Question: Lena can review any of the following EXCEPT

Answer: Mystery with George

Answer: Mystery with Karl

Answer: Retreat with Karl

Answer: Seasonings with Karl

Answer: Wolves with Jackie


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

Question: If Karl reviews the same movie as exactly one other reviewer, which one of the following is a complete and accurate list of the movies any one of which could be the movie that these two reviewers review?

Answer: Mystery, Retreat

Answer: Mystery, Seasonings

Answer: Retreat, Seasonings

Answer: Mystery, Seasonings, Wolves

Answer: Retreat, Seasonings, Wolves


Question: Which one of the following is an acceptable assignment of reviewers to movies? Mystery Retreat Seasonings Wolves

Answer: George Frank, Hilda Jackie, Lena Karl

Answer: George Frank, Hilda Karl, Lena Jackie

Answer: George Karl, Lena Jackie Frank, Hilda

Answer: George, Karl Frank, Hilda Lena Jackie

Answer: Jackie George, Lena Frank, Hilda Karl


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

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

Answer: bzeak bleak leak peak pea

Answer: crbek creek reek seek sxeek

Answer: dteam gleam glean lean mean

Answer: feed freed reed seed seeg

Answer: food fool fools fopls opls


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

Answer: t

Answer: w

Answer: x

Answer: y

Answer: z


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

Answer: bender

Answer: gender

Answer: lender

Answer: sender

Answer: tender


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

Answer: four

Answer: five

Answer: six

Answer: seven

Answer: eight


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

Answer: second

Answer: third

Answer: fourth, fifth

Answer: second, third, fourth

Answer: third, fourth, fifth


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

Answer: four

Answer: five

Answer: six

Answer: seven

Answer: eight


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

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

Answer: H Z M N Y K

Answer: K J Y O Z N

Answer: K Y P J Z M

Answer: P Y J H X O

Answer: X N K O J Z


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

Answer: J

Answer: K

Answer: O

Answer: Y

Answer: Z


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

Answer: H

Answer: K

Answer: N

Answer: P

Answer: X


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

Answer: J

Answer: K

Answer: M

Answer: N

Answer: X


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

Answer: J

Answer: K

Answer: O

Answer: Y

Answer: Z


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

Answer: M

Answer: O

Answer: P

Answer: X

Answer: Z


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

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

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

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

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

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

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


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

Answer: George and Nathan

Answer: George and Olga

Answer: Joan and Kathy

Answer: Joan and Nathan

Answer: Joan and Olga


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

Answer: Fran and Kathy

Answer: George and Nathan

Answer: Henry and Lewis

Answer: Joan and Nathan

Answer: Joan and Olga


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

Answer: Fran supervises swimming.

Answer: Henry supervises tennis.

Answer: Joan supervises volleyball.

Answer: Lewis supervises volleyball.

Answer: Nathan supervises tennis.


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

Answer: George supervises volleyball.

Answer: Henry supervises volleyball.

Answer: Joan supervises tennis.

Answer: Kathy supervises swimming.

Answer: Nathan supervises tennis.


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

Answer: Fran supervises swimming.

Answer: George supervises swimming.

Answer: Kathy supervises volleyball.

Answer: Lewis supervises volleyball.

Answer: Nathan supervises tennis.


Context: A fire chief is determining the work schedules of five firefighters: Fuentes, Graber, Howell, Iman, and Jackson. The schedule must meet the following conditions: Except for Saturday and Sunday, when none of them works, exactly one of the firefighters works each day. None of the firefighters can work more than two days per week. No firefighter works on two consecutive days. Fuentes never works later in the week than Jackson. If Howell works, then Graber must work on the following day.

Question: Which one of the following CANNOT be a Monday-to-Friday work schedule?

Answer: Fuentes, Iman, Fuentes, Jackson, Iman

Answer: Fuentes, Jackson, Howell, Graber, Fuentes

Answer: Graber, Fuentes, Graber, Fuentes, Jackson

Answer: Graber, Howell, Graber, Fuentes, Jackson

Answer: Howell, Graber, Iman, Graber, Iman


Question: If each firefighter is required to have at least two consecutive days off during the Monday-to-Friday workweek, which one of the following could be a possible work schedule?

Answer: Howell, Graber, Howell, Graber, Iman

Answer: Howell, Howell, Graber, Fuentes, Iman

Answer: Iman, Fuentes, Jackson, Iman, Iman

Answer: Fuentes, Howell, Graber, Fuentes, Jackson

Answer: Jackson, Howell, Graber, Iman, Fuentes


Question: If both Fuentes and Jackson work during a week, which one of the following statements CANNOT be true?

Answer: Fuentes works on Monday and Wednesday.

Answer: Jackson works on Monday and Wednesday.

Answer: Fuentes works on Tuesday and Thursday.

Answer: Jackson works on Tuesday and Thursday.

Answer: Jackson works on Wednesday and Friday.


Question: If Fuentes works two days during the week and Jackson works on Thursday, which one of the following statements could be true?

Answer: Fuentes works on Tuesday.

Answer: Graber works on Tuesday.

Answer: Howell works on Tuesday.

Answer: Graber works on Wednesday.

