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

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

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


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

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

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

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


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

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

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

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


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


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

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


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

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

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


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

Paton was hired exactly one year after Orozco.

Exactly one professor was hired in 1994.

Exactly two professors were hired in 1993.


Question: Which one of the following must be false?

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


Question: Which one of the following must be true?

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


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

Orozco, Paton, and Togo share a specialty.

Madison, Paton, and Togo share a specialty.

Exactly two professors were hired in 1991.

Exactly two professors were hired in 1993.


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

Nilsson does not share a specialty with Paton.

Exactly one professor was hired in 1990.

Exactly one professor was hired in 1991.

Exactly two professors were hired in each of two years.

Paton was hired at least one year before Sarkis.


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

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

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


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

figs oranges pears tangerines watermelons


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

figs, kiwis, oranges, pears, watermelons


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

The stand carries at least two kinds of fruit.

The stand carries at most three kinds of fruit.

The stand carries neither oranges nor pears.

The stand carries neither oranges nor kiwis.


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

The stand carries pears but not oranges.

The stand carries pears but not tangerines.


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

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


A radio talk show host airs five telephone calls sequentially. The calls, one from each of Felicia, Gwen, Henry, Isaac, and Mel, are each either live or taped (but not both). Two calls are from Vancouver, two are from Seattle, and one is from Kelowna. The following conditions must apply: Isaac's and Mel's calls are the first two calls aired, but not necessarily in that order. The third call aired, from Kelowna, is taped. Both Seattle calls are live. Both Gwen's and Felicia's calls air after Henry's. Neither Mel nor Felicia calls from Seattle.

Question: Which one of the following could be an accurate list of the calls, listed in the order in which they are aired?

Isaac's, Henry's, Felicia's, Mel's, Gwen's

Isaac's, Mel's, Gwen's, Henry's, Felicia's

Mel's, Gwen's, Henry's, Isaac's, Felicia's

Mel's, Isaac's, Gwen's, Henry's, Felicia's

Mel's, Isaac's, Henry's, Felicia's, Gwen's


Question: Which one of the following could be true?

Felicia's call airs fifth.
Gwen's call airs first.
Henry's call airs second.
Isaac's call airs third.
Mel's call airs fifth.


Question: If the first call aired is from Seattle, then which one of the following could be true?

Felicia's call is the next call aired after Isaac's.

Henry's call is the next call aired after Felicia's.

Henry's call is the next call aired after Mel's.

Henry's call is the next call aired after Isaac's.

Isaac's call is the next call aired after Mel's.


Question: If a taped call airs first, then which one of the following CANNOT be true?

Felicia's call airs fourth.
Gwen's call airs fifth.
A taped call airs second.
A taped call airs third.
A taped call airs fourth.


Question: Which one of the following must be true?

Gwen's call is live.
Henry's call is live.
Mel's call is live.
Felicia's call is taped.
Isaac's call is taped.


Question: If no two live calls are aired consecutively and no two taped calls are aired consecutively, then in exactly how many distinct orders could the calls from the five people be aired?


Question: If a taped call airs second, then which one of the following CANNOT be true?

The first call aired is from Seattle.
The first call aired is from Vancouver.
The fourth call aired is from Seattle.
The fifth call aired is from Seattle.
The fifth call aired is from Vancouver.


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

Question: Which one of the following could be true?

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

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

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

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


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

Imamura occupies the window seat in row 3.

Gutierrez sits in the same row as Kelly.

Gutierrez sits in the same row as Moore.


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

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


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

Gutierrez sits in the same row as Imamura.


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

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


An airline has four flights from New York to Sarasota—flights 1, 2, 3, and 4. On each flight there is exactly one pilot and exactly one co-pilot. The pilots are Fazio, Germond, Kyle, and Lopez; the co-pilots are Reich, Simon, Taylor, and Umlas. Each pilot and co-pilot is assigned to exactly one flight. The flights take off in numerical order. Fazio's flight takes off before Germond's, and at least one other flight takes off between their flights. Kyle is assigned to flight 2. Lopez is assigned to the same flight as Umlas.

Question: Which one of the following pilot and co-pilot teams could be assigned to flight 1?

Fazio and Reich
Fazio and Umlas
Germond and Reich
Germond and Umlas
Lopez and Taylor


Question: If Reich's flight is later than Umlas's, which one of the following statements cannot be true?

Fazio's flight is earlier than Simon's.
Kyle's flight is earlier than Reich's.
Kyle's flight is earlier than Taylor's.
Simon's flight is earlier than Reich's.
Taylor's flight is earlier than Kyle's.


Question: If Lopez's flight is earlier than Germond's, which one of the following statements could be false?

Either Reich's or Taylor's flight is earlier than Umlas's.


Question: What is the maximum possible number of different pilot and co-pilot teams, any one of which could be assigned to flight 4?


Question: If Simon's flight is later than Lopez's, then which one of the following statements could be false?

Germond's flight is later than Taylor's.


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

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

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


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

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


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

Richards South
Wisteria South
Tuscarora South
Veblen South
Veblen North


Question: If males are assigned to Veblen South, which one of the following is a complete and accurate list of the wings that CANNOT be assigned males?

Richards North, Tuscarora North, Wisteria South

Richards North, Tuscarora North, Veblen North, Wisteria South

Richards North, Richards South, Tuscarora North, Veblen North, Wisteria South


Question: If Tuscarora South is assigned females, then it could be true that females are assigned to both

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


In a single day, exactly seven trucks—S, T, U, W, X, Y, and Z—are the only arrivals at a warehouse. No truck arrives at the same time as any other truck, and no truck arrives more than once that day. Each truck is either green or red (but not both). The following conditions apply: No two consecutive arrivals are red. Y arrives at some time before both T and W. Exactly two of the trucks that arrive before Y are red. S is the sixth arrival. Z arrives at some time before U.

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

X, Z, U, Y, W, S, T
X, Y, Z, U, W, S, T
Z, W, U, T, Y, S, X
Z, U, T, Y, W, S, X
U, Z, Y, T, S, W, X


Question: For which one of the following pairs of trucks is it the case that they CANNOT both be red?


Question: If X is the third arrival, then which one of the following trucks must be green?


Question: If exactly three of the trucks are green, then which one of the following trucks must be green?


Question: For exactly how many of the seven trucks can one determine exactly how many trucks arrived before it?


Question: Which one of the following pairs of trucks CANNOT arrive consecutively at the warehouse?


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

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

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

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

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

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

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


Question: Which one of the following CANNOT be true?

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

The novels are on the same shelf as each other.

Neither linguistics monograph is on the first shelf.


Question: Which one of the following must be true?

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

A novel and a grammar are on the second shelf.

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

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

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


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

The phonology monograph is on the third shelf.

The Farsi grammar is on the second shelf.

The phonology monograph is on the first shelf.


Question: Which one of the following must be true?

A linguistics monograph is on the first shelf.

No more than one novel is on each shelf.

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

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

The Woolf novel is not on the first shelf.


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

The phonology monograph is on the second shelf.

The Hausa grammar is on the second shelf.

The semantics monograph is on the third shelf.

The Vonnegut novel is on the third shelf.


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

The phonology monograph is on the third shelf.

The Vonnegut novel is on the second shelf.

The semantics monograph is on the second shelf.

The semantics monograph is on the first shelf.


A swim team with exactly five members—Jacobson, Kruger, Lu, Miller, Ortiz—swims a ten-lap relay race. Each team member swims exactly two of the laps: one swims laps 1 and 6, one swims laps 2 and 7, one swims laps 3 and 8, one swims laps 4 and 9, and one swims laps 5 and 10. The following conditions apply: Neither of Kruger's laps is immediately before either of Lu's. Jacobson does not swim lap 9. Ortiz's first lap is after (but not necessarily immediately after) Miller's. At least one of Jacobson's laps is immediately after one of Ortiz's laps.

Question: Which one of the following could be an accurate list of the swimmers of the first five laps, in order from lap 1 through lap 5?

Jacobson, Kruger, Miller, Lu, Ortiz
Kruger, Miller, Ortiz, Jacobson, Lu
Lu, Miller, Jacobson, Kruger, Ortiz
Ortiz, Kruger, Miller, Lu, Jacobson
Miller, Ortiz, Jacobson, Kruger, Lu


Question: If Jacobson swims lap 8, then for exactly how many of the ten laps can one determine which team member swims the lap?


Question: If Ortiz swims lap 4, then which one of the following could be true?

