LSAT Logic Games : Solving two-variable logic games

Example Questions

Example Question #21 : Solving Two Variable Logic Games

A school is holding tryouts for seven athletes – Eric, Fred, Greg, Ian, John, Kevin, and Merlin – for the varsity and JV track teams. Which team the athletes can join is determined by their 40 yard dash time; the three fastest will join the varsity team and the four slowest the JV team, subject to the following conditions:

Fred has a faster time than Ian.
Eric has a faster time than Ian, but a slower time than Greg
Greg has a faster time than Fred, but a slower time than John.
Kevin is part of the JV team.

Which of the following could be an accurate list of the team rosters, arranged from fastest to slowest?

Varsity: John, Merlin, Ian;
JV: Greg, Fred, Eric, Kevin.

Varsity: Greg, John, Fred;
JV: Eric, Ian, Kevin, Merlin.

Varsity: Merlin, John, Greg;
JV: Kevin, Eric, Ian, Fred.

Varsity: John, Fred, Greg;
JV: Merlin, Eric, Ian, Kevin.

Varsity: John, Merlin, Greg;
JV: Fred, Eric, Kevin, Ian.

Varsity: John, Merlin, Greg;
JV: Fred, Eric, Kevin, Ian.

Explanation:

Each of the incorrect answers violates one of the stated conditions:

(Varsity: John, Fred, Greg;
JV: Merlin, Eric, Ian, Kevin.) - Greg has a faster time than Fred.

(Varsity: Merlin, John, Greg;
JV: Kevin, Eric, Ian, Fred.) - Fred has a faster time than Ian.

(Varsity: Greg, John, Fred;
JV: Eric, Ian, Kevin, Merlin.) - John has a faster time than Greg.

(Varsity: John, Merlin, Ian;
JV: Greg, Fred, Eric, Kevin.) - Ian has a slower time than both Fred and Greg.

The correct answer does not violate any of the conditions.

Example Question #21 : Two Variable

A school is holding tryouts for seven athletes – Eric, Fred, Greg, Ian, John, Kevin, and Merlin – for the varsity and JV track teams. Which team the athletes can join is determined by their 40 yard dash time; the three fastest will join the varsity team and the four slowest the JV team, subject to the following conditions:

Fred has a faster time than Ian.
Eric has a faster time than Ian, but a slower time than Greg
Greg has a faster time than Fred, but a slower time than John.
Kevin is part of the JV team.

If K has the fourth fastest recorded time, each of the following could have a slower time, EXCEPT:

Greg

Eric

Merlin

Ian

Fred

Greg

Explanation:

If one writes out the first three rules we get the following, shortening the names to initials:

F - I

G - E - I

J - G - F

Combining these three, we get:

J - G - E/F - I

If K has the fourth fastest recorded time, that means it has the first spot on the JV team and there are three athletes that can be slower than him. The only athlete not taken into account in the above model is M, who has no restrictions. As a result, the latest that J could be in this case is second since no other athlete can have a faster time than him.

The incorrect answers can all be placed on the JV team within the scope of the stated conditions.

Example Question #21 : Solving Two Variable Logic Games

A school is holding tryouts for seven athletes – Eric, Fred, Greg, Ian, John, Kevin, and Merlin – for the varsity and JV track teams. Which team the athletes can join is determined by their 40 yard dash time; the three fastest will join the varsity team and the four slowest the JV team, subject to the following conditions:

Fred has a faster time than Ian.
Eric has a faster time than Ian, but a slower time than Greg
Greg has a faster time than Fred, but a slower time than John.
Kevin is part of the JV team.

Which of the following athletes CANNOT be on the varsity team?

Ian

Merlin

Eric

Greg

Fred

Ian

Explanation:

Using the J - G - E/F - I combination of the first three rules, we can see that there are at least four athletes that must have faster times than Ian. As there are only three spots on the varsity team, it is impossible for Ian to be placed onto the varsity team in any scenario.

