Exactly six trade representatives negotiate a treaty: Klosnik, Londi, Manley, Neri, Osata, Poirier. There are exactly six chairs evenly spaced around a circular table. The chairs are numbered 1 through 6, with successively numbered chairs next to each other and chair number 1 next to chair number 6. Each chair is occupied by exactly one of the representatives. The following conditions apply: Poirier sits immediately next to Neri. Londi sits immediately next to Manley, Neri, or both. Klosnik does not sit immediately next to Manley. If Osata sits immediately next to Poirier, Osata does not sit immediately next to Manley.

Question: Which one of the following seating arrangements of the six representatives in chairs 1 through 6 would NOT violate the stated conditions?

Klosnik, Poirier, Neri, Manley, Osata, Londi

Klosnik, Londi, Manley, Poirier, Neri, Osata

Klosnik, Londi, Manley, Osata, Poirier, Neri

Klosnik, Osata, Poirier, Neri, Londi, Manley

Klosnik, Neri, Londi, Osata, Manley, Poirier


Question: If Londi sits immediately next to Poirier, which one of the following is a pair of representatives who must sit immediately next to each other?

Klosnik and Osata
Londi and Neri
Londi and Osata
Manley and Neri
Manley and Poirier


Question: If Klosnik sits directly between Londi and Poirier, then Manley must sit directly between

Londi and Neri
Londi and Osata
Neri and Osata
Neri and Poirier
Osata and Poirier


Question: If Neri sits immediately next to Manley, then Klosnik can sit directly between

Londi and Manley
Londi and Poirier
Neri and Osata
Neri and Poirier
Poirier and Osata


Question: If Londi sits immediately next to Manley, then which one of the following is a complete and accurate list of representatives any one of whom could also sit immediately next to Londi?

Klosnik
Klosnik, Neri
Neri, Poirier
Klosnik, Osata, Poirier
Klosnik, Neri, Osata, Poirier


Question: If Londi sits immediately next to Neri, which one of the following statements must be false?

Neri sits directly between Londi and Poirier.

Osata sits directly between Klosnik and Manley.


Question: If Klosnik sits immediately next to Osata, then Londi CANNOT sit directly between

Klosnik and Manley
Klosnik and Neri
Manley and Neri
Manley and Poirier
Neri and Osata


Hannah spends 14 days, exclusive of travel time, in a total of six cities. Each city she visits is in one of three countries—X, Y, or Z. Each of the three countries has many cities. Hannah visits at least one city in each of the three countries. She spends at least two days in each city she visits. She spends only whole days in any city.

Question: If Hannah spends exactly eight days in the cities of country X, then which one of the following CANNOT be true?

She visits exactly two cities in country X.

She visits exactly two cities in country Y.

She visits exactly two cities in country Z.

She visits more cities in country Y than in country Z.

She visits more cities in country Z than in country Y.


Question: If Hannah visits an equal number of cities in each of the countries, what is the greatest total number of days she can spend visiting cities in country X?


Question: If Hannah spends three days in the cities of country Y and seven days in the cities of country Z, then which one of the following must be false?

She visits more cities in country X than in country Y.

She visits exactly two cities in country X.

She visits more cities in country Z than in country X.

She visits exactly two cities in country Z.

She visits exactly three cities in country Z.


Question: If the city of Nomo is in country X, and if Hannah spends as many days as possible in Nomo and as few days as possible in each of the other cities that she visits, then which one of the following must be true?

Hannah cannot visit any other cities in country X.

Hannah can visit four cities in country Y.

Hannah cannot spend more than four days in country Z.

Hannah can visit, at most, a total of four cities in countries Y and Z.


Question: If Hannah visits a combined total of four cities in countries X and Y, what is the greatest total number of days she can spend visiting cities in country Y?


J, K, L, M, N, and O are square ski chalets of the same size, which are positioned in two straight rows as shown below: J K L row 1: ■ ■ ■ row 2: ■ ■ ■ M N O J is directly opposite M; K is directly opposite N; and L is directly opposite O. After a snowstorm, residents shovel a single continuous path that connects all of the chalets and meets the following conditions: The path is composed of five straight segments, each of which directly connects exactly two of the chalets. Each chalet is directly connected by a segment of the path to another chalet. No chalet is directly connected by segments of the path to more than two other chalets. No segment of the path crosses any other segment. One segment of the path directly connects chalets J and N, and another segment directly connects chalets K and L.

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

One segment of the path directly connects chalets M and K.

One segment of the path directly connects chalets M and L.

One segment of the path directly connects chalets M and O.

One segment of the path directly connects chalets J and K and another segment directly connects chalets K and M.

One segment of the path directly connects chalets O and L and another segment directly connects chalets O and N.


Question: If one segment of the path directly connects chalets K and N, then the two chalets in which one of the following pairs must be directly connected to each other by a segment?


Question: If a segment of the path directly connects chalets J and K, then the two chalets in which one of the following pairs must be directly connected to each other by a segment?


Question: If one segment of the path directly connects chalets K and O, then which one of the following statements could be true?

Chalet J is directly connected to chalet M.

Chalet K is directly connected to chalet N.

Chalet L is directly connected to chalet O.

Chalet L is directly connected to exactly two chalets.

Chalet O is directly connected to exactly one chalet.


Question: Which one of the following statements, if true, guarantees that one segment of the path directly connects chalets M and N?

One segment of the path directly connects chalets K and J.

One segment of the path directly connects chalets N and O.

One segment of the path directly connects chalet K and a chalet in row 2.

One segment of the path directly connects chalet L and a chalet in row 2.

One segment of the path directly connects chalet O and a chalet in row 1.


Question: Which one of the following chalets cannot be directly connected by segments of the path to exactly two other chalets?


Question: If no segment of the path directly connects any chalet in row 1 with the chalet in row 2 that is directly opposite it, then each of the following statements must be true EXCEPT:

A segment of the path directly connects chalets M and N.

A segment of the path directly connects chalets N and O.

Chalet L is directly connected to exactly one other chalet.

Chalet N is directly connected to exactly two other chalets.

Chalet O is directly connected to exactly two other chalets.


Eight benches—J, K, L, T, U, X, Y, and Z are arranged along the perimeter of a park as shown below: The following is true: J, K, and L are green; T and U are red; X, Y, and Z are pink. The green benches stand next to one another along the park's perimeter. The pink benches stand next to one another along the park's perimeter. No green bench stands next to a pink bench. The bench on the southeast corner is T. J stands at the center of the park's north side. If T stands next to X, then T does not also stand next to L.

Question: Which one of the following benches could be on the northeast corner of the park?


Question: Each of the following statements must be true EXCEPT:

The bench on the northwest corner is pink.

The bench on the northeast corner is green.

The bench on the southwest corner is pink.

The middle bench on the east side of the park is green.

The middle bench on the west side of the park is pink.


Question: Which one of the following benches must be next to J?


Question: For which one of the following benches are there two and no more than two locations either one of which could be the location the bench occupies?


Question: If Z is directly north of Y, which one of the following statements must be true?

J is directly west of K.
K is directly east of U.
U is directly north of X.
X is directly south of J.
Z is directly south of J.


Question: If Y is in the middle of the west side of the park, then the two benches in which one of the following pairs CANNOT be two of the corner benches?


Question: If Y is farther south than L and farther north than T, then the benches in each of the following pairs must be next to each other EXCEPT


A lake contains exactly five islands—J, K, L, M, O—which are unconnected by bridges. Contractors will build a network of bridges that satisfies the following specifications: Each bridge directly connects exactly two islands with each other, and no two bridges intersect. No more than one bridge directly connects any two islands. No island has more than three bridges that directly connect it with other islands. J, K, and L are each directly connected by bridge with one or both of M and O. J is directly connected by bridge with exactly two islands. K is directly connected by bridge with exactly one island. A bridge directly connects J with O, and a bridge directly connects M with O.

Question: Which one of the following is a complete and accurate list of the islands any one of which could be directly connected by bridge with L ?


Question: Which one of the following could be true about the completed network of bridges?

J is directly connected by bridge both with L and with M.

K is directly connected by bridge both with M and with O.

L is directly connected by bridge both with J and with M.

M is directly connected by bridge with J, with K, and with L.

O is directly connected by bridge with K, with L, and with M.


Question: If a bridge directly connects K with O, then which one of the following could be true?

There are exactly three bridges directly connecting L with other islands.

There are exactly two bridges directly connecting O with other islands.


Question: If a bridge directly connects L with M and a bridge directly connects L with O, then which one of the following must be true?

There are exactly two bridges directly connecting L with other islands.

There are exactly two bridges directly connecting M with other islands.


