LSAT Logic Games : Solving grouping games
Study concepts, example questions & explanations for LSAT Logic Games
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Example Questions
Example Question #191 : Grouping Games
Each of seven baseball players—G, H, K, L, M, N, and O—will be placed on the active roster for one of two teams, the Angels and the Reds. The following conditions govern the roster with respect to these players.
If G is on the roster for the Angels, then H will play for the Reds.
If K plays for the Angels, then L and M will play for the Reds.
N plays on a different team than O.
M plays on a different team than G.
If O plays for the Angels, then H will also play for the Angels.
If G and L are both on the roster for the Angels, then all of the following are true, EXCEPT?
K is on the roster for the Reds.
Only two of the players are on the roster for the Angels.
M is on the roster for the Reds
N is on the roster for the Angels.
Only three of the players are on the roster for the Angels.
Only two of the players are on the roster for the Angels.
If G and L are on the roster for the Angels, then:
H must be on the roster for the Reds by virtue of the first condition.
K cannot be on the roster for the Angels by virtue of the second condition (K and L can't both play for the Reds).
O can't be on the roster for the Angels, because the fifth condition states that if O plays for the Angels, so does H, which can't be true given the first condition. Furthermore, N must be on the roster for the Angels because N can't be on the same team as O.
M must be on the Reds' roster because the fourth condition states M and G can't be on the same team.
When all permutations are accounted for, it is clear that only three players can be assigned to the Angels if G and L are on that roster.
Example Question #701 : Lsat Logic Games
The university philosophy department is holding a dinner for a select group of professors and students, each of whom has exactly one seat at exactly one of the three available tables-- 1, 2, and 3. There are four professors-- W, X, Y, and Z-- and five students-- B, C, D, E, and F. The seating arrangements must adhere to the following conditions without exception:
There is at least one professor and one student at each of the three tables.
Two of the tables seat two individuals, and one of the tables seats five individuals.
If W is at a table with C, then E is at a table with B.
If D is at a table with B, then X is not sitting with E.
F is never sitting at a table with more than one professor.
W always sits at the table with the most seated individuals.
Y is always sitting at a higher-numbered table than Z.
Which of the following is an acceptable seating arrangement?
Table 1: Y, W, C, E, B
Table 2: X, D
Table 3: Z, F
Table 1: W, Z, C, D, F
Table 2: Y, E
Table 3: X, B
Table 1: W, X, C, B, D
Table 2: Z, E
Table 3: Y, F
Table 1: X, W, C, D
Table 2: Z, E, B
Table 3: Y, F
Table 1:Z, F
Table 2:W, Y, D, B, E
Table 3:X, C
Table 1:Z, F
Table 2:W, Y, D, B, E
Table 3:X, C
This is a relatively easy question that simply tests your basic grasp of the game rules. Each of the incorrect answers breaks one or more rules in some way.
Table 1: Y, W, C, E, B
Table 2: Z, D
Table 3: X, F
This arrangement breaks the rule that Y must be at a higher numbered table than Z.
Table 1: X, W, C, D
Table 2: Z, E, B
Table 3: Y, F
This arrangement breaks the rule that there must always be more students than professors at any given table. There are an equal number of professors and students at Table 1.
Table 1: W, Z, C, D, F
Table 2: Y, E
Table 3: X, B
This arrangement breaks the rule that F never sits with more than one professor.
Table 1: W, X, C, B, D
Table 2: Z, E
Table 3: Y, F
This arrangement breaks the rule that E and B sit at the same table if W and C do.
Example Question #702 : Lsat Logic Games
The university philosophy department is holding a dinner for a select group of professors and students, each of whom has exactly one seat at exactly one of the three available tables-- 1, 2, and 3. There are four professors-- W, X, Y, and Z-- and five students-- B, C, D, E, and F. The seating arrangements must adhere to the following conditions without exception:
There is at least one professor and one student at each of the three tables.
Two of the tables seat two individuals, and one of the tables seats five individuals.
If W is at a table with C, then E is at a table with B.
If D is at a table with B, then X is not sitting with E.
F is never sitting at a table with more than one professor.
W always sits at the table with the most seated individuals.
Y is always sitting at a higher-numbered table than Z.
If W is seated at Table 3, then which two individuals MUST be seated at the same table?
E and B
Z and F
X and C
C and B
W and X
E and B
It is possible to simply brute force this answer, however, it is possible to reason it out as well.
W is at the largest table, and the largest table always has two professors and three students (since the large table seats 5 and must accommodate two professors in order to get all of the professors seated with at least one professor and one student at each table). Z may never sit at Table 3, since Y must be seated at a higher table.
F never sits with more than one professor, so he doesn't sit at this table (and he also never sits with W). Thus, W sits with three of B, C, D, and E. If W sits with C, then E and B must also sit together. Groups of multiple students must sit with W. So, Table 3 MUST contain C, E and B if C is seated with W. Either X or Z may sit as well, but that doesn't really matter for this question.
