Question: If R speaks second at meeting 2 and first at meeting 3, which one of the following is a complete and accurate list of those time slots any one of which could be the time slot in which R speaks at meeting 1?

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


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

Question: If the order in which the candidates speak at meeting 1 is R, U, S, T, Q, and the order in which they speak at meeting 2 is Q, R, U, S, T, which one of the following could be true of meeting 3?

Q speaks first.
R speaks third.
S speaks first.
T speaks second.
U speaks fifth.


Question: If R speaks first at meetings 1 and 2, and S speaks first at meeting 3, which one of the following must be true?

S speaks second at at least one of the meetings.

S speaks fifth at exactly one of the meetings.

S speaks fifth at exactly two of the meetings.


Question: It could be true that at all three meetings T speaks

in some time slot after the time slot in which R speaks

in some time slot after the time slots in which S and U speak

in some time slot before the time slots in which R and U speak


Question: If S, T, and U speak second at meetings 1, 2, and 3, respectively, which one of the following must be true?

The fifth speaker at at least one of the meetings is either Q or R.

Either Q speaks first at exactly two of the meetings or else R does so.

Neither S nor T speaks fifth at any of the meetings.

Q speaks third at one of the meetings, and R speaks third at another of the meetings.

Q speaks fourth at one of the meetings, and R speaks fourth at another of the meetings.


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

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

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


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

ginger lemongrass paprika saffron turmeric


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

fenugreek, lemongrass, paprika, turmeric


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

ginger lemongrass nutmeg saffron turmeric


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

fenugreek, ginger, lemongrass, paprika, saffron

fenugreek, ginger, lemongrass, saffron, turmeric

fenugreek, lemongrass, nutmeg, paprika, saffron


Seven singers—Jamie, Ken, Lalitha, Maya, Norton, Olive, and Patrick—will be scheduled to perform in the finals of a singing competition. During the evening of the competition, each singer, performing alone, will give exactly one performance. The schedule for the evening must conform to the following requirements: Jamie performs immediately after Ken. Patrick performs at some time after Maya. Lalitha performs third only if Norton performs fifth. If Patrick does not perform second, he performs fifth.

Question: Which one of the following is an acceptable schedule for the evening's performers, from first through seventh?

Ken, Jamie, Maya, Lalitha, Patrick, Norton, Olive

Lalitha, Patrick, Norton, Olive, Maya, Ken, Jamie

Norton, Olive, Ken, Jamie, Maya, Patrick, Lalitha

Olive, Maya, Ken, Lalitha, Patrick, Norton, Jamie

Olive, Maya, Lalitha, Norton, Patrick, Ken, Jamie


Question: If Lalitha is scheduled for the third performance, which one of the following must be scheduled for the sixth performance?


Question: If Norton is scheduled for the fifth performance, which one of the following could be true?

Jamie is scheduled for the sixth performance.

Ken is scheduled for the second performance.

Lalitha is scheduled for the fourth performance.

Maya is scheduled for the third performance.

Olive is scheduled for the first performance.


Question: If Maya is scheduled for the second performance, which one of the following could be true?

Jamie is scheduled for the sixth performance.

Ken is scheduled for the fourth performance.

Lalitha is scheduled for the third performance.

Norton is scheduled for the fifth performance.

Olive is scheduled for the fourth performance.


Question: If Jamie's performance is scheduled to be immediately before Lalitha's performance, Jamie's performance CANNOT be scheduled to be


At a small press, six textbooks, three introductory—F, G, and H—and three advanced—X, Y, and Z—will each be evaluated once by the editor, Juarez, and once by the publisher, Rosenberg, during six consecutive weeks—week 1 through week 6. Each evaluator evaluates exactly one textbook per week. No textbook will be evaluated by Juarez and Rosenberg during the same week. The following additional constraints apply: Rosenberg cannot evaluate any introductory textbook until Juarez has evaluated that textbook. Juarez cannot evaluate any advanced textbook until Rosenberg has evaluated that textbook. Rosenberg cannot evaluate any two introductory textbooks consecutively. Juarez must evaluate X during week 4.

Question: Which one of the following is an acceptable evaluation schedule, with the textbooks listed in order of evaluation from week 1 through week 6?

Juarez: F, G, X, Z, H, Y Rosenberg: X, F, Z, G, Y, H

Juarez: F, Y, G, X, H, Z Rosenberg Y, F, X, G, Z, H

Juarez: G, H, F, X, Y, Z Rosenberg: X, G, H, Y, Z, F

Juarez: G, Z, F, X, H, Y Rosenberg: Z, F, X, G, Y, H

Juarez: H, Y, F, X, G, Z Rosenberg: X, H, Z, F, Y, G


Question: If Juarez evaluates H during week 3 and Rosenberg evaluates G during week 6, which one of the following must be true?

Juarez evaluates F during week 1.
Juarez evaluates G during week 2.
Juarez evaluates Z during week 6.
Rosenberg evaluates X during week 1.
Rosenberg evaluates Y during week 5.


Question: If Juarez evaluates Z during week 2, then Rosenberg must evaluate which one of the following textbooks during week 5?


Question: Which one of the following must be true?

Rosenberg evaluates an advanced textbook during week 3.

Juarez evaluates an advanced textbook during week 2.

Juarez does not evaluate any two introductory textbooks consecutively.


Question: If Rosenberg evaluates X during week 1 and F during week 2, which one of the following could be true?

X is the third of the advanced textbooks to be evaluated by Juarez.

Y is the first of the advanced textbooks to be evaluated by Juarez.

Juarez does not evaluate any two introductory textbooks in a row.


Question: Which one of the following is a complete and accurate list of those weeks during which Juarez must evaluate an introductory textbook?

week 1
week 6
week 1, week 5
week 1, week 2, week 3
week 1, week 3, week 5


Question: Which one of the following could be true?

Juarez evaluates F during week 6.
Juarez evaluates Z during week 1.
Rosenberg evaluates F during week 3.
Rosenberg evaluates H during week 2.
Rosenberg evaluates X during week 5.


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

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

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


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

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


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


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


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


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


The members of two committees, a planting committee and a trails committee, are to be selected from among seven volunteers—F, G, H, J, K, L, and M. The following conditions govern the composition of the committees: Each committee must have at least three members. F cannot be on the same committee as K. If K is on a committee, J must also be on that committee. M must be on at least one of the committees. The two committees must have at least one member in common.

Question: Which one of the following represents an acceptable selection of volunteers for the committees?

planting: F, G, H; trails: G, J, K, L
planting: F, H, J; trails: G, H, L, M
planting: F, H, M; trails: G, K, L, M
planting: F, G, L, M; trails: F, H
planting: F, H, J, K; trails: H, L, M


Question: If the planting committee consists of F, H, L, and M, and if the trails committee consists of G, H, and J, then K could replace which one of the following committee members on a committee without violating any of the conditions governing the composition of the committees?


Question: If the only members of the planting committee are G, H, and L and if the two committees are to have as many members in common as the conditions allow, then which one of the following must be true?

The trails committee and the planting committee have exactly one member in common.

The trails committee and the planting committee have exactly two members in common.

The trails committee and the planting committee have an equal number of members.

The trails committee has at least one more member than the planting committee.

The planting committee has exactly two more members than the trails committee.


Question: If K is on both committees and L is also on both committees and if the planting committee has exactly three members, then which one of the following must be true?

F is on the planting committee.
F is on the trails committee.
G is on the planting committee.
M is on the planting committee.
M is on the trails committee.


Question: The largest number of members that the planting committee and the trails committee could have in common is


Exactly six tourists—Harry, Irene, Klaus, Laura, Michael, Norma—are to be assigned to four guides: Valois, Xerxes, Yossarian, Zalamea. Each tourist is assigned to exactly one guide, with at least one tourist assigned to each guide. Valois speaks only French. Xerxes speaks only Turkish and Spanish. Yossarian speaks only French and Turkish. Zalamea speaks only Spanish and Russian. Each tourist speaks exactly one of the languages spoken by his or her guide and speaks no other language. The following rules govern the assignment of the tourists to the guides: At least Harry and Irene are assigned to Yossarian. At least Laura is assigned to Zalamea. If Klaus is assigned to Xerxes, then Michael speaks French.

Question: Each of the following could be true EXCEPT:

Both Klaus and Harry speak Turkish.
Both Klaus and Michael speak French.
Both Klaus and Michael speak Russian.
Both Klaus and Norma speak French.
Both Klaus and Norma speak Spanish.


Question: Which one of the following must be true?

Zalamea is assigned fewer than three of the tourists.

Xerxes is assigned fewer than two of the tourists.

Yossarian is assigned exactly two of the tourists.

Valois is assigned exactly one of the tourists.

Zalamea is assigned exactly one of the tourists.


Question: Each of the following could be true of the assignment of tourists to guides EXCEPT:

It assigns Klaus to Valois and Michael to Xerxes.

It assigns Klaus to Yossarian and Norma to Zalamea.

It assigns Laura to Zalamea and Michael to Zalamea.

It assigns Michael to Valois and Klaus to Zalamea.

It assigns Michael to Xerxes and Klaus to Zalamea.


Question: If Klaus and Laura speak the same language as each other, then which one of the following must be true?

