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

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

Klosnik, Poirier, Neri, Manley, Osata, Londi

Klosnik, Londi, Manley, Poirier, Neri, Osata

Klosnik, Londi, Manley, Osata, Poirier, Neri

Klosnik, Osata, Poirier, Neri, Londi, Manley

Klosnik, Neri, Londi, Osata, Manley, Poirier


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

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


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

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


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

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


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

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


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

Neri sits directly between Londi and Poirier.

Osata sits directly between Klosnik and Manley.


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

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


A small software firm has four offices, numbered 1, 2, 3, and 4. Each of its offices has exactly one computer and exactly one printer. Each of these eight machines was bought in either 1987, 1988, or 1989. The eight machines were bought in a manner consistent with the following conditions: The computer in each office was bought either in an earlier year than or in the same year as the printer in that office. The computer in office 2 and the printer in office 1 were bought in the same year. The computer in office 3 and the printer in office 4 were bought in the same year. The computer in office 2 and the computer in office 3 were bought in different years. The computer in office 1 and the printer in office 3 were bought in 1988.

Question: If the computer in office 3 was bought in an earlier year than the printer in office 3 was, then which one of the following statements could be true?

The computer in office 2 was bought in 1987.

The computer in office 2 was bought in 1988.

The computer in office 4 was bought in 1988.

The printer in office 4 was bought in 1988.

The printer in office 4 was bought in 1989.


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

The printer in office 1 was bought in 1987.

The computer in office 2 was bought in 1987.

The computer in office 3 was bought in 1989.

The printer in office 4 was bought in 1988.

The printer in office 4 was bought in 1989.


Question: If as few of the eight machines as possible were bought in 1987, then what is the exact number of machines that were bought in 1987?


Question: If the computer in office 4 was bought in 1988, then which one of the following statements must be true?

The printer in office 1 was bought in 1988.

The printer in office 1 was bought in 1989.

The computer in office 2 was bought in 1988.

The computer in office 3 was bought in 1987.

The printer in office 4 was bought in 1989.


Question: If the computer in office 3 was bought in 1988, then which one of the following statements could be true?

The printer in office 1 was bought in 1988.

The computer in office 2 was bought in 1987.

The printer in office 2 was bought in 1988.

The computer in office 4 was bought in 1987.

The printer in office 4 was bought in 1989.


Question: Suppose that the computer in office 2 and the computer in office 3 had been bought in the same year as each other. If all of the other conditions remained the same, then which one of the following machines could have been bought in 1989?

the printer in office 1
the computer in office 2
the printer in office 2
the computer in office 4
the printer in office 4


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?


A railway company has exactly three lines: line 1, line 2, and line 3. The company prints three sets of tickets for January and three sets of tickets for February: one set for each of its lines for each of the two months. The company's tickets are printed in a manner consistent with the following conditions: Each of the six sets of tickets is exactly one of the following colors: green, purple, red, yellow. For each line, the January tickets are a different color than the February tickets. For each month, tickets for different lines are in different colors. Exactly one set of January tickets is red. For line 3, either the January tickets or the February tickets, but not both, are green. The January tickets for line 2 are purple. No February tickets are purple.

Question: If the line 3 tickets for January are red, then which one of the following statements must be true?

The line 1 tickets for January are green.

The line 1 tickets for January are yellow.

The line 1 tickets for February are red.

The line 2 tickets for February are yellow.

The line 3 tickets for February are green.


Question: If one set of the line 2 tickets is green, then which one of the following statements must be true?

The line 1 tickets for February are red.

The line 3 tickets for February are green.

The line 3 tickets for February are yellow.


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

One set of January tickets is green and one set of January tickets is yellow.

The line 2 tickets for January are the same color as the line 1 tickets for February.


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

Both the line 1 tickets for January and the line 2 tickets for February are green.

Both the line 1 tickets for January and the line 2 tickets for February are yellow.

Both the line 1 tickets for January and the line 3 tickets for February are yellow.

The line 1 tickets for January are green, and the line 3 tickets for February are red.

The line 3 tickets for January are yellow, and the line 1 tickets for February are red.


Question: If the line 3 tickets for February are yellow, then each of the following statements must be true EXCEPT:

The tickets in two of the six sets are red.

The tickets in two of the six sets are yellow.


Question: Suppose that none of the ticket sets are purple. If all of the other conditions remain the same, then which one of the following statements could be true?

None of the January tickets are green.
None of the February tickets are green.
None of the line 2 tickets are green.
No line 1 or line 2 tickets are yellow.
No line 2 or line 3 tickets are red.


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


An apartment building has five floors. Each floor has either one or two apartments. There are exactly eight apartments in the building. The residents of the building are J, K, L, M, N, O, P, and Q, who each live in a different apartment. J lives on a floor with two apartments. K lives on the floor directly above P. The second floor is made up of only one apartment. M and N live on the same floor. O does not live on the same floor as Q. L lives in the only apartment on her floor. Q does not live on the first or second floor.

Question: Which one of the following must be true?

Q lives on the third floor.
Q lives on the fifth floor.
L does not live on the fourth floor.
N does not live on the second floor.
J lives on the first floor.


Question: Which one of the following CANNOT be true?

K lives on the second floor.
M lives on the first floor.
N lives on the fourth floor.
O lives on the third floor.
P lives on the fifth floor.


Question: If J lives on the fourth floor and K lives on the fifth floor, which one of the following can be true?

O lives on the first floor.
Q lives on the fourth floor.
N lives on the fifth floor.
L lives on the fourth floor.
P lives on the third floor.


