Exactly eight computer processor chips—F, G, H, J, K, L, M, and O—are ranked according to their speed from first (fastest) to eighth (slowest). The ranking must be consistent with the following: There are no ties. Either F or G is ranked first. M is not the slowest. H is faster than J, with exactly one chip intermediate in speed between them. K is faster than L, with exactly two chips intermediate in speed between them. O is slower than both J and L.

Question: Which one of the following could be true?

F is ranked first and M is ranked eighth.

G is ranked fifth and O is ranked eighth.

J is ranked third and L is ranked seventh.

K is ranked second and H is ranked third.

M is ranked seventh and L is ranked eighth.


Question: H CANNOT be ranked


Question: If O is faster than F, then which one of the following chips could be ranked second?


Question: If M is faster than J, then the fastest ranking J could have is


Question: Which one of the following must be true?

J is ranked no faster than fifth.
K is ranked no faster than third.
L is ranked no faster than fifth.
M is ranked no faster than third.
O is ranked no faster than eighth.


At each of six consecutive stops—1, 2, 3, 4, 5, and 6—that a traveler must make in that order as part of a trip, she can choose one from among exactly four airlines—L, M, N, and O—on which to continue. Her choices must conform to the following constraints: Whichever airline she chooses at a stop, she chooses one of the other airlines at the next stop. She chooses the same airline at stop 1 as she does at stop 6. She chooses the same airline at stop 2 as she does at stop 4. Whenever she chooses either L or M at a stop, she does not choose N at the next stop. At stop 5, she chooses N or O.

Question: Which one of the following could be an accurate list of the airlines the traveler chooses at each stop, in order from 1 through 6?

L, M, M, L, O, L
M, L, O, M, O, M
M, N, O, N, O, M
M, O, N, O, N, M
O, M, L, M, O, N


Question: If the traveler chooses N at stop 5, which one of the following could be an accurate list of the airlines she chooses at stops 1, 2, and 3, respectively?


Question: If the only airlines the traveler chooses for the trip are M, N, and O, and she chooses O at stop 5, then the airlines she chooses at stops 1, 2, and 3, must be, respectively,

M, O, and N
M, N, and O
N, M, and O
N, O, and M
O, M, and N


Question: Which one of the following CANNOT be an accurate list of the airlines the traveler chooses at stops 1 and 2, respectively?


Question: If the traveler chooses O at stop 2, which one of the following could be an accurate list of the airlines she chooses at stops 5 and 6, respectively?


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

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

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


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


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


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


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


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


Within a five-year period from 1991 to 1995, each of three friends—Ramon, Sue, and Taylor—graduated. In that period, each bought his or her first car. The graduations and car purchases must be consistent with the following: Ramon graduated in some year before the year in which Taylor graduated. Taylor graduated in some year before the year in which he bought his first car. Sue bought her first car in some year before the year in which she graduated. Ramon and Sue graduated in the same year as each other. At least one of the friends graduated in 1993.

Question: Which one of the following could be an accurate matching of each friend and the year in which she or he graduated?


Question: Which one of the following could have taken place in 1995?

Ramon graduated.
Ramon bought his first car.
Sue graduated.
Sue bought her first car.
Taylor graduated.


Question: Which one of the following must be false?

Two of the friends each bought his or her first car in 1991.

Two of the friends each bought his or her first car in 1992.

Two of the friends each bought his or her first car in 1993.

Two of the friends each bought his or her first car in 1994.

Two of the friends each bought his or her first car in 1995.


Question: Which one of the following must be true?

None of the three friends graduated in 1991.

None of the three friends graduated in 1992.

None of the three friends bought his or her first car in 1993.

None of the three friends graduated in 1994.

None of the three friends bought his or her first car in 1995.


Question: If Taylor graduated in the same year that Ramon bought his first car, then each of the following could be true EXCEPT:

Sue bought her first car in 1991.
Ramon graduated in 1992.
Taylor graduated in 1993.
Taylor bought his first car in 1994.
Ramon bought his first car in 1995.


Question: If Sue graduated in 1993, then which one of the following must be true?

Sue bought her first car in 1991.
Ramon bought his first car in 1992.
Ramon bought his first car in 1993.
Taylor bought his first car in 1994.
Taylor bought his first car in 1995.


A child eating alphabet soup notices that the only letters left in her bowl are one each of these six letters: T, U, W, X, Y, and Z. She plays a game with the remaining letters, eating them in the next three spoonfuls in accord with certain rules. Each of the six letters must be in exactly one of the next three spoonfuls, and each of the spoonfuls must have at least one and at most three of the letters. In addition, she obeys the following restrictions: The U is in a later spoonful than the T. The U is not in a later spoonful than the X. The Y is in a later spoonful than the W. The U is in the same spoonful as either the Y or the Z, but not both.

Question: Which one of the following could be an accurate list of the spoonfuls and the letters in each of them?

first: Y second: T, W third: U, X, Z
first: T, W second: U, X, Y third: Z
first: T second: U, Z third: W, X, Y
first: T, U, Z second: W third: X, Y
first: W second: T, X, Z third: U, Y


Question: If the Y is the only letter in one of the spoonfuls, then which one of the following could be true?

The Y is in the first spoonful.
The Z is in the first spoonful.
The T is in the second spoonful.
The X is in the second spoonful.
The W is in the third spoonful.


Question: If the Z is in the first spoonful, then which one of the following must be true?

The T is in the second spoonful.
The U is in the third spoonful.
The W is in the first spoonful.
The W is in the second spoonful.
The X is in the third spoonful.


Question: Which one of the following is a complete list of letters, any one of which could be the only letter in the first spoonful?


Question: If the T is in the second spoonful, then which one of the following could be true?

Exactly two letters are in the first spoonful.

Exactly three letters are in the first spoonful.

Exactly three letters are in the second spoonful.

Exactly one letter is in the third spoonful.

Exactly two letters are in the third spoonful.


A clown will select a costume consisting of two pieces and no others: a jacket and overalls. One piece of the costume will be entirely one color, and the other piece will be plaid. Selection is subject to the following restrictions: If the jacket is plaid, then there must be exactly three colors in it. If the overalls are plaid, then there must be exactly two colors in them. The jacket and overalls must have exactly one color in common. Green, red, and violet are the only colors that can be in the jacket. Red, violet, and yellow are the only colors that can be in the overalls.

Question: Which one of the following could be a complete and accurate list of the colors in the costume? Jacket Overalls

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


Question: If there are exactly two colors in the costume, then which one of the following must be false?

At least part of the jacket is green.
At least part of the jacket is red.
The overalls are red and violet.
The overalls are red and yellow.
The overalls are violet and yellow.


Question: If at least part of the jacket is green, then which one of the following could be true?

At least part of the overalls are yellow.

At least part of the overalls are violet.


Question: Which one of the following must be false?

Both green and red are colors used in the costume.

Both green and violet are colors used in the costume.

Both green and yellow are colors used in the costume.

Both red and violet are colors used in the costume.

Both violet and yellow are colors used in the costume.


Question: If there are exactly three colors in the costume, the overalls must be

entirely red or else red and violet plaid

entirely yellow or else violet and yellow plaid

entirely violet or else red and violet plaid


Six hotel suites—F, G, H, J, K, L—are ranked from most expensive (first) to least expensive (sixth). There are no ties. The ranking must be consistent with the following conditions: H is more expensive than L. If G is more expensive than H, then neither K nor L is more expensive than J. If H is more expensive than G, then neither J nor L is more expensive than K. F is more expensive than G, or else F is more expensive than H, but not both.

Question: Which one of the following could be the ranking of the suites, from most expensive to least expensive?

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


Question: If G is the second most expensive suite, then which one of the following could be true?

H is more expensive than F.
H is more expensive than G.
K is more expensive than F.
K is more expensive than J.
L is more expensive than F.


Question: Which one of the following CANNOT be the most expensive suite?


Question: If L is more expensive than F, then which one of the following could be true?

F is more expensive than H.
F is more expensive than K.
G is more expensive than H.
G is more expensive than J.
G is more expensive than L.


Question: If H is more expensive than J and less expensive than K, then which one of the following could be true?

F is more expensive than H.
G is more expensive than F.
G is more expensive than H.
J is more expensive than L.
L is more expensive than K.


A locally known guitarist's demo CD contains exactly seven different songs—S, T, V, W, X, Y, and Z. Each song occupies exactly one of the CD's seven tracks. Some of the songs are rock classics; the others are new compositions. The following conditions must hold: S occupies the fourth track of the CD. Both W and Y precede S on the CD. T precedes W on the CD. A rock classic occupies the sixth track of the CD. Each rock classic is immediately preceded on the CD by a new composition. Z is a rock classic.

Question: Which one of the following could be the order of the songs on the CD, from the first track through the seventh?

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


Question: Which one of the following is a pair of songs that must occupy consecutive tracks on the CD?


Question: Which one of the following songs must be a new composition?


Question: If W precedes Y on the CD, then which one of the following must be true?

S is a rock classic.
V is a rock classic.
Y is a rock classic.
T is a new composition.
W is a new composition.


Question: If there are exactly two songs on the CD that both precede V and are preceded by Y, then which one of the following could be true?

V occupies the seventh track of the CD.
X occupies the fifth track of the CD.
Y occupies the third track of the CD.
T is a rock classic.
W is a rock classic.


A courier delivers exactly eight parcels—G, H, J, K, L, M, N, and O. No two parcels are delivered at the same time, nor is any parcel delivered more than once. The following conditions must apply: L is delivered later than H. K is delivered earlier than O. H is delivered earlier than M. O is delivered later than G. M is delivered earlier than G. Both N and J are delivered earlier than M.