At least one of Michael and Norma speaks Spanish.

At least one of Michael and Norma speaks French.


Question: If Laura and Norma speak the same language as each other, then the maximum number of the tourists who could speak Turkish is


Question: If exactly two tourists are assigned to Xerxes, then which one of the following could be true?

Norma speaks Russian and Laura speaks Russian.

Norma speaks French and Michael speaks French.

Norma speaks French and Klaus speaks Turkish.

Michael speaks Spanish and Klaus speaks Spanish.

Michael speaks French and Klaus speaks Spanish.


Question: If Harry, Irene, Michael, and Norma all speak the same language as each other, then which one of the following could be true?

Exactly two of the tourists speak Russian.

Exactly three of the tourists speak Spanish.

Exactly two of the tourists speak Turkish.


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

Question: Which one of the following could be true?

Maricella plays tennis and Shigeru plays golf.

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

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


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


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

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


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

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


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

Oliver and Maricella play the same sport as each other.

Paulo and Lina play the same sport as each other.

Paulo and Oliver play the same sport as each other.

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

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


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

Maricella and Kim play the same sport as each other.

Paulo and Kim play the same sport as each other.

Paulo and Maricella play the same sport as each other.

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

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


A disc jockey will play a sequence consisting of exactly seven different songs: three ballads—F, G, and H—and four dance tunes—R, S, V, and X. The following conditions must be met: No dance tune can be played immediately after another dance tune. H must be played earlier in the sequence than V. V and S must be separated from each other by exactly one song. S must be played immediately before or immediately after F. F must be played immediately after R, unless G is played earlier than R.

Question: Which one of the following could be the order of the songs in the sequence?

G, H, S, X, V, F, R
R, H, X, G, S, F, V
S, F, X, G, R, H, V
V, F, S, H, X, G, R
X, G, R, H, S, F, V


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

No ballad is played immediately after a dance tune.

No ballad is played immediately after another ballad.

No dance tune is played immediately after a ballad.


Question: Which one of the following could be the fourth song in the sequence?


Question: Which one of the following could be the first song in the sequence?


Question: If the third song in the sequence is S, which one of the following must be the sixth song?


Question: If the seventh song in the sequence is R, which one of the following could be the fifth song?


Eight physics students—four majors: Frank, Gwen, Henry, and Joan; and four nonmajors: Victor, Wanda, Xavier, and Yvette—are being assigned to four laboratory benches, numbered 1 through 4. Each student is assigned to exactly one bench, and exactly two students are assigned to each bench. Assignments of students to benches must conform to the following conditions: Exactly one major is assigned to each bench. Frank and Joan are assigned to consecutively numbered benches, with Frank assigned to the lower-numbered bench. Frank is assigned to the same bench as Victor. Gwen is not assigned to the same bench as Wanda.

Question: Which one of the following could be the assignment of students to benches?

1: Frank, Victor; 2: Joan, Gwen; 3: Henry, Wanda; 4: Xavier, Yvette

1: Gwen, Yvette; 2: Frank, Xavier; 3: Joan, Wanda; 4: Henry, Victor

1: Henry, Wanda; 2: Gwen, Xavier; 3: Frank, Victor; 4: Joan, Yvette

1: Henry, Xavier; 2: Joan, Wanda; 3: Frank, Victor; 4: Gwen, Yvette

1: Henry, Yvette; 2: Gwen, Wanda; 3: Frank, Victor, 4: Joan, Xavier


Question: If Victor is assigned to bench 2 and Wanda is assigned to bench 4, which one of the following must be true?

Frank is assigned to bench 1.
Gwen is assigned to bench 1.
Henry is assigned to bench 3.
Xavier is assigned to bench 1.
Yvette is assigned to bench 3.


Question: If Gwen and Henry are not assigned to consecutively numbered benches, which one of the following must be true?

Victor is assigned to bench 2.
Victor is assigned to bench 3.
Wanda is assigned to bench 1.
Wanda is assigned to bench 3.
Wanda is assigned to bench 4.


Question: If Henry and Yvette are both assigned to bench 1, which one of the following could be true?

Gwen is assigned to bench 3.
Joan is assigned to bench 2.
Wanda is assigned to bench 2.
Wanda is assigned to bench 3.
Xavier is assigned to bench 3.


Question: If Gwen is assigned to bench 4 and Xavier is assigned to bench 3, then any one of the following could be true EXCEPT:

Gwen is assigned to the same bench as Yvette.

Henry is assigned to the same bench as Wanda.

Henry is assigned to the same bench as Xavier.

Joan is assigned to the same bench as Xavier.

Joan is assigned to the same bench as Yvette.


Question: If Wanda is assigned to a lower-numbered bench than is Joan, then Henry must be assigned to a

lower-numbered bench than is Frank
lower-numbered bench than is Gwen
lower-numbered bench than is Xavier
higher-numbered bench than is Victor
higher-numbered bench than is Yvette


Question: Which one of the following could be the assignments for bench 2 and bench 4?

2: Gwen, Xavier 4: Henry, Yvette
2: Henry, Yvette 4: Joan, Xavier
2: Joan, Victor 4: Gwen, Xavier
2: Joan, Wanda 4: Gwen, Xavier
2: Joan, Xavier 4: Henry, Yvette


A messenger will deliver exactly seven packages—L, M, N, O, P, S, and T—one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions: P is delivered either first or seventh. The messenger delivers N at some time after delivering L. The messenger delivers T at some time after delivering M. The messenger delivers exactly one package between delivering L and delivering O, whether or not L is delivered before O. The messenger delivers exactly one package between delivering M and delivering P, whether or not M is delivered before P.

Question: Which one of the following is an order in which the messenger could make the deliveries, from first to seventh?

L, N, S, O, M, T, P
M, T, P, S, L, N, O
O, S, L, N, M, T, P
P, N, M, S, O, T, L
P, T, M, S, L, N, O


Question: Which one of the following could be true?

N is delivered first.
T is delivered first.
T is delivered second.
M is delivered fourth.
S is delivered seventh.


Question: If N is delivered fourth, which one of the following could be true?

L is delivered first.
L is delivered second.
M is delivered third.
O is delivered fifth.
S is delivered first.


Question: If T is delivered fourth, the seventh package delivered must be


Question: If the messenger delivers M at some time after delivering O, the fifth package delivered could be any one of the following EXCEPT:


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

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

movie, soccer game, soccer game, restaurant, movie

movie, restaurant, soccer game, soccer game, movie

soccer game, restaurant, movie, soccer game, movie

soccer game, restaurant, movie, soccer game, restaurant

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


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

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


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

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


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

Tyner and Valdez go to a restaurant together.


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

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


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


In each of two years exactly two of four lawmakers—Feld, Gibson, Hsu, and Ivins—and exactly two of three scientists—Vega, Young, and Zapora—will serve as members of a four-person panel. In each year, one of the members will be chairperson. The chairperson in the first year cannot serve on the panel in the second year. The chairperson in the second year must have served on the panel in the first year. Service on the panel must obey the following conditions: Gibson and Vega do not serve on the panel in the same year as each other. Hsu and Young do not serve on the panel in the same year as each other. Each year, either Ivins or Vega, but not both, serves on the panel.

Question: Which one of the following could be the list of the people who serve on the panel in the first year?

Feld, Gibson, Vega, Zapora
Feld, Hsu, Vega, Zapora
Feld, Ivins, Vega, Zapora
Gibson, Hsu, Ivins, Zapora
Hsu, Ivins, Young, Zapora


Question: If Vega is the chairperson in the first year, which one of the following is a pair of people who must serve on the panel in the second year?

Gibson and Young
Gibson and Zapora
Hsu and Ivins
Ivins and Young
Vega and Young


Question: If Hsu is the chairperson in the first year, which one of the following could be the chairperson in the second year?


Question: IF Feld serves on the panel in a given year, any one of the following could serve on the panel that year EXCEPT:


Question: If Ivins is the chairperson in the first year, which one of the following could be the chairperson in the second year?


Question: Which one of the following must be true?

Feld is on the panel in the second year.

Zapora is on the panel in the second year.


During a period of seven consecutive days—from day 1 through day 7—seven investors—Fennelly, Gupta, Hall, Jones, Knight, Lopez, and Moss—will each view a building site exactly once. Each day exactly one investor will view the site. The investors must view the site in accordance with the following conditions: Fennelly views the site on day 3 or else day 5. Lopez views the site on neither day 4 nor day 6. If Jones views the site on day 1, Hall views the site on day 2. If Knight views the site on day 4, Lopez views the site on day 5. Gupta views the site on the day after the day on which Hall views the site.

Question: Which one of the following could be the order in which the investors view the site, from day 1 through day 7?

Hall, Gupta, Fennelly, Moss, Knight, Lopez, Jones

Hall, Gupta, Lopez, Fennelly, Moss, Knight, Jones

Lopez, Gupta, Hall, Moss, Fennelly, Jones, Knight

Lopez, Jones, Fennelly, Knight, Hall, Gupta, Moss

Lopez, Jones, Knight, Moss, Fennelly, Hall, Gupta


Question: If Jones views the site on day 1, which one of the following investors must view the site on day 4?