Question: If no island that is directly connected by bridge with M is also directly connected by bridge with O, then there must be a bridge directly connecting

J with L
J with M
K with O
L with M
L with O


Greenburg has exactly five subway lines: Ll, L2, L3, L4, and L5. Along each of the lines, trains run in both directions, stopping at every station. Ll runs in a loop connecting exactly seven stations, their order being Rincon-Tonka-French-Semplain-Urstine-Quetzal-Park-Rincon in one direction of travel, and the reverse in the other direction. L2 connects Tonka with Semplain, and with no other station. L3 connects Rincon with Urstine, and with no other station. L4 runs from Quetzal through exactly one other station, Greene, to Rincon. L5 connects Quetzal with Tonka, and with no other station.

Question: How many different stations are there that a traveler starting at Rincon could reach by using the subway lines without making any intermediate stops?


Question: In order to go from Greene to Semplain taking the fewest possible subway lines and making the fewest possible stops, a traveler must make a stop at


Question: If L3 is not running and a traveler goes by subway from Urstine to Rincon making the fewest possible stops, which one of the following lists all of the intermediate stations in sequence along one of the routes that the traveler could take?

Quetzal, Tonka
Semplain, French
Semplain, Park
Quetzal, Park, Greene
Semplain, French, Tonka


Question: In order to go by subway from French to Greene, the minimum number of intermediate stops a traveler must make is


Question: If the tracks that directly connect Urstine and Quetzal are blocked in both directions, a traveler going from Semplain to Park and making the fewest possible intermediate stops must pass through

French or Tonka
Greene or Urstine
Quetzal or Tonka
Quetzal or Urstine or both
Rincon or Tonka or both


Question: If a sixth subway line is to be constructed so that all of the stations would have two or more lines reaching them, the stations connected by the new subway line must include at least

French, Greene, and Park
French, Greene, and Quetzal
French, Greene, and Rincon
Park, Tonka, and Urstine
Park, Semplain, and Tonka


Prior to this year's annual promotion review, the staff of a law firm consisted of partners Harrison and Rafael, associate Olivos, and assistants Ganz, Johnson, Lowry, Stefano, Turner, and Wilford. During each annual review, each assistant and associate is considered for promotion to the next higher rank, and at least one person is promoted from each of the two lower ranks. An assistant is promoted to associate when a majority of higherranking staff votes for promotion. An associate is promoted to partner when a majority of partners vote for promotion. Everyone eligible votes on every promotion. No one joins or leaves the firm. Olivos never votes for promoting Ganz, Johnson, or Turner. Rafael never votes for promoting Lowry or Stefano. Harrison never votes for promoting Johnson or Wilford.

Question: Which one of the following could be the distribution of staff resulting from this year's review?

Partner: Harrison, Olivos, Rafael. Associate: Ganz, Johnson, Lowry. Assistance: Stefano, Turner, Wilford

Partner: Harrison, Rafael. Associate: Lowry, Olivos, Stefano. Assistance: Ganz, Johnson, Turner, Wilford

Partner: Harrison, Olivos, Rafael, Stefano. Associate: Ganz, Lowry, Turner, Wilford. Assistance: Johnson

Partner: Harrison, Olivos, Rafael. Assistance: Ganz, Johnson, Lowry, Stefano, Turner, Wilford

Partner: Harrison, Olivos, Rafael. Associate: Ganz, Lowry Stefano, Turner. Assistance: Johnson, Wilford


Question: If Rafael votes for promoting only Ganz, Olivos, and Wilford, and if Harrison votes for promoting only Lowry, Olivos, and Stefano, then which one of the following could be the complete roster of associates resulting from this year's review?

Ganz, Lowry, Wilford
Johnson, Lowry, Stefano
Lowry, Stefano, Turner
Lowry, Stefano, Wilford
Olivos, Turner, Wilford


Question: If Johnson is to be promoted to associate during next year's review, which one of the following is the smallest number of assistants who must be promoted during this year's review?


Question: Which one of the following must be true after next year's review?

Lowry is an assistant.
Wilford is a partner.
There are no assistants.
There are at least two assistants.
There are no more than four assistants.


Question: What is the smallest possible number of associates in the firm immediately after next year's review?


A square parking lot has exactly eight lights—numbered 1 through 8—situated along its perimeter as diagramed below. The lot must always be illuminated in such a way that the following specifications are met: At least one of any three consecutively numbered lights is off. Light 8 is on. Neither light 2 nor light 7 is on when light 1 is on. At least one of the three lights on each side is on. If any side has exactly one of its three lights on, then that light is its center light. Two of the lights on the north side are on.

Question: Which one of the following could be a complete and accurate list of lights that are on together?


Question: Which one of the following lights must be on?


Question: If light 1 is off, which one of the following is a light that must also be off?


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

If light 2 is on, then light 6 is off.
If light 3 is on, then light 2 is on.
If light 4 is on, then light 3 is off.
If light 5 is off, then light 4 is on.
If light 6 is off, then light 1 is on.


Question: If light 5 is on, which one of the following could be true?

Light 1 is off and light 6 is off.
Light 1 is on and light 7 is on.
Light 2 is off and light 4 is on.
Light 2 is off and light 6 is off.
Light 6 is on and light 7 is on.


Question: If light 4 is on, each of the following statements must be true EXCEPT:

Light 1 is on.
Light 2 is on.
Light 5 is off.
Light 6 is on.
Light 7 is off.


Question: Suppose that it is no longer part of the specifications that two lights on the north side be on. If all of the other original specifications remain the same, and if exactly one light on the north side is on, which one of the following statements could be false?

Light 1 is off.
Light 2 is on.
Light 3 is off.
Light 4 is on.
Light 5 is on.


Six cities are located within the numbered areas as follows: Within the six-city area there are exactly four hospitals, two jails, and two universities. These eight institutions are located as follows: No institution is in more than one of the cities. None of the cities contains more than one jail, and none contains more than one university. None of the cities contains both a jail and a university. Each jail is located in a city that contains at least one hospital. The universities are located in two cities that do not share a common boundary. City 3 contains a university, and city 6 contains a jail.

Question: Which one of the following could be true?

City 5 contains a university.
City 6 contains a university.
City 2 contains a jail.
City 3 contains a jail.
City 3 contains a hospital.


Question: Which one of the following could be true?

City 1 contains exactly one hospital.
City 1 contains exactly one university.
City 2 contains exactly one jail.
City 5 contains exactly one university.
City 6 contains exactly one university.


Question: Which one of the following is a complete and accurate list of the cities any one of which could contain the jail that is not in city 6?


Question: If each of the six cities contains at least one of the eight institutions, then which one of the following must be true?

There is a jail in city 1.
There is a hospital in city 2.
There is a hospital in city 3.
There is a hospital in city 4.
There is a jail in city 4.


Question: In which one of the following cities must there be fewer than three hospitals?


Question: If one of the cities contains exactly two hospitals and exactly one university, then which one of the following lists three cities that might, among them, contain no hospital?


In a game, "words" (real or nonsensical) consist of any combination of at least four letters of the English alphabet. Any "sentence" consists of exactly five words and satisfies the following conditions: The five words are written from left to right on a single line in alphabetical order. The sentence is started by any word, and each successive word is formed by applying exactly one of three operations to the word immediately to its left: delete one letter; add one letter; replace one letter with another letter. At most three of the five words begin with the same letter as one another. Except for the leftmost word, each word is formed by a different operation from that which formed the word immediately to its left.

Question: Which one of the following could be a sentence in the word game?

bzeak bleak leak peak pea
crbek creek reek seek sxeek
dteam gleam glean lean mean
feed freed reed seed seeg
food fool fools fopls opls


Question: The last letter of the alphabet that the first word of a sentence in the word game can begin with is


Question: If the first word in a sentence is "blender" and the third word is "slender", then the second word can be


Question: If the first word in a sentence consists of nine letters, then the minimum number of letters that the fourth word can contain is


Question: If "clean" is the first word in a sentence and "learn" is another word in the sentence, then which one of the following is a complete and accurate list of the positions each of which could be the position in which "learn" occurs in the sentence?

second
third
fourth, fifth
second, third, fourth
third, fourth, fifth


Question: If the first word in a sentence consists of four letters, then the maximum number of letters that the fifth word in this sentence could contain is


Four apprentices—Louis, Madelyn, Nora, and Oliver—are initially assigned to projects Q, R, S, and T, respectively. During the year in which they are apprentices, two reassignments of apprentices to projects will be made, each time according to a different one of the following plans, which can be used in any order: Plan 1. The apprentice assigned to project Q switches projects with the apprentice assigned to project S and the apprentice assigned to project R switches projects with the apprentice assigned to project T. Plan 2. The apprentice assigned to project S switches projects with the apprentice assigned to project T. Plan 3. Louis and Madelyn switch projects with each other.

Question: Which one of the following must be true after the second reassignment of apprentices to projects during the year if that reassignment assigns Nora to project T ?

Louis is assigned to project S.
Madelyn is assigned to project R.
Madelyn is assigned to project S.
Oliver is assigned to project R.
Oliver is assigned to project S.


Question: Which one of the following could be true after only one reassignment during the year?

Louis and Nora each remain assigned to the same projects as before.