Jacobson swims lap 1.
Jacobson swims lap 3.
Kruger swims lap 5.
Lu swims lap 3.
Miller swims lap 5.


Question: Which one of the following could be true?

Jacobson swims lap 4.
Kruger swims lap 5.
Lu swims lap 5.
Miller swims lap 10.
Ortiz swims lap 6.


Question: Jacobson CANNOT swim which one of the following laps?


Question: Which one of the following could be an accurate list of the swimmers of the last five laps, in order from lap 6 through lap 10?

Jacobson, Miller, Kruger, Ortiz, Lu
Kruger, Lu, Miller, Ortiz, Jacobson
Lu, Kruger, Miller, Ortiz, Jacobson
Miller, Kruger, Ortiz, Jacobson, Lu
Ortiz, Jacobson, Kruger, Miller, Lu


A car drives into the center ring of a circus and exactly eight clowns—Q, R, S, T, V, W, Y, and Z—get out of the car, one clown at a time. The order in which the clowns get out of the car is consistent with the following conditions: V gets out at some time before both Y and Q. Q gets out at some time after Z. T gets out at some time before V but at some time after R. S gets out at some time after V. R gets out at some time before W.

Question: Which one of the following could be the order, from first to last, in which the clowns get out of the car?

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


Question: Which one of the following could be true?

Y is the second clown to get out of the car.

R is the third clown to get out of the car.

Q is the fourth clown to get out of the car.

S is the fifth clown to get out of the car.

V is the sixth clown to get out of the car.


Question: If Z is the seventh clown to get out of the car, then which one of the following could be true?

R is the second clown to get out of the car.

T is the fourth clown to get out of the car.

W is the fifth clown to get out of the car.

V is the sixth clown to get out of the car.

Y is the eighth clown to get out of the car.


Question: If T is the fourth clown to get out of the car, then which one of the following must be true?

R is the first clown to get out of the car.

Z is the second clown to get out of the car.

W is the third clown to get out of the car.

V is the fifth clown to get out of the car.

Y is the seventh clown to get out of the car.


Question: If Q is the fifth clown to get out of the car, then each of the following could be true EXCEPT:

Z is the first clown to get out of the car.

T is the second clown to get out of the car.

V is the third clown to get out of the car.

W is the fourth clown to get out of the car.

Y is the sixth clown to get out of the car.


Question: If R is the second clown to get out of the car, which one of the following must be true?

S gets out of the car at some time before T does.

T gets out of the car at some time before W does.

W gets out of the car at some time before V does.

Y gets out of the car at some time before Q does.

Z gets out of the car at some time before W does.


Question: If V gets out of the car at some time before Z does, then which one of the following could be true?

R is the second clown to get out of the car.

T is the fourth clown to get out of the car.

Q is the fourth clown to get out of the car.

V is the fifth clown to get out of the car.

Z is the sixth clown to get out of the car.


Each of six tasks—harvesting, milling, plowing, spinning, threshing, and weaving—will be demonstrated exactly once at a farm exhibition. No two tasks will be demonstrated concurrently. Three volunteers—Frank, Gladys, and Leslie—will each demonstrate exactly two of the tasks. The tasks must be demonstrated in accordance with the following conditions: Frank demonstrates exactly one task before Gladys demonstrates any of the tasks. Frank performs neither the first nor the last demonstration. Gladys demonstrates neither harvesting nor milling. Leslie demonstrates neither harvesting nor threshing. Milling is the next task demonstrated after threshing is demonstrated.

Question: Which one of the following is an acceptable list of the volunteers and the tasks each demonstrates, in order from the first to the last demonstration?

Frank: weaving; Gladys: threshing; Leslie: milling; Leslie: spinning; Frank: harvesting; Gladys: plowing

Leslie: plowing; Frank: harvesting; Frank: threshing; Leslie: milling; Gladys: spinning; Gladys: weaving

Leslie: plowing; Frank: spinning; Gladys: threshing; Leslie: milling; Frank: harvesting; Gladys: weaving

Leslie: spinning; Leslie: weaving; Frank: plowing; Gladys: harvesting; Frank: threshing; Gladys: milling

Leslie: weaving; Frank: threshing; Gladys: spinning; Leslie: milling; Frank: harvesting; Gladys: plowing


Question: Which one of the following must be true?

Frank demonstrates harvesting.
Frank demonstrates milling.
Frank demonstrates threshing.
Gladys demonstrates plowing.
Gladys demonstrates weaving.


Question: If Leslie performs the fourth demonstration, then harvesting could be the demonstration performed


Question: If Gladys demonstrates plowing immediately before Frank demonstrates threshing, which one of the following must be true?

Frank demonstrates harvesting for the second demonstration.

Gladys demonstrates spinning for the fifth demonstration.

Leslie demonstrates weaving for the first demonstration.

Gladys performs the fourth demonstration.

Leslie performs the sixth demonstration.


Question: Which one of the following must be true?

Frank performs the second demonstration.

Gladys performs the fourth demonstration.

Gladys performs the sixth demonstration.

Leslie performs the first demonstration.

Leslie performs the second demonstration.


Question: Which one of the following could be true?

Harvesting is demonstrated first.
Milling is demonstrated second.
Threshing is demonstrated first.
Threshing is demonstrated last.
Weaving is demonstrated first.


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

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

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

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

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

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

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


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

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


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

Feng and Weiss are both hired for production positions.

Garcia and Yates are both hired for sales positions.

Ilias and Weiss are both hired for sales positions.

Ilias and Weiss are both hired for production positions.

Ilias and Xavier are both hired for production positions.


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

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


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

Herrera is hired for a production position.

Weiss is hired for the management position.

Weiss is hired for a production position.


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

Feng and Herrera are both hired for sales positions.

Herrera and Weiss are both hired for sales positions.

Feng and Yates are both hired for production positions.

Garcia and Weiss are both hired for production positions.

Herrera and Weiss are both hired for production positions.


Musicians perform each of exactly five pieces—Nexus, Onyx, Synchrony, Tailwind, and Virtual—once, and one at a time; the pieces are performed successively (though not necessarily in that order). Each piece is performed with exactly two instruments: Nexus with fiddle and lute, Onyx with harp and mandolin, Synchrony with guitar and harp, Tailwind with fiddle and guitar, and Virtual with lute and mandolin. The following conditions must apply: Each piece shares one instrument with the piece performed immediately before it or after it (or both). Either Nexus or Tailwind is performed second.

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

Nexus, Synchrony, Onyx, Virtual, Tailwind

Synchrony, Tailwind, Onyx, Nexus, Virtual

Tailwind, Nexus, Onyx, Virtual, Synchrony

Tailwind, Nexus, Synchrony, Onyx, Virtual

Virtual, Nexus, Synchrony, Onyx, Tailwind


Question: Which one of the following instruments CANNOT be shared by the third and fourth pieces performed?


Question: If each piece (except the fifth) shares one instrument with the piece performed immediately after it, then which one of the following could be true?

Virtual is performed first.
Synchrony is performed second.
Onyx is performed third.
Nexus is performed fourth.
Tailwind is performed fifth.


Question: Each of the following could be the piece performed first EXCEPT:


Question: If Synchrony is performed fifth, then which one of the following could be true?

Nexus is performed third.
Onyx is performed third.
Tailwind is performed fourth.
Virtual is performed first.
Virtual is performed second.


Eight files will be ordered from first to eighth. Each file falls into exactly one of three categories: red files (H, M, O), green files (P, V, X), or yellow files (T, Z). The files must be ordered according to the following conditions: H must be placed into some position before O, but H cannot immediately precede O. X must be placed into some position before V. X and V must be separated by the same number of files as separate H and O. Z must immediately precede M. The first file cannot be a red file.

Question: Which one of the following is an acceptable ordering of the files from first to eighth?

H X O V Z M P T
P M Z H X O V T
P Z M H O T X V
X Z M V H T P O
Z M H P O X V T


Question: The largest possible number of files that can separate Z from H is


Question: If each of the three red files is immediately followed by a green file, which one of the following must be a yellow file?

the first
the second
the third
the fourth
the fifth


Question: The largest possible number of files that can separate X from V is


Question: If Z is placed in the fifth position, then which one of the following is a complete and accurate list of the positions, any one of which could be H's position?

first, third, fourth
first, second, third
second, third, fourth
second, third, fourth, sixth
third, fourth, sixth, seventh


Exactly three employees of Capital Enterprises—Maria, Suki, and Tate—attend a three-day conference together. Each day, there are exactly three sessions on the three topics of the conference—one on hiring, one on investing, and one on regulations. The following rules govern the conference: Each conference participant attends exactly two sessions, which are on different topics and on different days. Neither Maria nor Suki attends any session on investing. Tate does not attend any session on the third day. At most two Capital employees attend any given session together.

