The eight partners of a law firm are Gregg, Hodges, Ivan, James, King, MacNeil, Nader, and Owens. In each of the years 1961 through 1968, exactly one of the partners joined the firm. Hodges joined the firm before Nader. King joined the firm before James. Nader and James joined the firm before Gregg. Nader joined the firm before Owens. James joined the firm before MacNeil. Gregg joined the firm before Ivan.

Question: Which one of the following CANNOT be true?

Hodges joined the law firm in 1961.
Hodges joined the law firm in 1963.
Gregg joined the law firm in 1964.
MacNeil joined the law firm in 1964.
Owens joined the law firm in 1964.


Question: If James joined the firm in 1962, which one of the following CANNOT be true?

Hodges joined the firm in 1963.
MacNeil joined the firm in 1963.
Hodges joined the firm in 1964.
Nader joined the firm in 1964.
Owens joined the firm in 1964.


Question: Of the following, which one is the latest year in which James could have joined the firm?


Question: If Owens joined the firm in 1965 and MacNeil joined it in 1967, one can determine the years in which exactly how many of the other partners joined the firm?


Question: Assume that Owens joined the law firm before MacNeil. Of the following, which one is the earliest year in which MacNeil could have joined it?


The Mammoth Corporation has just completed hiring nine new workers: Brandt, Calva, Duvall, Eberle, Fu, Garcia, Haga, Irving, and Jessup. Fu and Irving were hired on the same day as each other, and no one else was hired that day. Calva and Garcia were hired on the same day as each other, and no one else was hired that day. On each of the other days of hiring, exactly one worker was hired. Eberle was hired before Brandt. Haga was hired before Duvall. Duvall was hired after Irving but before Eberle. Garcia was hired after both Jessup and Brandt. Brandt was hired before Jessup.

Question: Who were the last two workers to be hired?

Eberle and Jessup
Brandt and Garcia
Brandt and Calva
Garcia and Calva
Jessup and Brandt


Question: Who was hired on the fourth day of hiring?


Question: Exactly how many workers were hired before Jessup?


Question: Which one of the following must be true?

Duvall was the first worker to be hired.

Haga and Fu were the first two workers to be hired.

Either Haga was the first worker to be hired or Fu and Irving were the first two workers to be hired.


Question: If Eberle was hired on a Monday, what is the earliest day on which Garcia could have been hired?

Monday Tuesday Wednesday Thursday Friday


Exactly six dogs—P, Q, R, S, T, and U—are entered in a dog show. The judge of the show awards exactly four ribbons, one for each of first, second, third, and fourth places, to four of the dogs. The information that follows is all that is available about the six dogs: Each dog is either a greyhound or a labrador, but not both. Two of the six dogs are female and four are male. The judge awards ribbons to both female dogs, exactly one of which is a labrador. Exactly one labrador wins a ribbon. Dogs P and R place ahead of dog S, and dog S places ahead of dogs Q and T. Dogs P and R are greyhounds. Dogs S and U are labradors.

Question: Which one of the following is a complete and accurate list of the dogs that can be greyhounds?


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

A female greyhound wins the second place ribbon.

A female labrador wins the second place ribbon.

A female labrador wins the third place ribbon.

A male greyhound wins the fourth place ribbon.

A female greyhound wins the fourth place ribbon.


Question: Which one of the following dogs must be male?


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

Dog P places ahead of dog R.
Dog P places ahead of dog T.
Dog R places ahead of dog U.
Dog R places ahead of dog T.
Dog S places ahead of dog U.


Question: If dog Q is female, which one of the following statements can be false?

Dog P is male.
Dog R is male.
Dog Q wins the fourth place ribbon.
Dog Q is a greyhound.
Dog T is a greyhound.


Question: If dog T wins the fourth place ribbon, then which one of the following statements must be true?

Dog P is male.
Dog Q is male.
Dog T is male.
Dog Q is a labrador.
Dog T is a labrador.


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

Dog P does not win a ribbon.
Dog R does not win a ribbon.
Dog S does not win a ribbon.
Dog T wins a ribbon.
Dog U wins a ribbon.


There are exactly seven houses on a street. Each house is occupied by exactly one of seven families: the Kahns, Lowes, Muirs, Newmans, Owens, Piatts, Rutans. All the houses are on the same side of the street, which runs from west to east. The Rutans do not live in the first or the last house on the street. The Kahns live in the fourth house from the west end of the street. The Muirs live next to the Kahns. The Piatts live east of both the Kahns and the Muirs but west of the Lowes.

Question: Which one of the following families could live in the house that is the farthest east?

the Kahns
the Muirs
the Newmans
the Piatts
the Rutans


Question: Which one of the following families CANNOT live next to the Kahns?

the Lowes
the Newmans
the Owens
the Piatts
the Rutans


Question: If the Muirs live west of the Kahns, then the Rutans CANNOT live next to both

the Kahns and the Piatts
the Lowes and the Piatts
the Muirs and the Piatts
the Muirs and the Owens
the Muirs and the Newmans


Question: If the Newmans live immediately west of the Kahns, which one of the following statements must be false?

The Owens live next to the Newmans.
The Owens live next to the Rutans.
The Piatts live next to the Lowes.
The Piatts live next to the Muirs.
The Rutans live next to the Newmans.


Question: If the Owens live east of the Muirs, which one of the following statements must be true?

The Kahns live east of the Muirs.
The Kahns live west of the Rutans.
The Owens live west of the Lowes.
The Owens live east of the Piatts.
The Owens live west of the Piatts.


Question: If the Owens live east of the Kahns, which one of the following pairs of families must live next to each other?

the Kahns and the Piatts
the Lowes and the Owens
the Muirs and the Newmans
the Newmans and the Rutans
the Owens and the Piatts


A law firm has exactly nine partners: Fox, Glassen, Hae, Inman, Jacoby, Kohn, Lopez, Malloy, and Nassar. Kohn's salary is greater than both Inman's and Lopez's. Lopez's salary is greater than Nassar's. Inman's salary is greater than Fox's. Fox's salary is greater than Malloy's. Malloy's salary is greater than Glassen's. Glassen's salary is greater than Jacoby's. Jacoby's salary is greater than Hae's.

Question: Which one of the following partners cannot have the third highest salary?


Question: If Malloy and Nassar earn the same salary, at least how many of the partners must have lower salaries than Lopez?


Question: The salary rankings of each of the nine partners could be completely determined if which one of the following statements were true?

Nassar's salary is greater than Inman's.

Nassar's salary is greater than Malloy's.


Question: If Nassar's salary is the same as that of one other partner of the firm, which one of the following must be false?

Inman's salary is less than Lopez's.
Jacoby's salary is less than Lopez's.
Lopez's salary is less than Fox's.
Lopez's salary is less than Hae's.
Nassar's salary is less than Glassen's.


Question: What is the minimum number of different salaries earned by the nine partners of the firm?


Question: Assume that the partners of the firm are ranked according to their salaries, from first (highest) to ninth (lowest), and that no two salaries are the same. Which one of the following is a complete and accurate list of Glassen's possible ranks?

fifth
fifth, sixth
fifth, seventh
fifth, sixth, seventh
fifth, sixth, seventh, eighth


A committee ranks five towns—Palmdale, Quietville, Riverdale, Seaside, Tidetown—from first (best) to fifth (worst) on each of three criteria: climate, location, friendliness. For each of the three criteria, none of the five towns receives the same ranking as any other town does. In climate, Tidetown is ranked third, and Seaside fourth. In location, Quietville is ranked second, Riverdale third, Palmdale fourth. In friendliness, Tidetown's ranking is better than Palmdale's, Quietville is ranked fourth and Seaside fifth. Riverdale receives a better ranking in climate than in friendliness. Quietville's three ranking are all different from each other.

Question: Which of the following is a complete and accurate list of the rankings any one of which could be the ranking on climate given to Riverdale?

first
first, second
first, fifth
second, fifth
first, second, fifth


Question: Which of the following is a town that CANNOT be ranked fifth on any one of the three criteria?

