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

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

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


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

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


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


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


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


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


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

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

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

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

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

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

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


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


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

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


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

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


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

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

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


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


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

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

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

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

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

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

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


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

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


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

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


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

Sharon must visit Montreal if Paul visits Vancouver.

Regina must visit Vancouver if Paul visits Vancouver.

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

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

Lori visits a city with Paul or else with Sharon.


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

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


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

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

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

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

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

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


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

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

No conservative and exactly two liberals voted for Datalog.

Exactly one conservative and exactly one liberal voted for Datalog.

Exactly one conservative and all three liberals voted for Datalog.

Exactly two conservatives and exactly one liberal voted for Datalog.

Exactly two conservatives and exactly two liberals voted for Datalog.


Question: Which one of the following must be true?

At least one conservative voted for Datalog.

At least one liberal voted against Datalog.

At least one moderate voted against Datalog.

At least one moderate voted for Datalog.


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

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

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


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

Exactly one conservative voted for Datalog.

Exactly three liberals voted for Datalog.


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

one conservative, two moderates, two liberals

one conservative, two moderates, three liberals


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

Both conservatives voted against Datalog.

At least one liberal voted against Datalog.

Exactly five of the judges voted against Datalog.


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

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

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


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

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


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


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


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


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


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

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

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


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

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


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

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


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

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

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


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


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


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


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


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


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

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

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

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

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

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

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


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

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


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

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


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

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


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

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


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

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


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

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

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


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


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


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


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


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

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


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

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


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


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

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

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


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

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


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

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


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

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


Question: If G is the only child in group 1, which one of the following must be true?

F is in group 3.
K is in group 3.
Q is in group 2.
R is in group 1.
S is in group 2.


Exactly eight consumers—F, G, H, J, K, L, M, and N—will be interviewed by market researchers. The eight will be divided into exactly two 4-person groups—group 1 and group 2—before interviews begin. Each person is assigned to exactly one of the two groups according to the following conditions: F must be in the same group as J. G must be in a different group from M. If H is in group 1, then L must be in group 1. If N is in group 2, then G must be in group 1.

Question: Group 1 could consist of

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


Question: If K is in the same group as N, which one of the following must be true?

G is in group 1.
H is in group 2.
J is in group 1.
K is in group 2.
M is in group 1.


Question: If F is in the same group as H, which one of the following must be true?

G is in group 2.
J is in group 1.
K is in group 1.
L is in group 2.
M is in group 2.


Question: If L and M are in group 2, then a person who could be assigned either to group 1 or, alternatively, to group 2 is


Question: Each of the following is a pair of people who could be in group 1 together EXCEPT


Question: If L is in group 2, then each of the following is a pair of people who could be in group 1 together EXCEPT


A breeder has ten birds: Kind Male Female Goldfinches H J, K Lovebirds M N Parakeets Q, R, S T, W The breeder exhibits pairs of birds consisting of one male and one female of the same kind. At most two pairs can be exhibited at a time; the remaining birds must be distributed between two cages. The breeder is constrained by the following conditions: Neither cage can contain more than four birds. Any two birds that are both of the same sex and of the same kind as each other cannot be caged together. Whenever either J or W is exhibited, S cannot be exhibited.

Question: Which one of the following is a possible assignment of the birds? First Cage Second Cage Exhibition

H, M, N J, K, S Q, R, T, W
K, M, Q N, R, W H, J, S, T
K, Q, S R, T, W H, J, M, N
H, J, M, R K, N, S, W Q, T
H, J, M, R, W K, N, S Q, T, W


Question: Which one of the following lists two pairs of birds that the breeder can exhibit at the same time?

H and J; M and N
H and J; S and T
H and K; M and N
H and K; R and W
M and N; S and W


Question: If Q and R are among the birds that are assigned to the cages, then it must be true that

H is exhibited
K is exhibited
N is exhibited
J is assigned to one of the cages
T is assigned to one of the cages


Question: If Q and T are among the birds assigned to the cages, which one of the following is a pair of birds that must be exhibited?


Question: Which one of the following CANNOT be true?

One pair of parakeets are the only birds exhibited together.

One pair of goldfinches and one pair of lovebirds are exhibited together.

One pair of goldfinches and one pair of parakeets are exhibited together.

One pair of lovebirds and one pair of parakeets are exhibited together.

Two pairs of parakeets are exhibited together.


Question: If S is one of the birds exhibited, it must be true that

H is exhibited
M is exhibited
K is assigned to a cage
N is assigned to a cage
R is assigned to a cage


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

Question: Which one of the following is an acceptable assignment of students to the three classes?

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


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

class 1
class 3
class 1, class 3
class 2, class 3
class 1, class 2, class 3


Question: If X is added to class 1, which one of the following is a student who must be added to class 2?


Question: If X is added to class 3, each of the following is a pair of students who can be added to class 1 EXCEPT


Question: If T is added to class 3, which one of the following is a student who must be added to class 2?


Each of two boats, boat 1 and boat 2, will be assigned exactly four people. Exactly eight people, three adults—F, G, and H—and five children—V, W, X, Y, and Z—must be assigned to the boats according to the following conditions: Each boat is assigned at least one adult. If F is assigned to boat 2, G is assigned to boat 2. If V is assigned to boat 1, W is assigned to boat 2. X and Z are assigned to different boats.

Question: Which one of the following is an acceptable assignment of people to boat I ?

F, G, H, X
F, H, W, Y
F, H, Y, Z
F, V, W, X
G, H, X, Y


Question: If F is assigned to boat 2, which one of the following is a pair of people who could be assigned to the same boat as each other?


Question: If exactly three children are assigned to boat 1, which one of the following is a pair of people who could both be assigned to boat 2?


Question: If G is assigned to boat 1, which one of the following must be true?

Exactly one adult is assigned to boat 1.

Exactly two adults are assigned to boat 2.

Exactly two children are assigned to boat 2.


Question: If V and W are assigned to the same boat as each other, which one of the following is a pair of people who must also be assigned to the same boat as each other?


Question: If H is assigned to a different boat than Y, which one of the following must be assigned to boat 1?


Question: If exactly one adult is assigned to boat 1, which one of the following must be true?

F is assigned to boat 1.
G is assigned to boat 2.
H is assigned to boat 2.
V is assigned to boat 1.
Z is assigned to boat 2.


Each of nine students—Faith, Gregory, Harlan, Jennifer, Kenji, Lisa, Marcus, Nari, and Paul—will be assigned to exactly one of three panels: Oceans, Recycling, and Wetlands. Exactly three of the students will be assigned to each panel. The assignment of students to panels must meet the following conditions: Faith is assigned to the same panel as Gregory. Kenji is assigned to the same panel as Marcus. Faith is not assigned to the same panel as Paul. Gregory is not assigned to the same panel as Harlan. Jennifer is not assigned to the same panel as Kenji. Harlan is not assigned to the Oceans panel if Paul is not assigned to the Oceans panel.

Question: Which one of the following is an acceptable assignment of students to the panels?

Oceans: Faith, Gregory, Jennifer Recycling: Kenji, Lisa, Nari Wetlands: Harlan, Marcus, Paul

Oceans: Faith, Jennifer, Lisa Recycling: Harlan, Kenji, Marcus Wetlands: Gregory, Nari, Paul

Oceans: Harlan, Kenji, Marcus Recycling: Faith, Gregory, Jennifer Wetlands: Lisa, Nari, Paul

Oceans: Jennifer, Kenji, Marcus Recycling: Faith, Gregory, Nari Wetlands: Harlan, Lisa, Paul

Oceans: Kenji, Marcus, Paul Recycling: Harlan, Jennifer, Nari Wetlands: Faith, Gregory, Lisa


Question: If Marcus and Paul are both assigned to the Wetlands panel, which one of the following must be true?

Harlan is assigned to the Recycling panel.

Jennifer is assigned to the Oceans panel.