Question: If O lives on the second floor, which one of the following CANNOT be true?

K lives on the fourth floor.
K lives on the fifth floor.
L lives on the first floor.
L lives on the third floor.
L lives on the fourth floor.


Question: If M lives on the fourth floor, which one of the following must be false?

O lives on the fifth floor.
J lives on the first floor.
L lives on the second floor.
Q lives on the third floor.
P lives on the first floor.


Question: Which one of the following must be true?

If J lives on the fourth floor, then Q does not live on the fifth floor.

If O lives on the second floor, then L does not live on the fourth floor.

If N lives on the fourth floor, then K does not live on the second floor.

If K lives on the third floor, then O does not live on the fifth floor.

If P lives on the fourth floor, then M does not live on the third floor.


Question: If O lives on the fourth floor and P lives on the second floor, which one of the following must be true?

L lives on the first floor.
M lives on the third floor.
Q lives on the third floor.
N lives on the fifth floor.
Q lives on the fifth floor.


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

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

She visits exactly two cities in country X.

She visits exactly two cities in country Y.

She visits exactly two cities in country Z.

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

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


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


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

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

She visits exactly two cities in country X.

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

She visits exactly two cities in country Z.

She visits exactly three cities in country Z.


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

Hannah cannot visit any other cities in country X.

Hannah can visit four cities in country Y.

Hannah cannot spend more than four days in country Z.

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


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


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.


Three couples—John and Kate, Lewis and Marie, and Nat and Olive have dinner in a restaurant together. Kate, Marie, and Olive are women; the other three are men. Each person orders one and only one of the following kinds of entrees: pork chops, roast beef, swordfish, tilefish, veal cutlet. The six people order in a manner consistent with the following conditions: The two people in each couple do not order the same kind of entree as each other. None of the men orders the same kind of entree as any of the other men. Marie orders swordfish. Neither John nor Nat orders a fish entree. Olive orders roast beef.

Question: Which one of the following is a complete and accurate list of the entrees any one of which Lewis could order?

pork chops, roast beef, tilefish, veal cutlet


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

John orders the same kind of entree as Marie does.

Kate orders the same kind of entree as Nat does.

Lewis orders the same kind of entree as Nat does.

Marie orders the same kind of entree as Olive does.

Nat orders the same kind of entree as Olive does.


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

One of the men orders pork chops or veal cutlet.

One of the men orders swordfish or veal cutlet.

Exactly one of the women orders a fish entree.


Question: If John orders veal cutlet, then which one of the following statements must be true?

Kate orders roast beef.
Kate orders swordfish.
Lewis orders tilefish.
Lewis orders veal cutlet.
Nat orders pork chops.


Question: If none of the six people orders pork chops, then which one of the following statements must be true?

John orders veal cutlet.
Kate orders tilefish.
Lewis orders tilefish.
One of the men orders swordfish.
One of the women orders tilefish.


Question: If Lewis orders pork chops, then which one of the following is a complete and accurate list of the entrees any one of which John could order?

roast beef
veal cutlet
roast beef, veal cutlet
roast beef, swordfish
pork chops, roast beef, swordfish


Question: Suppose that the people in each couple both order the same kind of entree as each other rather than order different kinds of entrees. If all other conditions remain the same, and no two women order the same kind of entree, then which one of the following statements could be true?

John orders roast beef.
John orders swordfish.
Kate orders roast beef.
Two of the people order pork chops.
Two of the people order tilefish.


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


At an automobile exhibition, cars are displayed on each floor of a three-floor building. On each floor the cars are either all family cars or all sports cars, either all new or all used, and either all production models or all research models. The following conditions apply to this exhibition: If the exhibition includes both family cars and sports cars, then each family car is displayed on a lower numbered floor than any sports car. The exhibition includes no used research models. The exhibition includes no research models that are sports cars. There are new cars on floor 1. There are used cars on floor 3.

Question: If there are sports cars on exactly two floors, then which one of the following statements could be true?

There are research models on floor 1.
There are sports cars on floor 1.
There are family cars on floor 2.
There are research models on floor 2.
There are family cars on floor 3.


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

The exhibition includes new research model sports cars.

The exhibition includes used research model family cars.

The exhibition includes used research model sports cars.

There are research models on exactly one floor.

There are research models on all three floors.


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

There are production models on floor 1.
There are research models on floor 1.
There are production models on floor 2.
There are production models on floor 3.
There are research models on floor 3.


Question: If there are research models on exactly two floors, then which one of the following statements can be false?

There are family cars on floor 1.
There are research models on floor 1.
There are new cars on floor 2.
There are research models on floor 2.
There are family cars on floor 3.


Question: If all the new cars in the exhibition are research models, then which one of the following statements must be true?

All the family cars in the exhibition are new.

All the family cars in the exhibition are research models.

All the family cars in the exhibition are used.

All the new cars in the exhibition are family cars.

All the production models in the exhibition are family cars.


Question: If all the production models in the exhibition are used, then which one of the following statements must be true?

There are family cars on floor 1.
There are new cars on floor 2.
There are research models on floor 2.
There are family cars on floor 3.
There are sports cars on floor 3.


Planes 1, 2, 3, and 4—and no others—are available to fly in an air show. Pilots Anna, Bob, and Cindy are all aboard planes that are flying in the show and they are the only qualified pilots in the show. Copilots Dave, Ed, and Fran are all aboard planes that are flying in the show and they are the only qualified copilots in the show. No plane flies in the show without a qualified pilot aboard. No one but qualified pilots and qualified copilots flies in the show. Anna will only fly in either plane 1 or plane 4. Dave will only fly in either plane 2 or plane 3.