Answer: Howell works on Wednesday.


Question: If Graber does not work during the week, which one of the following statements must be true?

Answer: Fuentes works exactly one day during the week.

Answer: Fuentes works exactly two days during the week.

Answer: Iman works exactly one day during the week.

Answer: Iman works exactly two days during the week.

Answer: Jackson works exactly one day during the week.


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

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

Answer: F, G, Q, R, S

Answer: F, J, K, P, Q

Answer: F, P, Q, R, S

Answer: J, K, M, Q, S

Answer: J, M, P, Q, S


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

Answer: F, G, J

Answer: F, G, M

Answer: F, J, M

Answer: G, J, K

Answer: G, J, M


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

Answer: F

Answer: G

Answer: K

Answer: P

Answer: R


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

Answer: G

Answer: K

Answer: P

Answer: R

Answer: S


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

Answer: G

Answer: K

Answer: P

Answer: Q

Answer: S


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

Answer: G is selected.

Answer: P is selected.

Answer: J is the chairperson.

Answer: Q is the chairperson.

Answer: S is the chairperson.


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

Answer: If G is selected, Q is also selected.

Answer: If G is selected, R is also selected.

Answer: If J is selected, F is also selected.

Answer: If J is selected, Q is also selected.

Answer: If J is selected, R is also selected.


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

Answer: F, P

Answer: G, J

Answer: K, Q

Answer: M, P

Answer: R, S


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

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

Answer: Louis is assigned to project S.

Answer: Madelyn is assigned to project R.

Answer: Madelyn is assigned to project S.

Answer: Oliver is assigned to project R.

Answer: Oliver is assigned to project S.


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

Answer: Louis is assigned to project T.

Answer: Nora is assigned to project R.

Answer: Oliver is assigned to project Q.

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

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


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

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

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

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

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

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


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

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

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

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

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

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


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

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

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

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

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

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


Context: A piano instructor will schedule exactly one lesson for each of six students—Grace, Henry, Janet, Steve, Tom, and Una—one lesson per day for six consecutive days. The schedule must conform to the following conditions: Henry's lesson is later in the schedule than Janet's lesson. Una's lesson is later in the schedule than Steve's lesson. Steve's lesson is exactly three days after Grace's lesson. Janet's lesson is on the first day or else the third day.

Question: If Janet's lesson is scheduled for the first day, then the lesson for which one of the following students must be scheduled for the sixth day?

Answer: Grace

Answer: Henry

Answer: Steve

Answer: Tom

Answer: Una


Question: For which one of the following students is there an acceptable schedule in which the student's lesson is on the third day and another acceptable schedule in which the student's lesson is on the fifth day?

Answer: Grace

Answer: Henry

Answer: Steve

Answer: Tom

Answer: Una


Question: Which one of the following is a complete and accurate list of the students any one of whom could be the student whose lesson is scheduled for the second day?

Answer: Grace

Answer: Tom

Answer: Grace, Tom

Answer: Henry, Tom

Answer: Grace, Henry, Tom


Question: If Henry's lesson is scheduled for a day either immediately before or immediately after Tom's lesson, then Grace's lesson must be scheduled for the

Answer: first day

Answer: second day

Answer: third day

Answer: fourth day

Answer: fifth day


Question: If Janet's lesson is scheduled for the third day, which one of the following could be true?

Answer: Grace's lesson is scheduled for a later day than Henry's lesson.

Answer: Grace's lesson is scheduled for a later day than Una's lesson.

Answer: Henry's lesson is scheduled for a later day than Una's lesson.

Answer: Tom's lesson is scheduled for a later day than Henry's lesson.

Answer: Tom's lesson is scheduled for a later day than Una's lesson.


Question: Which one of the following is a complete and accurate list of days any one of which could be the day for which Tom's lesson is scheduled?

Answer: first, second, third

Answer: second, third, fourth

Answer: second, fifth, sixth

Answer: first, second, third, fourth

Answer: second, third, fourth, sixth


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

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

Answer: G and K are in group 3.

Answer: G and R are in group 3.

Answer: J and S are in group 2.

Answer: K and R are in group 1.

Answer: Q and S are in group 2.


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

Answer: G is in group 2.

Answer: H is in group 3.

Answer: K is in group 1.

Answer: Q is in group 2.

Answer: R is in group 1.


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

Answer: H is in group 3.

Answer: J is in group 1.

Answer: R is in group 2.

Answer: S is in group 3.

Answer: T is in group 1.


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

Answer: G is in group 2.

Answer: T is in group 1.

Answer: There is exactly one child in group 1.

Answer: There is exactly one child in group 2.

Answer: There is exactly one child in group 3.


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

Answer: F is in group 3.

Answer: K is in group 3.

Answer: Q is in group 2.

Answer: R is in group 1.

Answer: S is in group 2.


Context: 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?

Answer: Lara buys a hot dog.

Answer: Lara buys a shish kebab.

Answer: Mendel buys a hot dog.

Answer: Mendel buys a pretzel.

Answer: 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?

