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

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

The computer in office 2 was bought in 1987.

The computer in office 2 was bought in 1988.

The computer in office 4 was bought in 1988.

The printer in office 4 was bought in 1988.

The printer in office 4 was bought in 1989.


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

The printer in office 1 was bought in 1987.

The computer in office 2 was bought in 1987.

The computer in office 3 was bought in 1989.

The printer in office 4 was bought in 1988.

The printer in office 4 was bought in 1989.


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


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

The printer in office 1 was bought in 1988.

The printer in office 1 was bought in 1989.

The computer in office 2 was bought in 1988.

The computer in office 3 was bought in 1987.

The printer in office 4 was bought in 1989.


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

The printer in office 1 was bought in 1988.

The computer in office 2 was bought in 1987.

The printer in office 2 was bought in 1988.

The computer in office 4 was bought in 1987.

The printer in office 4 was bought in 1989.


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

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


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

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

The line 1 tickets for January are green.

The line 1 tickets for January are yellow.

The line 1 tickets for February are red.

The line 2 tickets for February are yellow.

The line 3 tickets for February are green.


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

The line 1 tickets for February are red.

The line 3 tickets for February are green.

The line 3 tickets for February are yellow.


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

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

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


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

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

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

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

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

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


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

The tickets in two of the six sets are red.

The tickets in two of the six sets are yellow.


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

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


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

Question: Which one of the following must be true?

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


Question: Which one of the following CANNOT be true?

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


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

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


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

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


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

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


Question: Which one of the following must be true?

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

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

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

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

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


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

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


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

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

pork chops, roast beef, tilefish, veal cutlet


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

John orders the same kind of entree as Marie does.

Kate orders the same kind of entree as Nat does.

Lewis orders the same kind of entree as Nat does.

Marie orders the same kind of entree as Olive does.

Nat orders the same kind of entree as Olive does.


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

One of the men orders pork chops or veal cutlet.

One of the men orders swordfish or veal cutlet.

Exactly one of the women orders a fish entree.


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

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


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

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


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

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


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

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


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

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

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


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

The exhibition includes new research model sports cars.

The exhibition includes used research model family cars.

The exhibition includes used research model sports cars.

There are research models on exactly one floor.

There are research models on all three floors.


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

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


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

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


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

All the family cars in the exhibition are new.

All the family cars in the exhibition are research models.

All the family cars in the exhibition are used.

All the new cars in the exhibition are family cars.

All the production models in the exhibition are family cars.


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

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


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

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

Cindy flies in either plane 1 or plane 3.

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

Bob and one other person fly in plane l.

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

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


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

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


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

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


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

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


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

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


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

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

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


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


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

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

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


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


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

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


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

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

First Street
Second Street
Third Street
Fifth Street
Eighth Street


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


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


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

The crew cleaned First Street on Tuesday afternoon.

The crew cleaned Second Street on Thursday afternoon.

The crew cleaned Third Street on Wednesday morning.

The crew cleaned Fifth Street on Thursday afternoon.

The crew cleaned Sixth Street on Friday afternoon.


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


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

The crew cleaned First Street before Second Street.

The crew cleaned Second Street before Fifth Street.

The crew cleaned Third Street before Second Street.

The crew cleaned Sixth Street before Fifth Street.

The crew cleaned Seventh Street before Second Street.


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

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

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


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

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

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


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

His grades in history and Italian are identical.

His grades in history and Russian are identical.

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


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


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

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


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

He receives a lower grade in Italian than in economics.

He receives a lower grade in Italian than in physics.

He receives a lower grade in physics than in Italian.

He receives a lower grade in Russian than in economics.

He receives a lower grade in Russian than in history.


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

Question: Which one of the following must be false?

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

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

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

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

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


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

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


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

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

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

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

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

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


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

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


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

either a medium red shirt or a medium blue shirt

either a large yellow shirt or a medium blue shirt


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

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

Monday Tuesday Wednesday Friday Saturday


Question: On Wednesday Doctor Yamata could be scheduled to

conduct research in the morning and operate in the afternoon

lecture in the morning and treat patients in the afternoon

operate in the morning and lecture in the afternoon

operate in the morning and conduct research in the afternoon

treat patients in the morning and treat patients in the afternoon


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

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

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

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

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

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


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

Monday morning, Monday afternoon, Friday morning, Friday afternoon

Monday morning, Friday afternoon, Saturday morning, Saturday afternoon

Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon

Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon

Wednesday afternoon, Friday afternoon, Saturday morning, Saturday afternoon


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

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


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

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


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

Monday Tuesday Wednesday Thursday Friday


Question: Which one of the following must be true?

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

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

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

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

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


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

Monday Tuesday Wednesday Thursday Friday


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

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

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


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

Question: Each of the following can be true EXCEPT:

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


Question: Which one of the following could be true?

W and exactly one other organism respond to ganocyclene.

W responds to more of the antibiotics than X does.

More of the organisms respond to ferromycin than to ganocyclene.


Question: Which one of the following could be true?

Exactly one of the organisms responds to ferromycin.

All four of the organisms respond to heptocillin.

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

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

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


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

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


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

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


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

Exactly three of the organisms respond to ganocyclene.

Exactly four of the organisms respond to ganocyclene.


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

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

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


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

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

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

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

2 orchids 3 roses 1 gardenia 1 rose 2 violets

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


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


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


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

two orchids
three gardenias
three roses
five roses
five violets


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

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


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

exactly one rose and exactly one gardenia

exactly one orchid and exactly four violets


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

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


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

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


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

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


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

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


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

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


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

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


Lara, Mendel, and Nastassia each buy at least one kind of food from a street vendor who sells only fruit cups, hot dogs, pretzels, and shish kebabs. They make their selections in accordance with the following restrictions: None of the three buys more than one portion of each kind of food. If any of the three buys a hot dog, that person does not also buy a shish kebab. At least one of the three buys a hot dog, and at least one buys a pretzel. Mendel buys a shish kebab. Nastassia buys a fruit cup. Neither Lara nor Nastassia buys a pretzel. Mendel does not buy any kind of food that Nastassia buys.

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

Lara buys a hot dog.
Lara buys a shish kebab.
Mendel buys a hot dog.
Mendel buys a pretzel.
Nastassia buys a hot dog.


Question: If the vendor charges $1 for each portion of food, what is the minimum amount the three people could spend?


Question: If the vendor charges $1 for each portion of food, what is the greatest amount the three people could spend?


Question: If Lara and Mendel buy exactly two kinds of food each, which one of the following statements must be true.

There is exactly one kind of food that Lara and Mendel both buy.

There is exactly one kind of food that Lara and Nastassia both buy.


Question: If Lara buys a shish kebab, which one of the following statements must be true?