Nora and Oliver each remain assigned to the same projects as before.


Question: If at some time during the year, Louis is reassigned to project R, which one of the following could have been the assignment of apprentices to the projects immediately before the reassignment?

Q: Louis; R: Madelyn; S: Oliver; T: Nora

Q: Louis; R: Nora; S: Oliver; T: Madelyn

Q: Nora; R: Madelyn; S: Louis; T: Oliver

Q: Nora; R: Oliver; S: Louis; T: Madelyn

Q: Oliver; R: Nora; S: Louis; T: Madelyn


Question: Which one of the following is an acceptable assignment of apprentices to the projects after only one reassignment during the year?

Q: Louis; R: Madelyn; S: Nora; T: Oliver

Q: Madelyn; R: Louis; S: Nora; T: Oliver

Q: Madelyn; R: Oliver; S: Nora; T: Louis

Q: Nora; R: Louis; S: Oliver; T: Madelyn

Q: Nora; R: Madelyn; S: Oliver; T: Louis


Question: If the first reassignment is made according to plan 1, which one of the following must be true?

Louis is assigned to project T as a result of the second reassignment.

Madelyn is assigned to project Q as a result of the second reassignment.

Madelyn is assigned to project T as a result of the second reassignment.

Oliver is assigned to project S as a result of the second reassignment.

Oliver is assigned to project T as a result of the second reassignment.


A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply: The product of an experiment cannot be used in further experiments. Mixing the contents of 1 and 2 produces a red chemical. Mixing the contents of 2 and 3 produces an orange chemical. Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical. Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical.

Question: If the student performs exactly one experiment, which one of the following could be the colors of the chemicals in the resulting three nonempty flasks?

blue, blue, green
blue, orange, orange
blue, orange, red
green, green, red
green, orange, orange


Question: If the student performs exactly two experiments, which one of the following could be the colors of the chemicals in the resulting two nonempty flasks?

blue, blue
blue, orange
blue, red
green, red
orange, orange


Question: If the student performs exactly one experiment and none of the resulting three nonempty flasks contains a red chemical, which one of the following could be the colors of the chemicals in the three flasks?

blue, blue, green
blue, green, green
blue, green, orange
blue, orange, orange
green, green, orange


Question: If the student performs exactly one experiment and exactly one of the resulting three nonempty flasks contains a blue chemical, which one of the following must be the colors of the chemicals in the other two flasks?

both green
both orange
both red
one green and one red
one orange and one red


Question: If the student will perform exactly two experiments and after the first experiment exactly one of the resulting three nonempty flasks contains an orange chemical, then in the second experiment the student could mix together the contents of flasks


Question: If the student performs exactly one experiment and none of the resulting three nonempty flasks contains an orange chemical, then the student must have mixed the contents of

flask 1 with flask 2
flask 1 with flask 4
flask 2 with flask 4
flask 2 with one of the other flasks
flask 4 with one of the other flasks


Question: If the student performs exactly two experiments and exactly one of the resulting two nonempty flasks contains an orange chemical, then it must be true that the contents of the other nonempty flask is

obtained by mixing flasks 1 and 2
obtained by mixing flasks 2 and 4
blue
green
red


The population of a small country is organized into five clans—N, O, P, S, and T. Each year exactly three of the five clans participate in the annual harvest ceremonies. The rules specifying the order of participation of the clans in the ceremonies are as follows: Each clan must participate at least once in any two consecutive years. No clan participates for three consecutive years. Participation takes place in cycles, with each cycle ending when each of the five clans has participated three times. Only then does a new cycle begin. No clan participates more than three times within any cycle.

Question: If the clans participating in the first year of a given cycle are N, O, and P, which one of the following could be the clans participating in the second year of that cycle?


Question: Which one of the following can be true about the clans' participation in the ceremonies?

N participates in the first, second, and third years.

N participates in the second, third, and fourth years.

Both O and S participate in the first and third years.

Both N and S participate in the first, third, and fifth years.

Both S and T participate in the second, third, and fifth years.


Question: Any cycle for the clans' participation in the ceremonies must be completed at the end of exactly how many years?


Question: Which one of the following must be true about the three clans that participate in the ceremonies in the first year?

At most two of them participate together in the third year.

At least two of them participate together in the second year.

All three of them participate together in the fourth year.

All three of them participate together in the fifth year.

None of them participates in the third year.


Question: If, in a particular cycle, N, O, and S participate in the ceremonies in the first year, which one of the following must be true?

N participates in the second and third years.

O participates in the third and fourth years.

N and O both participate in the third year.

P and T both participate in the fifth year.

S and T both participate in the fifth year.


Question: If, in a particular cycle, N, O, and T participate in the first year and if O and P participate in the fourth year, any of the following could be a clan that participates in the third year EXCEPT


Question: If, in a particular cycle, N, O, and S participate in the ceremonies in the first year and O, S, and T participate in the third year, then which one of the following could be the clans that participate in the fifth year?


The country of Zendu contains exactly four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Zendu. Part of R intersects T; part of S also intersects T; R does not intersect S. Area U is completely within R and also completely within T. At noon exactly four planes J, K, L, M—are over Zendu, in a manner consistent with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas.

Question: Which one of the following could be a complete listing of the planes located in the four areas at noon, with each plane listed in every area in which it is located?

R: J, L; S: J, M; T: L; U: L
R: J, L; S: K; T: M; U: none
R: K; S: J; T: L; U: M
R: K, M; S: J, L; T: J; U: none
R: M; S: J, K; T: J, L; U: none


Question: If at noon K is within exactly two of the four areas, then which one of the following CANNOT be true at that time?

J is within area T.
K is within area R.
K is within area T.
L is within area R.
L is within area T.


Question: Which one of the following is a complete and accurate list of those planes any one of which could be within area T at noon?


Question: Which one of the following statements CANNOT be true at noon about the planes?

K is within area T.
K is within area U.
L is within area R.
M is within area R.
M is within area U.


Question: It CANNOT be true that at noon there is at least one plane that is within both area

R and area T
R and area U
S and area T
S and area U
T and area U


Question: If at noon M is within area T, then which one of the following statements CANNOT be true at that time?

J is within area T.
L is within area R.
L is within area S.
K is within exactly two areas.
L is within exactly two areas.


Question: If at noon plane L is within exactly three of the areas, which one of the following could be true at that time?

J is within exactly two of the areas.
J is within exactly three of the areas.
K is within area S.
M is within area R.
M is within area T.


Five experienced plumbers—Frank, Gene, Jill, Kathy, and Mark—and four inexperienced plumbers—Roberta, Sally, Tim, and Vernon—must decide which of them will be assigned to four work teams of exactly two plumbers each. Assignments must meet the following restrictions: Each plumber is assigned to at most one team. At least one plumber on each team must be experienced. Neither Mark nor Roberta nor Vernon can be assigned to a team with Frank. If Tim is assigned to a team, either Gene or Kathy must be assigned to that team. Jill cannot be assigned to a team with Roberta.

Question: If all of the inexperienced plumbers are assigned to teams, and neither Roberta nor Tim nor Vernon is assigned to a team with Gene, then Sally must be assigned to a team with either

Frank or else Gene
Frank or else Mark
Gene or else Mark
Jill or else Kathy
Jill or else Mark


Within a tennis league each of five teams occupies one of five positions, numbered 1 through 5 in order of rank, with number 1 as the highest position. The teams are initially in the order R, J, S, M, L, with R in position 1. Teams change positions only when a lower-positioned team defeats a higher-positioned team. The rules are as follows: Matches are played alternately in odd-position rounds and in even-position rounds. In an odd-position round, teams in positions 3 and 5 play against teams positioned immediately above them. In an even-position round, teams in positions 2 and 4 play against teams positioned immediately above them. When a lower-positioned team defeats a higher-positioned team, the two teams switch positions after the round is completed.

Question: Which one of the following could be the order of teams, from position 1 through position 5 respectively, after exactly one round of even-position matches if no odd-position round has yet been played?

J, R, M, L, S
J, R, S, L, M
R, J, M, L, S
R, J, M, S, L
R, S, J, L, M


Question: If exactly two rounds of matches have been played, beginning with an odd-position round, and if the lower-positioned teams have won every match in those two rounds, then each of the following must be true EXCEPT:

L is one position higher than J.
R is one position higher than L.
S is one position higher than R.
J is in position 4.
M is in position 3.


Question: Which one of the following could be true after exactly two rounds of matches have been played?

J has won two matches.
L has lost two matches.
R has won two matches.
L's only match was played against J.
M played against S in two matches.


Question: If after exactly three rounds of matches M is in position 4, and J and L have won all of their matches, then which one of the following can be true?

J is in position 2.
J is in position 3.
L is in position 2.
R is in position 1.
S is in position 3.


Question: If after exactly three rounds M has won three matches and the rankings of the other four teams relative to each other remain the same, then which one of the following must be in position 3?


