Solving grouping games - LSAT

Card 0 of 2168

Question

A dance teacher is creating a set list for an upcoming dance recital. There must be five numbers, performed in sequence. The numbers can be solos, duets or trios, made up of eight students: Amy, Belle, Carrie, Dana, Linda, Monique, Nicole and Ona. Each student will perform only once and the set list must conform to the follwing conditions:

Amy and Ona must perform solo

Carrie cannot perform in the second number unless Belle performs in the fourth

Nicole and Linda must perform together

Ona must perform at some time before Dana

The first and fifth numbers must be solos

Which of the following must be true?

Answer

We can figure this one out from the initial set-up of the game. If we are placing eight dancers into five numbers, we know there has to be one girl in each spot. This takes care of five dancers. We have three left over. Our options are to place all three in different numbers, yielding a 1:1:2:2:2 ratio OR to place two in one number and one in another, yielding a 1:1:1:2:3 ratio. Therefore the only correct answer is that there is at most one trio.

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Question

The chairman of the board is creating a finance committee from a group of seven representatives: Harris, Innis, Jenkins, Kenzi, Lawrence, McHenry and Nin. The committe must conform to the following restrictions:

If Harris is chosen for the committee, Innis must also be chosen

If McHenry is chosen, Harris is not

If Nin is chosen, McHenry is also chosen but Innis is not

If Innis is chosen, Kenzi is also chosen

If Jenkins is not chosen, Harris is chosen

Which of the following is a possible complete and accurate list of representatives NOT chosen for the committee?

Answer

This is a simple list question turned inside out. In order to answer this question we need to figure out who is chosen for the committe in each answer and elminate answers based on rule violations. We know that Harris and McHenry cannot both be chosen and Nin and Innis cannot both be chosen. If Innis is chosen, Kenzi must also be chosen, as when Harris is chosen Innis must also be chosen. We also know that at least one of Harris and Jenkins must always be chosen, so any answer that has both of them out is wrong. The only correct possibility leaves this committee: Harris, Innis, Kenzi.

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Question

The chairman of the board is creating a finance committee from a group of seven representatives: Harris, Innis, Jenkins, Kenzi, Lawrence, McHenry and Nin. The committe must conform to the following restrictions:

If Harris is chosen for the committee, Innis must also be chosen

If McHenry is chosen, Harris is not

If Nin is chosen, McHenry is also chosen but Innis is not

If Innis is chosen, Kenzi is also chosen

If Jenkins is not chosen, Harris is chosen

If Harris is chosen for the committee, which of the following could be true?

Answer

We know that when Harris is chosen, Innis must also be chosen. If Innis is chosen, Kenzi must also be chosen. So the smallest possible group is Harris, Innis and Kenzi. Nin and Innis cannot both be chosen, so Nin cannot be in this group. McHenry and Harris cannot both be chosen, so McHenry also cannot be in this group. The only answer that could be true is that Jenkins is chosen - Jenkins does not have to be in this group but could be.

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Question

The chairman of the board is creating a finance committee from a group of seven representatives: Harris, Innis, Jenkins, Kenzi, Lawrence, McHenry and Nin. The committe must conform to the following restrictions:

If Harris is chosen for the committee, Innis must also be chosen

If McHenry is chosen, Harris is not

If Nin is chosen, McHenry is also chosen but Innis is not

If Innis is chosen, Kenzi is also chosen

If Jenkins is not chosen, Harris is chosen

What is the smallest possible number of representatives chosen for the committee?

Answer

We know that if Jenkins is not chosen, Harris is. Therefore if Harris is not chosen, Jenkins is. This means that we must always have at least one or the other of these two in the game. If Harris is chosen this leads to several other members being chosen as well, but if Jenkins is chosen he could be the only representative on the committee.

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Question

The chairman of the board is creating a finance committee from a group of seven representatives: Harris, Innis, Jenkins, Kenzi, Lawrence, McHenry and Nin. The committe must conform to the following restrictions:

If Harris is chosen for the committee, Innis must also be chosen

If McHenry is chosen, Harris is not

If Nin is chosen, McHenry is also chosen but Innis is not

If Innis is chosen, Kenzi is also chosen

If Jenkins is not chosen, Harris is chosen

If there are excatly three people on the committee, each of the following could be true EXCEPT:

Answer

The only answer that would exceed three people is Harris and Jenkins are both chosen. When Harris is chosen we must also choose Innis and then Kenzi. Choosing Jenkins as well would require four people to be on the committee. The other answers yield the following groups: Harris, Kenzi, Innis; Kenzi, Lawrence, Jenkins; Nin, McHenry, Jenkins; McHenry, Lawrence, Jenkins

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Question

The chairman of the board is creating a finance committee from a group of seven representatives: Harris, Innis, Jenkins, Kenzi, Lawrence, McHenry and Nin. The committe must conform to the following restrictions:

If Harris is chosen for the committee, Innis must also be chosen

If McHenry is chosen, Harris is not

If Nin is chosen, McHenry is also chosen but Innis is not

If Innis is chosen, Kenzi is also chosen

If Jenkins is not chosen, Harris is chosen

If Nin is chosen, which of the following is a complete and accurate list of all other possible representatives who could also be chosen?

