Stratosphere 6
Tough Logic Games
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Tough Logic Games
What Makes Tough Games Tough
Easy Games: The Overview
Six racehorses—K, L, M, N, O, and P—will be assigned
to six positions arranged in a straight line and numbered
consecutively 1 through 6. The horses are assigned to
the positions, one horse per position, according to the
following conditions:
A showroom contains exactly six new cars—T, V, W, X,
Y, and Z—each equipped with at least one of the following
three options: power windows, leather interior, and sunroof.
No car has any other options. The following conditions
must apply:
On a Tuesday, an accountant has exactly seven bills—
numbered 1 through 7—to pay by Thursday of the same week.
The accountant will pay each bill only once according to the
following rules:
Either three or four of the seven bills must be paid on
Wednesday, the rest on Thursday.
Why are these easy games?
Sources: PrepTest 28, Section 2, Game 1
PrepTest 35, Section 3, Game 2
PrepTest 29, Section 3, Game 1
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Difficult Sequencing Games: The Overview
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, nonhostile 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.
What makes this game more difficult?
Test Day TipS
• Don’t skip the SEAL questions. They are a crucial part of the Kaplan Method for Logic Games,
especially in more difficult games.
• Use the Limitations step of SEAL to work the numbers, starting by counting the numbers of
entities and slots.
• Take your time setting up the sketch for difficult games, particularly when a twist in the game
forces you to alter Kaplan’s basic sketches for the game’s action. Analyze, then draw.
Source: PrepTest 21, Section 1, Game 3
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Tough Logic Games
Difficult Questions
The Minimum is a Must
1. If R is interviewed at some time after Y, which one of the
following must be a day reserved for interviewing hostile
witnesses?
(A) (B) (C) (D) (E) Monday
Tuesday
Wednesday
Thursday
Friday
Which entities can you definitely place?
How many of the entities must be placed before X?
What does this tell you about the hostile witnesses?
Game Strategy
• Think in terms of minimums to determine what must be true.
Source: PrepTest 21, Section 1, Question 15
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Try These at Home
2. Which one of the following is a sequence, from first
to last, in which the nonhostile witnesses could be
interviewed?
(A) (B) (C) (D) (E) Q with R, U, X, Y, Z
Q, U, R, X with Y, Z
U, X, Q, with R, X, Z
U, Y, Q with R, X, Z
X, Q with U, Z, R, Y
3. Which one of the following is acceptable as a complete
schedule of witnesses for Tuesday morning, Tuesday
afternoon, and Wednesday morning, respectively?
(A) (B) (C) (D) (E) Q, R, none
R, none, Y
U, none, X
U, Y, none
Y, Z, none
5. If on Wednesday afternoon and on Monday the attorney
conducts no interviews, which one of the following must
be true?
(A) (B) (C) (D) (E) Q is interviewed on the same day as U.
R is interviewed on the same day as Y.
Y is interviewed at some time before U.
Y is interviewed at some time before Wednesday.
Z is interviewed at some time before Friday.
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.
4. If Y is interviewed at some time after X, which one of
the following must be a day reserved for interviewing
hostile witnesses?
(A) (B) (C) (D) (E) Monday
Tuesday
Wednesday
Friday
Saturday
Source: PrepTest 21, Section 1, Questions 12–14, 16, and 17
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Tough Logic Games
Difficult Games
An Impure Game
Exactly seven professors—Madison, Nilsson, Orozco, Paton,
Robinson, Sarkis, and Togo—were hired in the years 1989
through 1995. Each professor has one or more specialities, and
any two professors hired in the same year or in consecutive
years do not have a specialty in common. The professors were
hired according to the following conditions:
Madison was hired in 1993, Robinson in 1991.
There is at least one specialty that Madison, Orozco, and
Togo have in common.
Nilsson shares a specialty with Robinson.
Paton and Sarkis were each hired at least one year before
Madison and at least one year after Nilsson.
Orozco, who shares a specialty with Sarkis, was hired
in 1990.
What makes this game more difficult?
Game Strategies
• An Impure game is one that adds an element that changes how the main action will work.
