LSAT Logic Games : Solving four- and five-variable logic games

Study concepts, example questions & explanations for LSAT Logic Games

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Example Questions

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Example Question #1 : Solving Four And Five Variable Logic Games

Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom.  Five trains are lined up, each a different color.  They are, from left to right:  Blue, Green, Orange, Red, and Yellow.  Each child plays with one train.  Caleb doesn't like orange or yellow colors.  At most one train separates Everett from his older brother Dan.  Amanda sits in between two boys.  Dan grabs the blue train right away and won't share.

Which train is Caleb playing with?

Possible Answers:

The orange train.

The blue train.

The green train.

The yellow train.

The red train.

Correct answer:

The red train.

Explanation:

Caleb doesn't like orange or yellow, so he can't be playing with those trains.  Dan is playing with the blue train.  Everett must be either next to Dan so that Everett is playing with the green train, or two spaces away, in which case Amanda must be playing with the green train because that would be the only way she could be between two boys.  That leaves the red train.

Example Question #1 : Solving Four And Five Variable Logic Games

Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom.  Five trains are lined up, each a different color.  They are, from left to right:  Blue, Green, Orange, Red, and Yellow.  Each child plays with one train.  Caleb doesn't like orange or yellow colors.  At most one train separates Everett from his older brother Dan.  Amanda sits in between two boys.  Dan grabs the blue train right away and won't share.

Who is playing with the yellow train?

Possible Answers:

Everett

Dan

Beatrice

Amanda

Caleb

Correct answer:

Beatrice

Explanation:

Dan is playing with the blue train.  Everett is playing with either the green or the orange train.  Caleb is playing with the red train.  Amanda is in between two boys so she can't be playing with the yellow train on the far right.  Beatrice is the only child who could be playing with the yellow train.

Example Question #2 : Four & Five Variable

Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom.  Five trains are lined up, each a different color.  They are, from left to right:  Blue, Green, Orange, Red, and Yellow.  Each child plays with one train.  Caleb doesn't like orange or yellow colors.  At most one train separates Everett from his older brother Dan.  Amanda sits in between two boys.  Dan grabs the blue train right away and won't share.

Which is a possible arrangement of children playing with trains?

Possible Answers:

Dan with the blue train, Amanda with the green train, Everett with the orange train, Caleb with the red train, and Beatrice with the yellow train.

Dan with the blue train, Amanda with the green train, Everett with the orange train, Beatrice with the red train, Caleb with the yellow train.

Everett with the blue train, Beatrice with the green train, Amanda with the orange train, Dan with the red train, and Everett with the yellow train.

Dan with the blue train, Caleb with the green train, Everett with the orange train, Amanda with the red train, and Beatrice with the yellow train.

Caleb with the blue train, Amanda with the green train, Everett with the orange train, Caleb with the red train, and Beatrice with the yellow train.

Correct answer:

Dan with the blue train, Amanda with the green train, Everett with the orange train, Caleb with the red train, and Beatrice with the yellow train.

Explanation:

Dan must be playing with the blue train.  Beatrice must be playing with the yellow train.  That excludes all other answer choices but one, which also meets all of the conditions.

Example Question #3 : Four & Five Variable

Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom.  Five trains are lined up, each a different color.  They are, from left to right:  Blue, Green, Orange, Red, and Yellow.  Each child plays with one train.  Caleb doesn't like orange or yellow colors.  At most one train separates Everett from his older brother Dan.  Amanda sits in between two boys.  Dan grabs the blue train right away and won't share.

If in addition to the above conditions, Amanda is three spaces away from Beatrice, which kids are playing with with trains?

Possible Answers:

Dan with blue train, Amanda with green train, Everett with orange train, Caleb with red train, and Beatrice with yellow train.

Dan with blue train, Beatrice with green train, Amanda with orange train, Everett with red train, and Caleb with yellow train.

Dan with blue train, Everett with green train, Amanda with orange train, Caleb with red train, and Beatrice with yellow train.

Everett with blue train, Dan with green train, Caleb with orange train, Amanda with red train, and Beatrice with yellow train.

Dan with blue train, Amanda with green train, Beatrice with orange train, Caleb with red train, and Everett with yellow train.

Correct answer:

Dan with blue train, Amanda with green train, Everett with orange train, Caleb with red train, and Beatrice with yellow train.

