Context: 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?

Answer: Klosnik, Poirier, Neri, Manley, Osata, Londi

Answer: Klosnik, Londi, Manley, Poirier, Neri, Osata

Answer: Klosnik, Londi, Manley, Osata, Poirier, Neri

Answer: Klosnik, Osata, Poirier, Neri, Londi, Manley

Answer: 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?

Answer: Klosnik and Osata

Answer: Londi and Neri

Answer: Londi and Osata

Answer: Manley and Neri

Answer: Manley and Poirier


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

Answer: Londi and Neri

Answer: Londi and Osata

Answer: Neri and Osata

Answer: Neri and Poirier

Answer: Osata and Poirier


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

Answer: Londi and Manley

Answer: Londi and Poirier

Answer: Neri and Osata

Answer: Neri and Poirier

Answer: 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?

Answer: Klosnik

Answer: Klosnik, Neri

Answer: Neri, Poirier

Answer: Klosnik, Osata, Poirier

Answer: Klosnik, Neri, Osata, Poirier


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

Answer: Klosnik sits immediately next to Osata.

Answer: Londi sits immediately next to Manley.

Answer: Osata sits immediately next to Poirier.

Answer: Neri sits directly between Londi and Poirier.

Answer: Osata sits directly between Klosnik and Manley.


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

Answer: Klosnik and Manley

Answer: Klosnik and Neri

Answer: Manley and Neri

Answer: Manley and Poirier

Answer: Neri and Osata


Context: 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?

Answer: The computer in office 2 was bought in 1987.

Answer: The computer in office 2 was bought in 1988.

Answer: The computer in office 4 was bought in 1988.

Answer: The printer in office 4 was bought in 1988.

Answer: The printer in office 4 was bought in 1989.


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

Answer: The printer in office 1 was bought in 1987.

Answer: The computer in office 2 was bought in 1987.

Answer: The computer in office 3 was bought in 1989.

Answer: The printer in office 4 was bought in 1988.

Answer: 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?

Answer: 0

Answer: 1

Answer: 2

Answer: 3

Answer: 4


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

Answer: The printer in office 1 was bought in 1988.

Answer: The printer in office 1 was bought in 1989.

Answer: The computer in office 2 was bought in 1988.

Answer: The computer in office 3 was bought in 1987.

Answer: 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?

Answer: The printer in office 1 was bought in 1988.

Answer: The computer in office 2 was bought in 1987.

Answer: The printer in office 2 was bought in 1988.

Answer: The computer in office 4 was bought in 1987.

Answer: 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?

Answer: the printer in office 1

Answer: the computer in office 2

Answer: the printer in office 2

Answer: the computer in office 4

Answer: the printer in office 4


Context: 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?

Answer: Hodges joined the law firm in 1961.

Answer: Hodges joined the law firm in 1963.

Answer: Gregg joined the law firm in 1964.

Answer: MacNeil joined the law firm in 1964.

Answer: Owens joined the law firm in 1964.


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

Answer: Hodges joined the firm in 1963.

Answer: MacNeil joined the firm in 1963.

Answer: Hodges joined the firm in 1964.

Answer: Nader joined the firm in 1964.

Answer: Owens joined the firm in 1964.


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

Answer: 1962

Answer: 1963

Answer: 1964

Answer: 1965

Answer: 1966


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?

Answer: 1

Answer: 2

Answer: 3

Answer: 4

Answer: 5


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?

Answer: 1963

Answer: 1964

Answer: 1965

Answer: 1966

Answer: 1967


Context: 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?

Answer: The line 1 tickets for January are green.

Answer: The line 1 tickets for January are yellow.

Answer: The line 1 tickets for February are red.

Answer: The line 2 tickets for February are yellow.

Answer: 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?

Answer: The line 1 tickets for January are red.

Answer: The line 3 tickets for January are red.

Answer: The line 1 tickets for February are red.

Answer: The line 3 tickets for February are green.

Answer: The line 3 tickets for February are yellow.


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

Answer: No January ticket is green.

Answer: No February ticket is green.

Answer: Only line 2 tickets are red.

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

Answer: 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?

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

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

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

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

Answer: 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:

Answer: One set of January tickets is green.

Answer: One set of line 1 tickets is red.

Answer: One set of line 2 tickets is red.

Answer: The tickets in two of the six sets are red.

Answer: 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?

Answer: None of the January tickets are green.

Answer: None of the February tickets are green.

Answer: None of the line 2 tickets are green.

Answer: No line 1 or line 2 tickets are yellow.

Answer: No line 2 or line 3 tickets are red.


Context: 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?

Answer: Eberle and Jessup

Answer: Brandt and Garcia

Answer: Brandt and Calva

Answer: Garcia and Calva

Answer: Jessup and Brandt


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

Answer: Eberle

Answer: Brandt

Answer: Irving

Answer: Garcia

Answer: Jessup


Question: Exactly how many workers were hired before Jessup?

Answer: 6

Answer: 5

Answer: 4

Answer: 3

Answer: 2


Question: Which one of the following must be true?

Answer: Duvall was the first worker to be hired.

