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

Answer: lentils: second; mushrooms: third

Answer: mushrooms: fourth; lentils: last

Answer: onions: second; mushrooms: fifth

Answer: zucchini: first; lentils: last

Answer: zucchini: first; mushrooms: second


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

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

Answer: The kale is added second.

Answer: The tomatoes are added second.

Answer: The lentils are added third.

Answer: The lentils are added fourth.

Answer: The onions are added fourth.


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

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

Answer: F, I, L, H, G

Answer: F, L, G, H, M

Answer: F, L, I, G, M

Answer: F, L, I, H, M

Answer: F, L, K, I, G


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

Answer: G ranks better than M.

Answer: H ranks better than F.

Answer: I ranks better than F.

Answer: K ranks better than G.

Answer: M ranks better than G.


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

Answer: F

Answer: G

Answer: H

Answer: K

Answer: M


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

Answer: F, G, H, M

Answer: G, H, I, M

Answer: G, H, L, M

Answer: F, G, H, I, K

Answer: F, G, H, I, M


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

Answer: M ranks better than H.

Answer: K ranks better than G.

Answer: I ranks better than F.

Answer: H ranks better than M.

Answer: G ranks better than K.


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

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

Answer: Honolulu and Vancouver; Montreal and Toronto; Philadelphia and Vancouver; Toronto and Vancouver

Answer: Honolulu and Vancouver; Montreal and Philadelphia; Montreal and Toronto; Philadelphia and Toronto; Toronto and Vancouver

Answer: Honolulu and Philadelphia; Honolulu and Montreal; Philadelphia and Toronto; Toronto and Vancouver

Answer: Honolulu and Philadelphia; Montreal and Toronto; Philadelphia and Toronto; Philadelphia and Vancouver; Toronto and Vancouver

Answer: Honolulu and Philadelphia; Honolulu and Toronto; Montreal and Philadelphia; Philadelphia and Vancouver


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

Answer: Honolulu and Montreal

Answer: Honolulu and Vancouver

Answer: Montreal and Toronto

Answer: Montreal and Vancouver

Answer: Philadelphia and Vancouver


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

Answer: Honolulu and Montreal

Answer: Honolulu and Philadelphia

Answer: Montreal and Philadelphia

Answer: Montreal and Vancouver

Answer: Philadelphia and Toronto


Question: Which one of the following could be true?

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

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

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

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

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


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

Answer: Exactly one city is connected with Toronto.

Answer: Exactly one city is connected with Vancouver.

Answer: Exactly two cities are each connected with Honolulu.

Answer: Exactly two cities are each connected with Toronto.

Answer: Exactly four cities are each connected with Toronto.


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

Answer: four

Answer: five

Answer: six

Answer: seven

Answer: eight


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

Answer: Honolulu and Montreal

Answer: Honolulu and Philadelphia

Answer: Honolulu and Vancouver

Answer: Montreal and Philadelphia

Answer: Montreal and Toronto


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

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

Answer: F, G, K, N, T, V

Answer: F, H, K, N, V, Z

Answer: G, H, K, L, V, Z

Answer: G, H, K, N, V, Z

Answer: G, H, L, N, V, Z


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

Answer: F is selected.

Answer: T is selected.

Answer: Z is selected.

Answer: Exactly one panda is selected.

Answer: Exactly two pandas are selected.


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

Answer: F and G

Answer: H and K

Answer: K and T

Answer: L and N

Answer: T and V


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

Answer: K is selected.

Answer: L is selected.

Answer: Exactly one monkey is selected.

Answer: Exactly two pandas are selected.

Answer: All three of the monkeys are selected.


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

Answer: F and G

Answer: G and H

Answer: K and L

Answer: K and Z

Answer: L and N


Question: The selection of animals must include

Answer: at most two of each kind of animal

Answer: at least one of each kind of animal

Answer: at least two pandas

Answer: exactly two monkeys

Answer: exactly two raccoons


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

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

Answer: firefighters, puppeteers, veterans, musicians, gymnasts, jugglers

Answer: gymnasts, puppeteers, jugglers, musicians, firefighters, veterans

Answer: veterans, puppeteers, firefighters, gymnasts, jugglers, musicians

Answer: jugglers, puppeteers, gymnasts, firefighters, musicians, veterans

Answer: musicians, veterans, jugglers, firefighters, gymnasts, puppeteers


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

Answer: gymnasts

Answer: jugglers

Answer: musicians

Answer: puppeteers

Answer: veterans


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

Answer: firefighters

Answer: gymnasts

Answer: jugglers

Answer: musicians

Answer: veterans


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

Answer: The puppeteers are the first group.

Answer: The firefighters are the first group.

Answer: The veterans are the second group.

Answer: The gymnasts are the third group.

Answer: The musicians are the sixth group.


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

Answer: firefighters

Answer: jugglers

Answer: musicians

Answer: puppeteers

Answer: veterans


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

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

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

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

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

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

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


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

Answer: Miller rows at seat 1.

Answer: Singh rows at seat 2.

Answer: Zita rows at seat 3.

Answer: Lee rows at seat 4.

Answer: Ovitz rows at seat 6.


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

Answer: Zita rows immediately behind Valerio.

Answer: Ovitz rows immediately behind Valerio.

Answer: Ovitz rows immediately behind Zita.

Answer: Valerio rows immediately behind Lee.