Kenji is assigned to the Recycling panel.


Question: Which one of the following is a pair of students who could be assigned to the same panel as each other?

Faith and Harlan
Gregory and Paul
Harlan and Marcus
Faith and Marcus
Jennifer and Marcus


Question: If Kenji and Paul are both assigned to the Recycling panel, which one of the following could be true?

Faith is assigned to the Wetlands panel.

Gregory is assigned to the Recycling panel.

Jennifer is assigned to the Wetlands panel.

Lisa is assigned to the Recycling panel.


Question: Each of the following is a pair of students who could be assigned to the same panel as each other EXCEPT:

Gregory and Kenji
Gregory and Lisa
Kenji and Nari
Lisa and Marcus
Lisa and Paul


A university library budget committee must reduce exactly five of eight areas of expenditure—G, L, M, N, P, R, S, and W—in accordance with the following conditions: If both G and S are reduced, W is also reduced. If N is reduced, neither R nor S is reduced. If P is reduced, L is not reduced. Of the three areas L, M, and R, exactly two are reduced.

Question: Which one of the following could be a complete and accurate list of the areas of expenditure reduced by the committee?

G, L, M, N, W
G, L, M, P, W
G, M, N, R, W
G, M, P, R, S
L, M, R, S, W


Question: If W is reduced, which one of the following could be a complete and accurate list of the four other areas of expenditure to be reduced?

G, M, P, S
L, M, N, R
L, M, P, S
M, N, P, S
M, P, R, S


Question: If P is reduced, which one of the following is a pair of areas of expenditure both of which must be reduced?


Question: If both L and S are reduced, which one of the following could be a pair of areas of expenditure both of which are reduced?


Question: If R is not reduced, which one of the following must be true?

G is reduced.
N is not reduced.
P is reduced.
S is reduced.
W is not reduced.


Question: If both M and R are reduced, which one of the following is a pair of areas neither of which could be reduced?


Question: Which one of the following areas must be reduced?


At a benefit dinner, a community theater's seven sponsors—K, L, M, P, Q, V, and Z—will be seated at three tables—1, 2, and 3. Of the sponsors, only K, L, and M will receive honors, and only M, P, and Q will give a speech. The sponsors' seating assignments must conform to the following conditions: Each table has at least two sponsors seated at it, and each sponsor is seated at exactly one table. Any sponsor receiving honors is seated at table 1 or table 2. L is seated at the same table as V.

Question: Which one of the following is an acceptable assignment of sponsors to tables?

Table 1: K, P; Table 2: M, Q; Table 3: L, V, Z

Table 1: K, Q, Z; Table 2: L, V; Table 3: M, P

Table 1: L, P; Table 2: K, M; Table 3: Q, V, Z

Table 1: L, Q, V; Table 2: K, M; Table 3: P, Z

Table 1: L, V, Z; Table 2: K, M, P; Table 3: Q


Question: Which one of the following is a list of all and only those sponsors any one of whom could be among the sponsors assigned to table 3?


Question: If K is assigned to a different table than M, which one of the following must be true of the seating assignment?

Exactly two sponsors are seated at table 1.

Exactly two sponsors are seated at table 3.


Question: If Q is assigned to table 1 along with two other sponsors, which one of the following could be true of the seating assignment?

K is seated at the same table as L.
K is seated at the same table as Q.
M is seated at the same table as V.
M is seated at the same table as Z.
P Is seated at the same table as Q.


Question: If the sponsors assigned to table 3 include exactly one of the sponsors who will give a speech, then the sponsors assigned to table 1 could include any of the following EXCEPT:


Question: If three sponsors, exactly two of whom are receiving honors, are assigned to table 2, which one of the following could be the list of sponsors assigned to table 1?


Question: Which one of the following conditions, if added to the existing conditions, results in a set of conditions to which no seating assignment for the sponsors can conform?

At most two sponsors are seated at table 1.

Any sponsor giving a speech is seated at table 1 or else table 2.

Any sponsor giving a speech is seated at table 2 or else table 3.

Exactly three of the sponsors are seated at table 1.

Any table at which both L and V are seated also has a third sponsor seated at it.


Fu, Gunsel, Jackson, Kowalski, Lee, Mayer, and Ordoveza are the only applicants being considered for some positions at a nonprofit organization. Only applicants who are interviewed will be hired. The hiring process must meet the following constraints: If Gunsel is interviewed, Jackson is interviewed. If Jackson is interviewed, Lee is interviewed. Fu is interviewed. Fu is not hired, unless Kowalski is interviewed. Kowalski is not hired, unless Mayer is interviewed. If Mayer is hired, and Lee is interviewed, Ordoveza is hired.

Question: Which one of the following could be a complete and accurate list of the applicants that are interviewed?

Fu, Gunsel
Fu, Jackson
Fu, Lee
Fu, Gunsel, Lee
Fu, Gunsel, Jackson


Question: Which one of the following could be true?

Lee and Mayer are the only applicants interviewed.

Fu, Jackson, and Kowalski are the only applicants interviewed.

Gunsel and one other applicant are the only applicants interviewed.

Gunsel and two other applicants are the only applicants interviewed.

Gunsel and three other applicants are the only applicants interviewed.


Question: If Mayer is not interviewed, which one of the following must be true?

Fu is interviewed but Kowalski is not hired.


Question: If Gunsel and five other applicants are the only applicants interviewed, and if exactly three applicants are hired, then which one of the following could be an accurate list of the applicants hired?

Fu, Lee, Mayer
Fu, Kowalski, Mayer
Kowalski, Lee, Ordoveza
Gunsel, Jackson, Mayer
Gunsel, Jackson, Lee


Question: If every applicant that is interviewed is hired, and if Lee is hired, then each of the following applicants must be interviewed EXCEPT:


Question: If Ordoveza is not interviewed, and if exactly four applicants are hired, then which one of the following must be false?

Lee is hired.
Mayer is hired.
Jackson is interviewed.
Kowalski is interviewed.
Gunsel is interviewed.


Exactly six of seven researchers—three anthropologists: Franklin, Jones, and Marquez; and four linguists: Neil, Osborne, Rice, and Samuels—will be included in two three-person teams—team 1 and team 2. No researcher will be included in more than one team. Each team must include at least one anthropologist and at least one linguist. The teams' composition must conform to the following conditions: Neither team includes both Franklin and Samuels. Neither team includes both Neil and Rice. If a team includes Marquez, it includes neither Rice nor Samuels. If team 1 includes Jones, team 2 includes Rice.

Question: Which one of the following could be the list of the researchers on the two teams?

team 1: Franklin, Marquez, Osborne team 2: Jones, Neil, Rice

team 1: Franklin, Neil, Samuels team 2: Jones, Osborne, Rice

team 1: Franklin, Osborne, Rice team 2: Jones, Neil, Samuels

team 1: Jones, Marquez, Neil team 2: Osborne, Rice, Samuels

team 1: Jones, Osborne, Rice team 2: Franklin, Marquez, Neil


Question: If Jones is on team 1, which one of the following is a pair of researchers that must be on team 2 together?

Franklin and Rice
Marquez and Osborne
Neil and Osborne
Osborne and Samuels
Rice and Samuels


Question: If Neil is on team 1, which one of the following is a pair of researchers that could be on team 1 together with Neil?

Franklin and Jones
Jones and Osborne
Jones and Rice
Jones and Samuels
Osborne and Samuels


Question: If Franklin is on the same team as Marquez, which one of the following could be true?

Jones is on team 1.
Rice is on team 1.
Samuels is on team 2.
Both Neil and Osborne are on team 1.
Both Neil and Osborne are on team 2.


Question: Each of the following is a pair of researchers that could be on team 2 together EXCEPT:

Franklin and Jones
Franklin and Marquez
Franklin and Rice
Jones and Marquez
Jones and Rice


Question: Which one of the following could be true?

