is assigned females, then it could be true that females are assigned to both

Answer: Richards South and Wisteria North

Answer: Richards South and Wisteria South

Answer: Veblen North and Wisteria North

Answer: Veblen South and Wisteria South

Answer: Veblen South and Veblen North


Context: In a single day, exactly seven trucks—S, T, U, W, X, Y, and Z—are the only arrivals at a warehouse. No truck arrives at the same time as any other truck, and no truck arrives more than once that day. Each truck is either green or red (but not both). The following conditions apply: No two consecutive arrivals are red. Y arrives at some time before both T and W. Exactly two of the trucks that arrive before Y are red. S is the sixth arrival. Z arrives at some time before U.

Question: Which one of the following could be the order, from first to last, in which the trucks arrive?

Answer: X, Z, U, Y, W, S, T

Answer: X, Y, Z, U, W, S, T

Answer: Z, W, U, T, Y, S, X

Answer: Z, U, T, Y, W, S, X

Answer: U, Z, Y, T, S, W, X


Question: For which one of the following pairs of trucks is it the case that they CANNOT both be red?

Answer: S and X

Answer: T and S

Answer: U and W

Answer: W and T

Answer: X and Z


Question: If X is the third arrival, then which one of the following trucks must be green?

Answer: S

Answer: T

Answer: U

Answer: W

Answer: Z


Question: If exactly three of the trucks are green, then which one of the following trucks must be green?

Answer: S

Answer: T

Answer: U

Answer: W

Answer: Z


Question: For exactly how many of the seven trucks can one determine exactly how many trucks arrived before it?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


Question: Which one of the following pairs of trucks CANNOT arrive consecutively at the warehouse?

Answer: U and Y

Answer: X and Y

Answer: Y and T

Answer: Y and W

Answer: Y and Z


Context: A total of six books occupies three small shelves—one on the first shelf, two on the second shelf, and three on the third shelf. Two of the books are grammars—one of Farsi, the other of Hausa. Two others are linguistics monographs—one on phonology, the other on semantics. The remaining two books are novels—one by Vonnegut, the other by Woolf. The books' arrangement is consistent with the following: There is at least one novel on the same shelf as the Farsi grammar. The monographs are not both on the same shelf. The Vonnegut novel is not on the same shelf as either monograph.

Question: Which one of the following could be an accurate matching of the bookshelves to the books on each of them?

Answer: first shelf: Hausa grammar second shelf: semantics monograph, Vonnegut novel third shelf: Farsi grammar, phonology monograph, Woolf novel

Answer: first shelf: semantics monograph second shelf: Farsi grammar, Vonnegut novel third shelf: Hausa grammar, phonology monograph, Woolf novel

Answer: first shelf: Vonnegut novel second shelf: phonology monograph, Farsi grammar third shelf: Hausa grammar, semantics monograph, Woolf novel

Answer: first shelf: Woolf novel second shelf: phonology and semantics monographs third shelf: Farsi and Hausa grammars, Vonnegut novel

Answer: first shelf: Woolf novel second shelf: Farsi grammar, Vonnegut novel third shelf: Hausa grammar, phonology and semantics monographs


Question: Which one of the following CANNOT be true?

Answer: A grammar is on the first shelf.

Answer: A linguistics monograph is on the same shelf as the Hausa grammar.

Answer: A novel is on the first shelf.

Answer: The novels are on the same shelf as each other.

Answer: Neither linguistics monograph is on the first shelf.


Question: Which one of the following must be true?

Answer: A linguistics monograph and a grammar are on the second shelf.

Answer: A novel and a grammar are on the second shelf.

Answer: At least one linguistics monograph and at least one grammar are on the third shelf.

Answer: At least one novel and at least one grammar are on the third shelf.

Answer: At least one novel and at least one linguistics monograph are on the third shelf.


Question: If both grammars are on the same shelf, which one of the following could be true?

Answer: The phonology monograph is on the third shelf.