Answer: Haga was the first worker to be hired.

Answer: Fu and Irving were the first two workers to be hired.

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

Answer: 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?

Answer: Monday

Answer: Tuesday

Answer: Wednesday

Answer: Thursday

Answer: Friday


Context: 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?

Answer: Q lives on the third floor.

Answer: Q lives on the fifth floor.

Answer: L does not live on the fourth floor.

Answer: N does not live on the second floor.

Answer: J lives on the first floor.


Question: Which one of the following CANNOT be true?

Answer: K lives on the second floor.

Answer: M lives on the first floor.

Answer: N lives on the fourth floor.

Answer: O lives on the third floor.

Answer: 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?

Answer: O lives on the first floor.

Answer: Q lives on the fourth floor.

Answer: N lives on the fifth floor.

Answer: L lives on the fourth floor.

Answer: P lives on the third floor.


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

Answer: K lives on the fourth floor.

Answer: K lives on the fifth floor.

Answer: L lives on the first floor.

Answer: L lives on the third floor.

Answer: L lives on the fourth floor.


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

Answer: O lives on the fifth floor.

Answer: J lives on the first floor.

Answer: L lives on the second floor.

Answer: Q lives on the third floor.

Answer: P lives on the first floor.


Question: Which one of the following must be true?

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

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

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

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

Answer: 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?

Answer: L lives on the first floor.

Answer: M lives on the third floor.

Answer: Q lives on the third floor.

Answer: N lives on the fifth floor.

Answer: Q lives on the fifth floor.


Context: 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?

Answer: She visits exactly two cities in country X.

Answer: She visits exactly two cities in country Y.

Answer: She visits exactly two cities in country Z.

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

Answer: 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?

Answer: 3

Answer: 4

Answer: 5

Answer: 6

Answer: 7


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?

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

Answer: She visits exactly two cities in country X.

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

Answer: She visits exactly two cities in country Z.

Answer: 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?

Answer: Hannah cannot visit any other cities in country X.

Answer: Hannah can visit four cities in country Y.

Answer: Hannah can spend six days in Nomo.

Answer: Hannah cannot spend more than four days in country Z.

Answer: 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?

Answer: 6

Answer: 7

Answer: 8

Answer: 9

Answer: 10


Context: 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?

Answer: P, Q

Answer: P, R

Answer: P, Q, R

Answer: P, R, T

Answer: P, Q, R, T


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

Answer: A female greyhound wins the second place ribbon.

Answer: A female labrador wins the second place ribbon.

Answer: A female labrador wins the third place ribbon.

Answer: A male greyhound wins the fourth place ribbon.

Answer: A female greyhound wins the fourth place ribbon.


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

Answer: dog P

Answer: dog R

Answer: dog S

Answer: dog T

Answer: dog U


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

Answer: Dog P places ahead of dog R.

Answer: Dog P places ahead of dog T.

Answer: Dog R places ahead of dog U.

Answer: Dog R places ahead of dog T.

Answer: Dog S places ahead of dog U.


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

Answer: Dog P is male.

Answer: Dog R is male.

Answer: Dog Q wins the fourth place ribbon.

Answer: Dog Q is a greyhound.

Answer: Dog T is a greyhound.


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

Answer: Dog P is male.

Answer: Dog Q is male.

Answer: Dog T is male.

Answer: Dog Q is a labrador.

Answer: Dog T is a labrador.


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

Answer: Dog P does not win a ribbon.

Answer: Dog R does not win a ribbon.

Answer: Dog S does not win a ribbon.

Answer: Dog T wins a ribbon.

Answer: Dog U wins a ribbon.


Context: 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?

Answer: pork chops, roast beef

Answer: pork chops, veal cutlet

Answer: pork chops, swordfish, veal cutlet

Answer: pork chops, roast beef, tilefish, veal cutlet

Answer: pork chops, roast beef, swordfish, tilefish, veal cutlet


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

Answer: John orders the same kind of entree as Marie does.

Answer: Kate orders the same kind of entree as Nat does.

Answer: Lewis orders the same kind of entree as Nat does.

Answer: Marie orders the same kind of entree as Olive does.

Answer: Nat orders the same kind of entree as Olive does.


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

Answer: One of the men orders pork chops or veal cutlet.

Answer: One of the men orders swordfish or veal cutlet.

Answer: Two of the women order tilefish.

Answer: None of the men orders a fish entree.

Answer: 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?

Answer: Kate orders roast beef.

Answer: Kate orders swordfish.

Answer: Lewis orders tilefish.

Answer: Lewis orders veal cutlet.

Answer: Nat orders pork chops.


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

Answer: John orders veal cutlet.

Answer: Kate orders tilefish.

Answer: Lewis orders tilefish.

Answer: One of the men orders swordfish.

Answer: 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?

Answer: roast beef

Answer: veal cutlet

Answer: roast beef, veal cutlet

Answer: roast beef, swordfish

Answer: 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?

Answer: John orders roast beef.

Answer: John orders swordfish.

Answer: Kate orders roast beef.

Answer: Two of the people order pork chops.

Answer: Two of the people order tilefish.


Context: 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?