Question: If Anna flies in plane 4 and Dave flies in plane 2, which one of the following must be true?

Cindy flies in either plane 1 or plane 3.

If Cindy flies in plane 3, Bob flies in plane 2.

Bob and one other person fly in plane l.

If Bob is aboard plane 4, Cindy flies in plane 3.

If Cindy is in plane 2, Bob flies in plane 3.


Question: If Bob and Anna fly on the same plane, which one of the following must be true?

Cindy flies with Dave and Ed.
Cindy flies with Ed.
Dave flies with Cindy.
Dave flies with Cindy, Ed, and Fran.
Fran flies with Ed.


Question: If Cindy and Fran are the only people in one of the planes, which one of the following must be true?

Bob flies with Anna.
Dave flies with Ed.
Dave and Ed fly with Bob.
Dave flies with Bob.
Ed flies with Anna.


Question: If plane 1 is used, its crew could consist of

Anna, Bob, Cindy, Fran
Anna, Bob, Ed, Fran
Bob, Cindy, Ed, Fran
Bob, Cindy, Dave, Ed
Bob, Dave, Ed, Fran


Question: If as many of the pilots and copilots as possible fly in plane 4, that group will consist of

exactly two people
exactly three people
exactly four people
exactly five people
three pilots and two copilots


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


Each of five illnesses—J, K, L, M, and N—is characterized by at least one of the following three symptoms: fever, headache, and sneezing. None of the illnesses has any symptom that is not one of these three. Illness J is characterized by headache and sneezing. Illnesses J and K have no symptoms in common. Illnesses J and L have at least one symptom in common. Illness L has a greater number of symptoms than illness K. Illnesses L and N have no symptoms in common. Illness M has more symptoms than illness J.

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

Illness J has exactly two symptoms.
Illness K has exactly one symptom.
Illness L has exactly two symptoms.
Illness M has exactly three symptoms.
Illness N has exactly two symptoms.


Question: In which one of the following pairs could the first member of the pair be characterized by exactly the same number and types of symptoms as the second member of the pair?


Question: If illness L is characterized by a combination of symptoms different from any of the other illnesses, then which one of the following statements must be true?

Illnesses K and N are characterized by exactly the same symptoms.

Illnesses M and N are characterized by exactly the same symptoms.


Question: The illnesses in which one of the following pairs must have exactly one symptom in common?


Question: If Walter has exactly two of the three symptoms, then he cannot have all of the symptoms of

both illness J and illness L
both illness J and illness N
both illness K and illness L
both illness K and illness N
both illness L and illness N


A street cleaning crew works only Monday to Friday, and only during the day. It takes the crew an entire morning or an entire afternoon to clean a street. During one week the crew cleaned exactly eight streets—First, Second, Third, Fourth, Fifth, Sixth, Seventh, and Eighth streets. The following is known about the crew's schedule for the week: The crew cleaned no street on Friday morning. The crew cleaned no street on Wednesday afternoon. It cleaned Fourth Street on Tuesday morning. It cleaned Seventh Street on Thursday morning. It cleaned Fourth Street before Sixth Street and after Eighth Street. It cleaned Second, Fifth, and Eighth streets on afternoons.

Question: If the crew cleaned Second Street earlier in the week than Seventh Street, then it must have cleaned which one of the following streets on Tuesday afternoon?

First Street
Second Street
Third Street
Fifth Street
Eighth Street


Question: If the crew cleaned Sixth Street on a morning and cleaned Second Street before Seventh Street, then what is the maximum number of streets whose cleaning times cannot be determined?


Question: What is the maximum possible number of streets any one of which could be the one the crew cleaned on Friday afternoon?


Question: If the crew cleaned First Street earlier in the week than Third Street, then which one of the following statements must be false?

The crew cleaned First Street on Tuesday afternoon.

The crew cleaned Second Street on Thursday afternoon.

The crew cleaned Third Street on Wednesday morning.

The crew cleaned Fifth Street on Thursday afternoon.

The crew cleaned Sixth Street on Friday afternoon.


Question: If the crew cleaned Fifth, Sixth, and Seventh streets in numerical order, then what is the maximum number of different schedules any one of which the crew could have had for the entire week?


Question: Suppose the crew had cleaned Fourth Street on Tuesday afternoon instead of on Tuesday morning, but all other conditions remained the same. Which one of the following statements could be false?

The crew cleaned First Street before Second Street.

The crew cleaned Second Street before Fifth Street.

The crew cleaned Third Street before Second Street.

The crew cleaned Sixth Street before Fifth Street.

The crew cleaned Seventh Street before Second Street.


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

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

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

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

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

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

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


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


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


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

Chalet J is directly connected to chalet M.

Chalet K is directly connected to chalet N.

Chalet L is directly connected to chalet O.

Chalet L is directly connected to exactly two chalets.

Chalet O is directly connected to exactly one chalet.


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

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

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

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

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

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


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


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

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

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

Chalet L is directly connected to exactly one other chalet.

Chalet N is directly connected to exactly two other chalets.

Chalet O is directly connected to exactly two other chalets.


John receives one grade for each of the following six courses: economics, geology, history, Italian, physics, and Russian. From highest to lowest, the possible grades are A, B, C, D, and E. E is the only failing grade. Two letter grades are consecutive if and only if they are adjacent in the alphabet. John's grades in geology and physics are consecutive. His grades in Italian and Russian are consecutive. He receives a higher grade in economics than in history. He receives a higher grade in geology than in physics.