Answer: Singh rows immediately behind Zita.


Question: Which one of the following CANNOT be true?

Answer: Ovitz rows closer to the front than Singh.

Answer: Zita rows closer to the front than Miller.

Answer: Lee rows closer to the front than Valerio.

Answer: Singh rows closer to the front than Zita.

Answer: Valerio rows closer to the front than Lee.


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

Answer: two

Answer: three

Answer: four

Answer: five

Answer: six


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

Answer: Miller rows immediately in front of Singh.

Answer: Lee rows immediately in front of Valerio.

Answer: Zita rows immediately in front of Ovitz.

Answer: Singh rows immediately in front of Lee.

Answer: Singh rows immediately in front of Valerio.


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

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

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

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

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

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


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

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

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

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

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

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

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


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

Answer: Quarterion and Zelkova

Answer: Redemption and Tesseract

Answer: Redemption and Vale

Answer: Redemption and Zelkova

Answer: Tesseract and Zelkova


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

Answer: Quarterion, Redemption

Answer: Redemption, Sipapu

Answer: Quarterion, Sipapu, Tesseract

Answer: Quarterion, Redemption, Sipapu, Tesseract

Answer: Redemption, Sipapu, Tesseract, Zelkova


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

Answer: Redemption

Answer: Sipapu

Answer: Tesseract

Answer: Vale

Answer: Zelkova


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

Answer: Quarterion is sold to the museum.

Answer: Quarterion is from the artist's third period.

Answer: Redemption is sold to the private collector.

Answer: Redemption is from the artist's third period.

Answer: Redemption is sold to the same buyer as Vale.


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

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

Answer: X

Answer: X, Z

Answer: X, Y, Z

Answer: Y, Z

Answer: Z


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

Answer: the hot dog truck and the pita truck

Answer: the hot dog truck and the taco truck

Answer: the ice cream truck and the pita truck

Answer: the ice cream truck and the salad truck

Answer: the salad truck and the taco truck


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

Answer: the falafel truck and the hot dog truck

Answer: the falafel truck and the salad truck

Answer: the ice cream truck and the pita truck

Answer: the ice cream truck and the salad truck

Answer: the ice cream truck and the taco truck


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

Answer: the hot dog truck, the ice cream truck

Answer: the hot dog truck, the salad truck

Answer: the ice cream truck, the taco truck

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

Answer: the ice cream truck, the pita truck, the salad truck


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

Answer: the hot dog truck

Answer: the ice cream truck

Answer: the pita truck

Answer: the salad truck

Answer: the taco truck


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

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

Answer: Fuentes, Rhee, Tbahi, Soleimani, Fuentes, Matsuba, Rhee

Answer: Fuentes, Tbahi, Soleimani, Matsuba, Fuentes, Fuentes, Rhee

Answer: Fuentes, Rhee, Fuentes, Matsuba, Fuentes, Tbahi, Soleimani

Answer: Fuentes, Tbahi, Matsuba, Fuentes, Soleimani, Rhee, Fuentes

Answer: Fuentes, Tbahi, Soleimani, Fuentes, Rhee, Fuentes, Matsuba


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

Answer: Garibaldi's second meeting is with Soleimani.

Answer: Garibaldi's third meeting is with Matsuba.

Answer: Garibaldi's fourth meeting is with Soleimani.

Answer: Garibaldi's fifth meeting is with Matsuba.

Answer: Garibaldi's sixth meeting is with Soleimani.


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

Answer: Fuentes, Soleimani, Rhee

Answer: Matsuba, Rhee, Tbahi

Answer: Matsuba, Soleimani

Answer: Rhee, Tbahi

Answer: Fuentes, Soleimani


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

Answer: Garibaldi's third meeting is with Fuentes.

Answer: Garibaldi's fourth meeting is with Rhee.

Answer: Garibaldi's fifth meeting is with Fuentes.

Answer: Garibaldi's sixth meeting is with Rhee.

Answer: Garibaldi's seventh meeting is with Fuentes.


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

Answer: second meeting

Answer: third meeting

Answer: fifth meeting

Answer: sixth meeting

Answer: seventh meeting


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

Answer: Fuentes

Answer: Matsuba

Answer: Rhee

Answer: Soleimani

Answer: Tbahi


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

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

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

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

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

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

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


Question: Which one of the following must be true?

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

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

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

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

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


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

Answer: The greyhound is placed on Monday.

Answer: The keeshond is placed on Monday.

Answer: The Labrador retriever is placed on Monday.

Answer: The husky is placed on Tuesday.

Answer: The schnauzer is placed on Wednesday.


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

Answer: The husky is placed on Monday.

Answer: The Labrador retriever is placed on Monday.

Answer: The keeshond is placed on Tuesday.

Answer: The poodle is not placed on Wednesday.

Answer: The schnauzer is not placed on Wednesday.


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

Answer: The husky is placed on Monday.

Answer: The keeshond is placed on Monday.

Answer: The greyhound is placed on Tuesday.

Answer: The poodle is placed on Tuesday.

Answer: The poodle is placed on Wednesday.