Answer: A novel is on the first shelf.

Answer: Both novels are on the second shelf.

Answer: The Farsi grammar is on the second shelf.

Answer: The phonology monograph is on the first shelf.


Question: Which one of the following must be true?

Answer: A linguistics monograph is on the first shelf.

Answer: No more than one novel is on each shelf.

Answer: The Farsi grammar is not on the same shelf as the Hausa grammar.

Answer: The semantics monograph is not on the same shelf as the Woolf novel.

Answer: The Woolf novel is not on the first shelf.


Question: If the Farsi grammar is not on the third shelf, which one of the following could be true?

Answer: The phonology monograph is on the second shelf.

Answer: The Hausa grammar is on the second shelf.

Answer: The semantics monograph is on the third shelf.

Answer: The Vonnegut novel is on the third shelf.

Answer: The Woolf novel is on the second shelf.


Question: If the Hausa grammar and the phonology monograph are on the same shelf, which one of the following must be true?

Answer: The phonology monograph is on the third shelf.

Answer: The Vonnegut novel is on the second shelf.

Answer: The semantics monograph is on the second shelf.

Answer: The semantics monograph is on the first shelf.

Answer: The Woolf novel is on the third shelf.


Context: A swim team with exactly five members—Jacobson, Kruger, Lu, Miller, Ortiz—swims a ten-lap relay race. Each team member swims exactly two of the laps: one swims laps 1 and 6, one swims laps 2 and 7, one swims laps 3 and 8, one swims laps 4 and 9, and one swims laps 5 and 10. The following conditions apply: Neither of Kruger's laps is immediately before either of Lu's. Jacobson does not swim lap 9. Ortiz's first lap is after (but not necessarily immediately after) Miller's. At least one of Jacobson's laps is immediately after one of Ortiz's laps.

Question: Which one of the following could be an accurate list of the swimmers of the first five laps, in order from lap 1 through lap 5?

Answer: Jacobson, Kruger, Miller, Lu, Ortiz

Answer: Kruger, Miller, Ortiz, Jacobson, Lu

Answer: Lu, Miller, Jacobson, Kruger, Ortiz

Answer: Ortiz, Kruger, Miller, Lu, Jacobson

Answer: Miller, Ortiz, Jacobson, Kruger, Lu


Question: If Jacobson swims lap 8, then for exactly how many of the ten laps can one determine which team member swims the lap?

Answer: ten

Answer: eight

Answer: six

Answer: four

Answer: two


Question: If Ortiz swims lap 4, then which one of the following could be true?

Answer: Jacobson swims lap 1.

Answer: Jacobson swims lap 3.

Answer: Kruger swims lap 5.

Answer: Lu swims lap 3.

Answer: Miller swims lap 5.


Question: Which one of the following could be true?

Answer: Jacobson swims lap 4.

Answer: Kruger swims lap 5.

Answer: Lu swims lap 5.

Answer: Miller swims lap 10.

Answer: Ortiz swims lap 6.


Question: Jacobson CANNOT swim which one of the following laps?

Answer: lap 1

Answer: lap 2

Answer: lap 3

Answer: lap 6

Answer: lap 10


Question: Which one of the following could be an accurate list of the swimmers of the last five laps, in order from lap 6 through lap 10?

Answer: Jacobson, Miller, Kruger, Ortiz, Lu

Answer: Kruger, Lu, Miller, Ortiz, Jacobson

Answer: Lu, Kruger, Miller, Ortiz, Jacobson

Answer: Miller, Kruger, Ortiz, Jacobson, Lu

Answer: Ortiz, Jacobson, Kruger, Miller, Lu


Context: A car drives into the center ring of a circus and exactly eight clowns—Q, R, S, T, V, W, Y, and Z—get out of the car, one clown at a time. The order in which the clowns get out of the car is consistent with the following conditions: V gets out at some time before both Y and Q. Q gets out at some time after Z. T gets out at some time before V but at some time after R. S gets out at some time after V. R gets out at some time before W.