Question: What is the maximum number of sessions attended by at least one Capital employee?


Question: Which one of the following must be false?

Maria attends sessions only on the first two days.

Suki attends sessions only on the last two days.

Exactly two Capital employees attend a session together on the second day.

Exactly one session is attended by one or more Capital employees on the second day.

Exactly three sessions are attended by one or more Capital employees on the third day.


Question: If exactly two sessions on the third day are attended by one or more Capital employees, then which one of the following must be true?

Exactly two sessions on the first day are attended by one or more Capital employees.

Exactly two sessions on the second day are attended by one or more Capital employees.

Maria and Suki do not attend any session together.

Maria and Tate do not attend any session together.


Question: Each of the following is possible EXCEPT:

Every session attended by at least one Capital employee is attended by exactly one Capital employee.

Every session attended by at least one Capital employee is attended by exactly two Capital employees.

Every session attended by Maria is also attended by Suki.

Every session attended by Suki is also attended by Tate.

Every session attended by Tate is also attended by Maria.


Question: If all three sessions on the first day are attended by one or more Capital employees, then which one of the following must be false?

Maria and Suki attend a session together on the third day.

Suki and Tate attend a session together on the second day.

Maria attends a session on hiring on the second day.

Suki attends a session on regulations on the third day.

Tate attends a session on investing on the first day.


Question: If Maria and Tate are the only Capital employees to attend a session on the first day, then each of the following could be true EXCEPT:

Maria and Suki attend exactly two sessions together.

Maria and Tate attend exactly two sessions together.

Suki and Tate attend exactly one session together.

Maria attends a session on regulations on the second day.

Tate attends a session on hiring on the second day.


Of the five Pohl children—Sara, Theo, Uma, Will, and Zoe—three are left-handed and two are right-handed. Each of the five children was born in a different one of seven calendar years, 1990 through 1996. The following conditions apply: No two left-handed children were born in consecutive years. No two right-handed children were born in consecutive years. Sara, who is left-handed, was born before Uma. Zoe was born before both Theo and Will. A left-handed child was born in 1991. Uma, who is right-handed, was born in 1993.

Question: Which one of the following could be an accurate matching of each Pohl child with the year in which that child was born?


Question: If Sara was born before Zoe was born, then which one of the following statements CANNOT be true?

Will is left-handed.
Zoe is left-handed.
Theo was born after Will was born.
Uma was born after Zoe was born.
No child was born in 1990.


Question: Which one of the following must be false?

None of the children was born in 1990, nor was a child born in 1992.

None of the children was born in 1992, nor was a child born in 1995.

None of the children was born in 1994, nor was a child born in 1996.

One of the children was born in 1990, and another in 1993.

One of the children was born in 1993, and another in 1995.


Question: If Theo was born after Will was born, then how many sequential orderings of the children, from firstborn to lastborn, are possible?


Question: If none of the children was born in 1995, then which one of the following statements must be true?

Theo was born in 1994.
Will was born in 1994.
Will was born in 1996.
Zoe was born in 1990.
Zoe was born in 1994.


Question: If Theo is right-handed, then each of the following statements must be false EXCEPT:

Uma was born exactly three years before Theo was born.

Zoe was born exactly one year before Theo was born.


Question: If Zoe was born before Uma was born, then which one of the following statements must be false?

No child was born in 1992.
No child was born in 1995.
Theo is left-handed.
Zoe is left-handed.
Will is left-handed.


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

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

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


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

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


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


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

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

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

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

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

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


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


Charlie makes a soup by adding exactly six kinds of foods—kale, lentils, mushrooms, onions, tomatoes, and zucchini—to a broth, one food at a time. No food is added more than once. The order in which Charlie adds the foods to the broth must be consistent with the following: If the mushrooms are added third, then the lentils are added last. If the zucchini is added first, then the lentils are added at some time before the onions. Neither the tomatoes nor the kale is added fifth. The mushrooms are added at some time before the tomatoes or the kale, but not before both.

Question: Which one of the following could be the order in which the foods are added to the broth?

kale, mushrooms, onions, lentils, tomatoes, zucchini

kale, zucchini, mushrooms, tomatoes, lentils, onions

lentils, mushrooms, zucchini, kale, onions, tomatoes

zucchini, lentils, kale, mushrooms, onions, tomatoes

zucchini, tomatoes, onions, mushrooms, lentils, kale


Question: Which one of the following foods CANNOT be added first?


Question: If the lentils are added last, then which one of the following must be true?

At least one of the foods is added at some time before the zucchini.

At least two of the foods are added at some time before the kale.


Question: Which one of the following could be an accurate partial ordering of the foods added to the broth?

lentils: second; mushrooms: third
mushrooms: fourth; lentils: last
onions: second; mushrooms: fifth
zucchini: first; lentils: last
zucchini: first; mushrooms: second


Question: If the zucchini is added first, then which one of the following CANNOT be true?

The kale is added second.
The tomatoes are added second.
The lentils are added third.
The lentils are added fourth.
The onions are added fourth.


A study sponsored by a consumer group tests exactly five of seven cold medications—F, G, H, I, K, L, and M—and ranks the medications tested from first (best) to fifth (worst). There are no ties. The following conditions must apply: L ranks second. Either F or G ranks first. I is tested. H ranks better than G if both are tested. K ranks better than F if both are tested. If M is tested, both F and H are also tested.

Question: Which one of the following could be the five cold medications that the study ranks, listed from first to fifth?

F, I, L, H, G
F, L, G, H, M
F, L, I, G, M
F, L, I, H, M
F, L, K, I, G


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

G ranks better than M.
H ranks better than F.
I ranks better than F.
K ranks better than G.
M ranks better than G.


Question: Which one of the following cold medications must be among those tested in the study?


Question: Which one of the following is a complete and accurate list of the cold medications any one of which could be the cold medication ranked fifth?

F, G, H, M
G, H, I, M
G, H, L, M
F, G, H, I, K
F, G, H, I, M


Question: If I ranks third, each of the following could also be true of the study EXCEPT:

M ranks better than H.
K ranks better than G.
I ranks better than F.
H ranks better than M.
G ranks better than K.


Each nonstop flight offered by Zephyr Airlines departs from one and arrives at another of five cities: Honolulu, Montreal, Philadelphia, Toronto, and Vancouver. Any two cities are said to be connected with each other if Zephyr offers nonstop flights between them. Each city is connected with at least one other city. The following conditions govern Zephyr's nonstop flights: Montreal is connected with exactly one other city. Honolulu is not connected with Toronto. Any city that is connected with Honolulu is also connected with Toronto. If Philadelphia is connected with Toronto, then Philadelphia is not connected with Vancouver.

Question: Which one of the following could be a complete and accurate list of Zephyr Airlines' connected cities?

Honolulu and Vancouver; Montreal and Toronto; Philadelphia and Vancouver; Toronto and Vancouver

Honolulu and Vancouver; Montreal and Philadelphia; Montreal and Toronto; Philadelphia and Toronto; Toronto and Vancouver

Honolulu and Philadelphia; Honolulu and Montreal; Philadelphia and Toronto; Toronto and Vancouver

Honolulu and Philadelphia; Montreal and Toronto; Philadelphia and Toronto; Philadelphia and Vancouver; Toronto and Vancouver

Honolulu and Philadelphia; Honolulu and Toronto; Montreal and Philadelphia; Philadelphia and Vancouver


Question: If exactly three cities are each connected with Philadelphia, then which one of the following could be a pair of connected cities?

Honolulu and Montreal
Honolulu and Vancouver
Montreal and Toronto
Montreal and Vancouver
Philadelphia and Vancouver


Question: Which one of the following is a pair of cities that CANNOT be connected?

Honolulu and Montreal
Honolulu and Philadelphia
Montreal and Philadelphia
Montreal and Vancouver
Philadelphia and Toronto


Question: Which one of the following could be true?

Montreal and Philadelphia are connected with each other, but neither is connected with any other city.

Montreal and Toronto are connected with each other, but neither is connected with any other city.

Philadelphia and Toronto are connected with each other, but neither is connected with any other city.

Philadelphia and Vancouver are connected with each other, but neither is connected with any other city.

Toronto and Vancouver are connected with each other, but neither is connected with any other city.


