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

Answer: plastic, tin

Answer: newsprint, wood

Answer: newsprint, tin

Answer: glass, wood

Answer: glass, tin


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

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

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

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

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

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

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


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

Answer: H

Answer: I

Answer: K

Answer: N

Answer: O


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

Answer: G is the third valve opened.

Answer: H is the fourth valve opened.

Answer: P is the fifth valve opened.

Answer: O is the sixth valve opened.

Answer: G is the seventh valve opened.


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

Answer: G

Answer: I

Answer: K

Answer: N

Answer: P


Question: Which one of the following must be true?

Answer: At least one valve is opened before P is opened.

Answer: At least two valves are opened before G is opened.

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

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

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


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

Answer: I is the second valve opened.

Answer: N is the third valve opened.

Answer: G is the fifth valve opened.

Answer: O is the fifth valve opened.

Answer: P is the sixth valve opened.


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

Answer: K is the second valve opened.

Answer: N is the fourth valve opened.

Answer: H is the sixth valve opened.

Answer: O is the seventh valve opened.

Answer: L is the eighth valve opened.


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

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

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

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

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

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

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


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

Answer: Juana is accompanied by the same adult as Veronica.

Answer: Kyle is accompanied by the same adult as Salim.

Answer: Juana is accompanied by Mr. O'Connell.

Answer: Kyle is accompanied by Ms. Podorski.

Answer: Salim is accompanied by Ms. Podorski.


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

Answer: Kyle and Salim

Answer: Kyle and Thanh

Answer: Lucita and Salim

Answer: Lucita and Thanh

Answer: Salim and Thanh


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

Answer: Juana and Lucita

Answer: Juana and Salim

Answer: Kyle and Salim

Answer: Salim and Thanh

Answer: Salim and Veronica


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

Answer: Juana and Lucita

Answer: Juana and Veronica

Answer: Kyle and Thanh

Answer: Lucita and Thanh

Answer: Salim and Veronica


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

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

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

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

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

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

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


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

Answer: Negotiating is given on the first day.

Answer: Objections is given on the first day.

Answer: Persuasion is given on the first day.

Answer: Humor is given on the second day.

Answer: Telemarketing is given on the second day.


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

Answer: Negotiating is given at some time before Goals.

Answer: Persuasion is given at some time before Goals.

Answer: Persuasion is given at some time before Objections.

Answer: Humor is given at some time before Objections.

Answer: Negotiating is given at some time before Humor.


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

Answer: Humor

Answer: Persuasion

Answer: Objections

Answer: Negotiating

Answer: Goals


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

Answer: Telemarketing is given on the first day.

Answer: Negotiating is given on the second day.

Answer: Telemarketing is given on the second day.

Answer: Objections is given on the third day.

Answer: Persuasion is given on the third day.


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

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

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

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

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

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

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


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

Answer: Ginsberg's delivery is fifth.

Answer: Harris's delivery is second.

Answer: Harris's delivery is third.

Answer: Leacock's delivery is second.

Answer: Malpighi's delivery is first.


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

Answer: Figueroa's delivery is second.

Answer: Harris's delivery is second.

Answer: Harris's delivery is fourth.

Answer: Kanzaki's delivery is fifth.

Answer: Kanzaki's delivery is last.


Question: Which one of the following must be true?

Answer: Figueroa's delivery is earlier than Leacock's.

Answer: Ginsberg's delivery is earlier than Leacock's.

Answer: Harris's delivery is earlier than Kanzaki's.

Answer: Leacock's delivery is earlier than Ginsberg's.

Answer: Malpighi's delivery is earlier than Harris's.


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

Answer: Figueroa's delivery is first.

Answer: Ginsberg's delivery is third.

Answer: Harris's delivery is third.

Answer: Leacock's delivery is fifth.

Answer: Malpighi's delivery is second.


Question: Which one of the following must be false?

Answer: Figueroa's delivery is first.

Answer: Ginsberg's delivery is fifth.

Answer: Harris's delivery is third.

Answer: Leacock's delivery is second.

Answer: Malpighi's delivery is fourth.


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

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

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

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

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

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

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


Question: Which one of the following could be true?

Answer: West is the only performer who signs with Star Agency.

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

Answer: Xavier signs with the same agency as Zinser.

Answer: Zinser is the only performer who signs with Star Agency.

Answer: Three of the performers sign with Fame Agency.


Question: Which one of the following must be true?

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

Answer: Fame Agency signs at most two of the performers.

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

Answer: Traugott signs with the same agency as West.

Answer: West does not sign with Fame Agency.


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

Answer: Traugott signs with Fame Agency.

Answer: Traugott signs with Star Agency.

Answer: West signs with Premier Agency.

Answer: Xavier signs with Fame Agency.

Answer: Zinser signs with Premier Agency.


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

Answer: Premier Agency signs exactly one performer.

Answer: Star Agency signs exactly three of the performers.

Answer: Traugott signs with Star Agency.

Answer: West signs with Star Agency.

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


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

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

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

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

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

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

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


Question: Mertz's design CANNOT be presented

Answer: sixth

Answer: fifth

Answer: fourth

Answer: third

Answer: second


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

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

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

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

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

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


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

Answer: Jackson's design is presented second.

Answer: Peete's design is presented third.

Answer: Peete's design is presented fourth.

Answer: Jackson's design is presented fifth.

Answer: Liu's design is presented fifth.


