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Unformatted text preview: l Mapping Games Questions 1824 J, K, L, M, N, and O are square ski chalets of the same size,
which are positioned in two straight rows as shown below: JKL
row1:lll row2:lll
MNO J is directly opposite M; K is directly opposite N; and L is
directly opposite 0. After a snowstorm, residents shovel a
single continuous path that connects all of the chalets and
meets the following conditions:
The path is composed of ﬁve straight segments, each of
which directly connects exactly two of the chalets.
Each chalet is directly connected by a segment of the path
to another chalet.
No chalet is directly connected by segments of the path to
more than two other chalets.
No segment of the path crosses any other segment.
One segment of the path directly connects chalets J and N,
and another segment directly connects chalets K and L. 18. Which one of the following statements could be true? (A) One segment of the path directly connects chalets M and K. (B) One segment of the path directly connects chalets
M and L. (C) One segment of the path directly connects chalets
M and O. (D) One segment of the path directly connects chalets
J and K and another segment directly connects
chalets K and M. (B) One segment of the path directly connects chalets
O and L and another segment directly connects
chalets O and N. 19. If one segment of the path directly connects chalets K and
N, then the two chalets in which one of the following pairs
must be directly connected to each other by a segment? (A) J and K (B) K and O
(C) L and O
(D) M and N
(E) N and O 20. If a segment of the path directly connects chalets J and K,
then the two chalets in which one of the following pairs
must be directly connected to each other by a segment? (A) J and M
(B) K and N
(C) K and O
(D) L and O
(E) N and O 2 1. If one segment of the path directly connects chalets K and
0, then which one of the following statements could be
true? (A) Chalet J is directly connected to chalet M. (B) Chalet K is directly connected to chalet N. (C) Chalet L is directly connected to chalet O. (D) Chalet L is directly connected to exactly two
chalets. (E) Chalet 0 is directly connected to exactly one
chalet. 22. Which one of the following statements, if true, guarantees
that one segment of the path directly connects chalets M and N? (A) One segment of the path directly connects chalets
K and J. (B) One segment of the path directly connects chalets
N and O. (C) One segment of the path directly connects chalet
K and a chalet in row 2. (D) One segment of the path directly connects chalet
L and a chalet in row 2. (B) One segment of the path directly connects chalet
O and a chalet in row 1. 23. Which one of the following chalets cannot be directly
connected by segments of the path to exactly two other
chalets? (A) K
(B) L
(C) M
(D) N
(E) 0 24. If no segment of the path directly connects any chalet in
row 1 with the chalet in row 2 that is directly opposite it, then each of the following statements must be true
EXCEPT: (A) A segment of the path directly connects chalets M and N. (B) A segment of the path directly connects chalets N
and O. (C) Chalet L is directly connected to exactly one other
chalet. (D) Chalet N is directly connected to exactly two
other chalets. (E) Chalet 0 is directly connected to exactly two
other chalets.1 1 PT 4, Game 4 Mapping Games I Questions 13 19 Eight benchesiJ, K, L, T, U, X, Y, and Ziare arranged along the perimeter of a park as shown below: North West East South The following is true: 13. 14. J, K, and L are green; T and U are red; X, Y, and Z are
pink. The green benches stand next to one another along the
park’s perimeter. The pink benches stand next to one another along the
park’s perimeter. No green bench stands next to a pink bench. The bench on
the southeast comer is T. J stands at the center of the park’s north side. If T stands next to X, then T does not also stand next to L. Which one of the following benches could be on the
northeast corner of the park? (A) Z
(13) Y
(C) X
(D) T
(E) L Each of the following statements must be true EXCEPT: (A) The bench on the northwest corner is pink. (B) The bench on the northeast comer is green. (C) The bench on the southwest comer is pink. (D) The middle bench on the east side of the park is
green. (E) The middle bench on the west side of the park is
pink. 15. 16. 17. 18. 19. Which one of the following benches must be next to J? (A) K
(B) L
(C) T
(D) U
(E) X For which one of the following benches are there two and
no more than two locations either one of which could be
the location the bench occupies? (A) K
(B) T
(C) X
(D) Y
(E) Z If Z is directly north of Y, which one of the following
statements must be true? (A) J is directly west of K.
(B) K is directly east of U.
(C) U is directly north of X.
(D) X is directly south of J.
