Question: Which one of the following CANNOT be true?

Henson appears earlier than Geyer.
Henson appears sixth.
Lin appears fifth.
Paredes appears earlier than Mitchell.
Paredes appears second.


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

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


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

Geyer, Lin, Paredes, Henson
Geyer, Paredes, Henson, Lin
Lin, Henson, Geyer, Paredes
Lin, Paredes, Henson, Geyer
Paredes, Lin, Henson, Geyer


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

Geyer appears no later than third.
Henson appears last.
Lin appears no later than third.
Mitchell appears earlier than Geyer.
Paredes appears first.


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

Geyer appears fifth.
Henson appears third.
Jhalani appears sixth.
Lin appears second.
Paredes appears fourth.


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

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

the first and the third
the second and the third
the second and the sixth
the third and the sixth
the fourth and the sixth


Question: Which one of the following must be true?

The first and second loads are the same material.

The second and third loads are different materials.

At least two loads of mulch are hauled consecutively.

At least three loads of stone are hauled consecutively.


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

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

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


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

The second load is stone.
The third load is mulch.
The third load is stone.
The sixth load is mulch.
The seventh load is mulch.


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

The first load is stone.
The fourth load is stone.
The third load is mulch.
The sixth load is mulch.
The seventh load is mulch.


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

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

Romania: Farber Spain: Hall Tuscany: Jackson

Romania: Gombarick Spain: Hall Tuscany: Farber

Romania: Gombarick Spain: Hall Tuscany: Lha

Romania: Gombarick Spain: Lha Tuscany: Kanze

Romania: Hall Spain: Kanze Tuscany: Jackson


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

Gombarick is assigned to Spain.
Hall is assigned to Spain.
Kanze is assigned to Tuscany.
Lha is assigned to Spain.
Lha is assigned to Tuscany.


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

Farber is assigned to Tuscany.
Gombarick is assigned to Romania.
Hall is assigned to Romania.
Kanze is assigned to Tuscany.
Lha is assigned to Spain.


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

Farber and Gombarick
Gombarick and Hall
Hall and Kanze
Kanze and Lha
Lha and Hall


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

Farber is assigned to Romania.
Gombarick is assigned to Spain.
Hall is assigned to Romania.
Kanze is assigned to Tuscany.
Lha is assigned to Spain.


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


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

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

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

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

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

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

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


Question: The two workers who drive the cars CANNOT be

Faith and Gus
Faith and Kenneth
Faith and Lisa
Gus and Kenneth
Kenneth and Lisa


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

Faith travels in the same car as Kenneth.


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


Question: Which one of the following CANNOT be true?

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

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

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

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

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


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

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

figurine, headdress, jar, necklace, plaque, tureen

figurine, jar, plaque, headdress, tureen, necklace

figurine, necklace, plaque, headdress, jar, tureen

necklace, jar, figurine, headdress, plaque, tureen

plaque, tureen, figurine, necklace, jar, headdress


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


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


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


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


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

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

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

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

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

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


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

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

Uzoma, Ramirez, Quinn, Terrell
Terrell, Smith, Ramirez, Uzoma
Smith, Ramirez, Terrell, Quinn
Ramirez, Uzoma, Smith, Terrell
Quinn, Terrell, Smith, Ramirez


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


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

Ramirez runs in the first race.
Ramirez runs in the second race.
Ramirez runs in the third race.
Ramirez runs in the fourth race.
Ramirez does not run in the track meet.


Question: Which one of the following CANNOT be true?

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

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

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

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

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


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

Quinn does not run in the track meet.
Smith does not run in the track meet.
Quinn runs in the second race.
Terrell runs in the second race.
Ramirez runs in the fourth race.


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


From the 1st through the 7th of next month, seven nurses—Farnham, Griseldi, Heany, Juarez, Khan, Lightfoot, and Moreau—will each conduct one information session at a community center. Each nurse's session will fall on a different day. The nurses' schedule is governed by the following constraints: At least two of the other nurses' sessions must fall in between Heany's session and Moreau's session. Griseldi's session must be on the day before Khan's. Juarez's session must be on a later day than Moreau's. Farnham's session must be on an earlier day than Khan's but on a later day than Lightfoot's. Lightfoot cannot conduct the session on the 2nd.

Question: Which one of the following could be the order of the nurses' sessions, from first to last?

Farnham, Griseldi, Khan, Moreau, Juarez, Lightfoot, Heany

Heany, Lightfoot, Farnham, Moreau, Juarez, Griseldi, Khan

Juarez, Heany, Lightfoot, Farnham, Moreau, Griseldi, Khan

Lightfoot, Moreau, Farnham, Juarez, Griseldi, Khan, Heany

Moreau, Lightfoot, Heany, Juarez, Farnham, Griseldi, Khan


Question: Juarez's session CANNOT be on which one of the following days?


Question: If Juarez's session is on the 3rd, then which one of the following could be true?

Moreau's session is on the 1st.
Khan's session is on the 5th.
Heany's session is on the 6th.
Griseldi's session is on the 5th.
Farnham's session is on the 2nd.


Question: If Khan's session is on an earlier day than Moreau's, which one of the following could conduct the session on the 3rd?


Question: If Griseldi's session is on the 5th, then which one of the following must be true?

Farnham's session is on the 3rd.
Heany's session is on the 7th.
Juarez's session is on the 4th.
Lightfoot's session is on the 1st.
Moreau's session is on the 2nd.


Question: Lightfoot's session could be on which one of the following days?


A motel operator is scheduling appointments to start up services at a new motel. Appointments for six services—gas, landscaping, power, satellite, telephone, and water—will be scheduled, one appointment per day for the next six days. The schedule for the appointments is subject to the following conditions: The water appointment must be scheduled for an earlier day than the landscaping appointment. The power appointment must be scheduled for an earlier day than both the gas and satellite appointments. The appointments scheduled for the second and third days cannot be for either gas, satellite, or telephone. The telephone appointment cannot be scheduled for the sixth day.

Question: Which one of the following is an acceptable schedule of appointments, listed in order from earliest to latest?

gas, water, power, telephone, landscaping, satellite

power, water, landscaping, gas, satellite, telephone

telephone, power, landscaping, gas, water, satellite

telephone, water, power, landscaping, gas, satellite

water, telephone, power, gas, satellite, landscaping


Question: If neither the gas nor the satellite nor the telephone appointment is scheduled for the fourth day, which one of the following must be true?

The gas appointment is scheduled for the fifth day.

The power appointment is scheduled for the third day.

The satellite appointment is scheduled for the sixth day.

The telephone appointment is scheduled for the first day.

The water appointment is scheduled for the second day.


Question: Which one of the following must be true?

The landscaping appointment is scheduled for an earlier day than the telephone appointment.

The power appointment is scheduled for an earlier day than the landscaping appointment.

The telephone appointment is scheduled for an earlier day than the gas appointment.

The telephone appointment is scheduled for an earlier day than the water appointment.

The water appointment is scheduled for an earlier day than the gas appointment.


Question: Which one of the following CANNOT be the appointments scheduled for the fourth, fifth, and sixth days, listed in that order?

gas, satellite, landscaping
landscaping, satellite, gas
power, satellite, gas
telephone, satellite, gas
water, gas, landscaping


Question: If neither the gas appointment nor the satellite appointment is scheduled for the sixth day, which one of the following must be true?