Question: If after exactly three rounds the teams, in order from first to fifth position, are R, J, L, S, and M, then which one of the following could be the order, from first to fifth position, of the teams after the second round?

J, R, M, S, L
J, L, S, M, R
R, J, S, L, M
R, L, M, S, J
R, M, L, S, J


A contractor is scheduling construction of seven decks—F, G, H, J, K, L, and M—during a seven-week period: week 1 through week 7. Because of customers' requirements, exactly one deck must be built each week according to the following conditions: G must be built at some time before K is built. L must be built either immediately before or immediately after M is built. F must be built during week 5. J must be built during week 2 or week 6.

Question: Which one of the following is an acceptable construction schedule for the decks, in order from the deck built in week 1 to that built in week 7?

G, K, H, M, F, J, L
H, G, L, M, F, K, J
H, J, G, F, M, L, K
H, M, L, G, F, J, K
K, J, H, G, F, M, L


Question: If G is built at some time after F is built, which one of the following must be true?

G is built during week 7.
H is built during week 1.
J is built during week 6.
L is built during week 3.
M is built during week 1.


Question: Which one of the following is a complete and accurate list of the weeks any one of which could be the week in which K is built?


Question: Which one of the following is a complete and accurate list of decks any one of which could be the deck built in week 3?

K, L, M
F, G, H, K
F, H, K, M
G, H, K, L, M
H, J, K, L, M


Question: If G is built during week 4, then there are exactly how many acceptable orders any one of which could be the order in which the seven decks are built?


Each of five salespeople—F, G, H, I, and J—will present a different one of a company's products—L, M, N, O, and P—at a convention running from Monday through Wednesday. Exactly two products will be presented on Monday, exactly one on Tuesday, and exactly two on Wednesday. The scheduling of presentations is governed by the following conditions: F cannot present a product on the same day as H. Either I or else J must present product N on Tuesday. G must present a product on the day that product O is presented, whether or not G is the salesperson who presents product O.

Question: Which one of the following must be true?

If F presents a product on Monday, then G presents product O.

If I presents a product on Tuesday, then J presents a product on Monday.

If J presents a product on Tuesday, then G presents a product on Monday.

If both F and J present products on Monday, then H presents product O.

If both H and I present products on Wednesday, then product O is presented on Monday.


Question: If salespeople H and I present products on Monday, which one of the following must be true?

F presents product M.
G presents product L.
I presents product N.
Product O is presented on Wednesday.
Product P is presented on Wednesday.


Question: If G presents product P on Wednesday, then any of the following could be true EXCEPT:

H presents product O.
I presents product N.
I presents product O.
F makes a presentation on Monday.
F makes a presentation on Wednesday.


Question: If products M and P are presented on Monday, which one of the following could be true?

G presents product P.
I presents product O.
J presents product L.
F presents a product on Monday.
G presents a product on Monday.


Question: If product O is presented on the same day as product P, which one of the following must be true?

F presents neither product O nor product P.

J presents neither product O nor product P.


The seven members of an academic department are each to be assigned a different room as an office. The department members are professors F and G, lecturers Q, R, and S, and instructors V and W. The available rooms are seven consecutive rooms along one side of a straight hallway numbered sequentially 101 through 107. The assignment must conform to the following conditions: Neither instructor is assigned a room next to a professor's room. Neither professor is assigned room 101 and neither professor is assigned room 107. G is not assigned a room next to R's room. W is not assigned a room next to V's room unless R is also assigned a room next to V's room.

Question: If F and G are assigned rooms that have exactly one room between them, which one of the following is the list of department members each of whom could be assigned to the intervening room?


Question: Which one of the following is a possible assignment of rooms for members R, V, and W?


Question: If R is assigned room 104, which one of the following must be assigned either room 103 or else room 105?


Question: What is the greatest number of rooms that could be between the rooms to which F and G are assigned?


Question: Which one of the following CANNOT be assigned room 104?


Question: If no two faculty members of the same rank are assigned adjacent rooms, which one of the following must be true?

F is assigned either room 103 or else room 104.

Q is assigned either room 102 or else room 106.

R is assigned either room 102 or else room 105.

S is assigned either room 104 or else room 105.

V is assigned either room 101 or else room 107.


Question: If F and G are not assigned rooms that are next to each other, which one of the following CANNOT be assigned room 107?


The coordinator of an exhibition will select at least four and at most six rugs from a group of eight rugs made up of two oval wool rugs, three rectangular wool rugs, one oval silk rug, and two rectangular silk rugs according to the following conditions: At least two oval rugs must be selected. The number of wool rugs selected can be neither less than two nor more than three. If the oval silk rug is selected, at least one rectangular silk rug must be selected.

Question: Which one of the following is an acceptable selection of rugs for the exhibition?

one oval silk rug, one oval wool rug, and two rectangular wool rugs

one oval silk rug, one rectangular wool rug, and two rectangular silk rugs

two oval wool rugs, one rectangular silk rug, and two rectangular wool rugs

two oval wool rugs, one rectangular silk rug, and one rectangular wool rug

two rectangular silk rugs and three rectangular wool rugs


Question: If three wool rugs are selected, then any of the following could be a complete and accurate list of the other rugs selected EXCEPT:

one oval silk rug and one rectangular silk rug

one oval silk rug and two rectangular silk rugs


Question: The rugs selected for the exhibition can include any of the following EXCEPT:

one oval silk rug
two oval wool rugs
three oval rugs
two rectangular wool rugs
three rectangular wool rugs


Question: If only one silk rug is selected for the exhibition, then the other rugs selected must be a group made up of

two oval rugs and three rectangular rugs


Question: If exactly four rugs are selected, then the rugs selected could be

one oval rug and three rectangular wool rugs

two oval rugs and two rectangular wool rugs

three oval rugs and one rectangular silk rug

three oval rugs and one rectangular wool rug

two rectangular silk rugs and two rectangular wool rugs


Question: If all three silk rugs are selected, then each of the following could be a complete and accurate list of the other rugs selected EXCEPT:

one oval wool rug and one rectangular wool rug

one oval wool rug and two rectangular wool rugs

two oval wool rugs and one rectangular wool rug


Question: If exactly six rugs are selected, they must include

exactly one of the oval rugs
the two oval wool rugs
the two rectangular silk rugs
exactly three of the rectangular rugs
all three rectangular wool rugs


A jeweler makes a single strand of beads by threading onto a string in a single direction from a clasp a series of solid-colored beads. Each bead is either green, orange, purple, red, or yellow. The resulting strand satisfies the following specifications: If a purple bead is adjacent to a yellow bead, any bead that immediately follows and any bead that immediately precedes that pair must be red. Any pair of beads adjacent to each other that are the same color as each other must be green. No orange bead can be adjacent to any red bead. Any portion of the strand containing eight consecutive beads must include at least one bead of each color.

Question: If the strand has exactly eight beads, which one of the following is an acceptable order, starting from the clasp, for the eight beads?

green, red, purple, yellow, red, orange, green, purple

orange, yellow, red, red, yellow, purple, red, green

purple, yellow, red, green, green, orange, yellow, orange

red, orange, red, yellow, purple, green, yellow, green

red, yellow, purple, red, green, red, green, green


Question: If an orange bead is the fourth bead from the clasp, which one of the following is a pair that could be the second and third beads, respectively?

green, orange
green, red
purple, purple
yellow, green
yellow, purple


Question: If on an eight-bead strand the second, third, and fourth beads from the clasp are red, green, and yellow, respectively, and the sixth and seventh beads are purple and red, respectively, then which one of the following must be true?

The first bead is purple.
The fifth bead is green.
The fifth bead is orange.
The eighth bead is orange.
The eighth bead is yellow.


Question: If on a six-bead strand the first and second beads from the clasp are purple and yellow, respectively, then the fifth and sixth beads CANNOT be

green and orange, respectively
orange and green, respectively
orange and yellow, respectively
purple and orange, respectively
yellow and purple, respectively


Question: If on a nine-bead strand the first and fourth beads from the clasp are purple, and the second and fifth beads are yellow, which one of the following could be true?

The seventh bead is orange.
The eighth bead is green.
The eighth bead is red.
The ninth bead is red.
The ninth bead is yellow.


Question: If on an eight-bead strand the first, second, third, and fourth beads from the clasp are red, yellow, green, and red, respectively, then the fifth and sixth beads CANNOT be

green and orange, respectively
green and purple, respectively
purple and orange, respectively
purple and yellow, respectively
yellow and orange, respectively


A worker will insert colored light bulbs into a billboard equipped with exactly three light sockets, which are labeled lights 1, 2, and 3. The worker has three green bulbs, three purple bulbs, and three yellow bulbs. Selection of bulbs for the sockets is governed by the following conditions: Whenever light 1 is purple, light 2 must be yellow. Whenever light 2 is green, light 1 must be green. Whenever light 3 is either purple or yellow, light 2 must be purple.