If W does NOT sit with C, then we are left with D, E, and B which can also make valid diagrams.
Between C, E, and B and D, E, and B, E and B are the common factors. W, E, and B always sit together (this is, in fact, true regardless of whether or not they sit at Table 3).
Example Question #703 : Lsat Logic Games
The university philosophy department is holding a dinner for a select group of professors and students, each of whom has exactly one seat at exactly one of the three available tables-- 1, 2, and 3. There are four professors-- W, X, Y, and Z-- and five students-- B, C, D, E, and F. The seating arrangements must adhere to the following conditions without exception:
There is at least one professor and one student at each of the three tables.
Two of the tables seat two individuals, and one of the tables seats five individuals.
If W is at a table with C, then E is at a table with B.
If D is at a table with B, then X is not sitting with E.
F is never sitting at a table with more than one professor.
W always sits at the table with the most seated individuals.
Y is always sitting at a higher-numbered table than Z.
If W and X are sitting together, then how many possible valid seating arrangements are there?
1
5
3
4
2
2
If W and X are sitting together, then they must also be sitting with C, E, and B. (See previous answer explanation.)
Y always sits at a higher table than Z, so no matter which table W and X are sitting at, there is only one possible arrangement for Y and Z. (e.g. If W and X sit at Table 1, then Z sits at Table 2 and Y sits at Table 3. If W and X sit at Table 2, then Z sits at Table 1 and Y sits at Table 3, etc.)
The remaining letters, D and F can both sit with either Y or Z. Thus, there are two possible valid seating arrangements if X and W sit at the same table.
Example Question #704 : Lsat Logic Games
The university philosophy department is holding a dinner for a select group of professors and students, each of whom has exactly one seat at exactly one of the three available tables-- 1, 2, and 3. There are four professors-- W, X, Y, and Z-- and five students-- B, C, D, E, and F. The seating arrangements must adhere to the following conditions without exception:
There is at least one professor and one student at each of the three tables.
Two of the tables seat two individuals, and one of the tables seats five individuals.
If W is at a table with C, then E is at a table with B.
If D is at a table with B, then X is not sitting with E.
F is never sitting at a table with more than one professor.
W always sits at the table with the most seated individuals.
Y is always sitting at a higher numbered table than Z.
Which of the following two individuals can never sit at the same table together?
F and Z
C and D
W and Y
E and B
X and E
C and D
Because F never sits at the big table, W must sit with one other professor and three students out of B, C, D, and E. If C and D were to sit together, they MUST sit at the large table with W, since every other table seats one professor and one student. If C sits with W, then E and B must sit with W as well, since, again, no other table can accommodate a block of multiple students. Since there must be two professors at the large table, W, ?, C, B, and E completely fills the table with no room for D. C and D can never sit together.
Example Question #705 : Lsat Logic Games
The university philosophy department is holding a dinner for a select group of professors and students, each of whom has exactly one seat at exactly one of the three available tables-- 1, 2, and 3. There are four professors-- W, X, Y, and Z-- and five students-- B, C, D, E, and F. The seating arrangements must adhere to the following conditions without exception:
There is at least one professor and one student at each of the three tables.
Two of the tables seat two individuals, and one of the tables seats five individuals.
If W is at a table with C, then E is at a table with B.
If D is at a table with B, then X is not sitting with E.
F is never sitting at a table with more than one professor.
W always sits at the table with the most seated individuals.
Y is always sitting at a higher numbered table than Z.
Which of the following conditions, if added to the existing set of conditions, would still allow for a valid seating arrangement?
There are never more than two students seated together at a table.
E and F must be seated together.
If W and X are seated together at the same table, then D is seated with them at that table as well.
B is never seated at a table with more than one professor.
W and D must always sit together.
W and D must always sit together.
If W and D must always sit together, that simply collapses the possibilities for the large table to only W, Y, E, B, D. This is a valid seating arrangements.
[There are never more than two students seated together at a table.] Three students MUST be seated at the large table in order to accommodate all of the professors while maintaining the "at least one professor and one student at each table" rule.
[E and F must be seated together.] F always sits with one professor. E is not a professor, so F and E is not a valid seating arrangement for a small table with two seats. The large table with five seats MUST sit two professors in order to accomodate all of the professors.
[B is never seated at a table with more than one professor.] E and B MUST sit at the large table with W. The large table must seat two professors in order to accomodate them all.
[If W and X are seated together at the same table, then C is seated with them at that table as well.] If W and X are seated at the same table, then that table MUST have the arrangement W, X, C, E, B. If the arrangement was W, X, D, E, B, then we would be breaking the rule that X and E cannot sit together if D and B do.