Question: Which one of the following could be the order of deliveries from first to last?

N, H, K, M, J, G, O, L
H, N, J, K, G, O, L, M
J, H, N, M, K, O, G, L
N, J, H, L, M, K, G, O
K, N, J, M, G, H, O, L


Question: Which one of the following must be true?

At least one parcel is delivered earlier than K is delivered.

At least two parcels are delivered later than G is delivered.

At least four parcels are delivered later than H is delivered.

At least four parcels are delivered later than J is delivered.

At least four parcels are delivered earlier than M is delivered.


Question: If M is the fourth parcel delivered, then which one of the following must be true?

G is the fifth parcel delivered.
O is the seventh parcel delivered.
J is delivered later than H.
K is delivered later than N.
G is delivered later than L.


Question: If H is the fourth parcel delivered, then each of the following could be true EXCEPT:

K is the fifth parcel delivered.
L is the sixth parcel delivered.
M is the sixth parcel delivered.
G is the seventh parcel delivered.
O is the seventh parcel delivered.


Question: Each of the following could be true EXCEPT:

H is delivered later than K.
J is delivered later than G.
L is delivered later than O.
M is delivered later than L.
N is delivered later than H.


Question: If K is the seventh parcel delivered, then each of the following could be true EXCEPT:

G is the fifth parcel delivered.
M is the fifth parcel delivered.
H is the fourth parcel delivered.
L is the fourth parcel delivered.
J is the third parcel delivered.


Question: If L is delivered earlier than K, then which one of the following must be false?

N is the second parcel delivered.
L is the third parcel delivered.
H is the fourth parcel delivered.
K is the fifth parcel delivered.
M is the sixth parcel delivered.


A company employee generates a series of five-digit product codes in accordance with the following rules: The codes use the digits 0, 1, 2, 3, and 4, and no others. Each digit occurs exactly once in any code. The second digit has a value exactly twice that of the first digit. The value of the third digit is less than the value of the fifth digit.

Question: If the last digit of an acceptable product code is 1, it must be true that the

first digit is 2
second digit is 0
third digit is 3
fourth digit is 4
fourth digit is 0


Question: Which one of the following must be true about any acceptable product code?

The digit 1 appears in some position before the digit 2.

The digit 1 appears in some position before the digit 3.

The digit 2 appears in some position before the digit 3.

The digit 3 appears in some position before the digit 0.

The digit 4 appears in some position before the digit 3.


Question: If the third digit of an acceptable product code is not 0, which one of the following must be true?

The second digit of the product code is 2.

The third digit of the product code is 3.

The fourth digit of the product code is 0.

The fifth digit of the product code is 3.

The fifth digit of the product code is 1.


Question: Any of the following pairs could be the third and fourth digits, respectively, of an acceptable product code, EXCEPT:


Question: Which one of the following must be true about any acceptable product code?

There is exactly one digit between the digit 0 and the digit 1.

There is exactly one digit between the digit 1 and the digit 2.

There are at most two digits between the digit 1 and the digit 3.

There are at most two digits between the digit 2 and the digit 3.

There are at most two digits between the digit 2 and the digit 4.


Exactly three films—Greed, Harvest, and Limelight—are shown during a film club's festival held on Thursday, Friday, and Saturday. Each film is shown at least once during the festival but never more than once on a given day. On each day at least one film is shown. Films are shown one at a time. The following conditions apply: On Thursday Harvest is shown, and no film is shown after it on that day. On Friday either Greed or Limelight, but not both, is shown, and no film is shown after it on that day. On Saturday either Greed or Harvest, but not both, is shown, and no film is shown after it on that day.

Question: Which one of the following could be a complete and accurate description of the order in which the films are shown at the festival?

Thursday: Limelight, then Harvest; Friday: Limelight; Saturday: Harvest

Thursday: Harvest; Friday: Greed, then Limelight; Saturday: Limelight, then Greed

Thursday: Harvest; Friday: Limelight; Saturday: Limelight, then Greed

Thursday: Greed, then Harvest, then Limelight; Friday: Limelight; Saturday: Greed

Thursday: Greed, then Harvest; Friday: Limelight, then Harvest; Saturday: Harvest


Question: Which one of the following CANNOT be true?

Harvest is the last film shown on each day of the festival.

Limelight is shown on each day of the festival.

Greed is shown second on each day of the festival.

A different film is shown first on each day of the festival.

A different film is shown last on each day of the festival.


Question: If Limelight is never shown again during the festival once Greed is shown, then which one of the following is the maximum number of film showings that could occur during the festival?


Question: If Greed is shown exactly three times, Harvest is shown exactly twice, and Limelight is shown exactly once, then which one of the following must be true?

Exactly two films are shown on Saturday.

Limelight and Harvest are both shown on Thursday.

Greed is the only film shown on Saturday.

Harvest and Greed are both shown on Friday.


Question: If Limelight is shown exactly three times, Harvest is shown exactly twice, and Greed is shown exactly once, then which one of the following is a complete and accurate list of the films that could be the first film shown on Thursday?

Harvest
Limelight
Greed, Harvest
Greed, Limelight
Greed, Harvest, Limelight


A cruise line is scheduling seven week-long voyages for the ship Freedom. Each voyage will occur in exactly one of the first seven weeks of the season: weeks 1 through 7. Each voyage will be to exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad. Each destination will be scheduled for at least one of the weeks. The following conditions apply to Freedom's schedule: Jamaica will not be its destination in week 4. Trinidad will be its destination in week 7. Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages. Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica. No destination will be scheduled for consecutive weeks.

Question: Which one of the following is an acceptable schedule of destinations for Freedom, in order from week 1 through week 7?

Guadeloupe, Jamaica, Martinique, Trinidad, Guadeloupe, Martinique, Trinidad

Guadeloupe, Martinique, Trinidad, Martinique, Guadeloupe, Jamaica, Trinidad

Jamaica, Martinique, Guadeloupe, Martinique, Guadeloupe, Jamaica, Trinidad

Martinique, Trinidad, Guadeloupe, Jamaica, Martinique, Guadeloupe, Trinidad

Martinique, Trinidad, Guadeloupe, Trinidad, Guadeloupe, Jamaica, Martinique


Question: Which one of the following CANNOT be true about Freedom's schedule of voyages?

Freedom makes a voyage to Trinidad in week 6.

Freedom makes a voyage to Martinique in week 5.

Freedom makes a voyage to Jamaica in week 6.

Freedom makes a voyage to Jamaica in week 3.

Freedom makes a voyage to Guadeloupe in week 3.


Question: If Freedom makes a voyage to Trinidad in week 5, which one of the following could be true?

Freedom makes a voyage to Trinidad in week 1.

Freedom makes a voyage to Martinique in week 2.

Freedom makes a voyage to Guadeloupe in week 3.

Freedom makes a voyage to Martinique in week 4.

Freedom makes a voyage to Jamaica in week 6.


Question: If Freedom makes a voyage to Guadeloupe in week 1 and a voyage to Jamaica in week 5, which one of the following must be true?

Freedom makes a voyage to Jamaica in week 2.

Freedom makes a voyage to Trinidad in week 2.

Freedom makes a voyage to Martinique in week 3.

Freedom makes a voyage to Guadeloupe in week 6.

Freedom makes a voyage to Martinique in week 6.


Question: If Freedom makes a voyage to Guadeloupe in week 1 and to Trinidad in week 2, which one of the following must be true?

Freedom makes a voyage to Martinique in week 3.

Freedom makes a voyage to Martinique in week 4.

Freedom makes a voyage to Martinique in week 5.

Freedom makes a voyage to Guadeloupe in week 3.

Freedom makes a voyage to Guadeloupe in week 5.


Question: If Freedom makes a voyage to Martinique in week 3, which one of the following could be an accurate list of Freedom's destinations in week 4 and week 5, respectively?

Guadeloupe, Trinidad
Jamaica, Guadeloupe
Martinique, Trinidad
Trinidad, Jamaica
Trinidad, Martinique


Question: Which one of the following must be true about Freedom's schedule of voyages?

Freedom makes a voyage to Guadeloupe either in week 1 or else in week 2.

Freedom makes a voyage to Martinique either in week 2 or else in week 3.

Freedom makes at most two voyages to Guadeloupe.

Freedom makes at most two voyages to Jamaica.

Freedom makes at most two voyages to Trinidad.


There are exactly three recycling centers in Rivertown: Center 1, Center 2, and Center 3. Exactly five kinds of material are recycled at these recycling centers: glass, newsprint, plastic, tin, and wood. Each recycling center recycles at least two but no more than three of these kinds of material. The following conditions must hold: Any recycling center that recycles wood also recycles newsprint. Every kind of material that Center 2 recycles is also recycled at Center 1. Only one of the recycling centers recycles plastic, and that recycling center does not recycle glass.

Question: Which one of the following could be an accurate account of all the kinds of material recycled at each recycling center in Rivertown?

Center 1: newsprint, plastic, wood; Center 2: newsprint, wood; Center 3: glass, tin, wood

Center 1: glass, newsprint, tin; Center 2: glass, newsprint, tin; Center 3: newsprint, plastic, wood

Center 1: glass, newsprint, wood; Center 2: glass, newsprint, tin; Center 3: plastic, tin

Center 1: glass, plastic, tin; Center 2: glass, tin; Center 3: newsprint, wood

Center 1: newsprint, plastic, wood; Center 2: newsprint, plastic, wood; Center 3: glass, newsprint, tin


Question: Which one of the following is a complete and accurate list of the recycling centers in Rivertown any one of which could recycle plastic?

