Four boys—Fred, Juan, Marc, and Paul—and three girls—Nita, Rachel, and Trisha—will be assigned to a row of five adjacent lockers, numbered consecutively 1 through 5, arranged along a straight wall. The following conditions govern the assignment of lockers to the seven children: Each locker must be assigned to either one or two children, and each child must be assigned to exactly one locker. Each shared locker must be assigned to one girl and one boy. Juan must share a locker, but Rachel cannot share a locker. Nita's locker cannot be adjacent to Trisha's locker. Fred must be assigned to locker 3.

Question: Which one of the following is a complete and accurate list of the children who must be among those assigned to shared lockers?

Fred, Juan
Juan, Paul
Juan, Marc, Paul
Juan, Marc, Trisha
Juan, Nita, Trisha


Question: If Trisha is assigned to locker 3 and Marc alone is assigned to locker 1, then which one of the following must be true?

Juan is assigned to locker 4.
Juan is assigned to locker 5.
Paul is assigned to locker 2.
Rachel is assigned to locker 2.
Rachel is assigned to locker 5.


Question: If the four boys are assigned to consecutively numbered lockers and Juan is assigned to locker 5, then which one of the following is a complete and accurate list of lockers each of which CANNOT be a shared locker?

locker 2
locker 4
locker 1, locker 2
locker 1, locker 4
locker 2, locker 4


Question: Once Rachel has been assigned to a locker, what is the maximum number of different lockers each of which could be the locker to which Juan is assigned?


Question: If the first three lockers are assigned to girls, which one of the following must be true?

Juan is assigned to the same locker as Trisha.

Paul is assigned to the same locker as Trisha.


Question: If lockers 1 and 2 are each assigned to one boy and are not shared lockers, then locker 4 must be assigned to

Juan
Paul
Rachel
Juan and Nita
Marc and Trisha


A music store carries exactly ten types of CDs—both new and used of each of jazz, opera, pop, rap, and soul. The store is having a sale on some of these types of CDs. The following conditions must apply: Used pop is on sale; new opera is not. If both types of pop are on sale, then all soul is. If both types of jazz are on sale, then no rap is. If neither type of jazz is on sale, then new pop is. If either type of rap is on sale, then no soul is.

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

new jazz, used jazz, used opera, used pop, new rap

used jazz, used pop, new soul, used soul


Question: If new soul is not on sale, then which one of the following must be true?

At least one type of jazz is not on sale.

At least one type of pop is not on sale.


Question: If both types of jazz are on sale, then which one of the following is the minimum number of types of new CDs that could be included in the sale?


Question: Which one of the following CANNOT be true?

Neither type of opera and neither type of rap is on sale.

Neither type of jazz and neither type of opera is on sale.

Neither type of opera and neither type of soul is on sale.

Neither type of jazz and neither type of soul is on sale.

Neither type of jazz and neither type of rap is on sale.


Question: If neither type of jazz is on sale, then each of the following must be true EXCEPT:

Used opera is on sale.
New rap is not on sale.
Used rap is not on sale.
New soul is on sale.
Used soul is on sale.


Question: If new soul is the only type of new CD on sale, then which one of the following CANNOT be true?

Used jazz is not on sale.
Used opera is not on sale.
Used rap is not on sale.
Used soul is on sale.
Used soul is not on sale.


Question: If exactly four of the five types of used CDs are the only CDs on sale, then which one of the following could be true?

Neither type of rap and neither type of soul is on sale.


During a single week, from Monday through Friday, tours will be conducted of a company's three divisions—Operations, Production, and Sales. Exactly five tours will be conducted that week, one each day. The schedule of tours for the week must conform to the following restrictions: Each division is toured at least once. The Operations division is not toured on Monday. The Production division is not toured on Wednesday. The Sales division is toured on two consecutive days, and on no other days. If the Operations division is toured on Thursday, then the Production division is toured on Friday.

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

The division that is toured on Monday is also toured on Tuesday.

The division that is toured on Monday is also toured on Friday.

The division that is toured on Tuesday is also toured on Thursday.

The division that is toured on Wednesday is also toured on Friday.

The division that is toured on Thursday is also toured on Friday.


Question: If in addition to the Sales division one other division is toured on two consecutive days, then it could be true of the week's tour schedule both that the

Production division is toured on Monday and that the Operations division is toured on Thursday

Production division is toured on Tuesday and that the Sales division is toured on Wednesday

Operations division is toured on Tuesday and that the Production division is toured on Friday

Sales division is toured on Monday and that the Operations division is toured on Friday

Sales division is toured on Wednesday and that the Production division is toured on Friday


Question: If in the week's tour schedule the division that is toured on Tuesday is also toured on Friday, then for which one of the following days must a tour of the Production division be scheduled?

Monday Tuesday Wednesday Thursday Friday


Question: If in the week's tour schedule the division that is toured on Monday is not the division that is toured on Tuesday, then which one of the following could be true of the week's schedule?

A tour of the Sales division is scheduled for some day earlier in the week than is any tour of the Production division.

A tour of the Operations division is scheduled for some day earlier in the week than is any tour of the Production division.

The Production division is toured on Tuesday.

The Operations division is toured on Wednesday.


Question: If in the week's tour schedule the division that is toured on Tuesday is also toured on Wednesday, then which one of the following must be true of the week's tour schedule?

The Production division is toured on Monday.

The Operations division is toured on Tuesday.

The Sales division is toured on Wednesday.

The Sales division is toured on Thursday.

The Production division is toured on Friday.


A crew of up to five workers is to install a partition in at most three days. The crew completes five tasks in this order: framing, wallboarding, taping, sanding, priming. The crew is selected from the following list, which specifies exactly the tasks each person can do: George: taping Helena: sanding, priming Inga: framing, priming Kelly: framing, sanding Leanda: wallboarding, taping Maricita: sanding Olaf: wallboarding, priming The following conditions must apply: At least one task is done each day. Taping and priming are done on different days. Each crew member does at least one task during the installation, but no more than one task a day. Each task is done by exactly one worker, completed the day it is started and before the next task begins.

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

George, Helena, Inga, Kelly
George, Helena, Kelly, Leanda
Helena, Inga, Kelly, Olaf
Helena, Inga, Maricita, Olaf
George, Helena, Leanda, Maricita, Olaf


Question: If the installation takes three days, and if the same two crew members work on the first and third days, then which one of the following could be the pair of crew members who work on those two days?

Helena and Inga
Inga and Kelly
Inga and Leanda
Kelly and Olaf
Leanda and Olaf


Question: Each of the following could be a complete and accurate list of the members of the crew EXCEPT:

Helena, Inga, Kelly, Maricita
Inga, Kelly, Leanda, Olaf
George, Helena, Inga, Leanda
Inga, Leanda, Maricita, Olaf
Kelly, Leanda, Maricita, Olaf


Question: If the installation takes three days, and if the sanding is done on the third day, then which one of the following could be a list of all the crew members who work on the second day?

Inga
Kelly
Olaf
George and Helena
Leanda and Olaf


Question: Which one of the following could be a pair of members of the crew both of whom work on the same days as each other and each of whom perform two tasks?

George and Maricita
Helena and Kelly
Inga and Leanda
Kelly and Leanda
Leanda and Olaf


A closet contains exactly six hangers—1, 2, 3, 4, 5, and 6—hanging, in that order, from left to right. It also contains exactly six dresses—one gauze, one linen, one polyester, one rayon, one silk, and one wool—a different dress on each of the hangers, in an order satisfying the following conditions: The gauze dress is on a lower-numbered hanger than the polyester dress. The rayon dress is on hanger 1 or hanger 6. Either the wool dress or the silk dress is on hanger 3. The linen dress hangs immediately to the right of the silk dress.

Question: Which one of the following could be an accurate matching of the hangers to the fabrics of the dresses that hang on them?

1: wool; 2: gauze; 3: silk; 4: linen; 5: polyester; 6: rayon

1: rayon; 2: wool; 3: gauze; 4: silk; 5: linen; 6: polyester

1: polyester; 2: gauze; 3: wool; 4: silk; 5: linen; 6: rayon

1: linen; 2: silk; 3: wool; 4: gauze; 5: polyester; 6: rayon

1: gauze; 2: rayon; 3: silk; 4: linen; 5: wool; 6: polyester


Question: If both the silk dress and the gauze dress are on odd-numbered hangers, then which one of the following could be true?

The polyester dress is on hanger 1.
The wool dress is on hanger 2.
The polyester dress is on hanger 4.
The linen dress is on hanger 5.
The wool dress is on hanger 6.


Question: If the silk dress is on an even-numbered hanger, which one of the following could be on the hanger immediately to its left?

the gauze dress
the linen dress
the polyester dress
the rayon dress
the wool dress


Question: If the polyester dress is on hanger 2, then which one of the following must be true?

The silk dress is on hanger 1.
The wool dress is on hanger 3.
The linen dress is on hanger 4.
The linen dress is on hanger 5.
The rayon dress is on hanger 6.


Question: Which one of the following CANNOT be true?

The linen dress hangs immediately next to the gauze dress.

The polyester dress hangs immediately to the right of the rayon dress.

The rayon dress hangs immediately to the left of the wool dress.

The silk dress is on a lower-numbered hanger than the gauze dress.

The wool dress is on a higher-numbered hanger than the rayon dress.


Question: Which one of the following CANNOT hang immediately next to the rayon dress?

the gauze dress
the linen dress
the polyester dress
the silk dress
the wool dress


Question: Assume that the original condition that the linen dress hangs immediately to the right of the silk dress is replaced by the condition that the wool dress hangs immediately to the right of the silk dress. If all the other initial conditions remain in effect, which one of the following must be false?

The linen dress is on hanger 1.
The gauze dress is on hanger 2.
The wool dress is on hanger 4.
The silk dress is on hanger 5.
The polyester dress is on hanger 6.


At a children's festival, exactly four songs are performed, each exactly once: "Night's All Right," "Question Man," "Rhino Rock," and "Sammy." The songs are performed consecutively, each on a different one of exactly four instruments: flute, guitar, harmonica, or keyboard. The songs are performed in accordance with the following: The first song performed is not performed on the flute. If "Sammy" is performed on the keyboard, then "Rhino Rock" is performed on the harmonica. If "Question Man" is performed on the keyboard, then "Night's All Right" is performed on the flute. The song performed on the keyboard immediately follows "Rhino Rock" and immediately precedes "Night's All Right."