Answer: the Kahns

Answer: the Muirs

Answer: the Newmans

Answer: the Piatts

Answer: the Rutans


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

Answer: the Lowes

Answer: the Newmans

Answer: the Owens

Answer: the Piatts

Answer: the Rutans


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

Answer: the Kahns and the Piatts

Answer: the Lowes and the Piatts

Answer: the Muirs and the Piatts

Answer: the Muirs and the Owens

Answer: the Muirs and the Newmans


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

Answer: The Owens live next to the Newmans.

Answer: The Owens live next to the Rutans.

Answer: The Piatts live next to the Lowes.

Answer: The Piatts live next to the Muirs.

Answer: 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?

Answer: The Kahns live east of the Muirs.

Answer: The Kahns live west of the Rutans.

Answer: The Owens live west of the Lowes.

Answer: The Owens live east of the Piatts.

Answer: 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?

Answer: the Kahns and the Piatts

Answer: the Lowes and the Owens

Answer: the Muirs and the Newmans

Answer: the Newmans and the Rutans

Answer: the Owens and the Piatts


Context: 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?

Answer: There are research models on floor 1.

Answer: There are sports cars on floor 1.

Answer: There are family cars on floor 2.

Answer: There are research models on floor 2.

Answer: There are family cars on floor 3.


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

Answer: The exhibition includes new research model sports cars.

Answer: The exhibition includes used research model family cars.

Answer: The exhibition includes used research model sports cars.

Answer: There are research models on exactly one floor.

Answer: There are research models on all three floors.


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

Answer: There are production models on floor 1.

Answer: There are research models on floor 1.

Answer: There are production models on floor 2.

Answer: There are production models on floor 3.

Answer: 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?

Answer: There are family cars on floor 1.

Answer: There are research models on floor 1.

Answer: There are new cars on floor 2.

Answer: There are research models on floor 2.

Answer: 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?

Answer: All the family cars in the exhibition are new.

Answer: All the family cars in the exhibition are research models.

Answer: All the family cars in the exhibition are used.

Answer: All the new cars in the exhibition are family cars.

Answer: 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?

Answer: There are family cars on floor 1.

Answer: There are new cars on floor 2.

Answer: There are research models on floor 2.

Answer: There are family cars on floor 3.

Answer: There are sports cars on floor 3.


Context: 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?

Answer: Cindy flies in either plane 1 or plane 3.

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

Answer: Bob and one other person fly in plane l.

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

Answer: 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?

Answer: Cindy flies with Dave and Ed.

Answer: Cindy flies with Ed.

Answer: Dave flies with Cindy.

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

Answer: 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?

Answer: Bob flies with Anna.

Answer: Dave flies with Ed.

Answer: Dave and Ed fly with Bob.

Answer: Dave flies with Bob.

Answer: Ed flies with Anna.


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

Answer: Anna, Bob, Cindy, Fran

Answer: Anna, Bob, Ed, Fran

Answer: Bob, Cindy, Ed, Fran

Answer: Bob, Cindy, Dave, Ed

Answer: Bob, Dave, Ed, Fran


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

Answer: exactly two people

Answer: exactly three people

Answer: exactly four people

Answer: exactly five people

Answer: three pilots and two copilots


Context: 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?

Answer: Fox

Answer: Inman

Answer: Lopez

Answer: Malloy

Answer: Nassar


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

Answer: 3

Answer: 4

Answer: 5

Answer: 6

Answer: 7


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

Answer: Lopez's salary is greater than Fox's.

Answer: Lopez's salary is greater than Inman's.

Answer: Nassar's salary is greater than Fox's.

Answer: Nassar's salary is greater than Inman's.

Answer: 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?

Answer: Inman's salary is less than Lopez's.

Answer: Jacoby's salary is less than Lopez's.

Answer: Lopez's salary is less than Fox's.

Answer: Lopez's salary is less than Hae's.

Answer: 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?

Answer: 5

Answer: 6

Answer: 7

Answer: 8

Answer: 9


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?

Answer: fifth

Answer: fifth, sixth

Answer: fifth, seventh

Answer: fifth, sixth, seventh

Answer: fifth, sixth, seventh, eighth


Context: 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?

Answer: Illness J has exactly two symptoms.

Answer: Illness K has exactly one symptom.

Answer: Illness L has exactly two symptoms.

Answer: Illness M has exactly three symptoms.

Answer: 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?

Answer: J and N

Answer: K and L

Answer: K and N

Answer: L and M

Answer: M and N


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?

Answer: Fever is a symptom of illness L.

Answer: Sneezing is a symptom of illness L.

Answer: Headache is a symptom of illness L.

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

Answer: 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?

Answer: J and L

Answer: J and M

Answer: J and N

Answer: K and L

Answer: M and N


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

Answer: both illness J and illness L

Answer: both illness J and illness N

Answer: both illness K and illness L

Answer: both illness K and illness N

Answer: both illness L and illness N


Context: 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?

Answer: First Street

Answer: Second Street

Answer: Third Street

Answer: Fifth Street

Answer: 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?