Center 1 only
Center 3 only
Center 1, Center 2
Center 1, Center 3
Center 1, Center 2, Center 3


Question: If Center 2 recycles three kinds of material, then which one of the following kinds of material must Center 3 recycle?


Question: If each recycling center in Rivertown recycles exactly three kinds of material, then which one of the following could be true?

Only Center 2 recycles glass.
Only Center 3 recycles newsprint.
Only Center 1 recycles plastic.
Only Center 3 recycles tin.
Only Center 1 recycles wood.


Question: If Center 3 recycles glass, then which one of the following kinds of material must Center 2 recycle?


Question: If Center 1 is the only recycling center that recycles wood, then which one of the following could be a complete and accurate list of the kinds of material that one of the recycling centers recycles?

plastic, tin
newsprint, wood
newsprint, tin
glass, wood
glass, tin


Workers at a water treatment plant open eight valves—G, H, I, K, L, N, O, and P—to flush out a system of pipes that needs emergency repairs. To maximize safety and efficiency, each valve is opened exactly once, and no two valves are opened at the same time. The valves are opened in accordance with the following conditions: Both K and P are opened before H. O is opened before L but after H. L is opened after G. N is opened before H. I is opened after K.

Question: Which one of the following could be the order, from first to last, in which the valves are opened?

P, I, K, G, N, H, O, L
P, G, K, N, L, H, O, I
G, K, I, P, H, O, N, L
N, K, P, H, O, I, L, G
K, I, N, G, P, H, O, L


Question: Each of the following could be the fifth valve opened EXCEPT:


Question: If I is the second valve opened, then each of the following could be true EXCEPT:

G is the third valve opened.
H is the fourth valve opened.
P is the fifth valve opened.
O is the sixth valve opened.
G is the seventh valve opened.


Question: If L is the seventh valve opened, then each of the following could be the second valve opened EXCEPT:


Question: Which one of the following must be true?

At least one valve is opened before P is opened.

At least two valves are opened before G is opened.

No more than two valves are opened after O is opened.

No more than three valves are opened after H is opened.

No more than four valves are opened before N is opened.


Question: If K is the fourth valve opened, then which one of the following could be true?

I is the second valve opened.
N is the third valve opened.
G is the fifth valve opened.
O is the fifth valve opened.
P is the sixth valve opened.


Question: If G is the first valve opened and I is the third valve opened, then each of the following must be true EXCEPT:

K is the second valve opened.
N is the fourth valve opened.
H is the sixth valve opened.
O is the seventh valve opened.
L is the eighth valve opened.


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

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

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

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

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

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

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


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

Juana is accompanied by the same adult as Veronica.

Kyle is accompanied by the same adult as Salim.


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

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


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

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


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

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


Three short seminars—Goals, Objections, and Persuasion—and three long seminars—Humor, Negotiating, and Telemarketing—will be scheduled for a three-day sales training conference. On each day, two of the seminars will be given consecutively. Each seminar will be given exactly once. The schedule must conform to the following conditions: Exactly one short seminar and exactly one long seminar will be given each day. Telemarketing will not be given until both Goals and Objections have been given. Negotiating will not be given until Persuasion has been given.

Question: Which one of the following could be an accurate schedule for the sales training conference?

first day: Persuasion followed by Negotiating second day: Objections followed by Telemarketing third day: Goals followed by Humor

first day: Objections followed by Humor second day: Goals followed by Telemarketing third day: Persuasion followed by Negotiating

first day: Objections followed by Negotiating second day: Persuasion followed by Humor third day: Goals followed by Telemarketing

first day: Objections followed by Goals second day: Telemarketing followed by Persuasion third day: Negotiating followed by Humor

first day: Goals followed by Humor second day: Persuasion followed by Telemarketing third day: Objections followed by Negotiating


Question: If Goals is given on the first day of the sales training conference, then which one of the following could be true?

Telemarketing is given on the second day.


Question: If Negotiating is given at some time before Objections, then which one of the following must be true?

Negotiating is given at some time before Goals.

Persuasion is given at some time before Goals.

Persuasion is given at some time before Objections.

Humor is given at some time before Objections.

Negotiating is given at some time before Humor.


Question: Which one of the following CANNOT be the second seminar given on the second day of the sales training conference?

Humor Persuasion Objections Negotiating Goals


Question: If Humor is given on the second day of the sales training conference, then which one of the following could be true?

Telemarketing is given on the first day.

Telemarketing is given on the second day.


A bread truck makes exactly one bread delivery to each of six restaurants in succession—Figueroa's, Ginsberg's, Harris's, Kanzaki's, Leacock's, and Malpighi's—though not necessarily in that order. The following conditions must apply: Ginsberg's delivery is earlier than Kanzaki's but later than Figueroa's. Harris's delivery is earlier than Ginsberg's. If Figueroa's delivery is earlier than Malpighi's, then Leacock's delivery is earlier than Harris's. Either Malpighi's delivery is earlier than Harris's or it is later than Kanzaki's, but not both.

Question: Which one of the following accurately represents an order in which the deliveries could occur, from first to last?

Harris's, Figueroa's, Leacock's, Ginsberg's, Kanzaki's, Malpighi's

Leacock's, Harris's, Figueroa's, Ginsberg's, Malpighi's, Kanzaki's

Malpighi's, Figueroa's, Harris's, Ginsberg's, Leacock's, Kanzaki's

Malpighi's, Figueroa's, Kanzaki's, Harris's, Ginsberg's, Leacock's

Malpighi's, Figueroa's, Ginsberg's, Kanzaki's, Harris's, Leacock's


Question: If Figueroa's delivery is fourth, then which one of the following must be true?

Ginsberg's delivery is fifth.
Harris's delivery is second.
Harris's delivery is third.
Leacock's delivery is second.
Malpighi's delivery is first.


Question: If Malpighi's delivery is first and Leacock's delivery is third, then which one of the following must be true?

Figueroa's delivery is second.
Harris's delivery is second.
Harris's delivery is fourth.
Kanzaki's delivery is fifth.
Kanzaki's delivery is last.


Question: Which one of the following must be true?

Figueroa's delivery is earlier than Leacock's.

Ginsberg's delivery is earlier than Leacock's.

Harris's delivery is earlier than Kanzaki's.

Leacock's delivery is earlier than Ginsberg's.

Malpighi's delivery is earlier than Harris's.


Question: If Kanzaki's delivery is earlier than Leacock's, then which one of the following could be true?

Figueroa's delivery is first.
Ginsberg's delivery is third.
Harris's delivery is third.
Leacock's delivery is fifth.
Malpighi's delivery is second.


Question: Which one of the following must be false?

Figueroa's delivery is first.
Ginsberg's delivery is fifth.
Harris's delivery is third.
Leacock's delivery is second.
Malpighi's delivery is fourth.


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

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

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

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

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

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

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


Question: Which one of the following could be true?

West is the only performer who signs with Star Agency.

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

Xavier signs with the same agency as Zinser.

Zinser is the only performer who signs with Star Agency.

Three of the performers sign with Fame Agency.


Question: Which one of the following must be true?

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

Fame Agency signs at most two of the performers.

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

Traugott signs with the same agency as West.


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

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


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

Premier Agency signs exactly one performer.

Star Agency signs exactly three of the performers.

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


A competition is being held to select a design for Yancy College's new student union building. Each of six architects—Green, Jackson, Liu, Mertz, Peete, and Valdez—has submitted exactly one design. There are exactly six designs, and they are presented one at a time to the panel of judges, each design being presented exactly once, consistent with the following conditions: Mertz's design is presented at some time before Liu's and after Peete's. Green's design is presented either at some time before Jackson's or at some time after Liu's, but not both. Valdez's design is presented either at some time before Green's or at some time after Peete's, but not both.

Question: Which one of the following could be the order in which the designs are presented, from first to last?

Jackson's, Peete's, Mertz's, Green's, Valdez's, Liu's

Peete's, Jackson's, Liu's, Mertz's, Green's, Valdez's

Peete's, Mertz's, Jackson's, Liu's, Green's, Valdez's

Peete's, Mertz's, Valdez's, Green's, Liu's, Jackson's

Valdez's, Liu's, Jackson's, Peete's, Mertz's, Green's


Question: Mertz's design CANNOT be presented


Question: If Liu's design is presented sixth, then which one of the following must be true?

Green's design is presented at some time before Jackson's.

Jackson's design is presented at some time before Mertz's.

Peete's design is presented at some time before Green's.

Peete's design is presented at some time before Valdez's.

Valdez's design is presented at some time before Green's.


Question: If Jackson's design is presented at some time before Mertz's, then each of the following could be true EXCEPT:

Jackson's design is presented second.
Peete's design is presented third.
Peete's design is presented fourth.
Jackson's design is presented fifth.
Liu's design is presented fifth.


Question: Which one of the following designs CANNOT be the design presented first?

Green's Jackson's Liu's Peete's Valdez's


Question: Which one of the following could be an accurate partial list of the architects, each matched with his or her design's place in the order in which the designs are presented?

second: Green; third: Peete; fourth: Jackson

second: Mertz; fifth: Green; sixth: Jackson

fourth: Peete; fifth: Liu; sixth: Jackson

fourth: Valdez; fifth: Green; sixth: Liu


Detectives investigating a citywide increase in burglaries questioned exactly seven suspects—S, T, V, W, X, Y, and Z—each on a different one of seven consecutive days. Each suspect was questioned exactly once. Any suspect who confessed did so while being questioned. The investigation conformed to the following: T was questioned on day three. The suspect questioned on day four did not confess. S was questioned after W was questioned. Both X and V were questioned after Z was questioned. No suspects confessed after W was questioned. Exactly two suspects confessed after T was questioned.

