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.


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?


A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively. An experiment consists of mixing exactly two of these chemicals together by completely emptying the contents of one of the flasks into another of the flasks. The following conditions apply: The product of an experiment cannot be used in further experiments. Mixing the contents of 1 and 2 produces a red chemical. Mixing the contents of 2 and 3 produces an orange chemical. Mixing the contents of 3 with the contents of either 1 or 4 produces a blue chemical. Mixing the contents of 4 with the contents of either 1 or 2 produces a green chemical.

Question: If the student performs exactly one experiment, which one of the following could be the colors of the chemicals in the resulting three nonempty flasks?

blue, blue, green
blue, orange, orange
blue, orange, red
green, green, red
green, orange, orange


Question: If the student performs exactly two experiments, which one of the following could be the colors of the chemicals in the resulting two nonempty flasks?

blue, blue
blue, orange
blue, red
green, red
orange, orange


Question: If the student performs exactly one experiment and none of the resulting three nonempty flasks contains a red chemical, which one of the following could be the colors of the chemicals in the three flasks?

blue, blue, green
blue, green, green
blue, green, orange
blue, orange, orange
green, green, orange


Question: If the student performs exactly one experiment and exactly one of the resulting three nonempty flasks contains a blue chemical, which one of the following must be the colors of the chemicals in the other two flasks?

both green
both orange
both red
one green and one red
one orange and one red


Question: If the student will perform exactly two experiments and after the first experiment exactly one of the resulting three nonempty flasks contains an orange chemical, then in the second experiment the student could mix together the contents of flasks


Question: If the student performs exactly one experiment and none of the resulting three nonempty flasks contains an orange chemical, then the student must have mixed the contents of

flask 1 with flask 2
flask 1 with flask 4
flask 2 with flask 4
flask 2 with one of the other flasks
flask 4 with one of the other flasks


Question: If the student performs exactly two experiments and exactly one of the resulting two nonempty flasks contains an orange chemical, then it must be true that the contents of the other nonempty flask is

obtained by mixing flasks 1 and 2
obtained by mixing flasks 2 and 4
blue
green
red


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


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

Question: Victor can be scheduled for any day EXCEPT

Monday Tuesday Wednesday Thursday Friday


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

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


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

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

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

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


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

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


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

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

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

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

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

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


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.


The population of a small country is organized into five clans—N, O, P, S, and T. Each year exactly three of the five clans participate in the annual harvest ceremonies. The rules specifying the order of participation of the clans in the ceremonies are as follows: Each clan must participate at least once in any two consecutive years. No clan participates for three consecutive years. Participation takes place in cycles, with each cycle ending when each of the five clans has participated three times. Only then does a new cycle begin. No clan participates more than three times within any cycle.

Question: If the clans participating in the first year of a given cycle are N, O, and P, which one of the following could be the clans participating in the second year of that cycle?


Question: Which one of the following can be true about the clans' participation in the ceremonies?

N participates in the first, second, and third years.

N participates in the second, third, and fourth years.

Both O and S participate in the first and third years.

Both N and S participate in the first, third, and fifth years.

Both S and T participate in the second, third, and fifth years.


Question: Any cycle for the clans' participation in the ceremonies must be completed at the end of exactly how many years?


Question: Which one of the following must be true about the three clans that participate in the ceremonies in the first year?

At most two of them participate together in the third year.

At least two of them participate together in the second year.

All three of them participate together in the fourth year.

All three of them participate together in the fifth year.

None of them participates in the third year.


Question: If, in a particular cycle, N, O, and S participate in the ceremonies in the first year, which one of the following must be true?

N participates in the second and third years.

O participates in the third and fourth years.

N and O both participate in the third year.

P and T both participate in the fifth year.

S and T both participate in the fifth year.


Question: If, in a particular cycle, N, O, and T participate in the first year and if O and P participate in the fourth year, any of the following could be a clan that participates in the third year EXCEPT


Question: If, in a particular cycle, N, O, and S participate in the ceremonies in the first year and O, S, and T participate in the third year, then which one of the following could be the clans that participate in the fifth year?