Answer: $3

Answer: $4

Answer: $5

Answer: $6

Answer: $7


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

Answer: $5

Answer: $6

Answer: $7

Answer: $8

Answer: $9


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

Answer: Lara buys a fruit cup.

Answer: Lara buys a hot dog.

Answer: Mendel buys a fruit cup.

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

Answer: 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?

Answer: Lara buys a fruit cup.

Answer: Mendel buys a fruit cup.

Answer: Nastassia buys a hot dog.

Answer: Nastassia buys exactly one kind of food.

Answer: Exactly one person buys a fruit cup.


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?

Answer: $5

Answer: $6

Answer: $7

Answer: $8

Answer: $9


Context: 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?

Answer: blue, blue, green

Answer: blue, orange, orange

Answer: blue, orange, red

Answer: green, green, red

Answer: 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?

Answer: blue, blue

Answer: blue, orange

Answer: blue, red

Answer: green, red

Answer: 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?

Answer: blue, blue, green

Answer: blue, green, green

Answer: blue, green, orange

Answer: blue, orange, orange

Answer: 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?

Answer: both green

Answer: both orange

Answer: both red

Answer: one green and one red

Answer: 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

Answer: 1 and 2

Answer: 1 and 3

Answer: 1 and 4

Answer: 2 and 3

Answer: 3 and 4


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

Answer: flask 1 with flask 2

Answer: flask 1 with flask 4

Answer: flask 2 with flask 4

Answer: flask 2 with one of the other flasks

Answer: 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

Answer: obtained by mixing flasks 1 and 2

Answer: obtained by mixing flasks 2 and 4

Answer: blue

Answer: green

Answer: red


Context: 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

Answer: F, G, H, and J

Answer: F, H, L, and M

Answer: F, J, K, and L

Answer: G, H, L, and N

Answer: G, K, M, and N


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

Answer: G is in group 1.

Answer: H is in group 2.

Answer: J is in group 1.

Answer: K is in group 2.

Answer: M is in group 1.


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

Answer: G is in group 2.

Answer: J is in group 1.

Answer: K is in group 1.

Answer: L is in group 2.

Answer: 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

Answer: F

Answer: G

Answer: H

Answer: J

Answer: K


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

Answer: F and G

Answer: F and H

Answer: F and L

Answer: H and G

Answer: H and N


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

Answer: F and M

Answer: G and N

Answer: J and N

Answer: K and M

Answer: M and N


Context: 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

Answer: Monday

Answer: Tuesday

Answer: Wednesday

Answer: Thursday

Answer: 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?

Answer: Monday, Tuesday

Answer: Monday, Wednesday

Answer: Monday, Thursday

Answer: Monday, Tuesday, Wednesday

Answer: Monday, Wednesday, Thursday


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

Answer: Iris is scheduled for Friday.

Answer: Nancy is scheduled for Tuesday.

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

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

Answer: 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?

Answer: Harry is scheduled for Tuesday.

Answer: Harry is scheduled for Wednesday.

Answer: Iris is scheduled for Monday.

Answer: Iris is scheduled for Wednesday.

Answer: Nancy is scheduled for Wednesday.


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

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

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

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

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

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


Context: 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?

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

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

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

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

Answer: 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?

Answer: history

Answer: oils

Answer: pastels

Answer: sculpture

Answer: 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?

Answer: fresco

Answer: naturalism

Answer: oils

Answer: pastels

Answer: 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?

Answer: fresco

Answer: history

Answer: naturalism

Answer: pastels

Answer: sculpture


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

Answer: history

Answer: lithography

Answer: oils

Answer: pastels

Answer: 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?

Answer: Lithography is scheduled for day 3.

Answer: Naturalism is scheduled for day 2.

Answer: Fresco is scheduled for the same day as naturalism.

Answer: History is scheduled for the same day as naturalism.

Answer: History is scheduled for the same day as oils.


Context: 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?

Answer: N, O, S

Answer: N, O, T

Answer: N, P, S

Answer: O, P, T

Answer: O, S, T


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

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

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

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

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

Answer: 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?

Answer: five

Answer: six

Answer: seven

Answer: eight

Answer: nine


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

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

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

Answer: All three of them participate together in the fourth year.

Answer: All three of them participate together in the fifth year.

Answer: 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?

Answer: N participates in the second and third years.

Answer: O participates in the third and fourth years.

Answer: N and O both participate in the third year.

Answer: P and T both participate in the fifth year.

Answer: 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

Answer: N

Answer: O

Answer: P

Answer: S

Answer: T


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?

Answer: N, O, P

Answer: N, O, S

Answer: N, P, S

Answer: O, P, S

Answer: P, S, T


Context: 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

Answer: G H, K, L F

Answer: G H F, K, L

Answer: H F, G K, L

Answer: H, K G F, L

Answer: K F, G, H, L


Question: Which one of the following must be true?

Answer: There are at most three technicians.

Answer: There is exactly one technician.

Answer: There are at least two managers.

Answer: There are exactly two managers.

Answer: 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?

Answer: F, H

Answer: F, L

Answer: G, K

Answer: G, L

Answer: K, L


Question: Which one of the following could be true?

Answer: There is exactly one technician.

Answer: There are exactly two managers.