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

Answer: the husky

Answer: the keeshond

Answer: the Labrador retriever

Answer: the poodle

Answer: the schnauzer


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

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

Answer: Oliphant, Oliphant, Gallagher, Oliphant, Ferrara

Answer: Gallagher, Oliphant, Ferrara, Ferrara, Ferrara

Answer: Oliphant, Gallagher, Oliphant, Ferrara, Ferrara

Answer: Oliphant, Oliphant, Gallagher, Ferrara, Gallagher

Answer: Ferrara, Oliphant, Gallagher, Ferrara, Ferrara


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

Answer: the site visited first

Answer: the site visited second

Answer: the site visited third

Answer: the site visited fourth

Answer: the site visited fifth


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

Answer: the site visited first

Answer: the site visited second

Answer: the site visited third

Answer: the site visited fourth

Answer: the site visited fifth


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

Answer: third, fourth, fifth

Answer: second, third, fourth

Answer: first, fourth, fifth

Answer: first, second, fifth

Answer: first, second, fourth


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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

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

Answer: Y, Z, X, Y, Z

Answer: Y, Z, Z, Y, X

Answer: Z, Z, X, X, Y

Answer: Z, Z, X, X, Z

Answer: Z, Z, X, Z, Y


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

Answer: Monday

Answer: Tuesday

Answer: Wednesday

Answer: Thursday

Answer: Friday


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

Answer: Monday

Answer: Tuesday

Answer: Wednesday

Answer: Thursday

Answer: Friday


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

Answer: Monday

Answer: Tuesday

Answer: Wednesday

Answer: Thursday

Answer: Friday


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

Answer: Monday

Answer: Tuesday

Answer: Monday, Tuesday

Answer: Monday, Wednesday

Answer: Monday, Thursday


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

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

Answer: Yansky, workout, Upton, Reilly, Sanchez, Tang

Answer: Upton, Tang, Sanchez, Yansky, workout, Reilly

Answer: Upton, Reilly, Sanchez, workout, Tang, Yansky

Answer: Sanchez, Yansky, workout, Reilly, Tang, Upton

Answer: Sanchez, Upton, workout, Yansky, Tang, Reilly


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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: 1:00

Answer: 2:00

Answer: 3:00

Answer: 4:00

Answer: 5:00


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

Answer: Patterson meets with Reilly at 2:00.

Answer: Patterson meets with Yansky at 3:00.

Answer: Patterson meets with Tang at 4:00.

Answer: Patterson meets with Yansky at 5:00.

Answer: Patterson meets with Tang at 6:00.


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

Answer: Patterson meets with Reilly at 5:00.

Answer: Patterson meets with Upton at 5:00.

Answer: Patterson meets with Yansky at 2:00.

Answer: Patterson meets with Yansky at 3:00.

Answer: Patterson's workout is at 2:00.


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

Answer: Upton, Yansky, Sanchez, Reilly, Tang

Answer: Upton, Reilly, Sanchez, Tang, Yansky

Answer: Sanchez, Yansky, Reilly, Tang, Upton

Answer: Sanchez, Upton, Tang, Yansky, Reilly

Answer: Sanchez, Upton, Reilly, Yansky, Tang


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

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

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

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

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

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

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


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

Answer: Lulu

Answer: Nam

Answer: Ofelia

Answer: Santiago

Answer: Tyrone


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

Answer: Nam plays in the second game.

Answer: Ofelia plays in the third game.

Answer: Santiago plays in the second game.

Answer: Nam plays a game against Lulu.

Answer: Pachai plays a game against Lulu.


Question: Which one of the following could be true?

Answer: Pachai plays against Lulu in the first game.

Answer: Pachai plays against Nam in the second game.

Answer: Santiago plays against Ofelia in the second game.

Answer: Pachai plays against Lulu in the third game.

Answer: Nam plays against Santiago in the fourth game.


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

Answer: Lulu, Pachai

Answer: Nam, Ofelia

Answer: Nam, Pachai

Answer: Nam, Santiago

Answer: Ofelia, Pachai


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

Answer: Lulu plays in the third game.

Answer: Nam plays in the third game.

Answer: Pachai plays in the first game.

Answer: Pachai plays in the third game.

Answer: Tyrone plays in the second game.


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

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

Answer: Raimundo, Selma, Ty, Wendy

Answer: Raimundo, Ty, Yakira, Zack

Answer: Raimundo, Wendy, Yakira, Zack

Answer: Selma, Ty, Umiko, Yakira

Answer: Selma, Ty, Umiko, Zack


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

Answer: Selma also appears in the photograph.

Answer: Yakira also appears in the photograph.

Answer: Wendy also appears in the photograph.

Answer: Raimundo does not appear in the photograph.

Answer: Umiko does not appear in the photograph.


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

Answer: six

Answer: five

Answer: four

Answer: three

Answer: two


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

Answer: four

Answer: three

Answer: two

Answer: one

Answer: zero


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

Answer: Selma and Zack both appear in the photograph.

Answer: Ty and Yakira both appear in the photograph.

Answer: Wendy and Selma both appear in the photograph.

Answer: Yakira and Zack both appear in the photograph.

Answer: Zack and Raimundo both appear in the photograph.


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

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

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

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

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

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

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


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

Answer: Nation Y exports oranges.

Answer: Nation Y exports rice.

Answer: Nation Y exports tea.

Answer: Nation Z exports soybeans.

Answer: Nation Z exports tea.


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

Answer: Nation X exports oranges.

Answer: Nation X exports tea.

Answer: Nation X exports wheat.

Answer: Nation Y exports rice.