Answer: 1

Answer: 2

Answer: 3

Answer: 4

Answer: 5


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

Answer: 1

Answer: 2

Answer: 3

Answer: 4

Answer: 5


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

Answer: The crew cleaned First Street on Tuesday afternoon.

Answer: The crew cleaned Second Street on Thursday afternoon.

Answer: The crew cleaned Third Street on Wednesday morning.

Answer: The crew cleaned Fifth Street on Thursday afternoon.

Answer: 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?

Answer: 1

Answer: 2

Answer: 3

Answer: 4

Answer: 5


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?

Answer: The crew cleaned First Street before Second Street.

Answer: The crew cleaned Second Street before Fifth Street.

Answer: The crew cleaned Third Street before Second Street.

Answer: The crew cleaned Sixth Street before Fifth Street.

Answer: The crew cleaned Seventh Street before Second Street.


Context: 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?

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

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

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

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

Answer: 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?

Answer: J and K

Answer: K and O

Answer: L and O

Answer: M and N

Answer: N and O


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?

Answer: J and M

Answer: K and N

Answer: K and O

Answer: L and O

Answer: N and O


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

Answer: Chalet J is directly connected to chalet M.

Answer: Chalet K is directly connected to chalet N.

Answer: Chalet L is directly connected to chalet O.

Answer: Chalet L is directly connected to exactly two chalets.

Answer: 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?

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

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

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

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

Answer: 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?

Answer: K

Answer: L

Answer: M

Answer: N

Answer: O


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:

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

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

Answer: Chalet L is directly connected to exactly one other chalet.

Answer: Chalet N is directly connected to exactly two other chalets.

Answer: Chalet O is directly connected to exactly two other chalets.


Context: 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?

Answer: John's geology grade is a B.

Answer: John's history grade is a D.

Answer: John's history grade is an E.

Answer: John's physics grade is a B.

Answer: 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?

Answer: He receives exactly one A.

Answer: He receives exactly one B.

Answer: He receives exactly two Bs.

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

Answer: 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?

Answer: His grade in history is D.

Answer: His grade in Italian is D.

Answer: His grades in history and Italian are identical.

Answer: His grades in history and Russian are identical.

Answer: 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?

Answer: 2

Answer: 3

Answer: 4

Answer: 5

Answer: 6


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?

Answer: John receives both an A and a B.

Answer: John receives both an A and a C.

Answer: John receives both a B and a D.

Answer: John receives both a B and an E.

Answer: 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?

Answer: He receives a lower grade in Italian than in economics.

Answer: He receives a lower grade in Italian than in physics.

Answer: He receives a lower grade in physics than in Italian.

Answer: He receives a lower grade in Russian than in economics.

Answer: He receives a lower grade in Russian than in history.


Context: 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?

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

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

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

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

Answer: 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?

Answer: Casey buys two blue shirts.

Answer: Casey buys two red shirts.

Answer: Casey buys two yellow shirts.

Answer: Casey buys two small shirts.

Answer: Casey buys two medium shirts.


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

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

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

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

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

Answer: 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?

Answer: a medium red shirt

Answer: a medium yellow shirt

Answer: a medium blue shirt

Answer: a large red shirt

Answer: a large yellow shirt


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

Answer: a red shirt

Answer: a medium yellow shirt

Answer: either a large shirt or a small shirt

Answer: either a medium red shirt or a medium blue shirt

Answer: either a large yellow shirt or a medium blue shirt


Context: 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

Answer: G, H, K W, Y

Answer: G, J, K W, X

Answer: G, J, L X, Z

Answer: H, J, L W, Z

Answer: H, K, L Y, Z


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

Answer: She selects at least one W.

Answer: She selects at least one X.

Answer: She selects the J, but no Y's.

Answer: She selects the K, but no X's.

Answer: 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?

Answer: G, H, K

Answer: G, J, K

Answer: G, K, L

Answer: H, J, L

Answer: J, K, L


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

Answer: G, K, L

Answer: H, J, K

Answer: H, J, L

Answer: H, K, L

Answer: J, K, L


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

Answer: G, H, K

Answer: H, J, K

Answer: H, J, L

Answer: H, K, L

Answer: J, K, L


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

Answer: W and X

Answer: W and Y

Answer: W and Z

Answer: X and Y

Answer: X and Z


Context: 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?

Answer: first

Answer: first, second

Answer: first, fifth

Answer: second, fifth

Answer: first, second, fifth


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

Answer: Palmdale

Answer: Quietville

Answer: Riverdale

Answer: Seaside

Answer: Tidetown


Question: Which of the following could be true?

Answer: Palmdale is ranked first in both climate and friendliness.

Answer: Quietville is ranked second in both climate and location.

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

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

Answer: Tidetown is ranked third in both climate and friendliness.


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

Answer: Palmdale is ranked second in climate

Answer: Palmdale is ranked third in friendliness

Answer: Riverdale is ranked second in friendliness

Answer: Riverdale is ranked third in friendliness

Answer: Tidetown is ranked fifth in location


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

Answer: Palmdale is ranked second in friendliness.

Answer: Quietville is ranked first in climate.

Answer: Riverdale is ranked first in friendliness.