(E) Z is directly south of J. If Y is in the middle of the west side of the park, then the two benches in which one of the following pairs
CANNOT be two of the comer benches? (A) K and X
(B) K and Z
(C) L and U
(D) L and X
(E) L and Z If Y is farther south than L and farther north than T, then the benches in each of the following pairs must be next to
each other EXCEPT (A) J and L (B) K and T
(C) T and X
(D) U and Y
(E) x and z2 2 PT 6, Game 3 Mapping Games Questions 2024 A lake contains exactly ﬁve islandsiJ, K, L, M, Oiwhich
are unconnected by bridges. Contractors will build a network
of bridges that satisﬁes the following speciﬁcations:
Each bridge directly connects exactly two islands with each
other, and no two bridges intersect.
No more than one bridge directly connects any two islands.
No island has more than three bridges that directly connect
it with other islands.
J, K, and L are each directly connected by bridge with one
or both of M and O.
J is directly connected by bridge with exactly two islands.
K is directly connected by bridge with exactly one island.
A bridge directly connects J with O, and a bridge directly
connects M with O. 20. Which one of the following is a complete and accurate list
of the islands any one of which could be directly
connected by bridge with L ? (A) J, K (B) J, M (C) J, o (D) J, M, o
(E) J, K, M, o 21. Which one of the following could be true about the
completed network of bridges? (A) J is directly connected by bridge both with L and
with M. (B) K is directly connected by bridge both with M and
with O. (C) L is directly connected by bridge both with J and
with M. (D) M is directly connected by bridge with J, with K,
and with L. (E) O is directly connected by bridge with K, with L,
and with M. 22. 23. 24. If a bridge directly connects K with 0, then which one of
the following could be true? (A) No bridge directly connects L with M. (B) A bridge directly connects J with L. (C) A bridge directly connects L with O. (D) There are exactly three bridges directly
connecting L with other islands. (E) There are exactly two bridges directly connecting
O with other islands. If a bridge directly connects L with M and a bridge
directly connects L with 0, then which one of the
following must be true? (A) A bridge directly connects J with M. (B) A bridge directly connects K with M. (C) A bridge directly connects K with O. (D) There are exactly two bridges directly connecting
L with other islands. (E) There are exactly two bridges directly connecting
M with other islands. If no island that is directly connected by bridge with M is
also directly connected by bridge with 0, then there must
be a bridge directly connecting (A) J with L
(B) J with M
(C) K with o (D) L with M
(E) L with o3 3 PT 6, Game 4 Mapping Games I Questions 19724 Six cities are located within the numbered areas as follows: City City
1 2
City City
3 4
City City
5 6 Within the sixcity area there are exactly four hospitals, two jails, and two universities. These eight institutions are located as follows:
No institution is in more than one of the cities.
None of the cities contains more than one jail, and none
contains more than one university.
None of the cities contains both a jail and a university.
Each jail is located in a city that contains at least one
hospital. The universities are located in two cities that do not share a common boundary.
City 3 contains a university, and city 6 contains a jail. 19. Which one of the following could be true? (A) City 5 contains a university.
(B) City 6 contains a university.
(C) City 2 contains a jail. (D) City 3 contains a jail. (E) City 3 contains a hospital. 20. 21. 22. 23. 24. Which one of the following could be true? (A) City 1 contains exactly one hospital.
(B) City 1 contains exactly one university.
(C) City 2 contains exactly one jail. (D) City 5 contains exactly one university.
(E) City 6 contains exactly one university. Which one of the following is a complete and accurate list
of the cities any one of which could contain the jail that is
not in city 6? (A) l, 4 (B) 2, 4 (C) 4, 5 (D) l, 4, 5
(E) l, 2, 4, 5 If each of the six cities contains at least one of the eight
institutions, then which one of the following must be true? (A) There is a jail in city 1.
(B) There is a hospital in city 2.
(C) There is a hospital in city 3.
(D) There is a hospital in city 4.
(E) There is a jail in city 4. In which one of the following cities must there be fewer
than three hospitals? (A) 1
(B) 2
(C) 4
(D) 5
(E) 6 If one of the cities contains exactly two hospitals and
exactly one university, then which one of the following
lists three cities that might, among them, contain no
hospital? (A) 1, 3, 5
(B) 1, 4, 5
(C) 2, 3, 5
(D) 2, 4, 6
(E) 4, 5, 64 4 PT 9, Game 4 a Mapping Games Questions 713 The country of Zendu contains exactly four areas for radar
detection: R, S, T, and U. Each detection area is circular and
falls completely within Zendu. Part of R intersects T; part of S
also intersects T; R does not intersect S. Area U is completely
within R and also completely within T. At noon exactly four
planes J, K, L, Miare over Zendu, in a manner consistent
with the following statements: Each plane is in at least one of the four areas. J is in area S. K is not in any detection area that J is in. L is not in any detection area that M is in. M is in exactly one of the areas. 7. Which one of the following could be a complete listing of
the planes located in the four areas at noon, with each
plane listed in every area in which it is located? (A) R: J, L; S: J, M; T: L; U: L
(B) R: J, L; S: K; T: M; U: none
(C) R: K; S: J; T: L; U: M
(D) R: K, M; S: J, L; T: J; U: none
(E) R: M; S: J, K; T: J, L; U: none 8. If at noon K is within exactly two of the four areas, then
which one of the following CANNOT be true at that time? (A) J is within area T. (B) K is within area R.