Explanation:

Dan is playing with the blue train.  In order for Amanda and Beatrice to be three spaces apart from each other, they must play with the green and the yellow train.  Amanda can't be on the end because she's in between two boys, so Amanda must be playing with the green train and Beatrice must be playing with the yellow train.  Everett can't be separated from Dan by more than one train, so he must then be playing with the orange train.  That leaves Caleb playing with the red train.

Example Question #4 : Four & Five Variable

Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom.  Five trains are lined up, each a different color.  They are, from left to right:  Blue, Green, Orange, Red, and Yellow.  Each child plays with one train.  Caleb doesn't like orange or yellow colors.  At most one train separates Everett from his older brother Dan.  Amanda sits in between two boys.  Dan grabs the blue train right away and won't share.

If Dan and Everett are playing immediately next to each other, then which train is Everett playing with?

Possible Answers:

The blue train.

The orange train.

The yellow train.

The red train.

The green train.

Correct answer:

The green train.

Explanation:

This is an easy question.  Dan must be playing with the blue train.  The green train is next to the blue train.

Example Question #5 : Four & Five Variable

Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom. Five trains are lined up, each a different color. They are, from left to right:  Blue, Green, Orange, Red, and Yellow. Each child plays with one train. Caleb doesn't like orange or yellow colors and refuses to take them. At most one train separates Everett from his older brother Dan. Amanda sits in between two boys. Dan grabs the blue train right away and won't share.

Which train could Amanda be playing with?

Possible Answers:

The orange train.

The yellow train.

The blue train.

The red train.

None of the above answers.

Correct answer:

The orange train.

Explanation:

Dan is playing with the blue train. Caleb must be playing with the red train. Either Amanda is between Dan and Everett in which case she is playing with the green train, or she is between Everett and Caleb in which case she is playing with the orange train. Only the orange train is listed as an answer choice.

Possibilities that fulfill these conditions if we leave Amanda out for the time being (which keeps things simpler):

Blue: Dan

Green: Everett?/Caleb?/Beatrice?

Orange: Everett?/Beatrice?

Red: Caleb?/Beatrice?

Yellow: Beatrice?

 

Since Amanda must be between two boys, she cannot take yellow, and since no one else but Beatrice can take yellow, we have to put Beatrice there; since Beatrice has taken yellow, Amanda cannot take red, since she would not be between two boys either, so we now have this situation:

 

Blue: Dan

Green: Everett?/Caleb?

Orange: Everett?

Red: Caleb? (not Amanda)

Yellow: Beatrice (not Amanda)

 

Here we see that Caleb is the only option for the red train, so we have to eliminate him from the green train:

 

Blue: Dan

Green: Everett?

Orange: Everett?

Red: Caleb

Yellow: Beatrice

 

Now Everett can take either the green or the orange train, and his choice also presents two legal choices for Amanda: orange and green. Orange is the only available choice in the answers.

Example Question #6 : Four & Five Variable

The directors of a movie festival are deciding the lineup of their six films: Causes, Brothers, Willow, Above, Forged, and Monarchy. The festival will span Friday, Saturday, and Sunday evenings. At least one movie must be played each night, and there can be no more than three played the same evening. No movie is played more than once. The directors have decided on the following:

Monarchy is played on the night directly after Brothers.
Willow is played on the same night as Above.
If Causes is played on Saturday, then Above is played on Friday.
Brothers and Forged do not play on the same night.
Forged does not play by itself.

If Causes is played on Saturday, what could be true?

Possible Answers:

Monarchy could be played on Friday.

Brothers could be played on Friday.

Willow could be played on Saturday.

Forged could be played on Saturday.

Forged could be played on Sunday.

Correct answer:

Forged could be played on Sunday.

Explanation:

Let's look at the question. It asks which of the answers has the posibility of being true; it does not ask which of the answers must be true. We know that Causes is played on Saturday. Given our guidelines, that means that Above must be played on Friday. So Willow must also be played on Friday night; it cannot be played on Saturday. We can delete that answer. We know that Brothers must play on the night directly before Monarchy, so we know that Monarchy can thus not play on the first night of the festival. So Monarchy cannot be played on Friday. Delete that answer.