Question: If Knight views the site on day 4 and Moss views the site on some day after the day on which Jones views the site, which one of the following must be true?

Jones views the site on day 1.
Jones views the site on day 2.
Jones views the site on day 6.
Moss views the site on day 2.
Moss views the site on day 6.


Question: If Hall views the site on day 2, which one of the following is a complete and accurate list of investors any one of whom could be the investor who views the site on day 4?

Knight
Moss
Jones, Moss
Knight, Moss
Jones, Knight, Moss


Question: If Hall views the site on the day after the day Knight views the site and if Fennelly views the site on the day after the day Lopez views the site, then Jones must view the site on day


Question: If the day on which Gupta views the site and the day on which Lopez views the site both come at some time before the day on which Fennelly views the site, which one of the following is an investor who could view the site on day 3?


A zoo's reptile house has a straight row of exactly five consecutive habitats—numbered 1 through 5 from left to right—for housing exactly seven reptiles—four snakes and three lizards. Five of the reptiles are female and two are male. The reptiles must be housed as follows: No habitat houses more than two reptiles. No habitat houses both a snake and a lizard. No female snake is housed in a habitat that is immediately next to a habitat housing a male lizard.

Question: Which one of the following could be a complete and accurate matching of habitats to reptiles?

1: two female snakes; 2: one male snake; 3: one female lizard; 4: one male snake, one female lizard; 5: one female lizard

1: empty; 2: two female snakes; 3: two female lizards; 4: two male snakes; 5: one female lizard

1: one female snake, one male snake; 2: two female snakes; 3: one male lizard; 4: one female lizard; 5: one female lizard

1: two male snakes; 2: empty; 3: one female lizard; 4: one female lizard; 5: two female snakes, one female lizard

1: one female snake, one male snake; 2: one female snake, one male snake; 3: one male lizard; 4: one female lizard; 5: one female lizard


Question: If habitat 2 contains at least one female snake and habitat 4 contains two male lizards, then which one of the following could be true?

Habitat 3 contains two reptiles.
Habitat 5 contains two reptiles.
Habitat 1 contains a female lizard.
Habitat 2 contains a female lizard.
Habitat 5 contains a female lizard.


Question: Which one of the following must be true?

At least one female reptile is alone in a habitat.

At least one male reptile is alone in a habitat.

At least one lizard is alone in a habitat.


Question: Which one of the following CANNOT be the complete housing arrangement for habitats 1 and 2?

1: one female snake, one male snake; 2: one male snake

1: two female lizards; 2: one female snake


Question: If habitat 3 is empty, and no snake is housed in a habitat that is immediately next to a habitat containing a snake, then which one of the following could be false?

All snakes are housed in even-numbered habitats.

No lizard is housed in a habitat that is immediately next to a habitat containing a lizard.

Exactly one habitat contains exactly one reptile.


Question: If all snakes are female and each of the lizards has a habitat to itself, then which one of the following habitats CANNOT contain any snakes?

habitat 1
habitat 2
habitat 3
habitat 4
habitat 5


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

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

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

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

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

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

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


Question: Each of the following must be false EXCEPT:

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

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

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

Exactly two film buffs see the Kurosawa film.

Exactly three film buffs see the Hitchcock film.


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

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


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

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


Question: Which one of the following must be true?

Ginnie sees a different film than Ian does.

Ian sees a different film than Lianna does.

Ian sees a different film than Viktor does.

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

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


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

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


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

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


Six cars are to be arranged in a straight line, and will be numbered 1 through 6, in order, from the front of the line to the back of the line. Each car is exactly one color: two are green, two are orange, and two are purple. The arrangement of cars is restricted as follows: No car can be the same color as any car next to it in line. Either car 5 or car 6 must be purple. Car 1 cannot be orange. Car 4 cannot be green.

Question: The cars in which one of the following pairs CANNOT be the same color as each other?

cars 1 and 4
cars 1 and 5
cars 3 and 5
cars 3 and 6
cars 4 and 6


Question: If car 2 is the same color as car 4, then which one of the following statements must be true?

Car 1 is purple.
Car 2 is orange.
Car 3 is green.
Car 5 is purple.
Car 6 is green


Question: If car 4 is purple, which one of the following must be true?

Car 1 is orange.
Car 2 is green.
Car 3 is orange.
Car 5 is green.
Car 6 is purple.


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

Car 2 is green.
Car 4 is orange.
Car 5 is purple.
Car 6 is orange.
Car 6 is green.


Question: If one of the two orange cars is replaced by a third green car, and if the arrangement of cars in line must conform to the same restrictions as before, then which one of the following is a complete and accurate list of the cars each of which must be green?

car 1
car 3
car 5
car 1, car 3
car l, car 3, car 5


Exactly eight boats—Jewel, Kashmir, Neptune, Ojibwa, Pacific, Spain, Tornado, and Valhalla—arrived at a dock. No boat arrived at the same time as any other boat. The boats arrived in an order consistent with the following conditions: Tornado arrived before Spain but after Jewel. Neptune arrived before Tornado. Kashmir arrived after Jewel but before Spain. Spain arrived before Ojibwa.

Question: If Neptune arrived after Kashmir, which one of the following must be false?

Jewel was the second of the boats to arrive.

Kashmir was the fifth of the boats to arrive.

Neptune was the third of the boats to arrive.

Ojibwa was the sixth of the boats to arrive.

Spain was the seventh of the boats to arrive.


Question: Which one of the following must be true?

At least two of the boats arrived before Neptune.

At least five of the boats arrived before Pacific.

At least four of the boats arrived before Spain.

At least three of the boats arrived before Tornado.

At least two of the boats arrived before Valhalla.


Question: Of the eight boats, what is the maximum number that could have arrived before Jewel?


Question: Of the eight boats, if Valhalla was the second to arrive, then which one of the following CANNOT be true?

Jewel was the third to arrive.
Jewel was the first to arrive.
Kashmir was the third to arrive.
Pacific was the third to arrive.
Tornado was the third to arrive.


Question: If Valhalla arrived before Neptune but after Pacific, which one of the following could be true?

Ojibwa was not the last of the boats to arrive.

Spain was not the seventh of the boats to arrive.


Question: Of the boats, what are, respectively, the minimum number and the maximum number that could have arrived before Kashmir?

one, five
two, five
three, five
one, six
two, six


A park contains at most five of seven kinds of trees—firs, laurels, maples, oaks, pines, spruces, and yews—consistent with the following conditions: If maples are in the park, yews are not. If firs are in the park, pines are not. If yews are not in the park, then either laurels or oaks, but not both, are in the park. If it is not the case that the park contains both laurels and oaks, then it contains firs and spruces.

Question: Which one of the following could be a complete and accurate list of the kinds of trees in the park?

firs, maples
firs, laurels, oaks
firs, laurels, pines, spruces
firs, laurels, spruces, yews
firs, maples, oaks, spruces, yews


Question: If neither maples nor spruces are in the park, then which one of the following could be true?

Exactly four kinds of trees are in the park.

Exactly five kinds of trees are in the park.


Question: Which one of the following could be true?

Neither firs nor laurels are in the park.

Neither laurels, oaks, nor yews are in the park.

Neither laurels nor spruces are in the park.

Neither maples nor yews are in the park.

Neither oaks nor spruces are in the park.


Question: If firs are not in the park, then which one of the following must be true?

Maples are not in the park.
Spruces are not in the park.
Yews are not in the park.
Pines are in the park.
Spruces are in the park.


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

Exactly four kinds of trees are in the park.

Exactly five kinds of trees are in the park.

Neither firs nor maples are in the park.

Neither laurels nor maples are in the park.


Question: Each of the following could be an accurate, partial list of the kinds of trees in the park EXCEPT:

oaks, spruces
oaks, yews
firs, laurels, oaks
firs, maples, oaks
laurels, maples, oaks


Four married couples—Francisco and Gabrielle, Kyoko and Lee, Olivia and Peter, Raymond and Simone—will dine together at the same circular table. Each person will sit in a different one of the eight chairs evenly spaced around the table. The chairs are numbered from 1 through 8 with successively numbered chairs next to each other and chair 1 next to chair 8. Seating arrangements must meet the following conditions: No person sits next to her or his spouse. Simone sits in chair 1 and Raymond sits in chair 4. Neither Peter nor Olivia sits next to Raymond. Neither Kyoko nor Lee sits next to Gabrielle.

Question: Which one of the following could be the list of people sitting in chairs 5 through 8, respectively?

Francisco, Olivia, Gabrielle, Peter
Francisco, Gabrielle, Peter, Lee
Olivia, Gabrielle, Peter, Kyoko
Gabrielle, Lee, Olivia, Kyoko
Lee, Olivia, Francisco, Kyoko


Question: Each of the following could be true EXCEPT:

Peter and Gabrielle sit in chairs 2 and 3, respectively.

Peter and Kyoko sit in chairs 1 and 3, respectively.

Francisco, Kyoko, and Peter sit in chairs 5, 6, and 7, respectively.

Gabrielle, Olivia, and Kyoko sit in chairs 5, 6, and 7, respectively.

Gabrielle, Peter, and Lee sit in chairs 5, 6, and 7, respectively.