Answer: Riverdale is ranked fifth in climate.

Answer: 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?

Answer: One

Answer: Two

Answer: Three

Answer: Four

Answer: Five


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

Answer: Palmdale is ranked first in climate.

Answer: Quietville is ranked fifth in climate.

Answer: Riverdale is ranked third in friendliness.

Answer: Seaside is ranked first in location.

Answer: Tidetown is ranked second in friendliness.


Context: 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?

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

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

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

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

Answer: 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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: Cage Y contains exactly two lizards.

Answer: Cage Y contains exactly two snakes.

Answer: Cage Y contains exactly four animals.

Answer: Cage Z contains exactly three snakes.

Answer: 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?

Answer: Cage W contains exactly six animals.

Answer: Cage X contains exactly six animals.

Answer: Cage Y contains exactly one snake.

Answer: Cage Y contains exactly three snakes.

Answer: Cage Z contains exactly four snakes.


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

Answer: Cage W contains two gerbils.

Answer: Cage X contains four animals.

Answer: Cage Z contains two snakes.

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

Answer: 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?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


Context: 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?

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

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

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

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

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


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

Answer: Jazz received more votes than Nipi.

Answer: Kola received more votes than Nipi.

Answer: Luck received more votes than Jazz.

Answer: Nipi received more votes than Oboy.

Answer: 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?

Answer: Jazz received more votes than Luck.

Answer: Jazz received more votes than Ping.

Answer: Nipi received more votes than Oboy.

Answer: Nipi received more votes than Mist.

Answer: 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?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: three

Answer: four

Answer: five

Answer: six

Answer: seven


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

Answer: two

Answer: three

Answer: four

Answer: five

Answer: six


Context: 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?

Answer: Z

Answer: Y

Answer: X

Answer: T

Answer: L


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

Answer: The bench on the northwest corner is pink.

Answer: The bench on the northeast corner is green.

Answer: The bench on the southwest corner is pink.

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

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


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

Answer: K

Answer: L

Answer: T

Answer: U

Answer: X


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?

Answer: K

Answer: T

Answer: X

Answer: Y

Answer: Z


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

Answer: J is directly west of K.

Answer: K is directly east of U.

Answer: U is directly north of X.

Answer: X is directly south of J.

Answer: 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?

Answer: K and X

Answer: K and Z

Answer: L and U

Answer: L and X

Answer: L and Z


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

Answer: J and L

Answer: K and T

Answer: T and X

Answer: U and Y

Answer: X and Z


Context: 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 ?

Answer: J, K

Answer: J, M

Answer: J, O

Answer: J, M, O

Answer: J, K, M, O


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

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

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

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

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

Answer: 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?

Answer: No bridge directly connects L with M.

Answer: A bridge directly connects J with L.

Answer: A bridge directly connects L with O.

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

Answer: 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?

Answer: A bridge directly connects J with M.

Answer: A bridge directly connects K with M.

Answer: A bridge directly connects K with O.

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

Answer: 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

Answer: J with L

Answer: J with M

Answer: K with O

Answer: L with M

Answer: L with O


Context: 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?

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

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

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

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

Answer: 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?

Answer: Hubert visits the same city as Paul.

Answer: Lori visits the same city as Regina.

Answer: Paul visits the same city as Regina.

Answer: Paul visits Toronto.

Answer: Paul visits Vancouver.


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

Answer: Hubert visits Montreal.

Answer: Lori visits Montreal.

Answer: Paul visits Toronto.

Answer: Lori visits the same city as Paul.

Answer: Lori visits the same city as Regina.


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

Answer: Sharon must visit Montreal if Paul visits Vancouver.

Answer: Regina must visit Vancouver if Paul visits Vancouver.

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

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

Answer: 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?

Answer: Lori visits Toronto.

Answer: Lori visits Vancouver.

Answer: Paul visits Toronto.

Answer: Paul visits Vancouver.

Answer: Sharon visits Vancouver.


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

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

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

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

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

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


Context: 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 ?

Answer: fall mathematics, spring mathematics, fall oceanography, fall nutrition, spring nutrition, spring oceanography

Answer: fall oceanography, spring nutrition, fall nutrition, fall mathematics, spring mathematics, spring oceanography

Answer: spring mathematics, fall mathematics, spring nutrition, fall oceanography, fall nutrition, spring oceanography

Answer: spring oceanography, fall oceanography, fall nutrition, fall mathematics, spring mathematics, spring nutrition

Answer: spring oceanography, fall oceanography, spring mathematics, fall mathematics, fall nutrition, spring nutrition


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

Answer: The spring mathematics orders are in folder 3.

Answer: The fall nutrition orders are in folder 3.

Answer: The spring oceanography orders are in folder 1.

Answer: The spring nutrition orders are in folder 6.

Answer: 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?

Answer: The spring mathematics orders are in folder 4.

Answer: The spring mathematics orders are in folder 6.

Answer: The fall nutrition orders are in folder 1.

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

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


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

Answer: The spring mathematics orders are in folder 1.

Answer: The fall oceanography orders are in folder 1.

