LSAT Logic Games : Solving grouping games

Study concepts, example questions & explanations for LSAT Logic Games

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Example Questions

Example Question #591 : Lsat Logic Games

A saleswoman has exactly seven clients she must see by the end of February: Bruce, Cindy, Drew, Ellen, Gary, Harriet, and Karson. The saleswoman will see each of the seven clients exactly once by the February deadline according to the following guidelines:

            Either three or four of the clients must be seen in January. The remaining clients must be seen in February.

            Bruce cannot be seen in the same month as Cindy.

            Ellen must be seen in February.

            Harriet must be seen in the same month as Karson.

            If Drew is seen in January, Harriet must be seen in February.

If Karson is seen in February, which one of the following is a pair of clients who could also be seen in February?

Possible Answers:

Bruce and Cindy

Drew and Gary

Drew and Harriet

Cindy and Harriet

Bruce and Gary

Correct answer:

Cindy and Harriet

Explanation:

From the third global rule, you know Ellen must go in February. The question stem tells you Karson goes in February, and based on the fourth global rule, Harriet must also go in February.

You now have 3 people comitted to February, meaning only one spot is possibly open. Bruce and Cindy must go in different months. No matter who goes where, one must take the last February spot, and the other must go in January. Now that February is full, our two remaining clients - Drew and Gary - must go in January, the only month with room left:

January: Drew, Gary, Bruce or Cindy

February: Ellen, Karson, Harriet, Bruce or Cindy

The question asks you for a possible pair who can be seen together in February. You can eliminate the choice that pairs Bruce and Cindy, as they can never go together. You can eliminate the two answer choices that include Gary, since Gary must go in January. You can eliminate the remaining incorrect choice that includes Drew, since Drew must go in January.

This leaves you with the correct answer: Cindy and Harriet.

Example Question #91 : Solving Grouping Games

A saleswoman has exactly seven clients she must see by the end of February: Bruce, Cindy, Drew, Ellen, Gary, Harriet, and Karson. The saleswoman will see each of the seven clients exactly once by the February deadline according to the following guidelines:

            Either three or four of the clients must be seen in January. The remaining clients must be seen in February.

            Bruce cannot be seen in the same month as Cindy.

            Ellen must be seen in February.

            Harriet must be seen in the same month as Karson.

            If Drew is seen in January, Harriet must be seen in February.

Which one of the following must be true?

Possible Answers:

If Ellen is seen in February, Gary is seen in January.

Drew is seen in February, Gary is also seen in February.

If Karson is seen in February, Cindy is seen in January.

If Drew is seen in February, Karson is also seen in February.

If Karson is seen in February, Gary is seen in January.

Correct answer:

If Karson is seen in February, Gary is seen in January.

Explanation:

To eliminate the wrong answers in this problem, you need to show that they are not necessarily true given the global rules. You can do this by setting up a couple of hypothetical outcomes.

All outcomes must have Ellen in February, based on the third global rule.

Two of the answer choices start out with Drew in February. This puts Ellen and Drew in February, and Bruce and Cindy split up between the two months in some way. This means there is only room in January for the Harriet-Karson pair, as they must go together. There is room for Gary to go in January or February.

January: Harriet, Karson, Bruce or Cindy, [Gary]

February: Ellen, Drew, Bruce or Cindy, [Gary]

This allows you to eliminate "If Drew is seen in February, Gary is also seen in February" because it is possible for Drew to be in February and Gary to be in January. You can also eliminate "If Drew is seen in February, Karson is also seen in February" because it is possible for Drew to be in February and Karson to be in January.

Two of the answer choices start out with Karson in February. This puts Ellen and Karson in February, as well as Harriet in February because Harriet and Karson must go together. Bruce and Cindy will then be split up between the two months in some way, meaning February is full with four people. The remaining clients, Gary and Drew, must go in January:

January: Gary, Drew, Bruce or Cindy

February: Ellen, Karson, Harriet, Bruce or Cindy

This allows you to eliminate "If Karson is seen in February, Cindy is seen in January" because it is possible for Karson to be in February and Cindy to be in January.

This set-up tells you the correct answer is "Karson is seen in February, Gary is seen in January" because we started with Karson in February, and Gary was forced into January.

You can fully confirm this by drawing up another scenario to eliminate "If Ellen is seen in February, Gary is seen in January." You can create a possible set-up as such, to show Ellen and Gary can both go in February:

January: Harriet, Karson, Bruce or Cindy

February: Ellen, Gary, Bruce or Cindy, Drew

Example Question #92 : Solving Grouping Games

Seven college journalism students—Marco, Nora, Phillip, Roger, Sandra, Vicki, and Wallace—are required to write news items throughout the semester. For each of their news items, the students either write alone or with one another, in accordance with the following:

            Roger writes on every news item on which Marco writes.

            Marco writes on every news item on which Vicki writes.

            Phillip writes on every news item on which Nora does not write.

            Neither Phillip nor Sandra write on any news item on which Roger writes.

Which one of the following could be a complete and accurate list of the students who write together for a news item?