Example Question #21 : Solving Two Variable Logic Games

A school is holding tryouts for seven athletes – Eric, Fred, Greg, Ian, John, Kevin, and Merlin – for the varsity and JV track teams. Which team the athletes can join is determined by their 40 yard dash time; the three fastest will join the varsity team and the four slowest the JV team, subject to the following conditions:

Fred has a faster time than Ian.
Eric has a faster time than Ian, but a slower time than Greg
Greg has a faster time than Fred, but a slower time than John.
Kevin is part of the JV team.

If Merlin has the second fastest recorded time, which of the following must be true?

Ian has the seventh fastest recorded time.

Eric has the sixth fastest recorded time.

Greg has the third fastest recorded time.

Fred has the fourth fastest recorded time.

Kevin has the fifth fastest recorded time.

Greg has the third fastest recorded time.

Explanation:

Going off the J - G - E/F - I model, we see that the only unaccounted athletes are Merlin and Kevin. Since Kevin must be on the JV team and as a result, can only have the fourth spot as his fastest possible time, his placement has no effect on the side of the rule before E/F. Therefore, putting Merlin into the second spot produces the following rule:

J - M - G - E/F - I

The only answer choice that must be true is that Greg has the third fastest time, as it is the only spot that Kevin's placement on the JV team has no effect on.

Example Question #21 : Two Variable

A school is holding tryouts for seven athletes – Eric, Fred, Greg, Ian, John, Kevin, and Merlin – for the varsity and JV track teams. Which team the athletes can join is determined by their 40 yard dash time; the three fastest will join the varsity team and the four slowest the JV team, subject to the following conditions:

Fred has a faster time than Ian.
Eric has a faster time than Ian, but a slower time than Greg
Greg has a faster time than Fred, but a slower time than John.
Kevin is part of the JV team.

Which of the following is an accurate and complete list of the athletes that must be on the varsity team?

John, Greg, Merlin

John, Greg, Fred

Greg, Merlin

Greg, Eric

John, Greg

John, Greg

Explanation:

Again using the J - G - E/F - I combination of the first three rules, we are left with Kevin and Merlin as the remaining two wild cards. Since Kevin can only be part of the JV team, he can be at earliest the fourth fastest time, meaning he doesn't affect the J - G - E/F order, or at least, whichever of E or F comes first. Merlin, however, has no strings attached and can have any possible time. To eliminate the maximum number of choices, we can place him first, making a M - J - G - E/F order. In this scenario, both Eric and Fred will be on the JV team, but in every possible scenario, J and G are the only constants on the varsity team.

Example Question #21 : Solving Two Variable Logic Games

A school is holding tryouts for seven athletes – Eric, Fred, Greg, Ian, John, Kevin, and Merlin – for the varsity and JV track teams. Which team the athletes can join is determined by their 40 yard dash time; the three fastest will join the varsity team and the four slowest the JV team, subject to the following conditions:

Fred has a faster time than Ian.
Eric has a faster time than Ian, but a slower time than Greg
Greg has a faster time than Fred, but a slower time than John.
Kevin is part of the JV team.

If the rule that Kevin must be part of the JV team is replaced with one stating that Kevin must be part of the varsity team, which of the following must be true?

Eric is part of the JV team.

Fred is part of the varsity team.

Greg is part of the varsity team.

Merlin is part of the JV team.

Greg is part of the JV team.

Eric is part of the JV team.

Explanation:

Using the J - G - E/F - I combination of the last three rules, inserting Kevin into the first three means that only John is guaranteed to be on the varsity team, as inserting Merlin in any of the top three spots will push Greg into the JV team. Everyone after Greg in the J - G - E/F - I combination also must be part of the JV team since the only athletes that can be part of the varsity team now aside from John and Kevin are Greg and Merlin.

From this, we can determine the correct answer in that Eric must always be on the JV team, as there is no way for him to be on the varsity team.

Example Question #22 : Solving Two Variable Logic Games

Eight people are waiting for five buses at a bus stop. The eight people are Adrien, Brian, Carl, David, Eva, Faith, Glenda, and Henry. At least one person must get on each bus and everyone at the stop gets on one bus. The following conditions apply:

No more than two people get on any bus.

If two people get on the first bus, two people must get on the third bus.

Glenda gets on a bus alone.