The gas appointment is scheduled for the fifth day.

The landscaping appointment is scheduled for the sixth day.

The power appointment is scheduled for the third day.

The telephone appointment is scheduled for the fourth day.

The water appointment is scheduled for the second day.


Question: Which one of the following, if substituted for the condition that the telephone appointment cannot be scheduled for the sixth day, would have the same effect in determining the order of the appointments?

The telephone appointment must be scheduled for an earlier day than the gas appointment or the satellite appointment, or both.

The telephone appointment must be scheduled for the day immediately before either the gas appointment or the satellite appointment.

The telephone appointment must be scheduled for an earlier day than the landscaping appointment.

If the telephone appointment is not scheduled for the first day, it must be scheduled for the day immediately before the gas appointment.

Either the gas appointment or the satellite appointment must be scheduled for the sixth day.


An artisan has been hired to create three stained glass windows. The artisan will use exactly five colors of glass: green, orange, purple, rose, and yellow. Each color of glass will be used at least once, and each window will contain at least two different colors of glass. The windows must also conform to the following conditions: Exactly one of the windows contains both green glass and purple glass. Exactly two of the windows contain rose glass. If a window contains yellow glass, then that window contains neither green glass nor orange glass. If a window does not contain purple glass, then that window contains orange glass.

Question: Which one of the following could be the color combinations of the glass in the three windows?

window 1: green, purple, rose, and orange window 2: rose and yellow window 3: green and orange

window 1: green, purple, and rose window 2: green, rose, and orange window 3: purple and yellow

window 1: green, purple, and rose window 2: green, purple, and orange window 3: purple, rose, and yellow

window 1: green, purple, and orange window 2: rose, orange, and yellow window 3: purple and rose

window 1: green, purple, and orange window 2: purple, rose, and yellow window 3: purple and orange


Question: Which one of the following CANNOT be the complete color combination of the glass in one of the windows?

green and orange
green and purple
green and rose
purple and orange
rose and orange


Question: If two of the windows are made with exactly two colors of glass each, then the complete color combination of the glass in one of those windows could be

rose and yellow
orange and rose
orange and purple
green and rose
green and orange


Question: If the complete color combination of the glass in one of the windows is purple, rose, and orange, then the complete color combination of the glass in one of the other windows could be

green, orange, and rose
green, orange, and purple
orange and rose
orange and purple
green and orange


Question: If orange glass is used in more of the windows than green glass, then the complete color combination of the glass in one of the windows could be

orange and purple
green, purple, and rose
green and purple
green and orange
green, orange, and rose


Question: Which one of the following could be used in all three windows?

green glass
orange glass
purple glass
rose glass
yellow glass


Question: If none of the windows contains both rose glass and orange glass, then the complete color combination of the glass in one of the windows must be

green and purple
green, purple, and orange
green and orange
purple and orange
purple, rose, and yellow


A conference on management skills consists of exactly five talks, which are held successively in the following order: Feedback, Goal Sharing, Handling People, Information Overload, and Leadership. Exactly four employees of SoftCorp—Quigley, Rivera, Spivey, and Tran—each attend exactly two of the talks. No talk is attended by more than two of the employees, who attend the talks in accordance with the following conditions: Quigley attends neither Feedback nor Handling People. Rivera attends neither Goal Sharing nor Handling People. Spivey does not attend either of the talks that Tran attends. Quigley attends the first talk Tran attends. Spivey attends the first talk Rivera attends.

Question: Which one of the following could be a complete and accurate matching of the talks to the SoftCorp employees who attend them?

Feedback: Rivera, Spivey Goal Sharing: Quigley, Tran Handling People: None Information Overload: Quigley, Rivera Leadership: Spivey, Tran

Feedback: Rivera, Spivey Goal Sharing: Quigley, Tran Handling People: Rivera, Tran Information Overload: Quigley Leadership: Spivey

Feedback: Rivera, Spivey Goal Sharing: Quigley, Tran Handling People: Tran Information Overload: Quigley, Rivera Leadership: Spivey

Feedback: Rivera, Spivey Goal Sharing: Tran Handling People: Tran Information Overload: Quigley, Rivera Leadership: Quigley, Spivey

Feedback: Spivey Goal Sharing: Quigley, Tran Handling People: Spivey Information Overload: Quigley, Rivera Leadership: Rivera, Tran


Question: If none of the SoftCorp employees attends Handling People, then which one of the following must be true?

Rivera attends Feedback.
Rivera attends Leadership.
Spivey attends Information Overload.
Tran attends Goal Sharing.
Tran attends Information Overload.


Question: Which one of the following is a complete and accurate list of the talks any one of which Rivera and Spivey could attend together?

Feedback, Information Overload, Leadership

Feedback, Goal Sharing, Information Overload


Question: If Quigley is the only SoftCorp employee to attend Leadership, then which one of the following could be false?

Rivera attends Feedback.
Rivera attends Information Overload.
Spivey attends Feedback.
Spivey attends Handling People.
Tran attends Goal Sharing.


Question: If Rivera is the only SoftCorp employee to attend Information Overload, then which one of the following could be false?

Quigley attends Leadership.
Rivera attends Feedback.
Spivey attends Feedback.
Tran attends Goal Sharing.
Tran attends Handling People.


Exactly six witnesses will testify in a trial: Mangione, Ramirez, Sanderson, Tannenbaum, Ujemori, and Wong. The witnesses will testify one by one, and each only once. The order in which the witnesses testify is subject to the following constraints: Sanderson must testify immediately before either Tannenbaum or Ujemori. Ujemori must testify earlier than both Ramirez and Wong. Either Tannenbaum or Wong must testify immediately before Mangione.

Question: Which one of the following lists the witnesses in an order in which they could testify?

Ramirez, Sanderson, Tannenbaum, Mangione, Ujemori, Wong

Sanderson, Tannenbaum, Ujemori, Ramirez, Wong, Mangione

Sanderson, Ujemori, Tannenbaum, Wong, Ramirez, Mangione

Tannenbaum, Mangione, Ujemori, Sanderson, Ramirez, Wong

Wong, Ramirez, Sanderson, Tannenbaum, Mangione, Ujemori


Question: If Tannenbaum testifies first, then which one of the following could be true?

Ramirez testifies second.
Wong testifies third.
Sanderson testifies fourth.
Ujemori testifies fifth.
Mangione testifies sixth.


Question: If Sanderson testifies fifth, then Ujemori must testify


Question: Which one of the following pairs of witnesses CANNOT testify third and fourth, respectively?

Mangione, Tannenbaum
Ramirez, Sanderson
Sanderson, Ujemori
Tannenbaum, Ramirez
Ujemori, Wong


Question: Which one of the following pairs of witnesses CANNOT testify first and second, respectively?

Sanderson, Ujemori
Tannenbaum, Mangione
Tannenbaum, Sanderson
Ujemori, Tannenbaum
Ujemori, Wong


A movie studio is scheduling the release of six films—Fiesta, Glaciers, Hurricanes, Jets, Kangaroos, and Lovebird. No two of these films can be released on the same date. The release schedule is governed by the following conditions: Fiesta must be released earlier than both Jets and Lovebird. Kangaroos must be released earlier than Jets, and Jets must be released earlier than Hurricanes. Lovebird must be released earlier than Glaciers.