Franklin is on team 1 and Neil is on team 2.

Franklin is on team 2 and Jones is not on any team.

Franklin is on team 2 and Marquez is on team 2.

Franklin is not on any team and Jones is on team 1.

Jones is on team 1 and Neil is on team 2.


Question: If Marquez is on team 2, which one of the following must also be on team 2?


In a certain recipe contest, each contestant submits two recipes, one for an appetizer and one for a main dish. Together the two recipes must include exactly seven flavorings—fenugreek, ginger, lemongrass, nutmeg, paprika, saffron, and turmeric—with no flavoring included in more than one of the two recipes. Each contestant's recipes must satisfy the following conditions: The appetizer recipe includes at most three of the flavorings. Fenugreek is not included in the same recipe as nutmeg. Saffron is not included in the same recipe as turmeric. Ginger is included in the same recipe as nutmeg.

Question: Which one of the following could be a complete and accurate list of the flavorings included in one contestant's main-dish recipe?

fenugreek, lemongrass, saffron
fenugreek, ginger, nutmeg, turmeric
ginger, lemongrass, nutmeg, paprika
ginger, nutmeg, paprika, turmeric
lemongrass, nutmeg, saffron, turmeric


Question: If a contestant's appetizer recipe does not include fenugreek, then the contestant's appetizer recipe must include

ginger lemongrass paprika saffron turmeric


Question: Which one of the following could be a list of all of the flavorings included in one contestant's appetizer recipe?

fenugreek, lemongrass, paprika, turmeric


Question: If a contestant includes lemongrass in the same recipe as paprika, which one of the following is a flavoring that must be included in the contestant's main-dish recipe?

ginger lemongrass nutmeg saffron turmeric


Question: If the condition that requires ginger to be included in the same recipe as nutmeg is suspended but all of the other original conditions remain in effect, then which one of the following could be a list of all of the flavorings included in one contestant's main-dish recipe?

fenugreek, ginger, lemongrass, paprika, saffron

fenugreek, ginger, lemongrass, saffron, turmeric

fenugreek, lemongrass, nutmeg, paprika, saffron


Nine different treatments are available for a certain illness: three antibiotics—F, G, and H—three dietary regimens—M, N, and O—and three physical therapies—U, V, and W. For each case of the illness, a doctor will prescribe exactly five of the treatments, in accordance with the following conditions: If two of the antibiotics are prescribed, the remaining antibiotic cannot be prescribed. There must be exactly one dietary regimen prescribed. If O is not prescribed, F cannot be prescribed. If W is prescribed, F cannot be prescribed. G cannot be prescribed if both N and U are prescribed. V cannot be prescribed unless both H and M are prescribed.

Question: Which one of the following could be the five treatments prescribed for a given case?

F, G, H, M, V
F, G, M, O, V
F, H, M, O, W
G, H, N, U, W
G, H, O, U, W


Question: Which one of the following could be the antibiotics and physical therapies prescribed for a given case?

F, G, H, W
F, G, U, V
F, U, V, W
G, U, V, W
H, U, V, W


Question: If O is prescribed for a given case, which one of the following is a pair of treatments both of which must also be prescribed for that case?


Question: If G is prescribed for a given case, which one of the following is a pair of treatments both of which could also be prescribed for that case?


Question: Which one of the following is a list of three treatments that could be prescribed together for a given case?


Question: Which one of the following treatments CANNOT be prescribed for any case?


Each of six people—Kim, Lina, Maricella, Oliver, Paulo, and Shigeru—plays exactly one of two sports—golf, and tennis. If a sport is played by more than one of the six people, then the people who play that sport are ranked in order of ability from highest to lowest, with no ties. The following conditions must apply: Oliver plays tennis. Lina plays golf. There is no golf player ranked higher than Lina. If Maricella plays golf, then Paulo and Shigeru play golf, Paulo ranking lower than Maricella but higher than Shigeru. If Maricella plays tennis, then Shigeru plays tennis, Shigeru ranking lower than Oliver but higher than Maricella. If Paulo plays tennis, then Kim plays tennis, Oliver ranking lower than Kim but higher than Paulo.

Question: Which one of the following could be true?

Maricella plays tennis and Shigeru plays golf.

Paulo and Oliver play tennis, Paulo ranking higher than Oliver.

Maricella and Shigeru play tennis, Maricella ranking higher than Shigeru.


Question: Each of the following could be the lowest-ranking tennis player EXCEPT:


Question: Which one of the following could be a complete and accurate list of the people who play tennis, listed in order of rank from highest to lowest?

Shigeru, Paulo, Oliver
Oliver, Paulo, Kim
Shigeru, Oliver, Maricella
Oliver, Shigeru, Kim, Maricella
Paulo, Maricella, Shigeru, Kim


Question: If Shigeru plays golf, then each of the following are pairs of people who must play the same sport as each other EXCEPT:

Paulo and Maricella
Paulo and Shigeru
Kim and Maricella
Paulo and Lina
Maricella and Shigeru


Question: If Oliver is the highest-ranking tennis player, which one of the following must be true?

Oliver and Maricella play the same sport as each other.

Paulo and Lina play the same sport as each other.

Paulo and Oliver play the same sport as each other.

Kim and Lina do not play the same sport as each other.

Kim and Paulo do not play the same sport as each other.


Question: Suppose that the condition is added that Shigeru and Paulo do not play the same sport as each other. If all the other conditions remain in effect, then each of the following could be true EXCEPT:

Maricella and Kim play the same sport as each other.

Paulo and Kim play the same sport as each other.

Paulo and Maricella play the same sport as each other.

Kim and Paulo do not play the same sport as each other.

Maricella and Kim do not play the same sport as each other.


Each of exactly five persons—Nguyen, Olson, Pike, Tyner, and Valdez—participates in exactly one of three activities: going to a movie, going to a soccer game, or going to a restaurant. The following conditions must apply. Nguyen and Olson do not participate in the same activity as each other, nor does either one of them participate in the same activity as Pike. Exactly two persons go to a soccer game. Tyner and Pike do not participate in the same activity as each other. If Nguyen or Valdez goes to a movie, they both go to a movie.

Question: Which one of the following could be an accurate list of the activities participated in by Nguyen, Olson, Pike, Tyner, and Valdez, respectively?

movie, soccer game, soccer game, restaurant, movie

movie, restaurant, soccer game, soccer game, movie

soccer game, restaurant, movie, soccer game, movie

soccer game, restaurant, movie, soccer game, restaurant

soccer game, restaurant, movie, soccer game, soccer game


Question: If Valdez goes to a soccer game, then each of the following could be true EXCEPT:

Olson goes to a movie.
Nguyen goes to a restaurant.
Nguyen goes to a soccer game.
Tyner goes to a soccer game.
Tyner goes to a movie.


Question: Which one of the following is a pair of persons who could go to a movie together?

Nguyen and Tyner
Olson and Tyner
Olson and Valdez
Pike and Olson
Pike and Tyner


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

Tyner and Valdez go to a restaurant together.


Question: If Nguyen goes to a soccer game, then which one of the following is a complete and accurate list of the persons any one of whom could go to a movie?

Olson
Pike, Valdez
Olson, Tyner
Pike, Tyner, Valdez
Olson, Pike, Tyner


Question: If the condition that exactly two persons go to a soccer game is changed to require that exactly three persons go to a soccer game, but all other conditions remain the same, then which one of the following persons must participate in an activity other than going to a soccer game?


Exactly seven film buffs—Ginnie, Ian, Lianna, Marcos, Reveka, Viktor, and Yow—attend a showing of classic films. Three films are shown, one directed by Fellini, one by Hitchcock, and one by Kurosawa. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions must apply: Exactly twice as many of the film buffs see the Hitchcock film as see the Fellini film. Ginnie and Reveka do not see the same film as each other. Ian and Marcos do not see the same film as each other. Viktor and Yow see the same film as each other. Lianna sees the Hitchcock film. Ginnie sees either the Fellini film or the Kurosawa film.