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.


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

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

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


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

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


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

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


Question: It is NOT possible that Ron washed the knife


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

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


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

He washed the juice glass before the knife.

He washed the plate before the water glass.


A 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


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.


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

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

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


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

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


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

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


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

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

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

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


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

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

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

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

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

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


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


The country of Zendu contains exactly four areas for radar detection: R, S, T, and U. Each detection area is circular and falls completely within Zendu. Part of R intersects T; part of S also intersects T; R does not intersect S. Area U is completely within R and also completely within T. At noon exactly four planes J, K, L, M—are over Zendu, in a manner consistent with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas.

Question: Which one of the following could be a complete listing of the planes located in the four areas at noon, with each plane listed in every area in which it is located?

R: J, L; S: J, M; T: L; U: L
R: J, L; S: K; T: M; U: none
R: K; S: J; T: L; U: M
R: K, M; S: J, L; T: J; U: none
R: M; S: J, K; T: J, L; U: none


Question: If at noon K is within exactly two of the four areas, then which one of the following CANNOT be true at that time?

J is within area T.
K is within area R.
K is within area T.
L is within area R.
L is within area T.


Question: Which one of the following is a complete and accurate list of those planes any one of which could be within area T at noon?


Question: Which one of the following statements CANNOT be true at noon about the planes?

K is within area T.
K is within area U.
L is within area R.
M is within area R.
M is within area U.


Question: It CANNOT be true that at noon there is at least one plane that is within both area

R and area T
R and area U
S and area T
S and area U
T and area U


Question: If at noon M is within area T, then which one of the following statements CANNOT be true at that time?

J is within area T.
L is within area R.
L is within area S.
K is within exactly two areas.
L is within exactly two areas.


Question: If at noon plane L is within exactly three of the areas, which one of the following could be true at that time?

J is within exactly two of the areas.
J is within exactly three of the areas.
K is within area S.
M is within area R.
M is within area T.


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

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

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


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

Fritz drives on both Wednesday and Saturday.

Gina drives on both Monday and Wednesday.

Jerry drives on both Tuesday and Friday.

Gina drives on Monday and Jerry drives on Thursday.

Jerry drives on Wednesday and Gina drives on Saturday.


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

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


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

One other person besides Gina drives on exactly two days.

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

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

Either Helen or Jerry drives on Tuesday.


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

Fritz drives on Tuesday and Gina drives on Friday.

Gina drives on Monday and Jerry drives on Tuesday.

Gina drives on Monday and Jerry drives on Friday.

Helen drives on Monday and Jerry drives on Tuesday.

Helen drives on Tuesday and Jerry drives on Friday.


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

One person drives exactly three times during the week.

Three people drive exactly one time each during the week.

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


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


Question: If all of the inexperienced plumbers are assigned to teams, and neither Roberta nor Tim nor Vernon is assigned to a team with Gene, then Sally must be assigned to a team with either

Frank or else Gene
Frank or else Mark
Gene or else Mark
Jill or else Kathy
Jill or else Mark


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?


Question: Which one of the following must be true?

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

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

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

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

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


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


Within a tennis league each of five teams occupies one of five positions, numbered 1 through 5 in order of rank, with number 1 as the highest position. The teams are initially in the order R, J, S, M, L, with R in position 1. Teams change positions only when a lower-positioned team defeats a higher-positioned team. The rules are as follows: Matches are played alternately in odd-position rounds and in even-position rounds. In an odd-position round, teams in positions 3 and 5 play against teams positioned immediately above them. In an even-position round, teams in positions 2 and 4 play against teams positioned immediately above them. When a lower-positioned team defeats a higher-positioned team, the two teams switch positions after the round is completed.

Question: Which one of the following could be the order of teams, from position 1 through position 5 respectively, after exactly one round of even-position matches if no odd-position round has yet been played?