Question: Which one of the following could be true?

X was questioned on day one.
V was questioned on day two.
Z was questioned on day four.
W was questioned on day five.
S was questioned on day six.


Question: If Z was the second suspect to confess, then each of the following statements could be true EXCEPT:

T confessed.
T did not confess.
V did not confess.
X confessed.
Y did not confess.


Question: If Y was questioned after V but before X, then which one of the following could be true?

V did not confess.
Y confessed.
X did not confess.
X was questioned on day four.
Z was questioned on day two.


Question: Which one of the following suspects must have been questioned before T was questioned?


Question: If X and Y both confessed, then each of the following could be true EXCEPT:

V confessed.
X was questioned on day five.
Y was questioned on day one.
Z was questioned on day one.
Z did not confess.


Question: If neither X nor V confessed, then which one of the following must be true?

T confessed.
V was questioned on day two.
X was questioned on day four.
Y confessed.
Z did not confess.


The three highest-placing teams in a high school debate tournament are the teams from Fairview, Gillom, and Hilltop high schools. Each team has exactly two members. The individuals on these three teams are Mei, Navarro, O'Rourke, Pavlovich, Sethna, and Tsudama. The following is the case: Sethna is on the team from Gillom High. Tsudama is on the second-place team. Mei and Pavlovich are not on the same team. Pavlovich's team places higher than Navarro's team. The team from Gillom High places higher than the team from Hilltop High.

Question: Which one of the following could be an accurate list of the members of each of the three highest-placing teams?

first place: Mei and O'Rourke second place: Pavlovich and Sethna third place: Navarro and Tsudama

first place: Mei and Pavlovich second place: Sethna and Tsudama third place: Navarro and O'Rourke

first place: Navarro and Sethna second place: Pavlovich and Tsudama third place: Mei and O'Rourke

first place: O'Rourke and Pavlovich second place: Navarro and Tsudama third place: Mei and Sethna

first place: Pavlovich and Sethna second place: O'Rourke and Tsudama third place: Mei and Navarro


Question: If Pavlovich is on the team from Hilltop High, then which one of the following could be true?

O'Rourke is on the first-place team.
Pavlovich is on the first-place team.
Mei is on the second-place team.
Navarro is on the second-place team.
Sethna is on the second-place team.


Question: If O'Rourke is on the second-place team, then which one of the following could be true?

Navarro is on the team from Fairview High.

O'Rourke is on the team from Gillom High.

Pavlovich is on the team from Hilltop High.

Tsudama is on the team from Gillom High.


Question: If Pavlovich and Tsudama are teammates, then for how many of the individuals can it be exactly determined where his or her team places?


Question: If Mei is on a team that places higher than the Hilltop team, then which one of the following could be true?

The Fairview team places first.
The Gillom team places second.
Navarro is on the second-place team.
O'Rourke is on the first-place team.
Pavlovich is on the first-place team.


Question: Sethna's teammate could be any one of the following EXCEPT:


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

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

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


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

Felipe and Grant are the only men on stage.

Grant and Hassan are the only men on stage.

Jaclyn and Keiko are the only women on stage.


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

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


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


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


A critic has prepared a review of exactly six music CDs—Headstrong, In Flight, Nice, Quasi, Reunion, and Sounds Good. Each CD received a rating of either one, two, three, or four stars, with each CD receiving exactly one rating. Although the ratings were meant to be kept secret until the review was published, the following facts have been leaked to the public: For each of the ratings, at least one but no more than two of the CDs received that rating. Headstrong received exactly one more star than Nice did. Either Headstrong or Reunion received the same number of stars as In Flight did. At most one CD received more stars than Quasi did.

Question: Which one of the following could be an accurate matching of ratings to the CDs that received those ratings?

one star: In Flight, Reunion; two stars: Nice; three stars: Headstrong; four stars: Quasi, Sounds Good

one star: In Flight, Reunion; two stars: Quasi, Sounds Good; three stars: Nice; four stars: Headstrong

one star: Nice; two stars: Headstrong; three stars: In Flight, Sounds Good; four stars: Quasi, Reunion

one star: Nice, Sounds Good; two stars: In Flight, Reunion; three stars: Quasi; four stars: Headstrong

one star: Sounds Good; two stars: Reunion; three stars: Nice, Quasi; four stars: Headstrong, In Flight


Question: If Headstrong is the only CD that received a rating of two stars, then which one of the following must be true?

In Flight received a rating of three stars.

Sounds Good received a rating of one star.


Question: If Reunion received the same rating as Sounds Good, then which one of the following must be true?

Headstrong received a rating of two stars.

In Flight received a rating of three stars.

Sounds Good received a rating of one star.


Question: If Nice and Reunion each received a rating of one star, then which one of the following could be true?

Headstrong received a rating of three stars.

Headstrong received a rating of four stars.

In Flight received a rating of three stars.

Sounds Good received a rating of two stars.

Sounds Good received a rating of three stars.


Question: Which one of the following CANNOT be true?

Quasi is the only CD that received a rating of three stars.

Quasi is the only CD that received a rating of four stars.

Reunion is the only CD that received a rating of one star.

Reunion is the only CD that received a rating of two stars.

Reunion is the only CD that received a rating of three stars.


Question: If Reunion is the only CD that received a rating of one star, then which one of the following could be true?

Headstrong received a rating of four stars.

In Flight received a rating of two stars.

Sounds Good received a rating of two stars.


Question: Which one of the following CANNOT have received a rating of four stars?

Headstrong
In Flight
Quasi
Reunion
Sounds Good


A cake has exactly six layers—lemon, marzipan, orange, raspberry, strawberry, and vanilla. There is exactly one bottom layer (the first layer), and each succeeding layer (from second through sixth) completely covers the layer beneath it. The following conditions must apply: The raspberry layer is neither immediately above nor immediately below the strawberry layer. The marzipan layer is immediately above the lemon layer. The orange layer is above the marzipan layer but below the strawberry layer.

Question: Which one of the following could be an accurate list of the layers of the cake, from bottom to top?

lemon, marzipan, orange, strawberry, vanilla, raspberry

lemon, marzipan, orange, strawberry, raspberry, vanilla

marzipan, lemon, raspberry, vanilla, orange, strawberry

raspberry, lemon, marzipan, vanilla, strawberry, orange

raspberry, orange, lemon, marzipan, strawberry, vanilla


Question: If the strawberry layer is not immediately above the orange layer, then which one of the following could be true?

The raspberry layer is immediately above the vanilla layer.

The raspberry layer is immediately above the orange layer.

The raspberry layer is immediately below the marzipan layer.

The raspberry layer is the second layer.


Question: If the strawberry layer is not the top layer, then which one of the following is a complete and accurate list of the layers that could be the vanilla layer?

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


Question: If the lemon layer is third, then which one of the following could be true?

The vanilla layer is immediately above the raspberry layer.

The orange layer is not immediately above the marzipan layer.

The raspberry layer is above the marzipan layer.

The strawberry layer is not the top layer.


Question: Which one of the following could be an accurate list of the two lowest layers of the cake, listed in order from the bottom up?

lemon, raspberry
vanilla, raspberry
marzipan, raspberry
raspberry, marzipan
raspberry, strawberry


A panel reviews six contract bids—H, J, K, R, S, and T. No two bids have the same cost. Exactly one of the bids is accepted. The following conditions must hold: The accepted bid is either K or R and is either the second or the third lowest in cost. H is lower in cost than each of J and K. If J is the fourth lowest in cost, then J is lower in cost than each of S and T. If J is not the fourth lowest in cost, then J is higher in cost than each of S and T. Either R or S is the fifth lowest in cost.

Question: Which one of the following could be an accurate list of the bids in order from lowest to highest in cost?

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


Question: Which one of the following bids CANNOT be the fourth lowest in cost?


Question: Which one of the following bids CANNOT be the second lowest in cost?


Question: If R is the accepted bid, then which one of the following must be true?

T is the lowest in cost.
K is the second lowest in cost.
R is the third lowest in cost.
S is the fifth lowest in cost.
J is the highest in cost.


Question: Which one of the following must be true?

H is lower in cost than S.
H is lower in cost than T.
K is lower in cost than J.
S is lower in cost than J.
S is lower in cost than K.


Question: If R is the lowest in cost, then which one of the following could be false?

J is the highest in cost.
S is the fifth lowest in cost.
K is the third lowest in cost.
H is the second lowest in cost.
K is the accepted bid.


There are exactly six law students—Gambini, Little, Mitchum, Richardson, Saito, and Veracruz—in a trial advocacy class. The class is divided into three trial teams—team 1, team 2, and team 3—of exactly two students each. Each student is on exactly one of the teams. Each student prepares exactly one of either the opening argument or the final argument for his or her team. The teams must be formed according to the following specifications: Mitchum is on the same team as either Gambini or Veracruz. Little prepares an opening argument. Either Gambini or Richardson, but not both, prepares a final argument.

Question: Which one of the following could be the composition of each team and the argument each student prepares?

team 1: Little, opening; Gambini, final team 2: Veracruz, opening; Mitchum, final team 3: Saito, opening; Richardson, final

team 1: Mitchum, opening; Gambini, final team 2: Veracruz, opening; Little, final team 3: Richardson, opening; Saito, final

team 1: Richardson, opening; Gambini, final team 2: Mitchum, opening; Saito, final team 3: Little, opening; Veracruz, final

team 1: Gambini, opening; Mitchum, final team 2: Little, opening; Richardson, final team 3: Veracruz, opening; Saito, final

team 1: Gambini, opening; Mitchum, final team 2: Richardson, opening; Saito, final team 3: Little, opening; Veracruz, final


Question: If Gambini is on the same team as Mitchum, and if Gambini prepares the final argument for that team, then which one of the following could be true?