Question: Which one of the following could be an accurate matching of film buffs to films?

Ginnie: the Hitchcock film; Ian: the Kurosawa film; Marcos: the Hitchcock film

Ginnie: the Kurosawa film; Ian: the Fellini film; Viktor: the Fellini film

Ian: the Hitchcock film; Reveka: the Kurosawa film; Viktor: the Fellini film

Marcos: the Kurosawa film; Reveka: the Kurosawa film; Viktor: the Kurosawa film

Marcos: the Hitchcock film; Reveka: the Hitchcock film; Yow: the Hitchcock film


Question: Each of the following must be false EXCEPT:

Reveka is the only film buff to see the Fellini film.

Reveka is the only film buff to see the Hitchcock film.

Yow is the only film buff to see the Kurosawa film.

Exactly two film buffs see the Kurosawa film.

Exactly three film buffs see the Hitchcock film.


Question: Which one of the following could be a complete and accurate list of the film buffs who do NOT see the Hitchcock film?

Ginnie, Marcos
Ginnie Reveka
Ginnie, Ian, Reveka
Ginnie, Marcos, Yow
Ginnie, Viktor, Yow


Question: If exactly one film buff sees the Kurosawa film, then which one of the following must be true?

Viktor sees the Hitchcock film.
Ginnie sees the Fellini film.
Marcos sees the Fellini film.
Ian sees the Fellini film.
Reveka sees the Hitchcock film.


Question: Which one of the following must be true?

Ginnie sees a different film than Ian does.

Ian sees a different film than Lianna does.

Ian sees a different film than Viktor does.

Ian, Lianna, and Viktor do not all see the same film.

Ginnie, Lianna, and Marcos do not all see the same film.


Question: If Viktor sees the same film as Ginnie does, then which one of the following could be true?

Ginnie sees the Fellini film.
Ian sees the Hitchcock film.
Reveka sees the Kurosawa film.
Viktor sees the Hitchcock film.
Yow sees the Fellini film.


Question: Each of the following could be complete and accurate list of the film buffs who see the Fellini film EXCEPT:

Ginnie, Ian
Ginnie, Marcos
Ian, Reveka
Marcos, Reveka
Viktor, Yow


On a Tuesday, an accountant has exactly seven bills—numbered 1 through 7—to pay by Thursday of the same week. The accountant will pay each bill only once according to the following rules: Either three or four of the seven bills must be paid on Wednesday, the rest on Thursday. Bill 1 cannot be paid on the same day as bill 5. Bill 2 must be paid on Thursday. Bill 4 must be paid on the same day as bill 7. If bill 6 is paid on Wednesday, bill 7 must be paid on Thursday.

Question: If exactly four bills are paid on Wednesday, then those four bills could be


Question: Which one of the following is a complete and accurate list of the bills any one of which could be among the bills paid on Wednesday?


Question: If bill 2 and bill 6 are paid on different days from each other, which one of the following must be true?

Exactly three bills are paid on Wednesday.

Exactly three bills are paid on Thursday.

Bill 1 is paid on the same day as bill 4.

Bill 2 is paid on the same day as bill 3.

Bill 5 is paid on the same day as bill 7.


Question: If bill 6 is paid on Wednesday, which one of the following bills must also be paid on Wednesday?


Question: If bill 4 is paid on Thursday, which one of the following is a pair of bills that could also be paid on Thursday?


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

If bill 2 is paid on Thursday, bill 3 is paid on Wednesday.

If bill 4 is paid on Thursday, bill 1 is paid on Wednesday.

If bill 4 is paid on Thursday, bill 3 is paid on Wednesday.

If bill 6 is paid on Thursday, bill 3 is also paid on Thursday.

If bill 6 is paid on Thursday, bill 4 is also paid on Thursday.


Bird-watchers explore a forest to see which of the following six kinds of birds—grosbeak, harrier, jay, martin, shrike, wren—it contains. The findings are consistent with the following conditions: If harriers are in the forest, then grosbeaks are not. If jays, martins, or both are in the forest, then so are harriers. If wrens are in the forest, then so are grosbeaks. If jays are not in the forest, then shrikes are.

Question: Which one of the following could be a complete and accurate list of the birds NOT in the forest?

jays, shrikes
harriers, grosbeaks
grosbeaks, jays, martins
grosbeaks, martins, shrikes, wrens
martins, shrikes


Question: If both martins and harriers are in the forest, then which one of the following must be true?

Shrikes are the only other birds in the forest.

Jays are the only other birds in the forest.

The forest contains neither jays nor shrikes.

There are at least two other kinds of birds in the forest.

There are at most two other kinds of birds in the forest.


Question: If jays are not in the forest, then which one of the following must be false?

Neither martins nor harriers are in the forest.

Neither martins nor shrikes are in the forest.

Harriers and shrikes are the only birds in the forest.


Question: Which one of the following is the maximum number of the six kinds of birds the forest could contain?


Question: Which one of the following pairs of birds CANNOT be among those birds contained in the forest?

jays, wrens
jays, shrikes
shrikes, wrens
jays, martins
shrikes, martins


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

The forest contains both wrens and shrikes.

At most two kinds of birds are in the forest.

At least three kinds of birds are in the forest.


Question: Suppose the condition is added that if shrikes are in the forest, then harriers are not. If all other conditions remain in effect, then which one of the following could be true?

The forest contains both jays and shrikes.

The forest contains both wrens and shrikes.

The forest contains both martins and shrikes.

Jays are not in the forest, whereas martins are.

Only two of the six kinds of birds are not in the forest.


From among ten stones, a jeweler will select six, one for each of six rings. Of the stones, three—F, G, and H—are rubies; three—J, K, and M—are sapphires; and four—W, X, Y, and Z—are topazes. The selection of stones must meet the following restrictions: At least two of the topazes are selected. If exactly two of the sapphires are selected, exactly one of the rubies is selected. If W is selected, neither H nor Z is selected. If M is selected, W is also selected.

Question: Which one of the following could be the selection of stones?

F, G, H, M, X, Y
F, G, J, K, M, W
F, G, J, K, W, X
G, H, J, X, Y, Z
G, H, K, W, X, Z


Question: Which one of the following most be true?

Of at least one of the three types of stones, exactly one stone is selected.

Of at least one of the three types of stones, exactly three stones are selected.


Question: If Z is selected, which one of the following could be true?

All three of the sapphires are selected.


Question: If exactly two rubies are selected, which one of the following must be true?

H is selected.
J is selected.
Z is selected.
Exactly one sapphire is selected.
Exactly two topazes are selected.


Question: Which one of the following must be true?

The selection of stones includes at least one ruby.

The selection of stones includes at most two rubies.

The selection of stones includes either F or Z, or both.

The selection of stones includes either X or Y, or both.

The selection of stones includes either X or Z, or both.


Question: If J and M are the only sapphires selected, which one of the following could be true?

F and G are both selected.
F and X are both selected.
G and H are both selected.
G and K are both selected.
Y and Z are both selected.


Each of exactly six doctors—Juarez, Kudrow, Longtree, Nance, Onawa, and Palermo—is at exactly one of two clinics: Souderton or Randsborough. The following conditions must be satisfied: Kudrow is at Randsborough if Juarez is at Souderton. Onawa is at Souderton if Juarez is at Randsborough. If Longtree is at Souderton, then both Nance and Palermo are at Randsborough. If Nance is at Randsborough, then so is Onawa. If Palermo is at Randsborough, then both Kudrow and Onawa are at Souderton.

Question: Which one of the following could be a complete and accurate list of the doctors that are at Souderton?

Juarez, Kudrow, Onawa
Juarez, Nance, Onawa, Palermo
Kudrow, Longtree, Onawa
Nance, Onawa
Nance, Palermo


Question: If Palermo is at Randsborough, then which one of the following must be true?