Question: If Toronto is the only city that is connected with Philadelphia, then which one of the following could be true?

Exactly one city is connected with Toronto.

Exactly one city is connected with Vancouver.

Exactly two cities are each connected with Honolulu.

Exactly two cities are each connected with Toronto.

Exactly four cities are each connected with Toronto.


Question: At most how many pairs of cities could be connected?


Question: If four of the cities are each connected with the remaining city, then the cities in which one of the following pairs must be connected with each other?

Honolulu and Montreal
Honolulu and Philadelphia
Honolulu and Vancouver
Montreal and Philadelphia
Montreal and Toronto


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

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

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


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

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


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


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

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


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


Question: The selection of animals must include

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


There are exactly six groups in this year's Civic Parade: firefighters, gymnasts, jugglers, musicians, puppeteers, and veterans. Each group marches as a unit; the groups are ordered from first, at the front of the parade, to sixth, at the back. The following conditions apply: At least two groups march behind the puppeteers but ahead of the musicians. Exactly one group marches behind the firefighters but ahead of the veterans. The gymnasts are the first, third, or fifth group.

Question: Which one of the following could be an accurate list of the groups in the Civic Parade in order from first to last?

firefighters, puppeteers, veterans, musicians, gymnasts, jugglers

gymnasts, puppeteers, jugglers, musicians, firefighters, veterans

veterans, puppeteers, firefighters, gymnasts, jugglers, musicians

jugglers, puppeteers, gymnasts, firefighters, musicians, veterans

musicians, veterans, jugglers, firefighters, gymnasts, puppeteers


Question: If the gymnasts march immediately ahead of the veterans, then which one of the following could be the fourth group?

gymnasts jugglers musicians puppeteers veterans


Question: If the veterans march immediately behind the puppeteers, then which one of the following could be the second group?

firefighters gymnasts jugglers musicians veterans


Question: If the jugglers are the fifth group, then which one of the following must be true?

The puppeteers are the first group.
The firefighters are the first group.
The veterans are the second group.
The gymnasts are the third group.
The musicians are the sixth group.


Question: Which one of the following groups CANNOT march immediately behind the gymnasts?

firefighters jugglers musicians puppeteers veterans


A rowing team uses a boat with exactly six seats arranged in single file and numbered sequentially 1 through 6, from the front of the boat to the back. Six athletes—Lee, Miller, Ovitz, Singh, Valerio, and Zita—each row at exactly one of the seats. The following restrictions must apply: Miller rows closer to the front than Singh. Singh rows closer to the front than both Lee and Valerio. Valerio and Zita each row closer to the front than Ovitz.

Question: Which one of the following could be an accurate matching of athletes to seats?

Miller: seat 1; Valerio: seat 5; Lee: seat 6

Singh: seat 3; Valerio: seat 4; Zita: seat 5

Miller: seat 1; Valerio: seat 3; Lee: seat 6

Lee: seat 3; Valerio: seat 4; Ovitz: seat 5

Zita: seat 2; Valerio: seat 3; Ovitz: seat 6


Question: If Valerio rows at seat 5, then which one of the following must be true?

Miller rows at seat 1.
Singh rows at seat 2.
Zita rows at seat 3.
Lee rows at seat 4.
Ovitz rows at seat 6.


Question: If Lee rows at seat 3, then each of the following could be true EXCEPT:

Zita rows immediately behind Valerio.
Ovitz rows immediately behind Valerio.
Ovitz rows immediately behind Zita.
Valerio rows immediately behind Lee.
Singh rows immediately behind Zita.


Question: Which one of the following CANNOT be true?

Ovitz rows closer to the front than Singh.

Zita rows closer to the front than Miller.

Lee rows closer to the front than Valerio.

Singh rows closer to the front than Zita.

Valerio rows closer to the front than Lee.


Question: Exactly how many different seats could be the seat occupied by Zita?


Question: If Valerio rows closer to the front than Zita, then which one of the following must be true?

Miller rows immediately in front of Singh.

Lee rows immediately in front of Valerio.

Zita rows immediately in front of Ovitz.

Singh rows immediately in front of Valerio.


Question: Suppose the restriction that Miller rows closer to the front than Singh is replaced by the restriction that Singh rows closer to the front than Miller. If the other two restrictions remain in effect, then each of the following could be an accurate matching of athletes to seats EXCEPT:

Singh: seat 1; Zita: seat 2; Miller: seat 6

Singh: seat 1; Valerio: seat 3; Ovitz: seat 5

Singh: seat 3; Lee: seat 4; Valerio: seat 5

Valerio: seat 3; Miller: seat 4; Lee: seat 5

Valerio: seat 4; Miller: seat 5; Ovitz: seat 6


Exactly six of an artist's paintings, entitled Quarterion, Redemption, Sipapu, Tesseract, Vale, and Zelkova, are sold at auction. Three of the paintings are sold to a museum, and three are sold to a private collector. Two of the paintings are from the artist's first (earliest) period, two are from her second period, and two are from her third (most recent) period. The private collector and the museum each buy one painting from each period. The following conditions hold: Sipapu, which is sold to the private collector, is from an earlier period than Zelkova, which is sold to the museum. Quarterion is not from an earlier period than Tesseract. Vale is from the artist's second period.

Question: Which one of the following could be an accurate list of the paintings bought by the museum and the private collector, listed in order of the paintings' periods, from first to third?

museum: Quarterion, Vale, Zelkova private collector: Redemption, Sipapu, Tesseract

museum: Redemption, Zelkova, Quarterion private collector: Sipapu, Vale, Tesseract

museum: Sipapu, Zelkova, Quarterion private collector: Tesseract, Vale, Redemption

museum: Tesseract, Quarterion, Zelkova private collector: Sipapu, Redemption, Vale

museum: Zelkova, Tesseract, Redemption private collector: Sipapu, Vale, Quarterion


Question: If Sipapu is from the artist's second period, which one of the following could be two of the three paintings bought by the private collector?

Quarterion and Zelkova
Redemption and Tesseract
Redemption and Vale
Redemption and Zelkova
Tesseract and Zelkova


Question: Which one of the following is a complete and accurate list of the paintings, any one of which could be the painting from the artist's first period that is sold to the private collector?

Quarterion, Redemption, Sipapu, Tesseract


Question: If Sipapu is from the artist's second period, then which one of the following paintings could be from the period immediately preceding Quarterion's period and be sold to the same buyer as Quarterion?

Redemption Sipapu Tesseract Vale Zelkova


Question: If Zelkova is sold to the same buyer as Tesseract and is from the period immediately preceding Tesseract's period, then which one of the following must be true?

Quarterion is from the artist's third period.

Redemption is sold to the private collector.

Redemption is from the artist's third period.

Redemption is sold to the same buyer as Vale.


Each of exactly six lunch trucks sells a different one of six kinds of food: falafel, hot dogs, ice cream, pitas, salad, or tacos. Each truck serves one or more of exactly three office buildings: X, Y, or Z. The following conditions apply: The falafel truck, the hot dog truck, and exactly one other truck each serve Y. The falafel truck serves exactly two of the office buildings. The ice cream truck serves more of the office buildings than the salad truck. The taco truck does not serve Y. The falafel truck does not serve any office building that the pita truck serves. The taco truck serves two office buildings that are also served by the ice cream truck.

Question: Which one of the following could be a complete and accurate list of each of the office buildings that the falafel truck serves?


Question: For which one of the following pairs of trucks must it be the case that at least one of the office buildings is served by both of the trucks?

the hot dog truck and the pita truck
the hot dog truck and the taco truck
the ice cream truck and the pita truck
the ice cream truck and the salad truck
the salad truck and the taco truck


Question: If the ice cream truck serves fewer of the office buildings than the hot dog truck, then which one of the following is a pair of lunch trucks that must serve exactly the same buildings as each other?

the falafel truck and the hot dog truck
the falafel truck and the salad truck
the ice cream truck and the pita truck
the ice cream truck and the salad truck
the ice cream truck and the taco truck


Question: Which one of the following could be a complete and accurate list of the lunch trucks, each of which serves all three of the office buildings?

the hot dog truck, the ice cream truck, the pita truck

the ice cream truck, the pita truck, the salad truck


Question: Which one of the following lunch trucks CANNOT serve both X and Z?

the hot dog truck
the ice cream truck
the pita truck
the salad truck
the taco truck


In the course of one month Garibaldi has exactly seven different meetings. Each of her meetings is with exactly one of five foreign dignitaries: Fuentes, Matsuba, Rhee, Soleimani, or Tbahi. The following constraints govern Garibaldi's meetings: She has exactly three meetings with Fuentes, and exactly one with each of the other dignitaries. She does not have any meetings in a row with Fuentes. Her meeting with Soleimani is the very next one after her meeting with Tbahi. Neither the first nor last of her meetings is with Matsuba.