Answer: Nation Y exports soybeans.


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

Answer: oranges

Answer: rice

Answer: soybeans

Answer: tea

Answer: wheat


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

Answer: oranges and rice

Answer: oranges and soybeans

Answer: rice and tea

Answer: rice and wheat

Answer: soybeans and wheat


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

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

Answer: fox, lynx, grizzly, porcupine, moose, hare

Answer: fox, lynx, moose, hare, grizzly, porcupine

Answer: fox, moose, grizzly, lynx, hare, porcupine

Answer: lynx, fox, moose, grizzly, hare, porcupine

Answer: porcupine, fox, hare, grizzly, lynx, moose


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

Answer: fox

Answer: grizzly

Answer: lynx

Answer: moose

Answer: porcupine


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

Answer: guidepost 1

Answer: guidepost 2

Answer: guidepost 4

Answer: guidepost 5

Answer: guidepost 6


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

Answer: The lynx is pictured on guidepost 2.

Answer: The moose is pictured on guidepost 3.

Answer: The grizzly is pictured on guidepost 4.

Answer: The porcupine is pictured on guidepost 5.

Answer: The hare is pictured on guidepost 6.


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

Answer: fox

Answer: hare

Answer: lynx

Answer: moose

Answer: porcupine


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

Answer: Guidepost 5 pictures the hare.

Answer: Guidepost 4 pictures the moose.

Answer: Guidepost 4 pictures the porcupine.

Answer: Guidepost 3 pictures the lynx.

Answer: Guidepost 3 pictures the porcupine.


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

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

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

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

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

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

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


Question: Which one of the following must be true?

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

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

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

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

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


Question: Which one of the following could be true?

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

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

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

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

Answer: Tapes 2 and 3 each have jazz on one side.


Question: Which one of the following could be true?

Answer: Tape 1 has two sides of folk.

Answer: Tape 2 has both hip-hop and jazz.

Answer: Tape 4 has both folk and rock.

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

Answer: Tapes 3 and 4 each have a side of folk.


Question: Which one of the following CANNOT be true?

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

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

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

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

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


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

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

Answer: Lofton, Nordique, Plattesville, Oceana, Jackson

Answer: Lofton, Oceana, Plattesville, Nordique, Jackson

Answer: Nordique, Jackson, Plattesville, Oceana, Lofton

Answer: Nordique, Lofton, Plattesville, Jackson, Oceana

Answer: Nordique, Plattesville, Lofton, Oceana, Jackson


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

Answer: The first town the storm passes over is Oceana.

Answer: The fourth town the storm passes over is Lofton.

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

Answer: The fifth town the storm passes over is Jackson.

Answer: The fifth town the storm passes over receives only rain.


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

Answer: The first town the storm passes over is Oceana.

Answer: The fourth town the storm passes over receives only rain.

Answer: The fifth town the storm passes over is Jackson.

Answer: Jackson receives only rain.

Answer: Plattesville receives only rain.


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

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

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

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

Answer: The fourth town the storm passes over receives only rain.

Answer: The fifth town the storm passes over receives only rain.


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

Answer: The third town the storm passes over receives only rain.

Answer: The fourth town the storm passes over receives only rain.

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

Answer: The fifth town the storm passes over receives only rain.

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


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

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

Answer: French serves on a subcommittee with Hsia.

Answer: French serves on a subcommittee with Irving.

Answer: Irving serves on a subcommittee with Pinsky.

Answer: Magnus serves on a subcommittee with Ghauri.

Answer: Magnus serves on a subcommittee with Irving.


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

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

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

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

Answer: French serves on every subcommittee on which Pinsky serves.

Answer: Hsia serves on every subcommittee on which Pinsky serves.


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

Answer: Magnus serves on all of the subcommittees.

Answer: Irving serves on more than one subcommittee.

Answer: Irving serves on every subcommittee on which Pinsky serves.

Answer: French serves on a subcommittee with Magnus.

Answer: Ghauri serves on a subcommittee with Magnus.


Question: Which one of the following could be true?

Answer: French serves on all three subcommittees.

Answer: Hsia serves on all three subcommittees.

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

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

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


Question: Which one of the following must be true?

Answer: Ghauri serves on at least two subcommittees.

Answer: Irving serves on only one subcommittee.

Answer: French serves on a subcommittee with Hsia.

Answer: Ghauri serves on a subcommittee with Irving.

Answer: Magnus serves on a subcommittee with Pinsky.


Question: Which one of the following must be true?

Answer: Every subcommittee has either French or Ghauri as a member.

Answer: Every subcommittee has either Hsia or Irving as a member.

Answer: No subcommittee consists of French, Magnus, and Pinsky.

Answer: Some committee member serves on exactly two subcommittees.

Answer: Either Magnus or Pinsky serves on only one subcommittee.


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

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

Answer: P

Answer: Q

Answer: R

Answer: T

Answer: X


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

Answer: T is displayed first.

Answer: R is displayed fifth.

Answer: Q is displayed last.

Answer: Q is displayed second.

Answer: P is displayed second.


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

Answer: R

Answer: S

Answer: T

Answer: W

Answer: X


Question: Which one of the following could be true?

Answer: Q is displayed fifth.

Answer: Q is displayed seventh.

Answer: R is displayed third.

Answer: W is displayed third.

Answer: X is displayed fifth.