Little is on the same team as Veracruz, who prepares the opening argument for the team.

Richardson is on the same team as Saito, who prepares the opening argument for the team.

Richardson is on the same team as Saito, who prepares the final argument for the team.

Saito is on the same team as Veracruz, who prepares the opening argument for the team.

Saito is on the same team as Veracruz, who prepares the final argument for the team.


Question: Which one of the following could be true?

Gambini, who prepares a final argument, is on the same team as Richardson.

Gambini, who prepares a final argument, is on the same team as Veracruz.

Gambini, who prepares an opening argument, is on the same team as Little.

Little, who prepares an opening argument, is on the same team as Mitchum.

Mitchum, who prepares an opening argument, is on the same team as Saito.


Question: If Richardson is on the same team as Veracruz, then for exactly how many of the students can it be determined which of the arguments he or she prepares?


Question: If Little is on the same team as Richardson, then which one of the following must be true?

Saito is on the same team as Veracruz.
Gambini is on the same team as Mitchum.
Mitchum prepares a final argument.
Veracruz prepares a final argument.
Gambini prepares an opening argument.


Question: If Saito prepares an opening argument, then which one of the following pairs of students could be on the same team as each other?

Gambini and Little
Gambini and Saito
Little and Veracruz
Mitchum and Veracruz
Richardson and Veracruz


While on vacation, Sukanya receives several e-mail messages from work, each message from one of three associates: Hilary, Jerome, and Lula. Sukanya receives at least one and no more than two messages from each of them. Sukanya receives each message on the day it is sent. No more than one message is sent each day. The messages are received in a manner consistent with the following: The first message is not from Lula. Both the first and last messages are from the same person. Exactly once Sukanya receives a message from Jerome on the day after receiving one from Hilary. Of the first three messages, exactly one is from Jerome.

Question: Which one of the following could be an accurate list of the e-mail messages Sukanya receives, identified by the person each message is from and listed in the order she receives them?

Lula, Hilary, Jerome, Hilary, Jerome, Lula

Hilary, Lula, Lula, Jerome, Jerome, Hilary


Question: What is the maximum possible number of e-mail messages Sukanya receives after Jerome's first message but before Hilary's first message?


Question: If Sukanya receives exactly four e-mail messages, then which one of the following must be true?

Exactly one of the messages is from Lula.

Exactly two of the messages are from Jerome.


Question: Which one of the following e-mail messages CANNOT be from Lula?

the fifth message (if there is a fifth one)

the sixth message (if there is a sixth one)


Question: If Sukanya receives six e-mail messages, the fifth of which is from Lula, which one of the following must be true?

The first message is from Jerome.
The second message is from Lula.
The third message is from Hilary.
The fourth message is from Jerome.
The sixth message is from Lula.


Question: If Sukanya receives two e-mail messages from Lula, what is the maximum possible number of e-mail messages Sukanya receives after Lula's first message but before Lula's last message?


Mercotek carried out a study to compare the productivity of its night shift with that of its day shift. Every week the company's six crews—F, G, H, R, S, and T—were ranked from first (most productive) to sixth (least productive). There were no ties. For any given week, either G and T were the two night-shift crews or else S and H were—the four other crews were the day-shift crews for that week. The following relationships held for every week of the study: F is more productive than G. R is more productive than S. R is more productive than T. S is more productive than H. G is more productive than T.

Question: Which one of the following could be an accurate ranking of all the crews, in order from first to sixth, for a given week of the study?

F, G, T, R, S, H
F, R, G, T, H, S
G, R, T, S, H, F
R, F, G, S, H, T
R, S, H, T, F, G


Question: If F is ranked third for a given week of the study, then which one of the following could also be true of that week?

G ranks second.
H ranks fourth.
R ranks second.
S ranks fourth.
T ranks fourth.


Question: Which one of the following CANNOT be the crew ranked fifth for any given week of the study?


Question: For any given week of the study, the ranking of all the crews is completely determined if which one of the following is true?

F ranks second that week.
G ranks fifth that week.
H ranks third that week.
R ranks third that week.
S ranks third that week.


Question: If the night-shift crews rank fifth and sixth for a given week of the study, then which one of the following could also be true of that week?

G ranks fourth.
H ranks fifth.
R ranks third.
S ranks fourth.
T ranks fifth.


Question: Which one of the following is a complete and accurate list of the crews that CANNOT be ranked third for any given week of the study?


A shuttle van stops exactly four times—once at Fundy, once at Los Altos, once at Mineola, and once at Simcoe—not necessarily in that order. The van starts with exactly four passengers on board—Greg, Jasmine, Rosa, and Vijay—each of whom gets off at a different stop. The following conditions hold: Los Altos is the first or second stop. Rosa is still on board when the van reaches Mineola. Jasmine is on board longer than Vijay. If Jasmine is still on board when the van reaches Fundy, then Greg is still on board when the van reaches Simcoe; otherwise, Greg is not still on board when the van reaches Simcoe.

Question: Which one of the following could be a complete and accurate matching of stops, listed in the order in which the van stops at them, to the passengers who get off at them?

Los Altos: Greg Mineola: Vijay Fundy: Jasmine Simcoe: Rosa

Simcoe: Vijay Mineola: Greg Fundy: Rosa Los Altos: Jasmine

Los Altos: Jasmine Mineola: Vijay Fundy: Greg Simcoe: Rosa

Los Altos: Rosa Mineola: Vijay Fundy: Jasmine Simcoe: Greg

Los Altos: Vijay Fundy: Jasmine Mineola: Rosa Simcoe: Greg


Question: If Mineola is the first stop, which one of the following is a complete and accurate list of the passengers who could possibly get off there?

Rosa
Greg, Rosa
Greg, Vijay
Greg, Rosa, Vijay
Jasmine, Rosa, Vijay


Question: If Fundy is the first stop, then which one of the following could accurately list the passengers in order from first to last off?

Greg, Vijay, Jasmine, Rosa
Rosa, Vijay, Greg, Jasmine
Vijay, Greg, Rosa, Jasmine
Vijay, Jasmine, Greg, Rosa
Vijay, Rosa, Jasmine, Greg


Question: Which one of the following must be true if Greg is still on board both when the van reaches Los Altos and when it reaches Simcoe, not necessarily in that order, assuming he is the second one off the van?

Vijay is on board when the van reaches Simcoe.

Vijay is on board when the van reaches Los Altos.

Rosa is on board when the van reaches Simcoe.

Rosa is on board when the van reaches Fundy.

Jasmine is on board when the van reaches Mineola.


Question: If Greg is not on board when the van reaches Simcoe, then which one of the following must be false?

Greg is on board when the van reaches Fundy.

Jasmine is on board when the van reaches Mineola.

Rosa is on board when the van reaches Fundy.

Vijay is on board when the van reaches Fundy.

Vijay is on board when the van reaches Mineola.


Individual hour-long auditions will be scheduled for each of six saxophonists—Fujimura, Gabrieli, Herman, Jackson, King, and Lauder. The auditions will all take place on the same day. Each audition will begin on the hour, with the first beginning at 1 P.M. and the last at 6 P.M. The schedule of auditions must conform to the following conditions: Jackson auditions earlier than Herman does. Gabrieli auditions earlier than King does. Gabrieli auditions either immediately before or immediately after Lauder does. Exactly one audition separates the auditions of Jackson and Lauder.

Question: Which one of the following is an acceptable schedule for the auditions, listed in order from 1 P.M. through 6 P.M.?

Fujimura, Gabrieli, King, Jackson, Herman, Lauder

Fujimura, King, Lauder, Gabrieli, Jackson, Herman

Fujimura, Lauder, Gabrieli, King, Jackson, Herman

Herman, Jackson, Gabrieli, Lauder, King, Fujimura

Jackson, Gabrieli, Lauder, Herman, King, Fujimura


Question: Which one of the following must be true?

Lauder is scheduled to audition earlier than Herman.

Lauder is scheduled to audition earlier than King.

Jackson's audition is scheduled to begin at either 1 P.M. or 5 P.M.

Fujimura and Jackson are not scheduled to audition in consecutive hours.

Gabrieli and King are not scheduled to audition in consecutive hours.


Question: The earliest King's audition could be scheduled to begin is


Question: The order in which the saxophonists are scheduled to audition is completely determined if which one of the following is true?

Herman's audition is scheduled to begin at 4 P.M.

Jackson's audition is scheduled to begin at 1 P.M.

Jackson's audition is scheduled to begin at 5 P.M.

Lauder's audition is scheduled to begin at 1 P.M.

Lauder's audition is scheduled to begin at 2 P.M.


Question: If Fujimura's audition is not scheduled to begin at 1 P.M., which one of the following could be true?

Herman's audition is scheduled to begin at 6 P.M.

Gabrieli's audition is scheduled to begin at 5 P.M.

Herman's audition is scheduled to begin at 3 P.M.

Jackson's audition is scheduled to begin at 2 P.M.

Jackson's audition is scheduled to begin at 5 P.M.


Question: Which one of the following must be true?

Gabrieli's audition is scheduled to begin before 5 P.M.

Herman's audition is scheduled to begin after 2 P.M.

Herman's audition is scheduled to begin before 6 P.M.

King's audition is scheduled to begin before 6 P.M.

Lauder's audition is scheduled to begin before 5 P.M.