Question: Which one of the following could be an accurate matching of the four songs performed at the festival with the instruments on which they are performed, listed in order from the first song performed to the last?

"Night's All Right": guitar;" Question Man": keyboard; "Sammy": guitar;" Rhino Rock": flute

"Question Man": guitar;" Rhino Rock": harmonica; "Sammy": keyboard;" Night's All Right": flute

"Rhino Rock": flute;" Question Man": keyboard; "Night's All Right": harmonica;" Sammy": guitar

"Sammy": harmonica;" Night's All Right": guitar; "Question Man": keyboard;" Rhino Rock": flute

"Sammy": harmonica;" Rhino Rock": guitar; "Question Man": flute;" Night's All Right": keyboard


Question: Which one of the following could be true?

"Question Man" immediately follows the song performed on the keyboard.

"Night's All Right" immediately precedes the song performed on the keyboard.

"Question Man" immediately precedes the song performed on the guitar.

"Rhino Rock" immediately precedes the song performed on the harmonica.

"Sammy" immediately precedes the song performed on the guitar.


Question: Which one of the following CANNOT be true of the song performed on the flute?

It immediately follows "Night's All Right."


Question: If "Rhino Rock" is the second song performed at the festival, then which one of the following could be true?

The first song performed is performed on the keyboard.

The third song performed is performed on the guitar.

The third song performed is performed on the flute.

"Night's All Right" is performed on the guitar.

"Rhino Rock" is performed on the guitar.


Question: If "Question Man" is the third song performed at the festival, then each of the following could be true EXCEPT:

"Question Man" is performed on the guitar.

"Question Man" is performed on the keyboard.

"Rhino Rock" is performed on the guitar.


Each of the seven members of the board of directors—Guzman, Hawking, Lepp, Miyauchi, Upchurch, Wharton, and Zhu—serves on exactly one of two committees—the finance committee or the incentives committee. Only board members serve on these committees. Committee membership is consistent with the following conditions: If Guzman serves on the finance committee, then Hawking serves on the incentives committee. If Lepp serves on the finance committee, then Miyauchi and Upchurch both serve on the incentives committee. Wharton serves on a different committee from the one on which Zhu serves. Upchurch serves on a different committee from the one on which Guzman serves. If Zhu serves on the finance committee, so does Hawking.

Question: Which one of the following could be a complete and accurate list of the members of the finance committee?

Guzman, Hawking, Miyauchi, Wharton
Guzman, Lepp, Zhu
Hawking, Miyauchi, Zhu
Hawking, Upchurch, Wharton, Zhu
Miyauchi, Upchurch, Wharton


Question: Which one of the following pairs of board members CANNOT both serve on the incentives committee?

Guzman and Hawking
Guzman and Wharton
Hawking and Wharton
Miyauchi and Upchurch
Miyauchi and Wharton


Question: What is the maximum number of members on the finance committee?


Question: If Miyauchi and Wharton both serve on the finance committee, then which one of the following could be true?

Guzman and Lepp both serve on the finance committee.

Guzman and Upchurch both serve on the incentives committee.

Hawking and Zhu both serve on the finance committee.

Lepp and Upchurch both serve on the incentives committee.

Zhu and Upchurch both serve on the finance committee.


Question: If Guzman serves on the incentives committee, then which one of the following must be true?

Hawking serves on the finance committee.

Lepp serves on the incentives committee.

Miyauchi serves on the finance committee.

Wharton serves on the incentives committee.


Eight people—Fiona, George, Harriet, Ingrid, Karl, Manuel, Olivia, and Peter—are sitting, evenly spaced, around a circular picnic table. Any two of them are said to be sitting directly across from one another if and only if there are exactly three other people sitting between them, counting in either direction around the table. The following conditions apply: Fiona sits directly across from George. Harriet sits immediately next to neither Fiona nor Karl. Ingrid sits immediately next to, and immediately clockwise from, Olivia.

Question: Which one of the following could be the order in which four of the people are seated, with no one else seated between them, counting clockwise around the table?

George, Peter, Karl, Fiona
Harriet, Olivia, Ingrid, Karl
Ingrid, Fiona, Peter, Manuel
Olivia, Manuel, Karl, George
Peter, Harriet, Karl, Fiona


Question: If Harriet and Olivia each sits immediately next to George, then which one of the following could be the two people each of whom sits immediately next to Peter?

Fiona and Karl
Fiona and Olivia
Harriet and Ingrid
Harriet and Karl
Karl and Manuel


Question: If George does not sit immediately next to Harriet, then which one of the following could be the two people each of whom sits immediately next to Manuel?

Fiona and Harriet
Fiona and Peter
George and Karl
George and Peter
Harriet and Peter


Question: If Manuel sits immediately next to Olivia, then which one of the following people must sit immediately next to Fiona?


Question: What is the minimum possible number of people sitting between Ingrid and Manuel, counting clockwise from Ingrid around the table?


Question: If Karl sits directly across from Ingrid, then each of the following people could sit immediately next to Olivia EXCEPT:


Question: If Karl sits directly across from Harriet, then what is the minimum possible number of people sitting between George and Karl, counting clockwise from George to Karl?


Each of seven candidates for the position of judge—Hamadi, Jefferson, Kurtz, Li, McDonnell, Ortiz, and Perkins—will be appointed to an open position on one of two courts—the appellate court or the trial court. There are three open positions on the appellate court and six open positions on the trial court, but not all of them will be filled at this time. The judicial appointments will conform to the following conditions: Li must be appointed to the appellate court. Kurtz must be appointed to the trial court. Hamadi cannot be appointed to the same court as Perkins.

Question: Which one of the following is an acceptable set of appointments of candidates to courts?

appellate: Hamadi, Ortiz trial: Jefferson, Kurtz, Li, McDonnell, Perkins

appellate: Hamadi, Li, Perkins trial: Jefferson, Kurtz, McDonnell, Ortiz

appellate: Kurtz, Li, Perkins trial: Hamadi, Jefferson, McDonnell, Ortiz

appellate: Li, McDonnell, Ortiz trial: Hamadi, Jefferson, Kurtz, Perkins

appellate: Li, Perkins trial: Hamadi, Jefferson, Kurtz, McDonnell, Ortiz


Question: Which one of the following CANNOT be true?

Hamadi and McDonnell are both appointed to the appellate court.

McDonnell and Ortiz are both appointed to the appellate court.

Ortiz and Perkins are both appointed to the appellate court.

Hamadi and Jefferson are both appointed to the trial court.

Ortiz and Perkins are both appointed to the trial court.


Question: Which one of the following CANNOT be true?

Jefferson and McDonnell are both appointed to the appellate court.

Jefferson and McDonnell are both appointed to the trial court.

McDonnell and Ortiz are both appointed to the trial court.

McDonnell and Perkins are both appointed to the appellate court.

McDonnell and Perkins are both appointed to the trial court.


Question: If Ortiz is appointed to the appellate court, which one of the following must be true?

Hamadi is appointed to the appellate court.

Jefferson is appointed to the appellate court.

Jefferson is appointed to the trial court.

Perkins is appointed to the appellate court.

Perkins is appointed to the trial court.


Question: Which one of the following, if substituted for the condition that Hamadi cannot be appointed to the same court as Perkins, would have the same effect on the appointments of the seven candidates?

Hamadi and Perkins cannot both be appointed to the appellate court.

If Hamadi is not appointed to the trial court, then Perkins must be.

If Perkins is appointed to the same court as Jefferson, then Hamadi cannot be.

If Hamadi is appointed to the same court as Li, then Perkins must be appointed to the same court as Kurtz.

No three of Hamadi, Kurtz, Li, and Perkins can be appointed to the same court as each other.


Exactly six members of a skydiving team—Larue, Ohba, Pei, Trevino, Weiss, and Zacny—each dive exactly once, one at a time, from a plane, consistent with the following conditions: Trevino dives from the plane at some time before Weiss does. Larue dives from the plane either first or last. Neither Weiss nor Zacny dives from the plane last. Pei dives from the plane at some time after either Ohba or Larue but not both.

Question: Which one of the following could be an accurate list of the members in the order in which they dive from the plane, from first to last?

Larue, Trevino, Ohba, Zacny, Pei, Weiss
Larue, Trevino, Pei, Zacny, Weiss, Ohba
Weiss, Ohba, Trevino, Zacny, Pei, Larue
Trevino, Weiss, Pei, Ohba, Zacny, Larue
Trevino, Weiss, Zacny, Larue, Pei, Ohba


Question: Which one of the following must be true?

At least two of the members dive from the plane after Larue.

At least two of the members dive from the plane after Ohba.

At least two of the members dive from the plane after Pei.

At least two of the members dive from the plane after Trevino.

At least two of the members dive from the plane after Weiss.


Question: If Larue dives from the plane last, then each of the following could be true EXCEPT:

Trevino dives from the plane fourth.
Weiss dives from the plane fourth.
Ohba dives from the plane fifth.
Pei dives from the plane fifth.
Zacny dives from the plane fifth.


Question: If Zacny dives from the plane immediately after Weiss, then which one of the following must be false?

Larue dives from the plane first.
Trevino dives from the plane third.
Zacny dives from the plane third.
Pei dives from the plane fourth.
Zacny dives from the plane fourth.


Question: If Trevino dives from the plane immediately after Larue, then each of the following could be true EXCEPT:

Ohba dives from the plane third.
Weiss dives from the plane third.
Zacny dives from the plane third.
Pei dives from the plane fourth.
Weiss dives from the plane fourth.


A company's six vehicles—a hatchback, a limousine, a pickup, a roadster, a sedan, and a van—are serviced during a certain week—Monday through Saturday—one vehicle per day. The following conditions must apply: At least one of the vehicles is serviced later in the week than the hatchback. The roadster is serviced later in the week than the van and earlier in the week than the hatchback. Either the pickup and the van are serviced on consecutive days, or the pickup and the sedan are serviced on consecutive days, but not both. The sedan is serviced earlier in the week than the pickup or earlier in the week than the limousine, but not both.

