PRACTICE SET 3:
On Wednesday a physician will have
exactly one appointment with seven patients- P, Q, R, S, T, U, W- one
patient per appointment. The schedule of appointments, chronologically
numbered 1 through 7, must meet the following conditions:
Q’s appointment is at some time before W’s appointment.
U’s appointment is at some time before P’s appointment.
Either R or T has appointment 3.
S’s appointment is either the appointment immediately before or the appointment immediately after R’s appointment.
1. Which of the following is an acceptable schedule of appointments in order from 1 to 7?
A. Q, S, R, P, W, U, T
B. Q, U, W, S, R, T, P
C. S, Q, R, T, W, U, P
D. T, U, R, S, W, P, Q
E. U, Q, T, P, R, S, W
2. If W has appointment 2 and P has appointment 5, then which one of the following must be true?
A. R has appointment 6.
B. S has appointment 4.
C. S has appointment 7.
D. U has appointment 1.
E. U has appointment 4.
3. If U’s appointment is immediately
after T’s appointment and immediately before R’s appointment, then which
one of the following must be true?
A. Q’s appointment is at some time before P’s appointment.
B. S’s appointment is at some time before P’s appointment.
C. S’s appointment is immediately before Q’s appointment.
D. W’s appointment is immediately before P’s appointment.
E. W’s appointment is at some time before S’s appointment.
4. If P’s appointment is immediately before S’s appointment, then each of the following could be true EXCEPT:
A. R’s appointment is immediately before W’s appointment.
B. T’s appointment is immediately before Q’s appointment.
C. U’s appointment is immediately before P’s appointment.
D. U’s appointment is immediately before Q’s appointment.
E. W’s appointment is immediately before T’s appointment.
5. If T’s appointment is immediately
after P’s appointment and immediately before W’s appointment, then which
one of the following must be true?
A. W’s appointment is at some time before R’s appointment.
B. U’s appointment is at some time before R’s appointment.
C. S’s appointment is at some time before U’s appointment.
D. R’s appointment is at some time before P’s appointment.
E. Q’s appointment is at some time before S’s appointment.
PRACTICE SET 4:
The organizer of a reading club will
select at least five and at most six works from a group of nine works.
The group consists of three French novels, three Russian novels, two
French plays, and one Russian play. The organizer’s selection of works
must conform to the following requirements.
No more than four French works are selected.
At least three but no more than four novels are selected.
At least as many French novels as Russian novels are selected.
If both French plays are selected, then the Russian play is not selected.
1. Which of the following could be the organizer’s selection of works?
A. one French novel, two Russian novels, one French play, one Russian play
B. two French novels, one Russian novel, two French plays, one Russian play
C. two French novels, two Russian novels, two French plays
D. three French novels, one Russian novel, two French plays
E. three French novels, two Russian novels, one Russian play
2. Which of the following could be true about the organizer’s selection of works?
A. No Russian novels are selected.
B. Exactly one French novel is selected.
C. All three players are selected.
D. All three Russian novels are selected.
E. All five French for are selected
3. If the works selected include three
French novels, which one of the following could be a complete and
accurate list of the remaining works selected?
A. One Russian novel.
B. Two French Plays.
C. One Russian novel.
D. One Russian play one Russian novel,
E. Two French plays two Russian novels, one French play.
4. The organizer must at least select.
A. one French novel and one French play
B. One French novel and one Russian play
C. one Russian novel and one French play
D. two French novels
E. two Russian novels
5. Any one of the following could be true about the organizer’s selection of works EXCEPT:
A. No Russian novels and exactly one play are selected.
B. Exactly one Russian novel and both French plays are selected.
C. Exactly two French novels and the Russian plays are selected.
D. Exactly two French novels and exactly two plays are selected.
E. Exactly two Russian Novels and exactly one play are selected.
PRACTICE SET 5
Doctor Amara works only on Mondays,
Tuesdays, Wednesdays, Fridays and Saturdays. She performs four different
activities lecturing, operating, treating patients; and conducting
research. Each working day she performs exactly one activity in the
morning and exactly one activity in the afternoon. During each week her
work schedule must satisfy the following restrictions:
She performs operations on exactly two consecutive calendar days.
She treats patients on exactly one morning and exactly three afternoons.
She conducts research on exactly one morning.
On Saturday she neither lectures nor performs operations.