Question: If John receives the same grade in economics and Italian, and if he fails Russian, which one of the following must be true?

John's geology grade is a B.
John's history grade is a D.
John's history grade is an E.
John's physics grade is a B.
John's physics grade is a C.


Question: If John passes all his courses and receives a higher grade in geology than in either language, which one of the following must be true?

He receives at least one B and at least one C.

He receives at least one C and at least one D.


Question: If John receives a higher grade in physics than in economics and receives a higher grade in economics than in either language, which one of the following allows all six of his grades to be determined?

His grades in history and Italian are identical.

His grades in history and Russian are identical.

His grade in history is higher than his grade in Russian.


Question: If John receives a higher grade in physics than in economics and receives a higher grade in history than in Italian, exactly how many of his grades can be determined?


Question: Assume that John's grade in physics is higher than his grade in Italian and consecutive with it and that his grades in Russian and physics differ. Which one of the following must be true?

John receives both an A and a B.
John receives both an A and a C.
John receives both a B and a D.
John receives both a B and an E.
John receives both a D and an E.


Question: Assume that John receives a lower grade in economics than in physics. He must have failed at least one course if which one of the following is also true?

He receives a lower grade in Italian than in economics.

He receives a lower grade in Italian than in physics.

He receives a lower grade in physics than in Italian.

He receives a lower grade in Russian than in economics.

He receives a lower grade in Russian than in history.


A store sells shirts only in small, medium, and large sizes, and only in red, yellow, and blue colors. Casey buys exactly three shirts from the store. A shirt type consists of both a size and a color. Casey does not buy two shirts of the same type. Casey does not buy both a small shirt and a large shirt. No small red shirts are available. No large blue shirts are available.

Question: Which one of the following must be false?

Two of the shirts that Casey buys are small and two are red.

Two of the shirts that Casey buys are medium and two are red.

Two of the shirts that Casey buys are large and two are red.

Two of the shirts that Casey buys are small, one is yellow, and one is blue.

Two of the shirts that Casey buys are medium, one is yellow, and one is blue.


Question: If Casey buys a small blue shirt, which one of the following must be false?

Casey buys two blue shirts.
Casey buys two red shirts.
Casey buys two yellow shirts.
Casey buys two small shirts.
Casey buys two medium shirts.


Question: If Casey does not buy a medium yellow shirt, which one of the following must be true?

Casey buys either a medium red shirt or a small blue shirt.

Casey buys either a medium red shirt or a medium blue shirt.

Casey buys either a large red shirt or a small blue shirt.

Casey buys either a large red shirt or a medium red shirt.

Casey buys either a large yellow shirt or a small yellow shirt.


Question: If Casey buys exactly one medium shirt and does not buy two shirts of the same color, then she cannot buy which one of the following?

a medium red shirt
a medium yellow shirt
a medium blue shirt
a large red shirt
a large yellow shirt


Question: If neither large red shirts nor small blue shirts are available, which one of the following must Casey buy?

either a medium red shirt or a medium blue shirt

either a large yellow shirt or a medium blue shirt


A hobbyist is stocking her aquarium with exactly three fish of different types and with exactly two species of plants. The only fish under consideration are a G, an H, a J, a K, and an L, and the only kinds of plants under consideration are of the species W, X, Y, and Z. She will observe the following conditions: If she selects the G, she can select neither the H nor a Y. She cannot select the H unless she selects the K. She cannot select the J unless she selects a W. If she selects the K, she must select an X.

Question: Which one of the following is an acceptable selection of fish and plants for the aquarium? Fish Plants

G, H, K W, Y
G, J, K W, X
G, J, L X, Z
H, J, L W, Z
H, K, L Y, Z


Question: If the hobbyist selects the H, which one of the following must also be true?

She selects at least one W.
She selects at least one X.
She selects the J, but no Y's.
She selects the K, but no X's.
She selects at least one X, but no Y's.


Question: If the hobbyist selects both X's and Z's, which one of the following could be the group of fish she selects?


Question: The hobbyist could select any of the following groups of fish for the aquarium EXCEPT


Question: If the hobbyist selects a Y, which one of the following must be the group of fish she selects?


Question: The hobbyist could select any of the following plant combinations EXCEPT


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.


Petworld has exactly fourteen animals (three gerbils, three hamsters, three lizards, five snakes) that are kept in four separate cages (W, X, Y, Z) according to the following conditions: Each cage contains exactly two, four, or six animals. Any cage containing a gerbil also contains at least one hamster; any cage containing a hamster also contains at least one gerbil. Any cage containing a lizard also contains at least one snake; any cage containing a snake also contains at least one lizard. Neither cage Y nor cage Z contains a gerbil. Neither cage W nor cage X contains a lizard.

Question: Which one of the following could be a complete and accurate list of the animals kept in cages W and Y?

W: one gerbil and one hamster Y: two lizards and two snakes

W: one gerbil and two hamsters Y: one lizard and three snakes

W: two gerbils and two hamsters Y: one lizard and four snakes

W: two gerbils and two hamsters Y: three lizards and one snake

W: two gerbils and two lizards Y: two hamsters and two snakes


Question: If there are exactly two hamsters in cage W and the number of gerbils in cage X is equal to the number of snakes in cage Y, then the number of snakes in cage Z must be exactly


Question: If cage Z contains exactly twice as many lizards as cage Y, which one of the following can be true?