Answer: There are exactly two employees who are not supervised.

Answer: There are more managers than technicians.

Answer: The president supervises all of the other employees.


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

Answer: G is the president.

Answer: H is the president.

Answer: L is a technician.

Answer: There is exactly one manager.

Answer: There are exactly two technicians.


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

Answer: F is supervised by K.

Answer: G is a manager.

Answer: L is supervised.

Answer: There are exactly two managers.

Answer: There are exactly two technicians.


Context: 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?

Answer: Ron washed the fork first.

Answer: Ron washed the fork second.

Answer: Ron washed the mug first.

Answer: Ron washed the plate second.

Answer: Ron washed the plate third.


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

Answer: Ron washed the knife second.

Answer: Ron washed the knife seventh.

Answer: Ron washed the mug second.

Answer: Ron washed the mug third.

Answer: 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?

Answer: fork, spoon, water glass

Answer: knife, fork, juice glass

Answer: knife, spoon, juice glass

Answer: knife, spoon, water glass

Answer: plate, water glass, juice glass


Question: It is NOT possible that Ron washed the knife

Answer: first

Answer: second

Answer: third

Answer: fifth

Answer: sixth


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

Answer: He washed the knife second.

Answer: He washed the knife third.

Answer: He washed the plate third.

Answer: He washed the plate sixth.

Answer: 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?

Answer: He washed the fork before the plate.

Answer: He washed the fork before the spoon.

Answer: He washed the juice glass before the knife.

Answer: He washed the plate before the water glass.

Answer: He washed the spoon before the fork.


Context: 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

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

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

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

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

Answer: 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?

Answer: H and J; M and N

Answer: H and J; S and T

Answer: H and K; M and N

Answer: H and K; R and W

Answer: 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

Answer: H is exhibited

Answer: K is exhibited

Answer: N is exhibited

Answer: J is assigned to one of the cages

Answer: 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?

Answer: H and J

Answer: H and K

Answer: M and N

Answer: R and W

Answer: S and W


Question: Which one of the following CANNOT be true?

Answer: One pair of parakeets are the only birds exhibited together.

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

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

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

Answer: Two pairs of parakeets are exhibited together.


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

Answer: H is exhibited

Answer: M is exhibited

Answer: K is assigned to a cage

Answer: N is assigned to a cage

Answer: R is assigned to a cage


Context: 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?

Answer: Nikki's fall sport is running.

Answer: Nikki's winter sport is volleyball.

Answer: Nikki's spring sport is mountaineering.

Answer: Otto's fall sport is mountaineering.

Answer: 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?

Answer: hockey

Answer: kayaking

Answer: mountaineering

Answer: running

Answer: volleyball


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

Answer: Nikki's spring sport is kayaking.

Answer: Nikki's summer sport is mountaineering.

Answer: Otto's fall sport is mountaineering.

Answer: Otto's spring sport is kayaking.

Answer: Otto's spring sport is running.


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

Answer: Nikki's fall sport is neither mountaineering nor running.

Answer: Nikki's spring sport is neither mountaineering nor running.

Answer: Nikki's summer sport is neither kayaking nor mountaineering.

Answer: Otto's fall sport is neither mountaineering nor running.

Answer: 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?

Answer: Nikki's fall sport is running.

Answer: Nikki's spring sport is running.

Answer: Nikki's summer sport is kayaking.

Answer: Otto's fall sport is mountaineering.

Answer: Otto's spring sport is kayaking.


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

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

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

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

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

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


Context: 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?

Answer: H, J, R, S, T, K

Answer: H, R, T, K, S, J

Answer: K, J, T, H, S, R

Answer: R, J, K, T, H, S

Answer: T, R, J, S, K, H


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

Answer: H delivers the first speech.

Answer: J delivers the fifth speech.

Answer: K delivers the fourth speech.

Answer: R delivers the sixth speech.

Answer: 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?

Answer: H delivers the second speech.

Answer: J delivers the fifth speech.

Answer: K delivers the fifth speech.

Answer: K delivers the first speech.

Answer: 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?

Answer: R delivers the third speech.

Answer: T delivers the fourth speech.

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

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

Answer: 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?

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

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

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

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

Answer: 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

Answer: H

Answer: J

Answer: R

Answer: S

Answer: T


Context: 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?

Answer: R: J, L; S: J, M; T: L; U: L

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

Answer: R: K; S: J; T: L; U: M

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

Answer: 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?

Answer: J is within area T.

Answer: K is within area R.

Answer: K is within area T.

Answer: L is within area R.

Answer: 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?

Answer: M

Answer: J, L

Answer: J, L, M

Answer: K, L, M

Answer: J, K, L, M


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

Answer: K is within area T.

Answer: K is within area U.

Answer: L is within area R.

Answer: M is within area R.

Answer: M is within area U.


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

Answer: R and area T

Answer: R and area U

Answer: S and area T

Answer: S and area U

Answer: 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?

Answer: J is within area T.

Answer: L is within area R.

Answer: L is within area S.

Answer: K is within exactly two areas.

Answer: 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?

Answer: J is within exactly two of the areas.

Answer: J is within exactly three of the areas.

Answer: K is within area S.