1. Which of the following must be a day on which Doctor Amara lectures?
A. Monday
B. Tuesday
C. Wednesday
D. Friday
E. Saturday
2. On Wednesday Doctor Amara could be scheduled to
A. conduct research in the morning and operate in the afternoon
B. lectures in the morning and treat patients in the afternoon
C. operate in the morning and lecture in the afternoon
D. operate in the morning and conduct research in the afternoon
E. treats patients in the morning and treats patients in the afternoon
3. Which one of the following statement must be true?
A. There is one day on which the doctor treats patients both in the morning and in the afternoon.
B. The doctor conducts research on one of the days on which she lectures.
C. The doctor conducts research on one of the days on which she treats patients.
D. The doctor lectures on one of the days on which she treats patients.
E. The doctor lectures on one of the days on which she operates.
4. If Doctor Amara operates on Tuesday, then her schedule for treating patients could be?
A. Monday morning, Monday afternoon, Friday morning, Friday afternoon
B. Monday morning, Friday afternoon, Saturday morning, Saturday afternoon
C. Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon
D. Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon
E. Wednesday afternoon, Friday afternoon, Saturday morning, Saturday afternoon
5. Which one of the following is a pair of days on both of which Doctor Amara must treat patients?
A. Monday and Tuesday
B. Monday and Saturday
C. Tuesday and Friday
D. Tuesday and Saturday
E. Friday and Saturday
E
PRACTICE SET 6
Each of six people Kamal, Laiba, Mariam,
Omar, Pervaiz and Sameer plays exactly one of the sports golf and
tennis. If a sport is played by more than one of the six people, then
the people who play that sport are ranked in order of ability from
highest to lowest, with no ties. The following conditions must apply:
Omar plays tennis.
Laiba plays golf.
There is no golf player ranked higher than Laiba.
If Mariam plays tennis, then Sameer ranking lower than Omer but higher than Mariam.
If Pervaiz plays tennis, then Kamal plays tennis, Omar ranking lower than Kamal but higher than Pervaiz.
1. Which one of the following could be true?
A. Mariam plays tennis and Sameer plays golf.
B. Pervaiz plays tennis and Kamal plays golf.
C. Kamal plays tennis and Pervaiz plays golf.
D. Pervaiz and Omar play tennis, Pervaiz ranking higher than Omar.
E. Mariam and Sameer play tennis, Mariam ranking higher than Sameer.
2. Each of the following could be the lowest ranking tennis player EXCEPT:
A. Sameer
B. Kamal
C. Omar
D. Pervaiz
E. Mariam
3. Which one of the following could be a
complete and accurate list of the people who plays tennis, listed in
order of rank from highest to lowest?
A. Sameer, Pervaiz, Omar
B. Omar, Pervaiz, Kamal
C. Sameer, Omar, Mariam
D. Omar, Sameer, Kamal, Mariam
E. Pervaiz, Mariam, Sameer, Kamal
4. If Sameer plays golf, then each of the following are pairs of people who must play the same sport as each each other EXCEPT:
A. Pervaiz and Mariam
B. Pervaiz and Sameer
C. Kamal and Mariam
D. Pervaiz and Laiba
E. Mariam and Sameer
5. If Omar is the highest ranking tennis player, which one of the following must be true?
A. Omar and Mariam play the same sport as each other.
B. Pervaiz and Laiba play the same sport as each other.
C. Pervaiz and Omar play the same sport as each other.
D. Kamal and Laiba do not play the same sport as each other.
E. Kamal and Pervaiz do not play the same sport as each other.
6. Suppose that the conditions is added
that Sameer and Pervaiz do not play the same sport as each other. If all
other conditions remain in effect, then each of the following could be
true EXCEPT:
A. Mariam and Kamal play the same sport as each other.
B. Pervaiz and Mariam play the same sport as each other.
C. Pervaiz and Mariam play the same sport as each other.
D. Kamal and Pervaiz do not play the same sport as each other.
E. Mariam and Kamal do not play the same sport as each other.
PRACTICE 7
An attorney is scheduling interviews
with witnesses for a given week, Monday through Saturday. Two full
consecutive days of the week must be reserved for interviewing hostile
witnesses. In addition, non hostile witnesses Q, R, U, X , Y and Z will
each be interviewed exactly once for a full morning or afternoon. The
only witnesses who will be interviewed simultaneously with each other
are Q and R. The following conditions apply:
X must be interviewed on Thursday morning.
Q must be interviewed at some time before X.
U must be interviewed at some time before R.
Z must be interviewed at some time after X and at some time after Y.