Cage Y contains exactly two lizards.
Cage Y contains exactly two snakes.
Cage Y contains exactly four animals.
Cage Z contains exactly three snakes.
Cage Z contains exactly two animals.


Question: If the number of animals in cage W is equal to the number of animals in cage Z, then which one of the following can be true?

Cage W contains exactly six animals.
Cage X contains exactly six animals.
Cage Y contains exactly one snake.
Cage Y contains exactly three snakes.
Cage Z contains exactly four snakes.


Question: If cage Y contains six animals, which one of the following must be true?

The number of snakes in cage Y is equal to the number of lizards in cage Y.

The number of snakes in cage Z is equal to the number of lizards in cage Z.


Question: At most, how many snakes can occupy cage Y at any one time?


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?


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

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


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

The bench on the northwest corner is pink.

The bench on the northeast corner is green.

The bench on the southwest corner is pink.

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

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


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


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


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

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


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


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


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

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


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

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

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

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

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

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


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

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

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


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

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

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


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

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


Each of five students—Hubert, Lori, Paul, Regina, and Sharon—will visit exactly one of three cities—Montreal, Toronto, or Vancouver—for the month of March, according to the following conditions: Sharon visits a different city than Paul. Hubert visits the same city as Regina. Lori visits Montreal or else Toronto. If Paul visits Vancouver, Hubert visits Vancouver with him. Each student visits one of the cities with at least one of the other four students.

Question: Which one of the following could be true for March?

Hubert, Lori, and Paul visit Toronto, and Regina and Sharon visit Vancouver.

Hubert, Lori, Paul, and Regina visit Montreal, and Sharon visits Vancouver.

Hubert, Paul, and Regina visit Toronto, and Lori and Sharon visit Montreal.

Hubert, Regina, and Sharon visit Montreal, and Lori and Paul visit Vancouver.

Lori, Paul, and Sharon visit Montreal, and Hubert and Regina visit Toronto.


Question: If Hubert and Sharon visit a city together, which one of the following could be true in March?

Hubert visits the same city as Paul.
Lori visits the same city as Regina.
Paul visits the same city as Regina.
Paul visits Toronto.
Paul visits Vancouver.


Question: If Sharon visits Vancouver, which one of the following must be true for March?

Hubert visits Montreal.
Lori visits Montreal.
Paul visits Toronto.
Lori visits the same city as Paul.
Lori visits the same city as Regina.


Question: Which one of the following could be false in March?

Sharon must visit Montreal if Paul visits Vancouver.

Regina must visit Vancouver if Paul visits Vancouver.

Regina visits a city with exactly two of the other four students.

Lori visits a city with exactly one of the other four students.

Lori visits a city with Paul or else with Sharon.


Question: If Regina visits Toronto, which one of the following could be true in March?

Lori visits Toronto.
Lori visits Vancouver.
Paul visits Toronto.
Paul visits Vancouver.
Sharon visits Vancouver.


Question: Which one of the following must be true for March?

If any of the students visits Montreal, Lori visits Montreal.

If any of the students visits Montreal, exactly two of them do.

If any of the students visits Toronto, exactly three of them do.

If any of the students visits Vancouver, Paul visits Vancouver.

If any of the students visits Vancouver, exactly three of them do.


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.


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

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


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


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

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


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


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

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


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

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


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

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

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

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

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

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

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


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

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


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


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

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


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


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


Doctor Yamata works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities—lecturing, operating, treating patients, and conducting research. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. During each week her work schedule must satisfy the following restrictions: She performs operations on exactly three mornings. If she operates on Monday, she does not operate on Tuesday. She lectures in the afternoon on exactly two consecutive calendar days. She treats patients on exactly one morning and exactly three afternoons. She conducts research on exactly one morning. On Saturday she neither lectures nor performs operations.

Question: Which one of the following must be a day on which Doctor Yamata lectures?

Monday Tuesday Wednesday Friday Saturday


Question: On Wednesday Doctor Yamata could be scheduled to

conduct research in the morning and operate in the afternoon

lecture in the morning and treat patients in the afternoon

operate in the morning and lecture in the afternoon

operate in the morning and conduct research in the afternoon

treat patients in the morning and treat patients in the afternoon


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

There is one day on which the doctor treats patients both in the morning and in the afternoon.

The doctor conducts research on one of the days on which she lectures.

The doctor conducts research on one of the days on which she treats patients.

The doctor lectures on one of the days on which she treats patients.

The doctor lectures on one of the days on which she operates.


Question: If Doctor Yamata operates on Tuesday, then her schedule for treating patients could be

Monday morning, Monday afternoon, Friday morning, Friday afternoon

Monday morning, Friday afternoon, Saturday morning, Saturday afternoon

Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon

Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon

Wednesday afternoon, Friday afternoon, Saturday morning, Saturday afternoon


Question: Which one of the following is a pair of days on both of which Doctor Yamata must treat patients?

Monday and Tuesday
Monday and Saturday
Tuesday and Friday
Tuesday and Saturday
Friday and Saturday


Each of seven judges voted for or else against granting Datalog Corporation's petition. Each judge is categorized as conservative, moderate, or liberal, and no judge is assigned more than one of those labels. Two judges are conservatives, two are moderates, and three are liberals. The following is known about how the judges voted: If the two conservatives and at least one liberal voted the same way as each other, then both moderates voted that way. If the three liberals voted the same way as each other, then no conservative voted that way. At least two of the judges voted for Datalog, and at least two voted against Datalog. At least one conservative voted against Datalog.

Question: If the two moderates did not vote the same way as each other, then which one of the following could be true?