Palmdale Quietville Riverdale Seaside Tidetown


Question: Which of the following could be true?

Palmdale is ranked first in both climate and friendliness.

Quietville is ranked second in both climate and location.

Riverdale is ranked first in climate and third in both location and friendliness.

Seaside is ranked fifth in friendliness and fourth in both climate and location.

Tidetown is ranked third in both climate and friendliness.


Question: If Quietville is ranked first in climate, then it must be true that

Palmdale is ranked third in friendliness

Riverdale is ranked second in friendliness

Riverdale is ranked third in friendliness


Question: If Palmdale is ranked second in climate, then which one of the following can be true?

Palmdale is ranked second in friendliness.

Riverdale is ranked first in friendliness.

Tidetown is ranked third in friendliness.


Question: If Tidetown is ranked first in location and Riverdale is ranked second in friendliness, then it is possible to deduce with certainty all three rankings for exactly how many of the towns?


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

Riverdale is ranked third in friendliness.

Tidetown is ranked second in friendliness.


A soft drink manufacturer surveyed consumer preferences for exactly seven proposed names for its new soda: Jazz, Kola, Luck, Mist, Nipi, Oboy, and Ping. The manufacturer ranked the seven names according to the number of votes they received. The name that received the most votes was ranked first. Every name received a different number of votes. Some of the survey results are as follows: Jazz received more votes than Oboy. Oboy received more votes than Kola. Kola received more votes than Mist. Nipi did not receive the fewest votes. Ping received fewer votes than Luck but more votes than Nipi and more votes than Oboy.

Question: Which one of the following could be an accurate list of the seven names in rank order from first through seventh?

Jazz, Luck, Ping, Nipi, Kola, Oboy, Mist

Jazz, Luck, Ping, Oboy, Kola, Mist, Nipi

Luck, Ping, Jazz, Nipi, Oboy, Kola, Mist

Luck, Ping, Nipi, Oboy, Jazz, Kola, Mist

Ping, Luck, Jazz, Oboy, Nipi, Kola, Mist


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

Jazz received more votes than Nipi.
Kola received more votes than Nipi.
Luck received more votes than Jazz.
Nipi received more votes than Oboy.
Ping received more votes than Kola.


Question: If the ranks of Ping, Oboy, and Kola were consecutive, then which one of the following statements would have to be false?

Jazz received more votes than Luck.
Jazz received more votes than Ping.
Nipi received more votes than Oboy.
Nipi received more votes than Mist.
Oboy received more votes than Nipi.


Question: What is the total number of the soft drink names whose exact ranks can be deduced from the partial survey results?


Question: What is the maximum possible number of the soft drink names any one of which could be among the three most popular?


Question: If Ping received more votes than Jazz, then what is the maximum possible number of names whose ranks can be determined?


A college offers one course in each of three subjects—mathematics, nutrition, and oceanography—in the fall and again in the spring. Students' book orders for these course offerings are kept in six folders, numbered 1 through 6, from which labels identifying the folders' contents are missing. The following is known: Each folder contains only the orders for one of the six course offerings. Folder 1 contains orders for the same subject as folder 2 does. The orders in folder 3 are for a different subject than are the orders in folder 4. The fall mathematics orders are in folder 1 or else folder 4. The spring oceanography orders are in folder 1 or else folder 4. The spring nutrition orders are not in folder 5.

Question: Which one of the following could be the list of the contents of the folders, in order from folder 1 to folder 6 ?

fall mathematics, spring mathematics, fall oceanography, fall nutrition, spring nutrition, spring oceanography

fall oceanography, spring nutrition, fall nutrition, fall mathematics, spring mathematics, spring oceanography

spring mathematics, fall mathematics, spring nutrition, fall oceanography, fall nutrition, spring oceanography

spring oceanography, fall oceanography, fall nutrition, fall mathematics, spring mathematics, spring nutrition

spring oceanography, fall oceanography, spring mathematics, fall mathematics, fall nutrition, spring nutrition


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

The spring mathematics orders are in folder 3.

The fall nutrition orders are in folder 3.

The spring oceanography orders are in folder 1.

The spring nutrition orders are in folder 6.

The fall oceanography orders are in folder 5.


Question: If the fall oceanography orders are in folder 2, then which one of the following statements could be true?

The spring mathematics orders are in folder 4.

The spring mathematics orders are in folder 6.

The fall nutrition orders are in folder 1.

The spring nutrition orders are in neither folder 3 nor folder 6.

Neither the spring nor the fall nutrition orders are in folder 3.


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

The spring mathematics orders are in folder 1.

The fall oceanography orders are in folder 1.

The fall nutrition orders are in folder 4, and the fall oceanography orders are in folder 6.

The fall oceanography orders are in folder 2, and the spring oceanography orders are in folder 1.

The spring oceanography orders are in folder 1, and neither the spring nor the fall nutrition orders are in folder 3.


Question: If the fall oceanography orders are in folder 2, then for exactly how many of the remaining five folders can it be deduced which course offering's orders are in that folder?


Question: Which one of the following lists a pair of folders that must together contain orders for two different subjects?


Question: Which one of the following could be true?

The fall mathematics and spring oceanography orders are in folders with consecutive numbers.

Folder 5 contains the orders for a spring course in a subject other than mathematics.

Folder 6 contains the orders for a subject other than nutrition.

The mathematics orders are in folders 1 and 4.

The orders for the fall courses are in folders 1, 3, and 6.


Seven consecutive time slots for a broadcast, numbered in chronological order 1 through 7, will be filled by six song tapes—G, H, L, O, P, S—and exactly one news tape. Each tape is to be assigned to a different time slot, and no tape is longer than any other tape. The broadcast is subject to the following restrictions: L must be played immediately before O. The news tape must be played at some time after L. There must be exactly two time slots between G and P, regardless of whether G comes before P or whether G comes after P.

Question: If G is played second, which one of the following tapes must be played third?


Question: The news tape can be played in any one of the following time slots EXCEPT the


Question: If H and S are to be scheduled as far from each other as possible, then the first, the second, and the third time slots could be filled, respectively, by

G, H, and L
S, G, and the news
H, G, and L
H, L, and O
L, O, and S


Question: If P is played fifth, L must be played


Question: What is the maximum number of tapes that can separate S from the news?


Question: Which one of the following is the latest time slot in which L can be played?

the third
the fourth
the fifth
the sixth
the seventh


Question: The time slot in which O must be played is completely determined if G is assigned to which one of the following time slots?

the first
the third
the fourth
the fifth
the sixth


An official is assigning five runners—Larry, Ned, Olivia, Patricia, and Sonja—to parallel lanes numbered consecutively 1 through 5. The official will also assign each runner to represent a different charity—F, G, H, J, and K—not necessarily in order of the runner's names as given. The following ordering restrictions apply: The runner representing K is assigned to lane 4. Patricia is assigned to the only lane between the lanes of the runners representing F and G. There are exactly two lanes between Olivia's lane and the lane of the runner representing G. Sonja is assigned to a higher-numbered lane than the lane to which Ned is assigned.

Question: Which one of the following is a possible assignment of runners to lanes by the charity they represent?

F G H K J
G H J K F
G K F J H
H J G K F
J H F K G


Question: The lane to which Patricia is assigned must be a lane that is

next to the lane to which Larry is assigned

next to the lane to which Ned is assigned

separated by exactly one lane from the lane to which Ned is assigned

separated by exactly one lane from the lane to which Olivia is assigned

separated by exactly one lane from the lane to which Sonja is assigned


Question: If Olivia is assigned to lane 2, which one of the following assignments must be made? Charity Lane


Question: Which one of the following, is a complete and accurate list of runners each of whom could be the runner representing F?

Larry, Ned
Patricia, Sonja
Larry, Ned, Olivia
Larry, Ned, Sonja
Ned, Patricia, Sonja


Question: If Ned is the runner representing J, then it must be true that

the runner representing G is assigned to lane 1

the runner representing H is assigned to lane 2


Question: If Larry represents J, which one of the following could be the assignment of runners to lanes?