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

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

Answer: 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?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: 3 and 5

Answer: 4 and 5

Answer: 3 and 6

Answer: 4 and 6

Answer: 5 and 6


Question: Which one of the following could be true?

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

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

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

Answer: The mathematics orders are in folders 1 and 4.

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


Context: 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?

Answer: two

Answer: three

Answer: four

Answer: five

Answer: six


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

Answer: French

Answer: Park

Answer: Quetzal

Answer: Rincon

Answer: Tonka


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?

Answer: Quetzal, Tonka

Answer: Semplain, French

Answer: Semplain, Park

Answer: Quetzal, Park, Greene

Answer: 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

Answer: zero

Answer: one

Answer: two

Answer: three

Answer: four


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

Answer: French or Tonka

Answer: Greene or Urstine

Answer: Quetzal or Tonka

Answer: Quetzal or Urstine or both

Answer: 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

Answer: French, Greene, and Park

Answer: French, Greene, and Quetzal

Answer: French, Greene, and Rincon

Answer: Park, Tonka, and Urstine

Answer: Park, Semplain, and Tonka


Context: 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?

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

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

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

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

Answer: 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?

Answer: Ganz, Lowry, Wilford

Answer: Johnson, Lowry, Stefano

Answer: Lowry, Stefano, Turner

Answer: Lowry, Stefano, Wilford

Answer: 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?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: Lowry is an assistant.

Answer: Wilford is a partner.

Answer: There are no assistants.

Answer: There are at least two assistants.

Answer: 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?

Answer: none

Answer: one

Answer: two

Answer: three

Answer: four


Context: 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?

Answer: the news

Answer: H

Answer: L

Answer: O

Answer: S


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

Answer: second

Answer: third

Answer: fourth

Answer: fifth

Answer: sixth


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

Answer: G, H, and L

Answer: S, G, and the news

Answer: H, G, and L

Answer: H, L, and O

Answer: L, O, and S


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

Answer: first

Answer: second

Answer: third

Answer: fourth

Answer: sixth


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

Answer: 1

Answer: 2

Answer: 3

Answer: 4

Answer: 5


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

Answer: the third

Answer: the fourth

Answer: the fifth

Answer: the sixth

Answer: 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?

Answer: the first

Answer: the third

Answer: the fourth

Answer: the fifth

Answer: the sixth


Context: 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?

Answer: Monday

Answer: Tuesday

Answer: Wednesday

Answer: Friday

Answer: Saturday


Question: On Wednesday Doctor Yamata could be scheduled to

Answer: conduct research in the morning and operate in the afternoon

Answer: lecture in the morning and treat patients in the afternoon

Answer: operate in the morning and lecture in the afternoon

Answer: operate in the morning and conduct research in the afternoon

Answer: treat patients in the morning and treat patients in the afternoon


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

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

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

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

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

Answer: 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

Answer: Monday morning, Monday afternoon, Friday morning, Friday afternoon

Answer: Monday morning, Friday afternoon, Saturday morning, Saturday afternoon

Answer: Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon

Answer: Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon

Answer: 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?

Answer: Monday and Tuesday

Answer: Monday and Saturday

Answer: Tuesday and Friday

Answer: Tuesday and Saturday

Answer: Friday and Saturday


Context: 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?

Answer: No conservative and exactly two liberals voted for Datalog.

Answer: Exactly one conservative and exactly one liberal voted for Datalog.

Answer: Exactly one conservative and all three liberals voted for Datalog.

Answer: Exactly two conservatives and exactly one liberal voted for Datalog.

Answer: Exactly two conservatives and exactly two liberals voted for Datalog.


Question: Which one of the following must be true?

Answer: At least one conservative voted for Datalog.

Answer: At least one liberal voted against Datalog.

Answer: At least one liberal voted for Datalog.

Answer: At least one moderate voted against Datalog.

Answer: 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?

Answer: Both moderates voted for Datalog.

Answer: Both moderates voted against Datalog.

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

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

Answer: All three liberals voted for Datalog.


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

Answer: Both moderates voted for Datalog.

Answer: Exactly one conservative voted for Datalog.

Answer: No conservative voted for Datalog.

Answer: Exactly two liberals voted for Datalog.

Answer: 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

Answer: two liberals

Answer: one conservative, one liberal

Answer: two moderates, three liberals

Answer: one conservative, two moderates, two liberals

Answer: 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:

Answer: Both conservatives voted against Datalog.

Answer: Both moderates voted for Datalog.

Answer: At least one liberal voted against Datalog.

Answer: Exactly two liberals voted for Datalog.

Answer: Exactly five of the judges voted against Datalog.


Context: 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?