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

Answer: Green's

Answer: Jackson's

Answer: Liu's

Answer: Peete's

Answer: Valdez's


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

Answer: first: Mertz; fourth: Liu; fifth: Green

Answer: second: Green; third: Peete; fourth: Jackson

Answer: second: Mertz; fifth: Green; sixth: Jackson

Answer: fourth: Peete; fifth: Liu; sixth: Jackson

Answer: fourth: Valdez; fifth: Green; sixth: Liu


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

Question: Which one of the following could be true?

Answer: X was questioned on day one.

Answer: V was questioned on day two.

Answer: Z was questioned on day four.

Answer: W was questioned on day five.

Answer: S was questioned on day six.


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

Answer: T confessed.

Answer: T did not confess.

Answer: V did not confess.

Answer: X confessed.

Answer: Y did not confess.


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

Answer: V did not confess.

Answer: Y confessed.

Answer: X did not confess.

Answer: X was questioned on day four.

Answer: Z was questioned on day two.


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

Answer: V

Answer: W

Answer: X

Answer: Y

Answer: Z


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

Answer: V confessed.

Answer: X was questioned on day five.

Answer: Y was questioned on day one.

Answer: Z was questioned on day one.

Answer: Z did not confess.


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

Answer: T confessed.

Answer: V was questioned on day two.

Answer: X was questioned on day four.

Answer: Y confessed.

Answer: Z did not confess.


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

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

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

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

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

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

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


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

Answer: O'Rourke is on the first-place team.

Answer: Pavlovich is on the first-place team.

Answer: Mei is on the second-place team.

Answer: Navarro is on the second-place team.

Answer: Sethna is on the second-place team.


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

Answer: Mei is on the team from Gillom High.

Answer: Navarro is on the team from Fairview High.

Answer: O'Rourke is on the team from Gillom High.

Answer: Pavlovich is on the team from Hilltop High.

Answer: Tsudama is on the team from Gillom High.


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

Answer: two

Answer: three

Answer: four

Answer: five

Answer: six


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

Answer: The Fairview team places first.

Answer: The Gillom team places second.

Answer: Navarro is on the second-place team.

Answer: O'Rourke is on the first-place team.

Answer: Pavlovich is on the first-place team.


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

Answer: Mei

Answer: Navarro

Answer: O'Rourke

Answer: Pavlovich

Answer: Tsudama


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

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

Answer: Grant

Answer: Keiko, Lorena

Answer: Grant, Hassan, Lorena

Answer: Grant, Hassan, Jaclyn

Answer: Felipe, Grant, Jaclyn, Lorena


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

Answer: Felipe and Grant are the only men on stage.

Answer: Grant and Hassan are the only men on stage.

Answer: Jaclyn is the only woman on stage.

Answer: Keiko is the only woman on stage.

Answer: Jaclyn and Keiko are the only women on stage.


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

Answer: Lorena

Answer: Felipe, Lorena

Answer: Hassan, Lorena

Answer: Hassan, Keiko

Answer: Hassan, Keiko, Lorena


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

Answer: five

Answer: four

Answer: three

Answer: two

Answer: one


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

Answer: zero

Answer: one

Answer: two

Answer: three

Answer: four


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

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

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

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

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

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

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


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

Answer: In Flight received a rating of three stars.

Answer: Nice received a rating of three stars.

Answer: Quasi received a rating of three stars.

Answer: Reunion received a rating of one star.

Answer: Sounds Good received a rating of one star.


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

Answer: Headstrong received a rating of two stars.

Answer: In Flight received a rating of three stars.

Answer: Nice received a rating of two stars.

Answer: Quasi received a rating of four stars.

Answer: Sounds Good received a rating of one star.


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

Answer: Headstrong received a rating of three stars.

Answer: Headstrong received a rating of four stars.

Answer: In Flight received a rating of three stars.

Answer: Sounds Good received a rating of two stars.

Answer: Sounds Good received a rating of three stars.


Question: Which one of the following CANNOT be true?

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

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

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

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

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


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

Answer: Headstrong received a rating of four stars.

Answer: In Flight received a rating of two stars.

Answer: Nice received a rating of three stars.

Answer: Quasi received a rating of three stars.

Answer: Sounds Good received a rating of two stars.


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

Answer: Headstrong

Answer: In Flight

Answer: Quasi

Answer: Reunion

Answer: Sounds Good


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

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

Answer: lemon, marzipan, orange, strawberry, vanilla, raspberry

Answer: lemon, marzipan, orange, strawberry, raspberry, vanilla

Answer: marzipan, lemon, raspberry, vanilla, orange, strawberry

Answer: raspberry, lemon, marzipan, vanilla, strawberry, orange

Answer: raspberry, orange, lemon, marzipan, strawberry, vanilla


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

Answer: The raspberry layer is immediately above the vanilla layer.

Answer: The raspberry layer is immediately above the orange layer.

Answer: The raspberry layer is immediately below the marzipan layer.

Answer: The raspberry layer is the second layer.

Answer: The raspberry layer is the top layer.


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

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

Answer: the second, the third, the fourth, the fifth, the sixth

Answer: the third, the fourth, the fifth, the sixth

Answer: the fourth, the fifth, the sixth

Answer: the fifth, the sixth


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

Answer: The vanilla layer is fifth.

Answer: The vanilla layer is immediately above the raspberry layer.

Answer: The orange layer is not immediately above the marzipan layer.

Answer: The raspberry layer is above the marzipan layer.

Answer: The strawberry layer is not the top layer.