Question: If Francisco sits in chair 2 and Olivia sits next to Simone, Gabrielle must sit next to which one of the following persons?


Question: If neither Gabrielle nor Lee sits next to Raymond, which one of the following must be true?

Francisco sits next to Raymond.
Olivia sits next to Simone.
Francisco sits in chair 3.
Olivia sits in chair 6.
Olivia sits in chair 7.


Question: If Lee sits in chair 2, which one of the following must be true?

Peter sits next to Gabrielle.
Kyoko sits next to Simone.
Francisco sits next to Lee.
Gabrielle sits in chair 5.
Olivia sits in chair 6.


Question: If both Francisco and Gabrielle sit next to Raymond, which one of the following is a complete and accurate list of people any one of whom could sit next to Olivia?

Francisco, Gabrielle, Kyoko
Lee, Simone, Kyoko
Lee, Gabrielle, Kyoko
Francisco, Lee, Gabrielle, Kyoko
Lee, Simone, Gabrielle, Kyoko


Zeno's Unfinished Furniture sells exactly five types of furniture—footstools, hutches, sideboards, tables, and vanities. Irene buys just four items, each of a different type, and each made entirely of one kind of wood—maple, oak, pine, or rosewood. The following conditions govern Irene's purchases: Any vanity she buys is maple. Any rosewood item she buys is a sideboard. If she buys a vanity, she does not buy a footstool. If Irene buys a footstool, she also buys a table made of the same wood. Irene does not buy an oak table. Exactly two of the items she buys are made of the same kind of wood as each other.

Question: Which one of the following could be an accurate list of the items Irene buys?

Maple footstool, maple hutch, rosewood sideboard, maple table

oak hutch, rosewood sideboard, pine table, oak vanity

rosewood hutch, maple sideboard, oak table, maple vanity

pine footstool, rosewood sideboard, pine table, maple vanity

maple footstool, pine hutch, oak sideboard, maple table


Question: If Irene buys one item made of rosewood and two items made of maple, then which one of the following pairs could be two of the items she buys?

a rosewood sideboard and an oak footstool


Question: Which one of the following is a complete and accurate list of all the woods any footstool that Irene buys could be made of?

maple, oak
maple, pine
maple, rosewood
maple, oak, pine
maple, oak, pine, rosewood


Question: Suppose Irene buys a footstool. Then which one of the following is a complete and accurate list of items any one of which she could buy in maple?

footstool, hutch, sideboard, table, vanity


Question: Which one of the following CANNOT be the two items Irene buys that are made of the same wood as each other?

footstool, hutch
hutch, sideboard
hutch, table
sideboard, vanity
table, vanity


Question: If Irene does not buy an item made of maple, then each of the following must be true EXCEPT:

Irene buys exactly one item made of oak.

Irene buys exactly two items made of pine.


Six racehorses—K, L, M, N, O, and P—will be assigned to six positions arranged in a straight line and numbered consecutively 1 through 6. The horses are assigned to the positions, one horse per position, according to the following conditions: K and L must be assigned to positions that are separated from each other by exactly one position. K and N cannot be assigned to positions that are next to each other. N must be assigned to a higher-numbered position than M. P must be assigned to position 3.

Question: Which one of the following lists an acceptable assignment of horses to positions 1 though 6, respectively?

K, L, P, M, N, O
M, K, P, L, N, O
M, N, K, P, L, O
N, O, P, K, M, L
O, M, P, L, N, K


Question: Which one of the following is a complete and accurate list of the positions any one of which can be the position to which K is assigned?


Question: Which one of the following CANNOT be true?

K is assigned to position 2.
L is assigned to position 2.
M is assigned to position 1.
M is assigned to position 5.
O is assigned to position 2.


Question: Which one of the following must be true?

Either K or else L is assigned to position 2.

Either K or else L is assigned to position 4.

Either M or else N is assigned to position 2.

Either M or else N is assigned to position 5.

Either M or else O is assigned to position 6.


Question: Which one of the following CANNOT be true?

L and N are assigned to positions that are next to each other.

M and K are assigned to positions that are next to each other.

M and O are assigned to positions that are next to each other.

L and N are assigned to positions that are separated from each other by exactly one position.

M and P are assigned to positions that are separated from each other by exactly one position.


To prepare for fieldwork, exactly four different researchers—a geologist, a historian, a linguist, and a paleontologist—will learn at least one and at most three of four languages—Rundi, Swahili, Tigrinya, and Yoruba. They must learn the languages according to the following specifications: Exactly one researcher learns Rundi. Exactly two researchers learn Swahili. Exactly two researchers learn Tigrinya. Exactly three researchers learn Yoruba. Any language learned by the linguist or paleontologist is not learned by the geologist. Any language learned by the geologist is learned by the historian.

Question: Which one of the following could be true?

The linguist learns three languages—Rundi, Swahili, and Tigrinya.

The linguist learns three languages—Swahili, Tigrinya, and Yoruba.

The historian learns three languages—Rundi, Swahili, and Tigrinya.

The historian learns three languages—Swahili, Tigrinya, and Yoruba.

The paleontologist learns three languages—Rundi, Swahili, and Tigrinya.


Question: If the linguist learns three of the languages, then which one of the following must be true?

The linguist learns Tigrinya.
The linguist learns Rundi.
The linguist learns Swahili.
The paleontologist learns Rundi.
The paleontologist learns Swahili.


Question: Each of the following could be true of the researcher who learns Rundi EXCEPT:

The researcher also learns Tigrinya but not Swahili.

The researcher learns neither Tigrinya nor Swahili.

The researcher also learns Tigrinya but not Yoruba.

The researcher also learns both Tigrinya and Yoruba.

The researcher also learns Yoruba but not Tigrinya.


Question: Each of the following could be a complete and accurate list of the researchers who learn both Swahili and Yoruba EXCEPT:

the historian
the paleontologist
the historian, the linguist
the historian, the paleontologist
the linguist, the paleontologist


Question: If the geologist learns exactly two of the languages, then which one of the following could be true?

The paleontologist learns exactly three of the languages.

The historian learns exactly two of the languages.


Question: Which one of the following must be true?

Fewer of the languages are learned by the historian than are learned by the paleontologist.

Fewer of the languages are learned by the geologist than are learned by the historian.

Fewer of the languages are learned by the geologist than are learned by the linguist.

Fewer of the languages are learned by the paleontologist than are learned by the linguist.

Fewer of the languages are learned by the paleontologist than are learned by the historian.


Question: If exactly two of the languages are learned by the historian, then which one of the following must be true?

The paleontologist does not learn Rundi.

The paleontologist does not learn Swahili.


During three days—Monday through Wednesday—a health officer will inspect exactly six buildings—three hotels: Grace, Jacaranda, and Lido; and three restaurants: Seville, Vesuvio, and Zeno. Each day, exactly two buildings are inspected: one in the morning and one in the afternoon. Inspections must occur according to the following conditions: Hotels are not inspected on Wednesday. Grace is inspected at some time before Jacaranda. Grace is not inspected on the same day as Seville. If Zeno is inspected in the morning, Lido is also inspected in the morning.

Question: Which one of the following could be the order in which the buildings are inspected, listed in order from Monday morning through Wednesday afternoon?

Grace, Seville, Jacaranda, Lido, Vesuvio, Zeno

Grace, Vesuvio, Zeno, Jacaranda, Lido, Seville

Lido, Jacaranda, Grace, Vesuvio, Zeno, Seville

Lido, Seville, Grace, Jacaranda, Zeno, Vesuvio

Zeno, Grace, Jacaranda, Lido, Seville, Vesuvio


Question: Which one of the following could be the buildings inspected in the mornings, listed in order from Monday through Wednesday?

Grace, Jacaranda, Zeno
Jacaranda, Vesuvio, Seville
Lido, Jacaranda, Vesuvio
Seville, Jacaranda, Vesuvio
Seville, Lido, Zeno


Question: Which one of the following is a pair of buildings that, if inspected on the same day as each other, must be inspected on Monday?

Grace and Jacaranda
Grace and Vesuvio
Jacaranda and Lido
Lido and Seville
Lido and Vesuvio


Question: If Grace is inspected on Tuesday, which one of the following could be the buildings inspected in the afternoons, listed in order from Monday through Wednesday?

Lido, Jacaranda, Vesuvio
Lido, Jacaranda, Zeno
Lido, Vesuvio, Zeno
Seville, Grace, Vesuvio
Seville, Jacaranda, Lido


Question: If Seville is inspected on Monday morning, which one of the following must be true?

Grace is inspected on Tuesday afternoon.

Jacaranda is inspected on Monday afternoon.

Vesuvio is inspected on Wednesday morning.


Question: If Grace is inspected on Monday morning and Zeno is inspected on Wednesday morning, which one of the following must be true?

Jacaranda is inspected before Lido is inspected.

Jacaranda is inspected after Lido is inspected.

Jacaranda is inspected after Seville is inspected.

Lido is inspected before Seville is inspected.

Lido is inspected before Vesuvio is inspected.