Question: Which one of the following could be an accurate list of the colors of light bulbs selected for lights 1, 2, and 3, respectively?

green, green, yellow
purple, green, green
purple, purple, green
yellow, purple, green
yellow, yellow, yellow


Question: If light 1 is yellow, then any of the following can be true, EXCEPT:

Light 2 is green.
Light 2 is purple.
Light 3 is green.
Light 3 is purple.
Light 3 is yellow.


Question: There is exactly one possible color sequence of the three lights if which one of the following is true?

Light 1 is purple.
Light 2 is purple.
Light 2 is yellow.
Light 3 is purple.
Light 3 is yellow.


Question: If no green bulbs are selected, there are exactly how many possible different color sequences of the three lights?


Question: If no two lights are assigned light bulbs that are the same color as each other, then which one of the following could be true?

Light 1 is green, and light 2 is purple.

Light 1 is green, and light 2 is yellow.

Light 1 is purple, and light 3 is yellow.

Light 1 is yellow, and light 2 is green.

Light 1 is yellow, and light 3 is purple.


During a four-week period, each of seven previously unadvertised products—G, H, J, K, L, M, and O—will be advertised. A different pair of these products will be advertised each week. Exactly one of the products will be a member of two of these four pairs. The following constraints must be observed: J is not advertised during a given week unless H is advertised during the immediately preceding week. The product that is advertised during two of the weeks is advertised during week 4 but is not advertised during week 3. G is not advertised during a given week unless either J or else O is also advertised that week. K is advertised during one of the first two weeks. O is one of the products advertised during week 3.

Question: Which one of the following could be the schedule of advertisements?

week 1: G, J; week 2: K, L; week 3: O, M; week 4: H, L

week l: H, K; week 2: J, G; week 3: O, L; week 4: M, K

week 1: H, K; week 2: J, M; week 3: O, L; week 4: G, M

week 1: H, L; week 2: J, M; week 3: O, G; week 4: K, L

week 1: K, M; week 2: H, J; week 3: O, G; week 4: L, M


Question: Which one of the following is a pair of products that CANNOT be advertised during the same week as each other?


Question: Which one of the following must be advertised during week 2?


Question: Which one of the following CANNOT be the product that is advertised during two of the weeks?


Question: If L is the product that is advertised during two of the weeks, which one of the following is a product that must be advertised during one of the weeks in which L is advertised?


Question: Which one of the following is a product that could be advertised in any of the four weeks?


Question: Which one of the following is a pair of products that could be advertised during the same week as each other?


An upholsterer will do seven jobs—N, O, P, S, T, U, and X—during a given week on Monday through Friday. Each job is done on exactly one of the days, and no two jobs are done concurrently. Each job takes either one half day or an entire day. The following conditions apply: N is done on the same day as S. X is done on Wednesday, and T is done on Friday. S is done earlier than the day on which P is done. U and X are the only jobs that must take an entire day each.

Question: Which one of the following is an acceptable schedule for the seven jobs? Mon. Tues. Wed. Thurs. Fri.

N, S P X O, U T
O N, S X P U
P U X N, S O, T
S N, P X U O, T
U N, S X O P, T


Question: Which one of the following is a complete and accurate list of those jobs each of which CANNOT be done on Tuesday?


Question: If O is done on Thursday, N could be done on

Monday or else on Tuesday, but on no other day

Tuesday or else on Wednesday, but on no other day

Wednesday or else on Thursday, but on no other day


Question: Which one of the following must be true if the upholsterer does two jobs on Thursday and two jobs on Friday?

N is done on Monday.
O is done on Tuesday.
P is done on Friday.
O is done on the same day as P.
O is done on the same day as T.


Question: If P is not done on Friday, which one of the following must be true?

N is done on Monday or else on Thursday.

O is done on Wednesday or else on Thursday.

S is done on Monday or else on Thursday.

O is done on the same day as either P or T.


Question: If O is done on Monday, which one of the following must be true?

N is done on Tuesday.
P is done on Thursday.
P is done on Friday.
S is done on Thursday.
U is done on Friday.


Seven persons—G, H, I, K, L, M, and P—are going rock-climbing together. One person will be the organizer and not a member of any team. The remaining six will form three climbing teams, each consisting of two persons. No person can be on more than one team. The following conditions also apply: M and P cannot be on the same team as each other. If K is on a team, M must also be on that team. If G is on a team, either H or I must also be on that team. If H is on a team, K must be the organizer.

Question: Which one of the following can be a list of the members of the three teams?

Team 1: G, H; Team 2: I, L; Team 3: M, P

Team 1: G, H; Team 2: L, P; Team 3: K, M

Team 1: G, I; Team 2: H, M; Team 3: L, P

Team 1: G, P; Team 2: I, L; Team 3: K, M

Team 1: H, M; Team 2: I, L; Team 3: K, P


Question: Each of the following is a pair of persons who can constitute a team EXCEPT:


Question: Which one of the following can be the organizer, who is not on any team?


Question: If G and I form a team and if H is a member of a team, then H must be on the same team as either


Question: If L and M are on different teams, which one of the following must be true?

H is the organizer.
K is the organizer.
G is on the same team as H.
I is on the same team as M.
L is on the same team as P.


Question: Which one of the following lists three persons each of whom must be on a team and no two of whom can be on the same team as each other?


Question: There are how many different persons any one of whom could be paired with M to form a team?


A train makes five trips around a loop through five stations—P, Q, R, S, and T, in that order—stopping at exactly three of the stations on each trip. The train must conform to the following conditions: The train stops at any given station on exactly three trips, but not on three consecutive trips. The train stops at any given station at least once in any two consecutive trips.

Question: Which one of the following could be the list of stations at which the train stops on the first two trips?

first trip: P, Q, S; second trip: P, Q, R

first trip: P, Q, T; second trip: Q, R, T

first trip: Q, R, S; second trip: P, Q, S

first trip: Q, S, T; second trip: P, R, S

first trip: R, S, T; second trip: P, R, T


Question: If on the first and third trips the train is to stop at Q, R, and S, and at R, S, and T, respectively, which one of the following is the list of stations at which it must stop on the second trip?


Question: The train CANNOT stop at both P and Q on both the

first and third trips
first and fourth trips
second and fourth trips
second and fifth trips
fourth and fifth trips


Question: If the train is to stop at Q, R, and T on the first trip and at Q, R, and S on the fourth trip, then it could be true that the train

stops at Q on the second trip
stops at R on the fifth trip
stops at T on the second trip
does not stop at P on the third trip
does not stop at T on the fifth trip


Question: Suppose that the train's scheduler mistakenly scheduled the train to make the following stops on the first three trips: Q, R, and S on the first trip; P, Q, and S on the second trip; and R, S, and T on the third trip. Which one of the following is a substitution that results in a schedule for those three trips under which the train violates no condition?

on the first trip, P for Q
on the second trip, R for S
on the second trip, T for S
on the third trip, P for R
on the third trip, P for S


On a certain morning, each of six speakers—Feinberg, Guzman, Harrison, Jansen, Kim, and Mackey—will lecture for exactly one hour. Each lecture will take place in either the library or the studio, with exactly one speaker at a time lecturing in each of these two rooms. The lectures must be given in a manner consistent with the following conditions: Exactly three of the lectures are given in each room, the first beginning at precisely 8 A.M. , the second at precisely 9 A.M., and the third at precisely 10 A.M. Feinberg's lecture cannot begin earlier than Guzman's. Neither Jansen's lecture nor Mackey's lecture begins at the same time as Feinberg's. Harrison's lecture begins earlier than Feinberg's. Jansen and Mackey, not necessarily in that order, lecture in the studio.

Question: Which one of the following must be true?

Either Jansen or else Mackey lectures in the studio beginning at 8 A.M.

Either Harrison or else Mackey lectures in the studio beginning at 9 A.M.

Either Guzman or else Harrison lectures in the library beginning at 8 A.M.

Either Feinberg or else Guzman lectures in the library beginning at 9 A.M.

Either Feinberg or else Guzman lectures in the library beginning at 10 A.M.


Question: If both Kim's lecture and Mackey's lecture begin at 9 A.M. , which one of the following could be true?

Guzman's lecture begins at 8 A.M.
Harrison's lecture begins at 10 A.M.
Jansen's lecture begins at 10 A.M.
Guzman lectures in the library.
Harrison lectures in the studio.


Question: If Harrison's lecture begins at 9 A.M. , which one of the following must be true?

Feinberg lectures in the library.
Guzman lectures in the studio.
Harrison lectures in the library.
Kim lectures in the studio.
Mackey lectures in the library.


Question: Each of the following is a pair of speakers whose lectures could begin at the same time as each other EXCEPT:

Feinberg and Guzman
Feinberg and Kim
Guzman and Jansen
Guzman and Kim
Guzman and Mackey


Question: If Feinberg lectures in the library beginning at 9 A.M., which one of the following could be true?

Guzman lectures in the studio beginning at 10 A.M.