Juarez is at Randsborough.
Kudrow is at Randsborough.
Longtree is at Souderton.
Nance is at Randsborough.
Onawa is at Randsborough.


Question: What is the minimum number of doctors that could be at Souderton?


Question: If Nance and Onawa are at different clinics, which one of the following must be true?

Juarez is at Souderton.
Kudrow is at Souderton.
Palermo is at Randsborough.
Four doctors are at Souderton.
Four doctors are at Randsborough.


Question: Which one of the following CANNOT be a pair of the doctors at Randsborough?

Juarez and Kudrow
Juarez and Palermo
Kudrow and Onawa
Nance and Onawa
Nance and Palermo


Question: If Kudrow is at Souderton, then which one of the following must be true?

Juarez is at Souderton.
Nance is at Souderton.
Onawa is at Randsborough.
Palermo is at Souderton.
Palermo is at Randsborough.


A fruit stand carries at least one kind of the following kinds of fruit: figs, kiwis, oranges, pears, tangerines, and watermelons. The stand does not carry any other kind of fruit. The selection of fruits the stand carries is consistent with the following conditions: If the stand carries kiwis, then it does not carry pears. If the stand does not carry tangerines, then it carries kiwis. If the stand carries oranges, then it carries both pears and watermelons. If the stand carries watermelons, then it carries figs or tangerines or both.

Question: Which one of the following could be a complete and accurate list of the kinds of fruit the stand carries?

oranges, pears
pears, tangerines
oranges, pears, watermelons
oranges, tangerines, watermelons
kiwis, oranges, pears, watermelons


Question: Which one of the following could be the only kind of fruit the stand carries?

figs oranges pears tangerines watermelons


Question: Which one of the following CANNOT be a complete and accurate list of the kinds of fruit the stand carries?

figs, kiwis, oranges, pears, watermelons


Question: If the stand carries no watermelons, then which one of the following must be true?

The stand carries at least two kinds of fruit.

The stand carries at most three kinds of fruit.

The stand carries neither oranges nor pears.

The stand carries neither oranges nor kiwis.


Question: If the stand carries watermelons, then which one of the following must be false?

The stand carries pears but not oranges.

The stand carries pears but not tangerines.


Question: If the condition that if the fruit stand does not carry tangerines then it does carry kiwis is suspended, and all other conditions remain in effect, then which one of the following CANNOT be a complete and accurate list of the kinds of fruit the stand carries?

pears
figs, pears
oranges, pears, watermelons
figs, pears, watermelons
figs, oranges, pears, watermelons


A total of six books occupies three small shelves—one on the first shelf, two on the second shelf, and three on the third shelf. Two of the books are grammars—one of Farsi, the other of Hausa. Two others are linguistics monographs—one on phonology, the other on semantics. The remaining two books are novels—one by Vonnegut, the other by Woolf. The books' arrangement is consistent with the following: There is at least one novel on the same shelf as the Farsi grammar. The monographs are not both on the same shelf. The Vonnegut novel is not on the same shelf as either monograph.

Question: Which one of the following could be an accurate matching of the bookshelves to the books on each of them?

first shelf: Hausa grammar second shelf: semantics monograph, Vonnegut novel third shelf: Farsi grammar, phonology monograph, Woolf novel

first shelf: semantics monograph second shelf: Farsi grammar, Vonnegut novel third shelf: Hausa grammar, phonology monograph, Woolf novel

first shelf: Vonnegut novel second shelf: phonology monograph, Farsi grammar third shelf: Hausa grammar, semantics monograph, Woolf novel

first shelf: Woolf novel second shelf: phonology and semantics monographs third shelf: Farsi and Hausa grammars, Vonnegut novel

first shelf: Woolf novel second shelf: Farsi grammar, Vonnegut novel third shelf: Hausa grammar, phonology and semantics monographs


Question: Which one of the following CANNOT be true?

A linguistics monograph is on the same shelf as the Hausa grammar.

The novels are on the same shelf as each other.

Neither linguistics monograph is on the first shelf.


Question: Which one of the following must be true?

A linguistics monograph and a grammar are on the second shelf.

A novel and a grammar are on the second shelf.

At least one linguistics monograph and at least one grammar are on the third shelf.

At least one novel and at least one grammar are on the third shelf.

At least one novel and at least one linguistics monograph are on the third shelf.


Question: If both grammars are on the same shelf, which one of the following could be true?

The phonology monograph is on the third shelf.

The Farsi grammar is on the second shelf.

The phonology monograph is on the first shelf.


Question: Which one of the following must be true?

A linguistics monograph is on the first shelf.

No more than one novel is on each shelf.

The Farsi grammar is not on the same shelf as the Hausa grammar.

The semantics monograph is not on the same shelf as the Woolf novel.

The Woolf novel is not on the first shelf.


Question: If the Farsi grammar is not on the third shelf, which one of the following could be true?

The phonology monograph is on the second shelf.

The Hausa grammar is on the second shelf.

The semantics monograph is on the third shelf.

The Vonnegut novel is on the third shelf.


Question: If the Hausa grammar and the phonology monograph are on the same shelf, which one of the following must be true?

The phonology monograph is on the third shelf.

The Vonnegut novel is on the second shelf.

The semantics monograph is on the second shelf.

The semantics monograph is on the first shelf.


Seven job applicants—Feng, Garcia, Herrera, Ilias, Weiss, Xavier, and Yates—are hired to fill seven new positions at Chroma, Inc. One position is in the management department, three are in the production department, and three are in the sales department. The following conditions must apply: Herrera is hired for a position in the same department as Yates. Feng is hired for a position in a different department from Garcia. If Xavier is hired for a sales position, then Weiss is hired for a production position. Feng is hired for a production position.

Question: Which one of the following could be a complete and accurate matching of the applicants with the departments in which they were hired?

management: Weiss; production: Feng, Herrera, Yates; sales: Garcia, Ilias, Xavier

management: Weiss; production: Garcia, Ilias, Xavier; sales: Feng, Herrera, Yates

management: Xavier; production: Feng, Garcia, Herrera; sales: Ilias, Yates, Weiss

management: Xavier; production: Feng, Herrera, Ilias; sales: Garcia, Weiss, Yates

management: Xavier; production: Feng, Ilias, Weiss; sales: Garcia, Herrera, Yates


Question: Which one of the following is a complete and accurate list of the applicants, each of whom CANNOT be hired for a production position?

Feng, Ilias, Xavier
Garcia, Herrera, Yates
Herrera, Yates
Garcia
Ilias


Question: It can be determined in which department each of the seven applicants is hired if which one of the following statements is true?

Feng and Weiss are both hired for production positions.

Garcia and Yates are both hired for sales positions.

Ilias and Weiss are both hired for sales positions.

Ilias and Weiss are both hired for production positions.

Ilias and Xavier are both hired for production positions.


Question: Each of the following could be an accurate partial list of the applicants hired for sales positions EXCEPT:

Garcia, Ilias
Garcia, Xavier
Garcia, Yates
Herrera, Weiss
Herrera, Xavier


Question: If Feng is hired for a position in the same department as Xavier, then each of the following could be true EXCEPT:

Herrera is hired for a production position.

Weiss is hired for the management position.

Weiss is hired for a production position.


Question: If Xavier is not hired for one of the production positions, then which one of the following could be true?

Feng and Herrera are both hired for sales positions.

Herrera and Weiss are both hired for sales positions.

Feng and Yates are both hired for production positions.

Garcia and Weiss are both hired for production positions.

Herrera and Weiss are both hired for production positions.


Barbara is shopping at a pet store to select fish for her new aquarium from among the following species: J, K, L, M, N, O, and P. For each of the seven species, the store has several fish available. Barbara makes her selection in a manner consistent with the following conditions: If she selects one or more K, then she does not select any O. If she selects one or more M, then she does not select any N. If she selects one or more M, then she selects at least one O. If she selects one or more N, then she selects at least one O. If she selects one or more O, then she selects at least one P. If she selects one or more P, then she selects at least one O. If she selects any O at all, then she selects at least two O.