Question: Which one of the following could be the order, from first to last, in which the clowns get out of the car?

Answer: T, Z, V, R, W, Y, S, Q

Answer: Z, R, W, Q, T, V, Y, S

Answer: R, W, T, V, Q, Z, S, Y

Answer: Z, W, R, T, V, Y, Q, S

Answer: R, W, T, V, Z, S, Y, Q


Question: Which one of the following could be true?

Answer: Y is the second clown to get out of the car.

Answer: R is the third clown to get out of the car.

Answer: Q is the fourth clown to get out of the car.

Answer: S is the fifth clown to get out of the car.

Answer: V is the sixth clown to get out of the car.


Question: If Z is the seventh clown to get out of the car, then which one of the following could be true?

Answer: R is the second clown to get out of the car.

Answer: T is the fourth clown to get out of the car.

Answer: W is the fifth clown to get out of the car.

Answer: V is the sixth clown to get out of the car.

Answer: Y is the eighth clown to get out of the car.


Question: If T is the fourth clown to get out of the car, then which one of the following must be true?

Answer: R is the first clown to get out of the car.

Answer: Z is the second clown to get out of the car.

Answer: W is the third clown to get out of the car.

Answer: V is the fifth clown to get out of the car.

Answer: Y is the seventh clown to get out of the car.


Question: If Q is the fifth clown to get out of the car, then each of the following could be true EXCEPT:

Answer: Z is the first clown to get out of the car.

Answer: T is the second clown to get out of the car.

Answer: V is the third clown to get out of the car.

Answer: W is the fourth clown to get out of the car.

Answer: Y is the sixth clown to get out of the car.


Question: If R is the second clown to get out of the car, which one of the following must be true?

Answer: S gets out of the car at some time before T does.

Answer: T gets out of the car at some time before W does.

Answer: W gets out of the car at some time before V does.

Answer: Y gets out of the car at some time before Q does.

Answer: Z gets out of the car at some time before W does.


Question: If V gets out of the car at some time before Z does, then which one of the following could be true?

Answer: R is the second clown to get out of the car.

Answer: T is the fourth clown to get out of the car.

Answer: Q is the fourth clown to get out of the car.

Answer: V is the fifth clown to get out of the car.

Answer: Z is the sixth clown to get out of the car.


Context: Each of six tasks—harvesting, milling, plowing, spinning, threshing, and weaving—will be demonstrated exactly once at a farm exhibition. No two tasks will be demonstrated concurrently. Three volunteers—Frank, Gladys, and Leslie—will each demonstrate exactly two of the tasks. The tasks must be demonstrated in accordance with the following conditions: Frank demonstrates exactly one task before Gladys demonstrates any of the tasks. Frank performs neither the first nor the last demonstration. Gladys demonstrates neither harvesting nor milling. Leslie demonstrates neither harvesting nor threshing. Milling is the next task demonstrated after threshing is demonstrated.

Question: Which one of the following is an acceptable list of the volunteers and the tasks each demonstrates, in order from the first to the last demonstration?

Answer: Frank: weaving; Gladys: threshing; Leslie: milling; Leslie: spinning; Frank: harvesting; Gladys: plowing

Answer: Leslie: plowing; Frank: harvesting; Frank: threshing; Leslie: milling; Gladys: spinning; Gladys: weaving

Answer: Leslie: plowing; Frank: spinning; Gladys: threshing; Leslie: milling; Frank: harvesting; Gladys: weaving

Answer: Leslie: spinning; Leslie: weaving; Frank: plowing; Gladys: harvesting; Frank: threshing; Gladys: milling

Answer: Leslie: weaving; Frank: threshing; Gladys: spinning; Leslie: milling; Frank: harvesting; Gladys: plowing


Question: Which one of the following must be true?

Answer: Frank demonstrates harvesting.