Question: Which one of the following CANNOT be true?

Fiesta is released second.
Glaciers is released third.
Hurricanes is released fourth.
Kangaroos is released fourth.
Kangaroos is released fifth.


Question: Which one of the following must be true?

Fiesta is released earlier than Hurricanes.

Kangaroos is released earlier than Glaciers.

Lovebird is released earlier than Hurricanes.


Question: If Glaciers is released earlier than Hurricanes, then each of the following could be true EXCEPT:

Glaciers is released fourth.
Jets is released third.
Kangaroos is released second.
Lovebird is released third.
Lovebird is released fifth.


Question: If Lovebird is released earlier than Kangaroos, which one of the following could be true?

Hurricanes is released earlier than Lovebird.


Question: Which one of the following, if substituted for the condition that Fiesta must be released earlier than both Jets and Lovebird, would have the same effect on the order in which the films are released?

Only Kangaroos can be released earlier than Fiesta.

Kangaroos must be released earlier than Lovebird.

Fiesta must be released either first or second.

Fiesta must be released earlier than both Kangaroos and Lovebird.

Either Fiesta or Kangaroos must be released first.


The applications of seven job candidates—Farrell, Grant, Hong, Inman, Kent, Lopez, and Madsen—will be evaluated by four human resource officers—Rao, Smith, Tipton, and Ullman. Each application will be evaluated by exactly one officer, and each officer will evaluate at least one application, subject to the following constraints: Grant's application must be evaluated by Ullman. Farrell's application must be evaluated by the same officer who evaluates Lopez's application. Neither Hong's application nor Madsen's application can be evaluated by the same officer who evaluates Inman's application. The officer who evaluates Kent's application cannot evaluate any other applications. Smith must evaluate more of the applications than Tipton does.

Question: Which one of the following could be the assignment of applications to officers?

Rao: Hong Smith: Farrell, Lopez, Madsen Tipton: Kent Ullman: Grant, Inman

Rao: Inman Smith: Hong, Lopez, Madsen Tipton: Kent Ullman: Farrell, Grant

Rao: Madsen Smith: Farrell, Lopez Tipton: Kent Ullman: Grant, Hong, Inman

Rao: Farrell, Lopez Smith: Hong, Kent, Madsen Tipton: Inman Ullman: Grant

Rao: Farrell, Grant, Lopez Smith: Hong, Madsen Tipton: Kent Ullman: Inman


Question: If Hong's application is evaluated by Rao, which one of the following could be true?

Farrells application is evaluated by Rao.

Inmans application is evaluated by Smith.

Lopezs application is evaluated by Ullman.

Madsens application is evaluated by Tipton.


Question: If exactly two of the applications are evaluated by Tipton, then each of the following must be true EXCEPT:

Exactly one of the applications is evaluated by Rao.

Exactly one of the applications is evaluated by Ullman.

Farrells application is evaluated by Tipton.

Inmans application is evaluated by Smith.

Lopezs application is evaluated by Smith.


Question: If the officer who evaluates Madsens application does not evaluate any other application, which one of the following must be true?

Madsens application is evaluated by Tipton.

Lopezs application is evaluated by Smith.

Kents application is evaluated by Tipton.

Inmans application is evaluated by Smith.

Hongs application is evaluated by Smith.


Question: If Farrells application is evaluated by the same officer who evaluates Inmans application, then any of the following could be true EXCEPT:

Hongs application is evaluated by Ullman.

Kents application is evaluated by Tipton.

Lopezs application is evaluated by Ullman.

Madsens application is evaluated by Smith.

Madsens application is evaluated by Ullman.


Question: If Farrells application is evaluated by Rao, then for how many of the other applications is the identity of the officer who evaluates it fully determined?


A six-week literature course is being planned in which six books—F, K, N, O, R, and T—will be discussed. The books will be discussed one at a time, one book per week. In addition, written summaries will be required for one or more of the books. The order in which the books are discussed and the selection of books to be summarized is subject to the following conditions: No two books that are summarized are discussed in consecutive weeks. If N is not summarized, then both R and T are summarized. N is discussed earlier than T, and T is discussed earlier than O. F is discussed earlier than O, and O is discussed earlier than both K and R.

Question: Which one of the following could be the plan for the course, showing the order, from first to last, in which the books are discussed and the choice of books to be summarized?

F, N, T, O, R, K; with only T and R summarized

F, T, N, O, K, R; with only N and K summarized

N, F, T, O, K, R; with only T, O, and R summarized

N, T, F, O, K, R; with only T and O summarized

N, T, O, F, K, R; with only T and R summarized


Question: If N is the second book discussed and it is not summarized, which one of the following could be true?

The third book discussed is not summarized.


Question: If O is summarized, which one of the following CANNOT be true?

F is the first book discussed.
K is the sixth book discussed.
F is summarized.
K is not summarized.
N is not summarized.


Question: If neither of the last two books discussed is summarized, which one of the following could be true?

K is summarized
O is summarized
R is summarized
F and T summarized
N is not summarized


Question: Which one of the following, if substituted for the condition that F is discussed earlier than O, and O is discussed earlier than both K and R, would have the same effect in determining the plan for the literature course?

T is discussed third, and the last two books discussed are K and R, not necessarily in that order.

T is discussed earlier than F, and the last two books discussed are K and R, not necessarily in that order.

K and R are among the last three books discussed, and F is among the first three books discussed.

K and R are discussed in consecutive weeks, not necessarily in that order, and O is discussed fourth.

K and R are discussed in consecutive weeks, not necessarily in that order, and F is discussed third.


A museum curator is arranging seven paintings—a Morisot, a Pissarro, a Renoir, a Sisley, a Turner, a Vuillard, and a Whistler. The paintings will be arranged in a horizontal row of seven positions, with the first position being closest to the entrance and the seventh being furthest from the entrance. The arrangement is subject to the following constraints: The Turner must be closer to the entrance than the Whistler is. The Renoir must be closer to the entrance than the Morisot is, with exactly one other painting between them. The Pissarro and the Sisley must be next to each other. If the Vuillard is not in the third position, it must be in the fourth position.

Question: Which one of the following could be the arrangement of the paintings, listed in order from the first position to the seventh?

Morisot, Turner, Renoir, Vuillard, Whistler, Sisley, Pissarro

Pissarro, Sisley, Renoir, Vuillard, Morisot, Whistler, Turner

Renoir, Turner, Morisot, Vuillard, Whistler, Sisley, Pissarro

Sisley, Turner, Pissarro, Vuillard, Renoir, Whistler, Morisot

Turner, Vuillard, Pissarro, Sisley, Renoir, Whistler, Morisot


Question: If the Sisley is in the seventh position, which one of the following could be the position that the Turner is in?


Question: If the Pissarro is in the fifth position, which one of the following must be true?

The Morisot is in the fourth position.
The Renoir is in the second position.
The Sisley is in the sixth position.
The Turner is in the first position.
The Vuillard is in the third position.