• It’s great if you see Deductions as you work through the rules, but make sure that you
don’t skip any steps of the Kaplan Method. Analyze each rule and draw it out, then note
any Deductions you might have seen.
Source: PrepTest 35, Section 3, Game 4
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Try These at Home
7. Which one of the following is a complete and accurate
list of the professors who could have been hired in the
years 1989 through 1991?
(A)
(B)
(C)
(D)
(E)
Nilsson, Orozco, Robinson
Orozco, Robinson, Sarkis
Nilsson, Orozco, Paton, Robinson
Nilsson, Orozco, Paton, Sarkis
Orozco, Paton, Robinson, Sarkis
8. If exactly one professor was hired in 1991, then which
one of the following could be true?
(A)
(B)
(C)
(D)
(E)
Madison and Paton share a specialty.
Robinson and Sarkis share a specialty.
Paton was hired exactly one year after Orozco.
Exactly one professor was hired in 1994.
Exactly two professors were hired in 1993.
9. Which one of the following must be false?
(A)
(B)
(C)
(D)
(E)
Nilsson was hired in 1989.
Paton was hired in 1990.
Paton was hired in 1991.
Sarkis was hired in 1992.
Togo was hired in 1994.
10. Which one of the following must be true?
(A)
(B)
(C)
(D)
(E)
Orozco was hired before Paton.
Paton was hired before Sarkis.
Sarkis was hired before Robinson.
Robinson was hired before Sarkis.
Madison was hired before Sarkis.
11. If exactly two professors were hired in 1992, then which
one of the following could be true?
(A)
(B)
(C)
(D)
(E)
Orozco, Paton, and Togo share a specialty.
Madison, Paton, and Togo share a specialty.
Exactly two professors were hired in 1991.
Exactly two professors were hired in 1993.
Paton was hired in 1991.
12. If Paton and Madison have a specialty in common, then
which one of the following must be true?
(A)
(B)
(C)
(D)
(E)
Nilsson does not share a specialty with Paton.
Exactly one professor was hired in 1990.
Exactly one professor was hired in 1991.
Exactly two professors were hired in each of
two years.
Paton was hired at least one year before Sarkis.
Source: PrepTest 35, Section 3, Questions 18–23
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Tough Logic Games
Working the Numbers
To prepare for fieldwork, exactly four different researchers—a
geologist, a historian, a linguist, and a paleontologist—will
learn at least one and at most three of four languages—Rundi,
Swahili, Tigrinya, and Yoruba. They must learn the languages
according to the following specifications:
Exactly one researcher learns Rundi.
Exactly two researchers learn Swahili.
Exactly two researchers learn Tigrinya.
Exactly three researchers learn Yoruba.
Any language learned by the linguist or paleontologist is
not learned by the geologist.
Any language learned by the geologist is learned by the
historian.
How do you know that the arithmetic will be important in this game?
What else makes this game difficult?
How does the arithmetic allow you to make deductions?
Game Strategies
• Whenever a game’s Rules or Limitations involve numbers, do the arithmetic.
• Don’t stop deducing once you’ve done the math. Try to relate the numbers to the rest of
the game.
Source: PrepTest 28, Section 2, Game 2
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Identifying Difficult Questions
13. Which one of the following could be true?
(A)
(B)
(C)
(D)
(E)
The linguist learns three languages—
Rundi, Swahili, and Tigrinya.
The linguist learns three languages—
Swahili, Tigrinya, and Yoruba.
The historian learns three languages—
Rundi, Swahili, and Tigrinya.
The historian learns three languages—Swahili,
Tigrinya, and Yoruba.
The paleontologist learns three languages—
Rundi, Swahili, and Tigrinya.
14. If the linguist learns three of the languages, then which
one of the following must be true?
(A)
(B)
(C)
(D)
(E)
The linguist learns Tigrinya.
The linguist learns Rundi.
The linguist learns Swahili.
The paleontologist learns Rundi.
The paleontologist learns Swahili.
17. If the geologist learns exactly two of the languages, then
which one of the following could be true?