J, R, M, L, S
J, R, S, L, M
R, J, M, L, S
R, J, M, S, L
R, S, J, L, M


Question: If exactly two rounds of matches have been played, beginning with an odd-position round, and if the lower-positioned teams have won every match in those two rounds, then each of the following must be true EXCEPT:

L is one position higher than J.
R is one position higher than L.
S is one position higher than R.
J is in position 4.
M is in position 3.


Question: Which one of the following could be true after exactly two rounds of matches have been played?

J has won two matches.
L has lost two matches.
R has won two matches.
L's only match was played against J.
M played against S in two matches.


Question: If after exactly three rounds of matches M is in position 4, and J and L have won all of their matches, then which one of the following can be true?

J is in position 2.
J is in position 3.
L is in position 2.
R is in position 1.
S is in position 3.


Question: If after exactly three rounds M has won three matches and the rankings of the other four teams relative to each other remain the same, then which one of the following must be in position 3?


Question: If after exactly three rounds the teams, in order from first to fifth position, are R, J, L, S, and M, then which one of the following could be the order, from first to fifth position, of the teams after the second round?

J, R, M, S, L
J, L, S, M, R
R, J, S, L, M
R, L, M, S, J
R, M, L, S, J


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

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

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


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

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


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

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

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

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

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

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


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

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

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

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

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

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


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

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

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

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

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

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


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.


A contractor is scheduling construction of seven decks—F, G, H, J, K, L, and M—during a seven-week period: week 1 through week 7. Because of customers' requirements, exactly one deck must be built each week according to the following conditions: G must be built at some time before K is built. L must be built either immediately before or immediately after M is built. F must be built during week 5. J must be built during week 2 or week 6.

Question: Which one of the following is an acceptable construction schedule for the decks, in order from the deck built in week 1 to that built in week 7?

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


Question: If G is built at some time after F is built, which one of the following must be true?

G is built during week 7.
H is built during week 1.
J is built during week 6.
L is built during week 3.
M is built during week 1.


Question: Which one of the following is a complete and accurate list of the weeks any one of which could be the week in which K is built?


Question: Which one of the following is a complete and accurate list of decks any one of which could be the deck built in week 3?

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


Question: If G is built during week 4, then there are exactly how many acceptable orders any one of which could be the order in which the seven decks are built?


Each of five salespeople—F, G, H, I, and J—will present a different one of a company's products—L, M, N, O, and P—at a convention running from Monday through Wednesday. Exactly two products will be presented on Monday, exactly one on Tuesday, and exactly two on Wednesday. The scheduling of presentations is governed by the following conditions: F cannot present a product on the same day as H. Either I or else J must present product N on Tuesday. G must present a product on the day that product O is presented, whether or not G is the salesperson who presents product O.

Question: Which one of the following must be true?

If F presents a product on Monday, then G presents product O.

If I presents a product on Tuesday, then J presents a product on Monday.

If J presents a product on Tuesday, then G presents a product on Monday.

If both F and J present products on Monday, then H presents product O.

If both H and I present products on Wednesday, then product O is presented on Monday.


Question: If salespeople H and I present products on Monday, which one of the following must be true?

F presents product M.
G presents product L.
I presents product N.
Product O is presented on Wednesday.
Product P is presented on Wednesday.


Question: If G presents product P on Wednesday, then any of the following could be true EXCEPT:

H presents product O.
I presents product N.
I presents product O.
F makes a presentation on Monday.
F makes a presentation on Wednesday.


Question: If products M and P are presented on Monday, which one of the following could be true?

G presents product P.
I presents product O.
J presents product L.
F presents a product on Monday.
G presents a product on Monday.


Question: If product O is presented on the same day as product P, which one of the following must be true?

F presents neither product O nor product P.

J presents neither product O nor product P.


The seven members of an academic department are each to be assigned a different room as an office. The department members are professors F and G, lecturers Q, R, and S, and instructors V and W. The available rooms are seven consecutive rooms along one side of a straight hallway numbered sequentially 101 through 107. The assignment must conform to the following conditions: Neither instructor is assigned a room next to a professor's room. Neither professor is assigned room 101 and neither professor is assigned room 107. G is not assigned a room next to R's room. W is not assigned a room next to V's room unless R is also assigned a room next to V's room.