Question: Which one of the following could be the order in which the vehicles are serviced, from Monday through Saturday?

the hatchback, the pickup, the sedan, the limousine, the van, the roadster

the pickup, the sedan, the van, the roadster, the hatchback, the limousine

the pickup, the van, the sedan, the roadster, the limousine, the hatchback

the van, the roadster, the pickup, the hatchback, the sedan, the limousine

the van, the sedan, the pickup, the roadster, the hatchback, the limousine


Question: Which one of the following CANNOT be the vehicle serviced on Thursday?

the hatchback
the limousine
the pickup
the sedan
the van


Question: If neither the pickup nor the limousine is serviced on Monday, then which one of the following must be true?

The hatchback and the limousine are serviced on consecutive days.

The hatchback and the sedan are serviced on consecutive days.


Question: If the limousine is not serviced on Saturday, then each of the following could be true EXCEPT:

The limousine is serviced on Monday.
The roadster is serviced on Tuesday.
The hatchback is serviced on Wednesday.
The roadster is serviced on Wednesday.
The sedan is serviced on Wednesday.


Question: If the sedan is serviced earlier in the week than the pickup, then which one of the following could be true?

The limousine is serviced on Wednesday.
The sedan is serviced on Wednesday.
The van is serviced on Wednesday.
The hatchback is serviced on Friday.
The limousine is serviced on Saturday.


Question: If the limousine is serviced on Saturday, then which one of the following must be true?

The pickup is serviced earlier in the week than the roadster.

The pickup is serviced earlier in the week than the sedan.

The sedan is serviced earlier in the week than the roadster.

The hatchback and the limousine are serviced on consecutive days.

The roadster and the hatchback are serviced on consecutive days.


Question: Which one of the following could be the list of the vehicles serviced on Tuesday, Wednesday, and Friday, listed in that order?

the pickup, the hatchback, the limousine


A street entertainer has six boxes stacked one on top of the other and numbered consecutively 1 through 6, from the lowest box up to the highest. Each box contains a single ball, and each ball is one of three colors—green, red, or white. Onlookers are to guess the color of each ball in each box, given that the following conditions hold: There are more red balls than white balls. There is a box containing a green ball that is lower in the stack than any box that contains a red ball. There is a white ball in a box that is immediately below a box that contains a green ball.

Question: If there are exactly two white balls, then which one of the following boxes could contain a green ball?


Question: If there are green balls in boxes 5 and 6, then which one of the following could be true?

There are red balls in boxes 1 and 4.
There are red balls in boxes 2 and 4.
There is a white ball in box 1.
There is a white ball in box 2.
There is a white ball in box 3.


Question: The ball in which one of the following boxes must be the same color as at least one of the other balls?


Question: Which one of the following must be true?

There is a green ball in a box that is lower than box 4.

There is a green ball in a box that is higher than box 4.

There is a red ball in a box that is lower than box 4.

There is a red ball in a box that is higher than box 4.

There is a white ball in a box that is lower than box 4.


Question: If there are red balls in boxes 2 and 3, then which one of the following could be true?

There is a red ball in box 1.
There is a white ball in box 1.
There is a green ball in box 4.
There is a red ball in box 5.
There is a white ball in box 6.


Question: If boxes 2, 3, and 4 all contain balls that are the same color as each other, then which one of the following must be true?

Exactly two of the boxes contain a green ball.

Exactly three of the boxes contain a green ball.

Exactly three of the boxes contain a red ball.

Exactly one of the boxes contains a white ball.

Exactly two of the boxes contain a white ball.


A professor must determine the order in which five of her students—Fernando, Ginny, Hakim, Juanita, and Kevin—will perform in an upcoming piano recital. Each student performs one piece, and no two performances overlap. The following constraints apply: Ginny must perform earlier than Fernando. Kevin must perform earlier than Hakim and Juanita. Hakim must perform either immediately before or immediately after Fernando.

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

Ginny, Fernando, Hakim, Kevin, Juanita
Ginny, Juanita, Kevin, Hakim, Fernando
Ginny, Kevin, Hakim, Juanita, Fernando
Kevin, Ginny, Juanita, Fernando, Hakim
Kevin, Juanita, Fernando, Hakim, Ginny


Question: If Juanita performs earlier than Ginny, then which one of the following could be true?

Fernando performs fourth.
Ginny performs second.
Hakim performs third.
Juanita performs third.
Kevin performs second.


Question: Which one of the following CANNOT be true?

Fernando performs immediately before Juanita.

Ginny performs immediately before Hakim.

Hakim performs immediately before Ginny.

Juanita performs immediately before Ginny.

Kevin performs immediately before Hakim.


Question: The order in which the students perform is fully determined if which one of the following is true?

Fernando performs immediately before Hakim.

Ginny performs immediately before Fernando.

Hakim performs immediately before Juanita.

Juanita performs immediately before Hakim.

Kevin performs immediately before Fernando.


Question: How many of the students are there any one of whom could perform fourth?


As part of an open house at a crafts studio, three teachers—Jiang, Kudrow, and Lanning—will give six consecutive presentations on six different subjects. Jiang will present on needlework and origami; Kudrow on pottery, stenciling, and textile making; and Lanning on woodworking. The order of their presentations will meet the following conditions: Kudrow cannot give two presentations in a row. The presentation on stenciling must be given earlier than the one on origami. The presentation on textile making must be given earlier than the one on woodworking.

Question: Which one of the following could be the order of the presentations, from first to sixth?

stenciling, origami, needlework, textile making, pottery, woodworking

stenciling, origami, pottery, woodworking, needlework, textile making

stenciling, origami, textile making, woodworking, needlework, pottery

textile making, origami, stenciling, woodworking, needlework, pottery

textile making, stenciling, woodworking, needlework, pottery, origami


Question: If textile making is presented fifth, which one of the following could be true?

Needlework is presented sixth.
Pottery is presented fourth.
Stenciling is presented second.
Stenciling is presented third.
Woodworking is presented second.


Question: If needlework is presented first, which one of the following could be true?

Origami is presented sixth.
Pottery is presented second.
Stenciling is presented third.
Textile making is presented fifth.
Woodworking is presented third.


Question: Jiang CANNOT give both

the first and third presentations
the first and fourth presentations
the first and fifth presentations
the second and third presentations
the second and fourth presentations


Question: If needlework is presented sixth, which one of the following must be true?

Origami is presented fourth.
Pottery is presented fifth.
Stenciling is presented third.
Textile making is presented first.
Woodworking is presented fourth.


Question: Which one of the following CANNOT be the subject of the second presentation?

needlework
origami
pottery
textile making
woodworking


The organizer of a luncheon will select exactly five foods to be served from among exactly eight foods: two desserts—F and G; three main courses—N, O, and P; three side dishes—T, V, and W. Only F, N, and T are hot foods. The following requirements will be satisfied: At least one dessert, at least one main course, and at least one side dish must be selected. At least one hot food must be selected. If either P or W is selected, both must be selected. If G is selected, O must be selected. If N is selected, V cannot be selected.

Question: Which one of the following is a list of foods that could be the foods selected?

F, N, O, T, V
F, O, P, T, W
G, N, P, T, W
G, O, P, T, V
G, O, P, V, W


Question: Which one of the following is a pair of foods of which the organizer of the luncheon must select at least one?


Question: If O is the only main course selected, then which one of the following CANNOT be selected?


Question: If F is not selected, which one of the following could be true?

Exactly three main courses are selected.


Question: If T and V are the only side dishes selected, then which one of the following is a pair of foods each of which must be selected?


A television programming director is scheduling a three-hour block of programs beginning at 1 P.M. The programs that are to fill this time block include an hour-long program called Generations and four half-hour programs: Roamin', Sundown, Terry, and Waterloo. The programs will be shown one after the other, each program shown exactly once. The schedule must meet the following constraints: Generations starts on the hour rather than the half hour. Terry starts on the half hour rather than the hour. Roamin' is shown earlier than Sundown. If Waterloo is shown earlier than Terry, it is shown immediately before Terry.

Question: Which one of the following could be the order in which the programs are shown, from earliest to latest?

Generations, Roamin', Waterloo, Terry, Sundown

Roamin', Sundown, Waterloo, Terry, Generations

Roamin', Terry, Waterloo, Generations, Sundown

Waterloo, Roamin', Sundown, Terry, Generations

Waterloo, Terry, Sundown, Roamin', Generations


Question: If Waterloo is the first program, then how many orders are there in which the remaining programs could be shown?


Question: If Roamin' is the second program, then each of the following could be true EXCEPT:

Sundown is the third program.
Sundown is the fourth program.
Terry is the fifth program.
Waterloo is the third program.
Waterloo is the fifth program.


Question: If Sundown is the third program, then which one of the following must be true?

Generations is the first program.
Roamin' is the first program.
Roamin' is the second program.
Terry is the fifth program.
Waterloo is the fourth program.


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

Roamin' is the second program.
Roamin' is the fifth program.
Sundown is the fourth program.
Terry is the fourth program.
Waterloo is the second program.


Question: Which one of the following CANNOT be true?

Sundown is shown immediately before Generations.

Waterloo is shown immediately before Roamin'.

Generations is shown immediately before Sundown.

Roamin' is shown immediately before Terry.

Terry is shown immediately before Waterloo.


Question: Which one of the following, if substituted for the constraint that Generations starts on the hour rather than the half hour, would have the same effect in determining the order in which the programs are shown?

Generations is not shown immediately before Terry.

Generations is either the first program or the fifth.

Generations is neither the second program nor the fourth.

If Generations is shown third, then Roamin' is shown first.

If Generations is not shown first, then it is shown later than Terry.


Five students—Manolo, Nadia, Owen, Peng, and Rana—are each to deliver exactly one speech. Speeches are on exactly one of two topics—friendship and liberty. Each student has only one major: two major in geology, two in history, and one in journalism. The following conditions must apply: Exactly two of the students speak on friendship. A geology major and a history major speak on friendship. Manolo speaks on friendship. Rana speaks on liberty. Neither Peng nor Rana is a geology major. Nadia is a geology major.