Answer: Frank demonstrates milling.

Answer: Frank demonstrates threshing.

Answer: Gladys demonstrates plowing.

Answer: Gladys demonstrates weaving.


Question: If Leslie performs the fourth demonstration, then harvesting could be the demonstration performed

Answer: first

Answer: second

Answer: third

Answer: fourth

Answer: sixth


Question: If Gladys demonstrates plowing immediately before Frank demonstrates threshing, which one of the following must be true?

Answer: Frank demonstrates harvesting for the second demonstration.

Answer: Gladys demonstrates spinning for the fifth demonstration.

Answer: Leslie demonstrates weaving for the first demonstration.

Answer: Gladys performs the fourth demonstration.

Answer: Leslie performs the sixth demonstration.


Question: Which one of the following must be true?

Answer: Frank performs the second demonstration.

Answer: Gladys performs the fourth demonstration.

Answer: Gladys performs the sixth demonstration.

Answer: Leslie performs the first demonstration.

Answer: Leslie performs the second demonstration.


Question: Which one of the following could be true?

Answer: Harvesting is demonstrated first.

Answer: Milling is demonstrated second.

Answer: Threshing is demonstrated first.

Answer: Threshing is demonstrated last.

Answer: Weaving is demonstrated first.


Context: Seven job applicants—Feng, Garcia, Herrera, Ilias, Weiss, Xavier, and Yates—are hired to fill seven new positions at Chroma, Inc. One position is in the management department, three are in the production department, and three are in the sales department. The following conditions must apply: Herrera is hired for a position in the same department as Yates. Feng is hired for a position in a different department from Garcia. If Xavier is hired for a sales position, then Weiss is hired for a production position. Feng is hired for a production position.

Question: Which one of the following could be a complete and accurate matching of the applicants with the departments in which they were hired?

Answer: management: Weiss; production: Feng, Herrera, Yates; sales: Garcia, Ilias, Xavier

Answer: management: Weiss; production: Garcia, Ilias, Xavier; sales: Feng, Herrera, Yates

Answer: management: Xavier; production: Feng, Garcia, Herrera; sales: Ilias, Yates, Weiss

Answer: management: Xavier; production: Feng, Herrera, Ilias; sales: Garcia, Weiss, Yates

Answer: management: Xavier; production: Feng, Ilias, Weiss; sales: Garcia, Herrera, Yates


Question: Which one of the following is a complete and accurate list of the applicants, each of whom CANNOT be hired for a production position?

Answer: Feng, Ilias, Xavier

Answer: Garcia, Herrera, Yates

Answer: Herrera, Yates

Answer: Garcia

Answer: Ilias


Question: It can be determined in which department each of the seven applicants is hired if which one of the following statements is true?

Answer: Feng and Weiss are both hired for production positions.

Answer: Garcia and Yates are both hired for sales positions.

Answer: Ilias and Weiss are both hired for sales positions.

Answer: Ilias and Weiss are both hired for production positions.

Answer: Ilias and Xavier are both hired for production positions.


Question: Each of the following could be an accurate partial list of the applicants hired for sales positions EXCEPT:

Answer: Garcia, Ilias

Answer: Garcia, Xavier

Answer: Garcia, Yates

Answer: Herrera, Weiss

Answer: Herrera, Xavier


Question: If Feng is hired for a position in the same department as Xavier, then each of the following could be true EXCEPT:

Answer: Garcia is hired for a sales position.

Answer: Herrera is hired for a production position.

Answer: Ilias is hired for a sales position.

Answer: Weiss is hired for the management position.

Answer: Weiss is hired for a production position.


Question: If Xavier is not hired for one of the production positions, then which one of the following could be true?

Answer: Feng and Herrera are both hired for sales positions.

Answer: Herrera and Weiss are both hired for sales positions.

Answer: Feng and Yates are both hired for production positions.

Answer: Garcia and Weiss are both hired for production positions.