Question: Which one of the following could be the sequence of the meetings Garibaldi has with the dignitaries?

Fuentes, Rhee, Tbahi, Soleimani, Fuentes, Matsuba, Rhee

Fuentes, Tbahi, Soleimani, Matsuba, Fuentes, Fuentes, Rhee

Fuentes, Rhee, Fuentes, Matsuba, Fuentes, Tbahi, Soleimani

Fuentes, Tbahi, Matsuba, Fuentes, Soleimani, Rhee, Fuentes

Fuentes, Tbahi, Soleimani, Fuentes, Rhee, Fuentes, Matsuba


Question: If Garibaldi's last meeting is with Rhee, then which one of the following could be true?

Garibaldi's second meeting is with Soleimani.

Garibaldi's third meeting is with Matsuba.

Garibaldi's fourth meeting is with Soleimani.

Garibaldi's fifth meeting is with Matsuba.

Garibaldi's sixth meeting is with Soleimani.


Question: If Garibaldi's second meeting is with Fuentes, then which one of the following is a complete and accurate list of the dignitaries with any one of whom Garibaldi's fourth meeting could be?

Fuentes, Soleimani, Rhee
Matsuba, Rhee, Tbahi
Matsuba, Soleimani
Rhee, Tbahi
Fuentes, Soleimani


Question: If Garibaldi's meeting with Rhee is the very next one after Garibaldi's meeting with Soleimani, then which one of the following must be true?

Garibaldi's third meeting is with Fuentes.

Garibaldi's fourth meeting is with Rhee.

Garibaldi's fifth meeting is with Fuentes.

Garibaldi's seventh meeting is with Fuentes.


Question: If Garibaldi's first meeting is with Tbahi, then Garibaldi's meeting with Rhee could be the

second meeting
third meeting
fifth meeting
sixth meeting
seventh meeting


Question: If Garibaldi's meeting with Matsuba is the very next meeting after Garibaldi's meeting with Rhee, then with which one of the following dignitaries must Garibaldi's fourth meeting be?


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

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

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

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

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

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

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


Question: Which one of the following must be true?

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

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

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

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

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


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

The Labrador retriever is placed on Monday.


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

The Labrador retriever is placed on Monday.

The schnauzer is not placed on Wednesday.


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

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


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

the husky
the keeshond
the Labrador retriever
the poodle
the schnauzer


A tour group plans to visit exactly five archaeological sites. Each site was discovered by exactly one of the following archaeologists—Ferrara, Gallagher, Oliphant—and each dates from the eighth, ninth, or tenth century (A.D.). The tour must satisfy the following conditions: The site visited second dates from the ninth century. Neither the site visited fourth nor the site visited fifth was discovered by Oliphant. Exactly one of the sites was discovered by Gallagher, and it dates from the tenth century. If a site dates from the eighth century, it was discovered by Oliphant. The site visited third dates from a more recent century than does either the site visited first or that visited fourth.

Question: Which one of the following could be an accurate list of the discoverers of the five sites, listed in the order in which the sites are visited?

Oliphant, Oliphant, Gallagher, Oliphant, Ferrara

Gallagher, Oliphant, Ferrara, Ferrara, Ferrara

Oliphant, Gallagher, Oliphant, Ferrara, Ferrara

Oliphant, Oliphant, Gallagher, Ferrara, Gallagher

Ferrara, Oliphant, Gallagher, Ferrara, Ferrara


Question: If exactly one of the five sites the tour group visits dates from the tenth century, then which one of the following CANNOT be a site that was discovered by Ferrara?

the site visited first
the site visited second
the site visited third
the site visited fourth
the site visited fifth


Question: Which one of the following could be a site that dates from the eighth century?

the site visited first
the site visited second
the site visited third
the site visited fourth
the site visited fifth


Question: Which one of the following is a complete and accurate list of the sites each of which CANNOT be the site discovered by Gallagher?

third, fourth, fifth
second, third, fourth
first, fourth, fifth
first, second, fifth
first, second, fourth


Question: The tour group could visit at most how many sites that were discovered by Ferrara?


Each day of a five-day workweek (Monday through Friday), Anastasia parks for the entire day in exactly one of three downtown parking lots—X, Y, and Z. One of the lots costs $10 for the day, another costs $12, and the other costs $15. Anastasia parks in each of the three lots at least once during her workweek. The following conditions must apply: On Thursday, Anastasia parks in the $15 lot. Lot X costs more than lot Z. The lot Anastasia parks in on Wednesday costs more than the one she parks in on Friday. Anastasia parks in lot Z on more days of the workweek than she parks in lot X.

Question: Which one of the following could be a complete and accurate list of which lot Anastasia parks in each day, listed in order from Monday through Friday?

Y, Z, X, Y, Z
Y, Z, Z, Y, X
Z, Z, X, X, Y
Z, Z, X, X, Z
Z, Z, X, Z, Y


Question: Anastasia CANNOT park in the $15 lot on which one of the following days?

Monday Tuesday Wednesday Thursday Friday


Question: If lot Z is the $12 lot, then on which one of the following days must Anastasia park in lot Y?

Monday Tuesday Wednesday Thursday Friday


Question: Anastasia CANNOT park in lot Z on which one of the following days?

Monday Tuesday Wednesday Thursday Friday


Question: Which one of the following could be a complete and accurate list of the days on which Anastasia parks in the $10 lot?

Monday
Tuesday
Monday, Tuesday
Monday, Wednesday
Monday, Thursday


On one afternoon, Patterson meets individually with each of exactly five clients—Reilly, Sanchez, Tang, Upton, and Yansky—and also goes to the gym by herself for a workout. Patterson's workout and her five meetings each start at either 1:00, 2:00, 3:00, 4:00, 5:00, or 6:00. The following conditions must apply: Patterson meets with Sanchez at some time before her workout. Patterson meets with Tang at some time after her workout. Patterson meets with Yansky either immediately before or immediately after her workout. Patterson meets with Upton at some time before she meets with Reilly.

Question: Which one of the following could be an acceptable schedule of Patterson's workout and meetings, in order from 1:00 to 6:00?

Yansky, workout, Upton, Reilly, Sanchez, Tang

Upton, Tang, Sanchez, Yansky, workout, Reilly

Upton, Reilly, Sanchez, workout, Tang, Yansky

Sanchez, Yansky, workout, Reilly, Tang, Upton

Sanchez, Upton, workout, Yansky, Tang, Reilly


Question: How many of the clients are there, any one of whom could meet with Patterson at 1:00?


Question: Patterson CANNOT meet with Upton at which one of the following times?


Question: If Patterson meets with Sanchez the hour before she meets with Yansky, then each of the following could be true EXCEPT:

Patterson meets with Reilly at 2:00.
Patterson meets with Yansky at 3:00.
Patterson meets with Tang at 4:00.
Patterson meets with Yansky at 5:00.
Patterson meets with Tang at 6:00.


Question: If Patterson meets with Tang at 4:00, then which one of the following must be true?

Patterson meets with Reilly at 5:00.
Patterson meets with Upton at 5:00.
Patterson meets with Yansky at 2:00.
Patterson meets with Yansky at 3:00.
Patterson's workout is at 2:00.


Question: Which one of the following could be the order of Patterson's meetings, from earliest to latest?

Upton, Yansky, Sanchez, Reilly, Tang
Upton, Reilly, Sanchez, Tang, Yansky
Sanchez, Yansky, Reilly, Tang, Upton
Sanchez, Upton, Tang, Yansky, Reilly
Sanchez, Upton, Reilly, Yansky, Tang


Exactly six people—Lulu, Nam, Ofelia, Pachai, Santiago, and Tyrone—are the only contestants in a chess tournament. The tournament consists of four games, played one after the other. Exactly two people play in each game, and each person plays in at least one game. The following conditions must apply: Tyrone does not play in the first or third game. Lulu plays in the last game. Nam plays in only one game and it is not against Pachai. Santiago plays in exactly two games, one just before and one just after the only game that Ofelia plays in.