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

Answer: lemon, raspberry

Answer: vanilla, raspberry

Answer: marzipan, raspberry

Answer: raspberry, marzipan

Answer: raspberry, strawberry


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

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

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

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

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

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

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


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

Answer: H

Answer: J

Answer: K

Answer: R

Answer: T


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

Answer: H

Answer: J

Answer: K

Answer: R

Answer: T


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

Answer: T is the lowest in cost.

Answer: K is the second lowest in cost.

Answer: R is the third lowest in cost.

Answer: S is the fifth lowest in cost.

Answer: J is the highest in cost.


Question: Which one of the following must be true?

Answer: H is lower in cost than S.

Answer: H is lower in cost than T.

Answer: K is lower in cost than J.

Answer: S is lower in cost than J.

Answer: S is lower in cost than K.


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

Answer: J is the highest in cost.

Answer: S is the fifth lowest in cost.

Answer: K is the third lowest in cost.

Answer: H is the second lowest in cost.

Answer: K is the accepted bid.


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

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

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

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

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

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

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


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

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

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

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

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

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


Question: Which one of the following could be true?

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

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

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

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

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


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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: Saito is on the same team as Veracruz.

Answer: Gambini is on the same team as Mitchum.

Answer: Mitchum prepares a final argument.

Answer: Veracruz prepares a final argument.

Answer: Gambini prepares an opening argument.


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

Answer: Gambini and Little

Answer: Gambini and Saito

Answer: Little and Veracruz

Answer: Mitchum and Veracruz

Answer: Richardson and Veracruz


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

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

Answer: Lula, Hilary, Jerome, Hilary, Jerome, Lula

Answer: Jerome, Lula, Hilary, Lula, Jerome

Answer: Jerome, Lula, Hilary, Jerome, Hilary

Answer: Jerome, Lula, Hilary, Hilary, Jerome

Answer: Hilary, Lula, Lula, Jerome, Jerome, Hilary


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

Answer: zero

Answer: one

Answer: two

Answer: three

Answer: four


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

Answer: Exactly one of the messages is from Lula.

Answer: Exactly two of the messages are from Jerome.

Answer: The second message is from Lula.

Answer: The third message is from Hilary.

Answer: The fourth message is from Jerome.


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

Answer: the second message

Answer: the third message

Answer: the fourth message

Answer: the fifth message (if there is a fifth one)

Answer: the sixth message (if there is a sixth one)


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

Answer: The first message is from Jerome.

Answer: The second message is from Lula.

Answer: The third message is from Hilary.

Answer: The fourth message is from Jerome.

Answer: The sixth message is from Lula.


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

Answer: zero

Answer: one

Answer: two

Answer: three

Answer: four


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

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

Answer: F, G, T, R, S, H

Answer: F, R, G, T, H, S

Answer: G, R, T, S, H, F

Answer: R, F, G, S, H, T

Answer: R, S, H, T, F, G


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

Answer: G ranks second.

Answer: H ranks fourth.

Answer: R ranks second.

Answer: S ranks fourth.

Answer: T ranks fourth.


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

Answer: G

Answer: H

Answer: R

Answer: S

Answer: T


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

Answer: F ranks second that week.

Answer: G ranks fifth that week.

Answer: H ranks third that week.

Answer: R ranks third that week.

Answer: S ranks third that week.


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

Answer: G ranks fourth.

Answer: H ranks fifth.

Answer: R ranks third.

Answer: S ranks fourth.

Answer: T ranks fifth.


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

Answer: G, H, S

Answer: R, T

Answer: F, T

Answer: G, T

Answer: T


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

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

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

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

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

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

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


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

Answer: Rosa

Answer: Greg, Rosa

Answer: Greg, Vijay

Answer: Greg, Rosa, Vijay

Answer: Jasmine, Rosa, Vijay


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

Answer: Greg, Vijay, Jasmine, Rosa

Answer: Rosa, Vijay, Greg, Jasmine

Answer: Vijay, Greg, Rosa, Jasmine

Answer: Vijay, Jasmine, Greg, Rosa

Answer: Vijay, Rosa, Jasmine, Greg


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

Answer: Vijay is on board when the van reaches Simcoe.

Answer: Vijay is on board when the van reaches Los Altos.

Answer: Rosa is on board when the van reaches Simcoe.

Answer: Rosa is on board when the van reaches Fundy.

Answer: Jasmine is on board when the van reaches Mineola.


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

Answer: Greg is on board when the van reaches Fundy.

Answer: Jasmine is on board when the van reaches Mineola.

Answer: Rosa is on board when the van reaches Fundy.

Answer: Vijay is on board when the van reaches Fundy.

Answer: Vijay is on board when the van reaches Mineola.


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

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

Answer: Fujimura, Gabrieli, King, Jackson, Herman, Lauder

Answer: Fujimura, King, Lauder, Gabrieli, Jackson, Herman

Answer: Fujimura, Lauder, Gabrieli, King, Jackson, Herman

Answer: Herman, Jackson, Gabrieli, Lauder, King, Fujimura

Answer: Jackson, Gabrieli, Lauder, Herman, King, Fujimura


Question: Which one of the following must be true?

Answer: Lauder is scheduled to audition earlier than Herman.

Answer: Lauder is scheduled to audition earlier than King.

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

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

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


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

Answer: 5 P.M.

Answer: 4 P.M.

Answer: 3 P.M.

Answer: 2 P.M.

Answer: 1 P.M.


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

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

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

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

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

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


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

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

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

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

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

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


Question: Which one of the following must be true?

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

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

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

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

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


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

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

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

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

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

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

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


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

Answer: Heather helps move the sofa.

Answer: Josh helps move the sofa.

Answer: Maria helps move the sofa.

Answer: Grace helps move the table.