(C) K is within area T.
(D) L is within area R.
(E) L is within area T. 9. Which one of the following is a complete and accurate list
of those planes any one of which could be within area T at noon? (A) M (B) J, L (C) J, L, M
(D) K, L, M
(E) J, K, L, M 10. Which one of the following statements CANNOT be true 11. 12. 13. at noon about the planes? (A) K is within area T.
(B) K is within area U.
(C) L is within area R.
(D) M is within area R.
(E) M is within area U. It CANNOT be true that at noon there is at least one plane
that is within both area (A) R and area T
(B) R and area U
(C) S and area T
(D) S and area U
(E) T and area U If at noon M is within area T, then which one of the
following statements CANNOT be true at that time? (A) J is within area T.
(B) L is within area R.
(C) L is within area S.
(D) K is within exactly two areas.
(E) L is within exactly two areas. If at noon plane L is within exactly three of the areas,
which one of the following could be true at that time? (A) J is within exactly two of the areas.
(B) J is within exactly three of the areas.
(C) K is within area S. (D) M is within area R. (E) M is within area T.5 5 PT 15, Game 2 Mapping Games a Questions 1419 Greenburg has exactly ﬁve subway lines: L1, L2, L3, L4, and
L5. Along each of the lines, trains run in both directions,
stopping at every station. Ll runs in a loop connecting exactly seven stations, their
order being RinconTonkaFrenchSemplainUrstine
QuetzalParkRincon in one direction of travel, and the
reverse in the other direction. L2 connects Tonka with Semplain, and with no other
station. L3 connects Rincon with Urstine, and with no other station. L4 runs from Quetzal through exactly one other station,
Greene, to Rincon.
L5 connects Quetzal with Tonka, and with no other station. 14. How many different stations are there that a traveler 15. starting at Rincon could reach by using the subway lines
without making any intermediate stops? (A) two
(B) three
(C) four
(D) ﬁve
(E) six In order to go from Greene to Semplain taking the fewest
possible subway lines and making the fewest possible
stops, a traveler must make a stop at (A) French
(B) Park
(C) Quetzal
(D) Rincon
(E) Tonka l6. 17. 18. 19. If L3 is not running and a traveler goes by subway from
Urstine to Rincon making the fewest possible stops, which
one of the following lists all of the intermediate stations in
sequence along one of the routes that the traveler could
take? (A) Quetzal, Tonka (B) Semplain, French (C) Semplain, Park (D) Quetzal, Park, Greene
(E) Semplain, French, Tonka In order to go by subway from French to Greene, the
minimum number of intermediate stops a traveler must
make is (A) zero
(B) one
(C) two
(D) three
(E) four If the tracks that directly connect Urstine and Quetzal are
blocked in both directions, a traveler going from Semplain
to Park and making the fewest possible intermediate stops
must pass through (A) French or Tonka (B) Greene or Urstine (C) Quetzal or Tonka (D) Quetzal or Urstine or both
(E) Rincon or Tonka or both If a sixth subway line is to be constructed so that all of the
stations would have two or more lines reaching them, the
stations connected by the new subway line must include at
least (A) French, Greene, and Park
(B) French, Greene, and Quetzal
(C) French, Greene, and Rincon
(D) Park, Tonka, and Urstine
(E) Park, Semplain, and Tonka6 6 PT 18, Game 3 MAPPING GAMES
PT 4, Game 4 PT 6, Game 3 PT 6, Game 4 PT 9, Game 4 PT 15, Game 2 PT 18, Game 3
pg 1 pg 2 pg 3 pg 4 pg 5 pg 6
18. E 13. E 20. D 19. E 7. D 14. C
19. C 14. A 21. C 20. A 8. A 15. C
20. D 15. D 22. B 21. D 9. E 16. A
21. A 16. A 23. B 22. D 10. E 17. C
22. A 17. D 24. A 23. B 11. D 18. E
23. C 18. B 24. A 12. E 19. A
24. B 19. C 13. A ...
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