Morrisville's town council has exactly three members: Fu, Gianola, and Herstein. During one week, the council members vote on exactly three bills: a recreation bill, a school bill, and a tax bill. Each council member votes either for or against each bill. The following is known: Each member of the council votes for at least one of the bills and against at least one of the bills. Exactly two members of the council vote for the recreation bill. Exactly one member of the council votes for the school bill. Exactly one member of the council votes for the tax bill. Fu votes for the recreation bill and against the school bill. Gianola votes against the recreation bill. Herstein votes against the tax bill.

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

Fu and Gianola vote the same way on the tax bill.

Gianola and Herstein vote the same way on the recreation bill.

Gianola and Herstein vote the same way on the school bill.

Fu votes for one of the bills and Gianola votes for two of the bills.

Fu votes for two of the bills and Gianola votes for two of the bills.


Question: If the set of members of the council who vote against the school bill is the same set of members who vote against the tax bill, then which one of the following statements must be true?

Herstein votes against the recreation bill.


Question: If Gianola votes for the tax bill, then which one of the following statements could be true?

Fu and Gianola each vote for exactly one bill.

Gianola and Herstein each vote for exactly one bill.

Herstein votes against the recreation bill.


Question: If Gianola votes for exactly two of the three bills, which one of the following statements must be true?

Fu votes for the tax bill.
Gianola votes for the recreation bill.
Gianola votes for the school bill.
Gianola votes against the tax bill.
Herstein votes for the school bill.


Question: If one of the members of the council votes against exactly the same bills as does another member of the council, then which one of the following statements must be true?

Fu votes for the tax bill.
Gianola votes for the recreation bill.
Gianola votes against the school bill.
Gianola votes for exactly one bill
Herstein votes for exactly one bill.


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

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


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


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

Exactly three bills are paid on Wednesday.

Exactly three bills are paid on Thursday.

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

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

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


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


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


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

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

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

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

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

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


Two mannequins—1 and 2—will be dressed for display in outfits chosen from ten articles of clothing. Each article is in exactly one of three colors: navy, red, or yellow. There are three hats—one in each color; three jackets—one in each color; three skirts—one in each color; and one red tie. Each mannequin wears exactly one of the hats, one of the jackets, and one of the skirts. Furthermore, their outfits must meet the following restrictions: Neither mannequin wears all three colors. Each mannequin wears a hat in a different color from the jacket it wears. Mannequin 2 wears the navy skirt. Mannequin 1 wears the tie.

Question: Which one of the following could be complete outfits for the two mannequins?

mannequin 1: navy hat, red jacket, yellow skirt, red tie mannequin 2: red hat, navy jacket, navy skirt

mannequin 1: red hat, red jacket, yellow skirt, red tie mannequin 2: yellow hat, navy jacket, navy skirt

mannequin 1: red hat, yellow jacket, red skirt, red tie mannequin 2: yellow hat, navy jacket, yellow skirt

mannequin 1: yellow hat, red jacket, yellow skirt, red tie mannequin 2: red hat, navy jacket, navy skirt

mannequin 1: yellow hat, yellow jacket, red skirt mannequin 2: red hat, navy jacket, navy skirt


Question: Which one of the following could be true of the mannequins' outfits?

Mannequin 1 wears the navy jacket and the yellow skirt.

Mannequin 2 wears the red hat and the red jacket.

Mannequin 1 wears exactly one red article of clothing.

Mannequin 1 wears exactly three yellow articles of clothing.

Mannequin 2 wears no red articles of clothing.


Question: If mannequin 1 wears the navy jacket, which one of the following could be true?

Mannequin 1 wears the yellow hat.
Mannequin 1 wears the yellow skirt.
Mannequin 2 wears the red hat.
Mannequin 2 wears the yellow hat.
Mannequin 2 wears the yellow jacket.


Question: If all four of the red articles of clothing are included in the two mannequins' outfits, which one of the following must be true?

Mannequin 1 wears no navy articles of clothing.

Mannequin 2 wears no yellow articles of clothing.


Question: If mannequin 2 wears the red jacket, then mannequin 1 must wear the

navy hat
red hat
yellow hat
red skirt
yellow skirt


Question: If all three of the yellow articles of clothing are included in the two mannequins' outfits, which one of the following could be true?

Mannequin 1 wears the navy jacket.
Mannequin 1 wears the yellow jacket.
Mannequin 1 wears the red skirt.
Mannequin 2 wears the red hat.
Mannequin 2 wears the red jacket.


Question: If mannequin 1 wears the skirt that is the same color as the jacket that mannequin 2 wears, which one of the following must be true?

Mannequin 1 wears the yellow hat.
Mannequin 1 wears the yellow jacket.
Mannequin 2 wears the navy hat.
Mannequin 2 wears the red hat.
Mannequin 2 wears the red jacket.


A college dean will present seven awards for outstanding language research. The awards—one for French, one for German, one for Hebrew, one for Japanese, one for Korean, one for Latin, and one for Swahili—must be presented consecutively, one at a time, in conformity with the following constraints: The German award is not presented first. The Hebrew award is presented at some time before the Korean award is presented. The Latin award is presented at some time before the Japanese award is presented. The French award is presented either immediately before or immediately after the Hebrew award is presented. The Korean award is presented either immediately before or immediately after the Latin award is presented.

Question: Which one of the following must be true?

The French award is presented at some time before the Japanese award is presented.

The French award is presented at some time before the Swahili award is presented.

The German award is presented at some time before the Korean award is presented.

The German award is presented at some time before the Swahili award is presented.

The Swahili award is presented at some time before the Hebrew award is presented.


Question: If the Hebrew award is presented fourth, which one of the following must be true?

The French award is presented fifth.
The German award is presented third.
The Japanese award is presented sixth.
The Korean award is presented fifth.
The Swahili award is presented first.


Question: If the German award is presented third, which one of the following could be true?

The French award is presented fourth.
The Japanese award is presented fifth.
The Japanese award is presented sixth.
The Korean award is presented second.
The Swahili award is presented fifth.


Question: The earliest that the Japanese award could be presented is


Question: If the Japanese award is presented at some time before the Swahili award is presented, any of the following could be true EXCEPT:

The German award is presented immediately before the French award is presented.

The German award is presented immediately before the Japanese award is presented.

The Hebrew award is presented immediately before the Latin award is presented.

The Korean award is presented immediately before the Japanese award is presented.

The Swahili award is presented immediately before the German award is presented.


Question: The order in which the awards are presented is completely determined if which one of the following is true?

The French award is presented immediately before the German award is presented, and the Korean award is presented immediately before the Latin award is presented.

The French award is presented immediately before the Hebrew award is presented, and the Hebrew award is presented immediately before the Korean award is presented.

The French award is presented immediately before the Latin award is presented, and the Korean award is presented immediately before the Japanese award is presented.

The German award is presented immediately before the French award is presented, and the Latin award is presented immediately before the Japanese award is presented.

The German award is presented immediately before the Korean award is presented, and the Hebrew award is presented immediately before the French award is presented.


Exactly six piano classes are given sequentially on Monday: two with more than one student and four with exactly one student. Exactly four females—Gimena, Holly, Iyanna, and Kate—and five males—Leung, Nate, Oscar, Pedro, and Saul—attend these classes. Each student attends exactly one class. The following must obtain: Iyanna and Leung together constitute one class. Pedro and exactly two others together constitute one class. Kate is the first female, but not the first student, to attend a class. Gimena's class is at some time after Iyanna's but at sometime before Pedro's. Oscar's class is at some time after Gimena's.

Question: Which one of the following students could attend the first class?


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

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


Question: Which one of the following pairs of students could be in the class with Pedro?

Gimena and Holly
Holly and Saul
Kate and Nate
Leung and Oscar
Nate and Saul


Question: If Oscar and Pedro do not attend the same class as each other, then which one of the following could be true?

Gimena attends the fifth class.
Holly attends the third class.
Iyanna attends the fourth class.
Nate attends the fifth class.
Saul attends the second class.


Question: Suppose the condition that Oscar attends a class after Gimena is replaced with the condition that Oscar attends a class before Gimena and after Kate. If all the other conditions remain the same, then which class must Holly attend?

the second
the third
the fourth
the fifth
the sixth


This morning, a bakery makes exactly one delivery, consisting of exactly six loaves of bread. Each of the loaves is exactly one of three kinds: oatmeal, rye, or wheat, and each is either sliced or unsliced. The loaves that the bakery delivers this morning must be consistent with the following: There are at least two kinds of loaves. There are no more than three rye loaves. There is no unsliced wheat loaf. There is at least one unsliced oatmeal loaf. If two or more of the loaves are unsliced, then at least one of the unsliced loaves is rye.

Question: Which one of the following could be a complete and accurate list of the loaves that the bakery delivers?

five unsliced oatmeal loaves, one sliced rye loaf

five unsliced oatmeal loaves, one unsliced wheat loaf

four unsliced oatmeal loaves, two unsliced rye loaves

four unsliced oatmeal loaves, two sliced wheat loaves


Question: Each of the following could be a complete and accurate list of the unsliced loaves that the bakery delivers EXCEPT:

three oatmeal loaves
three oatmeal loaves, one rye loaf
two oatmeal loaves, two rye loaves
two oatmeal loaves, three rye loaves
one oatmeal loaf, one rye loaf


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

The only unsliced loaves are oatmeal loaves.