Question: If F and G are assigned rooms that have exactly one room between them, which one of the following is the list of department members each of whom could be assigned to the intervening room?


Question: Which one of the following is a possible assignment of rooms for members R, V, and W?


Question: If R is assigned room 104, which one of the following must be assigned either room 103 or else room 105?


Question: What is the greatest number of rooms that could be between the rooms to which F and G are assigned?


Question: Which one of the following CANNOT be assigned room 104?


Question: If no two faculty members of the same rank are assigned adjacent rooms, which one of the following must be true?

F is assigned either room 103 or else room 104.

Q is assigned either room 102 or else room 106.

R is assigned either room 102 or else room 105.

S is assigned either room 104 or else room 105.

V is assigned either room 101 or else room 107.


Question: If F and G are not assigned rooms that are next to each other, which one of the following CANNOT be assigned room 107?


The coordinator of an exhibition will select at least four and at most six rugs from a group of eight rugs made up of two oval wool rugs, three rectangular wool rugs, one oval silk rug, and two rectangular silk rugs according to the following conditions: At least two oval rugs must be selected. The number of wool rugs selected can be neither less than two nor more than three. If the oval silk rug is selected, at least one rectangular silk rug must be selected.

Question: Which one of the following is an acceptable selection of rugs for the exhibition?

one oval silk rug, one oval wool rug, and two rectangular wool rugs

one oval silk rug, one rectangular wool rug, and two rectangular silk rugs

two oval wool rugs, one rectangular silk rug, and two rectangular wool rugs

two oval wool rugs, one rectangular silk rug, and one rectangular wool rug

two rectangular silk rugs and three rectangular wool rugs


Question: If three wool rugs are selected, then any of the following could be a complete and accurate list of the other rugs selected EXCEPT:

one oval silk rug and one rectangular silk rug

one oval silk rug and two rectangular silk rugs


Question: The rugs selected for the exhibition can include any of the following EXCEPT:

one oval silk rug
two oval wool rugs
three oval rugs
two rectangular wool rugs
three rectangular wool rugs


Question: If only one silk rug is selected for the exhibition, then the other rugs selected must be a group made up of

two oval rugs and three rectangular rugs


Question: If exactly four rugs are selected, then the rugs selected could be

one oval rug and three rectangular wool rugs

two oval rugs and two rectangular wool rugs

three oval rugs and one rectangular silk rug

three oval rugs and one rectangular wool rug

two rectangular silk rugs and two rectangular wool rugs


Question: If all three silk rugs are selected, then each of the following could be a complete and accurate list of the other rugs selected EXCEPT:

one oval wool rug and one rectangular wool rug

one oval wool rug and two rectangular wool rugs

two oval wool rugs and one rectangular wool rug


Question: If exactly six rugs are selected, they must include

exactly one of the oval rugs
the two oval wool rugs
the two rectangular silk rugs
exactly three of the rectangular rugs
all three rectangular wool rugs


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

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

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


Question: Which one of the following must be false?

The inspection of G is scheduled for day 4.

The inspection of H is scheduled for day 6.

The inspection of J is scheduled for day 4.

The inspection of Q is scheduled for day 3.

The inspection of R is scheduled for day 2.


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


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


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

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

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

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

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

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


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


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

The inspection of G is scheduled for day 5.

The inspection of H is scheduled for day 6.

The inspection of J is scheduled for day 2.

The inspection of Q is scheduled for day 4.

The inspection of R is scheduled for day 3.


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 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


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.


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?


A jeweler makes a single strand of beads by threading onto a string in a single direction from a clasp a series of solid-colored beads. Each bead is either green, orange, purple, red, or yellow. The resulting strand satisfies the following specifications: If a purple bead is adjacent to a yellow bead, any bead that immediately follows and any bead that immediately precedes that pair must be red. Any pair of beads adjacent to each other that are the same color as each other must be green. No orange bead can be adjacent to any red bead. Any portion of the strand containing eight consecutive beads must include at least one bead of each color.