Nastassia buys exactly one kind of food.


Question: Assume that the condition is removed that prevents a customer who buys a hot dog from buying a shish kebab but all other conditions remain the same. If the vendor charges $1 for each portion of food, what is the maximum amount the three people could spend?


An art teacher will schedule exactly six of eight lectures—fresco, history, lithography, naturalism, oils, pastels, sculpture, and watercolors—for three days—1, 2, and 3. There will be exactly two lectures each day—morning and afternoon. Scheduling is governed by the following conditions: Day 2 is the only day for which oils can be scheduled. Neither sculpture nor watercolors can be scheduled for the afternoon. Neither oils nor pastels can be scheduled for the same day as lithography. If pastels is scheduled for day 1 or day 2, then the lectures scheduled for the day immediately following pastels must be fresco and history, not necessarily in that order.

Question: Which one of the following is an acceptable schedule of lectures for days 1, 2, and 3, respectively?

Morning: lithography, history, sculpture Afternoon: pastels, fresco, naturalism

Morning: naturalism, oils, fresco Afternoon: lithography, pastels, history

Morning: oils, history, naturalism Afternoon: pastels, fresco, lithography

Morning: sculpture, lithography, naturalism Afternoon: watercolors, fresco, pastels

Morning: sculpture, pastels, fresco Afternoon: lithography, history, naturalism


Question: If lithography and fresco are scheduled for the afternoons of day 2 and day 3, respectively, which one of the following is a lecture that could be scheduled for the afternoon of day 1?

history oils pastels sculpture watercolors


Question: If lithography and history are scheduled for the mornings of day 2 and day 3, respectively, which one of the following lectures could be scheduled for the morning of day 1?

fresco naturalism oils pastels sculpture


Question: If oils and lithography are scheduled for the mornings of day 2 and day 3, respectively, which one of the following CANNOT be scheduled for any day?

fresco history naturalism pastels sculpture


Question: If neither fresco nor naturalism is scheduled for any day, which one of the following must be scheduled for day 1?

history lithography oils pastels sculpture


Question: If the lectures scheduled for the mornings are fresco, history, and lithography, not necessarily in that order, which one of the following could be true?

Fresco is scheduled for the same day as naturalism.

History is scheduled for the same day as naturalism.

History is scheduled for the same day as oils.


A newly formed company has five employees—F, G, H, K, and L. Each employee holds exactly one of the following positions: president, manager, or technician. Only the president is not supervised. Other employees are each supervised by exactly one employee, who is either the president or a manager. Each supervised employee holds a different position than his or her supervisor. The following conditions apply: There is exactly one president. At least one of the employees whom the president supervises is a manager. Each manager supervises at least one employee. F does not supervise any employee. G supervises exactly two employees.

Question: Which one of the following is an acceptable assignment of employees to the positions? President Manager Technician

G H, K, L F
G H F, K, L
H F, G K, L
H, K G F, L
K F, G, H, L


Question: Which one of the following must be true?

There are exactly two employees who supervise no one.


Question: Which one of the following is a pair of employees who could serve as managers together?


Question: Which one of the following could be true?

There are exactly two employees who are not supervised.

There are more managers than technicians.

The president supervises all of the other employees.


Question: If F is supervised by the president, which one of the following must be true?

G is the president.
H is the president.
L is a technician.
There is exactly one manager.
There are exactly two technicians.


Question: If K supervises exactly two employees, which one of the following must be true?

F is supervised by K.
G is a manager.
L is supervised.
There are exactly two managers.
There are exactly two technicians.


During each of the fall, winter, spring, and summer seasons of one year, Nikki and Otto each participate in exactly one of the following five sports: hockey, kayaking, mountaineering, running, and volleyball. Each child participates in exactly four different sports during the year. In the fall, each child participates in mountaineering, running, or volleyball. In the winter, each child participates in hockey or volleyball. In the spring, each child participates in kayaking, mountaineering, running, or volleyball. In the summer, each child participates in kayaking, mountaineering, or volleyball. Nikki and Otto do not participate in the same sport during the same season. Otto's summer sport is volleyball.

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

Nikki's fall sport is running.
Nikki's winter sport is volleyball.
Nikki's spring sport is mountaineering.
Otto's fall sport is mountaineering.
Otto's spring sport is kayaking.


Question: It CANNOT be true that both Nikki and Otto participate during the year in which one of the following sports?

hockey kayaking mountaineering running volleyball


Question: If Nikki's fall sport is running, then which one of the following statements must be true?

Nikki's spring sport is kayaking.
Nikki's summer sport is mountaineering.
Otto's fall sport is mountaineering.
Otto's spring sport is kayaking.
Otto's spring sport is running.


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

Nikki's fall sport is neither mountaineering nor running.

Nikki's spring sport is neither mountaineering nor running.

Nikki's summer sport is neither kayaking nor mountaineering.

Otto's fall sport is neither mountaineering nor running.

Otto's spring sport is neither kayaking, nor mountaineering, nor running.


Question: If Otto does not run during the year, then which one of the following statements must be false?

Nikki's fall sport is running.
Nikki's spring sport is running.
Nikki's summer sport is kayaking.
Otto's fall sport is mountaineering.
Otto's spring sport is kayaking.


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

Nikki's fall sport is mountaineering and Otto's spring sport is running.

Nikki's spring sport is running and her summer sport is mountaineering.

Nikki's spring sport is mountaineering and Otto's fall sport is mountaineering.

Nikki's spring sport is running and Otto's fall sport is mountaineering.

Nikki's summer sport is mountaineering and Otto's spring sport is mountaineering.


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

Question: Which one of the following is an inexperienced plumber who can be assigned to a team with Frank?


Question: Which one of the following is a pair of plumbers who can be assigned together to a team?

Frank and Roberta
Frank and Vernon
Jill and Mark
Roberta and Tim
Sally and Vernon


Question: If Tim is assigned to a team, and if Sally is assigned to a team with a plumber who could have been assigned to a team with Tim, then the only plumber with whom Frank could be assigned to a team is


Question: If Gene is not assigned to a team, then Jill must be assigned to a team with


Four lions—F, G, H, J—and two tigers—K and M—will be assigned to exactly six stalls, one animal per stall. The stalls are arranged as follows: First Row: 1 2 3 Second Row: 4 5 6 The only stalls that face each other are stalls 1 and 4, stalls 2 and 5, and stalls 3 and 6. The following conditions apply: The tigers' stalls cannot face each other. A lion must be assigned to stall 1. H must be assigned to stall 6. J must be assigned to a stall numbered one higher than K's stall. K cannot be assigned to the stall that faces H's stall.

Question: Which one of the following must be true?