Larry Olivia Ned Patricia Sonja
Larry Ned Olivia Sonja Patricia
Larry Sonja Patricia Ned Olivia
Ned Olivia Larry Patricia Sonja
Ned Sonja Olivia Patricia Larry


Seven children are to be seated in seven chairs arranged in a row that runs from west to east. All seven children will face north. Four of the children are boys: Frank, Harry, Ivan, and Joel. Three are girls: Ruby, Sylvia, and Thelma. The children are assigned to chairs according to the following conditions: Exactly one child sits in each chair. No boy sits next to another boy. Ivan sits next to and east of the fourth child in the row. Sylvia sits east of Ivan. Frank sits next to Ruby.

Question: What is the maximum possible number of different pairs of chairs in which Frank and Ruby could sit?


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

Both Harry and Joel sit east of Frank.
Both Harry and Ruby sit east of Frank.
Both Harry and Joel sit west of Frank.
Both Harry and Ruby sit west of Frank.
Both Joel and Ruby sit east of Frank.


Question: If Thelma sits next to Ivan, and if Frank sits next to Thelma, which one of the following statements could be false?

Both Frank and Thelma sit west of Sylvia.


Question: If Frank does not sit next to any child who sits next to Ivan, which one of the following statements could be true?

Harry sits west of Frank.
Joel sits west of Ivan.
Ruby sits west of Frank.
Thelma sits west of Frank.
Thelma sits west of Ruby.


Question: If Frank sits east of Ruby, which one of the following pairs of children CANNOT sit next to each other?

Frank and Thelma
Harry and Ruby
Harry and Sylvia
Ivan and Ruby
Joel and Ruby


On the basis of an examination, nine students—Fred, Glen, Hilary, Ida, Jan, Kathy, Laura, Mike, and Nick—are each placed in one of three classes. The three highest scorers are placed in the level 1 class; the three lowest scorers are placed in the level 3 class. The remaining three are placed in the level 2 class. Each class has exactly three students. Ida scores higher than Glen. Glen scores higher than both Jan and Kathy. Jan scores higher than Mike. Mike scores higher than Hilary. Hilary scores higher than Nick. Kathy scores higher than both Fred and Laura.

Question: How many different combinations of students could form the level 1 class?


Question: Which one of the following students could be in the level 2 class but cannot be in the level 3 class?


Question: Which one of the following students could be placed in any one of the three classes?


Question: The composition of each class can be completely determined if which one of the following pairs of students is known to be in the level 2 class?

Fred and Kathy
Fred and Mike
Hilary and Jan
Kathy and Laura
Laura and Mike


Question: Which one of the following pairs of students cannot be in the same class as Fred?

Hilary and Nick
Jan and Laura
Kathy and Laura
Jan and Mike
Laura and Mike


Six reviewers—Frank, George, Hilda, Jackie, Karl, and Lena—will review four movies—Mystery, Retreat, Seasonings, and Wolves—according to the following conditions: Each reviewer reviews exactly one movie, and each movie is reviewed by at least one of the six reviewers. Hilda reviews the same movie as Frank. Lena reviews the same movie as exactly one other reviewer. George reviews Mystery. Jackie reviews either Mystery or else Wolves. Hilda does not review Wolves.

Question: Which one of the following can be true?

Karl reviews Wolves and Lena reviews Mystery.

Lena reviews Retreat and Frank reviews Seasonings.


Question: Lena can review any of the following EXCEPT

Mystery with George
Mystery with Karl
Retreat with Karl
Seasonings with Karl
Wolves with Jackie


Question: If Karl reviews the same movie as exactly one other reviewer, which one of the following is a complete and accurate list of the movies any one of which could be the movie that these two reviewers review?

Mystery, Retreat
Mystery, Seasonings
Retreat, Seasonings
Mystery, Seasonings, Wolves
Retreat, Seasonings, Wolves


Question: Which one of the following is an acceptable assignment of reviewers to movies? Mystery Retreat Seasonings Wolves

George Frank, Hilda Jackie, Lena Karl
George Frank, Hilda Karl, Lena Jackie
George Karl, Lena Jackie Frank, Hilda
George, Karl Frank, Hilda Lena Jackie
Jackie George, Lena Frank, Hilda Karl


A fire chief is determining the work schedules of five firefighters: Fuentes, Graber, Howell, Iman, and Jackson. The schedule must meet the following conditions: Except for Saturday and Sunday, when none of them works, exactly one of the firefighters works each day. None of the firefighters can work more than two days per week. No firefighter works on two consecutive days. Fuentes never works later in the week than Jackson. If Howell works, then Graber must work on the following day.

Question: Which one of the following CANNOT be a Monday-to-Friday work schedule?

Fuentes, Jackson, Howell, Graber, Fuentes

Graber, Fuentes, Graber, Fuentes, Jackson

Graber, Howell, Graber, Fuentes, Jackson


Question: If each firefighter is required to have at least two consecutive days off during the Monday-to-Friday workweek, which one of the following could be a possible work schedule?

Fuentes, Howell, Graber, Fuentes, Jackson


Question: If both Fuentes and Jackson work during a week, which one of the following statements CANNOT be true?

Fuentes works on Monday and Wednesday.
Jackson works on Monday and Wednesday.
Fuentes works on Tuesday and Thursday.
Jackson works on Tuesday and Thursday.
Jackson works on Wednesday and Friday.


Question: If Fuentes works two days during the week and Jackson works on Thursday, which one of the following statements could be true?

Fuentes works on Tuesday.
Graber works on Tuesday.
Howell works on Tuesday.
Graber works on Wednesday.
Howell works on Wednesday.


Question: If Graber does not work during the week, which one of the following statements must be true?

Fuentes works exactly one day during the week.

Fuentes works exactly two days during the week.

Iman works exactly one day during the week.

Iman works exactly two days during the week.

Jackson works exactly one day during the week.


A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Question: If Janet's lesson is scheduled for the first day, then the lesson for which one of the following students must be scheduled for the sixth day?


Question: For which one of the following students is there an acceptable schedule in which the student's lesson is on the third day and another acceptable schedule in which the student's lesson is on the fifth day?


Question: Which one of the following is a complete and accurate list of the students any one of whom could be the student whose lesson is scheduled for the second day?

Grace
Tom
Grace, Tom
Henry, Tom
Grace, Henry, Tom


Question: If Henry's lesson is scheduled for a day either immediately before or immediately after Tom's lesson, then Grace's lesson must be scheduled for the

first day
second day
third day
fourth day
fifth day


Question: If Janet's lesson is scheduled for the third day, which one of the following could be true?

Grace's lesson is scheduled for a later day than Henry's lesson.

Grace's lesson is scheduled for a later day than Una's lesson.

Henry's lesson is scheduled for a later day than Una's lesson.

Tom's lesson is scheduled for a later day than Henry's lesson.

Tom's lesson is scheduled for a later day than Una's lesson.


Question: Which one of the following is a complete and accurate list of days any one of which could be the day for which Tom's lesson is scheduled?

first, second, third
second, third, fourth
second, fifth, sixth
first, second, third, fourth
second, third, fourth, sixth


Five people—Harry, Iris, Kate, Nancy, and Victor—are to be scheduled as contestants on a television show, one contestant per day, for five consecutive days from Monday through Friday. The following restrictions governing the scheduling of contestants must be observed: Nancy is not scheduled for Monday. If Harry is scheduled for Monday, Nancy is scheduled for Friday. If Nancy is scheduled for Tuesday, Iris is scheduled for Monday. Kate is scheduled for the next day after the day for which Victor is scheduled.

Question: Victor can be scheduled for any day EXCEPT

Monday Tuesday Wednesday Thursday Friday


Question: If Iris is scheduled for the next day after Harry, which one of the following lists all those days any one of which could be the day for which Harry is scheduled?

Monday, Tuesday
Monday, Wednesday
Monday, Thursday
Monday, Tuesday, Wednesday
Monday, Wednesday, Thursday


Question: If Kate is scheduled for Wednesday, which one of the following could be true?

Nancy is scheduled for an earlier day than the day for which Harry is scheduled.