Answer

To answer this question we start by choosing Nin. We then automatically choose McHenry and eliminate Innis. Because we have chosen McHenry, we eliminate Harris. Eliminating Harris forces us to choose Jenkins. All that are left are Kenzi and Lawrence, who could or could not be chosen. Therefore, if we wanted to create the largest possibly committee starting with Nin, we could add in McHenry, Jenkins, Lawrence and Kenzi.

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Question

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.

Which one of the following could be a complete and accurate list of who among these seven players are on the Angels roster?

Answer

A violates the condition that G and H can’t both be on the Angels roster.

B violates the condition that if O plays for the Angels, then H must also play for the Angels. H is missing.

C violates the condition that M and G must be on different teams—this roster forces M and G onto the Reds roster.

D violates the condition that N and O can’t be on the same team.

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Question

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.

Which one of the following pairs of players CANNOT both play for the Reds?

Answer

If N plays for the Reds, then O must play for the Angels (N and O can’t be on the same team). But if O plays for the Angles, then H must also play for the Angels. So H can’t be with N on the Reds.

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Question

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.

What is the maximum number of players from these seven players who can be on the Angels roster?

Answer

H, M, O, and L can fit onto the Angels roster but it is impossible to fit any more players without violating at least one condition.

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Question

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 L and N both play for the Angels, then which one of the following could be true?

Answer

If L and N play for the Angels, then we can deduce immediately that O and K must play for the Reds. That allows us to eliminate the other answers. Note that G and M must be on different teams, so that option cannot be the credited response.

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Question

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?

Answer

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.

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Question

Each of eight parking lot attendants – F, G, H, J, K, L, N, and O – must be assigned to watch exactly one of three levels – X, Y, and Z - of a multi-level parking facility. Assignments must be made in accordance with the following conditions:

Each level is watched by either two or three of the attendants.

H watches X.

Neither K nor O watches Y.

Neither K nor N watches the same level as J.

If G watches X, both N and O watch Z.

Which one of the following is a pair of attendants that can be assigned to watch level Y together?

Answer

Only the correct answer does not violate any of the conditions.

Neither {F, K} nor {J, O} can be correct because neither K nor O can watch Y (Condition 3).

{H, L} cannot be correct because H must watch X, not Y (Condition 2).

{J, N} cannot be correct because J and N cannot watch the same level (Condition 4).

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Question

Four children and four adults attend a baseball game and sit in two sections. At least three members of the group must sit in each section--prime seating and the bleachers. The adults were Matthew, Nora, Olga, and Peter. The children were Sara, Tania, Ulric, and Victor. The following rules apply:

There must be at least one adult in each section

Nora and Sara cannot sit in the same section

Nora and Ulric must sit in the same section

Matthew must sit in the prime section

If the rules are changed so that there must be two adults and exactly four people in each section, which of the following could not be true?

Answer

If Tania sits with Nora and Victor, then Ulric must sit in the same section. This cannot be the case because all four seats would be taken but there would be only one adult.

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Question

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?

Answer

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.

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Question

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?

Answer

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).

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Question

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?

Answer

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.

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Question

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?

Answer

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.

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Question

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?

Answer

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.

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Question

A museum must choose five stuffed birds to be shown in their newest exhibit. Their choices include an Albatross, a Bluebird, a Condor, a Diver, an Eagle, a Flamingo, a Gull and a Hummingbird. They must choose the group according to the following restrictions:

If the Diver is chosen, the Albatross is not

The Eagle is chosen only if the Flamingo is not

If the Flamingo is chosen, the Albatross and the Hummingbird are also chosen

If the Gull is chosen, either the Hummingbird or the Bluebird are chosen, but not both

Which of the following is a complete and accurate list of birds that could be shown in the exhibit?

Answer

From the first two rules we know that the Diver and the Albatross, and the Eagle and the Flamingo can never appear in the same group together, which eliminates two choices immediately. We also know that if the Flamingo is chosen, both the Albatross and the Hummingbird must also be chosen, eliminating another incorrect answer. The last rule tells us that if the Gull is chosen, either the Hummingbird OR the Bluebird must be chosen, but not both. Therefore, we can deduce that if both the Hummingbird AND Bluebird are chosen, the Gull is not. This eliminates the last contender, leaving only the correct answer.

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Question

A museum must choose five stuffed birds to be shown in their newest exhibit. Their choices include an Albatross, a Bluebird, a Condor, a Diver, an Eagle, a Flamingo, a Gull and a Hummingbird. They must choose the group according to the following restrictions:

If the Diver is chosen, the Albatross is not

The Eagle is chosen only if the Flamingo is not

If the Flamingo is chosen, the Albatross and the Hummingbird are also chosen

If the Gull is chosen, either the Hummingbird or the Bluebird are chosen, but not both

If the Flamingo is chosen, how many different groups are possible?

Answer

If the Flamingo is chosen, we immediately also choose the Albatross and the Hummingbird. This leaves only two spots to be filled. We can eliminate the Eagle because it cannot appear with the Flamingo, and we can eliminate the Diver because it cannot appear with the Albatross. We are left to choose from the Bluebird, the Condor and the Gull. If we choose the Gull, we cannot also choose the Bluebird - since the Hummingbird is already present, this situation would violate the rule involving the Gull. Therefore, we must chose either the Gull OR the Bluebird, and then flll the remaining spot with the Condor. The two distinct possibilities are: Flamingo, Albatross, Hummingbird, Condor and Gull OR Flamingo, Albatross, Hummingbird, Condor and Bluebird.

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