Harrison lectures in the studio beginning at 8 A.M.

Jansen lectures in the studio beginning at 10 A.M.

Kim lectures in the studio beginning at 9 A.M.

Mackey lectures in the studio beginning at 9 A.M.


Question: Which one of the following could be a list of the speakers who give their lectures in the studio, in the order in which they give their lectures, from first to third, respectively?

Feinberg, Jansen, Mackey
Guzman, Kim, Mackey
Harrison, Jansen, Kim
Jansen, Mackey, Harrison
Mackey, Feinberg, Jansen


Exactly eight boats—Jewel, Kashmir, Neptune, Ojibwa, Pacific, Spain, Tornado, and Valhalla—arrived at a dock. No boat arrived at the same time as any other boat. The boats arrived in an order consistent with the following conditions: Tornado arrived before Spain but after Jewel. Neptune arrived before Tornado. Kashmir arrived after Jewel but before Spain. Spain arrived before Ojibwa.

Question: If Neptune arrived after Kashmir, which one of the following must be false?

Jewel was the second of the boats to arrive.

Kashmir was the fifth of the boats to arrive.

Neptune was the third of the boats to arrive.

Ojibwa was the sixth of the boats to arrive.

Spain was the seventh of the boats to arrive.


Question: Which one of the following must be true?

At least two of the boats arrived before Neptune.

At least five of the boats arrived before Pacific.

At least four of the boats arrived before Spain.

At least three of the boats arrived before Tornado.

At least two of the boats arrived before Valhalla.


Question: Of the eight boats, what is the maximum number that could have arrived before Jewel?


Question: Of the eight boats, if Valhalla was the second to arrive, then which one of the following CANNOT be true?

Jewel was the third to arrive.
Jewel was the first to arrive.
Kashmir was the third to arrive.
Pacific was the third to arrive.
Tornado was the third to arrive.


Question: If Valhalla arrived before Neptune but after Pacific, which one of the following could be true?

Ojibwa was not the last of the boats to arrive.

Spain was not the seventh of the boats to arrive.


Question: Of the boats, what are, respectively, the minimum number and the maximum number that could have arrived before Kashmir?

one, five
two, five
three, five
one, six
two, six


A park contains at most five of seven kinds of trees—firs, laurels, maples, oaks, pines, spruces, and yews—consistent with the following conditions: If maples are in the park, yews are not. If firs are in the park, pines are not. If yews are not in the park, then either laurels or oaks, but not both, are in the park. If it is not the case that the park contains both laurels and oaks, then it contains firs and spruces.

Question: Which one of the following could be a complete and accurate list of the kinds of trees in the park?

firs, maples
firs, laurels, oaks
firs, laurels, pines, spruces
firs, laurels, spruces, yews
firs, maples, oaks, spruces, yews


Question: If neither maples nor spruces are in the park, then which one of the following could be true?

Exactly four kinds of trees are in the park.

Exactly five kinds of trees are in the park.


Question: Which one of the following could be true?

Neither firs nor laurels are in the park.

Neither laurels, oaks, nor yews are in the park.

Neither laurels nor spruces are in the park.

Neither maples nor yews are in the park.

Neither oaks nor spruces are in the park.


Question: If firs are not in the park, then which one of the following must be true?

Maples are not in the park.
Spruces are not in the park.
Yews are not in the park.
Pines are in the park.
Spruces are in the park.


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

Exactly four kinds of trees are in the park.

Exactly five kinds of trees are in the park.

Neither firs nor maples are in the park.

Neither laurels nor maples are in the park.


Question: Each of the following could be an accurate, partial list of the kinds of trees in the park EXCEPT:

oaks, spruces
oaks, yews
firs, laurels, oaks
firs, maples, oaks
laurels, maples, oaks


Four married couples—Francisco and Gabrielle, Kyoko and Lee, Olivia and Peter, Raymond and Simone—will dine together at the same circular table. Each person will sit in a different one of the eight chairs evenly spaced around the table. The chairs are numbered from 1 through 8 with successively numbered chairs next to each other and chair 1 next to chair 8. Seating arrangements must meet the following conditions: No person sits next to her or his spouse. Simone sits in chair 1 and Raymond sits in chair 4. Neither Peter nor Olivia sits next to Raymond. Neither Kyoko nor Lee sits next to Gabrielle.

Question: Which one of the following could be the list of people sitting in chairs 5 through 8, respectively?

Francisco, Olivia, Gabrielle, Peter
Francisco, Gabrielle, Peter, Lee
Olivia, Gabrielle, Peter, Kyoko
Gabrielle, Lee, Olivia, Kyoko
Lee, Olivia, Francisco, Kyoko


Question: Each of the following could be true EXCEPT:

Peter and Gabrielle sit in chairs 2 and 3, respectively.

Peter and Kyoko sit in chairs 1 and 3, respectively.

Francisco, Kyoko, and Peter sit in chairs 5, 6, and 7, respectively.

Gabrielle, Olivia, and Kyoko sit in chairs 5, 6, and 7, respectively.

Gabrielle, Peter, and Lee sit in chairs 5, 6, and 7, respectively.


Question: If Francisco sits in chair 2 and Olivia sits next to Simone, Gabrielle must sit next to which one of the following persons?


Question: If neither Gabrielle nor Lee sits next to Raymond, which one of the following must be true?

Francisco sits next to Raymond.
Olivia sits next to Simone.
Francisco sits in chair 3.
Olivia sits in chair 6.
Olivia sits in chair 7.


Question: If Lee sits in chair 2, which one of the following must be true?

Peter sits next to Gabrielle.
Kyoko sits next to Simone.
Francisco sits next to Lee.
Gabrielle sits in chair 5.
Olivia sits in chair 6.


Question: If both Francisco and Gabrielle sit next to Raymond, which one of the following is a complete and accurate list of people any one of whom could sit next to Olivia?

Francisco, Gabrielle, Kyoko
Lee, Simone, Kyoko
Lee, Gabrielle, Kyoko
Francisco, Lee, Gabrielle, Kyoko
Lee, Simone, Gabrielle, Kyoko


Zeno's Unfinished Furniture sells exactly five types of furniture—footstools, hutches, sideboards, tables, and vanities. Irene buys just four items, each of a different type, and each made entirely of one kind of wood—maple, oak, pine, or rosewood. The following conditions govern Irene's purchases: Any vanity she buys is maple. Any rosewood item she buys is a sideboard. If she buys a vanity, she does not buy a footstool. If Irene buys a footstool, she also buys a table made of the same wood. Irene does not buy an oak table. Exactly two of the items she buys are made of the same kind of wood as each other.

Question: Which one of the following could be an accurate list of the items Irene buys?

Maple footstool, maple hutch, rosewood sideboard, maple table

oak hutch, rosewood sideboard, pine table, oak vanity

rosewood hutch, maple sideboard, oak table, maple vanity

pine footstool, rosewood sideboard, pine table, maple vanity

maple footstool, pine hutch, oak sideboard, maple table


Question: If Irene buys one item made of rosewood and two items made of maple, then which one of the following pairs could be two of the items she buys?

a rosewood sideboard and an oak footstool


Question: Which one of the following is a complete and accurate list of all the woods any footstool that Irene buys could be made of?

maple, oak
maple, pine
maple, rosewood
maple, oak, pine
maple, oak, pine, rosewood


Question: Suppose Irene buys a footstool. Then which one of the following is a complete and accurate list of items any one of which she could buy in maple?

footstool, hutch, sideboard, table, vanity


Question: Which one of the following CANNOT be the two items Irene buys that are made of the same wood as each other?

footstool, hutch
hutch, sideboard
hutch, table
sideboard, vanity
table, vanity


Question: If Irene does not buy an item made of maple, then each of the following must be true EXCEPT:

Irene buys exactly one item made of oak.

Irene buys exactly two items made of pine.


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?

five unsliced oatmeal loaves, one sliced rye loaf

five unsliced oatmeal loaves, one unsliced wheat loaf

four unsliced oatmeal loaves, two unsliced rye loaves

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:

three oatmeal loaves
three oatmeal loaves, one rye loaf
two oatmeal loaves, two rye loaves
two oatmeal loaves, three rye loaves
one oatmeal loaf, one rye loaf


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

The only unsliced loaves are oatmeal loaves.

The only unsliced loaves are rye loaves.

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

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?

No more than four oatmeal loaves are sliced.

No more than four wheat loaves are sliced.


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

one sliced rye loaf and one unsliced rye loaf

one sliced oatmeal loaf and one unsliced oatmeal loaf


Each nonstop flight offered by Zephyr Airlines departs from one and arrives at another of five cities: Honolulu, Montreal, Philadelphia, Toronto, and Vancouver. Any two cities are said to be connected with each other if Zephyr offers nonstop flights between them. Each city is connected with at least one other city. The following conditions govern Zephyr's nonstop flights: Montreal is connected with exactly one other city. Honolulu is not connected with Toronto. Any city that is connected with Honolulu is also connected with Toronto. If Philadelphia is connected with Toronto, then Philadelphia is not connected with Vancouver.