Question: Which one of the following could be a list of the majors of Manolo, Nadia, Owen, Peng, and Rana, respectively?

geology, geology, journalism, journalism, history

geology, geology, history, history, history

history, geology, geology, journalism, history

history, geology, journalism, geology, history

history, history, geology, journalism, history


Question: If Peng speaks on friendship, then which one of the following could be true?

Manolo is a history major.
Nadia speaks on friendship.
Owen speaks on friendship.
Owen is a journalism major.
Peng is a journalism major.


Question: If Owen is a geology major who speaks on friendship, then which one of the following must be true?

Manolo is a history major.
Nadia speaks on friendship.
Peng speaks on friendship.
Peng is a history major.
Rana is a journalism major.


Question: If Nadia speaks on friendship, then which one of the following must be false?

Manolo is a geology major.
Manolo is a history major.
Owen is a geology major.
Peng is a history major.
Rana is a history major.


Question: Rana must be a journalism major if which one of the following is true?

Manolo is a geology major and Peng is a history major.

Owen is a geology major and Manolo is a history major.

Owen is a geology major and Peng is a history major.

Both Manolo and Nadia speak on friendship.

Both Manolo and Peng speak on friendship.


Each of exactly seven professors—Powell, Shihab, Taylor, Vaughan, Wood, Young, and Zabel—gives exactly one guest lecture in the literary theory course. The lectures are ordered from first through seventh, and their order must conform to the following: Powell lectures before Wood. Taylor lectures before Shihab. Vaughan lectures before Zabel. Shihab is no later than third. Young is not seventh. Powell lectures first if, but only if, Young lectures before Vaughan.

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

Powell, Young, Taylor, Shihab, Vaughan, Zabel, Wood

Taylor, Powell, Shihab, Wood, Vaughan, Young, Zabel

Taylor, Vaughan, Shihab, Wood, Powell, Young, Zabel

Vaughan, Taylor, Shihab, Powell, Wood, Zabel, Young

Young, Taylor, Shihab, Powell, Vaughan, Zabel, Wood


Question: Which one of the following could lecture first?


Question: Which one of the following CANNOT given the second guest lecture?


Question: If Shihab lectures second and Zabel lectures fourth, then which one of the following could be true?

Powell lectures sixth
Taylor lectures third
Vaughan lectures fifth
Wood lectures fifth
Young lectures third


Question: Which one of the following CANNOT be the guest lecture that Vaughan gives?


Question: If Young lectures fourth and Taylor lectures first, then which one of the following must be true?

Powell lectures no earlier than sixth
Shihab lectures second.
Vaughan lectures no later than third.
Wood lectures seventh.
Zabel lectures no earlier than sixth.


Question: If Zabel lectures fourth, then which one of the following could be true?

Powell lectures second.
Powell lectures seventh.
Wood lectures third.
Young lectures second.
Young lectures sixth.


A toy retailer is opening a small satellite store with exactly three aisles, numbered from 1 (lowest) to 3 (highest). Six sections—Fantasy, Hobbies, Music, Puzzles, Reading, and Science—will each be confined to exactly one aisle, with each aisle containing at least one of the sections. The following conditions hold: Reading must be located in the same aisle as either Fantasy or Music. Fantasy must be located in a lower-numbered aisle than both Music and Puzzles. Science must be located in a lower-numbered aisle than Puzzles. Science cannot be located in a lower-numbered aisle than Hobbies.

Question: If aisle 1 contains Hobbies only, which one of the following could be true?

Fantasy is located in aisle 3.
Music is located in aisle 2.
Puzzles is located in aisle 2.
Reading is located in aisle 3.
Science is located in aisle 3.


Question: If aisle 3 contains Puzzles only, which one of the following must be true?

Fantasy is located in aisle 1.
Hobbies is located in aisle 1.
Music is located in aisle 1.
Reading is located in aisle 1.
Science is located in aisle 2.


Question: If each aisle contains exactly two of the six sections, then Science must be located in the same aisle as


Question: Which one of the following CANNOT be the list of the sections located in aisle 2?

Hobbies, Music
Music, Reading
Music, Science
Hobbies, Music, Science
Music, Reading, Science


Question: If aisle 2 contains Science only, then each of the following must be true EXCEPT:

Fantasy is located in aisle 1.
Hobbies is located in aisle 1.
Music is located in aisle 3.
Puzzles is located in aisle 3.
Reading is located in aisle 1.


Millville has created three new development zones: Z1, Z2, and Z3. Within these zones, subzones can be designated for housing, industrial, or retail use, with no subzone designated for more than one use. By city regulation, a total of no more than three subzones can be designated for each of the three uses. The following restrictions are in place: Retail subzones are not allowed in Z1. No more than two subzones for housing are allowed in any particular zone. No more than one retail subzone is allowed in any zone in which a subzone is designated for housing. Industrial subzones are not allowed in any zone in which a subzone is designated for housing or three subzones are designated for retail use.

Question: Which one of the following is an allowable way of designating subzones within the three zones?

Z1: no designated subzones Z2: one housing subzone, two retail subzones Z3: one industrial subzone, one retail subzone

Z1: one housing subzone, one industrial subzone Z2: two housing subzones, one retail subzone Z3: one industrial subzone, one retail subzone

Z1: one housing subzone, one retail subzone Z2: two housing subzones, one retail subzone Z3: one industrial subzone, one retail subzone

Z1: one industrial subzone Z2: three housing subzones Z3: three retail subzones

Z1: one industrial subzone Z2: two housing subzones, one retail subzone Z3: one industrial subzone, two retail subzones


Question: Which one of the following CANNOT be true within a single zone?

Two subzones are designated, one housing and one retail.

Two subzones are designated, one industrial and one retail.

Three subzones are designated, all of them retail.

Four subzones are designated, none of them industrial.

Four subzones are designated, two retail and two industrial.


Question: What is the maximum number of designated subzones allowed in Z3?


Question: If three subzones are designated for each use, then which one of the following is allowed?

Exactly one subzone in Z3 is designated for industrial use and exactly one subzone in Z3 is designated for retail use.

Exactly two subzones in Z2 are designated for housing.

Three subzones in Z1 are designated for industrial use.

Three subzones in Z2 are designated for industrial use and exactly one subzone in Z2 is designated for retail use.

Three subzones in Z3 are designated for retail use.


Question: If one subzone in each of the zones is designated for industrial use, then which one of the following is allowed?

More subzones are designated for retail use in Z2 than in Z3.

A subzone in one of the zones is designated for housing.

Exactly two subzones are designated in Z1.

Exactly three subzones each are designated in Z2 and Z3.

Exactly four subzones are designated in Z3.


Question: If three subzones in all are designated for retail use and a subzone in Z2 is designated for housing, then which one of the following is allowed?

Two subzones in Z1 are designated for housing.

More subzones are designated for industrial use in Z2 than in Z3.

More subzones are designated for retail use in Z2 than in Z3.

The same number of subzones are designated for retail use in Z2 and Z3.

A subzone in Z3 is designated for housing.


A researcher is studying seven manuscripts—F, G, H, L, M, P, and S—to determine their relative ages. It is known that no two manuscripts were written at the same time. The researcher has also determined the following: H was written earlier than S but later than F. P was the next manuscript written after G. At least four of the manuscripts were written earlier than L. At least four of the manuscripts were written later than M. H was not written fifth.

Question: Which one of the following could be the order in which the manuscripts were written, from first to last?

F, M, G, H, P, L, S
G, P, M, F, H, S, L
H, F, M, G, P, L, S
L, F, M, G, P, H, S
M, F, H, S, L, G, P


Question: Which one of the following manuscripts CANNOT have been written third?


Question: If H was the next manuscript written after M, which one of the following could be true?

F was written second.
G was written third.
H was written fourth.
P was written third.
S was written fourth.


Question: Which one of the following manuscripts CANNOT have been written fourth?


Question: If P was written earlier than H, then any of the following could be true EXCEPT:

F was written first.
G was written third.
H was written sixth.
L was written seventh.
M was written second.


Exactly six petri dishes—labeled dish 1 through dish 6—are to be stored in an otherwise empty refrigerator. There are three available shelves—the bottom shelf, the middle shelf, and the top shelf. The placement of the dishes must be consistent with the following conditions: No more than three dishes are stored on any shelf. Dish 2 is stored at least one shelf above dish 6. Dish 6 is stored either one shelf above or one shelf below dish 5. Dish 1 is not stored on the same shelf as dish 4.

Question: Which one of the following is an acceptable placement of dishes on the bottom, middle, and top shelves?

bottom: dish 1 middle: dish 6 top: dishes 2, 3, 4, 5

bottom: dishes 1, 3 middle: dish 6 top: dishes 2, 4, 5

bottom: dish 2 middle: dishes 4, 6 top: dishes 1, 3, 5

bottom: dishes 3, 5 middle: dish 6 top: dishes 1, 2, 4

bottom: dishes 4, 6 middle: dishes 1, 3 top: dishes 2, 5


Question: If dish 6 is the only dish stored on the bottom shelf, which one of the following could be the list of dishes that are stored together on the middle shelf?

dish 1, dish 3
dish 2, dish 4
dish 2, dish 3
dish 3, dish 5
dish 4, dish 5


Question: If dish 1, dish 2, and dish 3 are stored on the same shelf as each other, which one of the following could be true?

Exactly one of the dishes is stored on the top shelf.

Exactly two of the dishes are stored on the top shelf.

Exactly two of the dishes are stored on the middle shelf.

Exactly three of the dishes are stored on the middle shelf.

Exactly three of the dishes are stored on the bottom shelf.


Question: If exactly one of the shelves has no dish stored on it, which one of the following must be true?

Exactly three of the dishes are stored on the bottom shelf.

Exactly three of the dishes are stored on the middle shelf.

Dish 1 is stored on the same shelf as dish 5.

Dish 2 is stored on the same shelf as dish 3.

Dish 4 is stored on the same shelf as dish 5.