Question: Which one of the following could be a complete and accurate list of the fish Barbara selects for her aquarium?

three J, one K, two M
one J, one K, one M, three O
one J, one M, two O, one P
one J, one N, one O, two P
one M, one N, two O, one P


Question: If Barbara does not select any fish of species P, then it could be true that she selects fish of species

J and of species K
J and of species M
K and of species M
K and of species N
L and of species O


Question: If Barbara selects fish of as many species as possible, then she cannot select any fish of which one of the following species?


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

Barbara selects exactly four fish, at least one of which is a J.

Barbara selects exactly four fish, at least one of which is an L.

Barbara selects exactly three fish, at least one of which is an M.

Barbara selects exactly three fish, at least one of which is an O.

Barbara selects exactly three fish, at least one of which is a P.


Question: If Barbara selects at least one fish for her aquarium, then which one of the following lists the minimum and maximum possible numbers, respectively, of different species of fish that Barbara selects?


For a behavioral study, a researcher will select exactly six individual animals from among three monkeys—F, G, and H—three pandas—K, L, and N—and three raccoons—T, V, and Z. The selection of animals for the study must meet the following conditions: F and H are not both selected. N and T are not both selected. If H is selected, K is also selected. If K is selected, N is also selected.

Question: Which one of the following is an acceptable selection of animals for the study?

F, G, K, N, T, V
F, H, K, N, V, Z
G, H, K, L, V, Z
G, H, K, N, V, Z
G, H, L, N, V, Z


Question: If H and L are among the animals selected, which one of the following could be true?

F is selected.
T is selected.
Z is selected.
Exactly one panda is selected.
Exactly two pandas are selected.


Question: Each of the following is a pair of animals that could be selected together EXCEPT


Question: If all three of the raccoons are selected, which one of the following must be true?

K is selected.
L is selected.
Exactly one monkey is selected.
Exactly two pandas are selected.
All three of the monkeys are selected.


Question: If T is selected, which one of the following is a pair of animals that must be among the animals selected?


Question: The selection of animals must include

at most two of each kind of animal
at least one of each kind of animal
at least two pandas
exactly two monkeys
exactly two raccoons


During a certain week, an animal shelter places exactly six dogs—a greyhound, a husky, a keeshond, a Labrador retriever, a poodle, and a schnauzer—with new owners. Two are placed on Monday, two on Tuesday, and the remaining two on Wednesday, consistent with the following conditions: The Labrador retriever is placed on the same day as the poodle. The greyhound is not placed on the same day as the husky. If the keeshond is placed on Monday, the greyhound is placed on Tuesday. If the schnauzer is placed on Wednesday, the husky is placed on Tuesday.

Question: Which one of the following could be a complete and accurate matching of dogs to the days on which they are placed?

Monday: greyhound, Labrador retriever Tuesday: husky, poodle Wednesday: keeshond, schnauzer

Monday: greyhound, keeshond Tuesday: Labrador retriever, poodle Wednesday: husky, schnauzer

Monday: keeshond, schnauzer Tuesday: greyhound, husky Wednesday: Labrador retriever, poodle

Monday: Labrador retriever, poodle Tuesday: greyhound, keeshond Wednesday: husky, schnauzer

Monday: Labrador retriever, poodle Tuesday: husky, keeshond Wednesday: greyhound, schnauzer


Question: Which one of the following must be true?

The keeshond is not placed on the same day as the greyhound.

The keeshond is not placed on the same day as the schnauzer.

The schnauzer is not placed on the same day as the husky.

The greyhound is placed on the same day as the schnauzer.

The husky is placed on the same day as the keeshond.


Question: If the poodle is placed on Tuesday, then which one of the following could be true?

The Labrador retriever is placed on Monday.


Question: If the greyhound is placed on the same day as the keeshond, then which one of the following must be true?

The Labrador retriever is placed on Monday.

The schnauzer is not placed on Wednesday.


Question: If the husky is placed the day before the schnauzer, then which one of the following CANNOT be true?

The husky is placed on Monday.
The keeshond is placed on Monday.
The greyhound is placed on Tuesday.
The poodle is placed on Tuesday.
The poodle is placed on Wednesday.


Question: If the greyhound is placed the day before the poodle, then which one of the following CANNOT be placed on Tuesday?

the husky
the keeshond
the Labrador retriever
the poodle
the schnauzer


An album contains photographs picturing seven friends: Raimundo, Selma, Ty, Umiko, Wendy, Yakira, Zack. The friends appear either alone or in groups with one another, in accordance with the following: Wendy appears in every photograph that Selma appears in. Selma appears in every photograph that Umiko appears in. Raimundo appears in every photograph that Yakira does not appear in. Neither Ty nor Raimundo appears in any photograph that Wendy appears in.

Question: Which one of the following could be a complete and accurate list of the friends who appear together in a photograph?

Raimundo, Selma, Ty, Wendy
Raimundo, Ty, Yakira, Zack
Raimundo, Wendy, Yakira, Zack
Selma, Ty, Umiko, Yakira
Selma, Ty, Umiko, Zack


Question: If Ty and Zack appear together in a photograph, then which one of the following must be true?

Raimundo does not appear in the photograph.

Umiko does not appear in the photograph.


Question: What is the maximum number of friends who could appear in a photograph that Yakira does not appear in?


Question: If Umiko and Zack appear together in a photograph, then exactly how many of the other friends must also appear in that photograph?


Question: If exactly three friends appear together in a photograph, then each of the following could be true EXCEPT:

Selma and Zack both appear in the photograph.

Ty and Yakira both appear in the photograph.

Wendy and Selma both appear in the photograph.

Yakira and Zack both appear in the photograph.

Zack and Raimundo both appear in the photograph.


A lighting control panel has exactly seven switches, numbered from 1 to 7. Each switch is either in the on position or in the off position. The circuit load of the panel is the total number of its switches that are on. The control panel must be configured in accordance with the following conditions: If switch 1 is on, then switch 3 and switch 5 are off. If switch 4 is on, then switch 2 and switch 5 are off. The switch whose number corresponds to the circuit load of the panel is itself on.

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

switch 2, switch 3, switch 4, switch 7
switch 3, switch 6, switch 7
switch 2, switch 5, switch 6
switch 1, switch 3, switch 4
switch 1, switch 5


Question: If switch 1 and switch 3 are both off, then which one of the following could be two switches that are both on?

switch 2 and switch 7
switch 4 and switch 6
switch 4 and switch 7
switch 5 and switch 6
switch 6 and switch 7


Question: If exactly two of the switches are on, then which one of the following switches must be off?

switch 3
switch 4
switch 5
switch 6
switch 7


Question: If switch 6 and switch 7 are both off, then what is the maximum circuit load of the panel?


Question: If switch 5 and switch 6 are both on, then which one of the following switches must be on?

switch 1
switch 2
switch 3
switch 4
switch 7


Question: What is the maximum circuit load of the panel?


Henri has exactly five electrical appliances in his dormitory room: a hairdryer, a microwave oven, a razor, a television, and a vacuum. As a consequence of fire department regulations, Henri can use these appliances only in accordance with the following conditions: Henri cannot use both the hairdryer and the razor simultaneously. Henri cannot use both the hairdryer and the television simultaneously. When Henri uses the vacuum, he cannot at the same time use any of the following: the hairdryer, the razor, and the television.

Question: Which one of the following is a pair of appliances Henri could be using simultaneously?

the hairdryer and the razor
the hairdryer and the television
the razor and the television
the razor and the vacuum
the television and the vacuum


Question: Assume that Henri is using exactly two appliances and is not using the microwave oven. Which one of the following is a list of all the appliances, other than the microwave oven, that Henri CANNOT be using?

hairdryer
razor
vacuum
hairdryer, razor
hairdryer, vacuum


Question: Which one of the following CANNOT be true?