Four people—Grace, Heather, Josh, and Maria—will help each other move exactly three pieces of furniture—a recliner, a sofa, and a table. Each piece of furniture will be moved by exactly two of the people, and each person will help move at least one of the pieces of furniture, subject to the following constraints: Grace helps move the sofa if, but only if, Heather helps move the recliner. If Josh helps move the table, then Maria helps move the recliner. No piece of furniture is moved by Grace and Josh together.

Question: Which one of the following could be an accurate matching of each piece of furniture to the two people who help each other move it?

recliner: Grace and Maria; sofa: Heather and Josh; table: Grace and Heather

recliner: Grace and Maria; sofa: Heather and Maria; table: Grace and Josh

recliner: Heather and Josh; sofa: Grace and Heather; table: Josh and Maria

recliner: Heather and Josh; sofa: Heather and Maria; table: Grace and Maria

recliner: Josh and Maria; sofa: Grace and Heather; table: Grace and Maria


Question: If Josh and Maria help each other move the recliner, then which one of the following must be true?

Heather helps move the sofa.
Josh helps move the sofa.
Maria helps move the sofa.
Grace helps move the table.
Heather helps move the table.


Question: If Heather helps move each of the pieces of furniture, then which one of the following could be true?

Grace helps move the recliner.
Maria helps move the recliner.
Josh helps move the sofa.
Maria helps move the sofa.
Grace helps move the table.


Question: Which one of the following could be a pair of people who help each other move both the recliner and the table?

Grace and Josh
Grace and Maria
Heather and Josh
Heather and Maria
Josh and Maria


Question: If Josh and Maria help each other move the sofa, then which one of the following could be true?

Heather and Josh help each other move the recliner.

Heather and Maria help each other move the recliner.

Grace and Josh help each other move the table.

Grace and Maria help each other move the table.

Heather and Maria help each other move the table.


A town has exactly two public parks—Graystone Park and Landing Park—which are to be planted with North American trees. There are exactly four varieties of trees available—maples, oaks, sycamores, and tamaracks. The planting of the trees must be in accord with the following: Each of the parks is planted with exactly three of the varieties. At least one of the parks is planted with both maples and sycamores. Any park that is planted with oaks will also be planted with tamaracks. Graystone Park is planted with maples.

Question: Which one of the following could be a complete and accurate list of the varieties of trees planted in each of the parks?

Graystone Park: maples, oaks, sycamores Landing Park: maples, oaks, sycamores

Graystone Park: maples, oaks, tamaracks Landing Park: maples, oaks, tamaracks

Graystone Park: maples, sycamores, tamaracks Landing Park: maples, oaks, sycamores

Graystone Park: maples, sycamores, tamaracks Landing Park: maples, oaks, tamaracks

Graystone Park: oaks, sycamores, tamaracks Landing Park: maples, sycamores, tamaracks


Question: Which one of the following must be true?

Graystone Park is planted with sycamores.

The number of the parks planted with maples is equal to the number of the parks planted with sycamores.

The number of the parks planted with maples is greater than the number of the parks planted with sycamores.


Question: If both parks are planted with sycamores, which one of the following could be true?

The number of the parks planted with maples is equal to the number of the parks planted with oaks.

The number of the parks planted with maples is greater than the number of the parks planted with sycamores.

The number of the parks planted with oaks is equal to the number of the parks planted with sycamores.

Graystone Park is planted with both maples and oaks.

Landing Park is planted with both maples and oaks.


Question: Which one of the following must be false?

Exactly one of the parks is planted with maples.

Exactly one of the parks is planted with sycamores.


Question: Which one of the following could be true?

The number of the parks planted with oaks is equal to the number of the parks planted with tamaracks.

The number of the parks planted with oaks is greater than the number of the parks planted with sycamores.

Exactly one of the parks is planted with tamaracks.

Both parks contain exactly the same three varieties of trees as each other.


Five executives—Quinn, Rodriguez, Sasada, Taylor, and Vandercar—are being scheduled to make site visits to three of their company's manufacturing plants—Farmington, Homestead, and Morningside. Each site will be visited by at least one of the executives and each executive will visit just one site. Each of the three site visits will take place on a different day. The schedule of site visits must conform to the following requirements: The Farmington visit must take place before the Homestead visit. The Farmington visit will include only one of the executives. The site visit that includes Quinn must take place before any site visit that includes either Rodriguez or Taylor. The site visit that includes Sasada cannot take place after any site visit that includes Vandercar.

Question: Which one of the following could be the executives included in each of the site visits, with the sites listed in the order in which they are visited?

Farmington: Quinn Homestead: Rodriguez, Sasada Morningside: Taylor, Vandercar

Farmington: Quinn Homestead: Rodriguez, Vandercar Morningside: Sasada, Taylor

Farmington: Rodriguez Morningside: Quinn, Taylor Homestead: Sasada, Vandercar

Homestead: Sasada Farmington: Quinn Morningside: Rodriguez, Taylor, Vandercar

Morningside: Quinn Farmington: Rodriguez, Sasada Homestead: Taylor, Vandercar


Question: If the second of the three site visits includes both Rodriguez and Taylor, which one of the following must be true?

The second of the three site visits includes Sasada.

The second of the three site visits includes exactly three of the executives.


Question: If one of the site visits includes both Quinn and Sasada, which one of the following could be true?

The Farmington visit is the first of the three site visits.

The Homestead visit is the second of the three site visits.

One of the site visits includes only Vandercar.

The second of the three site visits includes Sasada.

The second of the three site visits includes exactly two of the executives.


Question: The executives who visit Homestead CANNOT be

Quinn and Vandercar only
Rodriguez and Taylor only
Sasada and Taylor only
Quinn, Sasada, and Vandercar
Rodriguez, Sasada, and Taylor


Question: If the Morningside visit includes both Quinn and Vandercar, which one of the following could be true?

One of the site visits includes both Rodriguez and Sasada.

The second of the three site visits includes exactly three of the executives.

The last of the three site visits includes exactly three of the executives.

The Homestead visit takes place earlier than the Morningside visit.

The Morningside visit takes place earlier than the Farmington visit.


Question: Which one of the following must be true?

The Farmington visit takes place earlier than the Morningside visit.

The site visit that includes Vandercar takes place earlier than the site visit that includes Rodriguez.

One of the first two site visits includes Sasada.

The second of the three site visits includes at least two of the executives.

At least one of the first two site visits includes only one of the executives.


Question: If the Farmington visit includes Sasada, which one of the following must be true?

One of the site visits includes exactly three of the executives.

The last of the three site visits includes Rodriguez.

The site visit that includes Vandercar also includes Quinn.


On a particular Saturday, a student will perform six activities—grocery shopping, hedge trimming, jogging, kitchen cleaning, laundry, and motorbike servicing. Each activity will be performed once, one at a time. The order in which the activities are performed is subject to the following conditions: Grocery shopping has to be immediately after hedge trimming. Kitchen cleaning has to be earlier than grocery shopping. Motorbike servicing has to be earlier than laundry. Motorbike servicing has to be either immediately before or immediately after jogging.

Question: Which one of the following could be the order, from first to last, of the student's activities?

jogging, kitchen cleaning, hedge trimming, grocery shopping, motorbike servicing, laundry

jogging, motorbike servicing, laundry, hedge trimming, grocery shopping, kitchen cleaning

kitchen cleaning, hedge trimming, grocery shopping, laundry, motorbike servicing, jogging

kitchen cleaning, jogging, motorbike servicing, laundry, hedge trimming, grocery shopping

motorbike servicing, jogging, laundry, hedge trimming, kitchen cleaning, grocery shopping


Question: Which one of the following activities CANNOT be third?

grocery shopping
hedge trimming
jogging
kitchen cleaning
motorbike servicing


Question: Which one of the following CANNOT be true?

Hedge trimming is fourth.
Jogging is fourth.
Kitchen cleaning is second.
Laundry is third.
Motorbike servicing is second.


Question: Which one of the following activities CANNOT be fifth?

grocery shopping
hedge trimming
jogging
laundry
motorbike servicing


Question: Which one of the following, if substituted for the condition that motorbike servicing has to be earlier than laundry, would have the same effect in determining the order of the student's activities?

Laundry has to be one of the last three activities.

Laundry has to be either immediately before or immediately after jogging.

Laundry has to be earlier than hedge trimming.


Each of exactly three actors—Gombrich, Otto, and Raines—auditions for parts on exactly two of the following days of a particular week: Wednesday, Thursday, Friday, and Saturday. On each of these days at least one of the actors auditions for parts. The order of that week's auditions must meet the following conditions: The first day on which Otto auditions is some day before the first day on which Raines auditions. There is at least one day on which both Gombrich and Raines audition. At least one of the actors auditions on both Thursday and Saturday.

Question: Which one of the following could be an accurate matching of the actors to the days on which they audition?

Gombrich: Thursday, Friday Otto: Wednesday, Saturday Raines: Friday, Saturday

Gombrich: Thursday, Saturday Otto: Wednesday, Friday Raines: Friday, Saturday

Gombrich: Friday, Saturday Otto: Thursday, Saturday Raines: Wednesday, Friday

Gombrich: Wednesday, Thursday Otto: Wednesday, Saturday Raines: Thursday, Saturday

Gombrich: Wednesday, Friday Otto: Wednesday, Thursday Raines: Thursday, Saturday


Question: If Otto auditions on both Thursday and Saturday, then Gombrich could audition on both

Wednesday and Thursday
Wednesday and Friday
Thursday and Friday
Thursday and Saturday
Friday and Saturday


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

Gombrich's last audition is on Thursday.