We know so far that Above and Willow play on Friday night and that Causes plays on Saturday night. Say Brothers plays on Friday night. Then Monarchy must play on Saturday night and Forged must play on Sunday night by itself, but that is impossible, so we can delete that answer choice. Say Forged plays on Saturday night, instead. Then Monarchy must play on Sunday night and Brothers must play on Saturday night, but that is impossible because Brothers and Forged cannot play on the same night. Delete that answer.

We are left with one choice. If Forged plays on Sunday night, Monarchy can also play on Sunday night, and Brothers can play on Saturday night. This is possible, and thus this is the correct answer.

Example Question #3 : Four & Five Variable

The directors of a movie festival are deciding the lineup of their six films: Causes, Brothers, Willow, Above, Forged, and Monarchy. The festival will span Friday, Saturday, and Sunday evenings. At least one movie must be played each night, and there can be no more than three played the same evening. No movie is played more than once. The directors have decided on the following:

Monarchy is played on the night directly after Brothers.
Willow is played on the same night as Above.
If Causes is played on Saturday, then Above is played on Friday.
Brothers and Forged do not play on the same night.
Forged does not play by itself.

If Monarchy plays the same night as Above, what could be true?

Possible Answers:

Causes could be played on Saturday.

Causes could be played on the same night as Brothers.

Causes could play on Sunday.

Forged could play on Saturday.

Willow could be played on Friday.

Correct answer:

Causes could play on Sunday.

Explanation:

Let's look at the question. It asks us which answer choice has the possibility of being true, not which one must be true. We know so far that Monarchy, Above, and Willow must all play on the same night. Given that Monarchy cannot be played on the first night (since Brothers must be played before it), these movies must be played on either Saturday or Sunday night. Thus Willow cannot be played on Friday night. Delete that answer.

Now, if Monarchy, Above, and Willow do not play on Saturday, they play on Sunday night, and thus Brothers must play on Saturday night. But Forged cannot play on the same night as Brothers, so it cannot be played on Saturday night. Also, since Forged cannot be played by itself, Causes must always be played with Forged, and thus Causes cannot be played the same evening as Brothers. Delete that answer.

Causes can either be played on Friday or on Sunday. We have our answer.

Example Question #4 : Four & Five Variable

There are five students sitting in a row while eating ice cream in the cafeteria. The students are Abby, Ben, Connie, David, and Emma. Each is eating a different flavor of ice cream. The order of the ice cream flavors is: vanilla, chocolate, mint chocolate chip, strawberry, and coffee.

Abby is not eating either mint chocolate chip or coffee ice cream.
Ben is sitting next to Emma and is not sitting next to Connie.
David is separated from Connie by exactly one person.
David is eating the coffee ice cream.

Which ice cream is Emma eating?

Possible Answers:

Mint chocolate chip

Chocolate

Coffee

Strawberry

Vanilla

Correct answer:

Chocolate

Explanation:

We know that David is eating coffee ice cream, so we can rule that answer out. Also, we know that Connie is separated from David by exactly one person, so she must be eating the mint chocolate chip ice cream. Ben and Emma are sitting next to one another, so they must be in the first two spots. Since Ben is not sitting next to Connie, he must be first in line. So, Emma must be the second in line. Thus she is eating the chocolate ice cream.

Example Question #2 : Solving Four And Five Variable Logic Games

There are five students sitting in a row while eating ice cream in the cafeteria. The students are Abby, Ben, Connie, David, and Emma. Each is eating a different flavor of ice cream. The order of the ice cream flavors is: vanilla, chocolate, mint chocolate chip, strawberry, and coffee.

Abby is not eating either mint chocolate chip or coffee ice cream.
Ben is sitting next to Emma and is not sitting next to Connie.
David is separated from Connie by exactly one person.
David is eating the coffee ice cream.

Who is eating the strawberry ice cream?

Possible Answers:

Abby

Connie

Emma

Ben

David

Correct answer:

Abby

Explanation:

We know that David is eating the coffee ice cream, so we can immediately rule him out. We also know that Connie is exactly one seat away from David, so she must be eating the mint chocolate chip. We can rule her out. Ben and Emma are seated beside each other, so they must be the first two in line. The person seated between David and Connie must then be Abby, meaning that she is eating the strawberry ice cream.

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