LSAT Logic Games : Grouping Games
Study concepts, example questions & explanations for LSAT Logic Games
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Example Questions
Example Question #71 : Grouping Games
A social psychologist is conducting a study involving six individuals who are from three regions in the country. Fred, Greg, and Helen are from the northeast. Kate, Lyle, and Norm are from the west. And Ted, Vickie, and Zach are from the south.
Due to certain demographic and other requirements for the study, the selection of these individuals for the study must meet the following conditions:
Fred and Helen are not both selected.
Norm and Ted are not both selected.
If Helen is selected, Kate must also be selected.
If Kate is selected, Norm must also be selected.
Each of the following is a pair of individuals that could be selected together EXCEPT:
Lyle and Norm
Ted and Vickie
Fred and Greg
Helen and Kate
Kate and Ted
Kate and Ted
Kate and Ted cannot both be selected because:
1) If Kate is selected, then Norm must be selected.
2) If Norm is selected, then Ted cannot be selected because Norm and Ted cannot both be selected together, according to one of the conditions.
Therefore, Kate and Ted cannot be selected together, for it leads to a violation of the condition that Norm and Ted cannot both be selected together.
Example Question #72 : Grouping Games
A social psychologist is conducting a study involving six individuals who are from three regions in the country. Fred, Greg, and Helen are from the northeast. Kate, Lyle, and Norm are from the west. And Ted, Vickie, and Zach are from the south.
Due to certain demographic and other requirements for the study, the selection of these individuals for the study must meet the following conditions:
Fred and Helen are not both selected.
Norm and Ted are not both selected.
If Helen is selected, Kate must also be selected.
If Kate is selected, Norm must also be selected.
If Norm is not selected, then who must also not be selected?
Zach
Fred
Greg
Helen
Lyle
Helen
If Helen is selected, then Kate must be selected. And if Kate is selected, Norm must be selected. Taking the contrapositives of both, we yield the inference that if Norm is not selected, then Kate is not selected; and if Kate is not selected, then Helen is not selected. Therefore, if Norm is not selected, then it follows that Helen cannot be selected.
Example Question #71 : Solving Grouping Games
A social psychologist is conducting a study involving six individuals who are from three regions in the country. Fred, Greg, and Helen are from the northeast. Kate, Lyle, and Norm are from the west. And Ted, Vickie, and Zach are from the south.
Due to certain demographic and other requirements for the study, the selection of these individuals for the study must meet the following conditions:
Fred and Helen are not both selected.
Norm and Ted are not both selected.
If Helen is selected, Kate must also be selected.
If Kate is selected, Norm must also be selected.
The selection of individuals must include:
at least two individuals from the west
exactly two individuals from the south
at least one individual from each of the regions
exactly two individuals from the northeast
at most two individuals from each of the regions
at least one individual from each of the regions
One quick way to answer this question is to canvas the responses from the previous questions (particularly the diagramming required for the other questions). But a more rigorous approach is to reason from the fact that there are only three "Out" slots and those three slots simply cannot be occupied by only individuals from one region. Any attempt to do this will reveal that some condition gets violated. Therefore, it must be true that at least one individual from each of the regions must be selected.
Example Question #71 : Solving Grouping Games
There are two movie theaters in the city of Aires, the Cineplex and the Triplex. The owners of these two movie theaters have made an arrangement as to the showing of various movie genres. There are exactly four genres that these owners have been discussing: action, comedy, drama, and horror.
The showing of movies within these genres must be in accord with the following:
Each movie theater must always show exactly three films from three of the four genres.
At least one of the theaters must show both an action film and a drama film.
Whichever theater shows a comedy film must also show a horror film.
The Cineplex always shows an action film.
If both theaters show a drama film, which one of the following could be true?
The Cineplex shows both an action film and a comedy film.
The number of action films is equal to the number of comedy films.
The Triplex shows both an action film and a comedy film.
The number of action films is greater than the number of drama films.
The number of comedy films is equal to the number of drama films.
The number of action films is equal to the number of comedy films.
This question calls for eliminating all the choices that must be false, leaving only one response that "could be true" (but need not necessarily be true).
The response specifying that action films are greater than drama films is absurd, since the question itself specifies that drama films are being shown in both theaters.
Likewise, the response that comedy films is equal to drama films must be rejected because there is no necessity to show comedy films in either theater; moreover, it would be impossible to show a comedy film in the Cineplex because there is only one empty slot---if that slot were filled with a comedy film, it would preclude adding in a horror film, which the rules require.
The above establishes that the Cineplex cannot show a comedy film, thus allowing us to eliminate the response that specifies that the Cineplex shows both an action and comedy film. The same reasoning allows us to reject the response that specifies that the Triplex shows both an action and comedy film, since doing so would violate the condition that a comedy film must bring with it a horror film.
This process of elimination leaves only the response that specifies that the number of comedy films equals the number of action films (namely, one of each). That arrangement could happen, though it need not happen (and thus, "could be true").
Example Question #75 : Solving Grouping Games
There are two movie theaters in the city of Aires, the Cineplex and the Triplex. The owners of these two movie theaters have made an arrangement as to the showing of various movie genres. There are exactly four genres that these owners have been discussing: action, comedy, drama, and horror.
The showing of movies within these genres must be in accord with the following:
Each movie theater must always show exactly three films from three of the four genres.
At least one of the theaters must show both an action film and a drama film.
Whichever theater shows a comedy film must also show a horror film.
The Cineplex always shows an action film.
Which one of the following could be true?
The number of comedy films is equal to the number of horror films.
The number of comedy films is greater than the number of drama films.
Both theaters are showing exactly the same three film genres.
Neither theater is showing a horror film.
Exactly one of the theaters is showing a horror film.
Both theaters are showing exactly the same three film genres.