Nancy is scheduled for an earlier day than the day for which Iris is scheduled.

Nancy is scheduled for an earlier day than the day for which Kate is scheduled.


Question: If Kate is scheduled for Friday, which one of the following must be true?

Harry is scheduled for Tuesday.
Harry is scheduled for Wednesday.
Iris is scheduled for Monday.
Iris is scheduled for Wednesday.
Nancy is scheduled for Wednesday.


Question: If Iris is scheduled for Wednesday, which one of the following must be true?

Harry is scheduled for an earlier day than the day for which Nancy is scheduled.

Harry is scheduled for an earlier day than the day for which Kate is scheduled.

Kate is scheduled for an earlier day than the day for which Harry is scheduled.

Nancy is scheduled for an earlier day than the day for which Kate is scheduled.

Nancy is scheduled for an earlier day than the day for which Iris is scheduled.


Ron washed a total of seven objects after eating his lunch. Two of the objects were pieces of china: a mug and a plate. Two were pieces of glassware: a water glass and a juice glass. Three were utensils: a fork, a knife, and a spoon. Ron washed the two pieces of china consecutively, the two glasses consecutively, and the three utensils consecutively. He washed the objects as follows: Ron washed each of the objects exactly once. Ron washed the glassware after either the china or the utensils but not after both. He washed the knife before the spoon, and he washed the mug before the plate. He did not wash any two objects at the same time.

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

Ron washed the fork first.
Ron washed the fork second.
Ron washed the mug first.
Ron washed the plate second.
Ron washed the plate third.


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

Ron washed the knife second.
Ron washed the knife seventh.
Ron washed the mug second.
Ron washed the mug third.
Ron washed the mug fourth.


Question: Which one of the following CANNOT be an accurate list of the objects Ron washed second, third, and fourth, respectively?

fork, spoon, water glass
knife, fork, juice glass
knife, spoon, juice glass
knife, spoon, water glass
plate, water glass, juice glass


Question: It is NOT possible that Ron washed the knife


Question: If Ron washed the spoon immediately before the fork, then which one of the following statements can be true?

He washed the knife second.
He washed the knife third.
He washed the plate third.
He washed the plate sixth.
He washed the plate seventh.


Question: If Ron washed a glass and the knife consecutively, but not necessarily in that order, then which one of the following statements must be false?

He washed the juice glass before the knife.

He washed the plate before the water glass.


A professor will listen to exactly one speech from each of six students—H, J, K, R, S, and T. The six speeches will be delivered one at a time, consecutively, according to the following conditions: The speeches delivered by H, J, and K, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. The speeches delivered by R, S, and T, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches. H's speech must be earlier than S's speech. J's speech can be neither first nor sixth. T's speech can be neither immediately before nor immediately after J's speech.

Question: Which one of the following could be the order, from first to last, in which the students deliver their speeches?

H, J, R, S, T, K
H, R, T, K, S, J
K, J, T, H, S, R
R, J, K, T, H, S
T, R, J, S, K, H


Question: If T delivers the third speech, which one of the following must be true?

H delivers the first speech.
J delivers the fifth speech.
K delivers the fourth speech.
R delivers the sixth speech.
S delivers the fourth speech.


Question: If S delivers the third speech and T delivers the fourth speech, then which one of the following must be true?

H delivers the second speech.
J delivers the fifth speech.
K delivers the fifth speech.
K delivers the first speech.
R delivers the first speech.


Question: If K delivers the first speech and H delivers the fifth speech, which one of the following must be true?

J's speech is immediately before H's speech.

K's speech is immediately before T's speech.

R's speech is immediately before J's speech.


Question: If R's speech is immediately after S's speech and immediately before K's speech, then which one of the following could be true?

H's speech is immediately before S's speech.

H's speech is immediately before T's speech.

K's speech is immediately before J's speech.

K's speech is immediately before T's speech.

T's speech is immediately before S's speech.


Question: If K delivers the third speech, any of the following could be the student who makes the fourth speech EXCEPT


Four people—Fritz, Gina, Helen, and Jerry—have formed a car pool to commute to work together six days a week from Monday through Saturday. Each day exactly one of the people drives. The schedule of the car pool's drivers for any given week must meet the following conditions: Each person drives on at least one day. No person drives on two consecutive days. Fritz does not drive on Monday. Jerry drives on Wednesday or Saturday or both, and he may also drive on other days. If Gina drives on Monday, then Jerry does not drive on Saturday.

Question: Which one of the following could be the schedule of drivers for one week, for the days Monday through Saturday, respectively?

Gina, Fritz, Jerry, Helen, Gina, Gina
Gina, Fritz, Jerry, Helen, Fritz, Jerry
Helen, Fritz, Gina, Jerry, Helen, Fritz
Helen, Gina, Jerry, Fritz, Helen, Fritz
Helen, Gina, Jerry, Helen, Jerry, Gina


Question: Which one of the following could be true of one week's schedule of drivers?

Fritz drives on both Wednesday and Saturday.

Gina drives on both Monday and Wednesday.

Jerry drives on both Tuesday and Friday.

Gina drives on Monday and Jerry drives on Thursday.

Jerry drives on Wednesday and Gina drives on Saturday.


Question: If during one week Jerry drives on Wednesday and Saturday only, which one of the following must be true of that week?

Fritz drives on Tuesday.
Gina drives on Friday.
Helen drives on Monday.
Fritz drives on exactly two days.
Helen drives on exactly two days.


Question: If during one week Gina drives on Monday and Saturday only, which one of the following must be true of that week?

One other person besides Gina drives on exactly two days.

The person who drives on Wednesday does not drive on Friday.

Helen drives on a day immediately before a day on which Fritz drives.

Either Helen or Jerry drives on Tuesday.


Question: Which one of the following CANNOT be true of one week's schedule of drivers?

Fritz drives on Tuesday and Gina drives on Friday.

Gina drives on Monday and Jerry drives on Tuesday.

Gina drives on Monday and Jerry drives on Friday.

Helen drives on Monday and Jerry drives on Tuesday.

Helen drives on Tuesday and Jerry drives on Friday.


Question: If during one week Fritz drives exactly twice but he drives on neither Tuesday nor Wednesday, which one of the following could be true of that week?

One person drives exactly three times during the week.

Three people drive exactly one time each during the week.

Jerry drives on no day that is immediately before a day on which Fritz drives.


Eight new students—R, S, T, V, W, X, Y, Z—are being divided among exactly three classes—class 1, class 2, and class 3. Classes 1 and 2 will gain three new students each; class 3 will gain two new students. The following restrictions apply: R must be added to class 1. S must be added to class 3. Neither S nor W can be added to the same class as Y. V cannot be added to the same class as Z. If T is added to class 1, Z must also be added to class 1.

Question: Which one of the following must be true?

If T and X are added to class 2, V is added to class 3.

If V and W are added to class 1, T is added to class 3.

If V and W are added to class 1, Z is added to class 3.

If V and X are added to class 1, W is added to class 3.

If Y and Z are added to class 2, X is added to class 2.


On Wednesday a physician will have exactly one appointment with seven patients—P, Q, R, S, T, U, W—one patient per appointment. The schedule of appointments, chronologically numbered 1 through 7, must meet the following conditions: Q's appointment is at some time before W's appointment. U's appointment is at some time before P's appointment. Either R or T has appointment 3. S's appointment is either the appointment immediately before or the appointment immediately after R's appointment.

Question: Which one of the following is an acceptable schedule of appointments in order from 1 to 7?

Q, S, R, P, W, U, T
Q, U, W, S, R, T, P
S, Q, R, T, W, U, P
T, U, R, S, W, P, Q
U, Q, T, P, R, S, W


Question: If W has appointment 2 and P has appointment 5, then which one of the following must be true?

R has appointment 6.
S has appointment 4.
S has appointment 7.
U has appointment 1.
U has appointment 4.


Question: If U's appointment is immediately after T's appointment and immediately before R's appointment, then which one of the following must be true?

Q's appointment is at some time before P's appointment.

S's appointment is at some time before P's appointment.

S's appointment is immediately before Q's appointment.