Question: Any one of the following could be in the third position EXCEPT:

the Morisot
the Renoir
the Sisley
the Turner
the Whistler


Question: If the Renoir and the Morisot are both between the Turner and the Whistler, which one of the following could be true?

The Pissarro is in the fifth position.
The Sisley is in the second position.
The Turner is in the third position.
The Vuillard is in the fourth position.
The Whistler is in the sixth position.


Question: If there is exactly one painting between the Turner and the Whistler, which one of the following must be true?

The Morisot is in the seventh position.
The Pissarro is in the first position.
The Renoir is in the fourth position.
The Turner is in the second position.
The Vuillard is in the third position.


Question: If the Turner is next to the Vuillard, which one of the following is a pair of paintings in which the one mentioned first must be closer to the entrance than the one mentioned second?

the Pissarro and the Sisley
the Renoir and the Whistler
the Turner and the Vuillard
the Vuillard and the Turner
the Whistler and the Renoir


A radio station airs hourly news updates every morning. Each update consists of exactly five reports—two of general interest: international and national; and three of local interest: sports, traffic, and weather. Each update must be structured as follows: There are exactly two segments, the first segment containing three reports and the second segment containing two. Within each segment, reports are ordered by length, from longest to shortest. Each segment contains at least one report of local interest. The national report is always the longest of the five reports. The sports report is always the shortest of the five reports. The international report is always longer than the weather report.

Question: Which one of the following could be an accurate matching of reports to their segments, with the reports listed in order from earliest to latest?

first segment: international, national, sports second segment: traffic, weather

first segment: national, international, sports second segment: weather, traffic

first segment: national, international, weather second segment: sports, traffic

first segment: national, weather, international second segment: traffic, sports

first segment: traffic, weather, sports second segment: national, international


Question: If the traffic report is the last report in the first segment, then which one of the following must be true?

The national report is the first report in the first segment.

The international report is the second report in the first segment.

The weather report is the second report in the first segment.

The national report is the first report in the second segment.

The sports report is the last report in the second segment.


Question: If the national report is the first report in the second segment, then exactly how many of the reports are there any one of which could be the first report in the first segment?


Question: Which one of the following CANNOT be true?

The international report is the first report in the first segment.

The national report is the first report in the first segment.

The national report is the first report in the second segment.

The weather report is the first report in the first segment.

The weather report is the last report in the second segment.


Question: The order of the reports is fully determined if which one of the following is true?

The international report is the last report in the first segment.

The national report is the first report in the first segment.

The national report is the first report in the second segment.

The sports report is the last report in the second segment.

The weather report is the last report in the first segment.


Question: If the traffic report is the first report in the first segment, then which one of the following could be true?

The international report is the first report in the second segment.

The national report is the second report in the first segment.

The weather report is the second report in the first segment.

The weather report is the first report in the second segment.

The weather report is the last report in the second segment.


On a single day, a realtor will show a client five houses, exactly one house in each of five neighborhoods—Quarry, Riverton, Shelburne, Townsend, and Valencia. Each house will be shown to the client exactly once. The order in which the houses are shown is subject to the following constraints: The house in Riverton must be shown either first or second. The house in Townsend must be shown either first or fifth. The third house shown must be the house in Quarry or the house in Valencia. The house in Quarry cannot be shown either immediately before or immediately after the house in Shelburne.

Question: If the house in Quarry is shown fourth, which one of the following must be true?

The house in Riverton is shown first.
The house in Riverton is shown second.
The house in Shelburne is shown second.
The house in Townsend is shown first.
The house in Valencia is shown third.


Question: The order in which the houses are shown is fully determined if which one of the following is true?

The house in Quarry is shown third.
The house in Riverton is shown first.
The house in Shelburne is shown second.
The house in Townsend is shown fifth.
The house in Valencia is shown fourth.


Question: If the house in Shelburne is shown earlier than the house in Quarry, which one of the following must be true?

The house in Quarry is shown fourth.
The house in Riverton is shown second.
The house in Shelburne is shown first.
The house in Townsend is shown fifth.
The house in Valencia is shown third.


Question: Which one of the following could be true?

The house in Quarry is shown first.
The house in Quarry is shown fifth.
The house in Valencia is shown first.
The house in Valencia is shown second.
The house in Valencia is shown fifth.


Question: If the house in Valencia is shown third, which one of the following must be true?

The house in Quarry is shown fourth.
The house in Riverton is shown second.
The house in Shelburne is shown first.
The house in Shelburne is shown fourth.
The house in Townsend is shown fifth.


Question: Which one of the following, if substituted for the constraint that the house in Riverton must be shown either first or second, would have the same effect on the order in which the houses are shown?

The house in Riverton cannot be shown fourth.

The house in Riverton must be shown earlier than the house in Valencia.

The house in Valencia must be shown either third or fourth.

The house in Quarry must be shown either immediately before or immediately after the house in Riverton.

If the house in Townsend is not shown fifth, then it must be shown immediately before the house in Riverton.


Five artifacts—V, W, X, Y, and Z—recovered from a sunken ship are each known to have originated in Iceland, Norway, or Sweden. These artifacts, together with the surviving fragments of a cargo list, have enabled historians to determine the following: W and Y originated in the same country. X originated in Norway or Sweden. More of the artifacts originated in Iceland than in Norway. If V originated in Iceland, then Z originated in Sweden.

Question: Which one of the following could be an accurate matching of the artifacts to their origins?

Iceland: W, Y Norway: none Sweden: V, X, Z


Question: If Y and Z originated in Iceland, then what is the minimum number of artifacts that originated in Sweden?


Question: Which one of the following CANNOT be true?

V and X both originated in Norway.
V and Y both originated in Iceland.
W and Z both originated in Iceland.
W and Z both originated in Sweden.
W and Y both originated in Norway.


Question: If W and X originated in Sweden, then which one of the following must be true?

None of the artifacts originated in Norway.

None of the artifacts originated in Iceland.


Question: Exactly how many of the artifacts are there any one of which could have originated in Norway?


Question: Which one of the following CANNOT be true?

Only V, W, X, and Y originated in Sweden.


The employees of the Summit Company—J, K, L, and M—work a four-day workweek from Monday through Thursday. Every Monday, work begins on four raw workpieces, each of which is worked on for four consecutive days. On any given day, an employee works on exactly one workpiece. At the beginning of each workday after Monday, each workpiece is transferred from the employee who worked on it the previous day to another one of the employees, who will work on it that day. Workpieces cannot be transferred in any of the following ways: From J to M. From K to J. From L to J.

Question: Which one of the following describes four transfers of workpieces that could all occur together at the beginning of a particular workday?

From J to K; from K to L; from L to M; from M to J

From J to K; from K to M; from L to K; from M to J

From J to L; from K to M; from L to J; from M to K

From J to L; from K to J; from L to M; from M to K

From J to M; from K to L; from L to K; from M to J


Question: Which one of the following transfers must occur at the beginning of any workday that is not a Monday?

From J to K
From J to L
From K to L
From L to M
From M to J


Question: If one workpiece is worked on by only two of the four employees in the course of an entire workweek, those two employees must be


Question: If L works on the same workpiece both on Tuesday and on Thursday, which one of the following must be true about that workpiece?