The only unsliced loaves are rye loaves.

The number of sliced loaves is exactly one greater than the number of sliced oatmeal loaves.

The number of unsliced loaves is exactly one greater than the number of unsliced oatmeal loaves.


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

No more than four oatmeal loaves are sliced.

No more than four wheat loaves are sliced.


Question: If the bakery delivers exactly four wheat loaves, then the bakery could also deliver

one sliced rye loaf and one unsliced rye loaf

one sliced oatmeal loaf and one unsliced oatmeal loaf


The six messages on an answering machine were each left by one of Fleure, Greta, Hildy, Liam, Pasquale, or Theodore, consistent with the following: At most one person left more than one message. No person left more than three messages. If the first message is Hildy's, the last is Pasquale's. If Greta left any message, Fleure and Pasquale did also. If Fleure left any message, Pasquale and Theodore did also, all of Pasquale's preceding any of Theodore's. If Pasquale left any message, Hildy and Liam did also, all of Hildy's preceding any of Liam's.

Question: Which one of the following could be a complete and accurate list of the messages left on the answering machine, from first to last?

Fleure's, Pasquale's, Theodore's, Hildy's, Pasquale's, Liam's

Greta's, Pasquale's, Theodore's, Theodore's, Hildy's, Liam's

Hildy's, Hildy's, Hildy's, Liam's, Pasquale's, Theodore's

Pasquale's, Hildy's, Fleure's, Liam's, Theodore's, Theodore's

Pasquale's, Hildy's, Theodore's, Hildy's, Liam's, Liam's


Question: The first and last messages on the answering machine could be the first and second messages left by which one of the following?


Question: If Greta left the fifth message, then which one of the following messages CANNOT have been left by Theodore?

the first message
the second message
the third message
the fourth message
the sixth message


Question: Each of the following must be true EXCEPT:

Exactly one person left at least two messages.


Question: If the only message Pasquale left is the fifth message, then which one of the following could be true?

Fleure left the third and fourth messages.


Exactly five cars—Frank's, Marquitta's, Orlando's, Taishah's, and Vinquetta's—are washed, each exactly once. The cars are washed one at a time, with each receiving exactly one kind of wash: regular, super, or premium. The following conditions must apply: The first car washed does not receive a super wash, though at least one car does. Exactly one car receives a premium wash. The second and third cars washed receive the same kind of wash as each other. Neither Orlando's nor Taishah's is washed before Vinquetta's. Marquitta's is washed before Frank's, but after Orlando's. Marquitta's and the car washed immediately before Marquitta's receive regular washes.

Question: Which one of the following could be an accurate list of the cars in the order in which they are washed, matched with type of wash received?

Orlando's: premium; Vinquetta's: regular; Taishah's: regular; Marquitta's: regular; Frank's: super

Vinquetta's: premium; Orlando's: regular; Taishah's: regular; Marquitta's: regular; Frank's: super

Vinquetta's: regular; Marquitta's: regular; Taishah's: regular; Orlando's: super; Frank's: super

Vinquetta's: super; Orlando's: regular; Marquitta's: regular; Frank's: regular; Taishah's: super

Vinquetta's: premium; Orlando's: regular; Marquitta's: regular; Frank's: regular; Taishah's: regular


Question: If Vinquetta's car does not receive a premium wash, which one of the following must be true?

Orlando's and Vinquetta's cars receive the same kind of wash as each other.

Marquitta's and Taishah's cars receive the same kind of wash as each other.

The fourth car washed receives a premium wash.


Question: If the last two cars washed receive the same kind of wash as each other, then which one of the following could be true?

Taishah's car is washed before Marquitta's car.

Vinquetta's car receives a regular wash.


Question: Which one of the following must be true?

Vinquetta's car receives a premium wash.

The fifth car washed receives a super wash.

The fourth car washed receives a super wash.

The second car washed receives a regular wash.


Question: Which one of the following is a complete and accurate list of the cars that must receive a regular wash?

Frank's, Marquitta's
Marquitta's, Orlando's
Marquitta's, Orlando's, Taishah's
Marquitta's, Taishah's
Marquitta's, Vinquetta's


Question: Suppose that in addition to the original five cars Jabrohn's car is also washed. If all the other conditions hold as given, which one of the following CANNOT be true?

Only the second and third cars washed receive a regular wash.

Jabrohn's car is washed after Frank's car.


Exactly seven toy-truck models—F, G, H, J, K, M, and S—are assembled on seven assembly lines, exactly one model to a line. The seven lines are arranged side by side and numbered consecutively 1 through 7. Assignment of models to lines must meet the following conditions: F is assembled on a lower-numbered line than J. M is assembled on the line numbered one lower than the line on which G is assembled. H is assembled on line 1 or else line 7. S is assembled on line 4.

Question: Which one of the following is an acceptable assignment of toy-truck models to lines, on order from line 1 through line 7?

F, J, K, S, H, M, G
F, K, J, S, M, G, H
F, M, K, S, G, J, H
H, K, S, M, G, F, J
H, M, G, S, J, F, K


Question: It must be true that the lowest-numbered line on which

F can be assembled is line 2
G can be assembled is line 3
J can be assembled is line 2
K can be assembled is line 3
M can be assembled is line 2


Question: If K is assembled on line 5, which one of the following is a pair of models that could be assembled, not necessarily in the order given, on lines whose numbers are consecutive to each other?


Question: There can be at most how many lines between the line on which F is assembled and the line on which J is assembled?


Question: If K is assembled on line 2, which one of the following must be true?

F is assembled on a lower-numbered line than S.

H is assembled on a lower-numbered line than G.

J is assembled on a lower-numbered line than H.

M is assembled on a lower-numbered line than J.

S is assembled on a lower-numbered line than J.


Question: If G is assembled on the line numbered one less than the line on which F is assembled, then which one of the following must be true?

F is assembled on line 3.
G is assembled on line 5.
H is assembled on line 1.
K is assembled on line 5.
M is assembled on line 6.


Question: If M is assembled on line 1, which one of the following could be true?

F is assembled on a line numbered one lower than the line on which H is assembled.

F is assembled on a line numbered one lower than the line on which K is assembled.

G is assembled on a line numbered one lower than the line on which J is assembled.

G is assembled on a line numbered one lower than the line on which K is assembled.

K is assembled on a line numbered one lower than the line on which G is assembled.


At a water carnival, each of the eight lifeguards—J, K, L, M, P, Q, R, and S—will participate in two events, a boat race and a rescue exercise. For each of these events the eight lifeguards are grouped into four two-person teams, subject to the following rules: If two lifeguards are teammates in the boat race, they cannot also be teammates in the rescue exercise. L and Q are teammates in the boat race. K and L are teammates in the rescue exercise. R and S are not teammates in either event.

Question: Which one of the following could be a list of the four teams participating in the boat race?

J and L; K and S; M and Q; P and R
J and M; K and P; L and Q; R and S
J and M; K and R; L and S; P and Q
J and M; K and S; L and Q; P and R
J and P; K and L; M and R; Q and S


Question: Which one of the following is a pair of lifeguards who cannot be teammates in the rescue exercise but who could be teammates in the boat race?


Question: If M and P are teammates in the boat race and J and R are teammates in the rescue exercise, which one of the following is a pair that must be teammates in the boat race?


Question: If P and K are teammates in the boat race and P and Q are teammates in the rescue exercise, then each of the following lists a pair of lifeguards who must be teammates in one of the two events EXCEPT:


Question: If J and P are teammates in the boat race, then M could be the teammate of

K in the boat race and S in the rescue exercise

L in the boat race and S in the rescue exercise

R in the boat race and L in the rescue exercise

S in the boat race and K in the rescue exercise

S in the boat race and P in the rescue exercise


A critic ranks exactly seven restaurants—Lautrec, Medici, Pastilla, Robusto, Scheherazade's, Tantoko, and Vistula—from highest (best) to lowest (worst). The ranking must meet the following conditions: Pastilla ranks higher than Lautrec but lower than Robusto. Medici ranks higher than Vistula but lower than Tantoko. If Scheherazade's ranks higher than Pastilla, Medici ranks higher than Scheherazade's. If Medici ranks higher than Scheherazade's, Scheherazade's ranks higher than Pastilla. There are no ties.

Question: Which one of the following could be an accurate ranking of the restaurants, from highest to lowest?

Tantoko, Medici, Scheherazade's, Pastilla, Vistula, Robusto, Lautrec

Robusto, Pastilla, Tantoko, Medici, Scheherazade's, Vistula, Lautrec

Tantoko, Medici, Scheherazade's, Robusto, Vistula, Pastilla, Lautrec

Tantoko, Robusto, Medici, Vistula, Pastilla, Scheherazade's, Lautrec

Robusto, Pastilla, Scheherazade's, Medici, Vistula, Tantoko, Lautrec


Question: If Pastilla ranks second highest, then which one of the following is a complete and accurate list of restaurants any one of which could be ranked fourth highest?

Lautrec
Lautrec, Vistula
Scheherazade's, Lautrec
Scheherazade's, Lautrec, Medici
Scheherazade's, Lautrec, Tantoko


Question: Which one of the following is the lowest ranking that Medici could have?

second highest
third highest
fourth highest
fifth highest
sixth highest


Question: If Medici ranks lower than Lautrec, then which one of the following must be true?