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

Answer: P

Answer: Q

Answer: T

Answer: W

Answer: X


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

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

Answer: switch 2, switch 3, switch 4, switch 7

Answer: switch 3, switch 6, switch 7

Answer: switch 2, switch 5, switch 6

Answer: switch 1, switch 3, switch 4

Answer: switch 1, switch 5


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

Answer: switch 2 and switch 7

Answer: switch 4 and switch 6

Answer: switch 4 and switch 7

Answer: switch 5 and switch 6

Answer: switch 6 and switch 7


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

Answer: switch 3

Answer: switch 4

Answer: switch 5

Answer: switch 6

Answer: switch 7


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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: switch 1

Answer: switch 2

Answer: switch 3

Answer: switch 4

Answer: switch 7


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

Answer: three

Answer: four

Answer: five

Answer: six

Answer: seven


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

Question: Which one of the following could be true?

Answer: S carries folk and rock but neither jazz nor opera.

Answer: T carries jazz but neither opera nor rock.

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

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

Answer: Z carries folk and opera but neither rock nor jazz.


Question: Which one of the following could be true?

Answer: S, V, and Z all carry folk.

Answer: S, X, and Z all carry jazz.

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

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

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


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

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

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

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

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

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


Question: Which one of the following must be true?

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

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

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

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

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


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

Answer: S and Z carry no types of music in common.

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

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

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

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


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

Answer: S and T carry no types of music in common.

Answer: S and Z carry no types of music in common.

Answer: T and Z carry no types of music in common.

Answer: S and Z carry two types of music in common.

Answer: T and V carry two types of music in common.


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

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

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

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

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

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

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


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

Answer: Janice

Answer: Kevin

Answer: Nan

Answer: Paul

Answer: Seymour


Question: Each of the following could be true EXCEPT:

Answer: Janice works Monday and Tuesday.

Answer: Kevin and Paul work Friday.

Answer: Seymour works Monday and Friday.

Answer: Janice and Kevin work Thursday.

Answer: Paul works Monday and Friday.


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

Answer: Janice and Seymour

Answer: Kevin and Paul

Answer: Paul and Seymour

Answer: Nan and Ophelia

Answer: Janice and Nan


Question: Which one of the following could be true?

Answer: Nan works Wednesday and Friday only.

Answer: Seymour works Monday and Paul works Tuesday.

Answer: Kevin works Monday, Wednesday, and Friday.

Answer: Nan works Wednesday with Ophelia and Thursday with Kevin.

Answer: Ophelia and Kevin work Tuesday.


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

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

Answer: the hairdryer and the razor

Answer: the hairdryer and the television

Answer: the razor and the television

Answer: the razor and the vacuum

Answer: the television and the vacuum


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

Answer: hairdryer

Answer: razor

Answer: vacuum

Answer: hairdryer, razor

Answer: hairdryer, vacuum


Question: Which one of the following CANNOT be true?

Answer: Henri uses the hairdryer while using the microwave oven.

Answer: Henri uses the microwave oven while using the razor.

Answer: Henri uses the microwave oven while using two other appliances.

Answer: Henri uses the television while using two other appliances.

Answer: Henri uses the vacuum while using two other appliances.


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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


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

Answer: Henri is using the hairdryer.

Answer: Henri is using the television.

Answer: Henri is not using the hairdryer.

Answer: Henri is not using the microwave oven.

Answer: Henri is not using the vacuum.


Question: Which one of the following must be true?

Answer: Henri uses at most three appliances simultaneously.

Answer: Henri uses at most four appliances simultaneously.

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

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

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


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

Question: Which one of the following could be true?

Answer: J is the first field harvested.

Answer: K is the second field harvested.

Answer: M is the sixth field harvested.

Answer: G is the seventh field harvested.

Answer: T is the eighth field harvested.


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

Answer: H

Answer: J

Answer: K

Answer: L

Answer: P


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

Answer: G

Answer: J

Answer: M

Answer: P

Answer: T


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

Answer: L is the first field harvested.

Answer: H is the second field harvested.

Answer: T is the fourth field harvested.

Answer: K is the seventh field harvested.

Answer: M is the eighth field harvested.


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

Answer: G is harvested at some time before T.

Answer: H is harvested at some time before K.

Answer: J is harvested at some time before M.

Answer: K is harvested at some time before J.

Answer: T is harvested at some time before K.


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

Answer: J is harvested at some time before G.

Answer: J is harvested at some time before T.

Answer: K is harvested at some time before T.

Answer: M is harvested at some time before H.

Answer: M is harvested at some time before J.


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

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

Answer: one

Answer: two

Answer: three

Answer: four

Answer: five


Question: Which one of the following must be true?

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

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

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

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

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


Question: Which one of the following must be false?

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

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

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

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

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


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

Answer: Stacy and Urma

Answer: Urma and Yolanda

Answer: Urma and Xena

Answer: Wim and Xena

Answer: Xena and Yolanda


Question: Which one of the following must be true?