J works on it on Monday.
K works on it on Monday.
M works on it on Monday.
J works on it on Wednesday.
K works on it on Wednesday.


Question: Which one of the following could be true about the Tuesday?

Transfer from J to K and from K to M occur.

Transfer from J to L and from L to M occur.

Transfer from J to M and from M to J occur.

Transfer from K to L and from L to K occur.

Transfer from K to L and from L to M occur.


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

first digit is 2
second digit is 0
third digit is 3
fourth digit is 4
fourth digit is 0


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

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

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

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

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

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?

The second digit of the product code is 2.

The third digit of the product code is 3.

The fourth digit of the product code is 0.

The fifth digit of the product code is 3.

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:


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

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

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

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

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

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


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?

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

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

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

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

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


Question: Which one of the following CANNOT be true?

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

Limelight is shown on each day of the festival.

Greed is shown second on each day of the festival.

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

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?


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?

Exactly two films are shown on Saturday.

Limelight and Harvest are both shown on Thursday.

Greed is the only film shown on Saturday.

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?

Harvest
Limelight
Greed, Harvest
Greed, Limelight
Greed, Harvest, Limelight


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?

Guadeloupe, Jamaica, Martinique, Trinidad, Guadeloupe, Martinique, Trinidad

Guadeloupe, Martinique, Trinidad, Martinique, Guadeloupe, Jamaica, Trinidad

Jamaica, Martinique, Guadeloupe, Martinique, Guadeloupe, Jamaica, Trinidad

Martinique, Trinidad, Guadeloupe, Jamaica, Martinique, Guadeloupe, Trinidad

Martinique, Trinidad, Guadeloupe, Trinidad, Guadeloupe, Jamaica, Martinique


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

Freedom makes a voyage to Trinidad in week 6.

Freedom makes a voyage to Martinique in week 5.

Freedom makes a voyage to Jamaica in week 6.

Freedom makes a voyage to Jamaica in week 3.

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?

Freedom makes a voyage to Trinidad in week 1.

Freedom makes a voyage to Martinique in week 2.

Freedom makes a voyage to Guadeloupe in week 3.

Freedom makes a voyage to Martinique in week 4.

Freedom makes a voyage to Jamaica in week 6.


Question: f 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?

Freedom makes a voyage to Jamaica in week 2.

Freedom makes a voyage to Trinidad in week 2.

Freedom makes a voyage to Martinique in week 3.

Freedom makes a voyage to Guadeloupe in week 6.

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?

Freedom makes a voyage to Martinique in week 3.

Freedom makes a voyage to Martinique in week 4.

Freedom makes a voyage to Martinique in week 5.

Freedom makes a voyage to Guadeloupe in week 3.

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?

Guadeloupe, Trinidad
Jamaica, Guadeloupe
Martinique, Trinidad
Trinidad, Jamaica
Trinidad, Martinique


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

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

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

Freedom makes at most two voyages to Guadeloupe.

Freedom makes at most two voyages to Jamaica.

Freedom makes at most two voyages to Trinidad.


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?

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

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

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

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

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


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

Center 1 only
Center 3 only
Center 1, Center 2
Center 1, Center 3
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?


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

Only Center 2 recycles glass.
Only Center 3 recycles newsprint.
Only Center 1 recycles plastic.
Only Center 3 recycles tin.
Only Center 1 recycles wood.


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


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

plastic, tin
newsprint, wood
newsprint, tin
glass, wood
glass, tin


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

first digit is 2
second digit is 0
third digit is 3
fourth digit is 4


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

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

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

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

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


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

The second digit of the product code is 2.

The third digit of the product code is 3.

The fourth digit of the product code is 0.

The fifth digit of the product code is 3.


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


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

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

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

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

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


Exactly three films—Gambhir, Haseen, and Lehenga—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 Haseen is shown, and no film is shown after it on that day. On Friday either Gambhir or Lehenga, but not both, is shown, and no film is shown after it on that day. On Saturday either Gambhir or Haseen, 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?

Thursday: Lehenga, then Haseen; Friday: Lehenga; Saturday: Haseen

Thursday: Haseen; Friday: Gambhir, then Lehenga; Saturday: Lehenga, then Gambhir

Thursday: Haseen; Friday: Lehenga; Saturday: Lehenga, then Gambhir

Thursday: Gambhir, then Haseen, then Lehenga; Friday: Lehenga; Saturday: Gambhir


Question: Which one of the following CANNOT be true?

Haseen is the last film shown on each day of the festival.

Lehenga is shown on each day of the festival.

Gambhir is shown second on each day of the festival.

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


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


Question: If Gambhir is shown exactly three times, Haseen is shown exactly twice, and Lehenga is shown exactly once, then which one of the following must be true?

Exactly two films are shown on Saturday.

Haseen and Gambhir are both shown on Friday.

Gambhir is the only film shown on Saturday.


Question: If Lehenga is shown exactly three times, Haseen is shown exactly twice, and Gambhir 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?

Haseen
Lehenga
Gambhir, Haseen
Gambhir, Lehenga


A cruise line is scheduling seven week-long voyages for the ship Azad. 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 Azad's schedule: Jamaica will not be its destination in week 4. Trinidad will be its destination in week 7. Azad 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 Azad, in order from week 1 through week 7?

Guadeloupe, Jamaica, Martinique, Trinidad, Guadeloupe, Martinique, Trinidad

Guadeloupe, Martinique, Trinidad, Martinique, Guadeloupe, Jamaica, Trinidad

Jamaica, Martinique, Guadeloupe, Martinique, Guadeloupe, Jamaica, Trinidad

Martinique, Trinidad, Guadeloupe, Jamaica, Martinique, Guadeloupe, Trinidad


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

Azad makes a voyage to Trinidad in week 6.

Azad makes a voyage to Martinique in week 5.

Azad makes a voyage to Jamaica in week 6.

Azad makes a voyage to Jamaica in week 3.


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

Azad makes a voyage to Trinidad in week 1.

Azad makes a voyage to Martinique in week 2.

Azad makes a voyage to Guadeloupe in week 3.

Azad makes a voyage to Martinique in week 4.


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

Azad makes a voyage to Jamaica in week 2.

Azad makes a voyage to Martinique in week 6.

Azad makes a voyage to Martinique in week 3.

Azad makes a voyage to Guadeloupe in week 6.


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

Azad makes a voyage to Martinique in week 3.

Azad makes a voyage to Martinique in week 4.

Azad makes a voyage to Martinique in week 5.

Azad makes a voyage to Guadeloupe in week 3.


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

Guadeloupe, Trinidad
Jamaica, Guadeloupe
Martinique, Trinidad
Trinidad, Jamaica


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

Azad makes a voyage to Guadeloupe either in week 1 or else in week 2.

Azad makes a voyage to Martinique either in week 2 or else in week 3.

Azad makes at most two voyages to Guadeloupe.

Azad makes at most two voyages to Jamaica.


There are exactly three recycling centers in Ganga Nagar: 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 Ganga Nagar?

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

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

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

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


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

Center 1 only
Center 3 only
Center 1, Center 2
Center 1, Center 3


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


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

Only Center 2 recycles glass.
Only Center 3 recycles newsprint.
Only Center 1 recycles plastic.
Only Center 3 recycles tin.