Question: Which one of the following could be a complete and accurate list of Zephyr Airlines' connected cities?

Honolulu and Vancouver; Montreal and Toronto; Philadelphia and Vancouver; Toronto and Vancouver

Honolulu and Vancouver; Montreal and Philadelphia; Montreal and Toronto; Philadelphia and Toronto; Toronto and Vancouver

Honolulu and Philadelphia; Honolulu and Montreal; Philadelphia and Toronto; Toronto and Vancouver

Honolulu and Philadelphia; Montreal and Toronto; Philadelphia and Toronto; Philadelphia and Vancouver; Toronto and Vancouver

Honolulu and Philadelphia; Honolulu and Toronto; Montreal and Philadelphia; Philadelphia and Vancouver


Question: If exactly three cities are each connected with Philadelphia, then which one of the following could be a pair of connected cities?

Honolulu and Montreal
Honolulu and Vancouver
Montreal and Toronto
Montreal and Vancouver
Philadelphia and Vancouver


Question: Which one of the following is a pair of cities that CANNOT be connected?

Honolulu and Montreal
Honolulu and Philadelphia
Montreal and Philadelphia
Montreal and Vancouver
Philadelphia and Toronto


Question: Which one of the following could be true?

Montreal and Philadelphia are connected with each other, but neither is connected with any other city.

Montreal and Toronto are connected with each other, but neither is connected with any other city.

Philadelphia and Toronto are connected with each other, but neither is connected with any other city.

Philadelphia and Vancouver are connected with each other, but neither is connected with any other city.

Toronto and Vancouver are connected with each other, but neither is connected with any other city.


Question: If Toronto is the only city that is connected with Philadelphia, then which one of the following could be true?

Exactly one city is connected with Toronto.

Exactly one city is connected with Vancouver.

Exactly two cities are each connected with Honolulu.

Exactly two cities are each connected with Toronto.

Exactly four cities are each connected with Toronto.


Question: At most how many pairs of cities could be connected?


Question: If four of the cities are each connected with the remaining city, then the cities in which one of the following pairs must be connected with each other?

Honolulu and Montreal
Honolulu and Philadelphia
Honolulu and Vancouver
Montreal and Philadelphia
Montreal and Toronto


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

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

car 1: Faith (driver), Hannah, and Juan car 2: Gus (driver), Kenneth, and Lisa

car 1: Faith (driver), Hannah, and Kenneth car 2: Lisa (driver), Gus, and Juan

car 1: Faith (driver), Juan, Kenneth, and Lisa car 2: Gus (driver) and Hannah

car 1: Faith (driver) and Juan car 2: Kenneth (driver), Gus, Hannah, and Lisa

car 1: Gus (driver), Hannah, and Lisa car 2: Juan (driver), Faith, and Kenneth


Question: The two workers who drive the cars CANNOT be

Faith and Gus
Faith and Kenneth
Faith and Lisa
Gus and Kenneth
Kenneth and Lisa


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

Faith travels in the same car as Kenneth.


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


Question: Which one of the following CANNOT be true?

Gus is the only person other than the driver in one of the cars.

Hannah is the only person other than the driver in one of the cars.

Juan is the only person other than the driver in one of the cars.

Kenneth is the only person other than the driver in one of the cars.

Lisa is the only person other than the driver in one of the cars.


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

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

figurine, headdress, jar, necklace, plaque, tureen

figurine, jar, plaque, headdress, tureen, necklace

figurine, necklace, plaque, headdress, jar, tureen

necklace, jar, figurine, headdress, plaque, tureen

plaque, tureen, figurine, necklace, jar, headdress


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


Question: Which one of the following artifacts CANNOT be fourth?


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


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


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

The tureen is older than the headdress but not as old as the figurine.

The figurine and the necklace are both older than the tureen.

The necklace is older than the tureen if and only if the jar is.

All of the artifacts except the headdress and the plaque must be older than the tureen.

The plaque is older than the necklace if and only if the plaque is older than the tureen.


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

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

Uzoma, Ramirez, Quinn, Terrell
Terrell, Smith, Ramirez, Uzoma
Smith, Ramirez, Terrell, Quinn
Ramirez, Uzoma, Smith, Terrell
Quinn, Terrell, Smith, Ramirez


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


Question: Which one of the following CANNOT be true?

Ramirez runs in the race immediately before the race in which Smith runs.

Smith runs in the race immediately before the race in which Quinn runs.

Smith runs in the race immediately before the race in which Terrell runs.

Terrell runs in the race immediately before the race in which Ramirez runs.

Uzoma runs in the race immediately before the race in which Terrell runs.


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

Quinn does not run in the track meet.
Smith does not run in the track meet.
Quinn runs in the second race.
Terrell runs in the second race.
Ramirez runs in the fourth race.


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


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

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

Farnham, Griseldi, Khan, Moreau, Juarez, Lightfoot, Heany

Heany, Lightfoot, Farnham, Moreau, Juarez, Griseldi, Khan

Juarez, Heany, Lightfoot, Farnham, Moreau, Griseldi, Khan

Lightfoot, Moreau, Farnham, Juarez, Griseldi, Khan, Heany

Moreau, Lightfoot, Heany, Juarez, Farnham, Griseldi, Khan


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


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

Moreau's session is on the 1st.
Khan's session is on the 5th.
Heany's session is on the 6th.
Griseldi's session is on the 5th.
Farnham's session is on the 2nd.


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


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

Farnham's session is on the 3rd.
Heany's session is on the 7th.
Juarez's session is on the 4th.
Lightfoot's session is on the 1st.
Moreau's session is on the 2nd.


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


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

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

gas, water, power, telephone, landscaping, satellite

power, water, landscaping, gas, satellite, telephone

telephone, power, landscaping, gas, water, satellite

telephone, water, power, landscaping, gas, satellite

water, telephone, power, gas, satellite, landscaping


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

The gas appointment is scheduled for the fifth day.

The power appointment is scheduled for the third day.

The satellite appointment is scheduled for the sixth day.

The telephone appointment is scheduled for the first day.

The water appointment is scheduled for the second day.


Question: Which one of the following must be true?

The landscaping appointment is scheduled for an earlier day than the telephone appointment.

The power appointment is scheduled for an earlier day than the landscaping appointment.

The telephone appointment is scheduled for an earlier day than the gas appointment.

The telephone appointment is scheduled for an earlier day than the water appointment.

The water appointment is scheduled for an earlier day than the gas appointment.


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

gas, satellite, landscaping
landscaping, satellite, gas
power, satellite, gas
telephone, satellite, gas
water, gas, landscaping


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

The gas appointment is scheduled for the fifth day.

The landscaping appointment is scheduled for the sixth day.

The power appointment is scheduled for the third day.

The telephone appointment is scheduled for the fourth day.

The water appointment is scheduled for the second day.


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

The telephone appointment must be scheduled for an earlier day than the gas appointment or the satellite appointment, or both.

The telephone appointment must be scheduled for the day immediately before either the gas appointment or the satellite appointment.

The telephone appointment must be scheduled for an earlier day than the landscaping appointment.

If the telephone appointment is not scheduled for the first day, it must be scheduled for the day immediately before the gas appointment.

Either the gas appointment or the satellite appointment must be scheduled for the sixth day.


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

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

window 1: green, purple, rose, and orange window 2: rose and yellow window 3: green and orange

window 1: green, purple, and rose window 2: green, rose, and orange window 3: purple and yellow

window 1: green, purple, and rose window 2: green, purple, and orange window 3: purple, rose, and yellow

window 1: green, purple, and orange window 2: rose, orange, and yellow window 3: purple and rose

window 1: green, purple, and orange window 2: purple, rose, and yellow window 3: purple and orange


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

green and orange
green and purple
green and rose
purple and orange
rose and orange


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

rose and yellow
orange and rose
orange and purple
green and rose
green and orange


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

green, orange, and rose
green, orange, and purple
orange and rose
orange and purple
green and orange


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

orange and purple
green, purple, and rose
green and purple
green and orange
green, orange, and rose


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

green glass
orange glass
purple glass
rose glass
yellow glass


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

green and purple
green, purple, and orange
green and orange
purple and orange
purple, rose, and yellow


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

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

Feedback: Rivera, Spivey Goal Sharing: Quigley, Tran Handling People: None Information Overload: Quigley, Rivera Leadership: Spivey, Tran

Feedback: Rivera, Spivey Goal Sharing: Quigley, Tran Handling People: Rivera, Tran Information Overload: Quigley Leadership: Spivey

Feedback: Rivera, Spivey Goal Sharing: Quigley, Tran Handling People: Tran Information Overload: Quigley, Rivera Leadership: Spivey

Feedback: Rivera, Spivey Goal Sharing: Tran Handling People: Tran Information Overload: Quigley, Rivera Leadership: Quigley, Spivey

Feedback: Spivey Goal Sharing: Quigley, Tran Handling People: Spivey Information Overload: Quigley, Rivera Leadership: Rivera, Tran


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

Rivera attends Feedback.
Rivera attends Leadership.
Spivey attends Information Overload.
Tran attends Goal Sharing.
Tran attends Information Overload.