Example Question #196 : Grouping Games
Six athletes -- Carter, Dalton, Engstrom, Franklin, Garcia, and Hooper -- are assigned to play for local sports teams. Each athlete will be assigned to play one of three sports -- basketball, rugby, or soccer. Two athletes are assigned to play each sport, and no athlete may play more than one sport. The assignments are subject to the following constraints:
If Carter and Dalton play the same sport, Engstrom and Garcia play the same sport.
Hooper cannot play soccer.
If Dalton plays rugby, then Garcia does not play basketball or rugby.
Carter and Hooper may play the same sport only if Engstrom plays soccer.
Dalton and Engstrom may play the same sport only if Garcia and Hooper play the same sport.
If Carter and Garcia both play basketball, then which one of the following must be true?
Franklin plays rugby.
Engstrom plays rugby.
Hooper plays soccer.
Engstrom plays soccer.
Dalton plays rugby.
Engstrom plays rugby.
Engstrom must play rugby under these circumstances. With Carter and Garcia playing basketball, Hooper must play rugby. Further, Dalton must play soccer because otherwise Garcia would have to play soccer. Engstrom, therefore, cannot play soccer because otherwise Garcia and Hooper would have to play the same sport. Thus, Engstrom and Hooper must play rugby, and Dalton and Franklin must play soccer.
Example Question #706 : Lsat Logic Games
Avery is selecting several lines of clothing to sell from her fashionable women's clothing boutique. She is selecting these clothing lines from the following seven fashion designers: A, B, C, D, E, F, and G. Each line of clothing has several items of women's wear. Avery selects clothing lines from among these seven designers according to the following conditions:
If she selects clothes from B, then she will not select any clothes from F.
If she selects clothes from D, then she will not select any clothes from E, but she will select clothes from F.
She will select clothes from F, so long as she selects clothes from E.
She also will select clothes from G if she selects clothes from F.
If she selects clothes from G, she will select clothes from F.
If she selects clothes from F, then she will select at least two clothing lines from F.
Which one of the following could be a complete and accurate list of the designers Avery selects from along with the number of clothing lines purchased from each of those designers?
One from A, one from E, one from F, two from G
One from A, one from B, one from D, three from F
Three from A, one from B, two from D
One from D, one from E, two from F, one from G
One from C, one from D, two from F, one from G
One from C, one from D, two from F, one from G
This is a twist on a typical grouping game. Essentially, it involves selecting what is "in" and what is "out." The best approach is to list the entities (the designers, in this case) and with each question, circle the ones that are "in" and cross out the ones that are "out." The rules are simply a series of conditional statements ("if-then" statements).
This is an "acceptability" question, so it is best to check each rule against the answer choices. By process of elimination (using each rule to eliminate choices that violate the rule), the correct list remains.
Example Question #191 : Solving Grouping Games
Avery is selecting several lines of clothing to sell from her fashionable women's clothing boutique. She is selecting these clothing lines from the following seven fashion designers: A, B, C, D, E, F, and G. Each line of clothing has several items of women's wear. Avery selects clothing lines from among these seven designers according to the following conditions:
If she selects clothes from B, then she will not select any clothes from F.
If she selects clothes from D, then she will not select any clothes from E, but she will select clothes from F.
She will select clothes from F, so long as she selects clothes from E.
She also will select clothes from G if she selects clothes from F.
If she selects clothes from G, she will select clothes from F.
If she selects clothes from F, then she will select at least two clothing lines from F.
If Avery does not purchase any clothing items from designer G, then it could be true that she selects clothing items from __________.
designers A and B
designers C and F
designers B and D
designers B and E
designers A and D
designers A and B
Start with the new rule—no G. The implication of that new rule: no F, D, and E. That eliminates all answer choices except the credited response.
Example Question #708 : Lsat Logic Games
Avery is selecting several lines of clothing to sell from her fashionable women's clothing boutique. She is selecting these clothing lines from the following seven fashion designers: A, B, C, D, E, F, and G. Each line of clothing has several items of women's wear. Avery selects clothing lines from among these seven designers according to the following conditions:
If she selects clothes from B, then she will not select any clothes from F.
If she selects clothes from D, then she will not select any clothes from E, but she will select clothes from F.
She will select clothes from F, so long as she selects clothes from E.
She also will select clothes from G if she selects clothes from F.
If she selects clothes from G, she will select clothes from F.
If she selects clothes from F, then she will select at least two clothing lines from F.
If Avery purchases clothing items from as many designers as possible, then she cannot select any clothing items from which one of the designers?
B
E
G
D
C
B
The question stem invokes a result, not a new rule. So, the task is to figure out how to achieve that mandated result. Look for the rule that limits the number of designers that can be selected. Rules that implicate F directly affect multiple other designers. If F is not selected, then D, E, and G will not be selected (deductions from the given rules). The credited response—B—precludes the selection of F, so B cannot be selected.
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