No conservative and exactly two liberals voted for Datalog.

Exactly one conservative and exactly one liberal voted for Datalog.

Exactly one conservative and all three liberals voted for Datalog.

Exactly two conservatives and exactly one liberal voted for Datalog.

Exactly two conservatives and exactly two liberals voted for Datalog.


Question: Which one of the following must be true?

At least one conservative voted for Datalog.

At least one liberal voted against Datalog.

At least one moderate voted against Datalog.

At least one moderate voted for Datalog.


Question: If the three liberals all voted the same way as each other, which one of the following must be true?

One conservative voted for Datalog and one conservative voted against Datalog.

One moderate voted for Datalog and one moderate voted against Datalog.


Question: If exactly two judges voted against Datalog, then which one of the following must be true?

Exactly one conservative voted for Datalog.

Exactly three liberals voted for Datalog.


Question: Each of the following could be a complete and accurate list of those judges who voted for Datalog EXCEPT

one conservative, two moderates, two liberals

one conservative, two moderates, three liberals


Question: If the two conservatives voted the same way as each other, but the liberals did not all vote the same way as each other, then each of the following must be true EXCEPT:

Both conservatives voted against Datalog.

At least one liberal voted against Datalog.

Exactly five of the judges voted against Datalog.


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


A gymnastics instructor is planning a weekly schedule, Monday through Friday, of individual coaching sessions for each of six students—H, I, K, O, U, and Z. The instructor will coach exactly one student each day, except for one day when the instructor will coach two students in separate but consecutive sessions. The following restrictions apply: H's session must take place at some time before Z's session. I's session is on Thursday. K's session is always scheduled for the day immediately before or the day immediately after the day for which O's session is scheduled. Neither Monday nor Wednesday can be a day for which two students are scheduled.

Question: Which one of the following is a pair of students whose sessions can both be scheduled for Tuesday, not necessarily in the order given?


Question: If K's session is scheduled for Tuesday, then which one of the following is the earliest day for which Z's session can be scheduled?

Monday Tuesday Wednesday Thursday Friday


Question: Which one of the following must be true?

If U's session is scheduled for Monday, H's session is scheduled for Tuesday.

If U's session is scheduled for Tuesday, O's session is scheduled for Wednesday.

If U's session is scheduled for Wednesday, Z's session is scheduled for Tuesday.

If U's session is scheduled for Thursday, Z's session is scheduled for Friday.

If U's session is scheduled for Friday, Z's session is scheduled for Thursday.


Question: Scheduling Z's session for which one of the following days determines the day for which U's session must be scheduled?

Monday Tuesday Wednesday Thursday Friday


Question: If H's session is scheduled as the next session after U's session, which one of the following could be true about H's session and U's session?

U's session is scheduled for Monday, and H's session is scheduled for Tuesday.

U's session is scheduled for Thursday, and H's session is scheduled for Friday.


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

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


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


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


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

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


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

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


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

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


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

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


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


The organisms W, X, Y, and Z respond to the antibiotics ferromycin, ganocyclene, and heptocillin in a manner consistent with the following: Each of the organisms responds to at least one of the antibiotics. No organism responds to all three antibiotics. At least two but not all four of the organisms respond to ferromycin. If W responds to any antibiotic, then X responds to that antibiotic. If an organism responds to ferromycin, then it responds to ganocyclene. Y responds to ferromycin.

Question: Each of the following can be true EXCEPT:

W responds to heptocillin.
X responds to ganocyclene.
X responds to heptocillin.
Y responds to heptocillin.
Z responds to ganocyclene.


Question: Which one of the following could be true?

W and exactly one other organism respond to ganocyclene.

W responds to more of the antibiotics than X does.

More of the organisms respond to ferromycin than to ganocyclene.


Question: Which one of the following could be true?

Exactly one of the organisms responds to ferromycin.

All four of the organisms respond to heptocillin.

At least one of the organisms responds both to ferromycin and to heptocillin.

At least one of the organisms responds neither to ganocyclene nor to heptocillin.

At least one of the organisms responds to ganocyclene but does not respond to ferromycin.


Question: If X does not respond to ferromycin, then which one of the following must be true?

W responds to ganocyclene.
X responds to ganocyclene.
X responds to heptocillin.
Z responds to ferromycin.
Z responds to heptocillin.


Question: If any of the organisms responds to two of the antibiotics, then which one of the following is true about such an organism?

It must respond to ferromycin.
It must respond to ganocyclene.
It must respond to heptocillin.
It cannot respond to ferromycin.
It cannot respond to ganocyclene.


Question: If none of the organisms responds to heptocillin, then which one of the following must be true?

Exactly three of the organisms respond to ganocyclene.

Exactly four of the organisms respond to ganocyclene.


Question: If three of the organisms respond to exactly the same set of antibiotics as each other, and if Z does not respond to ferromycin, then each of the following must be true EXCEPT:

W responds to exactly the same set of antibiotics as Y.

X responds to exactly the same set of antibiotics as Y.


A florist is making three corsages from four types of flowers: gardenias, orchids, roses, and violets. Each of the corsages will contain exactly three flowers. The nine flowers used in the corsages must include at least one flower from each of the four types, and at least twice as many roses as orchids must be used. The corsages must also meet the following specifications: Corsage 1 must contain exactly two types of flowers. Corsage 2 must contain at least one rose. Corsage 3 must contain at least one gardenia but no orchids.