Scheherazade's ranks higher than Vistula.

Tantoko ranks higher than Scheherazade's.


Question: If Vistula ranks higher than Robusto, then which one of the following restaurants could be ranked fifth highest?

Tantoko Medici Scheherazade's Vistula Pastilla


Question: Which one of the following CANNOT be true?

Pastilla ranks second highest.
Vistula ranks third highest.
Lautrec ranks third highest.
Robusto ranks fifth highest.
Scheherazade's ranks sixth highest.


Question: If Tantoko is ranked third highest, then which one of the following CANNOT be true?

Lautrec ranked fourth highest.
Pastilla is ranked fifth highest.
Medici is ranked fifth highest.
Scheherazade's is ranked fifth highest.
Medici is ranked sixth highest.


Each of exactly three parks—Jessup, Island, and Hilltop—has at least one attraction. Each attraction is exactly one of five different types: fountain, garden, museum, playground, or theater. Among the three parks at least one of each type of attraction is included. No two attractions of the same type are included in any park. The following conditions must apply: Each of exactly two parks has a garden. Jessup has a museum but not a theater. Island has exactly one attraction. No park has both a playground and a fountain. Each park that has a theater also has a garden. Each park that has a museum also has a playground.

Question: Which one of the following could be a complete and accurate matching of each park to its attractions?

Jessup: garden, museum; Island: playground; Hilltop: garden, theater

Jessup: museum, theater; Island: garden; Hilltop: fountain, garden, playground, theater

Jessup: garden, museum, playground; Island: theater; Hilltop: garden, museum, playground

Jessup: garden, museum, playground; Island: fountain; Hilltop: garden, theater

Jessup: museum, playground; Island: fountain, garden; Hilltop: garden, theater


Question: Which one of the following CANNOT be true?

Neither Island nor Hilltop has a museum.

Neither Island nor Hilltop has a playground.

Neither Jessup nor Hilltop has a fountain.

Neither Jessup nor Island has a theater.


Question: If each of exactly two of the parks has a fountain, then which one of the following could be true?

Island does not have a fountain.
Jessup does not have a garden.
Jessup has exactly two attractions.
Hilltop has exactly three attractions.
Hilltop has exactly four attractions.


Question: If Jessup has exactly three attractions, then it is possible to determine the exact set of attractions featured by which of the parks?

Island only
Jessup only
Island and Hilltop only
Island and Jessup only
Jessup, Island, and Hilltop


Question: If the attraction included in Island is of the same type as an attraction included in Jessup, then which one of the following must be true?

Hilltop has a playground.
Island has a museum.
Island has a fountain.
Island has a garden.
Jessup has a garden.


Question: Which one of the following could be true?

Both Hilltop and Island have a playground.


Question: If Hilltop has exactly three attractions, then each of the following could be true EXCEPT:

Hilltop has a museum.
Hilltop has a playground.
Island does not have a fountain.
Island has a garden.
Jessup has a garden.


Each year for the next three years, Dynamic Motors will assemble four new automobile models—the Volante, the Whisper, the Xavier, and the Ziggurat—in exactly five of its factories—F, G, H, I, and K. Each factory will assemble exactly one model in each year. Because of contractual obligations Dynamic will assemble all four models each year according to the following constraints: No model is manufactured in the same factory in consecutive years. Neither Volantes nor Whispers are assembled in any factory in which Xaviers were assembled the previous year. Neither Volantes nor Xaviers are assembled in any factory in which Ziggurats were assembled the previous year. In any year, only one factory assembles Zigurats.

Question: Which one of the following could be the assembly schedule for factories F and G for the first two years?

year 1: Volantes in F, Ziggurats in G year 2: Xaviers in F, Whispers in G

year 1: Whispers in F, Xaviers in G year 2: Whispers in F, Ziggurats in G

year 1: Xaviers in F, Volantes in G year 2: Ziggurats in F, Ziggurats in G

year 1: Xaviers in F, Xaviers in G year 2: Whispers in F, Ziggurats in G

year 1: Ziggurats in F, Whispers in G year 2: Volantes in F, Volantes in G


Question: If in the first year Volantes and Whispers are assembled in F and G, respectively, the models that are assembled in the second year in F and G, respectively, could be

Volantes and Whispers
Whispers and Volantes
Whispers and Ziggurats
Ziggurats and Whispers
Ziggurats and Ziggurats


Question: Which one of the following must be true?

Xaviers are assembled in exactly two of the factories in the first year.

Xaviers are assembled in exactly one of the factories in the second year.

Xaviers are assembled in exactly two of the factories in the second year.

Xaviers are assembled in exactly one of the factories in the third year.

Xaviers are assembled in exactly two of the factories in the third year.


Question: If in the second year Ziggurats are assembled in F, which one of the following must be true?

Volantes are assembled in exactly one of the factories in the third year.

Whispers are assembled in exactly one of the factories in the third year.

Volantes are assembled in F in the first year.

Whispers are assembled in F in the first year.

Xaviers are assembled in F in the first year.


Question: If in the second year Volantes and Whispers are assembled in F and G, respectively, the models that are assembled in the first year in F and G, respectively, could be

Whispers and Volantes
Whispers and Xaviers
Xaviers and Volantes
Xaviers and Ziggurats
Ziggurats and Volantes


Each of seven television programs—H, J, L, P, Q, S, V—is assigned a different rank: from first through seventh (from most popular to least popular). The ranking is consistent with the following conditions: J and L are each less popular than H. J is more popular than Q. S and V are each less popular than L. P and S are each less popular than Q. S is not seventh.

Question: Which one of the following could be the order of the programs, from most popular to least popular?

J, H, L, Q, V, S, P
H, L, Q, J, S, P, V
H, J, Q, L, S, V, P
H, J, V, L, Q, S, P
H, L, V, J, Q, P, S


Question: If J is more popular than L, and S is more popular than P, then which one of the following must be true of the ranking?

J is second.
J is third.
L is third.
Q is third.
P is seventh.


Question: Which one of the following programs CANNOT be ranked third?


Question: If V is more popular than Q and J is less popular than L, then which one of the following could be true of the ranking?

P is more popular than S.
S is more popular than V.
P is more popular than L.
J is more popular than V.
Q is more popular than V.


Question: If Q is more popular than L, then each of the following must be true of the ranking EXCEPT:

H is first.
L is fourth.
V is not fourth.
J is not third.
Q is third.


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

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

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


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

Shrikes are the only other birds in the forest.

Jays are the only other birds in the forest.

The forest contains neither jays nor shrikes.

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

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


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

Neither martins nor harriers are in the forest.

Neither martins nor shrikes are in the forest.

Harriers and shrikes are the only birds in the forest.


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


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

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


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

The forest contains both wrens and shrikes.

At most two kinds of birds are in the forest.

At least three kinds of birds are in the forest.


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

The forest contains both jays and shrikes.

The forest contains both wrens and shrikes.

The forest contains both martins and shrikes.

Jays are not in the forest, whereas martins are.

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


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

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

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


Question: Which one of the following most be true?

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

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


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

All three of the sapphires are selected.


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

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


Question: Which one of the following must be true?

The selection of stones includes at least one ruby.

The selection of stones includes at most two rubies.

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

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

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


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

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


There are exactly ten stores and no other buildings on Oak Street. On the north side of the street, from west to east, are stores 1, 3, 5, 7, and 9; on the south side of the street, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the north side are located directly across the street from those on the south side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colors: green, red, and yellow. The stores have been decorated with lights according to the following conditions: No store is decorated with lights of the same color as those of any store adjacent to it. No store is decorated with lights of the same color as those of the store directly across the street from it. Yellow lights decorate exactly one store on each side of the street. Red lights decorate store 4. Yellow lights decorate store 5.

Question: Which one of the following could be an accurate list of the colors of the lights that decorate stores 2, 4, 6, 8, and 10, respectively?

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


Question: If green lights decorate store 7, then each of the following statements could be false EXCEPT:

Green lights decorate store 2.
Green lights decorate store 10.
Red lights decorate store 8.
Red lights decorate store 9.
Yellow lights decorate store 2.


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

Green lights decorate store 10.
Red lights decorate store 1.
Red lights decorate store 8.
Yellow lights decorate store 8.
Yellow lights decorate store 10.


Question: If green lights decorate five stores on the street, then which one of the following statements must be true?

Green lights decorate store 9.
Red lights decorate store 2.
Red lights decorate store 7.
Red lights decorate store 10.
Yellow lights decorate store 8.


Question: Suppose that yellow lights decorate exactly two stores, not just one, on the south side of the street and decorate exactly one store on the north side. If all of the other conditions remain the same, then which one of the following statements must be true?

Green lights decorate store 1.
Red lights decorate store 7.
Red lights decorate store 10.
Yellow lights decorate store 2.
Yellow lights decorate store 8.