W's appointment is immediately before P's appointment.

W's appointment is at some time before S's appointment.


Question: If P's appointment is immediately before S's appointment, then each of the following could be true EXCEPT:

R's appointment is immediately before W's appointment.

T's appointment is immediately before Q's appointment.

U's appointment is immediately before P's appointment.

U's appointment is immediately before Q's appointment.

W's appointment is immediately before T's appointment.


Question: If T's appointment is immediately after P's appointment and immediately before W's appointment, then which one of the following must be true?

W's appointment is at some time before R's appointment.

U's appointment is at some time before R's appointment.

S's appointment is at some time before U's appointment.

R's appointment is at some time before P's appointment.

Q's appointment is at some time before S's appointment.


During a period of six consecutive days—day 1 through day 6—each of exactly six factories—F, G, H, J, Q, and R—will be inspected. During this period, each of the factories will be inspected exactly once, one factory per day. The schedule for the inspections must conform to the following conditions: F is inspected on either day 1 or day 6. J is inspected on an earlier day than Q is inspected. Q is inspected on the day immediately before R is inspected. If G is inspected on day 3, Q is inspected on day 5.

Question: Which one of the following could be a list of the factories in the order of their scheduled inspections, from day 1 thought day 6?

F, Q, R, H, J, G
G, H, J, Q, R, F
G, J, Q, H, R, F
G, J, Q, R, F, H
J, H, G, Q, R, F


Question: Which one of the following must be false?

The inspection of G is scheduled for day 4.

The inspection of H is scheduled for day 6.

The inspection of J is scheduled for day 4.

The inspection of Q is scheduled for day 3.

The inspection of R is scheduled for day 2.


Question: The inspection of which one of the following CANNOT be scheduled for day 5 ?


Question: The inspection scheduled for day 3 and day 5, respectively, could be those of


Question: If the inspection of R is scheduled for the day immediately before the inspection of F, which one of the following must be true about the schedule?

The inspection of either G or H is scheduled for day 1.

The inspection of either G or J is scheduled for day 1.

The inspection of either G or J is scheduled for day 2.

The inspection of either H or J is scheduled for day 3.

The inspection of either H or J is scheduled for day 4.


Question: If the inspection of G and of H are scheduled, not necessarily in that order, for days as far apart as possible, which one of the following is a complete and accurate list of the factories any one of which could be scheduled for inspection for day 1?


Question: If the inspection of G is scheduled for the day immediately before the inspection of Q, which one of the following could be true?

The inspection of G is scheduled for day 5.

The inspection of H is scheduled for day 6.

The inspection of J is scheduled for day 2.

The inspection of Q is scheduled for day 4.

The inspection of R is scheduled for day 3.


At an evening concert, a total of six songs—O, P, T, X, Y, and Z—will be performed by three vocalists—George, Helen, and Leslie. The songs will be sung consecutively as solos, and each will be performed exactly once. The following constraints govern the composition of the concert program: Y must be performed earlier than T and earlier than O. P must be performed earlier than Z and later than O. George can perform only X, Y, and Z. Helen can perform only T, P, and X. Leslie can perform only O, P, and X. The vocalist who performs first must be different from the vocalist who performs last.

Question: Which one of the following is an acceptable schedule for the performance of the songs, in order from the first to last song performed?

X, T, Y, O, P, Z
X, Z, Y, T, O, P
Y, O, P, X, T, Z
Y, P, O, Z, T, X
Y, X, O, P, Z, T


Question: Which one of the following must be true about the program?

George performs X.
Helen performs O.
Helen performs T.
Leslie performs P.
Leslie performs X.


Question: Which one of the following is a complete and accurate list of the songs any one of which could be the last song performed at the concert?


Question: If X is performed first, which one of the following must be true?

X is performed by George.
X is performed by Helen.
P is the fourth song performed.
Y is the second song performed.
Y is the third song performed.


Question: Each of the following is an acceptable schedule for the performance of the songs, in order from the first to last song performed, EXCEPT:

Y, O, P, T, Z, X
Y, T, O, P, X, Z
Y, X, O, P, Z, T
X, Y, O, P, Z, T
X, Y, O, T, P, Z


Question: If Y is performed first, the songs performed second, third, and fourth, respectively, could be

T, X, and O
T, Z, and O
X, O, and P
X, P, and Z
X, T, and O


Exactly four medical training sessions—M, O, R, and S—will be scheduled for four consecutive days—day 1 through day 4—one session each day. Six professionals—three nurses and three psychologists—will teach the sessions. The nurses are Fine, Johnson, and Leopold; the psychologists are Tyler, Vitale, and Wong. Each session will be taught by exactly one nurse and exactly one psychologist. The schedule must conform to the following conditions: Each professional teaches at least once. Day 3 is a day on which Leopold teaches. Neither Fine nor Leopold teaches with Tyler. Johnson teaches session S only. Session M is taught on the day after the day on which session S is taught.

Question: If session R is the only session for which Leopold is scheduled, which one of the following is a pair of professionals who could be scheduled for day 2 together?

Fine and Tyler
Fine and Wong
Johnson and Tyler
Johnson and Wong
Leopold and Wong


Question: Which one of the following must be false?

Session O is scheduled for day 1.
Session S is scheduled for day 3.
Leopold is scheduled for day 1.
Vitale is scheduled for day 4.
Wong is scheduled for day 1.


Question: Which one of the following could be the session and the professionals scheduled for day 4 ?

session M, Fine, Wong
session O, Fine, Tyler
session O, Johnson, Tyler
session R, Fine, Wong
session S, Fine, Vitale


Question: If session S is scheduled for day 2, which one of the following is a professional who must be scheduled to teach session M ?


Question: If session O and session R are scheduled for consecutive days, which one of the following is a pair of professionals who could be scheduled for day 2 together?

Fine and Leopold
Fine and Wong
Johnson and Tyler
Johnson and Vitale
Leopold and Tyler


Question: Which one of the following could be the order in which the nurses teach the sessions, listed from day 1 through day 4?

Fine, Johnson, Leopold, Leopold
Fine, Leopold, Leopold, Johnson
Johnson, Johnson, Leopold, Fine
Johnson, Leopold, Leopold, Johnson
Leopold, Leopold, Fine, Fine


Question: If session O is scheduled for day 3, which one of the following must be scheduled for day 4?


A producer is positioning exactly seven music pieces—F, G, H, J, K, L, and M—one after another on a music recording, not necessarily in that order. Each piece will fill exactly one of the seven sequential tracks on the recording, according to the following conditions: F must be second. J cannot be seventh. G can come neither immediately before nor immediately after H. H must be in some track before that of L. L must be in some track before that of M.

Question: Which one of the following could be the order, from first to seventh, of the pieces on the recording?

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


Question: If M fills some track before that of J and also before that of K on the recording, which one of the following must be true?

H comes either immediately before or immediately after F.

L comes either immediately before or immediately after G.


Question: Which one of the following is a complete and accurate list of the pieces any of which could be first on the recording?

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


Question: The earliest track that M can fill is the


Question: If G is to come immediately before H but all the other conditions remain in effect, any of the following could be true EXCEPT:

J comes immediately before F.
K comes immediately before G.
J comes immediately after L.
J comes immediately after K.
K comes immediately after M.


Five candidates for mayor—Q, R, S, T, and U—will each speak exactly once at each of three town meetings—meetings 1, 2, and 3. At each meeting, each candidate will speak in one of five consecutive time slots. No two candidates will speak in the same time slot as each other at any meeting. The order in which the candidates will speak will meet the following conditions: Each candidate must speak either first or second at at least one of the meetings. Any candidate who speaks fifth at any of the meetings must speak first at at least one of the other meetings. No candidate can speak fourth at more than one of the meetings.