Question: Which one of the following could be an accurate list of the contestants who play in each of the four games?

first game: Pachai, Santiago; second game: Ofelia, Tyrone; third game: Pachai, Santiago; fourth game: Lulu, Nam

first game: Lulu, Nam; second game: Pachai, Santiago; third game: Ofelia, Tyrone; fourth game: Lulu, Santiago

first game: Pachai, Santiago; second game: Lulu, Tyrone; third game: Nam, Ofelia; fourth game: Lulu, Nam

first game: Nam, Santiago; second game: Nam, Ofelia; third game: Pachai, Santiago; fourth game: Lulu, Tyrone

first game: Lulu, Nam; second game: Santiago, Tyrone; third game: Lulu, Ofelia; fourth game: Pachai, Santiago


Question: Which one of the following contestants could play in two consecutive games?


Question: If Tyrone plays in the fourth game, then which one of the following could be true?

Nam plays in the second game.
Ofelia plays in the third game.
Santiago plays in the second game.
Nam plays a game against Lulu.
Pachai plays a game against Lulu.


Question: Which one of the following could be true?

Pachai plays against Lulu in the first game.

Pachai plays against Nam in the second game.

Santiago plays against Ofelia in the second game.

Pachai plays against Lulu in the third game.

Nam plays against Santiago in the fourth game.


Question: Which one of the following is a complete and accurate list of the contestants who CANNOT play against Tyrone in any game?

Lulu, Pachai
Nam, Ofelia
Nam, Pachai
Nam, Santiago
Ofelia, Pachai


Question: If Ofelia plays in the third game, which one of the following must be true?

Lulu plays in the third game.
Nam plays in the third game.
Pachai plays in the first game.
Pachai plays in the third game.
Tyrone plays in the second game.


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

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

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


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

Raimundo does not appear in the photograph.

Umiko does not appear in the photograph.


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


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


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

Selma and Zack both appear in the photograph.

Ty and Yakira both appear in the photograph.

Wendy and Selma both appear in the photograph.

Yakira and Zack both appear in the photograph.

Zack and Raimundo both appear in the photograph.


The Export Alliance consists of exactly three nations: Nation X, Nation Y, and Nation Z. Each nation in the Alliance exports exactly two of the following five crops: oranges, rice, soybeans, tea, and wheat. Each of these crops is exported by at least one of the nations in the Alliance. The following conditions hold: None of the nations exports both wheat and oranges. Nation X exports soybeans if, but only if, Nation Y does also. If Nation Y exports rice, then Nations X and Z both export tea. Nation Y does not export any crop that Nation Z exports.

Question: Which one of the following could be an accurate list, for each of the nations, of the crops it exports?

Nation X: oranges, rice; Nation Y: oranges, tea; Nation Z: soybeans, wheat

Nation X: oranges, tea; Nation Y: oranges, rice; Nation Z: soybeans, wheat

Nation X: oranges, wheat; Nation Y: oranges, tea; Nation Z: rice, soybeans

Nation X: rice, wheat; Nation Y: oranges, tea; Nation Z: oranges, soybeans

Nation X: soybeans, rice; Nation Y: oranges, tea; Nation Z: soybeans, wheat


Question: If Nation X exports soybeans and tea, then which one of the following could be true?

Nation Y exports oranges.
Nation Y exports rice.
Nation Y exports tea.
Nation Z exports soybeans.
Nation Z exports tea.


Question: If Nation Z exports tea and wheat, then which one of the following must be true?

Nation X exports oranges.
Nation X exports tea.
Nation X exports wheat.
Nation Y exports rice.
Nation Y exports soybeans.


Question: It CANNOT be the case that both Nation X and Nation Z export which one of the following crops?


Question: Which one of the following pairs CANNOT be the two crops that Nation Y exports?

oranges and rice
oranges and soybeans
rice and tea
rice and wheat
soybeans and wheat


Exactly six guideposts, numbered 1 through 6, mark a mountain trail. Each guidepost pictures a different one of six animals—fox, grizzly, hare, lynx, moose, or porcupine. The following conditions must apply: The grizzly is pictured on either guidepost 3 or guidepost 4. The moose guidepost is numbered lower than the hare guidepost. The lynx guidepost is numbered lower than the moose guidepost but higher than the fox guidepost.

Question: Which one of the following could be an accurate list of the animals pictured on the guideposts, listed in order from guidepost 1 through guidepost 6?

fox, lynx, grizzly, porcupine, moose, hare

fox, lynx, moose, hare, grizzly, porcupine

fox, moose, grizzly, lynx, hare, porcupine

lynx, fox, moose, grizzly, hare, porcupine

porcupine, fox, hare, grizzly, lynx, moose


Question: Which one of the following animals CANNOT be the one pictured on guidepost 3?


Question: If the moose is pictured on guidepost 3, then which one of the following is the lowest numbered guidepost that could picture the porcupine?

guidepost 1
guidepost 2
guidepost 4
guidepost 5
guidepost 6


Question: If guidepost 5 does not picture the moose, then which one of the following must be true?

The porcupine is pictured on guidepost 5.


Question: Which one of the following animals could be pictured on any one of the six guideposts?


Question: If the moose guidepost is numbered exactly one higher than the lynx guidepost, then which one of the following could be true?

Guidepost 5 pictures the hare.
Guidepost 4 pictures the moose.
Guidepost 4 pictures the porcupine.
Guidepost 3 pictures the lynx.
Guidepost 3 pictures the porcupine.


Each side of four cassette tapes—Tapes 1 through 4—contains exactly one of the following four genres: folk, hip-hop, jazz, and rock. The following conditions must apply: Each genre is found on exactly two of the eight sides. Tape 1 has jazz on at least one side, but neither hip-hop nor rock. Tape 2 has no jazz. Folk is not on any tape numbered exactly one higher than a tape that has any rock on it.

Question: Which one of the following could be an accurate matching of tapes with the musical genres found on them?

Tape 1: folk and jazz; Tape 2: folk and jazz; Tape 3: hip-hop and rock; Tape 4: hip-hop and rock

Tape 1: folk and jazz; Tape 2: folk and rock; Tape 3: hip-hop and jazz; Tape 4: hip-hop and rock

Tape 1: folk and jazz; Tape 2: folk and rock; Tape 3: two sides of jazz; Tape 4: two sides of hip-hop

Tape 1: hip-hop and jazz; Tape 2: folk and hip-hop; Tape 3: folk and jazz; Tape 4: two sides of rock

Tape 1: two sides of jazz; Tape 2: folk and rock; Tape 3: hip-hop and rock; Tape 4: folk and hip-hop


Question: Which one of the following must be true?

If Tape 1 has two sides of jazz, Tape 4 has at least one side of rock.

If Tape 2 has two sides of folk, Tape 3 has at least one side of hip-hop.

If Tape 2 has two sides of rock, Tape 4 has at least one side of folk.

If Tape 3 has two sides of folk, Tape 2 has at least one side of jazz.

If Tape 4 has two sides of hip-hop, Tape 3 has at least one side of folk.


Question: Which one of the following could be true?

Tape 1 has jazz on both sides while Tape 4 has folk and hip-hop.

Tape 2 has hip-hop on one side while Tape 3 has hip-hop and jazz.

Tape 3 has folk on both sides while Tape 4 has jazz and rock.

Tape 3 has jazz on one side while Tape 4 has folk on both sides.

Tapes 2 and 3 each have jazz on one side.


Question: Which one of the following could be true?

Tapes 1 and 4 each have a side of hip-hop.


Question: Which one of the following CANNOT be true?

Tape 2 has rock on both sides while Tape 3 has hip-hop on both sides.

Tape 3 has rock on both sides while Tape 2 has hip-hop on both sides.

Tape 3 has rock on both sides while Tape 4 has hip-hop on both sides.

Tape 4 has rock on both sides while Tape 2 has hip-hop on both sides.

Tape 4 has rock on both sides while Tape 3 has hip-hop on both sides.


One afternoon, a single thunderstorm passes over exactly five towns—Jackson, Lofton, Nordique, Oceana, and Plattesville—dropping some form of precipitation on each. The storm is the only source of precipitation in the towns that afternoon. On some towns, it drops both hail and rain; on the remaining towns, it drops only rain. It passes over each town exactly once and does not pass over any two towns at the same time. The following must obtain: The third town the storm passes over is Plattesville. The storm drops hail and rain on the second town it passes over. The storm drops only rain on both Lofton and Oceana. The storm passes over Jackson at some time after it passes over Lofton and at some time after it passes over Nordique.

Question: Which one of the following could be the order, from first to fifth, in which the storm passes over the towns?