Question: Which one of the following pairs of days CANNOT be the two days on which Otto auditions?

Wednesday and Thursday
Wednesday and Friday
Wednesday and Saturday
Thursday and Friday
Thursday and Saturday


Question: Which one of the following could be true?

Otto auditions on Friday and on Saturday.

Raines auditions on Wednesday and on Friday.


Question: If Gombrich auditions on both Wednesday and Saturday, then which one of the following could be true?

Otto auditions on both Wednesday and Thursday.

Otto auditions on both Wednesday and Friday.

Otto auditions on both Wednesday and Saturday.

Raines auditions on both Wednesday and Saturday.

Raines auditions on both Thursday and Friday.


Each of seven toy dinosaurs—an iguanadon, a lambeosaur, a plateosaur, a stegosaur, a tyrannosaur, an ultrasaur, and a velociraptor—is completely colored either green, mauve, red, or yellow. A display is to consist entirely of exactly five of these toys. The display must meet the following specifications: Exactly two mauve toys are included. The stegosaur is red and is included. The iguanadon is included only if it is green. The plateosaur is included only if it is yellow. The velociraptor is included only if the ultrasaur is not. If both the lambeosaur and the ultrasaur are included, at least one of them is not mauve.

Question: Which one of the following could be the toys included in the display?

the lambeosaur, the plateosaur, the stegosaur, the ultrasaur, the velociraptor

the lambeosaur, the plateosaur, the stegosaur, the tyrannosaur, the ultrasaur

the iguanadon, the lambeosaur, the plateosaur, the stegosaur, the ultrasaur

the iguanadon, the lambeosaur, the plateosaur, the tyrannosaur, the velociraptor

the iguanadon, the lambeosaur, the stegosaur, the ultrasaur, the velociraptor


Question: If the tyrannosaur is not included in the display, then the display must contain each of the following EXCEPT:

a green iguanadon
a mauve velociraptor
a mauve lambeosaur
a mauve ultrasaur
a yellow plateosaur


Question: Which one of the following is a pair of toys that could be included in the display together?

a green lambeosaur and a mauve velociraptor

a green lambeosaur and a yellow tyrannosaur

a green lambeosaur and a yellow ultrasaur

a yellow tyrannosaur and a green ultrasaur

a yellow tyrannosaur and a red velociraptor


Question: If the display includes a yellow tyrannosaur, then which one of the following must be true?

The iguanadon is included in the display.

The plateosaur is not included in the display.

The display includes two yellow toy dinosaurs.

The display contains a green lambeosaur.

The display contains a mauve velociraptor.


Question: If both the iguanadon and the ultrasaur are included in the display, then the display must contain which one of the following?

a mauve tyrannosaur
a mauve ultrasaur
a yellow lambeosaur
a yellow plateosaur
a yellow ultrasaur


Question: If the display includes two green toys, then which one of the following could be true?

There is exactly one yellow toy included in the display.

The tyrannosaur is included in the display and it is green.

Neither the lambeosaur nor the velociraptor is included in the display.

Neither the tyrannosaur nor the velociraptor is included in the display.

Neither the ultrasaur nor the velociraptor is included in the display.


A charitable foundation awards grants in exactly four areas—medical services, theater arts, wildlife preservation, and youth services—each grant being in one of these areas. One or more grants are awarded in each of the four quarters of a calendar year. Additionally, over the course of a calendar year, the following must obtain: Grants are awarded in all four areas. No more than six grants are awarded. No grants in the same area are awarded in the same quarter or in consecutive quarters. Exactly two medical services grants are awarded. A wildlife preservation grant is awarded in the second quarter.

Question: Which one of the following is a possible allocation of grants in a particular calendar year?

first quarter: theater arts second quarter: wildlife preservation third quarter: medical services, youth services fourth quarter: theater arts

first quarter: wildlife preservation second quarter: medical services third quarter: theater arts fourth quarter: medical services, youth services

first quarter: youth services second quarter: wildlife preservation, medical services third quarter: theater arts fourth quarter: medical services, youth services

first quarter: medical services, theater arts second quarter: theater arts, wildlife preservation third quarter: youth services fourth quarter: medical services

first quarter: medical services, theater arts second quarter: wildlife preservation, youth services third quarter: theater arts fourth quarter: medical services, youth services


Question: Which one of the following CANNOT be true in a particular calendar year?

In each of the two quarters in which a medical services grant is awarded, no other grant is awarded.

Exactly two theater arts grants are awarded, one in the second quarter and one in the fourth quarter.

Exactly two youth services grants are awarded, one in the first quarter and one in the third quarter.

Two wildlife preservation grants and two youth services grants are awarded.

Three grants are awarded in the fourth quarter.


Question: If a wildlife preservation grant and a youth services grant are awarded in the same quarter of a particular calendar year, then any of the following could be true that year EXCEPT:

A medical services grant is awarded in the second quarter.

A theater arts grant is awarded in the first quarter.

A theater arts grant is awarded in the second quarter.

A wildlife preservation grant is awarded in the fourth quarter.

A youth services grant is awarded in the third quarter.


Question: If exactly two grants are awarded in just one of the four quarters of a particular calendar year, then which one of the following could be true that year?

Neither a medical services grant nor a youth services grant is awarded in the first quarter.

A wildlife preservation grant is awarded in the fourth quarter.

Both a youth services grant and a theater arts grant are awarded in the first quarter.

A youth services grant is awarded in the first quarter and a theater arts grant is awarded in the second quarter.


Question: Which one of the following CANNOT be true in a particular calendar year?

Three grants are awarded in a quarter, none of which is a medical services grant.

Exactly two grants are awarded in the first quarter and exactly two in the third quarter.

Exactly two grants are awarded in the first quarter and exactly two in the fourth quarter.

Theater arts grants are awarded in the first and fourth quarters, and no other grants are awarded in those two quarters.

Wildlife preservation grants are awarded in the second and fourth quarters, and no other grants are awarded in those two quarters.


Question: It is fully determined which grants are awarded for each quarter of a particular calendar year if which one of the following is true that year?

Three grants are awarded in the first quarter.

Three grants are awarded in the second quarter.

Three grants are awarded in the third quarter.


Historical records show that over the course of five consecutive years—601, 602, 603, 604, and 605—a certain emperor began construction of six monuments: F, G, H, L, M, and S. A historian is trying to determine the years in which the individual monuments were begun. The following facts have been established: L was begun in a later year than G, but in an earlier year than F. H was begun no earlier than 604. M was begun earlier than 604. Two of the monuments were begun in 601, and no other monument was begun in the same year as any of the other monuments.

Question: Which one of the following could be an accurate matching of monuments to the years in which they were begun?


Question: What is the latest year in which L could have been begun?


Question: The years in which each of the monuments were begun can be completely determined if which one of the following is discovered to be true?

F was begun in 603.
G was begun in 602.
H was begun in 605.
M was begun in 602.
S was begun in 604.


Question: Which one of the following must be true?

F was begun in a later year than M.
F was begun in a later year than S.
H was begun in a later year than F.
H was begun in a later year than S.
M was begun in a later year than G.


Question: L must be the monument that was begun in 602 if which one of the following is true?

F was begun in 605.
G was begun in 601.
H was begun in 604.
M was begun in 601.
S was begun in 603.


Question: If M was begun in a later year than L, then which one of the following could be true?

F was begun in 603.
G was begun in 602.
H was begun in 605.
L was begun in 603.
S was begun in 604.


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

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

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


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

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


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

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


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

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


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

Exactly three of the employees volunteer.

Exactly four of the employees volunteer.


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

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


Flyhigh Airlines owns exactly two planes: P and Q. Getaway Airlines owns exactly three planes: R, S, T. On Sunday, each plane makes exactly one flight, according to the following conditions: Only one plane departs at a time. Each plane makes either a domestic or an international flight, but not both. Plane P makes an international flight. Planes Q and R make domestic flights. All international flights depart before any domestic flight. Any Getaway domestic flight departs before Flyhigh's domestic flight.

Question: Which one of the following could be the order, from first to last, in which the five planes depart?

P, Q, R, S, T
P, Q, T, S, R
P, S, T, Q, R
P, S, T, R, Q
T, S, R, P, Q


Question: The plane that departs second could be any one of exactly how many of the planes?


Question: If plane S departs sometime before plane P, then which one of the following must be false?

Plane S departs first.
Plane S departs third.
Plane T departs second.
Plane T departs third.
Plane T departs fourth.


Question: Which one of the following must be true?

Plane P departs first.
Plane Q departs last.
Plane R departs second.
Plane S departs first.
Plane T departs fourth.


Question: If plane S departs third, then each of the following can be true EXCEPT:

Plane R departs sometime before plane S and sometime before plane T.

Plane S departs sometime before plane Q and sometime before plane T.

Plane S departs sometime before plane R and sometime before plane T.

Plane T departs sometime before plane P and sometime before plane S.

Plane T departs sometime before plane R and sometime before plane S.


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

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

linguistics, physics, theater, and writing


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


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

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


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

writing theater statistics physics linguistics


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

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


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

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

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

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

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

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


A law firm has seven departments—family law, health law, injury law, labor law, probate, securities, and tax law. The firm is to occupy a building with three floors—the bottom floor, the middle floor, and the top floor. Each floor can accommodate up to four departments, and no department is to be on more than one floor. Assignment of departments to floors is subject to the following constraints: Probate must be on the same floor as tax law. Health law must be on the floor immediately above injury law. Labor law must occupy an entire floor by itself.