Question: If dish 5 is the only dish stored on the bottom shelf and if exactly two of the dishes are stored on the middle shelf, then which one of the following is a pair of dishes that must be among the dishes stored on the top shelf?

dish 1 and dish 2
dish 1 and dish 6
dish 2 and dish 3
dish 2 and dish 4
dish 3 and dish 4


Question: If exactly one of the dishes is stored on the middle shelf, which one of the following could be the list of dishes stored on the top shelf?

dish 1, dish 2
dish 1, dish 5
dish 2, dish 3
dish 3, dish 4
dish 3, dish 5


A company operates vending machines in four schools: Ferndale, Gladstone, Hafford, and Isley. The company delivers juices in one of its two trucks and snacks in the other truck. Each week, exactly one delivery of juices and exactly one delivery of snacks is made to each school, subject to the following conditions: Snacks must be delivered to Ferndale at some time before they are delivered to Hafford. Gladstone cannot be the fourth school to which juices are delivered. Gladstone must be the third school to which snacks are delivered. The first school to which juices are delivered must be the fourth one to which snacks are delivered.

Question: Which one of the following could be the schedule of deliveries to the schools, from the first to the fourth?

Juices: Hafford, Ferndale, Gladstone, Isley Snacks: Ferndale, Isley, Gladstone, Hafford

Juices: Hafford, Isley, Ferndale, Gladstone Snacks: Isley, Ferndale, Gladstone, Hafford

Juices: Isley, Ferndale, Gladstone, Hafford Snacks: Hafford, Ferndale, Gladstone, Isley

Juices: Isley, Gladstone, Ferndale, Hafford Snacks: Ferndale, Gladstone, Hafford, Isley

Juices: Isley, Hafford, Gladstone, Ferndale Snacks: Ferndale, Isley, Gladstone, Hafford


Question: If Hafford is the fourth school to which juices are delivered, which one of the following must be true?

Ferndale is the second school to which juices are delivered.

Gladstone is the third school to which juices are delivered.

Ferndale is the second school to which snacks are delivered.

Hafford is the second school to which snacks are delivered.

Isley is the first school to which snacks are delivered.


Question: If Isley is the third school to which juices are delivered, which one of the following could be true?

Juices are delivered to Gladstone at some time before they are delivered to Hafford.

Juices are delivered to Isley at some time before they are delivered to Hafford.

Snacks are delivered to Ferndale at some time before they are delivered to Isley.

Snacks are delivered to Gladstone at some time before they are delivered to Isley.

Snacks are delivered to Hafford at some time before they are delivered to Gladstone.


Question: If Isley is the first school to which snacks are delivered, which one of the following could be true?

Ferndale is the second school to which juices are delivered.

Hafford is the second school to which juices are delivered.

Hafford is the third school to which juices are delivered.

Isley is the first school to which juices are delivered.

Hafford is the second school to which snacks are delivered.


Question: Which one of the following could be true?

Both juices and snacks are delivered to Gladstone at some time before they are delivered to Ferndale.

Both juices and snacks are delivered to Gladstone at some time before they are delivered to Isley.

Both juices and snacks are delivered to Hafford at some time before they are delivered to Isley.

Both juices and snacks are delivered to Isley at some time before they are delivered to Ferndale.

Both juices and snacks are delivered to Isley at some time before they are delivered to Hafford.


Question: Which one of the following, if substituted for the condition that Gladstone cannot be the fourth school to which juices are delivered, would have the same effect in determining the delivery schedule?

Ferndale must be either the second school or the fourth school to which juices are delivered.

Gladstone must be either the second school or the third school to which juices are delivered.

Hafford must be either the first school or the fourth school to which juices are delivered.

The first school to which juices are delivered must be either Ferndale or Isley.

The fourth school to which juices are delivered must be either Hafford or Isley.


Each of five paralegals—Frank, Gina, Hiro, Kevin, and Laurie—is being assigned to exactly one of three cases—the Raimes, Sicoli, or Thompson case. At least one paralegal will be assigned to each case. The following conditions must apply: Either Frank is assigned to Raimes and Kevin is assigned to Thompson, or Frank is not assigned to Raimes and Kevin is not assigned to Thompson. Either Frank is the sole paralegal assigned to his case or Gina is the sole paralegal assigned to her case, but not both. Hiro is assigned to Sicoli.

Question: Which one of the following could be the assignment of paralegals to cases?

Raimes: Frank Sicoli: Gina, Hiro, Kevin Thompson: Laurie

Raimes: Kevin Sicoli: Gina Thompson: Frank, Hiro, Laurie

Raimes: Gina, Kevin Sicoli: Frank, Hiro Thompson: Laurie

Raimes: Kevin, Laurie Sicoli: Gina, Hiro Thompson: Frank

Raimes: Frank, Kevin, Laurie Sicoli: Hiro Thompson: Gina


Question: Which one of the following CANNOT be the complete assignment of paralegals to the Sicoli case?

Frank, Hiro, Kevin
Frank, Hiro, Laurie
Gina, Hiro, Kevin
Gina, Hiro, Laurie
Hiro, Kevin, Laurie


Question: If exactly two of the paralegals are assigned to the Thompson case, then which one of the following could be the complete assignment of paralegals to the Raimes case?

Gina
Kevin
Laurie
Gina, Kevin
Kevin, Laurie


Question: If one of the cases has Gina and Laurie as the only paralegals assigned to it, then each of the following must be false EXCEPT:

Laurie is assigned to the Thompson case.


Question: Which one of the following CANNOT be the complete assignment of paralegals to the Thompson case?

Gina
Laurie
Gina, Kevin
Gina, Laurie
Kevin, Laurie


Question: If Kevin is the sole paralegal assigned to one of the cases then which one of the following lists all of the paralegals any one of

Frank, Kevin, Laurie
Frank, Kevin
Frank
Gina
Kevin


A record producer is planning the contents of a CD consisting of a sequence of exactly five instrumental pieces—Reciprocity, Salammbo, Trapezoid, Vancouver, and Wisteria. To create and sustain certain moods, the sequence of pieces will satisfy the following constraints: Salammbo must be earlier than Vancouver. Trapezoid must either be earlier than both Reciprocity and Salammbo or after than both Reciprocity and Salammbo. Wisteria must either be earlier than both Reciprocity and Trapezoid or after than both Reciprocity and Trapezoid.

Question: The five pieces could appear in which one of the following sequences on the CD, in order from first to last?

Reciprocity, Trapezoid, Wisteria, Salammbo, Vancouver

Salammbo, Reciprocity, Trapezoid, Vancouver, Wisteria

Trapezoid, Wisteria, Salammbo, Vancouver, Reciprocity

Vancouver, Wisteria, Salammbo, Reciprocity, Trapezoid

Wisteria, Salammbo, Vancouver, Trapezoid, Reciprocity


Question: If Salammbo is the fourth piece on the CD, then which one of the following must be true?

Reciprocity is earlier on the CD than Wisteria.

Salammbo is earlier on the CD than Trapezoid.

Trapezoid is earlier on the CD than Reciprocity.

Vancouver is earlier on the CD than Wisteria.

Wisteria is earlier on the CD than Trapezoid.


Question: If Reciprocity is the first piece on the CD, then which one of the following could be true?

Trapezoid is the second piece on the CD.


Question: If Trapezoid is the second piece on the CD, then which one of the following could be true?

Reciprocity is the first piece on the CD.

Reciprocity is the last piece on the CD.


Question: The first and second pieces on the CD, listed in order, could be

Reciprocity and Vancouver
Wisteria and Salammbo
Salammbo and Trapezoid
Trapezoid and Wisteria
Reciprocity and Wisteria


Question: If Vancouver is the second piece on the CD, then which one of the following could be true?

Reciprocity is the fourth piece on the CD.

Reciprocity is the last piece on the CD.


Question: If Wisteria is the first piece on the CD, then which one of the following CANNOT be true?

Trapezoid is the third piece on the CD.
Vancouver is the third piece on the CD.
Salammbo is the fourth piece on the CD.
Vancouver is the fourth piece on the CD
Trapezoid is the last piece on the CD.


At a business symposium there will be exactly five speakers: Long, Molina, Xiao, Yoshida, and Zimmerman. Each speaker will give exactly one speech, in either the Gold Room or the Rose Room. In each room, there will be exactly one speech at 1 P.M. and one speech at 2 P.M. In one of the rooms, yet to be determined, there will also be a speech at 3 P.M. The schedule of speeches is constrained by the following: Molina's speech must be earlier than Long's, and in the same room. Neither Xiao's speech nor Yoshida's speech can be earlier than Zimmerman's. If Long's speech is in the Gold Room, then Xiao's and Zimmerman's speeches must both be in the Rose Room.

Question: Which one of the following could be the speeches given in each room, listed in the order in which they occur?

Gold Room: Molina's, Long's Rose Room: Zimmerman's, Xiao's, Yoshida's

Gold Room: Molina's, Yoshida's, Long's Rose Room: Xiao's Zimmerman's

Gold Room: Xiao's, Molina's, Long's Rose Room: Zimmerman's, Yoshida's

Gold Room: Yoshida's, Long's, Molina's Rose Room: Zimmerman's, Xiao's

Gold Room: Zimmerman's, Molina's Rose Room: Xiao's, Yoshida's, Long's


Question: Which one of the following pairs of speeches CANNOT be given at the same time?

Long's and Yoshida's
Long's and Zimmerman's
Molina's and Xiao's
Xiao's and Yoshida's
Yoshida's and Zimmerman's


Question: If Xiao's speech is at 3 P.M., which one of the following CANNOT be true?

Long's speech is in the same room as Yoshida's.

Molina's speech is in the same room as Xiao's.

Xiao's speech is in the same room as Yoshida's.

Xiao's speech is in the same room as Zimmerman's.

Yoshida's speech is in the same room as Zimmerman's.


Question: Which one of the following could be a complete and accurate list of the speeches given in the Gold Room, in the order in which they occur?

Long's, Molina's
Molina's, Yoshida's
Molina's, Yoshida's, Long's
Yoshida's, Zimmerman's, Xiao's
Zimmerman's, Molina's, Long's


Question: If Yoshida's speech is at 1 P.M., which one of the following could be true?

Long's speech is at 1 P.M. in the Gold Room.

Long's speech is at 2 P.M. in the Rose Room.