Answer: F G H K J

Answer: G H J K F

Answer: G K F J H

Answer: H J G K F

Answer: J H F K G


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

Answer: next to the lane to which Larry is assigned

Answer: next to the lane to which Ned is assigned

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

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

Answer: 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

Answer: F 1

Answer: G 5

Answer: H 1

Answer: H 3

Answer: J 5


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

Answer: Larry, Ned

Answer: Patricia, Sonja

Answer: Larry, Ned, Olivia

Answer: Larry, Ned, Sonja

Answer: Ned, Patricia, Sonja


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

Answer: the runner representing G is assigned to lane 1

Answer: the runner representing H is assigned to lane 2

Answer: Larry is the runner representing K

Answer: Olivia is the runner representing F

Answer: Patricia is the runner representing H


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

Answer: Larry Olivia Ned Patricia Sonja

Answer: Larry Ned Olivia Sonja Patricia

Answer: Larry Sonja Patricia Ned Olivia

Answer: Ned Olivia Larry Patricia Sonja

Answer: Ned Sonja Olivia Patricia Larry


Context: 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?

Answer: H and U

Answer: H and Z

Answer: K and O

Answer: O and U

Answer: U and Z


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?

Answer: Monday

Answer: Tuesday

Answer: Wednesday

Answer: Thursday

Answer: Friday


Question: Which one of the following must be true?

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

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

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

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

Answer: 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?

Answer: Monday

Answer: Tuesday

Answer: Wednesday

Answer: Thursday

Answer: 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?

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

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

Answer: They are both scheduled for Tuesday.

Answer: They are both scheduled for Thursday.

Answer: They are both scheduled for Friday.


Context: 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?

Answer: 1, 3, 5, 7

Answer: 2, 4, 6, 8

Answer: 2, 3, 5, 6, 8

Answer: 3, 4, 6, 7, 8

Answer: 1, 2, 4, 5, 6, 8


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

Answer: light 2

Answer: light 3

Answer: light 4

Answer: light 5

Answer: light 6


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

Answer: light 3

Answer: light 4

Answer: light 5

Answer: light 6

Answer: light 7


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

Answer: If light 2 is on, then light 6 is off.

Answer: If light 3 is on, then light 2 is on.

Answer: If light 4 is on, then light 3 is off.

Answer: If light 5 is off, then light 4 is on.

Answer: If light 6 is off, then light 1 is on.


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

Answer: Light 1 is off and light 6 is off.

Answer: Light 1 is on and light 7 is on.

Answer: Light 2 is off and light 4 is on.

Answer: Light 2 is off and light 6 is off.

Answer: Light 6 is on and light 7 is on.


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

Answer: Light 1 is on.

Answer: Light 2 is on.

Answer: Light 5 is off.

Answer: Light 6 is on.

Answer: 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?

Answer: Light 1 is off.

Answer: Light 2 is on.

Answer: Light 3 is off.

Answer: Light 4 is on.

Answer: Light 5 is on.


Context: 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?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: Both Harry and Joel sit east of Frank.

Answer: Both Harry and Ruby sit east of Frank.

Answer: Both Harry and Joel sit west of Frank.

Answer: Both Harry and Ruby sit west of Frank.

Answer: 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?

Answer: Both Frank and Ivan sit east of Ruby.

Answer: Both Frank and Ruby sit west of Thelma.

Answer: Both Frank and Sylvia sit east of Ruby.

Answer: Both Frank and Thelma sit west of Sylvia.

Answer: Both Frank and Ruby sit west of Joel.


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

Answer: Harry sits west of Frank.

Answer: Joel sits west of Ivan.

Answer: Ruby sits west of Frank.

Answer: Thelma sits west of Frank.

Answer: 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?

Answer: Frank and Thelma

Answer: Harry and Ruby

Answer: Harry and Sylvia

Answer: Ivan and Ruby

Answer: Joel and Ruby


Context: 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:

Answer: W responds to heptocillin.

Answer: X responds to ganocyclene.

Answer: X responds to heptocillin.

Answer: Y responds to heptocillin.

Answer: Z responds to ganocyclene.


Question: Which one of the following could be true?

Answer: W, X, and Z all respond to ferromycin.

Answer: W, X, and Z all respond to ganocyclene.

Answer: W and exactly one other organism respond to ganocyclene.

Answer: W responds to more of the antibiotics than X does.

Answer: More of the organisms respond to ferromycin than to ganocyclene.


Question: Which one of the following could be true?

Answer: Exactly one of the organisms responds to ferromycin.

Answer: All four of the organisms respond to heptocillin.

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

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

Answer: 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?

Answer: W responds to ganocyclene.

Answer: X responds to ganocyclene.

Answer: X responds to heptocillin.

Answer: Z responds to ferromycin.

Answer: 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?

Answer: It must respond to ferromycin.

Answer: It must respond to ganocyclene.

Answer: It must respond to heptocillin.

Answer: It cannot respond to ferromycin.

Answer: It cannot respond to ganocyclene.


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

Answer: W responds to ferromycin.

Answer: X responds to ferromycin.

Answer: Z responds to ferromycin.

Answer: Exactly three of the organisms respond to ganocyclene.

Answer: 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:

Answer: W responds to ferromycin.

Answer: X responds to ganocyclene.

Answer: Z responds to ganocyclene.