F is assigned to an even-numbered stall.

J is assigned to stall 2 or else stall 3.

J is assigned to stall 3 or else stall 4.

K is assigned to stall 2 or else stall 4.


Question: Which one of the following could be true?

F's stall is numbered one higher than J's stall.

K's stall is in a different row than J's stall.


Question: Which one of the following must be true?

K's stall is in a different row from M's stall.

Each tiger is assigned to an even-numbered stall.

Each lion is assigned to a stall that faces a tiger's stall.


Question: If K's stall is in the same row as H's stall, which one of the following must be true?

F's stall is in the same row as J's stall.

F is assigned to a lower-numbered stall than G.

G is assigned to a lower-numbered stall than M.

M's stall is in the same row as G's stall.


Question: If J is assigned to stall 3, which one of the following could be true?

F is assigned to stall 2.
F is assigned to stall 4.
G is assigned to stall 1.
G is assigned to stall 4.
M is assigned to stall 5.


Question: Which one of the following must be true?

A tiger is assigned to stall 2.
A tiger is assigned to stall 4.
A tiger is assigned to stall 5.
A lion is assigned to stall 3.
A lion is assigned to stall 4.


On an undeveloped street, a developer will simultaneously build four houses on one side, numbered consecutively 1, 3, 5, and 7, and fos on the opposite side, numbered consecutively 2, 4, 6, and 8. Houses 2, 4, 6, and 8 will face houses 1, 3, 5, and 7, respectively. Each house will be exactly one of three styles—ranch, split-level, or Tudor—according to the following conditions: Adjacent houses are of different styles. No split-level house faces another split-level house. Every ranch house has at least one Tudor house adjacent to it. House 3 is a ranch house. House 6 is a split-level house.

Question: Any of the following could be a Tudor house EXCEPT house


Question: If there is one ranch house directly opposite another ranch house, which one of the following could be true?

House 8 is a ranch house.
House 7 is a split-level house.
House 4 is a Tudor house.
House 2 is a split-level house.
House 1 is a ranch house.


Question: If house 4 is a Tudor house, then it could be true that house

1 is a Tudor house
2 is a Tudor house
5 is a ranch house
7 is a Tudor house
8 is a ranch house


Question: On the street, there could be exactly

one ranch house
one Tudor house
two Tudor houses
four ranch houses
five ranch houses


Question: If no house faces a house of the same style, then it must be true that house

1 is a split-level house
1 is a Tudor house
2 is a ranch house
2 is a split-level house
4 is a Tudor house


Question: If the condition requiring house 6 to be a split-level house is suspended but all other original conditions remain the same, then any of the following could be an accurate list of the styles of houses 2, 4, 6, and 8, respectively, EXCEPT:

ranch, split-level, ranch, Tudor
split-level, ranch, Tudor, split-level
split-level, Tudor, ranch, split-level
Tudor, ranch, Tudor, split-level
Tudor, split-level, ranch, Tudor


Exactly six employees—officers F, G, and H, and supervisors K, L, and M—must be assigned to exactly three committees—Policy, Quality, and Sales—with exactly three employees per committee. Committee assignments must conform to the following conditions: Each committee must have at least one officer assigned to it. Each employee must be assigned to at least one committee. All three officers must be assigned to the Policy Committee. G cannot be assigned to the same committee as L. K must be assigned to the Sales Committee.

Question: Which one of the following is a group of three employees who can be assigned together to the Sales Committee?

F, G, and H
F, G, and M
G, K, and L
H, K, and L
K, L, and M


Question: If H is assigned to exactly one committee, and if no committee has both F and M assigned to it, then it must be true that

G and M are both assigned to the Quality Committee

K and L are both assigned to the Sales Committee


Question: Which one of the following CANNOT be true?

G is assigned to exactly three committees.

H is assigned to exactly three committees.

L is assigned to exactly two committees.


Question: If F is assigned to exactly three committees, and G is assigned to exactly two committees, then which one of the following must be true?

G is assigned to the Quality Committee.
G is assigned to the Sales Committee.
K is assigned to the Quality Committee.
L is assigned to the Sales Committee.
M is assigned to the Quality Committee.


Question: Which one of the following is a group of three employees who can be assigned together to the Quality Committee?

F, G, and H
F, G, and K
G, H, and K
G, K, and L
H, L, and M


Question: If L is assigned to exactly two committees, which of the following must be true?

F is assigned to the Sales Committee.
G is assigned to the Sales Committee.
H is assigned to the Quality Committee.
K is assigned to the Quality Committee.
M is assigned to the Quality Committee.


Question: Which one of the following CANNOT be true?

F and G are each assigned to exactly one committee.

F and H are each assigned to exactly one committee.

G and H are each assigned to exactly one committee.

F and M are both assigned to the Sales Committee.

G and K are both assigned to the Quality Committee.


On Tuesday Vladimir and Wendy each eat exactly four separate meals: breakfast, lunch, dinner, and a snack. The following is all that is known about what they eat during that day: At no meal does Vladimir eat the same kind of food as Wendy. Neither of them eats the same kind of food more than once during the day. For breakfast, each eats exactly one of the following: hot cakes, poached eggs, or omelet. For lunch, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For dinner, each eats exactly one of the following: fish, hot cakes, macaroni, or omelet. For a snack, each eats exactly one of the following: fish or omelet. Wendy eats an omelet for lunch.

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

Vladimir eats fish for lunch.
Vladimir eats fish for dinner.
Vladimir eats fish for his snack.
Wendy eats fish for dinner.
Wendy eats fish for her snack.


Question: Vladimir must eat which one of the following foods?

fish
hot cakes
macaroni
omelet
poached eggs


Question: If both Vladimir and Wendy eat macaroni on Tuesday, then which one of the following statements could be true?

Vladimir eats fish for lunch.
Vladimir eats hot cakes for lunch.
Vladimir eats macaroni for dinner.
Wendy eats hot cakes for breakfast.
Wendy eats hot cakes for dinner.


Question: If Wendy does not eat macaroni on Tuesday, then which one of the following statements could be true?

Vladimir eats poached eggs for breakfast.


Question: If Wendy eats poached eggs for breakfast, then which one of the following statements cannot be true?

Vladimir eats fish for lunch.
Vladimir eats hot cakes for lunch.
Vladimir eats macaroni for dinner.
Wendy eats hot cakes for dinner.
Wendy eats macaroni for dinner.


Eight people—Jack, Karen, Laura, Mark, Nick, Owen, Peggy, and Ruth—will be placed on two four-person teams—X and Y—for a relay race that is run in four successive legs: first, second, third, and fourth. The teams race concurrently. Each team member runs exactly one of the legs, one team member per leg, according to the following conditions: Jack is on the same team as Karen. Karen is not on the same team as Nick. Ruth runs an earlier leg of the race than Peggy runs, whether or not they are on the same team as each other. Mark and Nick are both on team Y. Neither Jack nor Mark runs third. Karen and Laura both run second. Owen runs fourth.