Answer: M is within area R.

Answer: M is within area T.


Context: 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?

Answer: Gina, Fritz, Jerry, Helen, Gina, Gina

Answer: Gina, Fritz, Jerry, Helen, Fritz, Jerry

Answer: Helen, Fritz, Gina, Jerry, Helen, Fritz

Answer: Helen, Gina, Jerry, Fritz, Helen, Fritz

Answer: Helen, Gina, Jerry, Helen, Jerry, Gina


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

Answer: Fritz drives on both Wednesday and Saturday.

Answer: Gina drives on both Monday and Wednesday.

Answer: Jerry drives on both Tuesday and Friday.

Answer: Gina drives on Monday and Jerry drives on Thursday.

Answer: 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?

Answer: Fritz drives on Tuesday.

Answer: Gina drives on Friday.

Answer: Helen drives on Monday.

Answer: Fritz drives on exactly two days.

Answer: 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?

Answer: One other person besides Gina drives on exactly two days.

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

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

Answer: Either Fritz or Helen drives on Friday.

Answer: Either Helen or Jerry drives on Tuesday.


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

Answer: Fritz drives on Tuesday and Gina drives on Friday.

Answer: Gina drives on Monday and Jerry drives on Tuesday.

Answer: Gina drives on Monday and Jerry drives on Friday.

Answer: Helen drives on Monday and Jerry drives on Tuesday.

Answer: 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?

Answer: One person drives exactly three times during the week.

Answer: Three people drive exactly one time each during the week.

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

Answer: Gina drives on Wednesday.

Answer: Jerry drives on Friday.


Context: 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?

Answer: Kathy

Answer: Roberta

Answer: Sally

Answer: Tim

Answer: Vernon


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

Answer: Frank and Roberta

Answer: Frank and Vernon

Answer: Jill and Mark

Answer: Roberta and Tim

Answer: 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

Answer: Gene

Answer: Jill

Answer: Mark

Answer: Roberta

Answer: Vernon


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

Answer: Vernon

Answer: Tim

Answer: Mark

Answer: Kathy

Answer: Frank


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

Answer: Frank or else Gene

Answer: Frank or else Mark

Answer: Gene or else Mark

Answer: Jill or else Kathy

Answer: Jill or else Mark


Context: 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?

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

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

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

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

Answer: 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?

Answer: class 1

Answer: class 3

Answer: class 1, class 3

Answer: class 2, class 3

Answer: 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?

Answer: T

Answer: V

Answer: W

Answer: Y

Answer: Z


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

Answer: Y and Z

Answer: W and Z

Answer: V and Y

Answer: V and W

Answer: T and Z


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

Answer: V

Answer: W

Answer: X

Answer: Y

Answer: Z


Question: Which one of the following must be true?

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

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

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

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

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


Context: 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?

Answer: F is assigned to an even-numbered stall.

Answer: F is assigned to stall 1.

Answer: J is assigned to stall 2 or else stall 3.

Answer: J is assigned to stall 3 or else stall 4.

Answer: K is assigned to stall 2 or else stall 4.


Question: Which one of the following could be true?

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

Answer: H's stall faces M's stall.

Answer: J is assigned to stall 4.

Answer: K's stall faces J's stall.

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


Question: Which one of the following must be true?

Answer: A tiger is assigned to stall 2.

Answer: A tiger is assigned to stall 5.

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

Answer: Each tiger is assigned to an even-numbered stall.

Answer: 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?

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

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

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

Answer: G's stall faces H's stall.

Answer: 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?

Answer: F is assigned to stall 2.

Answer: F is assigned to stall 4.

Answer: G is assigned to stall 1.

Answer: G is assigned to stall 4.

Answer: M is assigned to stall 5.


Question: Which one of the following must be true?

Answer: A tiger is assigned to stall 2.

Answer: A tiger is assigned to stall 4.

Answer: A tiger is assigned to stall 5.

Answer: A lion is assigned to stall 3.

Answer: A lion is assigned to stall 4.


Context: 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

Answer: 1

Answer: 2

Answer: 4

Answer: 7

Answer: 8


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

Answer: House 8 is a ranch house.

Answer: House 7 is a split-level house.

Answer: House 4 is a Tudor house.

Answer: House 2 is a split-level house.

Answer: House 1 is a ranch house.


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

Answer: 1 is a Tudor house

Answer: 2 is a Tudor house

Answer: 5 is a ranch house

Answer: 7 is a Tudor house

Answer: 8 is a ranch house


Question: On the street, there could be exactly

Answer: one ranch house

Answer: one Tudor house

Answer: two Tudor houses

Answer: four ranch houses

Answer: five ranch houses


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

Answer: 1 is a split-level house

Answer: 1 is a Tudor house

Answer: 2 is a ranch house

Answer: 2 is a split-level house

Answer: 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:

Answer: ranch, split-level, ranch, Tudor

Answer: split-level, ranch, Tudor, split-level

Answer: split-level, Tudor, ranch, split-level

Answer: Tudor, ranch, Tudor, split-level

Answer: Tudor, split-level, ranch, Tudor


Context: 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?

