LSAT Logic Games › Solving grouping games
A softball coach is assigning seven players to either the outfield or infield. The players are Aaron, Bethany, Cameron, David, Esther, Faith, and Glenda. There must be at least three players in the infield and at least three players in the outfield. The following rules apply:
If Aaron is in the outfield, then Bethany is in the infield
Esther and Glenda cannot be assigned together to either the outfield or infield
Faith and Esther must be assigned together to either the infield or outfield
When Bethany is assigned to the infield, Esther is assigned to the outfield
Which of the following could be a list of the players in the outfield and infield?
Outfield: Bethany, Faith, Esther, David
Infield: Aaron, Glenda, Cameron
Outfield: Aaron, Bethany, Glenda
Infield: Esther, David, Cameron, Faith
Outfield: Bethany, Faith, Esther, Glenda
Infield: Aaron, David, Cameron
Outfield: Aaron, Faith, Glenda
Infield: Bethany, David, Cameron, Esther
Outfield: Glenda, Bethany
Infield: Aaron, David, Cameron, Esther, Faith
Each of the incorrect answers violates one or more of the rules. Carefully apply the rules to eliminate the incorrect answers.
A new grocery store is deciding which brands of candy bars to sell in its opening stock. The store will select exactly five of the following eight brands to stock: Brighter, Charm, Delico, Flare, Handy, Joyful, Little, and Prospine. The selection of brands must follow these conditions:
If both Charm and Flare are selected, Delico is also selected.
If Handy is selected, neither Brighter nor Flare is selected.
If Little is selected, Joyful is not selected.
Of the brands Brighter, Joyful, and Prospine, exactly two are selected.
If both Flare and Joyful are selected, which of the following is a pair of brands both of which could also be selected?
Charm and Prospine
Charm and Little
Brighter and Handy
Delico and Handy
Flare and Little
Since you know Flare is selected, based off the second global rule, you know that Handy is not selected (by the contrapositive, if Flare is selected, Handy is not selected). This allows you to eliminate the two answer choices that include Handy.
Also, since you know Joyful is selected, based off the third global rule, you know that Little is not selected. This allows you to eliminate the two answer choices that include Little.
You are left with the correct answer: Charm and Prospine. You can verify this by filling the two spots with Charm and Prospine, which leads to the final spot being filled by Delico (via the first global rule).
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
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).
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:
Kate and Ted
Fred and Greg
Helen and Kate
Lyle and Norm
Ted and Vickie
Kate and Ted cannot both be selected because:
If Kate is selected, then Norm must be selected.
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.
Eight students-- Alyssa, Brian, Craig, Denzel, Erica, Felicia, Ginny, and Harmony-- decide to break into two groups to study for their upcoming exam. Alyssa and Ginny are the only freshmen; everyone else is a sophomore, junior, or senior. Each group has four students, and they must abide by the following requirements:
If Craig is in Group 2, which of the following is not possible?
Denzel and Harmony are in the same group.
Brian and Felicia are in the same group.
Alyssa and Denzel are in the same group.
Felicia and Harmony are in the same group.
Erica and Harmony are in the same group.
Craig and Denzel are both in Group 2. Since Craig and Harmony cannot be in the same group, Harmony must be in Group 1. Therefore, Denzel and Harmony are not in the same group.
Exactly Eight Classrooms—A, B, C, D, E, F, G, and H—are going on a field trip. Each classroom will go to either the museum or the observatory but not both. Exactly four classrooms go to the museum together and four go to the observatory together. The following conditions apply to the trips:
If G goes to the Observatory, then B also goes to the Observatory.
If C goes to the Museum, then E goes to the Observatory.
B and H go together.
D goes to the Museum.
If C goes to the Museum, how many different possible groups of classrooms are there that go to the Museum?
Three
Four
Two
Five
Six
If C goes to the museum the possible games can be mapped out as follows:
Museum: A, C, D, F
Observatory: B, E, G, H
And,
Museum: C, D, G, __
Observatory: B, E, H, __
A and F can thus be switched creating two possibilities. Add these two possibilities to the first game shown for a total of three possible groups.
Five students—Max, Nancy, Pete, Raina, and Trig—will each learn to play exactly one of three instruments—cello, flute, or violin—in their first semester of school. The instrument each student plays will be based on the following conditions:
Max learns to play the same instrument as Nancy.