Henri uses the hairdryer while using the microwave oven.

Henri uses the microwave oven while using the razor.

Henri uses the microwave oven while using two other appliances.

Henri uses the television while using two other appliances.

Henri uses the vacuum while using two other appliances.


Question: If Henri were to use exactly three appliances, then what is the total number of different groups of three appliances any one of which could be the group of appliances he is using?


Question: Which one of the following statements, if true, guarantees that Henri is using no more than one of the following: the hairdryer, the razor, the television?

Henri is using the hairdryer.
Henri is using the television.
Henri is not using the hairdryer.
Henri is not using the microwave oven.
Henri is not using the vacuum.


Question: Which one of the following must be true?

Henri uses at most three appliances simultaneously.

Henri uses at most four appliances simultaneously.

Henri uses at most one other appliance while using the microwave oven.

Henri uses at most one other appliance while using the razor.

Henri uses at least two other appliances while using the hairdryer.


There are exactly five pieces of mail in a mailbox: a flyer, a letter, a magazine, a postcard, and a survey. Each piece of mail is addressed to exactly one of three housemates: Georgette, Jana, or Rini. Each housemate has at least one of the pieces of mail addressed to her. The following conditions must apply: Neither the letter nor the magazine is addressed to Georgette. If the letter is addressed to Rini, then the postcard is addressed to Jana. The housemate to whom the flyer is addressed has at least one of the other pieces of mail addressed to her as well.

Question: Which one of the following could be a complete and accurate matching of the pieces of mail to the housemates to whom they are addressed?

Georgette: the flyer, the survey Jana: the letter Rini: the magazine

Georgette: the flyer, the postcard Jana: the letter, the magazine Rini: the survey

Georgette: the magazine, the survey Jana: the flyer, the letter Rini: the postcard

Georgette: the survey Jana: the flyer, the magazine Rini: the letter, the postcard

Georgette: the survey Jana: the letter, the magazine, the postcard Rini: the flyer


Question: Which one of the following is a complete and accurate list of the pieces of mail, any one of which could be the only piece of mail addressed to Jana?

the postcard
the letter, the postcard
the letter, the survey
the magazine, the survey
the letter, the magazine, the postcard


Question: Which one of the following CANNOT be a complete and accurate list of the pieces of mail addressed to Jana?

the flyer, the letter, the magazine
the flyer, the letter, the postcard
the flyer, the letter, the survey
the flyer, the magazine, the postcard
the flyer, the magazine, the survey


Question: Which one of the following CANNOT be a complete and accurate list of the pieces of mail addressed to Rini?

the magazine, the postcard
the letter, the survey
the letter, the magazine
the flyer, the magazine
the flyer, the letter


Question: If the magazine and the survey are both addressed to the same housemate, then which one of the following could be true?

The survey is addressed to Georgette.
The postcard is addressed to Rini.
The magazine is addressed to Jana.
The letter is addressed to Rini.
The flyer is addressed to Jana.


A summer program offers at least one of the following seven courses: geography, history, literature, mathematics, psychology, sociology, zoology. The following restrictions on the program must apply: If mathematics is offered, then either literature or sociology (but not both) is offered. If literature is offered, then geography is also offered but psychology is not. If sociology is offered, then psychology is also offered but zoology is not. If geography is offered, then both history and zoology are also offered.

Question: Which one of the following could be a complete and accurate list of the courses offered by the summer program?

history, literature, mathematics, sociology


Question: If the summer program offers literature, then which one of the following could be true?

Sociology is offered.
History is not offered.
Mathematics is not offered.
A total of two courses are offered.
Zoology is not offered.


Question: If history is not offered by the summer program, then which one of the following is another course that CANNOT be offered?

literature mathematics psychology sociology zoology


Question: If the summer program offers mathematics, then which one of the following must be true?

Literature is offered.
Psychology is offered.
Sociology is offered.
At least three courses are offered.
At most four courses are offered.


Question: Which one of the following must be false of the summer program?

Both geography and psychology are offered.

Both geography and mathematics are offered.

Both psychology and mathematics are offered.

Both history and mathematics are offered.

Both geography and sociology are offered.


The members of a five-person committee will be selected from among three parents—F, G, and H—three students—K, L, and M—and four teachers—U, W, X, and Z. The selection of committee members will meet the following conditions: The committee must include exactly one student. F and H cannot both be selected. M and Z cannot both be selected. U and W cannot both be selected. F cannot be selected unless Z is also selected. W cannot be selected unless H is also selected.

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

F, G, K, L, Z
F, G, K, U, X
G, K, W, X, Z
H, K, U, W, X
H, L, W, X, Z


Question: If W and Z are selected, which one of the following is a pair of people who could also be selected?


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


Question: If W is selected, then any one of the following could also be selected EXCEPT:


Question: If the committee is to include exactly one parent, which one of the following is a person who must also be selected?


Question: If M is selected, then the committee must also include both


On a field trip to the Museum of Natural History, each of six children—Juana, Kyle, Lucita, Salim, Thanh, and Veronica—is accompanied by one of three adults—Ms. Margoles, Mr. O'Connell, and Ms. Podorski. Each adult accompanies exactly two of the children, consistent with the following conditions: If Ms. Margoles accompanies Juana, then Ms. Podorski accompanies Lucita. If Kyle is not accompanied by Ms. Margoles, then Veronica is accompanied by Mr. O'Connell. Either Ms. Margoles or Mr. O'Connell accompanies Thanh. Juana is not accompanied by the same adult as Kyle; nor is Lucita accompanied by the same adult as Salim; nor is Thanh accompanied by the same adult as Veronica.

Question: Which one of the following could be an accurate matching of the adults to the children they accompany?

Ms. Margoles: Juana, Thanh; Mr. O'Connell: Lucita, Veronica; Ms. Podorski: Kyle, Salim

Ms. Margoles: Kyle, Thanh; Mr. O'Connell: Juana, Salim; Ms. Podorski: Lucita, Veronica

Ms. Margoles: Lucita, Thanh; Mr. O'Connell: Juana, Salim; Ms. Podorski: Kyle, Veronica

Ms. Margoles: Kyle, Veronica; Mr. O'Connell: Juana, Thanh; Ms. Podorski: Lucita, Salim

Ms. Margoles: Salim, Veronica; Mr. O'Connell: Kyle, Lucita; Ms. Podorski: Juana, Thanh


Question: If Ms. Margoles accompanies Lucita and Thanh, then which one of the following must be true?

Juana is accompanied by the same adult as Veronica.

Kyle is accompanied by the same adult as Salim.


Question: If Ms. Podorski accompanies Juana and Veronica, then Ms. Margoles could accompany which one of the following pairs of children?

Kyle and Salim
Kyle and Thanh
Lucita and Salim
Lucita and Thanh
Salim and Thanh


Question: Ms. Podorski CANNOT accompany which one of the following pairs of children?

Juana and Lucita
Juana and Salim
Kyle and Salim
Salim and Thanh
Salim and Veronica


Question: Mr. O'Connell CANNOT accompany which one of the following pairs of children?

Juana and Lucita
Juana and Veronica
Kyle and Thanh
Lucita and Thanh
Salim and Veronica


Five performers—Traugott, West, Xavier, Young, and Zinser—are recruited by three talent agencies—Fame Agency, Premier Agency, and Star Agency. Each performer signs with exactly one of the agencies and each agency signs at least one of the performers. The performers' signing with the agencies is in accord with the following: Xavier signs with Fame Agency. Xavier and Young do not sign with the same agency as each other. Zinser signs with the same agency as Young. If Traugott signs with Star Agency, West also signs with Star Agency.

Question: Which one of the following could be a complete and accurate list of the performers who sign with each agency?