(A)
(B)
(C)
(D)
(E)
18. Which one of the following must be true?
(A)
(B)
(C)
(D)
(E)
15. Each of the following could be true of the researcher
who learns Rundi EXCEPT:
(A)
(B)
(C)
(D)
(E)
The researcher also learns Tigrinya but
not Swahili.
The researcher learns neither Tigrinya
nor Swahili.
The researcher also learns Tigrinya but
not Yoruba.
The researcher also learns both Tigrinya
and Yoruba.
The researcher also learns Yoruba but
not Tigrinya.
The paleontologist learns Rundi.
The paleontologist learns Swahili.
The historian learns Rundi.
The paleontologist learns exactly three of
the languages.
The historian learns exactly two of the languages.
Fewer of the languages are learned by
the historian than are learned by the
paleontologist.
Fewer of the languages are learned by the
geologist than are learned by the historian.
Fewer of the languages are learned by the
geologist than are learned by the linguist.
Fewer of the languages are learned by the
paleontologist than are learned by the linguist.
Fewer of the languages are learned by
the paleontologist than are learned by
the historian.
19. If exactly two of the languages are learned by the
historian, then which one of the following must be true?
(A)
(B)
(C)
(D)
(E)
The paleontologist does not learn Rundi.
The geologist does not learn Swahili.
The linguist does not learn Rundi.
The historian does not learn Rundi.
The paleontologist does not learn Swahili.
16. Each of the following could be a complete and accurate
list of the researchers who learn both Swahili and
Yoruba EXCEPT:
(A)
(B)
(C)
(D)
(E)
the historian
the paleontologist
the historian, the linguist
the historian, the paleontologist
the linguist, the paleontologist
Which questions deal with the numbers?
Which questions are easier, and which are more difficult?
Source: PrepTest 28, Section 2, Questions 6–12
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Tough Logic Games
Complicated Question Stems
15. Each of the following could be true of the researcher who
learns Rundi EXCEPT:
(A)
(B)
(C)
(D)
(E)
The researcher also learns Tigrinya but
not Swahili.
The researcher learns neither Tigrinya nor Swahili.
The researcher also learns Tigrinya but not Yoruba.
The researcher also learns both Tigrinya
and Yoruba.
The researcher also learns Yoruba but not Tigrinya.
How would you characterize the choices for this question?
Source: PrepTest 28, Section 2, Question 8
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16. Each of the following could be a complete and
accurate list of the researchers who learn both
Swahili and Yoruba EXCEPT:
(A)
(B)
(C)
(D)
(E)
the historian
the paleontologist
the historian, the linguist
the historian, the paleontologist
the linguist, the paleontologist
How would you characterize the choices for this question?
Source: PrepTest 28, Section 2, Question 9
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Tough Logic Games
Relating the Groups
A newly formed company has five employees—F, G, H, K, and
L. Each employee holds exactly one of the following positions:
president, manager, or technician. Only the president is not
supervised. Other employees are each supervised by exactly
one employee, who is either the president or a manager. Each
supervised employee holds a different position than his or her
supervisor. The following conditions apply:
There is exactly one president.
At least one of the employees whom the president
supervises is a manager.
Each manager supervises at least one employee.
F does not supervise any employee.
G supervises exactly two employees.
How are the different groups in this game related to each other?
Game Strategies
• Numbers are crucial in Distribution games, especially difficult ones.
• Difficult games take time, even for the best students; think about pacing before you
tackle a game like this early.
• The Limitations make this an impure game, but don’t let that throw you. The LSAT will
always give you all the information you need to answer the questions.
Source: PrepTest 14, Section 1, Game 1
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Try These at Home
20. Which one of the following is an acceptable assignment
of employees to the positions?
President
Manager
Technician
(A)
G
H, K, L
F
(B)
G
H
F, K, L
(C)
H
F, G
K, L
(D)
H, K
G
F, L
(E)
K
F, G, H, L
—
21. Which one of the following must be true?
(A)
(B)
(C)
(D)
(E)
There are at most three technicians.
There is exactly one technician.
There are at least two managers.
There are exactly two managers.
There are exactly two employees who supervise
no one.
22. Which one of the following is a pair of employees who
could serve as managers together?