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

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

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

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

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


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

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

Answer: Glenside, Levon, Query

Answer: Glenside, Query, Hilltopper

Answer: Hilltopper, Query, Peasant

Answer: Peasant, Levon, Tinhead

Answer: Peasant, Query, Levon


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

Answer: Glenside

Answer: Hilltopper

Answer: Levon

Answer: Peasant

Answer: Tinhead


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

Answer: Glenside

Answer: Hilltopper

Answer: Levon

Answer: Query

Answer: Tinhead


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

Answer: Glenside, Levon, Query

Answer: Peasant, Hilltopper, Tinhead

Answer: Peasant, Tinhead, Glenside

Answer: Peasant, Tinhead, Hilltopper

Answer: Peasant, Tinhead, Levon


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

Answer: A folk group performs at 6.

Answer: A folk group performs at 8.

Answer: A folk group performs at 12.

Answer: A rock group performs at 8.

Answer: A rock group performs at 12.


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

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

Answer: French, Greek, Italian, Turkish, Norwegian, Hungarian

Answer: French, Hungarian, Italian, Norwegian, French, Hungarian

Answer: Hungarian, French, Norwegian, Greek, Norwegian, Italian

Answer: Norwegian, Turkish, Hungarian, Italian, French, Turkish

Answer: Turkish, French, Norwegian, Hungarian, French, Turkish


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

Answer: French

Answer: Greek

Answer: Hungarian

Answer: Norwegian

Answer: Turkish


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

Answer: A film in French is shown on day 3.

Answer: A film in Greek is shown on day 1.

Answer: A film in Hungarian is shown on day 6.

Answer: A film in Norwegian is shown on day 5.

Answer: A film in Turkish is shown on day 4.


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

Answer: day 1, day 3, day 5

Answer: day 2, day 4, day 5

Answer: day 2, day 5, day 6

Answer: day 1, day 3

Answer: day 2, day 4


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

Answer: a film in French, a film in Turkish

Answer: a film in Greek, a film in Hungarian

Answer: a film in Italian, a film in Norwegian

Answer: a film in Norwegian, a film in Turkish

Answer: a film in Turkish, a film in Greek


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

Answer: A film in Norwegian is shown on day 1.

Answer: A film in Norwegian is shown on day 5.

Answer: A film in Turkish is shown on day 4.

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

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


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

Answer: day 1

Answer: day 3

Answer: day 5

Answer: day 1 or else day 3

Answer: day 3 or else day 5


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

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

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

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

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

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

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


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

Answer: the postcard

Answer: the letter, the postcard

Answer: the letter, the survey

Answer: the magazine, the survey

Answer: the letter, the magazine, the postcard


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

Answer: the flyer, the letter, the magazine

Answer: the flyer, the letter, the postcard

Answer: the flyer, the letter, the survey

Answer: the flyer, the magazine, the postcard

Answer: the flyer, the magazine, the survey


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

Answer: the magazine, the postcard

Answer: the letter, the survey

Answer: the letter, the magazine

Answer: the flyer, the magazine

Answer: the flyer, the letter


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

Answer: The survey is addressed to Georgette.

Answer: The postcard is addressed to Rini.

Answer: The magazine is addressed to Jana.

Answer: The letter is addressed to Rini.

Answer: The flyer is addressed to Jana.


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

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

Answer: history, psychology

Answer: geography, history, literature

Answer: history, mathematics, psychology

Answer: literature, mathematics, psychology

Answer: history, literature, mathematics, sociology


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

Answer: Sociology is offered.

Answer: History is not offered.

Answer: Mathematics is not offered.

Answer: A total of two courses are offered.

Answer: Zoology is not offered.


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

Answer: literature

Answer: mathematics

Answer: psychology

Answer: sociology

Answer: zoology


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

Answer: Literature is offered.

Answer: Psychology is offered.

Answer: Sociology is offered.

Answer: At least three courses are offered.

Answer: At most four courses are offered.


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

Answer: Both geography and psychology are offered.

Answer: Both geography and mathematics are offered.

Answer: Both psychology and mathematics are offered.

Answer: Both history and mathematics are offered.

Answer: Both geography and sociology are offered.


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

Question: Which one of the following could be true?

Answer: F is ranked first and M is ranked eighth.

Answer: G is ranked fifth and O is ranked eighth.

Answer: J is ranked third and L is ranked seventh.

Answer: K is ranked second and H is ranked third.

Answer: M is ranked seventh and L is ranked eighth.


Question: H CANNOT be ranked

Answer: second

Answer: third

Answer: fourth

Answer: fifth

Answer: sixth


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

Answer: G

Answer: H

Answer: M

Answer: J

Answer: L


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

Answer: second

Answer: third

Answer: fourth

Answer: fifth

Answer: sixth


Question: Which one of the following must be true?

Answer: J is ranked no faster than fifth.

Answer: K is ranked no faster than third.

Answer: L is ranked no faster than fifth.

Answer: M is ranked no faster than third.

Answer: O is ranked no faster than eighth.