Molina's speech is at 2 P.M. in the Gold Room.

Xiao's speech is at 3 P.M. in the Gold Room.

Xiao's speech is at 1 P.M. in the Rose Room.


Question: Which one of the following, if substituted for the constraint that neither Xiao's speech nor Yoshida's speech can be earlier than Zimmerman's, would have the same effect in determining the schedule of speeches with regard to rooms and times?

Molina's speech cannot be earlier than Zimmerman's.

Either Xiao's speech or Yoshida's speech must be after Zimmerman's.

Either Xiao's speech or Yoshida's speech or both must be at 2 P.M.


During the seventeenth century, three families—the Trents, the Williamses, and the Yandells—owned the five buildings that constituted the center of their village—the forge, the granary, the inn, the mill, and the stable. Each family owned at least one of the buildings and each building was owned by exactly one of the families. The historical evidence establishes the following about the ownership of the buildings: The Williamses owned more of the buildings than the Yandells owned. Neither the inn nor the mill belonged to the owner of the forge. Either the Trents owned the stable or the Yandells owned the inn, or both.

Question: Which one of the following could be an accurate matching of each family to the building or buildings it owned?

Trents: the granary, the stable Williamses: the inn, the mill Yandells: the forge

Trents: the granary, the mill Williamses: the inn, the stable Yandells: the forge

Trents: the forge, the mill Williamses: the granary, the stable Yandells: the inn

Trents: the forge, the granary Williamses: the mill Yandells: the inn, the stable

Trents: the stable Williamses: the inn, the mill Yandells: the forge, the granary


Question: Which one of the following is a pair of buildings that CANNOT both have been owned by the Trents?

the forge, the granary
the granary, the mill
the granary, the stable
the inn, the mill
the inn, the stable


Question: If the Yandells owned the mill, which one of the following must be true?

The Trents owned the forge.
The Trents owned the inn.
The Williamses owned the forge.
The Williamses owned the granary.
The Williamses owned the inn.


Question: If one of the families owned both the granary and the inn, which one of the following could be true?

The Trents owned the granary.
The Trents owned the mill.
The Williamses owned the forge.
The Williamses owned the stable.
The Yandells owned the inn.


Question: If the Trents owned exactly one of the buildings, which one of the following is a complete and accurate list of the buildings any one of which could be the building that the Trents owned?

the forge
the forge, the mill
the inn, the stable
the forge, the granary, the mill
the forge, the mill, the stable


A florist is filling a customer's order for three bouquets—bouquet 1, bouquet 2, and bouquet 3. Each of the bouquets is to be composed of one or more of five kinds of flowers—lilies, peonies, roses, snapdragons, and tulips—subject to the following conditions: Bouquets 1 and 3 cannot have any kind of flower in common. Bouquets 2 and 3 must have exactly two kinds of flowers in common. Bouquet 3 must have snapdragons. If a bouquet has lilies, that bouquet must also have roses but cannot have snapdragons. If a bouquet has tulips, that bouquet must also have peonies.

Question: Which one of the following could be a complete and accurate list of the kinds of flowers in each of the bouquets?

bouquet 1: lilies, roses bouquet 2: peonies, roses, tulips bouquet 3: peonies, snapdragons, tulips

bouquet 1: peonies, roses bouquet 2: peonies, snapdragons bouquet 3: peonies, snapdragons, tulips

bouquet 1: peonies, tulips bouquet 2: roses, snapdragons, tulips bouquet 3: roses, snapdragons

bouquet 1: roses bouquet 2: peonies, snapdragons bouquet 3: lilies, peonies, snapdragons

bouquet 1: snapdragons bouquet 2: lilies, roses bouquet 3: lilies, roses


Question: If lilies are in bouquet 1, which one of the following must

Lilies are in bouquet 2.
Peonies are in bouquet 3.
Roses are in bouquet 2.
Tulips are in bouquet 2.
Tulips are in bouquet 3.


Question: If tulips are in bouquet 1, which one of the following could be a complete and accurate list of the kinds of flowers in bouquet 2?

peonies, tulips
peonies, snapdragons
peonies, snapdragons, tulips
peonies, roses, tulips
peonies, roses, snapdragons, tulips


Question: Which one of the following CANNOT be a complete and accurate list of the kinds of flowers in bouquet 2?

lilies, roses
peonies, tulips
peonies, roses, snapdragons
peonies, roses, tulips
peonies, roses, snapdragons, tulips


Question: Which one of the following CANNOT be true?

Lilies and roses are the only kinds of flowers in bouquet 1.

Peonies and tulips are the only kinds of flowers in bouquet 1.

Lilies, peonies, and roses are the only kinds of flowers in bouquet 2.

Peonies, roses, and snapdragons are the only kinds of flowers in bouquet 2.

Peonies, snapdragons, and tulips are the only kinds of flowers in bouquet 3.


A corporation's Human Resources department must determine annual bonuses for seven employees—Kimura, Lopez, Meng, and Peterson, who work in the Finance department; and Vaughan, Xavier, and Zane, who work in the Graphics department. Each employee will receive either a $1,000 bonus, a $3,000 bonus, or a $5,000 bonus, in accordance with the following: No one in the Graphics department receives a $1,000 bonus. Any employee who was rated Highly Effective receives a larger bonus than anyone in his or her department who was not rated Highly Effective. Only Lopez, Meng, and Xavier were rated Highly Effective.

Question: Which one of the following is an allowable distribution of bonuses to the seven employees?


Question: If Lopez does not receive the same bonus as Meng, which one of the following could be true?

Kimura receives the same bonus as Vaughan.

Peterson receives a larger bonus than Kimura.


Question: If only one of the employees receives a $1,000 bonus, which one of the following must be true?

The employee who receives a $1,000 bonus is Peterson.

The employee who receives a $1,000 bonus is Kimura.


Question: Which one of the following must be true?

At least one of the employees receives a $1,000 bonus.

At least three of the employees receives a $3,000 bonuses.

At most three of the employees receives a $3,000 bonuses.

At least two of the employees receives a $5,000 bonuses.

At most three of the employees receives a $5,000 bonuses.


Question: If exactly two of the employees receive $5,000 bonuses, which one of the following must be true?

Meng is one of the employees who receives a $5,000 bonus.


Question: Any of the following could be true of the seven employees EXCEPT:

The same number receive $1,000 bonuses as receive $3,000 bonuses.

More receive $1,000 bonuses than receive $3,000 bonuses.

The same number receive $1,000 bonuses as receive $5,000 bonuses.

More receive $1,000 bonuses than receive $5,000 bonuses.

More receive $3,000 bonuses than receive $5,000 bonuses.


A landscaper will plant exactly seven trees today—a hickory, a larch, a maple, an oak, a plum, a sycamore, and a walnut. Each tree must be planted on exactly one of three lots—1, 2, or 3—in conformity with the following requirements: The trees planted on one lot are the hickory, the oak, and exactly one other tree. The maple is not planted on the same lot as the walnut. Either the larch or the walnut, but not both, is planted on lot 1. Either the maple or the oak, but not both, is planted on lot 2. More trees are planted on lot 3 than on lot 1.

Question: Which one of the following could be the list of the trees that the landscaper plants on each of the lots today?

lot 1: the larch, the maple lot 2: the hickory, the oak lot 3: the plum, the sycamore, the walnut

lot 1: the larch, the maple lot 2: the hickory, the oak, the walnut lot 3: the plum, the sycamore

lot 1: the maple lot 2: the hickory, the larch, the oak lot 3: the plum, the sycamore, the walnut

lot 1: the sycamore, the walnut lot 2: the larch, the maple lot 3: the hickory, the oak, the plum

lot 1: the walnut lot 2: the plum, the sycamore lot 3: the hickory, the maple, the oak


Question: If the hickory is planted on lot 2, then which one of the following trees must be planted on lot 3?

the larch
the maple
the plum
the sycamore
the walnut


Question: Which one of the following is a complete and accurate list of the trees any of which could be planted on lot 1?

the hickory, the plum, the sycamore, the walnut

the larch, the plum, the sycamore, the walnut


Question: If the walnut is planted on lot 3, then which one of the following could be true?

The sycamore is planted on lot 1.
The hickory is planted on lot 2.
The larch is planted on lot 2.
The plum is planted on lot 3.
The sycamore is planted on lot 3.


Question: Where each of the trees is planted is completely determined if which one of the following trees is planted on lot 2?

the walnut
the sycamore
the plum
the maple
the larch


Seven librarians—Flynn, Gomez, Hill, Kitson, Leung, Moore, and Zahn—are being scheduled for desk duty for one week—Monday through Saturday. The librarians will be on duty exactly one day each. On each day except Saturday, there will be exactly one librarian on duty, with two on duty on Saturday, subject to the following constraints: Hill must be on desk duty earlier in the week than Leung. Both Hill and Moore must be on desk duty earlier in the week than Gomez. Flynn must be on desk duty earlier in the week than both Kitson and Moore. Kitson must be on desk duty earlier in the week than Zahn. Unless Leung is on desk duty on Saturday, Leung must be on desk duty earlier in the week than Flynn.

Question: Which one of the following is an acceptable schedule for the librarians, listed in order from Monday through Saturday?

Flynn; Hill; Moore; Kitson; Zahn; Gomez and Leung

Flynn; Moore; Hill; Leung; Kitson; Gomez and Zahn

Hill; Kitson; Moore; Flynn; Gomez; Leung and Zahn

Hill; Leung; Flynn; Moore; Zahn; Gomez and Kitson

Leung; Flynn; Kitson; Moore; Hill; Gomez and Zahn


Question: Which one of the following CANNOT be on desk duty on Tuesday?


Question: If Kitson is on desk duty earlier in the week than Moore, which one of the following CANNOT be true?

Flynn is on desk duty earlier in the week than Leung.

Gomez is on desk duty earlier in the week than Kitson.

Gomez is on desk duty earlier in the week than Zahn.

Hill is on desk duty earlier in the week than Kitson.

Zahn is on desk duty earlier in the week than Moore.


Question: If Zahn is on desk duty on Thursday, which one of the following must be true?

Flynn is on desk duty earlier in the week than Leung.