Answer: Heather helps move the table.


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

Answer: Grace helps move the recliner.

Answer: Maria helps move the recliner.

Answer: Josh helps move the sofa.

Answer: Maria helps move the sofa.

Answer: Grace helps move the table.


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

Answer: Grace and Josh

Answer: Grace and Maria

Answer: Heather and Josh

Answer: Heather and Maria

Answer: Josh and Maria


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

Answer: Heather and Josh help each other move the recliner.

Answer: Heather and Maria help each other move the recliner.

Answer: Grace and Josh help each other move the table.

Answer: Grace and Maria help each other move the table.

Answer: Heather and Maria help each other move the table.


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

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

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

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

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

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

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


Question: Which one of the following must be true?

Answer: Graystone Park is planted with sycamores.

Answer: Landing Park is planted with maples.

Answer: Landing Park is planted with tamaracks.

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

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


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

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

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

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

Answer: Graystone Park is planted with both maples and oaks.

Answer: Landing Park is planted with both maples and oaks.


Question: Which one of the following must be false?

Answer: Both parks are planted with oaks.

Answer: Both parks are planted with sycamores.

Answer: Both parks are planted with tamaracks.

Answer: Exactly one of the parks is planted with maples.

Answer: Exactly one of the parks is planted with sycamores.


Question: Which one of the following could be true?

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

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

Answer: Exactly one of the parks is planted with tamaracks.

Answer: Neither park is planted with tamaracks.

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


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

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

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

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

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

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

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


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

Answer: The Farmington visit includes Quinn.

Answer: The Homestead visit includes Vandercar.

Answer: The Morningside visit includes Sasada.

Answer: The second of the three site visits includes Sasada.

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


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

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

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

Answer: One of the site visits includes only Vandercar.

Answer: The second of the three site visits includes Sasada.

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


Question: The executives who visit Homestead CANNOT be

Answer: Quinn and Vandercar only

Answer: Rodriguez and Taylor only

Answer: Sasada and Taylor only

Answer: Quinn, Sasada, and Vandercar

Answer: Rodriguez, Sasada, and Taylor


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

Answer: One of the site visits includes both Rodriguez and Sasada.

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

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

Answer: The Homestead visit takes place earlier than the Morningside visit.

Answer: The Morningside visit takes place earlier than the Farmington visit.


Question: Which one of the following must be true?

Answer: The Farmington visit takes place earlier than the Morningside visit.

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

Answer: One of the first two site visits includes Sasada.

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

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


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

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

Answer: The last of the three site visits includes Rodriguez.

Answer: The Homestead visit includes Quinn.

Answer: The Morningside visit includes Taylor.

Answer: The site visit that includes Vandercar also includes Quinn.


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

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

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

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

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

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

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


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

Answer: grocery shopping

Answer: hedge trimming

Answer: jogging

Answer: kitchen cleaning

Answer: motorbike servicing


Question: Which one of the following CANNOT be true?

Answer: Hedge trimming is fourth.

Answer: Jogging is fourth.

Answer: Kitchen cleaning is second.

Answer: Laundry is third.

Answer: Motorbike servicing is second.


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

Answer: grocery shopping

Answer: hedge trimming

Answer: jogging

Answer: laundry

Answer: motorbike servicing


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

Answer: Laundry has to be one of the last three activities.

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

Answer: Jogging has to be earlier than laundry.

Answer: Laundry has to be earlier than hedge trimming.

Answer: Laundry has to be earlier than jogging.


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

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

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

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

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

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

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


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

Answer: Wednesday and Thursday

Answer: Wednesday and Friday

Answer: Thursday and Friday

Answer: Thursday and Saturday

Answer: Friday and Saturday


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

Answer: Gombrich's last audition is on Thursday.

Answer: Gombrich's last audition is on Friday.

Answer: Otto's last audition is on Saturday.

Answer: Raines's last audition is on Friday.

Answer: Raines's last audition is on Thursday.


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

Answer: Wednesday and Thursday

Answer: Wednesday and Friday

Answer: Wednesday and Saturday

Answer: Thursday and Friday

Answer: Thursday and Saturday


Question: Which one of the following could be true?

Answer: All three actors audition on Wednesday.

Answer: All three actors audition on Friday.

Answer: All three actors audition on Saturday.

Answer: Otto auditions on Friday and on Saturday.

Answer: Raines auditions on Wednesday and on Friday.


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

Answer: Otto auditions on both Wednesday and Thursday.

Answer: Otto auditions on both Wednesday and Friday.

Answer: Otto auditions on both Wednesday and Saturday.

Answer: Raines auditions on both Wednesday and Saturday.

Answer: Raines auditions on both Thursday and Friday.


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

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

Answer: the lambeosaur, the plateosaur, the stegosaur, the ultrasaur, the velociraptor

Answer: the lambeosaur, the plateosaur, the stegosaur, the tyrannosaur, the ultrasaur

Answer: the iguanadon, the lambeosaur, the plateosaur, the stegosaur, the ultrasaur

Answer: the iguanadon, the lambeosaur, the plateosaur, the tyrannosaur, the velociraptor

Answer: the iguanadon, the lambeosaur, the stegosaur, the ultrasaur, the velociraptor


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

Answer: a green iguanadon

Answer: a mauve velociraptor

Answer: a mauve lambeosaur

Answer: a mauve ultrasaur

Answer: a yellow plateosaur


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

Answer: a green lambeosaur and a mauve velociraptor

Answer: a green lambeosaur and a yellow tyrannosaur

Answer: a green lambeosaur and a yellow ultrasaur

Answer: a yellow tyrannosaur and a green ultrasaur

Answer: a yellow tyrannosaur and a red velociraptor


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

Answer: The iguanadon is included in the display.