Question: If the strand has exactly eight beads, which one of the following is an acceptable order, starting from the clasp, for the eight beads?

green, red, purple, yellow, red, orange, green, purple

orange, yellow, red, red, yellow, purple, red, green

purple, yellow, red, green, green, orange, yellow, orange

red, orange, red, yellow, purple, green, yellow, green

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


Question: If an orange bead is the fourth bead from the clasp, which one of the following is a pair that could be the second and third beads, respectively?

green, orange
green, red
purple, purple
yellow, green
yellow, purple


Question: If on an eight-bead strand the second, third, and fourth beads from the clasp are red, green, and yellow, respectively, and the sixth and seventh beads are purple and red, respectively, then which one of the following must be true?

The first bead is purple.
The fifth bead is green.
The fifth bead is orange.
The eighth bead is orange.
The eighth bead is yellow.


Question: If on a six-bead strand the first and second beads from the clasp are purple and yellow, respectively, then the fifth and sixth beads CANNOT be

green and orange, respectively
orange and green, respectively
orange and yellow, respectively
purple and orange, respectively
yellow and purple, respectively


Question: If on a nine-bead strand the first and fourth beads from the clasp are purple, and the second and fifth beads are yellow, which one of the following could be true?

The seventh bead is orange.
The eighth bead is green.
The eighth bead is red.
The ninth bead is red.
The ninth bead is yellow.


Question: If on an eight-bead strand the first, second, third, and fourth beads from the clasp are red, yellow, green, and red, respectively, then the fifth and sixth beads CANNOT be

green and orange, respectively
green and purple, respectively
purple and orange, respectively
purple and yellow, respectively
yellow and orange, respectively


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

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

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


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

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


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


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

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


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

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


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

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


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.


A worker will insert colored light bulbs into a billboard equipped with exactly three light sockets, which are labeled lights 1, 2, and 3. The worker has three green bulbs, three purple bulbs, and three yellow bulbs. Selection of bulbs for the sockets is governed by the following conditions: Whenever light 1 is purple, light 2 must be yellow. Whenever light 2 is green, light 1 must be green. Whenever light 3 is either purple or yellow, light 2 must be purple.

Question: Which one of the following could be an accurate list of the colors of light bulbs selected for lights 1, 2, and 3, respectively?

green, green, yellow
purple, green, green
purple, purple, green
yellow, purple, green
yellow, yellow, yellow


Question: If light 1 is yellow, then any of the following can be true, EXCEPT:

Light 2 is green.
Light 2 is purple.
Light 3 is green.
Light 3 is purple.
Light 3 is yellow.


Question: There is exactly one possible color sequence of the three lights if which one of the following is true?

Light 1 is purple.
Light 2 is purple.
Light 2 is yellow.
Light 3 is purple.
Light 3 is yellow.


Question: If no green bulbs are selected, there are exactly how many possible different color sequences of the three lights?


Question: If no two lights are assigned light bulbs that are the same color as each other, then which one of the following could be true?

Light 1 is green, and light 2 is purple.

Light 1 is green, and light 2 is yellow.

Light 1 is purple, and light 3 is yellow.

Light 1 is yellow, and light 2 is green.

Light 1 is yellow, and light 3 is purple.


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.


During a four-week period, each of seven previously unadvertised products—G, H, J, K, L, M, and O—will be advertised. A different pair of these products will be advertised each week. Exactly one of the products will be a member of two of these four pairs. The following constraints must be observed: J is not advertised during a given week unless H is advertised during the immediately preceding week. The product that is advertised during two of the weeks is advertised during week 4 but is not advertised during week 3. G is not advertised during a given week unless either J or else O is also advertised that week. K is advertised during one of the first two weeks. O is one of the products advertised during week 3.

Question: Which one of the following could be the schedule of advertisements?

week 1: G, J; week 2: K, L; week 3: O, M; week 4: H, L

week l: H, K; week 2: J, G; week 3: O, L; week 4: M, K

week 1: H, K; week 2: J, M; week 3: O, L; week 4: G, M

week 1: H, L; week 2: J, M; week 3: O, G; week 4: K, L

week 1: K, M; week 2: H, J; week 3: O, G; week 4: L, M


Question: Which one of the following is a pair of products that CANNOT be advertised during the same week as each other?