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

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

Answer: L, M, M, L, O, L

Answer: M, L, O, M, O, M

Answer: M, N, O, N, O, M

Answer: M, O, N, O, N, M

Answer: O, M, L, M, O, N


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

Answer: L, M, N

Answer: L, O, N

Answer: M, L, N

Answer: M, L, O

Answer: N, O, N


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

Answer: M, O, and N

Answer: M, N, and O

Answer: N, M, and O

Answer: N, O, and M

Answer: O, M, and N


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

Answer: L, M

Answer: L, O

Answer: M, L

Answer: M, O

Answer: O, N


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

Answer: M, N

Answer: N, L

Answer: N, O

Answer: O, L

Answer: O, N


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

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

Answer: F, G, K, L, Z

Answer: F, G, K, U, X

Answer: G, K, W, X, Z

Answer: H, K, U, W, X

Answer: H, L, W, X, Z


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

Answer: U and X

Answer: K and L

Answer: G and M

Answer: G and K

Answer: F and G


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

Answer: F and G

Answer: F and M

Answer: G and K

Answer: H and L

Answer: M and U


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

Answer: F

Answer: G

Answer: L

Answer: M

Answer: Z


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

Answer: K

Answer: L

Answer: M

Answer: U

Answer: X


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

Answer: F and G

Answer: G and H

Answer: H and K

Answer: K and U

Answer: U and X


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

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

Answer: Ramon: 1991; Sue: 1991; Taylor: 1993

Answer: Ramon: 1992; Sue: 1992; Taylor: 1993

Answer: Ramon: 1992; Sue: 1993; Taylor: 1994

Answer: Ramon: 1993; Sue: 1993; Taylor: 1992

Answer: Ramon: 1993; Sue: 1993; Taylor: 1995


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

Answer: Ramon graduated.

Answer: Ramon bought his first car.

Answer: Sue graduated.

Answer: Sue bought her first car.

Answer: Taylor graduated.


Question: Which one of the following must be false?

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

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

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

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

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


Question: Which one of the following must be true?

Answer: None of the three friends graduated in 1991.

Answer: None of the three friends graduated in 1992.

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

Answer: None of the three friends graduated in 1994.

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


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

Answer: Sue bought her first car in 1991.

Answer: Ramon graduated in 1992.

Answer: Taylor graduated in 1993.

Answer: Taylor bought his first car in 1994.

Answer: Ramon bought his first car in 1995.


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

Answer: Sue bought her first car in 1991.

Answer: Ramon bought his first car in 1992.

Answer: Ramon bought his first car in 1993.

Answer: Taylor bought his first car in 1994.

Answer: Taylor bought his first car in 1995.


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

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

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

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

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

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

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


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

Answer: The Y is in the first spoonful.

Answer: The Z is in the first spoonful.

Answer: The T is in the second spoonful.

Answer: The X is in the second spoonful.

Answer: The W is in the third spoonful.


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

Answer: The T is in the second spoonful.

Answer: The U is in the third spoonful.

Answer: The W is in the first spoonful.

Answer: The W is in the second spoonful.

Answer: The X is in the third spoonful.


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

Answer: T

Answer: T, W

Answer: T, X

Answer: T, W, Z

Answer: T, X, W, Z


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

Answer: Exactly two letters are in the first spoonful.

Answer: Exactly three letters are in the first spoonful.

Answer: Exactly three letters are in the second spoonful.

Answer: Exactly one letter is in the third spoonful.

Answer: Exactly two letters are in the third spoonful.


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

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

Answer: red red

Answer: red violet, yellow

Answer: violet green, violet

Answer: violet red, violet

Answer: violet red, violet, yellow


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

Answer: At least part of the jacket is green.

Answer: At least part of the jacket is red.

Answer: The overalls are red and violet.

Answer: The overalls are red and yellow.

Answer: The overalls are violet and yellow.


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

Answer: The overalls are plaid.

Answer: No part of the jacket is red.

Answer: No part of the jacket is violet.

Answer: At least part of the overalls are yellow.

Answer: At least part of the overalls are violet.


Question: Which one of the following must be false?

Answer: Both green and red are colors used in the costume.

Answer: Both green and violet are colors used in the costume.

Answer: Both green and yellow are colors used in the costume.

Answer: Both red and violet are colors used in the costume.

Answer: Both violet and yellow are colors used in the costume.


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

Answer: entirely red or else red and violet plaid

Answer: entirely yellow or else violet and yellow plaid

Answer: entirely violet or else red and violet plaid

Answer: entirely red or else entirely yellow

Answer: entirely red or else entirely violet


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

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

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

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

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

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

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


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

Answer: H is more expensive than F.

Answer: H is more expensive than G.

Answer: K is more expensive than F.

Answer: K is more expensive than J.

Answer: L is more expensive than F.


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

Answer: F

Answer: G

Answer: H

Answer: J

Answer: K


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

Answer: F is more expensive than H.

Answer: F is more expensive than K.

Answer: G is more expensive than H.

Answer: G is more expensive than J.

Answer: G is more expensive than L.


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

Answer: F is more expensive than H.

Answer: G is more expensive than F.

Answer: G is more expensive than H.

Answer: J is more expensive than L.

Answer: L is more expensive than K.


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

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

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

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

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

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

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


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

Answer: S and V

Answer: S and W

Answer: T and Z

Answer: T and Y

Answer: V and Z


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

Answer: S

Answer: T

Answer: W

Answer: X

Answer: Y


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

Answer: S is a rock classic.

Answer: V is a rock classic.

Answer: Y is a rock classic.

Answer: T is a new composition.

Answer: W is a new composition.


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

Answer: V occupies the seventh track of the CD.

Answer: X occupies the fifth track of the CD.

Answer: Y occupies the third track of the CD.

Answer: T is a rock classic.

Answer: W is a rock classic.


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

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

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

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

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

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

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


Question: Which one of the following must be true?

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

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

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

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

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


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

Answer: G is the fifth parcel delivered.