Answer: Herrera and Weiss are both hired for production positions.


Context: Musicians perform each of exactly five pieces—Nexus, Onyx, Synchrony, Tailwind, and Virtual—once, and one at a time; the pieces are performed successively (though not necessarily in that order). Each piece is performed with exactly two instruments: Nexus with fiddle and lute, Onyx with harp and mandolin, Synchrony with guitar and harp, Tailwind with fiddle and guitar, and Virtual with lute and mandolin. The following conditions must apply: Each piece shares one instrument with the piece performed immediately before it or after it (or both). Either Nexus or Tailwind is performed second.

Question: Which one of the following could be the order, from first to last, in which the pieces are performed?

Answer: Nexus, Synchrony, Onyx, Virtual, Tailwind

Answer: Synchrony, Tailwind, Onyx, Nexus, Virtual

Answer: Tailwind, Nexus, Onyx, Virtual, Synchrony

Answer: Tailwind, Nexus, Synchrony, Onyx, Virtual

Answer: Virtual, Nexus, Synchrony, Onyx, Tailwind


Question: Which one of the following instruments CANNOT be shared by the third and fourth pieces performed?

Answer: fiddle

Answer: guitar

Answer: harp

Answer: lute

Answer: mandolin


Question: If each piece (except the fifth) shares one instrument with the piece performed immediately after it, then which one of the following could be true?

Answer: Virtual is performed first.

Answer: Synchrony is performed second.

Answer: Onyx is performed third.

Answer: Nexus is performed fourth.

Answer: Tailwind is performed fifth.


Question: Each of the following could be the piece performed first EXCEPT:

Answer: Nexus

Answer: Onyx

Answer: Synchrony

Answer: Tailwind

Answer: Virtual


Question: If Synchrony is performed fifth, then which one of the following could be true?

Answer: Nexus is performed third.

Answer: Onyx is performed third.

Answer: Tailwind is performed fourth.

Answer: Virtual is performed first.

Answer: Virtual is performed second.


Context: Eight files will be ordered from first to eighth. Each file falls into exactly one of three categories: red files (H, M, O), green files (P, V, X), or yellow files (T, Z). The files must be ordered according to the following conditions: H must be placed into some position before O, but H cannot immediately precede O. X must be placed into some position before V. X and V must be separated by the same number of files as separate H and O. Z must immediately precede M. The first file cannot be a red file.

Question: Which one of the following is an acceptable ordering of the files from first to eighth?

Answer: H X O V Z M P T

Answer: P M Z H X O V T

Answer: P Z M H O T X V

Answer: X Z M V H T P O

Answer: Z M H P O X V T


Question: The largest possible number of files that can separate Z from H is

Answer: two

Answer: three

Answer: four

Answer: five

Answer: six


Question: If each of the three red files is immediately followed by a green file, which one of the following must be a yellow file?

Answer: the first

Answer: the second

Answer: the third

Answer: the fourth

Answer: the fifth


Question: The largest possible number of files that can separate X from V is

Answer: three

Answer: four

Answer: five

Answer: six

Answer: seven


Question: If Z is placed in the fifth position, then which one of the following is a complete and accurate list of the positions, any one of which could be H's position?

Answer: first, third, fourth

Answer: first, second, third

Answer: second, third, fourth

Answer: second, third, fourth, sixth

Answer: third, fourth, sixth, seventh


Context: Exactly three employees of Capital Enterprises—Maria, Suki, and Tate—attend a three-day conference together. Each day, there are exactly three sessions on the three topics of the conference—one on hiring, one on investing, and one on regulations. The following rules govern the conference: Each conference participant attends exactly two sessions, which are on different topics and on different days. Neither Maria nor Suki attends any session on investing. Tate does not attend any session on the third day. At most two Capital employees attend any given session together.

Question: What is the maximum number of sessions attended by at least one Capital employee?

Answer: three

Answer: four

Answer: five

Answer: six

Answer: seven


Question: Which one of the following must be false?