Question: Which one of the following could be the assignment of departments to floors?

top floor: labor law middle floor: injury law, probate, tax law bottom floor: family law, health law, securities

top floor: family law, health law, probate middle floor: injury law, securities, tax law bottom floor: labor law

top floor: health law, probate, tax law middle floor: family law, injury law, securities bottom floor: labor law

top floor: health law, probate, tax law middle floor: injury law, securities bottom floor: family law, labor law

top floor: family law, health law, probate, tax law middle floor: labor law bottom floor: injury law, securities


Question: If injury law and probate are both assigned to the middle floor, which one of the following could be true?

Family law is assigned to the middle floor.

Health law is assigned to the middle floor.

Securities is assigned to the bottom floor.


Question: Which one of the following CANNOT be the assignment for any of the floors?

family law, health law, probate, and tax law

family law, injury law, probate, and tax law

family law, probate, securities, and tax law

health law, probate, securities, and tax law

injury law, probate, securities, and tax law


Question: If family law is assigned to the same floor as securities, which one of the following could be true?

Exactly one department is assigned to the middle floor.

Exactly four departments are assigned to the middle floor.

Exactly two departments are assigned to the bottom floor.

Exactly three departments are assigned to the bottom floor.

Exactly four departments are assigned to the bottom floor.


Question: If probate is assigned to the middle floor along with exactly two other departments, then which one of the following must be true?

Family law is assigned to the floor immediately above health law.

Family law is assigned to the floor immediately below labor law.

Family law is assigned to the same floor as securities.

Probate is assigned to the same floor as health law.

Probate is assigned to the same floor as injury law.


A museum curator is arranging seven photographs—Fence, Gardenias, Hibiscus, Irises, Katydid, Lotus, and Magnolia—on a gallery wall in accordance with the photographer's requirements. The photographs are to be hung along the wall in a row, in seven positions sequentially numbered from first to seventh. The photographer's requirements are as follows: Gardenias must be immediately before Katydid. Hibiscus must be somewhere before Katydid but cannot be the first photograph. Irises and Lotus must be next to one another. Magnolia must be one of the first three photographs. Fence must be either first or seventh.

Question: Which one of the following could be the positions, from first to seventh, in which the photographs are hung?

Fence, Hibiscus, Gardenias, Magnolia, Katydid, Irises, Lotus

Hibiscus, Magnolia, Gardenias, Katydid, Irises, Lotus, Fence

Irises, Lotus, Magnolia, Hibiscus, Gardenias, Katydid, Fence

Lotus, Magnolia, Irises, Hibiscus, Gardenias, Katydid, Fence

Magnolia, Fence, Hibiscus, Gardenias, Katydid, Lotus, Irises


Question: If Irises is immediately before Gardenias, which one of the following could be true?

Gardenias is fourth.
Hibiscus is fourth.
Irises is third.
Lotus is second.
Magnolia is third.


Question: Where each photograph is hung is fully determined if which one of the following is true?

Gardenias is fourth.
Hibiscus is second.
Irises is second.
Lotus is first.
Magnolia is third.


Question: If Magnolia is second, which one of the following CANNOT be true?

Hibiscus is third.
Hibiscus is fourth.
Hibiscus is fifth.
Gardenias is fourth.
Gardenias is sixth.


Question: Which one of the following, if substituted for the condition that Hibiscus must be hung somewhere before Katydid but cannot be the first photograph, would have the same effect in determining the arrangement of the photographs?

If Fence is seventh, Hibiscus is second.

Gardenias is somewhere after Hibiscus, and either Fence or Magnolia is first.

Hibiscus must be somewhere between the first and sixth photographs.

Unless Hibiscus is second, it must be somewhere between Magnolia and Gardenias.

Katydid is somewhere after Hibiscus, which must be somewhere after Fence.


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

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

Geography, Japanese, Psychology, Russian

Geography, Macroeconomics, Psychology, Statistics

Geography, Japanese, Macroeconomics, Russian

Geography, Psychology, Russian, Statistics


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

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


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

World History
Statistics
Psychology
Macroeconomics
Japanese


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

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


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

Japanese
Macroeconomics
Psychology
Russian
World History


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

Psychology, Russian, Statistics, World History

Macroeconomics, Psychology, Statistics, World History

Macroeconomics, Psychology, Russian, World History

Geography, Psychology, Russian, World History

Geography, Macroeconomics, Russian, World History


An organization will hold its first six annual meetings in exactly six cities—Los Angeles, Montreal, New York, Toronto, Vancouver, and Washington—using each city only once. The following conditions govern the order in which the cities are used: Los Angeles must be used in some year after the year in which Toronto is used. Vancouver must be used either immediately before or immediately after Washington. The meeting in Toronto must be separated from the meeting in Montreal by meetings in exactly two other cities. The meeting in Vancouver must be separated from the meeting in Los Angeles by meetings in exactly two other cities.

Question: Which one of the following lists the cities in an order in which they could be used for the meetings, from the first year through the sixth?

Toronto, Vancouver, Washington, Montreal, Los Angeles, New York

Vancouver, Washington, Montreal, Los Angeles, New York, Toronto

Vancouver, Washington, Toronto, New York, Los Angeles, Montreal

Washington, Montreal, Vancouver, New York, Toronto, Los Angeles

Washington, Vancouver, New York, Toronto, Los Angeles, Montreal


Question: Which one of the following must be true?

Toronto is used at some time before Montreal is used.

New York is used either immediately before or immediately after Vancouver.

The meeting in New York is separated from the meeting in Washington by meetings in exactly two other cities.


Question: There is exactly one possible order in which the cities are used if which one of the following is true?

Los Angeles is used in the fifth year.
Montreal is used in the sixth year.
New York is used in the fifth year.
Vancouver is used in the first year.
Washington is used in the second year.


Question: Which one of the following is a complete and accurate list of the years in which Washington could be used?


Question: If Montreal is used in the first year, which one of the following CANNOT be true?

Washington is used in the third year.
Vancouver is used in the third year.
Toronto is used in the fourth year.
New York is used in the fifth year.
Los Angeles is used in the third year.


Question: Which one of the following could be true?

Los Angeles is used in the first year.
New York is used in the second year.
Montreal is used in the third year.
Vancouver is used in the fourth year.
Toronto is used in the sixth year.


Question: Which one of the following must be false?

Los Angeles is used either immediately before or immediately after New York.

Los Angeles is used either immediately before or immediately after Washington.

New York is used either immediately before or immediately after Toronto.

Toronto is used either immediately before or immediately after Vancouver.

Toronto is used either immediately before or immediately after Washington.


A community center will host six arts-and-crafts workshops—Jewelry, Kite-making, Needlepoint, Quilting, Rug-making, and Scrapbooking. The workshops will be given on three consecutive days: Wednesday, Thursday, and Friday. Each workshop will be given once, and exactly two workshops will be given per day, one in the morning and one in the afternoon. The schedule for the workshops is subject to the following constraints: Jewelry must be given in the morning, on the same day as either Kite-making or Quilting. Rug-making must be given in the afternoon, on the same day as either Needlepoint or Scrapbooking. Quilting must be given on an earlier day than both Kite-making and Needlepoint.

Question: Which one of the following is an acceptable schedule for the workshops, with each day's workshops listed in the order in which they are to be given?

Wednesday: Jewelry, Kite-making Thursday: Quilting, Scrapbooking Friday: Needlepoint, Rug-making

Wednesday: Jewelry, Quilting Thursday: Kite-making, Needlepoint Friday: Scrapbooking, Rug-making

Wednesday: Quilting, Needlepoint Thursday: Scrapbooking, Rug-making Friday: Jewelry, Kite-making

Wednesday: Quilting, Scrapbooking Thursday: Jewelry, Kite-making Friday: Rug-making, Needlepoint

Wednesday: Scrapbooking, Rug-making Thursday: Quilting, Jewelry Friday: Kite-making, Needlepoint


Question: Which one of the following workshops CANNOT be given on Thursday morning?

Jewelry Kite-making Needlepoint Quilting Scrapbooking


Question: Which one of the following pairs of workshops CANNOT be the ones given on Wednesday morning and Wednesday afternoon, respectively?

Jewelry, Kite-making
Jewelry, Quilting
Quilting, Scrapbooking
Scrapbooking, Quilting
Scrapbooking, Rug-making


Question: If Kite-making is given on Friday morning, then which one of the following could be true?

Needlepoint is given on Thursday afternoon.

Rug-making is given on Friday afternoon.

Scrapbooking is given on Wednesday afternoon.


Question: If Quilting is given in the morning, then which one of the following workshops CANNOT be given on Thursday?

Jewelry Kite-making Needlepoint Rug-making Scrapbooking


Question: How many of the workshops are there that could be the one given on Wednesday morning?


Exactly six actors—Geyer, Henson, Jhalani, Lin, Mitchell, and Paredes—will appear one after another in the opening credits of a television program. Their contracts contain certain restrictions that affect the order in which they can appear. Given these restrictions, the order in which the actors appear, from first to sixth, must conform to the following: Both Lin and Mitchell appear earlier than Henson. Both Lin and Paredes appear earlier than Jhalani. If Mitchell appears earlier than Paredes, then Henson appears earlier than Geyer. Geyer does not appear last.

Question: Which one of the following could be the order, from first to last, in which the actors appear?

Geyer, Lin, Jhalani, Paredes, Mitchell, Henson

Geyer, Mitchell, Paredes, Lin, Henson, Jhalani

Henson, Lin, Paredes, Jhalani, Geyer, Mitchell

Lin, Paredes, Mitchell, Henson, Jhalani, Geyer

Paredes, Mitchell, Lin, Jhalani, Geyer, Henson