(A)
(B)
(C)
(D)
(E)
F, H
F, L
G, K
G, L
K, L
23. Which one of the following could be true?
(A)
(B)
(C)
(D)
(E)
There is exactly one technician.
There are exactly two managers.
There are exactly two employees who are not
supervised.
There are more managers than technicians.
The president supervises all of the other
employees.
24. If F is supervised by the president, which one of the
following must be true?
(A)
(B)
(C)
(D)
(E)
G is the president.
H is the president.
L is a technician.
There is exactly one manager.
There are exactly two technicians.
25. If K supervises exactly two employees, which one of the
following must be true?
(A)
(B)
(C)
(D)
(E)
F is supervised by K.
G is a manager.
L is supervised.
There are exactly two managers.
There are exactly two technicians.
How do the Limited Options help you answer these questions?
Source: PrepTest 14, Section 1, Questions 1–6
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Tough Logic Games
The Minimum is a Must
The coordinator of an exhibition will select at least four and at
most six rugs from a group of eight rugs made up of two oval
wool rugs, three rectangular wool rugs, one oval silk rug, and
two rectangular silk rugs according to the following conditions:
At least two oval rugs must be selected.
The number of wool rugs selected can be neither less
than two nor more than three.
If the oval silk rug is selected, at least one rectangular
silk rug must be selected.
What, if anything, must be selected in this game?
Game Strategies
• Do the math to figure out what, at a minimum, must be selected.
• Don’t jot down every possibility.
• Make Formal Logic rules as concrete as possible.
Source: PrepTest A, Section 3, Game 4
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Working the Numbers
26. lf three wool rugs are selected, then any of the following
could be a complete and accurate list of the other rugs
selected EXCEPT:
(A)
(B)
(C)
(D)
(E)
one oval silk rug
one rectangular silk rug
two rectangular silk rugs
one oval silk rug and one rectangular silk rug
one oval silk rug and two rectangular silk rugs
27. If all three silk rugs are selected, then each of the
following could be a complete and accurate list of the
other rugs selected EXCEPT:
(A)
(B)
(C)
(D)
(E)
one oval wool rug
two oval wool rugs
one oval wool rug and one rectangular wool rug
one oval wool rug and two rectangular wool rugs
two oval wool rugs and one rectangular wool rug
How does our work with the numbers make these questions easier?
Source: PrepTest A, Section 3, Questions 19 and 23
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Tough Logic Games
Try These at Home
28. Which one of the following is an acceptable selection of
rugs for the exhibition?
(A)
(B)
(C)
(D)
(E)
one oval silk rug, one oval wool rug, and two
rectangular wool rugs
one oval silk rug, one rectangular wool rug, and
two rectangular silk rugs
two oval wool rugs, one rectangular silk rug, and
two rectangular wool rugs
two oval wool rugs, one rectangular silk rug, and
one rectangular wool rug
two rectangular silk rugs and three rectangular
wool rugs
29. The rugs selected for the exhibition can include any of
the following EXCEPT:
(A)
(B)
(C)
(D)
(E)
31. If exactly four rugs are selected, then the rugs selected
could be
(A)
(B)
(C)
(D)
(E)
one oval rug and three rectangular wool rugs
two oval rugs and two rectangular wool rugs
three oval rugs and one rectangular silk rug
three oval rugs and one rectangular wool rug
two rectangular silk rugs and two rectangular
wool rugs
32. If exactly six rugs are selected, they must include
(A)
(B)
(C)
(D)
(E)
exactly one of the oval rugs
the two oval wool rugs
the two rectangular silk rugs
exactly three of the rectangular rugs
all three rectangular wool rugs
one oval silk rug
two oval wool rugs
three oval rugs
two rectangular wool rugs
three rectangular wool rugs
30. If only one silk rug is selected for the exhibition, then
the other rugs selected must be a group made up of
(A)
(B)
(C)
(D)
(E)
one oval rug and two rectangular rugs
two oval rugs and one rectangular rug
two oval rugs and two rectangular rugs
two oval rugs and three rectangular rugs
three rectangular rugs
Source: PrepTest A, Section 3, Questions 18, 20–22, and 24
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