LSAT Logic Games : Solving two-variable logic games

Study concepts, example questions & explanations for LSAT Logic Games

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Example Questions

Example Question #81 : Solving Two Variable Logic Games

Three circus performers—Flo, Genie, and Kyle—will perform the following six circus acts: acrobatics; ball juggling; clowning; dunking; elephant demonstrations; fire twirling. Each act is performed only once in any given show, and only one act is performed at a time. The following conditions dictate the sequencing of these acts:

  • Flo performs exactly one act before Genie performs any of her acts
  • Flo does not perform first and he does not perform last
  • Genie does not do acrobatics and ball juggling
  • Kyle does not do acrobatics and elephant demonstrations
  • Ball juggling is performed immediately after the elephant demonstrations

If Kyle performs last, then which of the following must be true?

Possible Answers:

Genie does elephant demonstrations immediately before Kyle performs.

Genie performs some time after Kyle and Flo.

Genie performs second.

Genie performs immediately after Kyle.

Flo does ball juggling.

Correct answer:

Genie performs some time after Kyle and Flo.

Explanation:

This question calls for an answer that reflects what must happen, not what could happen.  We know that Kyle must go first, so Kyle occupies slots 1 and 6.  We know that Flo must go before Genie performs her first act.  So Genie cannot occupy slot 2.  That means Genie must perform after some time after Kyle and Flo, which is the credited response.

Example Question #343 : Linear Games

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

If Carlos dances on Monday, what must be true?

Possible Answers:

Eric dances on Tuesday.

Nicole dances on Wednesday.

Olivia dances on Thursday.

Ben dances on Tuesday.

Michelle dances on Thursday.

 

Correct answer:

Olivia dances on Thursday.

Explanation:

If Carlos dances on Monday, then Ben dances on Wednesday. Since Olivia dances one day after Ben, she must dance on Thursday.

Example Question #81 : Two Variable

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

Which is a possible and accurate order in which the women dance during the week starting with Monday?

Possible Answers:

Michelle, Olivia, Patricia, Liza, and Nicole

Nicole, Michelle, Patricia, Liza, and Olivia

Patricia, Nicole, Olivia, Liza, and Michelle

 

Olivia, Michelle, Nicole, Patricia, and Liza

Michelle, Olivia, Nicole, Patricia, and Liza

Correct answer:

Michelle, Olivia, Nicole, Patricia, and Liza

Explanation:

The key is to figure out where Olivia and Nicole can go based on where Carlos and Ben can be placed with one day in between them. For example:

 

The men being ordered B __ C __ A means the women would be ordered __ O N __ __

 

Additionally, Olivia and Nicole could be placed as follows:

__ __ O N __        

__ N __ __ O

N __ __ O __

 

Using this information, one finds only the correct answer conforms to one of these placement patterns.

 

Example Question #82 : Two Variable

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

Which is a possible and accurate order in which the men dance during the week starting with Monday?

Possible Answers:

Ben, Eric, Carlos, David, and Adam

Carlos, David, Ben, Adam, and Eric        

Carlos, David, Eric, Ben and Adam

 

Eric, David, Carlos, Ben, and Adam    

Ben, David, Eric, Carlos, and Adam

Correct answer:

Ben, Eric, Carlos, David, and Adam

Explanation:

The question gives enough information to figure out where Adam, Ben, and Carlos can possibly go. Thus listing out of the possibilities we get:

            __ B __ C A

            __ C __ B A

            B __ C __ A

            C __ B __ A

 Using this information, one finds that only the correct answer conforms to one of these placement patterns.

Example Question #85 : Two Variable

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

If Adam and Olivia dance on the same day, what must not be true?

Possible Answers:

Michelle dances Thursday.

Olivia dances on Friday.

Nicole dances on Tuesday.

Nicole dances on Wednesday.

Michelle dances on Monday.

Correct answer:

Nicole dances on Wednesday.

Explanation:

If Adam and Olivia dance on the same day (Friday), then Ben dances on Thursday (one day before Olivia) and Carlos and Nicole must dance on Tuesday (they dance on the same day and there is a day in-between Ben and Carlos). Thus it must not be true that Nicole dances on Wednesday.

Example Question #82 : Solving Two Variable Logic Games

Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:

Ben dances one day before Olivia.

Carlos and Nicole attend class on the same day.

Adam dances on Friday.

There is exactly one day between the days Ben and Carlos dance.

Which is a possible and acceptable partial schedule for the week?

Possible Answers:

Monday: Eric and Michelle

Tuesday: Carlos and Nicole

Wednesday: Ben and Patricia

Monday: Ben and Michelle

Tuesday: David and Olivia

Wednesday: Carlos and Nicole

Monday: David and Patricia

Tuesday: Ben and Michelle

Wednesday: Adam and Olivia

Monday: Carlos and Nicole                               

Tuesday: David and Olivia

Wednesday: Ben and Patricia

Monday: David and Patricia

Tuesday: Carlos and Michelle

Wednesday: Eric and Nicole

Correct answer:

Monday: Ben and Michelle

Tuesday: David and Olivia

Wednesday: Carlos and Nicole

Explanation:

All of the incorrect answers break one of the constraits placed on the order. 