Adrien must get on a bus with another person.

Only one person gets on the fourth bus.

David and Faith cannot get on the same bus.

Which of the following could be a list of the people who get on each bus?

1. Glenda; 2. David and Brian; 3. Adrien and Eva; 4. Henry; 5. Faith and Carl

1. Adrien and Eva; 2. Faith and Henry; 3. Glenda 4. David; 5. Brian and Carl

1. Glenda and David; 2. Faith; 3. Adrien and Eva; 4. Henry; 5. Brian and Carl

1. Adrien and Henry; 2. Glenda; 3. Eva and Faith 4. David and Carl; 5. Brian

1. Glenda; 2. David and Faith; 3. Adrien and Eva; 4. Carl; 5. Brian and Henry

1. Glenda; 2. David and Brian; 3. Adrien and Eva; 4. Henry; 5. Faith and Carl

Explanation:

This question requires only a straightforward application of the conditions because each of the incorrect answers directly violates one of the rules.  Carefully apply the rules to eliminate the incorrect answers.

Example Question #28 : Solving Two Variable Logic Games

Eight people are waiting for five buses at a bus stop. The eight people are Adrien, Brian, Carl, David, Eva, Faith, Glenda, and Henry. At least one person must get on each bus and everyone at the stop gets on one bus. The following conditions apply:

No more than two people get on any bus.

If two people get on the first bus, two people must get on the third bus.

Glenda gets on a bus alone.

Adrien must get on a bus with another person.

Only one person gets on the fourth bus.

David and Faith cannot get on the same bus.

If Adrien and David get on the first bus, and if Faith gets on the second bus alone, which of the following cannot be true?

Glenda gets on the fifth bus

Henry gets on the third bus

Carl gets on the third bus

Glenda gets on the fourth bus

Carl gets on the fifth bus

Glenda gets on the fifth bus

Explanation:

Since only one person got on the second bus and only one person got on the fourth bus, two people must get on each of the first, third, and fifth buses.  Since Glenda must get on a bus alone, she cannot be on the fifth bus.

Example Question #29 : Solving Two Variable Logic Games

Eight people are waiting for five buses at a bus stop. The eight people are Adrien, Brian, Carl, David, Eva, Faith, Glenda, and Henry. At least one person must get on each bus and everyone at the stop gets on one bus. The following conditions apply:

No more than two people get on any bus.

If two people get on the first bus, two people must get on the third bus.

Glenda gets on a bus alone.

Adrien must get on a bus with another person.

Only one person gets on the fourth bus.

David and Faith cannot get on the same bus.

Which of the following could be true?

Adrien and Henry get on the first bus and Faith gets on a bus alone

Adrien gets on the first bus while Glenda gets on the third

Adrien gets on the fourth bus

Adrien gets on a bus with Henry, Eva gets on a bus alone, and Brian and Carl get on a bus together

David and Faith each get on a bus alone

Adrien and Henry get on the first bus and Faith gets on a bus alone

Explanation:

You can eliminate several answer choices if you remember that only two people can get on a bus alone and one of those people must be Glenda.  Remember also that only one person can get on the fourth bus and that David and Faith cannot get on the same bus.  Faith can get on a bus alone, so long as Glenda is the only other one who does so, and Adrien can get on a bus with Henry.

Example Question #30 : Solving Two Variable Logic Games

Eight people are waiting for five buses at a bus stop. The eight people are Adrien, Brian, Carl, David, Eva, Faith, Glenda, and Henry. At least one person must get on each bus and everyone at the stop gets on one bus. The following conditions apply:

No more than two people get on any bus.

If two people get on the first bus, two people must get on the third bus.

Glenda gets on a bus alone.

Adrien must get on a bus with another person.

Only one person gets on the fourth bus.

David and Faith cannot get on the same bus.

If Adrien gets on the first bus, Henry gets on the fourth, and Carl gets on the second, which of the following must be true?

Eva, Brian, or both get on a bus after Carl

Eva or Brian get on the same bus as Henry

David, Faith, or both get on the third bus

Eva or Brian get on the same bus as Carl

David, Faith, or both get on the fifth bus