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

Feedback, Information Overload, Leadership

Feedback, Goal Sharing, Information Overload


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

Rivera attends Feedback.
Rivera attends Information Overload.
Spivey attends Feedback.
Spivey attends Handling People.
Tran attends Goal Sharing.


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

Quigley attends Leadership.
Rivera attends Feedback.
Spivey attends Feedback.
Tran attends Goal Sharing.
Tran attends Handling People.


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

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

Ramirez, Sanderson, Tannenbaum, Mangione, Ujemori, Wong

Sanderson, Tannenbaum, Ujemori, Ramirez, Wong, Mangione

Sanderson, Ujemori, Tannenbaum, Wong, Ramirez, Mangione

Tannenbaum, Mangione, Ujemori, Sanderson, Ramirez, Wong

Wong, Ramirez, Sanderson, Tannenbaum, Mangione, Ujemori


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

Ramirez testifies second.
Wong testifies third.
Sanderson testifies fourth.
Ujemori testifies fifth.
Mangione testifies sixth.


Question: If Sanderson testifies fifth, then Ujemori must testify


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

Mangione, Tannenbaum
Ramirez, Sanderson
Sanderson, Ujemori
Tannenbaum, Ramirez
Ujemori, Wong


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

Sanderson, Ujemori
Tannenbaum, Mangione
Tannenbaum, Sanderson
Ujemori, Tannenbaum
Ujemori, Wong


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

Question: Which one of the following CANNOT be true?

Fiesta is released second.
Glaciers is released third.
Hurricanes is released fourth.
Kangaroos is released fourth.
Kangaroos is released fifth.


Question: Which one of the following must be true?

Fiesta is released earlier than Hurricanes.

Kangaroos is released earlier than Glaciers.

Lovebird is released earlier than Hurricanes.


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

Glaciers is released fourth.
Jets is released third.
Kangaroos is released second.
Lovebird is released third.
Lovebird is released fifth.


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

Hurricanes is released earlier than Lovebird.


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

Only Kangaroos can be released earlier than Fiesta.

Kangaroos must be released earlier than Lovebird.

Fiesta must be released either first or second.

Fiesta must be released earlier than both Kangaroos and Lovebird.

Either Fiesta or Kangaroos must be released first.


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

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

Rao: Hong Smith: Farrell, Lopez, Madsen Tipton: Kent Ullman: Grant, Inman

Rao: Inman Smith: Hong, Lopez, Madsen Tipton: Kent Ullman: Farrell, Grant

Rao: Madsen Smith: Farrell, Lopez Tipton: Kent Ullman: Grant, Hong, Inman

Rao: Farrell, Lopez Smith: Hong, Kent, Madsen Tipton: Inman Ullman: Grant

Rao: Farrell, Grant, Lopez Smith: Hong, Madsen Tipton: Kent Ullman: Inman


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

Farrells application is evaluated by Rao.

Inmans application is evaluated by Smith.

Lopezs application is evaluated by Ullman.

Madsens application is evaluated by Tipton.


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

Exactly one of the applications is evaluated by Rao.

Exactly one of the applications is evaluated by Ullman.

Farrells application is evaluated by Tipton.

Inmans application is evaluated by Smith.

Lopezs application is evaluated by Smith.


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

Madsens application is evaluated by Tipton.

Lopezs application is evaluated by Smith.

Kents application is evaluated by Tipton.

Inmans application is evaluated by Smith.

Hongs application is evaluated by Smith.


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

Hongs application is evaluated by Ullman.

Kents application is evaluated by Tipton.

Lopezs application is evaluated by Ullman.

Madsens application is evaluated by Smith.

Madsens application is evaluated by Ullman.


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


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

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

F, N, T, O, R, K; with only T and R summarized

F, T, N, O, K, R; with only N and K summarized

N, F, T, O, K, R; with only T, O, and R summarized

N, T, F, O, K, R; with only T and O summarized

N, T, O, F, K, R; with only T and R summarized


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

The third book discussed is not summarized.


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

F is the first book discussed.
K is the sixth book discussed.
F is summarized.
K is not summarized.
N is not summarized.


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

K is summarized
O is summarized
R is summarized
F and T summarized
N is not summarized


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

T is discussed third, and the last two books discussed are K and R, not necessarily in that order.

T is discussed earlier than F, and the last two books discussed are K and R, not necessarily in that order.

K and R are among the last three books discussed, and F is among the first three books discussed.

K and R are discussed in consecutive weeks, not necessarily in that order, and O is discussed fourth.

K and R are discussed in consecutive weeks, not necessarily in that order, and F is discussed third.


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

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

Morisot, Turner, Renoir, Vuillard, Whistler, Sisley, Pissarro

Pissarro, Sisley, Renoir, Vuillard, Morisot, Whistler, Turner

Renoir, Turner, Morisot, Vuillard, Whistler, Sisley, Pissarro

Sisley, Turner, Pissarro, Vuillard, Renoir, Whistler, Morisot

Turner, Vuillard, Pissarro, Sisley, Renoir, Whistler, Morisot


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


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

The Morisot is in the fourth position.
The Renoir is in the second position.
The Sisley is in the sixth position.
The Turner is in the first position.
The Vuillard is in the third position.


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

the Morisot
the Renoir
the Sisley
the Turner
the Whistler


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

The Pissarro is in the fifth position.
The Sisley is in the second position.
The Turner is in the third position.
The Vuillard is in the fourth position.
The Whistler is in the sixth position.


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

The Morisot is in the seventh position.
The Pissarro is in the first position.
The Renoir is in the fourth position.
The Turner is in the second position.
The Vuillard is in the third position.


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

the Pissarro and the Sisley
the Renoir and the Whistler
the Turner and the Vuillard
the Vuillard and the Turner
the Whistler and the Renoir


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

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

first segment: international, national, sports second segment: traffic, weather

first segment: national, international, sports second segment: weather, traffic

first segment: national, international, weather second segment: sports, traffic

first segment: national, weather, international second segment: traffic, sports

first segment: traffic, weather, sports second segment: national, international


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

The national report is the first report in the first segment.

The international report is the second report in the first segment.

The weather report is the second report in the first segment.

The national report is the first report in the second segment.

The sports report is the last report in the second segment.


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


Question: Which one of the following CANNOT be true?

The international report is the first report in the first segment.

The national report is the first report in the first segment.

The national report is the first report in the second segment.

The weather report is the first report in the first segment.

The weather report is the last report in the second segment.


Question: The order of the reports is fully determined if which one of the following is true?

The international report is the last report in the first segment.

The national report is the first report in the first segment.

The national report is the first report in the second segment.

The sports report is the last report in the second segment.

The weather report is the last report in the first segment.


Question: If the traffic report is the first report in the first segment, then which one of the following could be true?

The international report is the first report in the second segment.

The national report is the second report in the first segment.

The weather report is the second report in the first segment.

The weather report is the first report in the second segment.

The weather report is the last report in the second segment.


On a single day, a realtor will show a client five houses, exactly one house in each of five neighborhoods—Quarry, Riverton, Shelburne, Townsend, and Valencia. Each house will be shown to the client exactly once. The order in which the houses are shown is subject to the following constraints: The house in Riverton must be shown either first or second. The house in Townsend must be shown either first or fifth. The third house shown must be the house in Quarry or the house in Valencia. The house in Quarry cannot be shown either immediately before or immediately after the house in Shelburne.

Question: If the house in Quarry is shown fourth, which one of the following must be true?

The house in Riverton is shown first.
The house in Riverton is shown second.
The house in Shelburne is shown second.
The house in Townsend is shown first.
The house in Valencia is shown third.


Question: The order in which the houses are shown is fully determined if which one of the following is true?

The house in Quarry is shown third.
The house in Riverton is shown first.
The house in Shelburne is shown second.
The house in Townsend is shown fifth.
The house in Valencia is shown fourth.


Question: If the house in Shelburne is shown earlier than the house in Quarry, which one of the following must be true?

The house in Quarry is shown fourth.
The house in Riverton is shown second.
The house in Shelburne is shown first.
The house in Townsend is shown fifth.
The house in Valencia is shown third.


Question: Which one of the following could be true?

The house in Quarry is shown first.
The house in Quarry is shown fifth.
The house in Valencia is shown first.
The house in Valencia is shown second.
The house in Valencia is shown fifth.


Question: If the house in Valencia is shown third, which one of the following must be true?

The house in Quarry is shown fourth.
The house in Riverton is shown second.
The house in Shelburne is shown first.
The house in Shelburne is shown fourth.
The house in Townsend is shown fifth.