Answer: J, R, M, L, S

Answer: J, R, S, L, M

Answer: R, J, M, L, S

Answer: R, J, M, S, L

Answer: 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:

Answer: L is one position higher than J.

Answer: R is one position higher than L.

Answer: S is one position higher than R.

Answer: J is in position 4.

Answer: M is in position 3.


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

Answer: J has won two matches.

Answer: L has lost two matches.

Answer: R has won two matches.

Answer: L's only match was played against J.

Answer: 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?

Answer: J is in position 2.

Answer: J is in position 3.

Answer: L is in position 2.

Answer: R is in position 1.

Answer: 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?

Answer: J

Answer: L

Answer: M

Answer: R

Answer: S


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?

Answer: J, R, M, S, L

Answer: J, L, S, M, R

Answer: R, J, S, L, M

Answer: R, L, M, S, J

Answer: R, M, L, S, J


Context: 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?

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

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

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

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

Answer: 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?

Answer: R has appointment 6.

Answer: S has appointment 4.

Answer: S has appointment 7.

Answer: U has appointment 1.

Answer: 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?

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

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

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

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

Answer: 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:

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

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

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

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

Answer: 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?

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

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

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

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

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


Context: 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?

Answer: F, G, and H

Answer: F, G, and M

Answer: G, K, and L

Answer: H, K, and L

Answer: 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

Answer: G and M are both assigned to the Quality Committee

Answer: K and L are both assigned to the Sales Committee

Answer: K is assigned to exactly two committees

Answer: L is assigned to exactly two committees

Answer: M is assigned to exactly two committees


Question: Which one of the following CANNOT be true?

Answer: F is assigned to exactly one committee.

Answer: G is assigned to exactly three committees.

Answer: H is assigned to exactly three committees.

Answer: K is assigned to exactly one committee.

Answer: 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?

Answer: G is assigned to the Quality Committee.

Answer: G is assigned to the Sales Committee.

Answer: K is assigned to the Quality Committee.

Answer: L is assigned to the Sales Committee.

Answer: 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?

Answer: F, G, and H

Answer: F, G, and K

Answer: G, H, and K

Answer: G, K, and L

Answer: H, L, and M


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

Answer: F is assigned to the Sales Committee.

Answer: G is assigned to the Sales Committee.

Answer: H is assigned to the Quality Committee.

Answer: K is assigned to the Quality Committee.

Answer: M is assigned to the Quality Committee.


Question: Which one of the following CANNOT be true?

Answer: F and G are each assigned to exactly one committee.

Answer: F and H are each assigned to exactly one committee.

Answer: G and H are each assigned to exactly one committee.

Answer: F and M are both assigned to the Sales Committee.

Answer: G and K are both assigned to the Quality Committee.


Context: 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?

Answer: Vladimir eats fish for lunch.

Answer: Vladimir eats fish for dinner.

Answer: Vladimir eats fish for his snack.

Answer: Wendy eats fish for dinner.

Answer: Wendy eats fish for her snack.


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

Answer: fish

Answer: hot cakes

Answer: macaroni

Answer: omelet

Answer: poached eggs


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

Answer: Vladimir eats fish for lunch.

Answer: Vladimir eats hot cakes for lunch.

Answer: Vladimir eats macaroni for dinner.

Answer: Wendy eats hot cakes for breakfast.

Answer: 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?

Answer: Vladimir eats poached eggs for breakfast.

Answer: Vladimir eats fish for lunch.

Answer: Vladimir eats hot cakes for lunch.

Answer: Wendy eats hot cakes for breakfast.

Answer: Wendy eats fish for dinner.


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

Answer: Vladimir eats fish for lunch.

Answer: Vladimir eats hot cakes for lunch.

Answer: Vladimir eats macaroni for dinner.

Answer: Wendy eats hot cakes for dinner.

Answer: Wendy eats macaroni for dinner.


Context: 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?

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

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

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

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

Answer: 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?

Answer: first

Answer: second

Answer: first, second

Answer: first, third

Answer: second, third


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

Answer: Mark runs fourth.

Answer: Nick runs first.

Answer: Nick runs fourth.

Answer: Peggy runs first.

Answer: Peggy runs fourth.


Question: Any of the following can be true EXCEPT:

Answer: Jack runs first.

Answer: Mark runs fourth.

Answer: Nick runs first.

Answer: Nick and Peggy both run third.

Answer: 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?

Answer: Jack runs first.

Answer: Mark runs fourth.

Answer: Nick runs third.

Answer: Peggy runs third.

Answer: Ruth runs first.


Question: Any of the following can be true EXCEPT:

Answer: Jack runs fourth.

Answer: Nick runs fourth.

Answer: Peggy runs fourth.

Answer: Ruth runs first.

Answer: 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?

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

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

Answer: Owen runs on the same team as Jack.

Answer: Owen runs on the same team as Mark.

Answer: Ruth runs on the same team as Mark.


Context: 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?

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

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

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

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

Answer: 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?

Answer: G is built during week 7.

Answer: H is built during week 1.

Answer: J is built during week 6.

Answer: L is built during week 3.

Answer: 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?