Question: Which one of the following must be advertised during week 2?


Question: Which one of the following CANNOT be the product that is advertised during two of the weeks?


Question: If L is the product that is advertised during two of the weeks, which one of the following is a product that must be advertised during one of the weeks in which L is advertised?


Question: Which one of the following is a product that could be advertised in any of the four weeks?


Question: Which one of the following is a pair of products that could be advertised during the same week as each other?


An upholsterer will do seven jobs—N, O, P, S, T, U, and X—during a given week on Monday through Friday. Each job is done on exactly one of the days, and no two jobs are done concurrently. Each job takes either one half day or an entire day. The following conditions apply: N is done on the same day as S. X is done on Wednesday, and T is done on Friday. S is done earlier than the day on which P is done. U and X are the only jobs that must take an entire day each.

Question: Which one of the following is an acceptable schedule for the seven jobs? Mon. Tues. Wed. Thurs. Fri.

N, S P X O, U T
O N, S X P U
P U X N, S O, T
S N, P X U O, T
U N, S X O P, T


Question: Which one of the following is a complete and accurate list of those jobs each of which CANNOT be done on Tuesday?


Question: If O is done on Thursday, N could be done on

Monday or else on Tuesday, but on no other day

Tuesday or else on Wednesday, but on no other day

Wednesday or else on Thursday, but on no other day


Question: Which one of the following must be true if the upholsterer does two jobs on Thursday and two jobs on Friday?

N is done on Monday.
O is done on Tuesday.
P is done on Friday.
O is done on the same day as P.
O is done on the same day as T.


Question: If P is not done on Friday, which one of the following must be true?

N is done on Monday or else on Thursday.

O is done on Wednesday or else on Thursday.

S is done on Monday or else on Thursday.

O is done on the same day as either P or T.


Question: If O is done on Monday, which one of the following must be true?

N is done on Tuesday.
P is done on Thursday.
P is done on Friday.
S is done on Thursday.
U is done on Friday.


Seven persons—G, H, I, K, L, M, and P—are going rock-climbing together. One person will be the organizer and not a member of any team. The remaining six will form three climbing teams, each consisting of two persons. No person can be on more than one team. The following conditions also apply: M and P cannot be on the same team as each other. If K is on a team, M must also be on that team. If G is on a team, either H or I must also be on that team. If H is on a team, K must be the organizer.

Question: Which one of the following can be a list of the members of the three teams?

Team 1: G, H; Team 2: I, L; Team 3: M, P

Team 1: G, H; Team 2: L, P; Team 3: K, M

Team 1: G, I; Team 2: H, M; Team 3: L, P

Team 1: G, P; Team 2: I, L; Team 3: K, M

Team 1: H, M; Team 2: I, L; Team 3: K, P


Question: Each of the following is a pair of persons who can constitute a team EXCEPT:


Question: Which one of the following can be the organizer, who is not on any team?


Question: If G and I form a team and if H is a member of a team, then H must be on the same team as either


Question: If L and M are on different teams, which one of the following must be true?

H is the organizer.
K is the organizer.
G is on the same team as H.
I is on the same team as M.
L is on the same team as P.


Question: Which one of the following lists three persons each of whom must be on a team and no two of whom can be on the same team as each other?


Question: There are how many different persons any one of whom could be paired with M to form a team?


A train makes five trips around a loop through five stations—P, Q, R, S, and T, in that order—stopping at exactly three of the stations on each trip. The train must conform to the following conditions: The train stops at any given station on exactly three trips, but not on three consecutive trips. The train stops at any given station at least once in any two consecutive trips.