Question: Which one of the following must be true?

If Jack and Owen are assigned to the same team as each other, Jack runs first.

If Jack and Peggy are assigned to the same team as each other, Jack runs fourth.

If Jack and Ruth are assigned to the same team as each other, Ruth runs third.

If Mark and Owen are assigned to the same team as each other, Mark runs fourth.

If Mark and Ruth are assigned to the same team as each other, Ruth runs third.


Question: If Ruth is assigned to team X, which one of the following is a complete and accurate list of the legs that she could run?

first
second
first, second
first, third
second, third


Question: If Owen and Ruth are assigned to the same team as each other, which one of the following must be true?

Mark runs fourth.
Nick runs first.
Nick runs fourth.
Peggy runs first.
Peggy runs fourth.


Question: Any of the following can be true EXCEPT:

Jack runs first.
Mark runs fourth.
Nick runs first.
Nick and Peggy both run third.
Owen and Peggy both run fourth.


Question: If Ruth and Peggy are assigned to the same team as each other, which one of the following must be true?

Jack runs first.
Mark runs fourth.
Nick runs third.
Peggy runs third.
Ruth runs first.


Question: Any of the following can be true EXCEPT:

Jack runs fourth.
Nick runs fourth.
Peggy runs fourth.
Ruth runs first.
Ruth runs third.


Question: If Peggy runs third on the same team to which Jack is assigned, which one of the following must be true?

Jack runs the first leg on the team to which he is assigned.

Ruth runs the first leg on the team to which she is assigned.


In a theater company, four two-day workshops—Lighting, Production, Rehearsals, and Staging—are conducted over the course of five days, Monday through Friday. The workshops are conducted in a manner consistent with the following constraints: The two days on which a given workshop is in session are consecutive. On each of the five days, at least one, but no more than two, of the workshops are in session. The workshops on Production and Rehearsals begin no earlier than the day immediately following the second day of the workshop on Lighting.

Question: Which one of the following could be true?

Only one workshop is in session on Thursday.

Only one workshop is in session on Friday.

The workshop on Rehearsals is in session on Tuesday.

The workshop on Staging is in session on Thursday.

The workshops in Rehearsals and Production are both in session on Wednesday.


Question: Which one of the following could be true?

The workshop on Lighting is in session on Wednesday, and the workshop on Rehearsals is in session on Tuesday.

The workshop on Lighting is in session on Wednesday, and the only workshop in session on Thursday is the workshop on Rehearsals.

The workshop on Lighting is in session on Wednesday, and the only workshop in session on Monday is the workshop on Staging.

The workshop on Lighting is in session on Monday, and the only workshop in session on Thursday is the workshop on Staging.

The workshops on Lighting and Production are both in session on Wednesday.


Question: If the workshop on Production is in session on Wednesday, which one of the following must be true?

The workshop on Lighting is in session on Monday.

The workshop on Rehearsals is in session on Wednesday.

The workshop on Staging is in session on Thursday .

The workshop on Staging is in session on Monday.

The workshop on Staging is in session on Wednesday.


Question: If the workshop on production is the only workshop in session on Friday, which one of the following must be false?

The workshop on Lighting is in session both on Tuesday and on Wednesday.

The workshop on Rehearsals is in session both on Wednesday and on Thursday.

The workshop on Staging is in session both on Monday and on Tuesday.

The workshop on Lighting is in session on the same two days as is the workshop on Staging.

The workshop on Rehearsals is in session on a day when the workshop on Staging is also in session.


Question: If the workshop on Lighting is the only workshop in session on Monday, which one of the following could be true?

The workshops on Rehearsals and Staging are both in session on Tuesday.

The workshop on Rehearsals is the only workshop in session on Wednesday.

The workshop on Staging is the only workshop in session on Wednesday.

The workshops on Staging and Rehearsals are both in session on Wednesday and on Thursday.

The workshops on Staging and Production are both in session on Thursday.


Each of seven travelers—Norris, Oribe, Paulsen, Rosen, Semonelli, Tan, and Underwood—will be assigned to exactly one of nine airplane seats. The seats are numbered from 1 through 9 and arranged in rows as follows: Front row: 1 2 3 Middle row: 4 5 6 Last row: 7 8 9 Only seats in the same row as each other are immediately beside each other. Seat assignments must meet the following conditions: Oribe's seat is in the last row. Paulsen's seat is immediately beside Rosen's seat and also immediately beside an unassigned seat. Rosen's seat is in the row immediately behind the row in which Norris' seat is located. Neither Semonelli nor Underwood is seated immediately beside Norris.

Question: Which one of the following is a pair of travelers who could be assigned to seats 2 and 8, respectively?

Norris, Semonelli
Oribe, Underwood
Paulsen, Oribe
Rosen, Semonelli
Underwood, Tan


Question: If Semonelli and Underwood are not assigned to seats in the same row as each other, which one of the following must be false?

Norris is assigned to seat 2.
Paulsen is assigned to seat 5.
Rosen is assigned to seat 4.
Tan is assigned to seat 2.
Underwood is assigned to seat 1.


Question: If Semonelli is assigned to a seat in the same row as Underwood, which one of the following travelers could be assigned to a seat immediately beside one of the unassigned seats?


Question: If the seat to which Tan is assigned is immediately beside a seat assigned to another traveler and also immediately beside one of the unassigned seats, which one of the following must be true?

Tan is assigned to a seat in the front row.

Tan is assigned to a seat in the last row.

Oribe is assigned to a seat immediately beside Semonelli.

Oribe is assigned to a seat immediately beside Tan.

Semonelli is assigned to a seat immediately beside Underwood.


Question: If Oribe is assigned to a seat immediately beside one of the unassigned seats, which one of the following must be true?

Oribe is assigned to seat 8.
Tan is assigned to seat 2.
Underwood is assigned to seat 1.
Seat 4 is unassigned.
Seat 9 is unassigned.


Seven students—fourth-year students Kim and Lee; third-year students Pat and Robin; and second-year students Sandy, Terry, and Val—and only those seven, are being assigned to rooms of equal size in a dormitory. Each room assigned must have either one, or two, or three students assigned to it, and will accordingly be called either a single, or a double, or a triple. The seven students are assigned to rooms in accordance with the following conditions: No fourth-year student can be assigned to a triple. No second-year student can be assigned to a single. Lee and Robin must not share the same room. Kim and Pat must share the same room.