Question: Which one of the following is an acceptable selection of flowers for the three corsages? Corsage 1 Corsage 2 Corsage 3

2 gardenias 1 orchid 1 gardenia 1 rose 1 rose 1 orchid 1 violet 1 violet

2 orchids 2 orchids 2 gardenias 1 rose 1 rose 1 rose

2 orchids 3 roses 1 gardenia 1 rose 2 violets

1 gardenia 1 gardenia 1 gardenia 1 orchid 1 rose 1 rose 1 rose 1 violet 1 violet


Question: The maximum total number of roses that can be used in the three corsages is


Question: If corsage 1 contains two orchids and one rose, what is the maximum total number of violets that the florist can use in making the three corsages?


Question: If corsage 2 is exactly the same as corsage 3, the nine flowers used in the corsages can include exactly

two orchids
three gardenias
three roses
five roses
five violets


Question: If two of the corsages contain at least one orchid each, then the flowers in corsage 2 must include at least

one gardenia and one orchid
one gardenia and one rose
one orchid and one rose
one orchid and one violet
one rose and one violet


Question: If the greatest possible number of violets is used in the three corsages, the florist must use

exactly one rose and exactly one gardenia

exactly one orchid and exactly four violets


Question: If corsage 1 contains at least one gardenia and at least one violet, and if corsage 3 contains three different types of flowers, which one of the following could be used to make corsage 2?

one rose, one orchid, and one gardenia
one rose and two orchids
one rose and two violets
two roses and one gardenia
two roses and one violet


From a group of seven people—J, K, L, M, N, P, and Q—exactly four will be selected to attend a diplomat's retirement dinner. Selection must conform to the following conditions: Either J or K must be selected, but J and K cannot both be selected. Either N or P must be selected, but N and P cannot both be selected. N cannot be selected unless L is selected. Q cannot be selected unless K is selected.

Question: Which one of the following could be the four people selected to attend the retirement dinner?

J, K, M, P
J, L, N, Q
J, M, N, Q
K, M, P, Q
L, M, N, P


Question: Among the people selected to attend the retirement dinner there must be

K or Q or both
L or M or both
N or M or both
N or Q or both
P or Q or both


Question: Which one of the following is a pair of people who CANNOT both be selected to attend the retirement dinner?


Question: If M is not selected to attend the retirement dinner, the four people selected to attend must include which one of the following pairs of people?


Question: If P is not selected to attend the retirement dinner, then exactly how many different groups of four are there each of which would be an acceptable selection?


Question: There is only one acceptable group of four that can be selected to attend the retirement dinner if which one of the following pairs of people is selected?


Three boys—Karl, Luis, and Miguel—and three girls—Rita, Sarah, and Tura—are giving a dance recital. Three dances—1, 2, and 3—are to be performed. Each dance involves three pairs of children, a boy and a girl partnering each other in each pair, according to the following conditions: Karl partners Sarah in either dance 1 or dance 2. Whoever partners Rita in dance 2 must partner Sarah in dance 3. No two children can partner each other in more than one dance.

Question: If Sarah partners Luis in dance 3, which one of the following is a complete and accurate list of the girls any one of whom could partner Miguel in dance 1?


Question: If Miguel partners Rita in dance 2, which one of the following could be true?

Karl partners Tura in dance 1.
Luis partners Sarah in dance 2.
Luis partners Sarah in dance 3.
Miguel partners Sarah in dance 1.
Miguel partners Tura in dance 3.


Question: If Miguel partners Sarah in dance 1, which one of the following is a pair of children who must partner each other in dance 3?

Karl and Rita
Karl and Tura
Luis and Rita
Luis and Tura
Miguel and Tura


Question: If Luis partners Sarah in dance 2, which one of the following is a pair of children who must partner each other in dance 1?

Karl and Rita
Karl and Tura
Luis and Rita
Luis and Tura
Miguel and Rita


Question: If Miguel partners Rita in dance 1, which one of the following must be true?

Karl partners Rita in dance 2.
Karl partners Sarah in dance 3.
Karl partners Tura in dance 1.
Luis partners Rita in dance 2.
Luis partners Tura in dance 3.


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

Question: Which one of the following could be true?

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


Question: Which one of the following could be true?

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


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


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

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


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


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


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: If Lena reviews Seasonings, which one of the following must be true?

Hilda reviews Retreat.
Jackie reviews Seasonings.
Karl reviews Mystery.
Karl reviews Retreat.
Karl reviews Wolves.


Question: If Karl does not review Seasonings, which one of the following must be true?

Lena reviews Mystery.
Lena reviews Retreat.
Lena reviews Seasonings.
Frank and Hilda review Retreat.
Frank and Hilda review Seasonings.


Question: Which one of the following is a complete and accurate list of the movies each of which could be the movie that Lena reviews?

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


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

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

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


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


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


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


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

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


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


A soloist will play six different guitar concertos, exactly one each Sunday for six consecutive weeks. Two concertos will be selected from among three concertos by Giuliani—H, J, and K; two from among four concertos by Rodrigo—M, N, O, and P; and two from among three concertos by Vivaldi—X, Y, and Z. The following conditions apply without exception: If N is selected, then J is also selected. If M is selected, then neither J nor O can be selected. If X is selected, then neither Z nor P can be selected. If both J and O are selected, then J is played at some time before O. X cannot be played on the fifth Sunday unless one of Rodrigo's concertos is played on the first Sunday.

Question: Which one of the following is an acceptable selection of concertos that the soloist could play on the first through the sixth Sunday?