The longer way to solve this particular question is to eliminate the responses that must be false (which is the flip-side of the task of finding the response that "could be true"). But it should be apparent that it is perfectly legitimate to have both theaters showing exactly the same film genres.
The comedy films cannot equal the horror films because both theaters must show horror films but only one can show a comedy film. The fact that only one theater can show a comedy film (at most) demonstrates that the number of comedy films cannot be greater than the number of drama films. These basic propositions that we can derive from the rules demands that we eliminate all of the responses except for the credited response.
Example Question #76 : Solving Grouping Games
A social psychologist is conducting a study involving six individuals who are from three regions in the country. Fred, Greg, and Helen are from the northeast. Kate, Lyle, and Norm are from the west. And Ted, Vickie, and Zach are from the south.
Due to certain demographic and other requirements for the study, the selection of these individuals for the study must meet the following conditions:
Fred and Helen are not both selected.
Norm and Ted are not both selected.
If Helen is selected, Kate must also be selected.
If Kate is selected, Norm must also be selected.
If all three individuals from the south are selected, which one of the following must be true?
All three of the individuals from the northeast are selected.
Exactly one individual from the northeast is selected.
Kyle is selected.
Lyle is selected.
Exactly two individuals from the west are selected.
Lyle is selected.
According to the question, Ted, Vickie, and Zach are selected (all southerners). Using contrapositives on the conditions set forth in this problem, we know that the "Out" group consists of Norm, Kate, and Helen (two westerners and and one northeasterner). Therefore, we can fill in the remaining "In" slots: F, G, and L.
All this reveals the correct response: Lyle is selected.
All of the other responses conflict with what we can deduce as to who is in the "In" group and who is in the "Out" group.
Example Question #73 : Grouping Games
A social psychologist is conducting a study involving six individuals who are from three regions in the country. Fred, Greg, and Helen are from the northeast. Kate, Lyle, and Norm are from the west. And Ted, Vickie, and Zach are from the south.
Due to certain demographic and other requirements for the study, the selection of these individuals for the study must meet the following conditions:
Fred and Helen are not both selected.
Norm and Ted are not both selected.
If Helen is selected, Kate must also be selected.
If Kate is selected, Norm must also be selected.
If Ted is selected, which one of the following is a pair of individuals who must be among the individuals selected?
Kate and Zach
Greg and Helen
Fred and Greg.
Lyle and Norm
Kate and Lyle
Fred and Greg.
With Ted selected, we can deduce who is in the "Out" group: Norm (because Norm and Ted cannot both be selected), as well as Kate and Helen (because selecting either one of those two will lead to the selection of Norm). This allows us to eliminate four of the responses---all the responses that contain Norm, Kate, or Helen. That leaves only the response, "Fred and Greg."
Example Question #74 : Grouping Games
Students are organizing a game of basketball. Two teams of four players are selected from eight students: Harold, Irene, Joe, Kevin, Laura, Maurene, Nate, and Oliver. The following conditions apply:
Laura cannot be on Team 2
If Nate is on Team 2, then Oliver must be on Team 1
Laura is on the same team as either Joe or Maurene, but not both
Kevin and Joe are on the same team
Which of the following could be true when Oliver is on Team 1?
Joe and Irene are on Team 1
Nate and Maurene are on Team 1
Kevin and Harold are on Team 1
Laura is on Team 2
Kevin and Maurene are on Team 1
Nate and Maurene are on Team 1
The key to this question is to recognize that Nate is not required to be on Team 2 when Oliver is on Team 1. When Nate is on Team 2, then Oliver must be on Team 1, but the reverse is not necessarily true.
Example Question #75 : Grouping Games
Students are organizing a game of basketball. Two teams of four players are selected from eight students: Harold, Irene, Joe, Kevin, Laura, Maurene, Nate, and Oliver. The following conditions apply:
Laura cannot be on Team 2
If Nate is on Team 2, then Oliver must be on Team 1
Laura is on the same team as either Joe or Maurene, but not both
Kevin and Joe are on the same team
If Maurene and Nate are on Team 2, which of the following cannot be true?
Harold is on Team 1
Harold is on Team 2
Oliver is on Team 1
Joe is on Team 1
Irene is on Team 2
Harold is on Team 1
When Nate is on Team 2, Oliver must be on Team 1. When Maurene is on team 2, Joe and Kevin also must be on Team 1. Of course, Laura always must be on Team 1. Since Oliver, Kevin, Joe, and Laura all must be on Team 1, Harold cannot be.
Example Question #76 : Grouping Games
Students are organizing a game of basketball. Two teams of four players are selected from eight students: Harold, Irene, Joe, Kevin, Laura, Maurene, Nate, and Oliver. The following conditions apply:
Laura cannot be on Team 2
If Nate is on Team 2, then Oliver must be on Team 1
Laura is on the same team as either Joe or Maurene, but not both
Kevin and Joe are on the same team
Which of the following could be a list of the students on each team?
Team 1: Harold, Joe, Kevin, Nate
Team 2: Oliver, Maurene, Laura, Irene
Team 1: Laura, Joe, Harold, Nate
Team 2: Oliver, Maurene, Kevin, Irene
Team 1: Laura, Joe, Kevin, Irene
Team 2: Oliver, Maurene, Harold, Nate
Team 1: Laura, Joe, Maurine, Oliver
Team 2: Nate, Kevin, Harold, Irene
Team 1: Laura, Joe, Kevin, Nate
Team 2: Oliver, Maurene, Harold, Irene
Team 1: Laura, Joe, Kevin, Nate
Team 2: Oliver, Maurene, Harold, Irene
Each of the incorrect answer choices directly violates one or more of the conditions. Carefully apply the rules to eliminate each incorrect answer choice.
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