Answer: O is the seventh parcel delivered.

Answer: J is delivered later than H.

Answer: K is delivered later than N.

Answer: G is delivered later than L.


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

Answer: K is the fifth parcel delivered.

Answer: L is the sixth parcel delivered.

Answer: M is the sixth parcel delivered.

Answer: G is the seventh parcel delivered.

Answer: O is the seventh parcel delivered.


Question: Each of the following could be true EXCEPT:

Answer: H is delivered later than K.

Answer: J is delivered later than G.

Answer: L is delivered later than O.

Answer: M is delivered later than L.

Answer: N is delivered later than H.


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

Answer: G is the fifth parcel delivered.

Answer: M is the fifth parcel delivered.

Answer: H is the fourth parcel delivered.

Answer: L is the fourth parcel delivered.

Answer: J is the third parcel delivered.


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

Answer: N is the second parcel delivered.

Answer: L is the third parcel delivered.

Answer: H is the fourth parcel delivered.

Answer: K is the fifth parcel delivered.

Answer: M is the sixth parcel delivered.


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

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

Answer: first digit is 2

Answer: second digit is 0

Answer: third digit is 3

Answer: fourth digit is 4

Answer: fourth digit is 0


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

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

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

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

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

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


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

Answer: The second digit of the product code is 2.

Answer: The third digit of the product code is 3.

Answer: The fourth digit of the product code is 0.

Answer: The fifth digit of the product code is 3.

Answer: The fifth digit of the product code is 1.


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

Answer: 0, 1

Answer: 0, 3

Answer: 1, 0

Answer: 3, 0

Answer: 3, 4


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

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

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

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

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

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


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

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

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

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

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

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

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


Question: Which one of the following CANNOT be true?

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

Answer: Limelight is shown on each day of the festival.

Answer: Greed is shown second on each day of the festival.

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

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


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

Answer: three

Answer: four

Answer: five

Answer: six

Answer: seven


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

Answer: All three films are shown on Thursday.

Answer: Exactly two films are shown on Saturday.

Answer: Limelight and Harvest are both shown on Thursday.

Answer: Greed is the only film shown on Saturday.

Answer: Harvest and Greed are both shown on Friday.


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

Answer: Harvest

Answer: Limelight

Answer: Greed, Harvest

Answer: Greed, Limelight

Answer: Greed, Harvest, Limelight


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

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

Answer: Guadeloupe, Jamaica, Martinique, Trinidad, Guadeloupe, Martinique, Trinidad

Answer: Guadeloupe, Martinique, Trinidad, Martinique, Guadeloupe, Jamaica, Trinidad

Answer: Jamaica, Martinique, Guadeloupe, Martinique, Guadeloupe, Jamaica, Trinidad

Answer: Martinique, Trinidad, Guadeloupe, Jamaica, Martinique, Guadeloupe, Trinidad

Answer: Martinique, Trinidad, Guadeloupe, Trinidad, Guadeloupe, Jamaica, Martinique


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

Answer: Freedom makes a voyage to Trinidad in week 6.

Answer: Freedom makes a voyage to Martinique in week 5.

Answer: Freedom makes a voyage to Jamaica in week 6.

Answer: Freedom makes a voyage to Jamaica in week 3.

Answer: Freedom makes a voyage to Guadeloupe in week 3.


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

Answer: Freedom makes a voyage to Trinidad in week 1.

Answer: Freedom makes a voyage to Martinique in week 2.

Answer: Freedom makes a voyage to Guadeloupe in week 3.

Answer: Freedom makes a voyage to Martinique in week 4.

Answer: Freedom makes a voyage to Jamaica in week 6.


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

Answer: Freedom makes a voyage to Jamaica in week 2.

Answer: Freedom makes a voyage to Trinidad in week 2.

Answer: Freedom makes a voyage to Martinique in week 3.

Answer: Freedom makes a voyage to Guadeloupe in week 6.

Answer: Freedom makes a voyage to Martinique in week 6.


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

Answer: Freedom makes a voyage to Martinique in week 3.

Answer: Freedom makes a voyage to Martinique in week 4.

Answer: Freedom makes a voyage to Martinique in week 5.

Answer: Freedom makes a voyage to Guadeloupe in week 3.

Answer: Freedom makes a voyage to Guadeloupe in week 5.


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

Answer: Guadeloupe, Trinidad

Answer: Jamaica, Guadeloupe

Answer: Martinique, Trinidad

Answer: Trinidad, Jamaica

Answer: Trinidad, Martinique


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

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

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

Answer: Freedom makes at most two voyages to Guadeloupe.

Answer: Freedom makes at most two voyages to Jamaica.

Answer: Freedom makes at most two voyages to Trinidad.


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

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

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

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

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

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

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


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

Answer: Center 1 only

Answer: Center 3 only

Answer: Center 1, Center 2

Answer: Center 1, Center 3

Answer: Center 1, Center 2, Center 3


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

Answer: glass

Answer: newsprint

Answer: plastic

Answer: tin

Answer: wood


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

Answer: Only Center 2 recycles glass.

Answer: Only Center 3 recycles newsprint.

Answer: Only Center 1 recycles plastic.

Answer: Only Center 3 recycles tin.

Answer: Only Center 1 recycles wood.


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

Answer: glass

Answer: newsprint

Answer: plastic

Answer: tin

Answer: wood