Answer: 2, 3, 6

Answer: 2, 3, 7

Answer: 2, 5, 6, 7

Answer: 1, 2, 3, 6, 7

Answer: 2, 3, 4, 6, 7


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?

Answer: K, L, M

Answer: F, G, H, K

Answer: F, H, K, M

Answer: G, H, K, L, M

Answer: 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?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


Context: 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?

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

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

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

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

Answer: 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?

Answer: F presents product M.

Answer: G presents product L.

Answer: I presents product N.

Answer: Product O is presented on Wednesday.

Answer: Product P is presented on Wednesday.


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

Answer: H presents product O.

Answer: I presents product N.

Answer: I presents product O.

Answer: F makes a presentation on Monday.

Answer: F makes a presentation on Wednesday.


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

Answer: G presents product P.

Answer: I presents product O.

Answer: J presents product L.

Answer: F presents a product on Monday.

Answer: 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?

Answer: F presents product O or else product P.

Answer: F presents neither product O nor product P.

Answer: H presents product O or else product P.

Answer: I presents product O or else product P.

Answer: J presents neither product O nor product P.


Context: 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?

Answer: Q, R

Answer: Q, S

Answer: Q, V

Answer: R, W

Answer: S, V


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

Answer: 101: V; 102: W; 103: R

Answer: 101: V; 102: W, 104: R

Answer: 101: V; 103: W; 104: R

Answer: 103: W; 104: V; 106: R

Answer: 105: R; 106: W; 107: V


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

Answer: F

Answer: G

Answer: Q

Answer: V

Answer: W


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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: F

Answer: G

Answer: Q

Answer: S

Answer: V


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

Answer: F is assigned either room 103 or else room 104.

Answer: Q is assigned either room 102 or else room 106.

Answer: R is assigned either room 102 or else room 105.

Answer: S is assigned either room 104 or else room 105.

Answer: 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?

Answer: W

Answer: V

Answer: S

Answer: R

Answer: Q


Context: 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?

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

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

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

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

Answer: 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:

Answer: one oval silk rug

Answer: one rectangular silk rug

Answer: two rectangular silk rugs

Answer: one oval silk rug and one rectangular silk rug

Answer: one oval silk rug and two rectangular silk rugs


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

Answer: one oval silk rug

Answer: two oval wool rugs

Answer: three oval rugs

Answer: two rectangular wool rugs

Answer: 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

Answer: one oval rug and two rectangular rugs

Answer: two oval rugs and one rectangular rug

Answer: two oval rugs and two rectangular rugs

Answer: two oval rugs and three rectangular rugs

Answer: three rectangular rugs


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

Answer: one oval rug and three rectangular wool rugs

Answer: two oval rugs and two rectangular wool rugs

Answer: three oval rugs and one rectangular silk rug

Answer: three oval rugs and one rectangular wool rug

Answer: 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:

Answer: one oval wool rug

Answer: two oval wool rugs

Answer: one oval wool rug and one rectangular wool rug

Answer: one oval wool rug and two rectangular wool rugs

Answer: two oval wool rugs and one rectangular wool rug


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

Answer: exactly one of the oval rugs

Answer: the two oval wool rugs

Answer: the two rectangular silk rugs

Answer: exactly three of the rectangular rugs

Answer: all three rectangular wool rugs


Context: 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?

Answer: F, Q, R, H, J, G

Answer: G, H, J, Q, R, F

Answer: G, J, Q, H, R, F

Answer: G, J, Q, R, F, H

Answer: J, H, G, Q, R, F


Question: Which one of the following must be false?

Answer: The inspection of G is scheduled for day 4.

Answer: The inspection of H is scheduled for day 6.

Answer: The inspection of J is scheduled for day 4.

Answer: The inspection of Q is scheduled for day 3.

Answer: The inspection of R is scheduled for day 2.


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

Answer: G

Answer: H

Answer: J

Answer: Q

Answer: R


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

Answer: G and H

Answer: G and R

Answer: H and G

Answer: R and J

Answer: R and H


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?

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

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

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

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

Answer: 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?

Answer: F, J

Answer: G, H

Answer: G, H, J

Answer: F, G, H

Answer: F, G, H, J


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?

Answer: The inspection of G is scheduled for day 5.

Answer: The inspection of H is scheduled for day 6.

Answer: The inspection of J is scheduled for day 2.

Answer: The inspection of Q is scheduled for day 4.

Answer: The inspection of R is scheduled for day 3.


Context: 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?

Answer: Only one workshop is in session on Thursday.

Answer: Only one workshop is in session on Friday.

Answer: The workshop on Rehearsals is in session on Tuesday.

Answer: The workshop on Staging is in session on Thursday.

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


Question: Which one of the following could be true?

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

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

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

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

Answer: 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?

Answer: The workshop on Lighting is in session on Monday.

Answer: The workshop on Rehearsals is in session on Wednesday.

Answer: The workshop on Staging is in session on Thursday .

Answer: The workshop on Staging is in session on Monday.

Answer: 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?

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

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

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

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

Answer: 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?

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

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

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

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

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


Context: 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 ?

Answer: F, G, H, X

Answer: F, H, W, Y

Answer: F, H, Y, Z

Answer: F, V, W, X

Answer: 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?