1. Which of the following is a sequence, from first to last, in which the non hostile witnesses could be interviewed?
A. Q with R, U, X, Y, Z
B. Q, U, R, X, with Y, Z
C. U, X, Q with R, Y, Z
D. U, Y, Q with R, X, Z
E. F, X, Q with U, Z, R, Y
2. Which one of the following is
acceptable as a complete schedule of witnesses for Tuesday morning,
Tuesday afternoon and Wednesday morning, respectively?
A. Q, R, none
B. R, none, Y
C. U, none, X
D. U, Y, none
E. Y, Z, none
3. If Y is interviewed at some time
after X, which one of the following must be a day reserved for
interviewing hostile witnesses?
A. Monday
B. Tuesday
C. Wednesday
D. Friday
E. Saturday
4. If R is interviewed at some time
after Y, which one of the following must be a day reserved for
interviewing hostile witnesses?
A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday
5. If on Wednesday afternoon and on Monday the attorney conducts no interviews, which one of the following must be true?
A. Q is interviewed on the same day as U.
B. R is interviewed on the same day as Y.
C. Y is interviewed at some time before U.
D. Y is interviewed at some time before Wednesday.
E. Z is interviewed at some time before Wednesday.
6. If Z is interviewed on Saturday morning, which one of the following can be true?
A. Wednesday is a day reserved for interviewing hostile witnesses.
B. Friday is a day reserved for interviewing hostile witnesses.
C. R is interviewed on Thursday.
D. U is interviewed on Tuesday.
E. Y is interviewed at some time before Thursday.
A
PRACTICE SET 8
The population of a small country is
organized into five clans N, O, P, S and T. Each year exactly three of
the five clans participate in annual harvest ceremonies. The rules
specifying the order of participation of the clans in the ceremonies are
as follows:
Each clan must participate at least once in two consecutive years.
No clans participate for three consecutive years.
Participation takes place in cycles, with each cycle ending when each of the five clans has participated three times.
Only then does a new cycle begin.
No clan participates more than three times within any cycle.
1. If the clan participating in the
first year of a given cycle are N, O, and P, which of the following
could be the clans participating in the second year of that cycle?
A. N, O, S
B. N, O, T
C. N, P, S
D. O, P, T
E. O, S, T
2. Which of the following can be true about the clan’s participation in the ceremonies?
A. N participates in the first, second, third and fourth years.
B. N participates in the second, third, and fourth years.
C. Both O and S participate in the first and third years.
D. Both N and S participate in the first, third and fifth years.
E. Both S and T participate in the second, third and fifth years.
3. Any cycle of the clans participation in the ceremonies must be completed at the end of exactly how many year?
A. five
B. six
C. seven
D. eight
E. nine
4. Which of the following must be true about three clans that participate in the ceremonies in the first year?
A. At most two of them participate together in the third year.
B. At least two of them participate together in the second year.
C. All three of them participate together in the fourth year.
D. All three of them participate together in the fifth year.
E. None of them participates in the third year.
5. If, in a particular cycle, N, O and S
participate in the ceremonies in the first year, which one of the
following must be true?
A. N participates in the second and third years.
B. O participates in the third and fourth years.
C. N and O both participate in the third year.
D. P and T both participate in the fifth year.
E. S and T both participate in the fifth year.
6. If, in a particular cycle, N, O, and T
participate in the first year and if O and P participate in the fourth
year, any of the following could be a clan that participates in the
third year EXCEPT
A. N
B. O
C. P
D. S
E. T
7. If, in a particular cycle N, O and S
participate in the ceremonies in the first year and O, S and T
participate in the third year, then which one of the following could be
the clans that participate in the fifth years.
A. N, O, P
B. N, O, S
C. N, P, S
D. O, P, S
E. P, S, T
PRACTICE SET 9
Exactly seven toy truck models—–F, G, H,
J, K, M and S are assembled on seven assembly lines, exactly one model
to a line. The seven lines are arranged side by side and numbered
consecutively 1 through 7. Assignment of models to lines must meet the
following conditions:
F is assembled on a lower numbered line than J.
M is assembled on the line numbered on lower than the line on which G is assembled.
H is assembled on line 1 or else line 7.
S is assembled on the line 4.
1. Which one of the following is an acceptable assignment of toy truck models to lines, on order from line 1 through line 7?