Question: Which one of the following could be the order, from first to fifth, in which the candidates speak at the meetings?

meeting 1: Q, U, R, T, S meeting 2: S, T, R, U, Q meeting 3: T, U, Q, R, S

meeting 1: R, S, Q, T, U meeting 2: U, T, S, R, Q meeting 3: Q, R, T, U, S

meeting 1: S, Q, U, T, R meeting 2: U, T, Q, R, S meeting 3: R, Q, S, T, U

meeting 1: T, R, S, U, Q meeting 2: Q, R, S, T, U meeting 3: U, S, R, Q, T

meeting 1: U, T, R, S, Q meeting 2: Q, R, S, T, U meeting 3: S, T, U, Q, R


Question: If R speaks second at meeting 2 and first at meeting 3, which one of the following is a complete and accurate list of those time slots any one of which could be the time slot in which R speaks at meeting 1?

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


Question: If the order in which the candidates speak at meeting 1 is R, U, S, T, Q, and the order in which they speak at meeting 2 is Q, R, U, S, T, which one of the following could be true of meeting 3?

Q speaks first.
R speaks third.
S speaks first.
T speaks second.
U speaks fifth.


Question: If R speaks first at meetings 1 and 2, and S speaks first at meeting 3, which one of the following must be true?

S speaks second at at least one of the meetings.

S speaks fifth at exactly one of the meetings.

S speaks fifth at exactly two of the meetings.


Question: It could be true that at all three meetings T speaks

in some time slot after the time slot in which R speaks

in some time slot after the time slots in which S and U speak

in some time slot before the time slots in which R and U speak


Question: If S, T, and U speak second at meetings 1, 2, and 3, respectively, which one of the following must be true?

The fifth speaker at at least one of the meetings is either Q or R.

Either Q speaks first at exactly two of the meetings or else R does so.

Neither S nor T speaks fifth at any of the meetings.

Q speaks third at one of the meetings, and R speaks third at another of the meetings.

Q speaks fourth at one of the meetings, and R speaks fourth at another of the meetings.


Seven singers—Jamie, Ken, Lalitha, Maya, Norton, Olive, and Patrick—will be scheduled to perform in the finals of a singing competition. During the evening of the competition, each singer, performing alone, will give exactly one performance. The schedule for the evening must conform to the following requirements: Jamie performs immediately after Ken. Patrick performs at some time after Maya. Lalitha performs third only if Norton performs fifth. If Patrick does not perform second, he performs fifth.

Question: Which one of the following is an acceptable schedule for the evening's performers, from first through seventh?

Ken, Jamie, Maya, Lalitha, Patrick, Norton, Olive

Lalitha, Patrick, Norton, Olive, Maya, Ken, Jamie

Norton, Olive, Ken, Jamie, Maya, Patrick, Lalitha

Olive, Maya, Ken, Lalitha, Patrick, Norton, Jamie

Olive, Maya, Lalitha, Norton, Patrick, Ken, Jamie


Question: If Lalitha is scheduled for the third performance, which one of the following must be scheduled for the sixth performance?


Question: If Norton is scheduled for the fifth performance, which one of the following could be true?

Jamie is scheduled for the sixth performance.

Ken is scheduled for the second performance.

Lalitha is scheduled for the fourth performance.

Maya is scheduled for the third performance.

Olive is scheduled for the first performance.


Question: If Maya is scheduled for the second performance, which one of the following could be true?

Jamie is scheduled for the sixth performance.

Ken is scheduled for the fourth performance.

Lalitha is scheduled for the third performance.

Norton is scheduled for the fifth performance.

Olive is scheduled for the fourth performance.


Question: If Jamie's performance is scheduled to be immediately before Lalitha's performance, Jamie's performance CANNOT be scheduled to be


At a small press, six textbooks, three introductory—F, G, and H—and three advanced—X, Y, and Z—will each be evaluated once by the editor, Juarez, and once by the publisher, Rosenberg, during six consecutive weeks—week 1 through week 6. Each evaluator evaluates exactly one textbook per week. No textbook will be evaluated by Juarez and Rosenberg during the same week. The following additional constraints apply: Rosenberg cannot evaluate any introductory textbook until Juarez has evaluated that textbook. Juarez cannot evaluate any advanced textbook until Rosenberg has evaluated that textbook. Rosenberg cannot evaluate any two introductory textbooks consecutively. Juarez must evaluate X during week 4.

Question: Which one of the following is an acceptable evaluation schedule, with the textbooks listed in order of evaluation from week 1 through week 6?

Juarez: F, G, X, Z, H, Y Rosenberg: X, F, Z, G, Y, H

Juarez: F, Y, G, X, H, Z Rosenberg Y, F, X, G, Z, H

Juarez: G, H, F, X, Y, Z Rosenberg: X, G, H, Y, Z, F

Juarez: G, Z, F, X, H, Y Rosenberg: Z, F, X, G, Y, H

Juarez: H, Y, F, X, G, Z Rosenberg: X, H, Z, F, Y, G


Question: If Juarez evaluates H during week 3 and Rosenberg evaluates G during week 6, which one of the following must be true?

Juarez evaluates F during week 1.
Juarez evaluates G during week 2.
Juarez evaluates Z during week 6.
Rosenberg evaluates X during week 1.
Rosenberg evaluates Y during week 5.


Question: If Juarez evaluates Z during week 2, then Rosenberg must evaluate which one of the following textbooks during week 5?


Question: Which one of the following must be true?

Rosenberg evaluates an advanced textbook during week 3.

Juarez evaluates an advanced textbook during week 2.

Juarez does not evaluate any two introductory textbooks consecutively.


Question: If Rosenberg evaluates X during week 1 and F during week 2, which one of the following could be true?

X is the third of the advanced textbooks to be evaluated by Juarez.

Y is the first of the advanced textbooks to be evaluated by Juarez.

Juarez does not evaluate any two introductory textbooks in a row.


Question: Which one of the following is a complete and accurate list of those weeks during which Juarez must evaluate an introductory textbook?

week 1
week 6
week 1, week 5
week 1, week 2, week 3
week 1, week 3, week 5


Question: Which one of the following could be true?

Juarez evaluates F during week 6.
Juarez evaluates Z during week 1.
Rosenberg evaluates F during week 3.
Rosenberg evaluates H during week 2.
Rosenberg evaluates X during week 5.


A disc jockey will play a sequence consisting of exactly seven different songs: three ballads—F, G, and H—and four dance tunes—R, S, V, and X. The following conditions must be met: No dance tune can be played immediately after another dance tune. H must be played earlier in the sequence than V. V and S must be separated from each other by exactly one song. S must be played immediately before or immediately after F. F must be played immediately after R, unless G is played earlier than R.

Question: Which one of the following could be the order of the songs in the sequence?

G, H, S, X, V, F, R
R, H, X, G, S, F, V
S, F, X, G, R, H, V
V, F, S, H, X, G, R
X, G, R, H, S, F, V


Question: Which one of the following must be true about the sequence?

No ballad is played immediately after a dance tune.

No ballad is played immediately after another ballad.

No dance tune is played immediately after a ballad.


Question: Which one of the following could be the fourth song in the sequence?


Question: Which one of the following could be the first song in the sequence?


Question: If the third song in the sequence is S, which one of the following must be the sixth song?


Question: If the seventh song in the sequence is R, which one of the following could be the fifth song?


Eight physics students—four majors: Frank, Gwen, Henry, and Joan; and four nonmajors: Victor, Wanda, Xavier, and Yvette—are being assigned to four laboratory benches, numbered 1 through 4. Each student is assigned to exactly one bench, and exactly two students are assigned to each bench. Assignments of students to benches must conform to the following conditions: Exactly one major is assigned to each bench. Frank and Joan are assigned to consecutively numbered benches, with Frank assigned to the lower-numbered bench. Frank is assigned to the same bench as Victor. Gwen is not assigned to the same bench as Wanda.

Question: Which one of the following could be the assignment of students to benches?

1: Frank, Victor; 2: Joan, Gwen; 3: Henry, Wanda; 4: Xavier, Yvette

1: Gwen, Yvette; 2: Frank, Xavier; 3: Joan, Wanda; 4: Henry, Victor

1: Henry, Wanda; 2: Gwen, Xavier; 3: Frank, Victor; 4: Joan, Yvette

1: Henry, Xavier; 2: Joan, Wanda; 3: Frank, Victor; 4: Gwen, Yvette

1: Henry, Yvette; 2: Gwen, Wanda; 3: Frank, Victor, 4: Joan, Xavier


Question: If Victor is assigned to bench 2 and Wanda is assigned to bench 4, which one of the following must be true?