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

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


Context: 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

Answer: 2 gardenias 1 orchid 1 gardenia 1 rose 1 rose 1 orchid 1 violet 1 violet

Answer: 2 orchids 2 orchids 2 gardenias 1 rose 1 rose 1 rose

Answer: 2 orchids 3 roses 1 gardenia 1 rose 2 violets

Answer: 1 gardenia 1 gardenia 1 gardenia 1 orchid 1 rose 1 rose 1 rose 1 violet 1 violet

Answer: 1 orchid 3 violets 3 gardenias 2 roses


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

Answer: three

Answer: four

Answer: five

Answer: six

Answer: seven


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?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: two orchids

Answer: three gardenias

Answer: three roses

Answer: five roses

Answer: five violets


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

Answer: one gardenia and one orchid

Answer: one gardenia and one rose

Answer: one orchid and one rose

Answer: one orchid and one violet

Answer: one rose and one violet


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

Answer: exactly one rose and exactly one gardenia

Answer: exactly one orchid and exactly four violets

Answer: exactly two orchids

Answer: exactly two roses

Answer: exactly six 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?

Answer: one rose, one orchid, and one gardenia

Answer: one rose and two orchids

Answer: one rose and two violets

Answer: two roses and one gardenia

Answer: two roses and one violet


Context: 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?

Answer: J, K, M, P

Answer: J, L, N, Q

Answer: J, M, N, Q

Answer: K, M, P, Q

Answer: L, M, N, P


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

Answer: K or Q or both

Answer: L or M or both

Answer: N or M or both

Answer: N or Q or both

Answer: 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?

Answer: J and N

Answer: J and Q

Answer: K and L

Answer: K and N

Answer: N and Q


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?

Answer: J and Q

Answer: K and L

Answer: K and P

Answer: L and P

Answer: N and Q


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?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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?

Answer: J and L

Answer: K and M

Answer: L and N

Answer: L and Q

Answer: M and Q


Context: 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?

Answer: Rita

Answer: Sarah

Answer: Tura

Answer: Rita, Sarah

Answer: Rita, Tura


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

Answer: Karl partners Tura in dance 1.

Answer: Luis partners Sarah in dance 2.

Answer: Luis partners Sarah in dance 3.

Answer: Miguel partners Sarah in dance 1.

Answer: 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?

Answer: Karl and Rita

Answer: Karl and Tura

Answer: Luis and Rita

Answer: Luis and Tura

Answer: 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?

Answer: Karl and Rita

Answer: Karl and Tura

Answer: Luis and Rita

Answer: Luis and Tura

Answer: Miguel and Rita


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

Answer: Karl partners Rita in dance 2.

Answer: Karl partners Sarah in dance 3.

Answer: Karl partners Tura in dance 1.

Answer: Luis partners Rita in dance 2.

Answer: Luis partners Tura in dance 3.


Context: 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?

Answer: City 5 contains a university.

Answer: City 6 contains a university.

Answer: City 2 contains a jail.

Answer: City 3 contains a jail.

Answer: City 3 contains a hospital.


Question: Which one of the following could be true?

Answer: City 1 contains exactly one hospital.

Answer: City 1 contains exactly one university.

Answer: City 2 contains exactly one jail.

Answer: City 5 contains exactly one university.

Answer: 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?

Answer: 1, 4

Answer: 2, 4

Answer: 4, 5

Answer: 1, 4, 5

Answer: 1, 2, 4, 5


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

Answer: There is a jail in city 1.

Answer: There is a hospital in city 2.

Answer: There is a hospital in city 3.

Answer: There is a hospital in city 4.

Answer: There is a jail in city 4.


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

Answer: 1

Answer: 2

Answer: 4

Answer: 5

Answer: 6


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?

Answer: 1, 3, 5

Answer: 1, 4, 5

Answer: 2, 3, 5

Answer: 2, 4, 6

Answer: 4, 5, 6


Context: 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?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: six


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

Answer: Fred

Answer: Glen

Answer: Jan

Answer: Kathy

Answer: Nick


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

Answer: Fred

Answer: Jan

Answer: Kathy

Answer: Laura

Answer: Mike


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?

Answer: Fred and Kathy

Answer: Fred and Mike

Answer: Hilary and Jan

Answer: Kathy and Laura

Answer: Laura and Mike


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

Answer: Hilary and Nick

Answer: Jan and Laura

Answer: Kathy and Laura

Answer: Jan and Mike

Answer: Laura and Mike


Context: 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?

Answer: Hilda reviews Retreat.

Answer: Jackie reviews Seasonings.

Answer: Karl reviews Mystery.

Answer: Karl reviews Retreat.

Answer: Karl reviews Wolves.


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

Answer: Lena reviews Mystery.

Answer: Lena reviews Retreat.

Answer: Lena reviews Seasonings.

Answer: Frank and Hilda review Retreat.

Answer: 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?

Answer: Mystery, Retreat

Answer: Retreat, Seasonings

Answer: Mystery, Seasonings, Wolves

Answer: Retreat, Seasonings, Wolves

Answer: Mystery, Retreat, Seasonings, Wolves


Question: Which one of the following can be true?

Answer: Frank and George review Mystery.

Answer: Frank and Lena review Wolves.

Answer: George and Jackie review Mystery.

Answer: Karl reviews Wolves and Lena reviews Mystery.

Answer: Lena reviews Retreat and Frank reviews Seasonings.