A. F, J, K, S, H, M, G
B. F, K, J, S, M, G, H
C. F, M, K, S, G, J, H
D. H, K, S, M, G, F, J
E. H, M, G, S, J, F, K
2. It must be true that the lowest numbered line on which
A. F can be assembled is line 2
B. G can be assembled in line 3
C. J can be assembled in line 2
D. K can be assembled in line 3
E. M can be assembled in line 2
3. If K is assembled on line 5, which
one of the following is a pair of models that could be assembled, not
necessarily in the order given, on lines whose numbers are consecutive
to each other?
A. G, H
B. G, J
C. H, J
D. J, M
E. M, S
4. There can be at most how many lines between the line on which F is assembled and the line on which J is assembled?
A. one
B. two
C. three
D. four
E. five
5. If K is assembled on line 2, which one of the following must be true?
A. F is assembled on a lower numbered line than S.
B. H is assembled on a lower numbered line than G.
C. J is assembled on a lower numbered line than 11.
D. M is assembled on a lower numbered line than J.
E. S is assembled on a lower numbered line than J.
6. If G is assembled on the line
numbered one less than the line on which F is assembled, then which one
of the following must be true?
A. F is assembled on line 3.
B. G is assembled on line 5.
C. H is assembled on line 1.
D. K is assembled on line 5.
E. M is assembled on line 6.
7. If M is assembled on line 1, which one of the following could be true?
A. F is assembled on a line numbered one lower than the line on which H is assembled.
B. F is assembled on a line numbered one lower than the line on which K is assembled.
C. G is assembled on a line numbered one lower than the line on which J is assembled.
D. G is assembled on a line numbered one lower than the line on which K is assembled.
E. K is assembled on a line numbered one lower than the line on which G is assembled.
D
PRACTICE SET 10
Five candidates for mayor—–Q, R, S, T
and U-will each speak exactly once at each of three town
meetings-meetings 1, 2, and 3. At each meeting, each candidate will
speak in one of five consecutive time slots. No two candidates will
speak in the same time slot as each other at any meeting. The order in
which the candidates will speak will meet the following conditions:
Each candidate must speak either first or second at least one of the meetings.
Any candidate who speaks fifth at any of
the meetings must speak first at least one of the other meetings. No
candidate can speak fourth at more than one of the meetings.
1. Which one of the following could be the order, from first to fifth, in which the candidates speak at the meetings?
A. meeting1: Q, U, R, T, S
meeting2: S, T, R, U, Q
meeting3: T, U, Q, R, S
B. meeting1: R, S, Q, T, U
meeting2: U, T, S, R, Q
meeting3: Q, R, T, U, S
C. meeting1: S, Q, U, T, R
meeting2: U, T, Q, R, S
meeting3: R, Q, S, T, U
D. meeting1: F, R, S, U, Q
meeting2: Q, R, S, T, U
meeting3: U, S, R, Q, T
E. meeting1: U, T, R, S, Q
meeting2: Q, R, S, T, U
meeting3: S, T, U, Q, R
2. If R speaks second at meeting 2 and
first at meeting 3, which one of the following is a complete and
accurate list of those time slots any one of which could be the time
slot in which R speaks at meeting 1?
A. fourth, fifth
B. first, second, fifth
C. second, third, fifth
D. third, fourth, fifth
E. second, third, fourth, fifth
3. If the order in which the candidates
speak at meeting 1 is R, U, S, T, Q and the order in which they speak at
meeting 2 is Q, R, U, S, T, which on e of the following could be true
of meeting 3?
A. Q speaks first.
B. R speaks third.
C. S speaks first.
D. T speaks second.
E. U speaks fifth.
4. If R speaks first at meetings 1 and 2, and S speaks first at meeting 3, which one of the following must be true?
A. R speaks second at meeting 3.
B. R speaks fourth at meeting 3.
C. S speaks second at least one of the meetings.
D. S speaks fifth at exactly one of the meetings.
E. S speaks fifth at exactly two of the meetings.
5. It could be true that at all three meetings T speaks
A. first
B. second
C. in some time slot after the time slot in which R speaks.
D. in some time slot after the time slot in which S and U speak.
E. in some time slot before the time slots in which R and U speak.
6. If S, T and U speak second at meeting 1, 2 and 3 respectively, which one of the following must be true?
A. The fifth speaker speaks at atleast one of the meetings is either Q or R.
B. Either Q speaks first at exactly two of the meetings or else R does so.
C. Neither S and T speak fifth at any of the meetings.
D. Q speaks third at one of the meetings, and R speaks third at another of the meetings.
E. Q speaks fourth at one of the meetings, and r speaks fourth at another of the meetings.
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