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


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

plastic, tin
newsprint, wood
newsprint, tin
glass, wood


A researcher is evaluating exactly four medicines: W, X, Y, and Z. The only side effects the medicines can have are fatigue, headaches, palpitations, and sweating. The researcher knows the following to be true of the medicines side effects: Each medicine has at least one side effect. No medicine has both fatigue and palpitations as side effects. Medicine Z has no side effect in common with any of the other medicines. Medicines W and X have exactly one side effect in common. Fatigue is a side effect of medicine W. Palpitations are a side effect of medicine X. Sweating is not a side effect of medicine Y.

Question: If sweating is not a side effect of medicine X, then which one of the following statements must be true?

Headaches are a side effect of medicine W.

Headaches are a side effect of medicine Y.

Headaches are a side effect of medicine Z.

Palpitations are a side effect of medicine Y.


Question: If sweating is not a side effect of medicine Z, then which one of the following statements must be true?

Headaches are a side effect of medicine W.

Headaches are a side effect of medicine Y.

Headaches are a side effect of medicine Z.

Palpitations are a side effect of medicine Y.


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

Headaches are a side effect of medicine X.

Palpitations are a side effect of medicine W.

Palpitations are a side effect of medicine Z.


Question: If medicines W, X, and Y have a side effect in common, then which one of the following statements must be true?

Headaches are a side effect of medicine W.

Headaches are a side effect of medicine Z.

Palpitations are a side effect of medicine Y.

Sweating is a side effect of medicine W.


Question: If medicine Y has more than one side effect, then which one of the following statements must be true?

Headaches are a side effect of medicine Y.

Palpitations are a side effect of medicine Y.

Sweating is a side effect of medicine W.

Palpitations are not a side effect of medicine Y.

Sweating is not a side effect of medicine Z.


Tracy's Flower Shop delivers exactly six types of flowers—lilacs, magnolias, orchids, roses, tulips, and violets. Exactly six deliveries are made over a period of two consecutive days—Friday and Saturday. Three deliveries are made each day, at three different times each day—10 A.M., 2 P.M., and 4 P.M. Each of the six deliveries involves only one of the six types of flowers. The deliveries are made in accord with the following: The violets are delivered on Friday. The lilacs are delivered at some time before the tulips. The violets are delivered at some time before the magnolias. The orchids and the roses are delivered on the same day as one another.

Question: Which one of the following could be an accurate list of the flowers in the order in which they are delivered, from first to last?

magnolias, lilacs, violets, orchids, tulips, roses

orchids, violets, roses, lilacs, magnolias, tulips

roses, orchids, lilacs, tulips, violets, magnolias

violets, orchids, magnolias, lilacs, tulips, roses

violets, roses, orchids, tulips, magnolias, lilacs


Question: If the roses are delivered on Friday at 2 P.M., then each of the following could be true EXCEPT:

The violets are delivered on Friday at 4 P.M.

The tulips are delivered on Saturday at 2 P.M.

The orchids are delivered on Friday at 4 P.M.

The magnolias are delivered on Friday at 4 P.M.

The lilacs are delivered on Saturday at 2 P.M.


Question: If the magnolias and the lilacs are delivered on Saturday, then which one of the following could be true?

The orchids are delivered on Friday at 2 P.M.

The orchids are delivered on Saturday at 10 A.M.

The roses are delivered on Saturday at 4 P.M.

The tulips are delivered on Friday at 4 P.M.

The tulips are delivered on Saturday at 10 A.M.


Question: Which one of the following could be an accurate list of the flowers in the order in which they are delivered, from first to last?

lilacs, roses, orchids, violets, tulips, magnolias

magnolias, violets, lilacs, orchids, roses, tulips

orchids, lilacs, violets, magnolias, roses, tulips

orchids, roses, violets, magnolias, tulips, lilacs

roses, violets, orchids, lilacs, tulips, magnolias


Question: Which one of the following could be true?

e lilacs are delivered on Saturday at 4 P.M.

The magnolias are delivered on Friday at 10 A.M.

The magnolias are delivered on Friday at 2 P.M.

The tulips are delivered on Friday at 10 A.M.

The violets are delivered on Saturday at 4 P.M.


Question: If the tulips are delivered on Friday, then which one of the following CANNOT be true?

The magnolias are delivered on Friday at 2 P.M.

The magnolias are delivered on Saturday at 4 P.M.

The orchids are delivered on Saturday at 10 A.M.

The roses are delivered on Saturday at 4 P.M.

The violets are delivered on Friday at 4 P.M.


Question: If the magnolias and the orchids are delivered on the same day, then which one of the following could be true?

The orchids are delivered before the violets.

The violets are delivered before the lilacs.


Question: If the tulips are delivered after the roses, then which one of the following must be true?

The magnolias and the tulips are delivered on different days.

The orchids and the tulips are delivered on different days.

The tulips are delivered after the orchids.


During a seven-year period, an amusement park builds exactly seven roller coasters—the Firecracker, the Gobbler, the Hurricane, the Jackrabbit, the Lasso, the Niagara, and the Pretzel. No two roller coasters are built in the same year. Each roller coaster is either steel or wooden. The following conditions must apply: The Pretzel is built in the second year. The roller coaster built in the first year is steel, and the one built in the seventh year is wooden. The Lasso is built after the Firecracker. The Jackrabbit and the Gobbler are built before the Hurricane. Exactly two of the roller coasters built after the Hurricane are steel. Wooden roller coasters are not built in any two consecutive years.

Question: Which one of the following could be the order, from first to last, in which the roller coasters are built?

Gobbler, Jackrabbit, Pretzel, Hurricane, Firecracker, Lasso, Niagara

Jackrabbit, Pretzel, Gobbler, Hurricane, Lasso, Firecracker, Niagara

Jackrabbit, Pretzel, Gobbler, Hurricane, Niagara, Firecracker, Lasso

Niagara, Pretzel, Gobbler, Jackrabbit, Hurricane, Firecracker, Lasso

Niagara, Pretzel, Jackrabbit, Hurricane, Gobbler, Firecracker, Lasso


Question: Which one of the following roller coasters must be steel?

Firecracker Gobbler Hurricane Jackrabbit Lasso


Question: If the Firecracker is built in a year immediately after a year in which a wooden roller coaster is built, then which one of the following must be true?

The Firecracker is built in the sixth year.

The Jackrabbit is built in the third year.


Question: Each of the following roller coasters must be built before the Lasso EXCEPT:

Firecracker Gobbler Hurricane Jackrabbit Niagara


Question: If the Jackrabbit, the Hurricane, and the Firecracker are built in three consecutive years, in that order, then each of the following must be true EXCEPT:

The Firecracker is built before the Niagara.

The Gobbler is built before the Jackrabbit.

The Hurricane is built before the Niagara.

The Pretzel is built before the Jackrabbit.