Lofton, Nordique, Plattesville, Oceana, Jackson

Lofton, Oceana, Plattesville, Nordique, Jackson

Nordique, Jackson, Plattesville, Oceana, Lofton

Nordique, Lofton, Plattesville, Jackson, Oceana

Nordique, Plattesville, Lofton, Oceana, Jackson


Question: If the storm passes over Oceana at some time before it passes over Jackson, then each of the following could be true EXCEPT:

The first town the storm passes over is Oceana.

The fourth town the storm passes over is Lofton.

The fourth town the storm passes over receives hail and rain.

The fifth town the storm passes over is Jackson.

The fifth town the storm passes over receives only rain.


Question: If the storm drops only rain on each town it passes over after passing over Lofton, then which one of the following could be false?

The first town the storm passes over is Oceana.

The fourth town the storm passes over receives only rain.

The fifth town the storm passes over is Jackson.


Question: If the storm passes over Jackson at some time before it passes over Oceana, then which one of the following could be false?

The storm passes over Lofton at some time before it passes over Jackson.

The storm passes over Lofton at some time before it passes over Oceana.

The storm passes over Nordique at some time before it passes over Oceana.

The fourth town the storm passes over receives only rain.

The fifth town the storm passes over receives only rain.


Question: If the storm passes over Oceana at some time before it passes over Lofton, then which one of the following must be true?

The third town the storm passes over receives only rain.

The fourth town the storm passes over receives only rain.

The fourth town the storm passes over receives hail and rain.

The fifth town the storm passes over receives only rain.

The fifth town the storm passes over receives hail and rain.


A reporter is trying to uncover the workings of a secret committee. The committee has six members—French, Ghauri, Hsia, Irving, Magnus, and Pinsky—each of whom serves on at least one subcommittee. There are three subcommittees, each having three members, about which the following is known: One of the committee members serves on all three subcommittees. French does not serve on any subcommittee with Ghauri. Hsia does not serve on any subcommittee with Irving.

Question: If French does not serve on any subcommittee with Magnus, which one of the following must be true?

French serves on a subcommittee with Hsia.

French serves on a subcommittee with Irving.

Irving serves on a subcommittee with Pinsky.

Magnus serves on a subcommittee with Ghauri.

Magnus serves on a subcommittee with Irving.


Question: If Pinsky serves on every subcommittee on which French serves and every subcommittee on which Ghauri serves, then which one of the following could be true?

Magnus serves on every subcommittee on which French serves and every subcommittee on which Ghauri serves.

Magnus serves on every subcommittee on which Hsia serves and every subcommittee on which Irving serves.

Hsia serves on every subcommittee on which French serves and every subcommittee on which Ghauri serves.

French serves on every subcommittee on which Pinsky serves.

Hsia serves on every subcommittee on which Pinsky serves.


Question: If Irving serves on every subcommittee on which Magnus serves, which one of the following could be true?

Magnus serves on all of the subcommittees.

Irving serves on more than one subcommittee.

Irving serves on every subcommittee on which Pinsky serves.

French serves on a subcommittee with Magnus.

Ghauri serves on a subcommittee with Magnus.


Question: Which one of the following could be true?

French serves on all three subcommittees.

Ghauri serves on every subcommittee on which Magnus serves and every subcommittee on which Pinsky serves.

Pinsky serves on every subcommittee on which Irving serves and every subcommittee on which Magnus serves.

Magnus serves on every subcommittee on which Pinsky serves, and Pinsky serves on every subcommittee on which Magnus serves.


Question: Which one of the following must be true?

Ghauri serves on at least two subcommittees.

French serves on a subcommittee with Hsia.

Ghauri serves on a subcommittee with Irving.

Magnus serves on a subcommittee with Pinsky.


Question: Which one of the following must be true?

Every subcommittee has either French or Ghauri as a member.

Every subcommittee has either Hsia or Irving as a member.

No subcommittee consists of French, Magnus, and Pinsky.

Some committee member serves on exactly two subcommittees.

Either Magnus or Pinsky serves on only one subcommittee.


Exactly seven products—P, Q, R, S, T, W, and X—are each to be advertised exactly once in a section of a catalog. The order in which they will be displayed is governed by the following conditions: Q must be displayed in some position before W. R must be displayed immediately before X. T cannot be displayed immediately before or immediately after W. S must be displayed either first or seventh. Either Q or T must be displayed fourth.

Question: Which one of the following CANNOT be the product that is displayed first?


Question: If X is displayed immediately before Q, then which one of the following could be true?

T is displayed first.
R is displayed fifth.
Q is displayed last.
Q is displayed second.
P is displayed second.


Question: If P is displayed second, then which one of the following could be displayed third?


Question: Which one of the following could be true?

Q is displayed fifth.
Q is displayed seventh.
R is displayed third.
W is displayed third.
X is displayed fifth.


Question: If R is displayed sixth, then which one of the following must be displayed fifth?


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

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

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


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

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


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

switch 3
switch 4
switch 5
switch 6
switch 7


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


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

switch 1
switch 2
switch 3
switch 4
switch 7


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


In Crescentville there are exactly five record stores, whose names are abbreviated S, T, V, X, and Z. Each of the five stores carries at least one of four distinct types of music: folk, jazz, opera, and rock. None of the stores carries any other type of music. The following conditions must hold: Exactly two of the five stores carry jazz. T carries rock and opera but no other type of music. S carries more types of music than T carries. X carries more types of music than any other store in Crescentville carries. Jazz is among the types of music S carries. V does not carry any type of music that Z carries.

Question: Which one of the following could be true?

S carries folk and rock but neither jazz nor opera.

T carries jazz but neither opera nor rock.

V carries folk, rock, and opera, but not jazz.

X carries folk, rock, and jazz, but not opera.

Z carries folk and opera but neither rock nor jazz.


Question: Which one of the following could be true?

Of the five stores, only S and V carry jazz.

Of the five stores, only T and X carry rock.

Of the five stores, only S, T, and V carry opera.


Question: If exactly one of the stores carries folk, then which one of the following could be true?

S and V carry exactly two types of music in common.

T and S carry exactly two types of music in common.

T and V carry exactly two types of music in common.

V and X carry exactly two types of music in common.

X and Z carry exactly two types of music in common.


Question: Which one of the following must be true?

T carries exactly the same number of types of music as V carries.

V carries exactly the same number of types of music as Z carries.

S carries at least one more type of music than Z carries.

Z carries at least one more type of music than T carries.

X carries exactly two more types of music than S carries.


Question: If V is one of exactly three stores that carry rock, then which one of the following must be true?

S and Z carry no types of music in common.

S and V carry at least one type of music in common.

S and Z carry at least one type of music in common.

T and Z carry at least one type of music in common.

T and V carry at least two types of music in common.


Question: If S and V both carry folk, then which one of the following could be true?

S and T carry no types of music in common.

S and Z carry no types of music in common.

T and Z carry no types of music in common.

S and Z carry two types of music in common.

T and V carry two types of music in common.


Maggie's Deli is open exactly five days every week: Monday through Friday. Its staff, each of whom works on at least one day each week, consists of exactly six people—Janice, Kevin, Nan, Ophelia, Paul, and Seymour. Exactly three of them—Janice, Nan, and Paul—are supervisors. The deli's staffing is consistent with the following: Each day's staff consists of exactly two people, at least one of whom is a supervisor. Tuesday's and Wednesday's staffs both include Ophelia. Of the days Nan works each week, at least two are consecutive. Seymour does not work on any day before the first day Paul works that week. Any day on which Kevin works is the first day during the week that some other staff member works.

Question: Which one of the following could be an accurate staffing schedule?

Monday: Janice, Kevin Tuesday: Nan, Ophelia Wednesday: Nan, Paul Thursday: Kevin, Paul Friday: Janice, Seymour

Monday: Paul, Seymour Tuesday: Ophelia, Paul Wednesday: Nan, Ophelia Thursday: Kevin, Nan Friday: Janice, Seymour

Monday: Janice, Kevin Tuesday: Nan, Ophelia Wednesday: Nan, Ophelia Thursday: Kevin, Paul Friday: Paul, Seymour

Monday: Janice, Kevin Tuesday: Janice, Ophelia Wednesday: Nan, Ophelia Thursday: Nan, Seymour Friday: Kevin, Paul

Monday: Paul, Seymour Tuesday: Ophelia, Paul Wednesday: Nan, Ophelia Thursday: Janice, Kevin Friday: Nan, Paul


Question: If Kevin and Paul work Thursday, who must work Friday?