Question: Which one of the following is a combination of rooms to which the seven students could be assigned?

two triples and one single
one triple and four singles
three doubles and a single
two doubles and three singles
one double and five singles


Question: If the room assigned to Robin is a single, which one of the following could be true?

There is exactly one double that has a second-year student assigned to it.

Sandy, Pat and one other student are assigned to a triple together.

Exactly three of the rooms assigned to the students are singles.

Exactly two of the rooms assigned to the students are doubles.


Question: Which one of the following must be true?

Pat shares a double with another student.

Robin shares a double with another student.

Two of the second-year students share a double with each other.

Neither of the third-year students is assigned to a single.


Question: If Robin is assigned to a triple, which one of the following must be true?

Two second-year students share a double with each other.

None of the rooms assigned to the students is a single.

Two of the rooms assigned to the students are singles.

Three of the rooms assigned to the students are singles.


Question: If Terry and Val are assigned to different doubles from each other, then it must be true of the students' rooms that exactly

one is a single
two are singles
two are doubles
one is a triple
two are triples


Question: Which one of the following could be true?

The two fourth-year students are assigned to singles.

The two fourth-year students share a double with each other.

Lee shares a room with a second-year student.

Lee shares a room with a third-year student

Pat shares a triple with two other students.


An attorney is scheduling interviews with witnesses for a given week, Monday through Saturday. Two full consecutive days of the week must be reserved for interviewing hostile witnesses. In addition, nonhostile witnesses Q, R, U, X, Y, and Z will each be interviewed exactly once for a full morning or afternoon. The only witnesses who will be interviewed simultaneously with each other are Q and R. The following conditions apply: X must be interviewed on Thursday morning. Q must be interviewed at some time before X. U must be interviewed at some time before R. Z must be interviewed at some time after X and at some time after Y.

Question: Which one of the following is a sequence, from first to last, in which the nonhostile witnesses could be interviewed?

Q with R, U, X, Y, Z
Q, U, R, X with Y, Z
U, X, Q, with R, X, Z
U, Y, Q with R, X, Z
X, Q with U, Z, R, Y


Question: Which one of the following is acceptable as a complete schedule of witnesses for Tuesday morning, Tuesday afternoon, and Wednesday morning, respectively?

Q, R, none
R, none, Y
U, none, X
U, Y, none
Y, Z, none


Question: If Y is interviewed at some time after X, which one of the following must be a day reserved for interviewing hostile witnesses?

Monday Tuesday Wednesday Friday Saturday


Question: If R is interviewed at some time after Y, which one of the following must be a day reserved for interviewing hostile witnesses?

Monday Tuesday Wednesday Thursday Friday


Question: If on Wednesday afternoon and on Monday the attorney conducts no interviews, which one of the following must be true?

Y is interviewed at some time before Wednesday.

Z is interviewed at some time before Friday.


Question: If Z is interviewed on Saturday morning, which one of the following can be true?

Wednesday is a day reserved for interviewing hostile witnesses.

Friday is a day reserved for interviewing hostile witnesses.

Y is interviewed at some time before Thursday.


Six paintings hang next to each other as shown below: Each of the paintings is an oil or else a watercolor. Each oil is directly beside, directly above, or directly below another oil. Each watercolor is directly beside, directly above, or directly below another watercolor. Each painting is a nineteenth-century painting or else a twentieth-century painting. Each painting is directly beside, directly above, or directly below another painting painted in the same century. Painting 2 is a nineteenth-century painting. Painting 3 is an oil. Painting 5 is a twentieth-century painting.

Question: If all of the nineteenth-century paintings are watercolors, which one of the following must be true?

Painting 3 is a nineteenth-century painting.

Painting 6 is a twentieth-century painting.


Question: It is possible that the only two watercolors among the six paintings are

paintings 1 and 5
paintings 1 and 6
paintings 2 and 4
paintings 4 and 5
paintings 4 and 6


Question: If there are exactly three oils and three watercolors, which one of the following must be true?

Painting 1 is a watercolor.
Painting 2 is a watercolor.
Painting 4 is a watercolor.
Painting 5 is a watercolor.
Painting 6 is a watercolor.


Question: If exactly two paintings are oils and exactly two paintings are nineteenth-century paintings, which one of the following must be false?

Painting 1 is a nineteenth-century painting, and painting 6 is an oil.

Painting 2 is both a nineteenth-century painting and an oil.

Painting 3 is a nineteenth-century painting.

Paintings 1 and 2 are both nineteenth-century paintings.

Painting 2 is an oil, and painting 4 is a nineteenth-century painting.


Question: Which one of the following could be true?

Paintings 1 and 4 are two of exactly three twentieth-century paintings.

Paintings 1 and 6 are two of exactly three twentieth-century paintings.

Paintings 1 and 6 are two of exactly three nineteenth-century paintings.

Paintings 3 and 4 are two of exactly three nineteenth-century paintings.

Paintings 4 and 6 are two of exactly three nineteenth-century paintings.


Exactly six of seven jugglers—G, H, K, L, N, P, and Q—are each assigned to exactly one of three positions—front, middle, and rear—on one of two teams—team 1 and team 2. For each team, exactly one juggler must be assigned to each position according to the following conditions: If either G or H or both are assigned to teams, they are assigned to front positions. If assigned to a team, K is assigned to a middle position. If assigned to a team, L is assigned to team 1. Neither P nor K is on the same team as N. P is not on the same team as Q. If H is on team 2, then Q is assigned to the middle position on team 1.

Question: Which one of the following is an acceptable list of assignments of jugglers to team 2?

front: Q; middle: K; rear: N
front: H; middle: P; rear: K
front: H; middle: L; near: N
front: G; middle: Q; rear: P
front: G; middle: Q; rear: N


Question: If H is assigned to team 2, which one of the following is an acceptable assignment of jugglers to team 1?

front: G; middle: K; rear: L
front: G; middle: K; rear: N
front: L; middle: K; rear: P
front: L; middle: Q; rear: G
front: L; middle: Q; rear: N


Question: Which one of the following is an acceptable list of assignments of jugglers to team 1?

front: G; middle: K; rear: L
front: G; middle: K; rear: P
front: L; middle: K; rear: Q
front: Q; middle: K; rear: P
front: Q; middle: L; rear: N


Question: If G is assigned to team 1, which one of the following is a pair of jugglers who could also be assigned to team 1?


Question: If G is assigned to team 1 and K is assigned to team 2, which one of the following must be assigned the rear position on team 2?


The members of two committees, a planting committee and a trails committee, are to be selected from among seven volunteers—F, G, H, J, K, L, and M. The following conditions govern the composition of the committees: Each committee must have at least three members. F cannot be on the same committee as K. If K is on a committee, J must also be on that committee. M must be on at least one of the committees. The two committees must have at least one member in common.