Answer: Maria attends sessions only on the first two days.

Answer: Suki attends sessions only on the last two days.

Answer: Exactly two Capital employees attend a session together on the second day.

Answer: Exactly one session is attended by one or more Capital employees on the second day.

Answer: Exactly three sessions are attended by one or more Capital employees on the third day.


Question: If exactly two sessions on the third day are attended by one or more Capital employees, then which one of the following must be true?

Answer: Exactly two sessions on the first day are attended by one or more Capital employees.

Answer: Exactly two sessions on the second day are attended by one or more Capital employees.

Answer: Maria and Suki do not attend any session together.

Answer: Maria and Tate do not attend any session together.

Answer: Tate attends a session on investing.


Question: Each of the following is possible EXCEPT:

Answer: Every session attended by at least one Capital employee is attended by exactly one Capital employee.

Answer: Every session attended by at least one Capital employee is attended by exactly two Capital employees.

Answer: Every session attended by Maria is also attended by Suki.

Answer: Every session attended by Suki is also attended by Tate.

Answer: Every session attended by Tate is also attended by Maria.


Question: If all three sessions on the first day are attended by one or more Capital employees, then which one of the following must be false?

Answer: Maria and Suki attend a session together on the third day.

Answer: Suki and Tate attend a session together on the second day.

Answer: Maria attends a session on hiring on the second day.

Answer: Suki attends a session on regulations on the third day.

Answer: Tate attends a session on investing on the first day.


Question: If Maria and Tate are the only Capital employees to attend a session on the first day, then each of the following could be true EXCEPT:

Answer: Maria and Suki attend exactly two sessions together.

Answer: Maria and Tate attend exactly two sessions together.

Answer: Suki and Tate attend exactly one session together.

Answer: Maria attends a session on regulations on the second day.

Answer: Tate attends a session on hiring on the second day.


Context: Of the five Pohl children—Sara, Theo, Uma, Will, and Zoe—three are left-handed and two are right-handed. Each of the five children was born in a different one of seven calendar years, 1990 through 1996. The following conditions apply: No two left-handed children were born in consecutive years. No two right-handed children were born in consecutive years. Sara, who is left-handed, was born before Uma. Zoe was born before both Theo and Will. A left-handed child was born in 1991. Uma, who is right-handed, was born in 1993.

Question: Which one of the following could be an accurate matching of each Pohl child with the year in which that child was born?

Answer: Sara: 1990; Zoe: 1992; Uma: 1993; Will: 1994; and Theo: 1995

Answer: Sara: 1991; Uma: 1993; Theo: 1994; Zoe: 1995; and Will: 1996

Answer: Zoe: 1990; Sara: 1991; Uma: 1992; Theo: 1994; and Will: 1995

Answer: Zoe: 1990; Sara: 1991; Uma: 1993; Theo: 1994; and Will: 1995

Answer: Zoe: 1990; Sara: 1991; Uma: 1993; Theo: 1994; and Will: 1996


Question: If Sara was born before Zoe was born, then which one of the following statements CANNOT be true?

Answer: Will is left-handed.

Answer: Zoe is left-handed.

Answer: Theo was born after Will was born.

Answer: Uma was born after Zoe was born.

Answer: No child was born in 1990.


Question: Which one of the following must be false?

Answer: None of the children was born in 1990, nor was a child born in 1992.

Answer: None of the children was born in 1992, nor was a child born in 1995.

Answer: None of the children was born in 1994, nor was a child born in 1996.

Answer: One of the children was born in 1990, and another in 1993.

Answer: One of the children was born in 1993, and another in 1995.


Question: If Theo was born after Will was born, then how many sequential orderings of the children, from firstborn to lastborn, are possible?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


Question: If none of the children was born in 1995, then which one of the following statements must be true?

Answer: Theo was born in 1994.

Answer: Will was born in 1994.