Hill is on desk duty earlier in the week than Flynn.

Hill is on desk duty earlier in the week than Moore.

Hill is on desk duty earlier in the week than Zahn.

Kitson is on desk duty earlier in the week than Moore.


Question: If Moore is on desk duty on Tuesday, which one of the following must be true?

Hill is on desk duty on Thursday.
Kitson is on desk duty on Thursday.
Leung is on desk duty on Saturday.
Zahn is on desk duty on Friday.
Zahn is on desk duty on Saturday.


Question: If Flynn is on desk duty earlier in the week than Hill, which one of the following must be true?

Hill is on desk duty earlier in the week than Kitson.

Hill is on desk duty earlier in the week than Zahn.

Kitson is on desk duty earlier in the week than Moore.

Moore is on desk duty earlier in the week than Leung.

Moore is on desk duty earlier in the week than Zahn.


Question: Which one of the following, if substituted for the constraint that Flynn must be on desk duty earlier in the week than both Kitson and Moore, would have the same effect in determining the schedule for the librarians?

Flynn cannot be on desk duty on Thursday.

Only Flynn or Hill can be on desk duty on Monday.

Only Hill and Leung can be on desk duty earlier than Flynn.

Flynn must be on desk duty earlier in the week than both Gomez and Kitson.

Flynn must be on desk duty earlier in the week than both Moore and Zahn.


Each issue of a business newsletter has five slots, numbered 1 through 5. The policy of the newsletter requires that there are at least three features per issue, with each feature completely occupying one or more of the slots. Each feature can be one of four types—finance, industry, marketing, or technology. Any slot not containing a feature contains a graphic. The newsletters policy further requires that each issue be structured as follows: Any feature occupying more than one slot must occupy consecutively numbered slots. If an issue has any finance or technology feature, then a finance or technology feature must occupy slot 1. An issue can have at most one industry feature.

Question: Which one of the following is an allowable structure for an issue of the newsletter?

slot 1: a finance feature; slot 2: an industry feature; slot 3: a second industry feature; slot 4: a graphic; slot 5: a graphic

slot 1: a graphic; slot 2: a technology feature; slot 3: a second technology feature; slot 4: a graphic; slot 5: a third technology feature

slots 1 and 2: a single industry feature; slots 3 and 4: a single marketing feature; slot 5: a finance feature

slot 1: a technology feature; slots 2 and 3: a single industry feature; slot 4: a finance feature; slot 5: a graphic

slot 1: a technology feature; slots 2 and 4: a single marketing feature; slot 3: an industry feature; slot 5: a graphic


Question: If an issue of the newsletter has no technology feature and if there is a finance feature that occupies both slots 4 and 5, then which one of the following is required for that issue?

A finance feature occupies slot 2 or slot 3 or both.

An industry feature or a marketing feature occupies slot 2.

An industry feature or a marketing feature occupies slot 3.


Question: Which one of the following is NOT allowed for an issue of the newsletter?

There is exactly one industry feature, and it occupies slot 1.

There is exactly one finance feature, and it occupies slot 2.

There is exactly one technology feature, and it occupies slot 3.

Each feature except the feature occupying slot 1 is either a finance feature or a marketing feature.

Each feature except the feature occupying slot 5 is either an industry feature or a marketing feature.


Question: If, in a particular issue of the newsletter, slot 1 is occupied by the only industry feature in that issue, then which one of the following is required for that issue?

There is an industry feature that occupies slots 1 and 2, and only those slots.

There is an industry feature that occupies slots 1, 2, and 3, and only those slots.

There is a marketing feature that occupies slot 2 or slot 3 or both.

There is a marketing feature that occupies one or more of slots 2, 3, and 4.

There is a marketing feature that occupies slot 3 or slot 5 or both.


Question: Any of the following is allowed for an issue of the newsletter EXCEPT:

There is exactly one finance feature and no industry or marketing feature.

There is exactly one industry feature and no finance or marketing feature.

There is exactly one industry feature and no marketing or technology feature.

There is exactly one marketing feature and no finance or technology feature.

There is exactly one marketing feature and no industry or technology feature.


Six entertainers—Robinson, Shahpari, Tigay, Wu, Yeaton, and Zane—are being scheduled for the six performances on the opening day of a community festival. Each entertainer will perform at one of six times—in the morning at 9:00 A.M., 10:00 A.M., or 11:00 A.M., or in the afternoon at 2:00 P.M., 3:00 P.M., or 4:00 P.M.—with no two entertainers performing at the same scheduled time. The order in which the entertainers perform is subject to the following constraints: Robinson must perform at some time before Zane. Yeaton's performance must be the next performance after Wu's. Tigay must perform in the afternoon. Zane must perform in the morning.

Question: Which one of the following could be the order, from first to last, in which the entertainers are scheduled to perform?

Robinson, Shahpari, Zane, Tigay, Wu, Yeaton

Robinson, Wu, Yeaton, Zane, Shahpari, Tigay

Robinson, Zane, Tigay, Shahpari, Wu, Yeaton

Shahpari, Robinson, Zane, Wu, Tigay, Yeaton

Wu, Yeaton, Zane, Shahpari, Tigay, Robinson


Question: If Wu is scheduled to perform in the morning, then which one of the following could be true?

Robinson is scheduled to perform at 10:00 A.M.

Shahpari is scheduled to perform at 3:00 P.M.

Tigay is scheduled to perform at 2:00 P.M.

Yeaton is scheduled to perform at 3:00 P.M.

Zane is scheduled to perform at 11:00 A.M.


Question: Shahpari CANNOT be scheduled to perform at which one of the following times?


Question: What is the earliest time that Wu could be scheduled to perform?


Question: Which one of the following is a complete and accurate list of the entertainers who must be scheduled to perform in the afternoon?

Tigay
Tigay, Wu
Tigay, Yeaton
Tigay, Wu, Yeaton
Tigay, Shahpari, Yeaton


Exactly six of eight ceramic bowls, each crafted by exactly one of eight potters—Larsen, Mills, Neiman, Olivera, Park, Reigel, Serra, and Vance—will be displayed in a row in positions consecutively numbered 1 through 6, one bowl per position. The display is subject to the following conditions: If Larsen's bowl is displayed, Mills's bowl cannot be displayed. Park's bowl can be displayed only if it is next to Olivera's bowl and next to Serra's bowl. Reigel's bowl can be displayed only in either position 1 or position 6. Serra's bowl cannot be displayed in either position 2 or position 4. Neiman's bowl can be displayed only in position 5.

Question: Which one of the following could be the display of bowls, listed by potters name, in order from position 1 through position 6?

Larsen, Mills, Serra, Park, Olivera, Reigel

Larsen, Neiman, Olivera, Park, Serra, Vance

Mills, Olivera, Park, Serra, Reigel, Vance

Reigel, Park, Serra, Olivera, Neiman, Mills

Serra, Park, Olivera, Vance, Larsen, Reigel


Question: If Neiman's bowl and Park's bowl are both displayed, which one of the following is a potter whose bowl could be displayed in position 1?


Question: If Larsen's bowl is displayed in position 6 and Olivera's bowl is displayed in position 2, which one of the following must be true?

Mills's bowl is displayed in position 3.

Serra's bowl is displayed in position 1.

Serra's bowl is displayed in position 3.

Vance's bowl is displayed in position 1.

Vance's bowl is displayed in position 3.


Question: If Park's bowl is displayed in position 4, then the bowl displayed in position 2 must be

Larsen's, Mills's, or Vance's
Larsen's, Neiman's, or Vance's
Larsen's, Serra's, or Vance's
Mills's, Reigel's, or Vance's
Mills's, Serra's, or Vance's


Question: If Larsen's bowl is displayed in position 1 and Olivera's bowl is displayed in position 4, which one of the following is a potter whose bowl CANNOT be displayed?


Question: Which one of the following is a potter whose bowl must be displayed?


Question: If Neiman's bowl, Park's bowl, and Reigel's bowl are all displayed, which one of the following must be true?

Neiman's bowl is displayed next to Reigel's bowl.

Neiman's bowl is displayed next to Vance's bowl.

Olivera's bowl is displayed next to Reigel's bowl.

Olivera's bowl is displayed next to Vance's bowl.

Serra's bowl is displayed next to Vance's bowl.


Four employees—Jackson, Larabee, Paulson, and Torillo—are to select from among four offices—W, X, Y, and Z. The order in which they select, from first to fourth, is to be decided by a random drawing. Each employee has ranked the offices from first (highest) to fourth (lowest) as follows: Jackson: Y, X, Z, W Larabee: X, Z, W, Y Paulson: Y, Z, X, W Torillo: X, Y, Z, W The following restrictions must apply: Each employee selects an office that has not been selected previously. Each employee selects only one office. Each employee selects the office that he or she ranks highest among the unselected offices.

Question: Which one of the following is a possible matching of employees with the offices they select?

Jackson: W; Larabee: Y; Paulson: X; Torillo: Z

Jackson: Z; Larabee: X; Paulson: W; Torillo: Y

Jackson: X; Larabee: W; Paulson: Z; Torillo: Y

Jackson: Y; Larabee: W; Paulson: X; Torillo: Z

Jackson: Y; Larabee: Z; Paulson: X; Torillo: W


Question: Which one of the following must be true?

At most one of the employees selects the office he or she ranks first.

At most one of the employees selects the office he or she ranks second.

At least one of the employees selects the office he or she ranks first.

At least one of the employees selects the office he or she ranks second.

At least one of the employees selects the office he or she ranks third.


Question: Which one of the following could be true?

Exactly two of the employees each selects the office he or she ranks third.

Exactly two of the employees each selects the office he or she ranks fourth.

Exactly three of the employees each selects the office he or she ranks second.

Exactly three of the employees each selects the office he or she ranks third.

Exactly three of the employees each selects the office he or she ranks fourth.


Question: If Paulson selects office W, then which one of the following could be true?

Exactly two of the employees each selects the office he or she ranks second.

Exactly two of the employees each selects the office he or she ranks third.

Exactly three of the employees each selects the office he or she ranks first.


Question: Which one of the following must be true?