Frank is assigned to bench 1.
Gwen is assigned to bench 1.
Henry is assigned to bench 3.
Xavier is assigned to bench 1.
Yvette is assigned to bench 3.


Question: If Gwen and Henry are not assigned to consecutively numbered benches, which one of the following must be true?

Victor is assigned to bench 2.
Victor is assigned to bench 3.
Wanda is assigned to bench 1.
Wanda is assigned to bench 3.
Wanda is assigned to bench 4.


Question: If Henry and Yvette are both assigned to bench 1, which one of the following could be true?

Gwen is assigned to bench 3.
Joan is assigned to bench 2.
Wanda is assigned to bench 2.
Wanda is assigned to bench 3.
Xavier is assigned to bench 3.


Question: If Gwen is assigned to bench 4 and Xavier is assigned to bench 3, then any one of the following could be true EXCEPT:

Gwen is assigned to the same bench as Yvette.

Henry is assigned to the same bench as Wanda.

Henry is assigned to the same bench as Xavier.

Joan is assigned to the same bench as Xavier.

Joan is assigned to the same bench as Yvette.


Question: If Wanda is assigned to a lower-numbered bench than is Joan, then Henry must be assigned to a

lower-numbered bench than is Frank
lower-numbered bench than is Gwen
lower-numbered bench than is Xavier
higher-numbered bench than is Victor
higher-numbered bench than is Yvette


Question: Which one of the following could be the assignments for bench 2 and bench 4?

2: Gwen, Xavier 4: Henry, Yvette
2: Henry, Yvette 4: Joan, Xavier
2: Joan, Victor 4: Gwen, Xavier
2: Joan, Wanda 4: Gwen, Xavier
2: Joan, Xavier 4: Henry, Yvette


A messenger will deliver exactly seven packages—L, M, N, O, P, S, and T—one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions: P is delivered either first or seventh. The messenger delivers N at some time after delivering L. The messenger delivers T at some time after delivering M. The messenger delivers exactly one package between delivering L and delivering O, whether or not L is delivered before O. The messenger delivers exactly one package between delivering M and delivering P, whether or not M is delivered before P.

Question: Which one of the following is an order in which the messenger could make the deliveries, from first to seventh?

L, N, S, O, M, T, P
M, T, P, S, L, N, O
O, S, L, N, M, T, P
P, N, M, S, O, T, L
P, T, M, S, L, N, O


Question: Which one of the following could be true?

N is delivered first.
T is delivered first.
T is delivered second.
M is delivered fourth.
S is delivered seventh.


Question: If N is delivered fourth, which one of the following could be true?

L is delivered first.
L is delivered second.
M is delivered third.
O is delivered fifth.
S is delivered first.


Question: If T is delivered fourth, the seventh package delivered must be


Question: If the messenger delivers M at some time after delivering O, the fifth package delivered could be any one of the following EXCEPT:


During a period of seven consecutive days—from day 1 through day 7—seven investors—Fennelly, Gupta, Hall, Jones, Knight, Lopez, and Moss—will each view a building site exactly once. Each day exactly one investor will view the site. The investors must view the site in accordance with the following conditions: Fennelly views the site on day 3 or else day 5. Lopez views the site on neither day 4 nor day 6. If Jones views the site on day 1, Hall views the site on day 2. If Knight views the site on day 4, Lopez views the site on day 5. Gupta views the site on the day after the day on which Hall views the site.

Question: Which one of the following could be the order in which the investors view the site, from day 1 through day 7?

Hall, Gupta, Fennelly, Moss, Knight, Lopez, Jones

Hall, Gupta, Lopez, Fennelly, Moss, Knight, Jones

Lopez, Gupta, Hall, Moss, Fennelly, Jones, Knight

Lopez, Jones, Fennelly, Knight, Hall, Gupta, Moss

Lopez, Jones, Knight, Moss, Fennelly, Hall, Gupta


Question: If Jones views the site on day 1, which one of the following investors must view the site on day 4?


Question: If Knight views the site on day 4 and Moss views the site on some day after the day on which Jones views the site, which one of the following must be true?

Jones views the site on day 1.
Jones views the site on day 2.
Jones views the site on day 6.
Moss views the site on day 2.
Moss views the site on day 6.


Question: If Hall views the site on day 2, which one of the following is a complete and accurate list of investors any one of whom could be the investor who views the site on day 4?

Knight
Moss
Jones, Moss
Knight, Moss
Jones, Knight, Moss


Question: If Hall views the site on the day after the day Knight views the site and if Fennelly views the site on the day after the day Lopez views the site, then Jones must view the site on day


Question: If the day on which Gupta views the site and the day on which Lopez views the site both come at some time before the day on which Fennelly views the site, which one of the following is an investor who could view the site on day 3?


Six cars are to be arranged in a straight line, and will be numbered 1 through 6, in order, from the front of the line to the back of the line. Each car is exactly one color: two are green, two are orange, and two are purple. The arrangement of cars is restricted as follows: No car can be the same color as any car next to it in line. Either car 5 or car 6 must be purple. Car 1 cannot be orange. Car 4 cannot be green.

Question: The cars in which one of the following pairs CANNOT be the same color as each other?

cars 1 and 4
cars 1 and 5
cars 3 and 5
cars 3 and 6
cars 4 and 6


Question: If car 2 is the same color as car 4, then which one of the following statements must be true?

Car 1 is purple.
Car 2 is orange.
Car 3 is green.
Car 5 is purple.
Car 6 is green


Question: If car 4 is purple, which one of the following must be true?

Car 1 is orange.
Car 2 is green.
Car 3 is orange.
Car 5 is green.
Car 6 is purple.


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

Car 2 is green.
Car 4 is orange.
Car 5 is purple.
Car 6 is orange.
Car 6 is green.


Question: If one of the two orange cars is replaced by a third green car, and if the arrangement of cars in line must conform to the same restrictions as before, then which one of the following is a complete and accurate list of the cars each of which must be green?

car 1
car 3
car 5
car 1, car 3
car l, car 3, car 5


Six racehorses—K, L, M, N, O, and P—will be assigned to six positions arranged in a straight line and numbered consecutively 1 through 6. The horses are assigned to the positions, one horse per position, according to the following conditions: K and L must be assigned to positions that are separated from each other by exactly one position. K and N cannot be assigned to positions that are next to each other. N must be assigned to a higher-numbered position than M. P must be assigned to position 3.

Question: Which one of the following lists an acceptable assignment of horses to positions 1 though 6, respectively?

K, L, P, M, N, O
M, K, P, L, N, O
M, N, K, P, L, O
N, O, P, K, M, L
O, M, P, L, N, K


Question: Which one of the following is a complete and accurate list of the positions any one of which can be the position to which K is assigned?


Question: Which one of the following CANNOT be true?

K is assigned to position 2.
L is assigned to position 2.
M is assigned to position 1.
M is assigned to position 5.
O is assigned to position 2.


Question: Which one of the following must be true?

Either K or else L is assigned to position 2.

Either K or else L is assigned to position 4.

Either M or else N is assigned to position 2.

Either M or else N is assigned to position 5.

Either M or else O is assigned to position 6.


Question: Which one of the following CANNOT be true?

L and N are assigned to positions that are next to each other.

M and K are assigned to positions that are next to each other.

M and O are assigned to positions that are next to each other.

L and N are assigned to positions that are separated from each other by exactly one position.

M and P are assigned to positions that are separated from each other by exactly one position.


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

Question: Which one of the following must be true?

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

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

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

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

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


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

The French award is presented fifth.
The German award is presented third.
The Japanese award is presented sixth.
The Korean award is presented fifth.
The Swahili award is presented first.


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

The French award is presented fourth.
The Japanese award is presented fifth.
The Japanese award is presented sixth.
The Korean award is presented second.
The Swahili award is presented fifth.