Answer: The plateosaur is not included in the display.

Answer: The display includes two yellow toy dinosaurs.

Answer: The display contains a green lambeosaur.

Answer: The display contains a mauve velociraptor.


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

Answer: a mauve tyrannosaur

Answer: a mauve ultrasaur

Answer: a yellow lambeosaur

Answer: a yellow plateosaur

Answer: a yellow ultrasaur


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

Answer: There is exactly one yellow toy included in the display.

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

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

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

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


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

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

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

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

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

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

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


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

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

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

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

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

Answer: Three grants are awarded in the fourth quarter.


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

Answer: A medical services grant is awarded in the second quarter.

Answer: A theater arts grant is awarded in the first quarter.

Answer: A theater arts grant is awarded in the second quarter.

Answer: A wildlife preservation grant is awarded in the fourth quarter.

Answer: A youth services grant is awarded in the third quarter.


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

Answer: Two youth services grants are awarded.

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

Answer: A wildlife preservation grant is awarded in the fourth quarter.

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

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


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

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

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

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

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

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


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

Answer: Two theater arts grants are awarded.

Answer: Two youth services grants are awarded.

Answer: Three grants are awarded in the first quarter.

Answer: Three grants are awarded in the second quarter.

Answer: Three grants are awarded in the third quarter.


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

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

Answer: 601: G; 602: L, S; 603: M; 604: H; 605: F

Answer: 601: G, M; 602: L; 603: H; 604: S; 605: F

Answer: 601: G, M; 602: S; 603: F; 604: L; 605: H

Answer: 601: G, S; 602: L; 603: F; 604: M; 605: H

Answer: 601: G, S; 602: L; 603: M; 604: H; 605: F


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

Answer: 601

Answer: 602

Answer: 603

Answer: 604

Answer: 605


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

Answer: F was begun in 603.

Answer: G was begun in 602.

Answer: H was begun in 605.

Answer: M was begun in 602.

Answer: S was begun in 604.


Question: Which one of the following must be true?

Answer: F was begun in a later year than M.

Answer: F was begun in a later year than S.

Answer: H was begun in a later year than F.

Answer: H was begun in a later year than S.

Answer: M was begun in a later year than G.


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

Answer: F was begun in 605.

Answer: G was begun in 601.

Answer: H was begun in 604.

Answer: M was begun in 601.

Answer: S was begun in 603.


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

Answer: F was begun in 603.

Answer: G was begun in 602.

Answer: H was begun in 605.

Answer: L was begun in 603.

Answer: S was begun in 604.


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

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

Answer: Felicia, Salman

Answer: Masatomo, Rochelle

Answer: Leah, Salman, Terry

Answer: Salman, Rochelle, Veena

Answer: Leah, Salman, Terry, Veena


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

Answer: Felicia and Rochelle also volunteer.

Answer: Felicia and Salman also volunteer.

Answer: Leah and Masatomo also volunteer.

Answer: Leah and Terry also volunteer.

Answer: Salman and Terry also volunteer.


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

Answer: Felicia volunteers.

Answer: Leah volunteers.

Answer: Rochelle volunteers.

Answer: Salman volunteers.

Answer: Veena volunteers.


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

Answer: Felicia volunteers.

Answer: Leah volunteers.

Answer: Veena volunteers.

Answer: Salman does not volunteer.

Answer: Terry does not volunteer.


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

Answer: Leah volunteers.

Answer: Salman volunteers.

Answer: Veena does not volunteer.

Answer: Exactly three of the employees volunteer.

Answer: Exactly four of the employees volunteer.


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

Answer: Felicia and Terry

Answer: Leah and Masatomo

Answer: Leah and Veena

Answer: Rochelle and Salman

Answer: Salman and Terry


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

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

Answer: P, Q, R, S, T

Answer: P, Q, T, S, R

Answer: P, S, T, Q, R

Answer: P, S, T, R, Q

Answer: T, S, R, P, Q


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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: Plane S departs first.

Answer: Plane S departs third.

Answer: Plane T departs second.

Answer: Plane T departs third.

Answer: Plane T departs fourth.


Question: Which one of the following must be true?

Answer: Plane P departs first.

Answer: Plane Q departs last.

Answer: Plane R departs second.

Answer: Plane S departs first.

Answer: Plane T departs fourth.


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

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

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

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

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

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


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

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

Answer: history, linguistics, and statistics

Answer: history, music, and physics

Answer: history, physics, and theater

Answer: linguistics, physics, theater, and writing

Answer: music, theater, and writing


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

Answer: seven

Answer: six

Answer: five

Answer: four

Answer: three


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

Answer: history nor linguistics

Answer: history nor music

Answer: history nor statistics

Answer: linguistics nor music

Answer: statistics nor theater


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

Answer: writing

Answer: theater

Answer: statistics

Answer: physics

Answer: linguistics


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

Answer: history or statistics

Answer: linguistics or theater

Answer: linguistics or writing

Answer: music or physics

Answer: theater or writing


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

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

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

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

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

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


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

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

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

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

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

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

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


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

Answer: Family law is assigned to the middle floor.

Answer: Health law is assigned to the middle floor.

Answer: Labor law is assigned to the top floor.

Answer: Securities is assigned to the bottom floor.

Answer: Tax law is assigned to the top floor.