On Tuesday evenings, the Community Center offers one session of each of the following six introductory classes: gymnastics, jazz dance, kung fu, meditation, tennis, and yoga. No other introductory classes are offered on Tuesdays. Each class is scheduled for exactly one hour, beginning at 5 P.M., 6 P.M., 7 P.M., or 8 P.M. Tuesdays schedule conforms to the following conditions: Yoga begins later than jazz dance but no later than kung fu. Meditation begins at the same time as exactly one other introductory class. No other introductory class begins at the same time as gymnastics. At most one of the other introductory classes begins later than gymnastics.

Question: Which one of the following could be an accurate schedule of the Tuesday introductory classes?

5 P.M.: jazz dance, meditation 6 P.M.: yoga 7 P.M.: gymnastics 8 P.M.: kung fu, tennis

5 P.M.: jazz dance 6 P.M.: meditation, tennis 7 P.M.: yoga 8 P.M.: gymnastics, kung fu

5 P.M.: jazz dance, meditation 6 P.M.: yoga 7 P.M.: kung fu, tennis 8 P.M.: gymnastics

5 P.M.: jazz dance, tennis 6 P.M.: meditation 7 P.M.: kung fu, yoga 8 P.M.: gymnastics

5 P.M.: tennis, yoga 6 P.M.: jazz dance, meditation 7 P.M.: gymnastics 8 P.M.: kung fu


Question: If meditation is scheduled to begin later than tennis, then which one of the following could be true of the schedule?

Jazz dance begins later than meditation.


Question: Which one of the following introductory classes could be the only class scheduled to begin at 5 P.M.?

yoga
tennis
meditation
kung fu
gymnastics


Question: Which one of the following introductory classes CANNOT be scheduled to start at 6 P.M.?

gymnastics
jazz dance
kung fu
meditation
tennis


Each of five experts—a lawyer, a naturalist, an oceanographer, a physicist, and a statistician—individually gives exactly one presentation at a conference. The five presentations are given consecutively. Each presentation is in exactly one of the four following languages: French, Hindi, Japanese, or Mandarin. Each expert speaks exactly one of the languages. The following conditions must hold: Exactly two of the presentations are in the same language as each other. The statistician gives the second presentation in Hindi. The lawyer gives the fourth presentation in either Mandarin or French. The oceanographer presents in either French or Japanese; the same is true of the physicist. The first presentation and the last presentation are in Japanese.

Question: Which one of the following could be the order in which the experts give their presentations, from first to last?

the physicist, the statistician, the lawyer, the naturalist, the oceanographer

the physicist, the naturalist, the oceanographer, the lawyer, the statistician

the oceanographer, the statistician, the naturalist, the lawyer, the physicist

the oceanographer, the statistician, the lawyer, the naturalist, the physicist


Question: Which one of the following is a complete and accurate list of the experts any one of whom could be one of the two who present in Japanese?

the naturalist, the oceanographer, the statistician

the naturalist, the oceanographer, the physicist, the statistician


Question: If the naturalist presents in French, which one of the following could be true?

The oceanographer presents third.
The oceanographer presents fifth.
The lawyer presents in French.
The oceanographer presents in French.


Question: Which one of the following is a complete and accurate list of the languages any one of which could be the language of the third presentation?

French
Mandarin
French, Hindi
French, Mandarin


Question: Suppose the condition that the statistician gives the second presentation in Hindi is replaced with the condition that the statistician gives either of the presentations given in Japanese. If all the other original conditions remain in effect, which one of the following could be the order, from first to last, in which the experts present?

the naturalist, the oceanographer, the physicist, the lawyer, the statistician

the oceanographer, the statistician, the naturalist, the lawyer, the physicist

the physicist, the oceanographer, the lawyer, the naturalist, the statistician

the statistician, the oceanographer, the naturalist, the lawyer, the physicist


Shanti interviews exactly five out of a total of seven job applicants—Gopi, Irfan, Lata, Nasser, Oscar, Rohit, and Tarun. She interviews the five one at a time, once each. Interviewing must meet the following conditions: Lata is interviewed second or third. Nasser or Tarun is interviewed last. Gopi, if interviewed, is interviewed first. Irfan is interviewed immediately after Rohit if both are interviewed. Oscar is interviewed immediately after Rohit if both are interviewed. Tarun is interviewed immediately after Nasser if both are interviewed.

Question: Which one of the following could be a complete and accurate list of the applicants interviewed, listed in the order in which they are interviewed?

Gopi, Lata, Irfan, Nasser, Tarun
Gopi, Rohit, Oscar, Lata, Tarun
Irfan, Gopi, Lata, Oscar, Tarun
Oscar, Rohit, Lata, Nasser, Tarun


Question: Which one of the following is a complete and accurate list of the applicants each of whom must be interviewed?


Question: If Irfan is interviewed fourth, then which one of the following must be true?

Gopi is interviewed.
Oscar is interviewed.
Rohit is interviewed.
Nasser is interviewed last.


Question: If Gopi is interviewed first and Oscar is interviewed second, each of the following could be true EXCEPT:

Irfan is interviewed fourth.
Rohit is interviewed fourth.
Nasser is interviewed last.
Both Nasser and Tarun are interviewed.


Question: Suppose the condition that Nasser or Tarun is interviewed last is replaced with the condition that neither Nasser nor Tarun is interviewed last. If all the other initial conditions remain in effect, then which one of the following must be true if Rohit is interviewed last?

Exactly one of Irfan and Oscar is interviewed.

Exactly one of Nasser and Tarun is interviewed.


An industrial electrician attaches exactly seven components designated S, T, V, W, X, Y, and Z to a circuit board in exactly seven consecutive steps; exactly one component is attached per step. Each component is attached exactly once, and each is attached either by hand or by machine, but not both. X is the fourth component attached. Exactly two components are attached by hand at some time before X is attached. No component is attached by hand before T is attached. W is attached at some time before T. Y is attached at some time after both Z and S. The sixth component attached is attached by hand.

Question: Which one of the following could be an accurate list, in order, of the first three components attached?


Question: Which one of the following components must be attached by machine?


Question: If V is the seventh component attached, each of the following components could be attached by machine EXCEPT:


Question: Which one of the following is a complete and accurate list of the components, any one of which could be the sixth component attached?

S, W, Z
S, T, Y, Z
S, V, Y, Z
S, W, Y, Z


Question: Which one of the following components must be attached by hand?


Question: If S is attached by machine, which one of the following must be true?

Z is attached by hand.
X is attached by hand.
V is attached by hand.
Y is the seventh component attached.


The Darshan Advertising Agency has exactly seven representatives—Faizal, John, Lekha, Monica, Pooja, Qadir, Shobhit. Its new campaign is presented to exactly one client by one or more of the representatives in accordance with the following conditions: If Faizal presents, then so do Monica and Pooja. If John presents, then Qadir does not. If Qadir does not present, then Pooja does. If Lekha presents, then either John, Shobhit, or both present. If both Lekha and Shobhit present, then Monica does not.

Question: Which one of the following could be a complete and accurate list of the representatives who present?

Monica, Shobhit
Faizal, Monica, Qadir
Faizal, Lekha, Monica, Pooja
Monica, Pooja, Qadir, Shobhit


Question: If Lekha and Qadir both present, then which one of the following could be true?

Exactly two of the seven representatives present.

Exactly three of the seven representatives present.


Question: Which one of the following representatives could be the only representative who presents?


Question: Which one of the following CANNOT be true?