Monday: Carlos and Nicole                               

Tuesday: David and Olivia

Wednesday: Ben and Patricia

(Ben must dance one day before Olivia)

 

Monday: David and Patricia

Tuesday: Carlos and Michelle

Wednesday: Eric and Nicole

(Carlos and Nicole must dance on the same day)

 

Monday: David and Patricia

Tuesday: Ben and Michelle

Wednesday: Adam and Olivia

(Adam must dance on Friday)

 

Monday: Eric and Michelle

Tuesday: Carlos and Nicole

Wednesday: Ben and Patricia

 (The must be one day between Ben and Carlos)

 

Example Question #82 : Two Variable

Five friends: Lenny, Monica, Nathan, Olivia, and Peter, take turns doing the following five chores: dishes, sweeping, mopping, dusting, and trash removal. Each person does exacly one chore, and each chore is done by exactly one person. To determine which friend does each chore, they apply the following rules:

  • Lenny cannot sweep.
  • Peter must either dust or mop.
  • If Monica does dishes, then Lenny does trash removal.
  • If Olivia does not do trash removal, then Peter dusts.

If Monica does dishes, which of the following must be true?

Possible Answers:

Nathan does trash removal.

Peter dusts.

Olivia sweeps.

Peter mops.

Nathan sweeps.

Correct answer:

Peter dusts.

Explanation:

Since Monica does dishes, Lenny does trash removal. Therefore, Olivia does not do trash removal, so Peter dusts.

Example Question #83 : Two Variable

Five friends: Lenny, Monica, Nathan, Olivia, and Peter, take turns doing the following five chores: dishes, sweeping, mopping, dusting, and trash removal. Each person does exacly one chore, and each chore is done by exactly one person. To determine which friend does each chore, they apply the following rules:

  • Lenny cannot sweep.
  • Peter must either dust or mop.
  • If Monica does dishes, then Lenny does trash removal.
  • If Olivia does not do trash removal, then Peter dusts.

If Peter mops, all of the following are possible except:

Possible Answers:

Monica dusts.

Nathan sweeps.

Lenny dusts.

Nathan does dishes.

Monica does dishes.

Correct answer:

Monica does dishes.

Explanation:

Since Peter mops, he does not dust. Employing the contrapositive of the last statement (ie: P -> Q means ~Q -> ~P), if Peter does not dust, then Olivia does trash removal. This means that Lenny does not do trash removal, so (again, employing the contrapositive), Monica does not do dishes.

Example Question #81 : Solving Two Variable Logic Games

A college is having an event for alumni who graduated in the years 2005-2010, inclusive. Six friends-- Harry, Inez, Jack, Katie, Lou, and Maria-- attend the event.
  • Katie graduated in 2006.
  • Harry and Maria graduated the same year.
  • Nobody graduated in 2007.
  • Katie graduated before Jack, but after Lou.

If Inez is the only person who graduated in 2010, and Jack did not graduate the same year as Maria, which of the following could be a correct assessment of each person's graduation year?

Possible Answers:

Lou ('05), Katie ('06), Harry ('08), Maria ('08), Jack ('09), Inez ('10)

Lou ('05), Katie ('06), Maria ('08), Jack ('09), Harry ('09), Inez ('10)

Lou ('05), Katie ('06), Jack ('08), Maria ('10), Harry ('10), Inez ('10)

Lou ('05), Katie ('06), Jack ('07), Harry ('08), Maria ('08), Inez ('10)

Lou ('05), Katie ('06), Jack ('06), Harry ('08), Maria ('08), Inez ('10)

Correct answer:

Lou ('05), Katie ('06), Harry ('08), Maria ('08), Jack ('09), Inez ('10)

Explanation:

Lou ('05), Katie ('06), Harry ('08), Maria ('08), Jack ('09), Inez ('10) is the only sequence of possibilities among the given choices that adheres to all the requirements.

Example Question #83 : Solving Two Variable Logic Games

A family is having a yard sale and pricing each type of item at $0.25, $0.50, $1.00, or $2.00. The types of items they sell are: books, CDs, dolls, flowerpots, paintbrushes, and towels.

  • Flowerpots cost at least as much as dolls.
  • The total price of one doll with one CD is less than the total price of one doll with one book.
  • Books are the same price as paintbrushes.
  • Towels cost $2.00.

If books cost $0.50 and dolls cost more than books, which of the following could be true?

Possible Answers:

CDs are the same price as dolls.

Flowerpots are the same price as CDs.

Flowerpots are the same price as towels.

Paintbrushes are the same price as dolls.

Towels are the same price as CDs.

Correct answer:

Flowerpots are the same price as towels.

Explanation:

Since dolls cost more than books, dolls must cost either $1.00 or $2.00.

  • If dolls cost $1.00, flowerpots cost either $1.00 or $2.00 because flowerpots cost at least as much as dolls.
  • If dolls cost $2.00, flowerpots cost $2.00 for the same reason.

In either case, flowerpots could cost $2.00 (the same price as towels).

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