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

Answer: family law, health law, probate, and tax law

Answer: family law, injury law, probate, and tax law

Answer: family law, probate, securities, and tax law

Answer: health law, probate, securities, and tax law

Answer: injury law, probate, securities, and tax law


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

Answer: Exactly one department is assigned to the middle floor.

Answer: Exactly four departments are assigned to the middle floor.

Answer: Exactly two departments are assigned to the bottom floor.

Answer: Exactly three departments are assigned to the bottom floor.

Answer: Exactly four departments are assigned to the bottom floor.


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

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

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

Answer: Family law is assigned to the same floor as securities.

Answer: Probate is assigned to the same floor as health law.

Answer: Probate is assigned to the same floor as injury law.


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

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

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

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

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

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

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


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

Answer: Gardenias is fourth.

Answer: Hibiscus is fourth.

Answer: Irises is third.

Answer: Lotus is second.

Answer: Magnolia is third.


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

Answer: Gardenias is fourth.

Answer: Hibiscus is second.

Answer: Irises is second.

Answer: Lotus is first.

Answer: Magnolia is third.


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

Answer: Hibiscus is third.

Answer: Hibiscus is fourth.

Answer: Hibiscus is fifth.

Answer: Gardenias is fourth.

Answer: Gardenias is sixth.


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

Answer: If Fence is seventh, Hibiscus is second.

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

Answer: Hibiscus must be somewhere between the first and sixth photographs.

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

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


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

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

Answer: Geography, Japanese, Psychology, Russian

Answer: Geography, Macroeconomics, Psychology, Statistics

Answer: Geography, Japanese, Macroeconomics, Russian

Answer: Geography, Psychology, Russian, Statistics

Answer: Macroeconomics, Psychology, Russian, Statistics


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

Answer: Geography, Statistics, World History

Answer: Japanese, Macroeconomics, Statistics

Answer: Japanese, Psychology, World History

Answer: Psychology, Russian, World History

Answer: Russian, Statistics, World History


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

Answer: World History

Answer: Statistics

Answer: Psychology

Answer: Macroeconomics

Answer: Japanese


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

Answer: Geography and Japanese

Answer: Geography and Psychology

Answer: Japanese and World History

Answer: Psychology and Russian

Answer: Russian and World History


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

Answer: Japanese

Answer: Macroeconomics

Answer: Psychology

Answer: Russian

Answer: World History


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

Answer: Psychology, Russian, Statistics, World History

Answer: Macroeconomics, Psychology, Statistics, World History

Answer: Macroeconomics, Psychology, Russian, World History

Answer: Geography, Psychology, Russian, World History

Answer: Geography, Macroeconomics, Russian, World History


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

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

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

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

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

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

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


Question: Which one of the following must be true?

Answer: Toronto is used in the first year.

Answer: Montreal is used in the fourth year.

Answer: Toronto is used at some time before Montreal is used.

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

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


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

Answer: Los Angeles is used in the fifth year.

Answer: Montreal is used in the sixth year.

Answer: New York is used in the fifth year.

Answer: Vancouver is used in the first year.

Answer: Washington is used in the second year.


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

Answer: 1, 3, 5

Answer: 2, 3, 4, 5

Answer: 2, 3, 4, 6

Answer: 1, 2, 4, 6

Answer: 1, 2, 3, 4, 5, 6


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

Answer: Washington is used in the third year.

Answer: Vancouver is used in the third year.

Answer: Toronto is used in the fourth year.

Answer: New York is used in the fifth year.

Answer: Los Angeles is used in the third year.


Question: Which one of the following could be true?

Answer: Los Angeles is used in the first year.

Answer: New York is used in the second year.

Answer: Montreal is used in the third year.

Answer: Vancouver is used in the fourth year.

Answer: Toronto is used in the sixth year.


Question: Which one of the following must be false?

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

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

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

Answer: Toronto is used either immediately before or immediately after Vancouver.

Answer: Toronto is used either immediately before or immediately after Washington.


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

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

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

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

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

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

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


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

Answer: Jewelry

Answer: Kite-making

Answer: Needlepoint

Answer: Quilting

Answer: Scrapbooking


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

Answer: Jewelry, Kite-making

Answer: Jewelry, Quilting

Answer: Quilting, Scrapbooking

Answer: Scrapbooking, Quilting

Answer: Scrapbooking, Rug-making


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

Answer: Jewelry is given on Thursday morning.

Answer: Needlepoint is given on Thursday afternoon.

Answer: Quilting is given on Wednesday morning.

Answer: Rug-making is given on Friday afternoon.

Answer: Scrapbooking is given on Wednesday afternoon.


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

Answer: Jewelry

Answer: Kite-making

Answer: Needlepoint

Answer: Rug-making

Answer: Scrapbooking


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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

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

Answer: Geyer, Lin, Jhalani, Paredes, Mitchell, Henson

Answer: Geyer, Mitchell, Paredes, Lin, Henson, Jhalani

Answer: Henson, Lin, Paredes, Jhalani, Geyer, Mitchell

Answer: Lin, Paredes, Mitchell, Henson, Jhalani, Geyer

Answer: Paredes, Mitchell, Lin, Jhalani, Geyer, Henson


Question: Which one of the following CANNOT be true?

Answer: Henson appears earlier than Geyer.

Answer: Henson appears sixth.

Answer: Lin appears fifth.

Answer: Paredes appears earlier than Mitchell.

Answer: Paredes appears second.


Question: Exactly how many of the actors are there any one of whom could appear sixth?

Answer: 5

Answer: 4

Answer: 3

Answer: 2

Answer: 1


Question: If Jhalani appears earlier than Mitchell, then which one of the following could be the order in which the other four actors appear, from earliest to latest?