Jill, Kurt, Larisa, Manny, and Olga are the clerks in a supermarket. The supermarket has exactly nine parallel aisles, numbered consecutively 1 through 9 from one end of the store to the other. Each aisle is stocked by exactly one clerk and no clerk stocks more than two aisles. Stocking assignments must meet the following conditions: Olga stocks exactly one aisle. Kurt stocks aisle 2. Manny does not stock aisle 1. Jill does not stock consecutive aisles. Kurt stocks the only aisle between the two aisles Manny stocks. Exactly one of Larisa's aisles is an end aisle. Olga's aisle is numbered higher than either of Kurt's aisles, and lower than at least one of Larisa's.

Question: Which one of the following clerks could stock two consecutive aisles?


Question: Which one of the following is a pair of clerks, neither of whom could stock aisle 5?

Jill and Manny
Kurt and Olga
Larisa and Manny
Kurt and Manny
Larisa and Olga


Question: Which one of the following is a complete and accurate list of clerks, any one of whom could stock aisle 3?

Jill, Kurt, Larisa
Jill, Larisa, Manny
Jill, Larisa, Olga
Jill, Kurt, Larisa, Manny
Jill, Kurt, Larisa, Olga


Question: Which one of the following is a complete and accurate list of aisles, any one of which could be one of the aisles Manny stocks?


Question: If Larisa's aisles are separated by the maximum number of aisles that could separate her aisles, which one of the following could be true?

Both of Jill's aisles are numbered lower than Olga's.

Only one clerk stocks a higher numbered aisle than Olga does.


Question: If Jill stocks aisle 3, then which one of the following CANNOT be true?

Jill stocks aisle 9.
Kurt stocks aisle 6.
Larisa stocks aisle 4.
Manny stocks aisle 4.
Olga stocks aisle 6.


Question: Suppose that, rather than just one, Larisa stocks both end aisles; all other conditions remaining in effect, which one of the following CANNOT be true?

Olga stocks the only aisle between the two aisles that Jill stocks.

One of Larisa's aisles is immediately next to Olga's.


A five-week adult education course consists of exactly five lectures with a different lecture given each week. No lecture is given more than once. Each lecture is delivered by a different speaker. The following conditions are true about the speakers and their lectures: Each speaker lectures on a philosopher in whom he or she specializes. No two speakers lecture on the same philosopher. The first week's speaker specializes in Kant, Locke, and Mill, and no other philosophers. The second week's speaker specializes in Kant, Locke, Mill, and Nietzsche, and no other philosophers. The third week's and fourth week's speakers each specialize in Mill and Nietzsche, and no other philosophers. The fifth week's speaker specializes in Nietzsche, Ockham, and Plato, and no other philosophers.

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

The second speaker lectures on Nietzsche.

The fifth speaker lectures on Nietzsche.


Question: What is the maximum possible number of different schedules for the five lectures in which those philosophers who are discussed are discussed in alphabetical order?


Question: Which one of the following, if known, would allow one to determine the entire lecture schedule and identify for each week the philosopher who is lectured on that week?

the weeks that Kant, Locke, and Mill are lectured on

the weeks that Kant, Mill, and Nietzsche are lectured on

the weeks that Kant, Mill, and Ockham are lectured on

the weeks that Mill, Nietzsche, and Ockham are lectured on

the weeks that Mill, Nietzsche, and Plato are lectured on


Question: Assume that, of the six philosophers, Kant and Nietzsche are the only German philosophers, and Locke, Mill, and Ockham are the only British philosophers. Each of the following statements could be true EXCEPT:

The first and fourth speakers lecture on British philosophers.

The first and fourth speakers lecture on German philosophers.

The second and third speakers lecture on British philosophers.

The third and fourth speakers lecture on German philosophers.

The fourth and fifth speakers lecture on British philosophers.


Question: Suppose the third speaker were a specialist not only in Mill and Nietzsche, but also in Sartre. If all of the other conditions remained the same, then each of the following could be true EXCEPT:

Mill is lectured on in the first lecture and Nietzsche in the fourth.

Mill is lectured on in the second lecture and Nietzsche in the third.

Mill is lectured on in the second lecture and Nietzsche in the fourth.

Mill is lectured on in the fourth lecture and Nietzsche in the fifth.

Nietzsche is lectured on in the second lecture and Mill in the fourth.


Exactly seven different trains—Quigley, Rockville, Sunnydale, Tilbury, Victoria, Wooster, and York—arrive at Middlebrook Station on Saturday. The following conditions govern their arrivals: The trains arrive one at a time. Either the York or the Wooster arrives fourth. The Sunnydale arrives at some time after the Wooster but at some time before the York. Both the Tilbury and the Victoria arrive at some time after the Rockville. The Tilbury does not arrive next after the Victoria; nor does the Victoria arrive next after the Tilbury.

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

Rockville, Tilbury, Victoria, Wooster, Sunnydale, York, Quigley

Rockville, Wooster, Quigley, York, Tilbury, Sunnydale, Victoria

Rockville, Tilbury, Quigley, Wooster, Sunnydale, York, Victoria

Quigley, Rockville, Wooster, Sunnydale, Victoria, York, Tilbury

Tilbury, Rockville, Quigley, Wooster, Sunnydale, York, Victoria


Question: If the Wooster arrives at some time before the Rockville, then exactly how many different orders are there in which the seven trains could arrive?


Question: Which one of the following must be true?

The first train to arrive is the Rockville.

The Quigley arrives at some time before the Sunnydale.

The Rockville arrives at some time before the Wooster.

The Victoria arrives at some time before the York.

The Wooster arrives at some time before the York.


Question: Which one of the following could be true?

The Sunnydale is the next train to arrive after the Quigley.

The Rockville is the next train to arrive after the Sunnydale.

The Rockville is the next train to arrive after the Tilbury.

The Quigley is the next train to arrive after the Sunnydale.

The Quigley is the next train to arrive after the Wooster.


Question: If exactly one of the trains arrives after the Wooster but before the York, then which one of the following could be true?

The sixth train to arrive is the Sunnydale.

The sixth train to arrive is the Tilbury.

The third train to arrive is the Rockville.

The second train to arrive is the Sunnydale.

The first train to arrive is the Rockville.


Question: If the Quigley arrives at some time before the Rockville, then the Wooster must arrive


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

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

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


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

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


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


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

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


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

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


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

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


From among eight candidates, four astronauts will be selected for a space flight. Four of the candidates—F, J, K, and L—are experienced astronauts and four—M, N, P, and T—are inexperienced astronauts. F, M, P, and T are geologists whereas J, K, L, and N are radiobiologists. The astronauts must be selected according to the following conditions: Exactly two experienced astronauts and two inexperienced astronauts are selected. Exactly two geologists and two radiobiologists are selected. Either P or L or both are selected.

Question: Which one of the following is an acceptable selection of astronauts for the space flight?

F, J, N, and T
F, L, M, and P
F, M, N, and P
J, L, M, and T
K, L, N, and T


Question: If F and P are selected for the space flight, the other two astronauts selected must be

a radiobiologist who is an experienced astronaut and a radiobiologist who is an inexperienced astronaut

a radiobiologist who is an experienced astronaut and a geologist who is an inexperienced astronaut

a radiobiologist and a geologist, both of whom are experienced astronauts

two radiobiologists, both of whom are experienced astronauts

two radiobiologists, both of whom are inexperienced astronauts


Question: If F and J are selected for the space flight, which one of the following must also be selected?


Question: If M and T are selected for the space flight, which one of the following could be, but need not be, selected for the flight?


Question: If N is selected for the space flight, which one of the following must also be selected?


A showroom contains exactly six new cars—T, V, W, X, Y, and Z—each equipped with at least one of the following three options: power windows, leather interior, and sunroof. No car has any other options. The following conditions must apply: V has power windows and a sunroof. W has power windows and a leather interior. W and Y have no options in common. X has more options than W. V and Z have exactly one option in common. T has fewer options than Z.

Question: For exactly how many of the six cars is it possible to determine exactly which options each one has?


Question: Which one of the following must be false?

Exactly five of the six cars have leather interiors.

Exactly five of the six cars have sunroofs.

Exactly four of the six cars have leather interiors.

Exactly four of the six cars have power windows.

Exactly four of the six cars have sunroofs.


Question: If all the cars that have leather interiors also have power windows, which one of the following must be false?

T has power windows.
T has a sunroof.
V has power windows.
Z has power windows.
Z has a sunroof.


Question: If Z has no options in common with T but has at least one option in common with every other car, then which one of the following must be false?

Exactly four of the six cars have power windows.

Exactly four of the six cars have leather interiors.

Exactly four of the six cars have sunroofs.


Question: Suppose that no two cars have exactly the same options as one another. In that case, each of the following could be true EXCEPT:

Exactly three of the six cars have power windows.

Exactly four of the six cars have power windows.

Exactly three of the six cars have sunroofs.

Exactly four of the six cars have sunroofs.

Exactly four of the six cars have leather interiors.


Question: If exactly four of the six cars have leather interiors, and exactly four of the six cars have power windows, then each of the following must be true EXCEPT:

T and Z have exactly one option in common.

W and Z have exactly one option in common.


Question: Suppose that the condition requiring that X has more options than W is replaced by a new condition requiring that X and W have exactly two options in common. If all of the other original conditions remain in effect, which one of the following must be false?

V and X have exactly one option in common.

V and X have exactly two options in common.

X and Z have exactly two options in common.