Question: Which one of the following represents an acceptable selection of volunteers for the committees?

planting: F, G, H; trails: G, J, K, L
planting: F, H, J; trails: G, H, L, M
planting: F, H, M; trails: G, K, L, M
planting: F, G, L, M; trails: F, H
planting: F, H, J, K; trails: H, L, M


Question: If the planting committee consists of F, H, L, and M, and if the trails committee consists of G, H, and J, then K could replace which one of the following committee members on a committee without violating any of the conditions governing the composition of the committees?


Question: If the only members of the planting committee are G, H, and L and if the two committees are to have as many members in common as the conditions allow, then which one of the following must be true?

The trails committee and the planting committee have exactly one member in common.

The trails committee and the planting committee have exactly two members in common.

The trails committee and the planting committee have an equal number of members.

The trails committee has at least one more member than the planting committee.

The planting committee has exactly two more members than the trails committee.


Question: If K is on both committees and L is also on both committees and if the planting committee has exactly three members, then which one of the following must be true?

F is on the planting committee.
F is on the trails committee.
G is on the planting committee.
M is on the planting committee.
M is on the trails committee.


Question: The largest number of members that the planting committee and the trails committee could have in common is


Exactly six tourists—Harry, Irene, Klaus, Laura, Michael, Norma—are to be assigned to four guides: Valois, Xerxes, Yossarian, Zalamea. Each tourist is assigned to exactly one guide, with at least one tourist assigned to each guide. Valois speaks only French. Xerxes speaks only Turkish and Spanish. Yossarian speaks only French and Turkish. Zalamea speaks only Spanish and Russian. Each tourist speaks exactly one of the languages spoken by his or her guide and speaks no other language. The following rules govern the assignment of the tourists to the guides: At least Harry and Irene are assigned to Yossarian. At least Laura is assigned to Zalamea. If Klaus is assigned to Xerxes, then Michael speaks French.

Question: Each of the following could be true EXCEPT:

Both Klaus and Harry speak Turkish.
Both Klaus and Michael speak French.
Both Klaus and Michael speak Russian.
Both Klaus and Norma speak French.
Both Klaus and Norma speak Spanish.


Question: Which one of the following must be true?

Zalamea is assigned fewer than three of the tourists.

Xerxes is assigned fewer than two of the tourists.

Yossarian is assigned exactly two of the tourists.

Valois is assigned exactly one of the tourists.

Zalamea is assigned exactly one of the tourists.


Question: Each of the following could be true of the assignment of tourists to guides EXCEPT:

It assigns Klaus to Valois and Michael to Xerxes.

It assigns Klaus to Yossarian and Norma to Zalamea.

It assigns Laura to Zalamea and Michael to Zalamea.

It assigns Michael to Valois and Klaus to Zalamea.

It assigns Michael to Xerxes and Klaus to Zalamea.


Question: If Klaus and Laura speak the same language as each other, then which one of the following must be true?

At least one of Michael and Norma speaks Spanish.

At least one of Michael and Norma speaks French.


Question: If Laura and Norma speak the same language as each other, then the maximum number of the tourists who could speak Turkish is


Question: If exactly two tourists are assigned to Xerxes, then which one of the following could be true?

Norma speaks Russian and Laura speaks Russian.

Norma speaks French and Michael speaks French.

Norma speaks French and Klaus speaks Turkish.

Michael speaks Spanish and Klaus speaks Spanish.

Michael speaks French and Klaus speaks Spanish.


Question: If Harry, Irene, Michael, and Norma all speak the same language as each other, then which one of the following could be true?

Exactly two of the tourists speak Russian.

Exactly three of the tourists speak Spanish.

Exactly two of the tourists speak Turkish.


In each of two years exactly two of four lawmakers—Feld, Gibson, Hsu, and Ivins—and exactly two of three scientists—Vega, Young, and Zapora—will serve as members of a four-person panel. In each year, one of the members will be chairperson. The chairperson in the first year cannot serve on the panel in the second year. The chairperson in the second year must have served on the panel in the first year. Service on the panel must obey the following conditions: Gibson and Vega do not serve on the panel in the same year as each other. Hsu and Young do not serve on the panel in the same year as each other. Each year, either Ivins or Vega, but not both, serves on the panel.

Question: Which one of the following could be the list of the people who serve on the panel in the first year?

Feld, Gibson, Vega, Zapora
Feld, Hsu, Vega, Zapora
Feld, Ivins, Vega, Zapora
Gibson, Hsu, Ivins, Zapora
Hsu, Ivins, Young, Zapora


Question: If Vega is the chairperson in the first year, which one of the following is a pair of people who must serve on the panel in the second year?

Gibson and Young
Gibson and Zapora
Hsu and Ivins
Ivins and Young
Vega and Young


Question: If Hsu is the chairperson in the first year, which one of the following could be the chairperson in the second year?


Question: IF Feld serves on the panel in a given year, any one of the following could serve on the panel that year EXCEPT:


Question: If Ivins is the chairperson in the first year, which one of the following could be the chairperson in the second year?


Question: Which one of the following must be true?

Feld is on the panel in the second year.

Zapora is on the panel in the second year.


A zoo's reptile house has a straight row of exactly five consecutive habitats—numbered 1 through 5 from left to right—for housing exactly seven reptiles—four snakes and three lizards. Five of the reptiles are female and two are male. The reptiles must be housed as follows: No habitat houses more than two reptiles. No habitat houses both a snake and a lizard. No female snake is housed in a habitat that is immediately next to a habitat housing a male lizard.

Question: Which one of the following could be a complete and accurate matching of habitats to reptiles?

1: two female snakes; 2: one male snake; 3: one female lizard; 4: one male snake, one female lizard; 5: one female lizard

1: empty; 2: two female snakes; 3: two female lizards; 4: two male snakes; 5: one female lizard

1: one female snake, one male snake; 2: two female snakes; 3: one male lizard; 4: one female lizard; 5: one female lizard

1: two male snakes; 2: empty; 3: one female lizard; 4: one female lizard; 5: two female snakes, one female lizard

1: one female snake, one male snake; 2: one female snake, one male snake; 3: one male lizard; 4: one female lizard; 5: one female lizard


Question: If habitat 2 contains at least one female snake and habitat 4 contains two male lizards, then which one of the following could be true?

Habitat 3 contains two reptiles.
Habitat 5 contains two reptiles.
Habitat 1 contains a female lizard.
Habitat 2 contains a female lizard.
Habitat 5 contains a female lizard.


Question: Which one of the following must be true?

At least one female reptile is alone in a habitat.

At least one male reptile is alone in a habitat.