Answer: Will was born in 1996.

Answer: Zoe was born in 1990.

Answer: Zoe was born in 1994.


Question: If Theo is right-handed, then each of the following statements must be false EXCEPT:

Answer: Theo was born in 1996.

Answer: Will was born in 1995.

Answer: Uma was born exactly three years before Theo was born.

Answer: Zoe was born exactly one year before Theo was born.

Answer: Will is right-handed.


Question: If Zoe was born before Uma was born, then which one of the following statements must be false?

Answer: No child was born in 1992.

Answer: No child was born in 1995.

Answer: Theo is left-handed.

Answer: Zoe is left-handed.

Answer: Will is left-handed.


Context: Barbara is shopping at a pet store to select fish for her new aquarium from among the following species: J, K, L, M, N, O, and P. For each of the seven species, the store has several fish available. Barbara makes her selection in a manner consistent with the following conditions: If she selects one or more K, then she does not select any O. If she selects one or more M, then she does not select any N. If she selects one or more M, then she selects at least one O. If she selects one or more N, then she selects at least one O. If she selects one or more O, then she selects at least one P. If she selects one or more P, then she selects at least one O. If she selects any O at all, then she selects at least two O.

Question: Which one of the following could be a complete and accurate list of the fish Barbara selects for her aquarium?

Answer: three J, one K, two M

Answer: one J, one K, one M, three O

Answer: one J, one M, two O, one P

Answer: one J, one N, one O, two P

Answer: one M, one N, two O, one P


Question: If Barbara does not select any fish of species P, then it could be true that she selects fish of species

Answer: J and of species K

Answer: J and of species M

Answer: K and of species M

Answer: K and of species N

Answer: L and of species O


Question: If Barbara selects fish of as many species as possible, then she cannot select any fish of which one of the following species?

Answer: K

Answer: L

Answer: M

Answer: N

Answer: P


Question: Which one of the following statements must be false?

Answer: Barbara selects exactly four fish, at least one of which is a J.

Answer: Barbara selects exactly four fish, at least one of which is an L.

Answer: Barbara selects exactly three fish, at least one of which is an M.

Answer: Barbara selects exactly three fish, at least one of which is an O.

Answer: Barbara selects exactly three fish, at least one of which is a P.


Question: If Barbara selects at least one fish for her aquarium, then which one of the following lists the minimum and maximum possible numbers, respectively, of different species of fish that Barbara selects?

Answer: 1, 4

Answer: 1, 5

Answer: 1, 6

Answer: 2, 5

Answer: 2, 6


Context: Charlie makes a soup by adding exactly six kinds of foods—kale, lentils, mushrooms, onions, tomatoes, and zucchini—to a broth, one food at a time. No food is added more than once. The order in which Charlie adds the foods to the broth must be consistent with the following: If the mushrooms are added third, then the lentils are added last. If the zucchini is added first, then the lentils are added at some time before the onions. Neither the tomatoes nor the kale is added fifth. The mushrooms are added at some time before the tomatoes or the kale, but not before both.

Question: Which one of the following could be the order in which the foods are added to the broth?

Answer: kale, mushrooms, onions, lentils, tomatoes, zucchini

Answer: kale, zucchini, mushrooms, tomatoes, lentils, onions

Answer: lentils, mushrooms, zucchini, kale, onions, tomatoes

Answer: zucchini, lentils, kale, mushrooms, onions, tomatoes

Answer: zucchini, tomatoes, onions, mushrooms, lentils, kale


Question: Which one of the following foods CANNOT be added first?

Answer: kale

Answer: lentils

Answer: mushrooms

Answer: onions

Answer: tomatoes


Question: If the lentils are added last, then which one of the following must be true?

Answer: At least one of the foods is added at some time before the zucchini.

Answer: At least two of the foods are added at some time before the kale.

Answer: The mushrooms are added third.

Answer: The zucchini is added third.

Answer: The tomatoes are added fourth.