Answer: Geyer, Lin, Paredes, Henson

Answer: Geyer, Paredes, Henson, Lin

Answer: Lin, Henson, Geyer, Paredes

Answer: Lin, Paredes, Henson, Geyer

Answer: Paredes, Lin, Henson, Geyer


Question: If Lin appears immediately before Geyer, then which one of the following must be true?

Answer: Geyer appears no later than third.

Answer: Henson appears last.

Answer: Lin appears no later than third.

Answer: Mitchell appears earlier than Geyer.

Answer: Paredes appears first.


Question: If Mitchell appears first, then which one of the following must be true?

Answer: Geyer appears fifth.

Answer: Henson appears third.

Answer: Jhalani appears sixth.

Answer: Lin appears second.

Answer: Paredes appears fourth.


Context: Over the course of one day, a landscaper will use a truck to haul exactly seven loads—three loads of mulch and four loads of stone. The truck's cargo bed will be cleaned in between carrying any two loads of different materials. To meet the landscaper's needs as efficiently as possible, the following constraints apply: The cargo bed cannot be cleaned more than three times. The fifth load must be mulch.

Question: Which one of the following is a pair of loads that can both be mulch?

Answer: the first and the third

Answer: the second and the third

Answer: the second and the sixth

Answer: the third and the sixth

Answer: the fourth and the sixth


Question: Which one of the following must be true?

Answer: The second load is stone.

Answer: The first and second loads are the same material.

Answer: The second and third loads are different materials.

Answer: At least two loads of mulch are hauled consecutively.

Answer: At least three loads of stone are hauled consecutively.


Question: If the third load is mulch, which one of the following must be true?

Answer: The sixth load is a different material than the seventh load.

Answer: The first load is a different material than the second load.

Answer: The seventh load is mulch.

Answer: The sixth load is mulch.

Answer: The first load is stone.


Question: If the cargo bed is cleaned exactly twice, which one of the following must be true?

Answer: The second load is stone.

Answer: The third load is mulch.

Answer: The third load is stone.

Answer: The sixth load is mulch.

Answer: The seventh load is mulch.


Question: If no more than two loads of the same material are hauled consecutively, then which one of the following could be true?

Answer: The first load is stone.

Answer: The fourth load is stone.

Answer: The third load is mulch.

Answer: The sixth load is mulch.

Answer: The seventh load is mulch.


Context: A travel magazine has hired six interns—Farber, Gombarick, Hall, Jackson, Kanze, and Lha—to assist in covering three stories—Romania, Spain, and Tuscany. Each intern will be trained either as a photographer's assistant or as a writer's assistant. Each story is assigned a team of two interns—one photographer's assistant and one writer's assistant—in accordance with the following conditions: Gombarick and Lha will be trained in the same field. Farber and Kanze will be trained in different fields. Hall will be trained as a photographer's assistant. Jackson is assigned to Tuscany. Kanze is not assigned to Spain.

Question: Which one of the following could be an acceptable assignment of photographer's assistants to stories?

Answer: Romania: Farber Spain: Hall Tuscany: Jackson

Answer: Romania: Gombarick Spain: Hall Tuscany: Farber

Answer: Romania: Gombarick Spain: Hall Tuscany: Lha

Answer: Romania: Gombarick Spain: Lha Tuscany: Kanze

Answer: Romania: Hall Spain: Kanze Tuscany: Jackson


Question: If Farber is assigned to Romania, then which one of the following must be true?

Answer: Gombarick is assigned to Spain.

Answer: Hall is assigned to Spain.

Answer: Kanze is assigned to Tuscany.

Answer: Lha is assigned to Spain.

Answer: Lha is assigned to Tuscany.


Question: If Farber and Hall are assigned to the same story as each other, then which one of the following could be true?

Answer: Farber is assigned to Tuscany.

Answer: Gombarick is assigned to Romania.

Answer: Hall is assigned to Romania.

Answer: Kanze is assigned to Tuscany.

Answer: Lha is assigned to Spain.


Question: If Farber is a writer's assistant, then which one of the following pairs could be the team of interns assigned to Romania?

Answer: Farber and Gombarick

Answer: Gombarick and Hall

Answer: Hall and Kanze

Answer: Kanze and Lha

Answer: Lha and Hall


Question: If Gombarick and Kanze are assigned to the same story as each other, then which one of the following could be true?

Answer: Farber is assigned to Romania.

Answer: Gombarick is assigned to Spain.

Answer: Hall is assigned to Romania.

Answer: Kanze is assigned to Tuscany.

Answer: Lha is assigned to Spain.


Question: Which one of the following interns CANNOT be assigned to Tuscany?

Answer: Farber

Answer: Gombarick

Answer: Hall

Answer: Kanze

Answer: Lha


Context: Exactly six workers—Faith, Gus, Hannah, Juan, Kenneth, and Lisa—will travel to a business convention in two cars—car 1 and car 2. Each car must carry at least two of the workers, one of whom will be assigned to drive. For the entire trip, the workers will comply with an assignment that also meets the following constraints: Either Faith or Gus must drive the car in which Hannah travels. Either Faith or Kenneth must drive the car in which Juan travels. Gus must travel in the same car as Lisa.

Question: Which one of the following is a possible assignment of the workers to the cars?