At least one lizard is alone in a habitat.


Question: Which one of the following CANNOT be the complete housing arrangement for habitats 1 and 2?

1: one female snake, one male snake; 2: one male snake

1: two female lizards; 2: one female snake


Question: If habitat 3 is empty, and no snake is housed in a habitat that is immediately next to a habitat containing a snake, then which one of the following could be false?

All snakes are housed in even-numbered habitats.

No lizard is housed in a habitat that is immediately next to a habitat containing a lizard.

Exactly one habitat contains exactly one reptile.


Question: If all snakes are female and each of the lizards has a habitat to itself, then which one of the following habitats CANNOT contain any snakes?

habitat 1
habitat 2
habitat 3
habitat 4
habitat 5


To prepare for fieldwork, exactly four different researchers—a geologist, a historian, a linguist, and a paleontologist—will learn at least one and at most three of four languages—Rundi, Swahili, Tigrinya, and Yoruba. They must learn the languages according to the following specifications: Exactly one researcher learns Rundi. Exactly two researchers learn Swahili. Exactly two researchers learn Tigrinya. Exactly three researchers learn Yoruba. Any language learned by the linguist or paleontologist is not learned by the geologist. Any language learned by the geologist is learned by the historian.

Question: Which one of the following could be true?

The linguist learns three languages—Rundi, Swahili, and Tigrinya.

The linguist learns three languages—Swahili, Tigrinya, and Yoruba.

The historian learns three languages—Rundi, Swahili, and Tigrinya.

The historian learns three languages—Swahili, Tigrinya, and Yoruba.

The paleontologist learns three languages—Rundi, Swahili, and Tigrinya.


Question: If the linguist learns three of the languages, then which one of the following must be true?

The linguist learns Tigrinya.
The linguist learns Rundi.
The linguist learns Swahili.
The paleontologist learns Rundi.
The paleontologist learns Swahili.


Question: Each of the following could be true of the researcher who learns Rundi EXCEPT:

The researcher also learns Tigrinya but not Swahili.

The researcher learns neither Tigrinya nor Swahili.

The researcher also learns Tigrinya but not Yoruba.

The researcher also learns both Tigrinya and Yoruba.

The researcher also learns Yoruba but not Tigrinya.


Question: Each of the following could be a complete and accurate list of the researchers who learn both Swahili and Yoruba EXCEPT:

the historian
the paleontologist
the historian, the linguist
the historian, the paleontologist
the linguist, the paleontologist


Question: If the geologist learns exactly two of the languages, then which one of the following could be true?

The paleontologist learns exactly three of the languages.

The historian learns exactly two of the languages.


Question: Which one of the following must be true?

Fewer of the languages are learned by the historian than are learned by the paleontologist.

Fewer of the languages are learned by the geologist than are learned by the historian.

Fewer of the languages are learned by the geologist than are learned by the linguist.

Fewer of the languages are learned by the paleontologist than are learned by the linguist.

Fewer of the languages are learned by the paleontologist than are learned by the historian.


Question: If exactly two of the languages are learned by the historian, then which one of the following must be true?

The paleontologist does not learn Rundi.

The paleontologist does not learn Swahili.


During three days—Monday through Wednesday—a health officer will inspect exactly six buildings—three hotels: Grace, Jacaranda, and Lido; and three restaurants: Seville, Vesuvio, and Zeno. Each day, exactly two buildings are inspected: one in the morning and one in the afternoon. Inspections must occur according to the following conditions: Hotels are not inspected on Wednesday. Grace is inspected at some time before Jacaranda. Grace is not inspected on the same day as Seville. If Zeno is inspected in the morning, Lido is also inspected in the morning.

Question: Which one of the following could be the order in which the buildings are inspected, listed in order from Monday morning through Wednesday afternoon?

Grace, Seville, Jacaranda, Lido, Vesuvio, Zeno

Grace, Vesuvio, Zeno, Jacaranda, Lido, Seville

Lido, Jacaranda, Grace, Vesuvio, Zeno, Seville

Lido, Seville, Grace, Jacaranda, Zeno, Vesuvio

Zeno, Grace, Jacaranda, Lido, Seville, Vesuvio


Question: Which one of the following could be the buildings inspected in the mornings, listed in order from Monday through Wednesday?

Grace, Jacaranda, Zeno
Jacaranda, Vesuvio, Seville
Lido, Jacaranda, Vesuvio
Seville, Jacaranda, Vesuvio
Seville, Lido, Zeno


Question: Which one of the following is a pair of buildings that, if inspected on the same day as each other, must be inspected on Monday?

Grace and Jacaranda
Grace and Vesuvio
Jacaranda and Lido
Lido and Seville
Lido and Vesuvio


Question: If Grace is inspected on Tuesday, which one of the following could be the buildings inspected in the afternoons, listed in order from Monday through Wednesday?

Lido, Jacaranda, Vesuvio
Lido, Jacaranda, Zeno
Lido, Vesuvio, Zeno
Seville, Grace, Vesuvio
Seville, Jacaranda, Lido


Question: If Seville is inspected on Monday morning, which one of the following must be true?

Grace is inspected on Tuesday afternoon.

Jacaranda is inspected on Monday afternoon.

Vesuvio is inspected on Wednesday morning.


Question: If Grace is inspected on Monday morning and Zeno is inspected on Wednesday morning, which one of the following must be true?

Jacaranda is inspected before Lido is inspected.

Jacaranda is inspected after Lido is inspected.

Jacaranda is inspected after Seville is inspected.

Lido is inspected before Seville is inspected.

Lido is inspected before Vesuvio is inspected.


Morrisville's town council has exactly three members: Fu, Gianola, and Herstein. During one week, the council members vote on exactly three bills: a recreation bill, a school bill, and a tax bill. Each council member votes either for or against each bill. The following is known: Each member of the council votes for at least one of the bills and against at least one of the bills. Exactly two members of the council vote for the recreation bill. Exactly one member of the council votes for the school bill. Exactly one member of the council votes for the tax bill. Fu votes for the recreation bill and against the school bill. Gianola votes against the recreation bill. Herstein votes against the tax bill.

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

Fu and Gianola vote the same way on the tax bill.

Gianola and Herstein vote the same way on the recreation bill.

Gianola and Herstein vote the same way on the school bill.

Fu votes for one of the bills and Gianola votes for two of the bills.

Fu votes for two of the bills and Gianola votes for two of the bills.


Question: If the set of members of the council who vote against the school bill is the same set of members who vote against the tax bill, then which one of the following statements must be true?

Herstein votes against the recreation bill.


Question: If Gianola votes for the tax bill, then which one of the following statements could be true?

Fu and Gianola each vote for exactly one bill.