Question: Each of the following could be true EXCEPT:

Janice works Monday and Tuesday.
Kevin and Paul work Friday.
Seymour works Monday and Friday.
Janice and Kevin work Thursday.
Paul works Monday and Friday.


Question: Which one of the following CANNOT be the pair of staff that works Monday?

Janice and Seymour
Kevin and Paul
Paul and Seymour
Nan and Ophelia
Janice and Nan


Question: Which one of the following could be true?

Seymour works Monday and Paul works Tuesday.

Kevin works Monday, Wednesday, and Friday.

Nan works Wednesday with Ophelia and Thursday with Kevin.


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

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

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


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

hairdryer
razor
vacuum
hairdryer, razor
hairdryer, vacuum


Question: Which one of the following CANNOT be true?

Henri uses the hairdryer while using the microwave oven.

Henri uses the microwave oven while using the razor.

Henri uses the microwave oven while using two other appliances.

Henri uses the television while using two other appliances.

Henri uses the vacuum while using two other appliances.


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


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

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


Question: Which one of the following must be true?

Henri uses at most three appliances simultaneously.

Henri uses at most four appliances simultaneously.

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

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

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


A farmer harvests eight separate fields—G, H, J, K, L, M, P, and T. Each field is harvested exactly once, and no two fields are harvested simultaneously. Once the harvesting of a field begins, no other fields are harvested until the harvesting of that field is complete. The farmer harvests the fields in an order consistent with the following conditions: Both P and G are harvested at some time before K. Both H and L are harvested at some time before J. K is harvested at some time before M but after L. T is harvested at some time before M.

Question: Which one of the following could be true?

J is the first field harvested.
K is the second field harvested.
M is the sixth field harvested.
G is the seventh field harvested.
T is the eighth field harvested.


Question: If M is the seventh field harvested, then any one of the following could be the fifth field harvested EXCEPT:


Question: Which one of the following CANNOT be the field that is harvested fifth?


Question: If J is the third field harvested, then which one of the following must be true?

L is the first field harvested.
H is the second field harvested.
T is the fourth field harvested.
K is the seventh field harvested.
M is the eighth field harvested.


Question: If H is the sixth field harvested, then which one of the following must be true?

G is harvested at some time before T.
H is harvested at some time before K.
J is harvested at some time before M.
K is harvested at some time before J.
T is harvested at some time before K.


Question: If L is the fifth field harvested, then which one of the following could be true?

J is harvested at some time before G.
J is harvested at some time before T.
K is harvested at some time before T.
M is harvested at some time before H.
M is harvested at some time before J.


In a repair facility there are exactly six technicians: Stacy, Urma, Wim, Xena, Yolanda, and Zane. Each technician repairs machines of at least one of the following three types—radios, televisions, and VCRs—and no other types. The following conditions apply: Xena and exactly three other technicians repair radios. Yolanda repairs both televisions and VCRs. Stacy does not repair any type of machine that Yolanda repairs. Zane repairs more types of machines than Yolanda repairs. Wim does not repair any type of machine that Stacy repairs. Urma repairs exactly two types of machines.

Question: For exactly how many of the six technicians is it possible to determine exactly which of the three types of machines each repairs?


Question: Which one of the following must be true?

Of the types of machines repaired by Stacy there is exactly one type that Urma also repairs.

Of the types of machines repaired by Yolanda there is exactly one type that Xena also repairs.

Of the types of machines repaired by Wim there is exactly one type that Xena also repairs.

There is more than one type of machine that both Wim and Yolanda repair.

There is more than one type of machine that both Urma and Wim repair.


Question: Which one of the following must be false?

Exactly one of the six technicians repairs exactly one type of machine.

Exactly two of the six technicians repair exactly one type of machine each.

Exactly three of the six technicians repair exactly one type of machine each.

Exactly one of the six technicians repairs exactly two types of machines.

Exactly three of the six technicians repair exactly two types of machines each.


Question: Which one of the following pairs of technicians could repair all and only the same types of machines as each other?

Stacy and Urma
Urma and Yolanda
Urma and Xena
Wim and Xena
Xena and Yolanda


Question: Which one of the following must be true?

There is exactly one type of machine that both Urma and Wim repair.

There is exactly one type of machine that both Urma and Xena repair.

There is exactly one type of machine that both Urma and Yolanda repair.

There is exactly one type of machine that both Wim and Yolanda repair.

There is exactly one type of machine that both Xena and Yolanda repair.


Three folk groups—Glenside, Hilltopper, Levon—and three rock groups—Peasant, Query, Tinhead—each perform on one of two stages, north or south. Each stage has three two-hour performances: north at 6, 8, and 10; south at 8, 10, and 12. Each group performs individually and exactly once, consistent with the following conditions: Peasant performs at 6 or 12. Glenside performs at some time before Hilltopper. If any rock group performs at 10, no folk group does. Levon and Tinhead perform on different stages. Query performs immediately after a folk group, though not necessarily on the same stage.

Question: Which one of the following could be a complete and accurate ordering of performances on the north stage, from first to last?

Glenside, Levon, Query
Glenside, Query, Hilltopper
Hilltopper, Query, Peasant
Peasant, Levon, Tinhead
Peasant, Query, Levon


Question: Which one of the following groups must perform earlier than 10?

Glenside Hilltopper Levon Peasant Tinhead


Question: Which one of the following groups could perform at 6?


Question: If Query performs at 12, then which one of the following could be an accurate ordering of the performances on the north stage, from first to last?

Glenside, Levon, Query
Peasant, Hilltopper, Tinhead
Peasant, Tinhead, Glenside
Peasant, Tinhead, Hilltopper
Peasant, Tinhead, Levon


Question: If a rock group performs at 10, then which one of the following must be true?

A folk group performs at 6.
A folk group performs at 8.
A folk group performs at 12.
A rock group performs at 8.
A rock group performs at 12.


During an international film retrospective lasting six consecutive days—day 1 through day 6—exactly six different films will be shown, one each day. Twelve films will be available for presentation, two each in French, Greek, Hungarian, Italian, Norwegian, and Turkish. The presentation of the films must conform to the following conditions: Neither day 2 nor day 4 is a day on which a film in Norwegian is shown. A film in Italian is not shown unless a film in Norwegian is going to be shown the next day. A film in Greek is not shown unless a film in Italian is going to be shown the next day.

Question: Which one of the following is an acceptable order of films for the retrospective, listed by their language, from day 1 through day 6?

French, Greek, Italian, Turkish, Norwegian, Hungarian

French, Hungarian, Italian, Norwegian, French, Hungarian

Hungarian, French, Norwegian, Greek, Norwegian, Italian

Norwegian, Turkish, Hungarian, Italian, French, Turkish

Turkish, French, Norwegian, Hungarian, French, Turkish


Question: If two films in Italian are going to be shown, one on day 2 and one on day 5, then the film shown on day 1 could be in any one of the following languages EXCEPT:

French Greek Hungarian Norwegian Turkish


Question: If two films in Italian are shown during the retrospective, which one of the following must be false?

A film in French is shown on day 3.
A film in Greek is shown on day 1.
A film in Hungarian is shown on day 6.
A film in Norwegian is shown on day 5.
A film in Turkish is shown on day 4.


Question: Which one of the following is a complete and accurate list of the days, any one of which is a day on which a film in Italian could be shown?

day 1, day 3, day 5
day 2, day 4, day 5
day 2, day 5, day 6
day 1, day 3
day 2, day 4


Question: If two films in French are going to be shown, one on day 3 and one on day 5, which one of the following is a pair of films that could be shown on day 1 and day 6, respectively?

a film in French, a film in Turkish
a film in Greek, a film in Hungarian
a film in Italian, a film in Norwegian
a film in Norwegian, a film in Turkish
a film in Turkish, a film in Greek


Question: If neither a film in French nor a film in Italian is shown during the retrospective, which one of the following must be true?

A film in Hungarian or else a film in Norwegian is shown on day 3.

A film in Hungarian or else a film in Turkish is shown on day 2.


Question: If a film in Greek is going to be shown at some time after a film in Norwegian, then a film in Norwegian must be shown on

day 1
day 3
day 5
day 1 or else day 3
day 3 or else day 5


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

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

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

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

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

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

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


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

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


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

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


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

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


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

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


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

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

history, literature, mathematics, sociology


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

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


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

literature mathematics psychology sociology zoology


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

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


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

Both geography and psychology are offered.

Both geography and mathematics are offered.

Both psychology and mathematics are offered.

Both history and mathematics are offered.

Both geography and sociology are offered.