H Z M N Y K
K J Y O Z N
K Y P J Z M
P Y J H X O
X N K O J Z


Question: If the six concertos to be played are J, K, N, O, Y, and Z and if N is to be played on the first Sunday, then which one of the following concertos CANNOT be played on the second Sunday?


Question: If J, O, and Y are the first three concertos to be played, not necessarily in the order given, which one of the following is a concerto that CANNOT be played on the fifth Sunday?


Question: If O is selected for the first Sunday, which one of the following is a concerto that must also be selected?


Question: Which one of the following is a concerto that must be selected?


Question: Which one of the following is a concerto that CANNOT be selected together with N?


Eight camp counselors—Fran, George, Henry, Joan, Kathy, Lewis, Nathan, and Olga—must each be assigned to supervise exactly one of three activities—swimming, tennis, and volleyball. The assignment of counselors must conform to the following conditions: Each activity is supervised by at least two, but not more than three, of the eight counselors. Henry supervises swimming. Neither Kathy nor Olga supervises tennis. Neither Kathy nor Nathan supervises the same activity as Joan. If George supervises swimming, both Nathan and Olga supervise volleyball.

Question: Which one of the following is an acceptable assignment of the counselors to the activities?

Swimming: Fran, George, Henry; Tennis: Joan, Lewis; Volleyball: Kathy, Nathan, Olga

Swimming: George, Henry, Olga; Tennis: Fran, Joan, Lewis; Volleyball: Kathy, Nathan

Swimming: Henry; Tennis: Fran, George, Joan, Lewis; Volleyball: Kathy, Nathan, Olga

Swimming: Henry, Joan, Kathy; Tennis: George, Nathan; Volleyball: Fran, Lewis, Olga

Swimming: Henry, Nathan; Tennis: Fran, Kathy, Lewis; Volleyball: George, Joan, Olga


Question: Which one of the following is a pair of counselors who could be two of three counselors assigned to supervise swimming?

George and Nathan
George and Olga
Joan and Kathy
Joan and Nathan
Joan and Olga


Question: Which one of the following is a pair of counselors who could together be assigned to supervise tennis?

Fran and Kathy
George and Nathan
Henry and Lewis
Joan and Nathan
Joan and Olga


Question: If George and Kathy are two of three counselors assigned to supervise swimming, which one of the following could be true of the assignment?

Fran supervises swimming.
Henry supervises tennis.
Joan supervises volleyball.
Lewis supervises volleyball.
Nathan supervises tennis.


Question: If Fran and Lewis are two of three counselors assigned to supervise swimming, which one of the following must be true of the assignment?

George supervises volleyball.
Henry supervises volleyball.
Joan supervises tennis.
Kathy supervises swimming.
Nathan supervises tennis.


Question: If Joan is assigned to supervise the same activity as Olga, which one of the following CANNOT be true of the assignment?

Fran supervises swimming.
George supervises swimming.
Kathy supervises volleyball.
Lewis supervises volleyball.
Nathan supervises tennis.


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 housing committee will consist of exactly five representatives, one of whom will be its chairperson. The representatives will be selected from among a group of five tenants—F, G, J, K, and M—and a group of four homeowners—P, Q, R, and S. The following conditions must be met: The committee must include at least two representatives from each group. The chairperson must be a representative belonging to the group from which exactly two representatives are selected. If F is selected, Q must be selected. If G is selected, K must be selected. If either J or M is selected, the other must also be selected. M and P cannot both be selected.

Question: Which one of the following is an acceptable selection of representatives for the committee?

F, G, Q, R, S
F, J, K, P, Q
F, P, Q, R, S
J, K, M, Q, S
J, M, P, Q, S


Question: Which one of the following lists three representatives who could be selected together for the committee?


Question: If M is the chairperson of the committee, which one of the following is among the people who must also be on the committee?


Question: If F is the chairperson of the committee, which one of the following is among the people who must also be on the committee?


Question: If F is selected, any one of the following people could be the chairperson of the committee EXCEPT:


Question: If neither F nor K is selected for the committee, which one of the following can be true?

G is selected.
P is selected.
J is the chairperson.
Q is the chairperson.
S is the chairperson.


Question: If the chairperson of the committee is to be a homeowner, which one of the following must be true?

If G is selected, Q is also selected.
If G is selected, R is also selected.
If J is selected, F is also selected.
If J is selected, Q is also selected.
If J is selected, R is also selected.


Question: The committee must include at least one representative from which one of the following pairs?


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

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

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


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

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

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


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

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

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

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

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

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


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

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

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

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

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

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


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

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

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

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

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

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


A 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 children—F, G, H, J, and K—and four adults—Q, R, S, and T—are planning a canoeing trip. The canoeists will be divided into three groups—groups 1, 2, and 3—of three canoeists each, according to the following conditions: There must be at least one adult in each group. F must be in the same group as J. G cannot be in the same group as T. H cannot be in the same group as R. Neither H nor T can be in group 2.

Question: If F is in group 1, which one of the following could be true?

G and K are in group 3.
G and R are in group 3.
J and S are in group 2.
K and R are in group 1.
Q and S are in group 2.


Question: If F and S are in group 3, which one of the following must be true?

G is in group 2.
H is in group 3.
K is in group 1.
Q is in group 2.
R is in group 1.


Question: If G and K are in group 3, which one of the following must be true?

H is in group 3.
J is in group 1.
R is in group 2.
S is in group 3.
T is in group 1.


Question: If Q is in group 1 and S is in group 3, which one of the following CANNOT be true?

G is in group 2.
T is in group 1.
There is exactly one child in group 1.
There is exactly one child in group 2.
There is exactly one child in group 3.