Possible Answers:

Marco, Nora, Sandra, Vicki

Nora, Phillip, Roger, Wallace

Marco, Phillip, Roger, Sandra

Marco, Sandra, Vicki, Wallace

Nora, Phillip, Sandra, Wallace

Correct answer:

Nora, Phillip, Sandra, Wallace

Explanation:

You can eliminate wrong answers here by checking against the global rules.

The first global rule tells you Roger must write on any news item on which Marco writes. So anywhere you see Marco, Roger must also be there (for it to be valid). You can eliminate two lists that break this rule: "Marco, Nora, Sandra, Vicki" and "Marco, Sandra, Vicki, Wallace."

The fourth global rule tells you if Roger writes on a news item, neither Philip nor Sandra can also write on that news item. You can eliminate "Marco, Phillip, Roger, Sandra" because it pairs Phillip and Sandra with Roger, breaking the global rule. You can also eliminate "Nora, Phillip, Roger, Wallace" because it pairs Phillip with Roger, breaking the global rule.

This leaves you with the correct answer: "Nora, Phillip, Sandra, Wallace" - which follows all global rules.

(Some might think the third global rule states that Phillip and Nora can never go together, but this is not the case. The global rule is actually stating that for each news item, at least one of Phillip or Nora must write - but it is also possible for both to write.)

Example Question #93 : Solving Grouping Games

Seven college journalism students—Marco, Nora, Phillip, Roger, Sandra, Vicki, and Wallace—are required to write news items throughout the semester. For each of their news items, the students either write alone or with one another, in accordance with the following:

            Roger writes on every news item on which Marco writes.

            Marco writes on every news item on which Vicki writes.

            Phillip writes on every news item on which Nora does not write.

            Neither Phillip nor Sandra write on any news item on which Roger writes.

What is the maximum number of students who could write on a news item on which Nora does not write?

Possible Answers:

three

five

two

four

six

Correct answer:

three

Explanation:

The question stem first tells you that Nora will not write for the news item at hand. Based on the third global rule, this means Phillip must write for this news item.

The fourth global rule tells you Phillip cannot write on any news item on which Roger writes. So based on the contrapositive of this rule, Roger cannot write on any news item on which Phillip writes - which is what's going on here. Thus, Roger cannot write on this news item.

From the first global rule, Roger must write on any news item on which Marco writes. Using the contrapositive, this means when Roger does not write on a news item, Marco also does not write on a news item. Thus, Marco cannot write on this news item.

From the second global rule, Marco must write on any news item on which Vicki writes. Using the contrapositive, this means when Marco does note write on a news item, Vicki also does not write on a news item. Thus, Vicki cannot write on this news item.

So far, in our goal of determining the maximum number of writers, we have shown that Nora, Roger, Marco, and Vicki all cannot write for this news item.

We know Phillip must write for this news item. No rules prohibit the remaining writers - Sandra and Wallace - from writing with Phillip. So our maximum number of writers for this news item is three.

Example Question #94 : Solving Grouping Games

Seven college journalism students—Marco, Nora, Phillip, Roger, Sandra, Vicki, and Wallace—are required to write news items throughout the semester. For each of their news items, the students either write alone or with one another, in accordance with the following:

            Roger writes on every news item on which Marco writes.

            Marco writes on every news item on which Vicki writes.

            Phillip writes on every news item on which Nora does not write.

            Neither Phillip nor Sandra write on any news item on which Roger writes.

If Vicki and Wallace write together on a news item, then exactly how many of the other students must also write on that news item?

Possible Answers:

zero

two

one

four

three

Correct answer:

three

Explanation:

Here we are looking for how many additional students must write on a news item on which Vicki and Wallace write.

The second global rule tells you that since Vicki writes on the news item, that Marco also writes on the news item. The first global rule tells you that since Marco writes on the news item, Roger also writes on the news item.

So far, the following write on this news item: Vicki, Wallace, Marco, Roger

The fourth global rule tells you that since Roger writes on this news item, Phillip and Sandra do not write on this news item.

The third global rule tells you that since Phillip does not write on this news item, Nora must write on this news item. This covers all of the students.

The following must write on this news item: Vicki, Wallace, Marco, Roger, Nora

The question asked for how many additional students write on this news item, so the correct answer is three.

Example Question #95 : Solving Grouping Games

Seven college journalism students—Marco, Nora, Phillip, Roger, Sandra, Vicki, and Wallace—are required to write news items throughout the semester. For each of their news items, the students either write alone or with one another, in accordance with the following:

            Roger writes on every news item on which Marco writes.

            Marco writes on every news item on which Vicki writes.

            Phillip writes on every news item on which Nora does not write.

            Neither Phillip nor Sandra write on any news item on which Roger writes.

If exactly three students write together on a news item, then each of the following could be true of that news item EXCEPT:

Possible Answers:

Marco and Roger both write on the news item.

Nora and Wallace both write on the news item.

Phillip and Wallace both write on the news item.

Marco and Wallace both write on the news item.

Nora and Sandra both write on the news item.

Correct answer:

Marco and Wallace both write on the news item.