Pete and Raina do not learn to play the same instrument.
Trig learns to play either the cello or the flute.
If Pete learns to play the violin, Max also learns to play the violin.
Each student learns to play his/her instrument along with at least one other student.
Which one of the following could be false?
Raina must learn cello if Pete learns violin.
Nancy must learn violin if Pete learns violin.
Nancy learns the same instrument as exactly two of the other four students.
Trig learns the same instrument as exactly one of the other four students.
Trig learns an instrument with Pete or else with Raina.
For this problem, you are looking for an outcome that can be false. Another way of looking at this is something that can be untrue or something that could possibly not happen. If the outcome must be true then it is not the correct answer here.
"Nancy must learn violin if Pete learns violin" is always true, so this is not the correct answer. If Pete learns to play violin, the fourth global rule tells you that Max must also learn to play violin. Then, the first global rule tells you that Nancy must also learn to play violin. So this outcome cannot be false.
This also leads you to your correct answer: Raina must learn cello if Pete learns violin. You just showed that if Pete learns violin, Max and Nancy must also learn to play violin. This means that Raina and Trig must learn the same instrument, to keep with the fifth global rule.
Since the third global rule tells you that Trig can learn either cello or flute, the two of them could learn either instrument. Since they can learn to play flute, this makes the statement that "Raina must learn cello if Pete learns violin" a can-be-false outcome.
A zoo has four exhibition regions---labelled R, T, V, and W---and each region consists of a vegetarian wing and a carnivore wing. The following conditions apply:
Each exhibition wing houses only mammals or amphibians.
Three of the wings have mammals.
R's vegetarian wing and T's vegetarian wing house amphibians.
If an exhibition region has mammals in one of its wings, then the other wing in that exhibition region has amphibians.
If mammals are housed in V's carnivore wing, then W's vegetarian wing has mammals, too.
If mammals are housed in V's carnivore wing, which one of the following is a complete and accurate list of the wings that CANNOT house mammals?
R's vegetarian wing, T's vegetarian wing, V's vegetarian wing, W's carnivore wing.
R's vegetarian wing, T's vegetarian wing
R's vegetarian wing, T's vegetarian wing, V's vegetarian wing
R's vegetarian wing, T's vegetarian wing, W's carnivore wing
R's vegetarian wing, R's carnivore wing, T's vegetarian wing, V's vegetarian wing, W's carnivore wing
R and T's vegetarian wings are already designated locations for amphibians, so they are included in any correct response. Because mammals cannot occupy both wings, V's vegetarian wing cannot house mammals, since V's carnivore wing houses mammals. A rule dictates that if mammals are housed in V's carnivore wing, then W's vegetarian wing must house mammals. Therefore, mammals cannot be housed in V's vegetarian wing and W's carnivore wing, in addition to the wings already noted. Hence, the credited response is: R's vegetarian wing, T's vegetarian wing, V's vegetarian wing, W's carnivore wing.
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:Z, F
Table 2:W, Y, D, B, E
Table 3:X, C
Table 1: Y, W, C, E, B
Table 2: X, D
Table 3: Z, F
Table 1: X, W, C, D
Table 2: Z, E, B
Table 3: Y, 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
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.
A corporate conference is held with three breakout sessions: motivational interviewing (MI), sales optimizing (SO), and research and development (RD). Each of exactly five persons from one regional office---Nora, Oscar, Paul, Tim, and Vick---attend exactly one breakout session. The following conditions must apply:
Nora and Oscar do not attend the same breakout session.
Exactly two persons from the above-noted regional office attend the sales optimizing (SO) session.
Tim and Paul do not attend the same breakout session.
Neither Nora nor Oscar attend a session with Paul.
If Nora or Vick attend the MI session, then the other also attends that same session.
If Vick attends the SO session, then each of the following could be true EXCEPT:
Tim attends the SO session.
Oscar attends the MI session.
Nora attends the RD session.
Nora attends the SO session
Tim attends the MI session.
Tim cannot attend the SO session because the SO session only has two slots, and one slot is taken by Vick (by virtue of the question itself), and the other slot must be taken by Nora, Oscar, or Paul. The key deduction in this problem is the fact that Nora, Oscar, or Paul must occupy a single slot in each of the sessions, by virtue of the fact that none of them can attend the same session together.