Gianola and Herstein each vote for exactly one bill.

Herstein votes against the recreation bill.


Question: If Gianola votes for exactly two of the three bills, which one of the following statements must be true?

Fu votes for the tax bill.
Gianola votes for the recreation bill.
Gianola votes for the school bill.
Gianola votes against the tax bill.
Herstein votes for the school bill.


Question: If one of the members of the council votes against exactly the same bills as does another member of the council, then which one of the following statements must be true?

Fu votes for the tax bill.
Gianola votes for the recreation bill.
Gianola votes against the school bill.
Gianola votes for exactly one bill
Herstein votes for exactly one bill.


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

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

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

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

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

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

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


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

Mannequin 1 wears the navy jacket and the yellow skirt.

Mannequin 2 wears the red hat and the red jacket.

Mannequin 1 wears exactly one red article of clothing.

Mannequin 1 wears exactly three yellow articles of clothing.

Mannequin 2 wears no red articles of clothing.


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

Mannequin 1 wears the yellow hat.
Mannequin 1 wears the yellow skirt.
Mannequin 2 wears the red hat.
Mannequin 2 wears the yellow hat.
Mannequin 2 wears the yellow jacket.


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

Mannequin 1 wears no navy articles of clothing.

Mannequin 2 wears no yellow articles of clothing.


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

navy hat
red hat
yellow hat
red skirt
yellow skirt


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

Mannequin 1 wears the navy jacket.
Mannequin 1 wears the yellow jacket.
Mannequin 1 wears the red skirt.
Mannequin 2 wears the red hat.
Mannequin 2 wears the red jacket.


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

Mannequin 1 wears the yellow hat.
Mannequin 1 wears the yellow jacket.
Mannequin 2 wears the navy hat.
Mannequin 2 wears the red hat.
Mannequin 2 wears the red jacket.


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

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


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

the fourth, the fifth
the fourth, the sixth
the second, the fourth, the fifth
the third, the fifth, the sixth
the second, the third, the fourth


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

Gimena and Holly
Holly and Saul
Kate and Nate
Leung and Oscar
Nate and Saul


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

Gimena attends the fifth class.
Holly attends the third class.
Iyanna attends the fourth class.
Nate attends the fifth class.
Saul attends the second class.


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

the second
the third
the fourth
the fifth
the sixth


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

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

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


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

Green lights decorate store 2.
Green lights decorate store 10.
Red lights decorate store 8.
Red lights decorate store 9.
Yellow lights decorate store 2.


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

Green lights decorate store 10.
Red lights decorate store 1.
Red lights decorate store 8.
Yellow lights decorate store 8.
Yellow lights decorate store 10.


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

Green lights decorate store 9.
Red lights decorate store 2.
Red lights decorate store 7.
Red lights decorate store 10.
Yellow lights decorate store 8.


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

Green lights decorate store 1.
Red lights decorate store 7.
Red lights decorate store 10.
Yellow lights decorate store 2.
Yellow lights decorate store 8.


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

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

F, J, N, and T
F, L, M, and P
F, M, N, and P
J, L, M, and T
K, L, N, and T


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

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

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

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

two radiobiologists, both of whom are experienced astronauts

two radiobiologists, both of whom are inexperienced astronauts


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


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


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


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

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


Question: Which one of the following must be false?

Exactly five of the six cars have leather interiors.

Exactly five of the six cars have sunroofs.

Exactly four of the six cars have leather interiors.

Exactly four of the six cars have power windows.

Exactly four of the six cars have sunroofs.


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

T has power windows.
T has a sunroof.
V has power windows.
Z has power windows.
Z has a sunroof.


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

Exactly four of the six cars have power windows.

Exactly four of the six cars have leather interiors.

Exactly four of the six cars have sunroofs.


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

Exactly three of the six cars have power windows.

Exactly four of the six cars have power windows.

Exactly three of the six cars have sunroofs.

Exactly four of the six cars have sunroofs.

Exactly four of the six cars have leather interiors.


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

T and Z have exactly one option in common.

W and Z have exactly one option in common.


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

V and X have exactly one option in common.

V and X have exactly two options in common.

X and Z have exactly two options in common.


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

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

Seat G3 is empty.
Seat H2 is empty.
Shiro sits in a seat numbered 3.
Tony sits in a seat numbered 1.
Umeko sits in a seat numbered 3.


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

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

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

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


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

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

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

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


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


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

Quentin
Shiro, Umeko
Robert, Shiro, Umeko
Tony, Shiro, Umeko
Quentin, Shiro, Tony, Umeko


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

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

Nilsson, Orozco, Robinson
Orozco, Robinson, Sarkis
Nilsson, Orozco, Paton, Robinson
Nilsson, Orozco, Paton, Sarkis
Orozco, Paton, Robinson, Sarkis


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

Paton was hired exactly one year after Orozco.

Exactly one professor was hired in 1994.

Exactly two professors were hired in 1993.


Question: Which one of the following must be false?

Nilsson was hired in 1989.
Paton was hired in 1990.
Paton was hired in 1991.
Sarkis was hired in 1992.
Togo was hired in 1994.


Question: Which one of the following must be true?

Orozco was hired before Paton.
Paton was hired before Sarkis.
Sarkis was hired before Robinson.
Robinson was hired before Sarkis.
Madison was hired before Sarkis.


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

Orozco, Paton, and Togo share a specialty.

Madison, Paton, and Togo share a specialty.

Exactly two professors were hired in 1991.

Exactly two professors were hired in 1993.


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

Nilsson does not share a specialty with Paton.

Exactly one professor was hired in 1990.

Exactly one professor was hired in 1991.

Exactly two professors were hired in each of two years.

Paton was hired at least one year before Sarkis.


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

Question: Which one of the following could be true?

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

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

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

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


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

Imamura occupies the window seat in row 3.

Gutierrez sits in the same row as Kelly.

Gutierrez sits in the same row as Moore.


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

Hoffman sits in row 2.
Imamura sits in row 2.
Imamura sits in row 3.
Kelly sits in row 1.
Lapas sits in row 3.


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

Gutierrez sits in the same row as Imamura.


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

Hoffman sits in row 2.
Kelly sits in row 2.
Moore sits in row 2.
Imamura occupies an aisle seat.
Moore occupies an aisle seat.


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

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

Richards North and Tuscarora South
Richards South and Wisteria South
Richards South and Tuscarora North
Tuscarora North and Wisteria South
Tuscarora South and Wisteria South


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

Richards South and Wisteria South
Richards South and Tuscarora South
Richards South and Veblen North
Tuscarora South and Wisteria South
Veblen North and Wisteria South


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

Richards South
Wisteria South
Tuscarora South
Veblen South
Veblen North