Explanation:

Since the question stem ends with "EXCEPT," we are looking for the answer choice that cannot be true. You can go through and eliminate wrong answers (which in this case, are instances that can be true) by filling in possible 3-student scenarios.

Nora and Sandra can both write on this news item. A possible outcome is Nora, Sandra, and Phillip. Since this can be true, it is incorrect.

Marco and Roger can both write on this news item. A possible outcome is Marco, Roger, and Nora. Since this can be true, it is incorrect.

Nora and Wallace can both write on this news item. A possible outcome is Nora, Wallace, and Phillip. Since this can be true, it is incorrect.

You can use the same outcome of Nora, Wallace, and Phillip to prove that Phillip and Wallace can both write on this news item. Since this can be true, it is incorrect.

Marco and Wallace cannot write on the same news item. If Marco writes on a news item, so does Roger - giving you Marco, Roger, and Wallace. But at least either Phillip or Nora must write on every news item, and adding even just one of those two for this news item requires more than 3 students, which defies the limits set by the question's stem.

So this is your correct answer (remember the "EXCEPT" in the question stem): Marco and Wallace both write on the news item.

Example Question #96 : 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?

Possible Answers:

Outfield: Glenda, Bethany

Infield: Aaron, David, Cameron, Esther, Faith

Outfield: Aaron, Faith, Glenda

Infield: Bethany, David, Cameron, Esther

Outfield: Bethany, Faith, Esther, Glenda

Infield: Aaron, David, Cameron

Outfield: Bethany, Faith, Esther, David

Infield: Aaron, Glenda, Cameron

Outfield: Aaron, Bethany, Glenda

Infield: Esther, David, Cameron, Faith

Correct answer:

Outfield: Bethany, Faith, Esther, David

Infield: Aaron, Glenda, Cameron

Explanation:

Each of the incorrect answers violates one or more of the rules.  Carefully apply the rules to eliminate the incorrect answers.

Example Question #97 : 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 cannot be true?

Possible Answers:

Aaron, Bethany, and Glenda are in the infield

Cameron, David, and Faith are in the infield

Aaron, Glenda, and Cameron are in the infield

Glenda, Cameron, and David are in the infield

Cameron, David, and Bethany are in the infield

Correct answer:

Cameron, David, and Faith are in the infield

Explanation:

When Cameron, David, and Faith are in the infield, Esther must also be in the infield.  As a result, Aaron and Bethany both would need to be in the outfield.  However, when Aaron is in the outfield, Bethany must be in the infield.

Example Question #98 : 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

If the rules are changed so that there must be two players in the outfield and five in the infield, which of the following could be true?

Possible Answers:

Aaron is in the outfield

David is in the outfield

Bethany is in the outfield

Faith and Cameron are in the outfield

Esther and David are in the outfield

Correct answer:

Bethany is in the outfield

Explanation:

The key to this problem is to notice that there are only two options for the pair of players in the outfield--either Esther and Faith or Glenda and Bethany. If any other pair of players were in the outfield, one or more rules would need to be violated.

Example Question #605 : Lsat Logic Games

Three rock bands---Glee, Hellraiser, and Indigo---will be playing gigs at a music festival taking place over a three day period.  Each band must play at least one gig during the festival but never playing more than once on a given day.  At least one band must play on any given day.  There is only one stage for the musical performances.  The following restrictions apply:

On Day 1, Hellraiser performs and no other band plays after it.

On Day 2, either Glee or Indigo perform, and no other band plays after whichever of them performs.

On Day 3, either Glee or Hellraiser perform, and no other band plays after whichever of them performs.

Which one of the following could be a complete and accurate list of the bands playing, in the proper sequence?

Possible Answers:

Day 1:  Indigo, then Hellraiser; Day 2:  Indigo; Day 3:  Hellraiser

Day 1:  Hellraiser; Day 2:  Glee, then Indigo; Day 3:  Indigo, then Glee

Day 1:  Glee, then Hellraiser; Day 2:  Indigo, then Hellraiser; Day 3:  Hellraiser

Day 1:  Hellraiser; Day 2:  Indigo; Day 3:  Indigo, then Glee

Day 1:  Glee, then Hellraiser, then Indigo; Day 2:  Indigo; Day 3:  Glee

Correct answer:

Day 1:  Hellraiser; Day 2:  Indigo; Day 3:  Indigo, then Glee

Explanation:

Day 1:  Indigo, then Hellraiser; Day 2:  Indigo; Day 3:  Hellraiser  [This arrangement omits Glee, so it is invalid].

Day 1:  Hellraiser; Day 2:  Glee, then Indigo; Day 3:  Indigo, then Glee [Glee and Indigo cannot both play on Day 2---either one or the other plays.  So this arrangment can be eliminated.]

Day 1:  Glee, then Hellraiser, then Indigo; Day 2:  Indigo; Day 3:  Glee [This arrangement violates the restriction for Day 1 that Hellraiser plays last].

Day 1:  Glee, then Hellraiser; Day 2:  Indigo, then Hellraiser; Day 3:  Hellraiser [This arrangement violates the restriction for Day 2 that no band follow either Glee or Indigo, whichever of those two happen to be playing on that day.]

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