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


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

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

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

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

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

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


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

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

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

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

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

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


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

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

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

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

Hildy's, Hildy's, Hildy's, Liam's, Pasquale's, Theodore's

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

Pasquale's, Hildy's, Theodore's, Hildy's, Liam's, Liam's


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


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

the first message
the second message
the third message
the fourth message
the sixth message


Question: Each of the following must be true EXCEPT:

Exactly one person left at least two messages.


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

Fleure left the third and fourth messages.


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

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

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

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

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

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

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


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

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

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

The fourth car washed receives a premium wash.


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

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

Vinquetta's car receives a regular wash.


Question: Which one of the following must be true?

Vinquetta's car receives a premium wash.

The fifth car washed receives a super wash.

The fourth car washed receives a super wash.

The second car washed receives a regular wash.


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

Frank's, Marquitta's
Marquitta's, Orlando's
Marquitta's, Orlando's, Taishah's
Marquitta's, Taishah's
Marquitta's, Vinquetta's


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

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

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


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

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

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


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

F can be assembled is line 2
G can be assembled is line 3
J can be assembled is line 2
K can be assembled is line 3
M can be assembled is line 2


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


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


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

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

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

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

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

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


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

F is assembled on line 3.
G is assembled on line 5.
H is assembled on line 1.
K is assembled on line 5.
M is assembled on line 6.


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

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

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

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

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

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


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

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

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


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


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


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


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

K in the boat race and S in the rescue exercise

L in the boat race and S in the rescue exercise

R in the boat race and L in the rescue exercise

S in the boat race and K in the rescue exercise

S in the boat race and P in the rescue exercise


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

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

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

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

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

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

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


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

Lautrec
Lautrec, Vistula
Scheherazade's, Lautrec
Scheherazade's, Lautrec, Medici
Scheherazade's, Lautrec, Tantoko


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

second highest
third highest
fourth highest
fifth highest
sixth highest


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

Scheherazade's ranks higher than Vistula.

Tantoko ranks higher than Scheherazade's.


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

Tantoko Medici Scheherazade's Vistula Pastilla


Question: Which one of the following CANNOT be true?

Pastilla ranks second highest.
Vistula ranks third highest.
Lautrec ranks third highest.
Robusto ranks fifth highest.
Scheherazade's ranks sixth highest.


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

Lautrec ranked fourth highest.
Pastilla is ranked fifth highest.
Medici is ranked fifth highest.
Scheherazade's is ranked fifth highest.
Medici is ranked sixth highest.


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

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

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

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

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

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

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


Question: Which one of the following CANNOT be true?

Neither Island nor Hilltop has a museum.

Neither Island nor Hilltop has a playground.

Neither Jessup nor Hilltop has a fountain.

Neither Jessup nor Island has a theater.


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

Island does not have a fountain.
Jessup does not have a garden.
Jessup has exactly two attractions.
Hilltop has exactly three attractions.
Hilltop has exactly four attractions.


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

Island only
Jessup only
Island and Hilltop only
Island and Jessup only
Jessup, Island, and Hilltop


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

Hilltop has a playground.
Island has a museum.
Island has a fountain.
Island has a garden.
Jessup has a garden.


Question: Which one of the following could be true?

Both Hilltop and Island have a playground.


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

Hilltop has a museum.
Hilltop has a playground.
Island does not have a fountain.
Island has a garden.
Jessup has a garden.


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

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

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

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

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

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

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


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

Volantes and Whispers
Whispers and Volantes
Whispers and Ziggurats
Ziggurats and Whispers
Ziggurats and Ziggurats


Question: Which one of the following must be true?

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

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

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

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

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


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

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

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

Volantes are assembled in F in the first year.

Whispers are assembled in F in the first year.

Xaviers are assembled in F in the first year.


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

Whispers and Volantes
Whispers and Xaviers
Xaviers and Volantes
Xaviers and Ziggurats
Ziggurats and Volantes


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

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

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


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

J is second.
J is third.
L is third.
Q is third.
P is seventh.


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


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

P is more popular than S.
S is more popular than V.
P is more popular than L.
J is more popular than V.
Q is more popular than V.


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

H is first.
L is fourth.
V is not fourth.
J is not third.
Q is third.


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

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


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

Jill and Manny
Kurt and Olga
Larisa and Manny
Kurt and Manny
Larisa and Olga


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

Jill, Kurt, Larisa
Jill, Larisa, Manny
Jill, Larisa, Olga
Jill, Kurt, Larisa, Manny
Jill, Kurt, Larisa, Olga


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


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

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

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


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

Jill stocks aisle 9.
Kurt stocks aisle 6.
Larisa stocks aisle 4.
Manny stocks aisle 4.
Olga stocks aisle 6.


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

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

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


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

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

The second speaker lectures on Nietzsche.

The fifth speaker lectures on Nietzsche.


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


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

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

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

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

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

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


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

The first and fourth speakers lecture on British philosophers.

The first and fourth speakers lecture on German philosophers.

The second and third speakers lecture on British philosophers.

The third and fourth speakers lecture on German philosophers.

The fourth and fifth speakers lecture on British philosophers.


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

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

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

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

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

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


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

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

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

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

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

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

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


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


Question: Which one of the following must be true?

The first train to arrive is the Rockville.

The Quigley arrives at some time before the Sunnydale.

The Rockville arrives at some time before the Wooster.

The Victoria arrives at some time before the York.

The Wooster arrives at some time before the York.


Question: Which one of the following could be true?

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

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

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

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

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


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

The sixth train to arrive is the Sunnydale.

The sixth train to arrive is the Tilbury.

The third train to arrive is the Rockville.

The second train to arrive is the Sunnydale.

The first train to arrive is the Rockville.


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


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

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

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

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

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

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

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


Question: Which one of the following could be true?

Felicia's call airs fifth.
Gwen's call airs first.
Henry's call airs second.
Isaac's call airs third.
Mel's call airs fifth.


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

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

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

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

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

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


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

Felicia's call airs fourth.
Gwen's call airs fifth.
A taped call airs second.
A taped call airs third.
A taped call airs fourth.


Question: Which one of the following must be true?

Gwen's call is live.
Henry's call is live.
Mel's call is live.
Felicia's call is taped.
Isaac's call is taped.


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


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

The first call aired is from Seattle.
The first call aired is from Vancouver.
The fourth call aired is from Seattle.
The fifth call aired is from Seattle.
The fifth call aired is from Vancouver.


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

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

Fazio and Reich
Fazio and Umlas
Germond and Reich
Germond and Umlas
Lopez and Taylor


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

Fazio's flight is earlier than Simon's.
Kyle's flight is earlier than Reich's.
Kyle's flight is earlier than Taylor's.
Simon's flight is earlier than Reich's.
Taylor's flight is earlier than Kyle's.


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

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


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


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

Germond's flight is later than Taylor's.


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

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

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


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


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


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


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


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


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

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

Jacobson, Kruger, Miller, Lu, Ortiz
Kruger, Miller, Ortiz, Jacobson, Lu
Lu, Miller, Jacobson, Kruger, Ortiz
Ortiz, Kruger, Miller, Lu, Jacobson
Miller, Ortiz, Jacobson, Kruger, Lu


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


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

Jacobson swims lap 1.
Jacobson swims lap 3.
Kruger swims lap 5.
Lu swims lap 3.
Miller swims lap 5.


Question: Which one of the following could be true?

Jacobson swims lap 4.
Kruger swims lap 5.
Lu swims lap 5.
Miller swims lap 10.
Ortiz swims lap 6.


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


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

Jacobson, Miller, Kruger, Ortiz, Lu
Kruger, Lu, Miller, Ortiz, Jacobson
Lu, Kruger, Miller, Ortiz, Jacobson
Miller, Kruger, Ortiz, Jacobson, Lu
Ortiz, Jacobson, Kruger, Miller, Lu


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

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

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


Question: Which one of the following could be true?

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

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

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

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

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


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

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

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

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

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

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


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

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

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

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

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

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


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

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

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

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

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

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


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

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

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

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

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

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