Fame Agency: Xavier Premier Agency: West Star Agency: Traugott, Young, Zinser

Fame Agency: Xavier Premier Agency: Traugott, West Star Agency: Young, Zinser

Fame Agency: Xavier Premier Agency: Traugott, Young Star Agency: West, Zinser

Fame Agency: Young, Zinser Premier Agency: Xavier Star Agency: Traugott, West

Fame Agency: Xavier, Young, Zinser Premier Agency: Traugott Star Agency: West


Question: Which one of the following could be true?

West is the only performer who signs with Star Agency.

West, Young, and Zinser all sign with Premier Agency.

Xavier signs with the same agency as Zinser.

Zinser is the only performer who signs with Star Agency.

Three of the performers sign with Fame Agency.


Question: Which one of the following must be true?

West and Zinser do not sign with the same agency as each other.

Fame Agency signs at most two of the performers.

Fame Agency signs the same number of the performers as Star Agency.

Traugott signs with the same agency as West.


Question: The agency with which each of the performers signs is completely determined if which one of the following is true?

Traugott signs with Fame Agency.
Traugott signs with Star Agency.
West signs with Premier Agency.
Xavier signs with Fame Agency.
Zinser signs with Premier Agency.


Question: If Zinser signs with Star Agency, which one of the following must be false?

Premier Agency signs exactly one performer.

Star Agency signs exactly three of the performers.

None of the other performers signs with the same agency as Xavier.


A dance is being choreographed for six dancers: three men—Felipe, Grant, and Hassan—and three women—Jaclyn, Keiko, and Lorena. At no time during the dance will anyone other than the dancers be on stage. Who is on stage and who is off stage at any particular time in the dance is determined by the following constraints: If Jaclyn is on stage, Lorena is off stage. If Lorena is off stage, Jaclyn is on stage. If Felipe is off stage, Jaclyn is also off stage. If any of the women are on stage, Grant is also on stage.

Question: Which one of the following is a list of all of the dancers who could be on stage at a particular time?

Grant
Keiko, Lorena
Grant, Hassan, Lorena
Grant, Hassan, Jaclyn
Felipe, Grant, Jaclyn, Lorena


Question: Which one of the following CANNOT be true at any time during the dance?

Felipe and Grant are the only men on stage.

Grant and Hassan are the only men on stage.

Jaclyn and Keiko are the only women on stage.


Question: Which one of the following is a complete and accurate list of the dancers any one of whom could be off stage when Jaclyn is on stage?

Lorena
Felipe, Lorena
Hassan, Lorena
Hassan, Keiko
Hassan, Keiko, Lorena


Question: If there are more women than men on stage, then exactly how many dancers must be on stage?


Question: What is the minimum number of dancers that must be on stage at any given time?


A company organizing on-site day care consults with a group of parents composed exclusively of volunteers from among the seven employees—Felicia, Leah, Masatomo, Rochelle, Salman, Terry, and Veena—who have become parents this year. The composition of the volunteer group must be consistent with the following: If Rochelle volunteers, then so does Masatomo. If Masatomo volunteers, then so does Terry. If Salman does not volunteer, then Veena volunteers. If Rochelle does not volunteer, then Leah volunteers. If Terry volunteers, then neither Felicia nor Veena volunteers.

Question: Which one of the following could be a complete and accurate list of the volunteers?

Felicia, Salman
Masatomo, Rochelle
Leah, Salman, Terry
Salman, Rochelle, Veena
Leah, Salman, Terry, Veena


Question: If Veena volunteers, then which one of the following could be true?

Felicia and Rochelle also volunteer.
Felicia and Salman also volunteer.
Leah and Masatomo also volunteer.
Leah and Terry also volunteer.
Salman and Terry also volunteer.


Question: If Terry does not volunteer, then which one of the following CANNOT be true?

Felicia volunteers.
Leah volunteers.
Rochelle volunteers.
Salman volunteers.
Veena volunteers.


Question: If Masatomo volunteers, then which one of the following could be true?

Felicia volunteers.
Leah volunteers.
Veena volunteers.
Salman does not volunteer.
Terry does not volunteer.


Question: If Felicia volunteers, then which one of the following must be true?

Exactly three of the employees volunteer.

Exactly four of the employees volunteer.


Question: Which one of the following pairs of employees is such that at least one member of the pair volunteers?

Felicia and Terry
Leah and Masatomo
Leah and Veena
Rochelle and Salman
Salman and Terry


A student is choosing courses to take during a summer school session. Each summer school student must take at least three courses from among the following seven: history, linguistics, music, physics, statistics, theater, and writing. The summer school schedule restricts the courses a student can take in the following ways: If history is taken, then neither statistics nor music can be taken. If music is taken, then neither physics nor theater can be taken. If writing is taken, then neither physics nor statistics can be taken.

Question: The student could take which one of the following groups of courses during the summer school session?

linguistics, physics, theater, and writing


Question: What is the maximum number of courses the student could take during the summer school session?


Question: If the student takes neither physics nor writing, then it could be true that the student also takes neither

history nor linguistics
history nor music
history nor statistics
linguistics nor music
statistics nor theater


Question: If the student takes music, then which one of the following must the student also take?

writing theater statistics physics linguistics


Question: The student must take one or the other or both of

history or statistics
linguistics or theater
linguistics or writing
music or physics
theater or writing


Question: Which one of the following, if substituted for the restriction that if music is taken, then neither physics nor theater can be taken, would have the same effect in determining which courses the student can take?

If music is taken, then either statistics or writing must also be taken.

The only courses that are eligible to be taken together with music are linguistics, statistics, and writing.

The only courses that are eligible to be taken together with physics are history and linguistics.

The only courses that are eligible to be taken together with theater are history, linguistics, and writing.

If both physics and theater are taken, then music cannot be taken.


Alicia will take exactly four courses this semester. She must choose from the following seven courses—Geography, Japanese, Macroeconomics, Psychology, Russian, Statistics (which is offered twice, once each on Tuesdays at 9 A.M. and 3 P.M.), and World History. No one is allowed to take any course more than once per semester. Because of university requirements and time conflicts, the following restrictions apply to Alicia's choices: She must take Japanese if she does not take Russian. She cannot take Japanese if she takes Macroeconomics. She cannot take World History if she takes Statistics at 9 A.M. She must take Statistics at 9 A.M. if she takes Psychology. She must take either Geography or World History but cannot take both.

Question: Which one of the following could be the list of the four courses Alicia takes?

Geography, Japanese, Psychology, Russian

Geography, Macroeconomics, Psychology, Statistics

Geography, Japanese, Macroeconomics, Russian

Geography, Psychology, Russian, Statistics


Question: Which one of the following could be an accurate list of three of the courses Alicia takes?

Geography, Statistics, World History
Japanese, Macroeconomics, Statistics
Japanese, Psychology, World History
Psychology, Russian, World History
Russian, Statistics, World History


Question: Which courses Alicia takes is fully determined if she takes Russian and which one of the following?

World History
Statistics
Psychology
Macroeconomics
Japanese


Question: Alicia could take Statistics at either of the available times if she takes which one of the following pairs of courses?

Geography and Japanese
Geography and Psychology
Japanese and World History
Psychology and Russian
Russian and World History


Question: If Alicia takes Statistics at 3 P.M. and Geography, then which one of the following courses must she also take?

Japanese
Macroeconomics
Psychology
Russian
World History


Question: Suppose that Alicia must take Statistics if she takes Psychology, but rather than being restricted to taking Statistics at 9 A.M. she can take it at either 9 A.M. or at 3 P.M. If all the other restrictions remain the same, then which one of the following could be the list of the four courses Alicia takes?

Psychology, Russian, Statistics, World History

Macroeconomics, Psychology, Statistics, World History

Macroeconomics, Psychology, Russian, World History

Geography, Psychology, Russian, World History

Geography, Macroeconomics, Russian, World History