Faizal and Qadir both present.
John presents but Pooja does not.
Neither John nor Qadir presents.
Only Monica and Pooja present.


Question: If exactly two of the representatives present, then which one of the following representatives CANNOT be one of the two who present?


Question: If Faizal presents, then which one of the following must be true?

At least three of the representatives present.

At most four of the representatives present.

Exactly one of Lekha or Shobhit presents.


Meena has six colored pencils—green, maroon, orange, red, white, and yellow. She sketches a drawing using exactly five of the six pencils, one pencil at a time. The following conditions must hold: No pencil is used more than once. Either the maroon or the yellow pencil is not used. The red pencil is used at some time before the green. The red pencil is used at some time before either the orange or the yellow, but not before both. The green pencil is used at some time before either the maroon or the white, but not before both.

Question: Which one of the following could be an accurate list of the pencils used, from first to fifth?

orange, green, red, maroon, yellow
red, green, orange, white, maroon
red, orange, maroon, white, green
white, red, orange, green, maroon
white, yellow, orange, green, red


Question: Which one of the following could be true?

The maroon pencil is used first, whereas the white is used second.

The white pencil is used first, whereas the green is used second.

The yellow pencil is used first, whereas the orange is used second.

The yellow pencil is used first, whereas the orange is used fourth.

The yellow pencil is used fourth, whereas the maroon is used fifth.


Question: Which one of the following CANNOT be the color of the fifth pencil used?


Question: Which one of the following could be an accurate list of the pencils used, from first to fifth?

maroon, green, white, red, orange
maroon, red, green, white, yellow
red, green, orange, white, yellow
red, white, orange, green, maroon
white, red, maroon, green, orange


Question: Which one of the following CANNOT be the color of the third pencil used?


Question: Suppose that the condition that either the maroon or the yellow pencil is not used no longer holds. If all other conditions remain in effect, then which one of the following could be an accurate list of the pencils used, from first to fifth?

maroon, red, green, orange, yellow
maroon, yellow, red, green, white
orange, green, red, yellow, maroon
orange, red, maroon, green, white
white, red, green, maroon, yellow


A bird sanctuary contains birds of at least two of the following six kinds—kingfishers, mynas, peacocks, robins, sparrows, and woodpeckers. No other kinds of birds are in the sanctuary. The following conditions must hold: Woodpeckers are not in the sanctuary if mynas are. Peacocks are not in the sanctuary if robins are. Either robins or woodpeckers, but not both, are in the sanctuary. Woodpeckers are in the sanctuary if kingfishers, sparrows, or both are in the sanctuary

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

kingfishers, mynas
peacocks, woodpeckers
kingfishers, robins, sparrows
mynas, peacocks, robins
mynas, peacocks, sparrows


Question: What is the maximum number of the kinds of birds that could be in the sanctuary?


Question: If both kingfishers and sparrows are in the sanctuary, then each of the following could be true EXCEPT:

Exactly three kinds of birds are in the sanctuary.

Exactly four kinds of birds are in the sanctuary.


Question: If there are no kingfishers in the sanctuary, then which one of the following must be true?

There are no woodpeckers in the sanctuary.

At least three kinds of birds are in the sanctuary.

At most three kinds of birds are in the sanctuary


Question: If there are no robins in the sanctuary, then which one of the following is a kind of bird that CANNOT be in the sanctuary?

kingfishers mynas peacocks sparrows woodpeckers


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

Exactly two kinds of birds are in the sanctuary.

Exactly three kinds of birds are in the sanctuary.

Exactly four kinds of birds are in the sanctuary.

There are no kingfishers in the sanctuary.


Last year, seven stores—Faroj's Appliances, Good Buy, Intelligent Office, LANs for Less, Networks Unlimited, Silicon Village, and Uptown Computing—each sold exactly 100, 200, 300, 400, or 500 computers, consistent with the following conditions: Good Buy sold exactly the same number of computers as Networks Unlimited did. Intelligent Office sold exactly the same number of computers as Uptown Computing did. Neither Faroj's Appliances nor Silicon Village sold exactly the same number of computers as any other store. LANs for Less sold more computers than Uptown Computing did. Intelligent Office sold more computers than Good Buy did.

Question: Which one of the following could be an accurate matching of the stores to the exact number of computers each sold last year?

Faroj's Appliances: 100; Good Buy: 200; Intelligent Office: 300; LANs for Less: 400; Networks Unlimited: 200; Silicon Village: 500; Uptown Computing: 300

Faroj's Appliances: 100; Good Buy: 200; Intelligent Office: 400; LANs for Less: 300; Networks Unlimited: 200; Silicon Village: 500; Uptown Computing: 400

Faroj's Appliances: 500; Good Buy: 200; Intelligent Office: 300; LANs for Less: 400; Networks Unlimited: 500; Silicon Village: 100; Uptown Computing: 300

Faroj's Appliances: 500; Good Buy: 300; Intelligent Office: 200; LANs for Less: 400; Networks Unlimited: 300; Silicon Village: 100; Uptown Computing: 200

Faroj's Appliances: 500; Good Buy: 300; Intelligent Office: 400; LANs for Less: 200; Networks Unlimited: 300; Silicon Village: 500; Uptown Computing: 100


Question: Which one of the following stores CANNOT have sold exactly 400 computers last year?

Faroj's Appliances
Good Buy
Intelligent Office
Silicon Village
Uptown Computing


Question: Which one of the following stores CANNOT have sold exactly 200 computers last year?

Faroj's Appliances
Good Buy
Intelligent Office
LANs for Less
Silicon Village


Question: Which one of the following must be true?

Faroj's Appliances sold more computers last year than Good Buy did.

Intelligent Office sold more computers last year than Silicon Village did.

LANs for Less sold more computers last year than Faroj's Appliances did.

Silicon Village sold more computers last year than Good Buy did.

Uptown Computing sold more computers last year than Networks Unlimited did.


Arbutus College owns exactly four houses that it leases to faculty or students. Of these houses, no two are exactly the same distance from Arbutus's campus, and each house is either a student house (occupied entirely by students) or a faculty house (occupied entirely by faculty). The lease length for each house is one, two, or three semesters. The following conditions must hold: No student house has a three-semester lease. At least two houses each have longer leases than does the house closest to campus. Every student house (if there are any) is farther from campus than any faculty house (if there are any).

Question: Which one of the following could be a complete and accurate list of the leases of the student houses, ordered from the student house closest to campus to the student house farthest from campus?

one semester, two semesters, one semester

one semester, two semesters, two semesters, one semester

one semester, two semesters, three semesters, two semesters


Question: If the house farthest from campus has a lease longer than that of each of the other houses, then which one of the following could be true?

Each faculty house has a two-semester lease.

Exactly two houses each have a one-semester lease.

Exactly three houses each have a two-semester lease.

None of the houses has a one-semester lease.

None of the houses has a two-semester lease


Question: What is the maximum number of houses that could all be student houses with two-semester leases?


Question: Which one of the following must be true of the two houses that are neither the house farthest from campus nor the house closest to campus?

At least one of them has a lease the same length as that of the house closest to campus.

At least one of them has a lease longer than that of the house closest to campus.

At least one of them has a lease shorter than three semesters.