Jackson does not select office X.
Larabee does not select office W.
Larabee does not select office Z.
Torillo does not select office X.
Paulson does not select office X.


Exactly five volunteers—Haddad, Joslin, Kwon, Molina, and Nash—are being assigned to three community committees—X, Y, and Z. Each committee will have three volunteers assigned to it, with each volunteer on a committee holding exactly one of three positions—leader, secretary, or treasurer. The following conditions apply: If Nash is assigned to a committee, Nash must be the leader for that committee. Molina must be assigned to exactly one committee. Kwon must be assigned to Y but cannot be assigned to Z. Joslin must be the secretary for Y but cannot be assigned to X or Z.

Question: Which one of the following could be the assignment of volunteers to Z?

leader: Haddad; secretary: Molina; treasurer: Joslin

leader: Joslin; secretary: Haddad; treasurer: Molina

leader: Kwon; secretary: Haddad; treasurer: Molina

leader: Molina; secretary: Nash; treasurer: Haddad

leader: Nash; secretary: Molina; treasurer: Haddad


Question: If Kwon is assigned to be treasurer for exactly two of the committees, then any of the following could be true EXCEPT:

Haddad is assigned to be secretary for Z.

Haddad is assigned to be treasurer for X.

Molina is assigned to be treasurer for Z.


Question: Each of the following must be true EXCEPT:

Haddad is assigned to X.
Haddad is assigned to Y.
Kwon is assigned to X.
Molina is assigned to Z.
Nash is assigned to X.


Question: If Kwon is assigned to be leader for exactly one of the committees, then for which of the committees is the assignment of volunteers to positions fully determined?

X only
Y only
X and Y, but not Z
Y and Z, but not X
X and Z, but not Y


Question: The assignment of volunteers to committees and positions is fully determined if which one of the following is true?

Haddad is assigned to be leader for exactly one of the committees.

Haddad is assigned to be secretary for exactly two of the committees.

Haddad is assigned to be treasurer for all three of the committees.

Kwon is assigned to be treasurer for exactly two of the committees.

Nash is assigned to be leader for all three of the committees.


Question: Which one of the following, if substituted for the condition that Molina must be assigned to exactly one committee, would have the same effect in determining the assignment of volunteers to committees?

Haddad must be assigned to more committees than Molina.

Joslin must be assigned to more committees than Molina.

Kwon must be assigned to more committees than Molina.

Molina must be assigned to more committees than Haddad.

Nash must be assigned to more committees than Molina.


In one week—Monday through Friday—a library's bookmobile will visit five of the following six neighborhoods—Hidden Hills, Lakeville, Nottingham, Oldtown, Park Plaza, and Sunnyside. Exactly one neighborhood will be visited on each of the five days, and none of the neighborhoods will be visited on more than one day. The bookmobile's schedule must conform to the following conditions: Hidden Hills is visited, but not on Friday. If Oldtown is visited, then it is visited on the day immediately before Hidden Hills is visited. If Lakeville is visited, then it is visited on Wednesday. Nottingham and Sunnyside are both visited, but not on consecutive days.

Question: The five neighborhoods visited by the bookmobile, listed in order from Monday through Friday, could be

Nottingham, Lakeville, Oldtown, Hidden Hills, and Sunnyside

Nottingham, Oldtown, Hidden Hills, Sunnyside, and Park Plaza

Oldtown, Hidden Hills, Lakeville, Nottingham, and Sunnyside

Sunnyside, Oldtown, Lakeville, Hidden Hills, and Nottingham

Sunnyside, Park Plaza, Nottingham, Oldtown, and Hidden Hills


Question: Which one of the following neighborhoods CANNOT be visited on Thursday?

Hidden Hills
Nottingham
Oldtown
Park Plaza
Sunnyside


Question: If Hidden Hills is visited on Monday, which one of the following must be true?

Lakeville is visited on Wednesday.
Nottingham is visited on Tuesday.
Park Plaza is visited on Thursday.
Sunnyside is visited on Tuesday.
Sunnyside is visited on Friday


Question: If Hidden Hills is visited on Wednesday, which one of the following must be true?

Nottingham is visited on Monday.
Oldtown is visited on Tuesday.
Park Plaza is visited on Friday.
Sunnyside is visited on Monday.
Sunnyside is visited on Thursday


Question: If Nottingham is visited on Thursday, which one of the following must be true?

Hidden Hills is visited on Wednesday.
Lakeville is visited on Wednesday.
Oldtown is visited on Monday.
Park Plaza is visited on Friday.
Sunnyside is visited on Tuesday.


Six park rangers—Jefferson, Koguchi, Larson, Mendez, Olsen, and Pruitt—are each to be assigned to monitor one of three areas—area 1, area 2, and area 3—in a national park. At least one ranger, but no more than three, is assigned to each area. The assignment must conform to the following conditions: Mendez is assigned to area 3. Neither Olsen nor Pruitt is assigned to area 1. Larson is assigned to the same area as either Koguchi or Mendez but not to the same area as both. If Olsen is assigned to area 2, then Jefferson is assigned to the same area as Koguchi; otherwise, Jefferson is assigned to a different area than Koguchi.

Question: Which one of the following is a permissible assignment of rangers to park areas?

area 1: Jefferson, Koguchi; area 2: Larson, Olsen; area 3: Mendez, Pruitt

area 1: Koguchi, Larson; area 2: Olsen, Pruitt; area 3: Jefferson, Mendez

area 1: Koguchi, Pruitt; area 2: Jefferson; area 3: Larson, Mendez, Olsen

area 1: Jefferson, Koguchi, Larson; area 2: Mendez, Olsen; area 3: Pruitt

area 1: Jefferson, Koguchi, Larson; area 2: Olsen, Pruitt; area 3: Mendez


Question: If Olsen is the sole ranger assigned to area 2, then which one of the following could be the complete assignment of rangers to area 3?

Mendez
Larson, Mendez
Mendez, Pruitt
Jefferson, Koguchi, Mendez
Jefferson, Mendez, Pruitt


Question: If exactly one ranger is assigned to area 1, then which one of the following must be true?

Jefferson is assigned to area 1.
Koguchi is assigned to area 2.
Larson is assigned to area 3.
Olsen is assigned to area 3.
Pruitt is assigned to area 2.


Question: Which one of the following rangers CANNOT be assigned to area 3?


Question: If Koguchi is assigned to area 2, then which one of the following could be true?

Jefferson is assigned to area 2.
Jefferson is assigned to area 3.
Larson is assigned to area 1.
Olsen is assigned to area 2.
Pruitt is assigned to area 3


Question: If Larson and Olsen are assigned to the same area, then which one of the following could be true?

Jefferson is assigned to area 3.
Koguchi is assigned to area 2.
Larson is assigned to area 1.
Olsen is assigned to area 2.
Pruitt is assigned to area 3


Question: If Jefferson is assigned to area 2, then which one of the following must be true?

Koguchi is assigned to area 1.
Larson is assigned to area 1.
Olsen is assigned to area 2.
Pruitt is assigned to area 2.
Pruitt is assigned to area 3


An economics department is assigning six teaching assistants—Ramos, Smith, Taj, Vogel, Yi, and Zane—to three courses—Labor, Markets, and Pricing. Each assistant will be assigned to exactly one course, and each course will have at least one assistant assigned to it. The assignment of assistants to courses is subject to the following conditions: Markets must have exactly two assistants assigned to it. Smith and Taj must be assigned to the same course as each other. Vogel and Yi cannot be assigned to the same course as each other. Yi and Zane must both be assigned to Pricing if either one of them is.

Question: Which one of the following could be the complete assignment of assistants to Pricing?

Ramos, Yi, and Zane
Smith, Taj, and Yi
Smith, Taj, Yi, and Zane
Taj, Yi, and Zane
Vogel, Yi, and Zane


Question: Which one of the following CANNOT be the complete assignment of assistants to Labor?

Ramos, Vogel
Ramos, Zane
Smith, Taj
Vogel, Zane
Yi, Zane


Question: Which one of the following could be true?

Ramos and Vogel are both assigned to Markets.

Ramos and Taj are both assigned to Markets.

Smith and Vogel are both assigned to Markets.

Smith and Zane are both assigned to Pricing.

Vogel and Zane are both assigned to Pricing.


Question: If Vogel is assigned to the same course as Zane, which one of the following CANNOT be true?

Ramos is assigned to Labor.
Smith is assigned to Labor.
Taj is assigned to Markets.
Ramos is assigned to Pricing.
Smith is assigned to Pricing.


Question: If no other assistant is assigned to the same course as Ramos, which one of the following must be true?

Taj is assigned to Labor.
Vogel is assigned to Labor.
Yi is assigned to Markets.
Zane is assigned to Markets.
Smith is assigned to Pricing


There are exactly six computers—P, Q, R, S, T, and U—on a small network. Exactly one of those computers was infected by a virus from outside the network, and that virus was then transmitted between computers on the network. Each computer received the virus exactly once. The following pieces of information concerning the spread of the virus have been established: No computer transmitted the virus to more than two other computers on the network. S transmitted the virus to exactly one other computer on the network. The computer that transmitted the virus to R also transmitted it to S. Either R or T transmitted the virus to Q. Either T or U transmitted the virus to P.

Question: One possible route of the virus from the first computer in the network infected to Q is

from R to P to T to Q
from T to S to R to Q
from T to S to U to Q
from U to P to R to Q
from U to T to P to R to Q


Question: Which one of the following could be the computer that was infected from outside the network?


Question: If T did not transmit the virus to any other computer on the network, which one of the following must be true?

P did not transmit the virus to any other computer on the network.

R did not transmit the virus to any other computer on the network.


Question: Any of the following computers could have transmitted the virus to two other computers on the network EXCEPT:


Question: The spread of the virus among the computers is completely determined if which one of the following is true?

R transmitted the virus to Q.
T transmitted the virus to Q.
T transmitted the virus to S.
U transmitted the virus to P.
U transmitted the virus to R


Question: If P is the only computer that transmitted the virus to two other computers on the network, which one of the following must be true?

Q did not transmit the virus to any other computer on the network.

R did not transmit the virus to any other computer on the network.

U did not transmit the virus to any other computer on the network.