Question: Which one of the following could be the list of stations at which the train stops on the first two trips?

first trip: P, Q, S; second trip: P, Q, R

first trip: P, Q, T; second trip: Q, R, T

first trip: Q, R, S; second trip: P, Q, S

first trip: Q, S, T; second trip: P, R, S

first trip: R, S, T; second trip: P, R, T


Question: If on the first and third trips the train is to stop at Q, R, and S, and at R, S, and T, respectively, which one of the following is the list of stations at which it must stop on the second trip?


Question: The train CANNOT stop at both P and Q on both the

first and third trips
first and fourth trips
second and fourth trips
second and fifth trips
fourth and fifth trips


Question: If the train is to stop at Q, R, and T on the first trip and at Q, R, and S on the fourth trip, then it could be true that the train

stops at Q on the second trip
stops at R on the fifth trip
stops at T on the second trip
does not stop at P on the third trip
does not stop at T on the fifth trip


Question: Suppose that the train's scheduler mistakenly scheduled the train to make the following stops on the first three trips: Q, R, and S on the first trip; P, Q, and S on the second trip; and R, S, and T on the third trip. Which one of the following is a substitution that results in a schedule for those three trips under which the train violates no condition?

on the first trip, P for Q
on the second trip, R for S
on the second trip, T for S
on the third trip, P for R
on the third trip, P for S


On a certain morning, each of six speakers—Feinberg, Guzman, Harrison, Jansen, Kim, and Mackey—will lecture for exactly one hour. Each lecture will take place in either the library or the studio, with exactly one speaker at a time lecturing in each of these two rooms. The lectures must be given in a manner consistent with the following conditions: Exactly three of the lectures are given in each room, the first beginning at precisely 8 A.M. , the second at precisely 9 A.M., and the third at precisely 10 A.M. Feinberg's lecture cannot begin earlier than Guzman's. Neither Jansen's lecture nor Mackey's lecture begins at the same time as Feinberg's. Harrison's lecture begins earlier than Feinberg's. Jansen and Mackey, not necessarily in that order, lecture in the studio.

Question: Which one of the following must be true?

Either Jansen or else Mackey lectures in the studio beginning at 8 A.M.

Either Harrison or else Mackey lectures in the studio beginning at 9 A.M.

Either Guzman or else Harrison lectures in the library beginning at 8 A.M.

Either Feinberg or else Guzman lectures in the library beginning at 9 A.M.

Either Feinberg or else Guzman lectures in the library beginning at 10 A.M.


Question: If both Kim's lecture and Mackey's lecture begin at 9 A.M. , which one of the following could be true?

Guzman's lecture begins at 8 A.M.
Harrison's lecture begins at 10 A.M.
Jansen's lecture begins at 10 A.M.
Guzman lectures in the library.
Harrison lectures in the studio.


Question: If Harrison's lecture begins at 9 A.M. , which one of the following must be true?

Feinberg lectures in the library.
Guzman lectures in the studio.
Harrison lectures in the library.
Kim lectures in the studio.
Mackey lectures in the library.


Question: Each of the following is a pair of speakers whose lectures could begin at the same time as each other EXCEPT:

Feinberg and Guzman
Feinberg and Kim
Guzman and Jansen
Guzman and Kim
Guzman and Mackey


Question: If Feinberg lectures in the library beginning at 9 A.M., which one of the following could be true?

Guzman lectures in the studio beginning at 10 A.M.

Harrison lectures in the studio beginning at 8 A.M.

Jansen lectures in the studio beginning at 10 A.M.

Kim lectures in the studio beginning at 9 A.M.

Mackey lectures in the studio beginning at 9 A.M.


Question: Which one of the following could be a list of the speakers who give their lectures in the studio, in the order in which they give their lectures, from first to third, respectively?

Feinberg, Jansen, Mackey
Guzman, Kim, Mackey
Harrison, Jansen, Kim
Jansen, Mackey, Harrison
Mackey, Feinberg, Jansen


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.


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

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

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


Question: Which one of the following must be false?

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


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

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


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


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

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


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

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


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


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?


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

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

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


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

H comes either immediately before or immediately after F.

L comes either immediately before or immediately after G.


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

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


Question: The earliest track that M can fill is the


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

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


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?


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

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

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

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

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

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

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