Answer: car 1: Faith (driver), Hannah, and Juan car 2: Gus (driver), Kenneth, and Lisa

Answer: car 1: Faith (driver), Hannah, and Kenneth car 2: Lisa (driver), Gus, and Juan

Answer: car 1: Faith (driver), Juan, Kenneth, and Lisa car 2: Gus (driver) and Hannah

Answer: car 1: Faith (driver) and Juan car 2: Kenneth (driver), Gus, Hannah, and Lisa

Answer: car 1: Gus (driver), Hannah, and Lisa car 2: Juan (driver), Faith, and Kenneth


Question: The two workers who drive the cars CANNOT be

Answer: Faith and Gus

Answer: Faith and Kenneth

Answer: Faith and Lisa

Answer: Gus and Kenneth

Answer: Kenneth and Lisa


Question: If Lisa drives one of the cars, then which one of the following could be true?

Answer: Faith travels in the same car as Kenneth.

Answer: Faith travels in the same car as Lisa.

Answer: Gus travels in the same car as Hannah.

Answer: Gus travels in the same car as Juan.

Answer: Hannah travels in the same car as Lisa.


Question: If Faith travels with two other workers in car 1, and if Faith is not the driver, then the person in car 1 other than Faith and the driver must be

Answer: Gus

Answer: Hannah

Answer: Juan

Answer: Kenneth

Answer: Lisa


Question: Which one of the following CANNOT be true?

Answer: Gus is the only person other than the driver in one of the cars.

Answer: Hannah is the only person other than the driver in one of the cars.

Answer: Juan is the only person other than the driver in one of the cars.

Answer: Kenneth is the only person other than the driver in one of the cars.

Answer: Lisa is the only person other than the driver in one of the cars.


Context: An archaeologist has six ancient artifacts—a figurine, a headdress, a jar, a necklace, a plaque, and a tureen—no two of which are the same age. She will order them from first (oldest) to sixth (most recent). The following has already been determined: The figurine is older than both the jar and the headdress. The necklace and the jar are both older than the tureen. Either the plaque is older than both the headdress and the necklace, or both the headdress and the necklace are older than the plaque.

Question: Which one of the following could be the artifacts in the order of their age, from first to sixth?

Answer: figurine, headdress, jar, necklace, plaque, tureen

Answer: figurine, jar, plaque, headdress, tureen, necklace

Answer: figurine, necklace, plaque, headdress, jar, tureen

Answer: necklace, jar, figurine, headdress, plaque, tureen

Answer: plaque, tureen, figurine, necklace, jar, headdress


Question: Exactly how many of the artifacts are there any one of which could be first?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


Question: Which one of the following artifacts CANNOT be fourth?

Answer: figurine

Answer: headdress

Answer: jar

Answer: necklace

Answer: plaque


Question: If the figurine is third, which one of the following must be second?

Answer: headdress

Answer: jar

Answer: necklace

Answer: plaque

Answer: tureen


Question: If the plaque is first, then exactly how many artifacts are there any one of which could be second?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


Question: Which one of the following, if substituted for the information that the necklace and the jar are both older than the tureen, would have the same effect in determining the order of the artifacts?

Answer: The tureen is older than the headdress but not as old as the figurine.

Answer: The figurine and the necklace are both older than the tureen.

Answer: The necklace is older than the tureen if and only if the jar is.

Answer: All of the artifacts except the headdress and the plaque must be older than the tureen.

Answer: The plaque is older than the necklace if and only if the plaque is older than the tureen.


Context: The coach of a women's track team must determine which four of five runners—Quinn, Ramirez, Smith, Terrell, and Uzoma—will run in the four races of an upcoming track meet. Each of the four runners chosen will run in exactly one of the four races—the first, second, third, or fourth. The coach's selection is bound by the following constraints: If Quinn runs in the track meet, then Terrell runs in the race immediately after the race in which Quinn runs. Smith does not run in either the second race or the fourth race. If Uzoma does not run in the track meet, then Ramirez runs in the second race. If Ramirez runs in the second race, then Uzoma does not run in the track meet.

Question: Which one of the following could be the order in which the runners run, from first to fourth?

Answer: Uzoma, Ramirez, Quinn, Terrell

Answer: Terrell, Smith, Ramirez, Uzoma

Answer: Smith, Ramirez, Terrell, Quinn

Answer: Ramirez, Uzoma, Smith, Terrell

Answer: Quinn, Terrell, Smith, Ramirez


Question: Which one of the following runners must the coach select to run in the track meet?

Answer: Quinn

Answer: Ramirez

Answer: Smith

Answer: Terrell

Answer: Uzoma


Question: The question of which runners will be chosen to run in the track meet and in what races they will run can be completely resolved if which one of the following is true?

Answer: Ramirez runs in the first race.

Answer: Ramirez runs in the second race.

Answer: Ramirez runs in the third race.

Answer: Ramirez runs in the fourth race.

Answer: Ramirez does not run in the track meet.


Question: Which one of the following CANNOT be true?

Answer: Ramirez runs in the race immediately before the race in which Smith runs.

Answer: Smith runs in the race immediately before the race in which Quinn runs.

Answer: Smith runs in the race immediately before the race in which Terrell runs.

Answer: Terrell runs in the race immediately before the race in which Ramirez runs.

Answer: Uzoma runs in the race immediately before the race in which Terrell runs.


Question: If Uzoma runs in the first race, then which one of the following must be true?

Answer: Quinn does not run in the track meet.

Answer: Smith does not run in the track meet.

Answer: Quinn runs in the second race.

Answer: Terrell runs in the second race.

Answer: Ramirez runs in the fourth race.


Question: If both Quinn and Smith run in the track meet, then how many of the runners are there any one of whom could be the one who runs in the first race?

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five