Answer: F and Y

Answer: G and H

Answer: G and Y

Answer: V and W

Answer: Y and Z


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?

Answer: F and H

Answer: G and Y

Answer: H and W

Answer: V and W

Answer: W and Y


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

Answer: H is assigned to boat 2.

Answer: V is assigned to boat 2.

Answer: Exactly one adult is assigned to boat 1.

Answer: Exactly two adults are assigned to boat 2.

Answer: 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?

Answer: F and H

Answer: F and Y

Answer: G and X

Answer: W and X

Answer: Y and Z


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

Answer: F

Answer: G

Answer: H

Answer: V

Answer: Y


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

Answer: F is assigned to boat 1.

Answer: G is assigned to boat 2.

Answer: H is assigned to boat 2.

Answer: V is assigned to boat 1.

Answer: Z is assigned to boat 2.


Context: 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?

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

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

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

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

Answer: 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?

Answer: Harlan is assigned to the Recycling panel.

Answer: Jennifer is assigned to the Oceans panel.

Answer: Kenji is assigned to the Recycling panel.

Answer: Lisa is assigned to the Wetlands panel.

Answer: Nari is assigned to the Oceans panel.


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

Answer: Faith and Harlan

Answer: Gregory and Paul

Answer: Harlan and Marcus

Answer: Faith and Marcus

Answer: Jennifer and Marcus


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

Answer: Faith is assigned to the Wetlands panel.

Answer: Gregory is assigned to the Recycling panel.

Answer: Harlan is assigned to the Oceans panel.

Answer: Jennifer is assigned to the Wetlands panel.

Answer: 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:

Answer: Gregory and Kenji

Answer: Gregory and Lisa

Answer: Kenji and Nari

Answer: Lisa and Marcus

Answer: Lisa and Paul


Context: 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?

Answer: Norris, Semonelli

Answer: Oribe, Underwood

Answer: Paulsen, Oribe

Answer: Rosen, Semonelli

Answer: 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?

Answer: Norris is assigned to seat 2.

Answer: Paulsen is assigned to seat 5.

Answer: Rosen is assigned to seat 4.

Answer: Tan is assigned to seat 2.

Answer: 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?

Answer: Oribe

Answer: Rosen

Answer: Semonelli

Answer: Tan

Answer: Underwood


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?

Answer: Tan is assigned to a seat in the front row.

Answer: Tan is assigned to a seat in the last row.

Answer: Oribe is assigned to a seat immediately beside Semonelli.

Answer: Oribe is assigned to a seat immediately beside Tan.

Answer: 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?

Answer: Oribe is assigned to seat 8.

Answer: Tan is assigned to seat 2.

Answer: Underwood is assigned to seat 1.

Answer: Seat 4 is unassigned.

Answer: Seat 9 is unassigned.


Context: 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?

Answer: G, L, M, N, W

Answer: G, L, M, P, W

Answer: G, M, N, R, W

Answer: G, M, P, R, S

Answer: 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?

Answer: G, M, P, S

Answer: L, M, N, R

Answer: L, M, P, S

Answer: M, N, P, S

Answer: 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?

Answer: G, M

Answer: M, R

Answer: N, R

Answer: R, S

Answer: S, W


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?

Answer: G, M

Answer: G, P

Answer: N, R

Answer: N, W

Answer: P, S


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

Answer: G is reduced.

Answer: N is not reduced.

Answer: P is reduced.

Answer: S is reduced.

Answer: 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?

Answer: G, L

Answer: G, N

Answer: L, N

Answer: L, P

Answer: P, S


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

Answer: G

Answer: L

Answer: N

Answer: P

Answer: W


Context: 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?

Answer: green, red, purple, yellow, red, orange, green, purple

Answer: orange, yellow, red, red, yellow, purple, red, green

Answer: purple, yellow, red, green, green, orange, yellow, orange

Answer: red, orange, red, yellow, purple, green, yellow, green

Answer: 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?

Answer: green, orange

Answer: green, red

Answer: purple, purple

Answer: yellow, green

Answer: 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?

Answer: The first bead is purple.

Answer: The fifth bead is green.

Answer: The fifth bead is orange.

Answer: The eighth bead is orange.

Answer: 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

Answer: green and orange, respectively

Answer: orange and green, respectively

Answer: orange and yellow, respectively

Answer: purple and orange, respectively

Answer: 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?

Answer: The seventh bead is orange.

Answer: The eighth bead is green.

Answer: The eighth bead is red.

Answer: The ninth bead is red.

Answer: 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

Answer: green and orange, respectively

Answer: green and purple, respectively

Answer: purple and orange, respectively

Answer: purple and yellow, respectively

Answer: yellow and orange, respectively


Context: 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?

Answer: X, T, Y, O, P, Z

Answer: X, Z, Y, T, O, P

Answer: Y, O, P, X, T, Z

Answer: Y, P, O, Z, T, X

Answer: Y, X, O, P, Z, T


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

Answer: George performs X.

Answer: Helen performs O.

Answer: Helen performs T.

Answer: Leslie performs P.

Answer: Leslie performs X.