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

## Example Questions

### Example Question #21 : Four & Five Variable

Adam, Bill, Chris, Don, Eric, Fred, and George ran in a race.  There were no other competitors and there were no ties.  The ranking of the racers met the following conditions:

Fred finished before Eric and George.

Bill and Adam finished consecutively with Bill finishing before Adam.

Chris finished before George but after Don.

Adam finished before Chris.

Assume Don finished fifth.  How many racers could potentially have finished first?

Three

One

Two

Four

None of the other answers

Two

Explanation:

The correct answer is: Two.

Don finished before Chris.  Adam, and therefore Bill, also finished before Chris.  Chris finished before George.  If Don finished fifth, Chris must have finished sixth and George must have finished seventh.  Bill, Adam, Fred and Eric remain.  Adam could not have been first because Bill finished before him.  Eric could not have finished first because Fred finished before him.  Bill and Fred, meanwhile, could have finished first.  Therefore, the correct answer is two.

### Example Question #21 : Solving Four And Five Variable Logic Games

Adam, Bill, Chris, Don, Eric, Fred, and George ran in a race.  There were no other competitors and there were no ties.  The ranking of the racers met the following conditions:

Fred finished before Eric and George.

Bill and Adam finished consecutively with Bill finishing before Adam.

Chris finished before George but after Don.

Adam finished before Chris.

Which racer could have potentially finished in first and potentially finished in last?

Bill

Eric

Don

None of the other answers

None of the other answers

Explanation:

The correct answer is: None of the other answers.

Bill could have finished first but could not have finished last because Bill had to finish in front of Adam.  Eric could have finished last but could not have finished first because Fred had to finish before Eric.  Don could have finished first but could not have finished last because Chris had to finish after Don.  Finally, Adam could not have finished first or last because he had to finish behind Bill and ahead of Chris.  In fact, no racer could have potentially finished first and also potentially finished last.  Therefore, the correct answer is no one or "none of the other answers."

### Example Question #21 : Solving Four And Five Variable Logic Games

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.

What is the possible order of the six films?

Friday: Above, Willow

Saturday: Causes, Brothers

Sunday: Monarchy, Forged

Friday: Brothers, Above, Willow

Saturday: Causes, Monarchy

Sunday: Forged

Friday: Brothers, Forged

Saturday: Causes, Monarchy

Sunday: Above, Willow

Friday: Brothers, Above

Saturday: Monarchy, Causes

Sunday: Forged, Willow

Friday: Causes, Brothers

Saturday: Willow, Above

Sunday: Monarchy, Forged

Friday: Above, Willow

Saturday: Causes, Brothers

Sunday: Monarchy, Forged

Explanation:

First, consider what we're given. Forged cannot be played on a night by itself; we can delete that answer. Willow and Above must be played on the same evening, so we can delete the answer where they're not. Monarchy must be played directly after Brothers, so delete the answer where that is not the case. And lastly, Brothers and Forged cannot be played on the same evening. Delete that. We are left with the correct answer choice.

### Example Question #22 : 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 Forged plays on Friday, what must be true?

Brothers is played on Sunday.

Willow is played on Friday.

Monarchy is played on Sunday.

Causes is played on Saturday.

Causes is played on Friday.

Monarchy is played on Sunday.

Explanation:

Let's look at the question. It asks what must be true, not what can be true. In this scenario, Willow can be played on any of the days, so it does not have to be played on Friday. The same goes for Causes: it can be played on Friday or Saturday, so does not have to be played on Friday specifically or on Saturday specifically. Based on the information, because Brothers cannot play on the same night as Forged, it cannot play Friday night. But it must play one night before Monarchy, so it cannot play on Sunday night either, and it must be played on Saturday. Thus, Monarchy can and must be played on Sunday night since it must be played the night directly after Brothers.

### Example Question #21 : Solving Four And Five Variable Logic Games

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 Sunday night is cancelled, but the same restrictions apply, what could be the possible order of the six films?

Friday: Brothers, Causes, Willow

Saturday: Forged, Above, Monarchy

Friday: Causes, Brothers

Saturday: Willow, Above, Forged, Monarchy

Friday: Causes, Brothers, Forged

Saturday: Monarchy, Willow, Above

Friday: Brothers, Monarchy, Causes

Saturday: Forged, Willow, Above

Friday: Brothers, Willow, Above

Saturday: Causes, Monarchy, Forged

Friday: Brothers, Willow, Above

Saturday: Causes, Monarchy, Forged

Explanation:

Looking at our restrictions, we know that there can be no more than three movies played each night. We can delete the answer choice with four movies on Saturday night. We also know that Monarchy must be played directly after Brothers. Delete the answer where it is not. Willow and Above must be played the same night. Delete the answer where they are not. And lastly, Brothers and Forged cannot be played the same night. Delete that answer choice. We are thus left with one answer choice, and it abides by all of our restrictions.

### Example Question #21 : Four & Five Variable

A popular band is preparing for a nationwide music tour.  The tour must include the following five states: California, Florida, Illinois, New York, and Texas.  The tour will conclude in one state before moving to the next state.  The following restrictions apply to the tour dates:

The tour must start in New York or California.

Texas cannot be the final state.

Texas and Illinois must be consecutive, with either coming first.

Florida must be after New York.

New York and California must not be consecutive to each other.

How many possible positions in the tour sequence can California be in?

Five

One

Two

Three

Four

Four

Explanation:

California can be in four possible positions: First, Third, Fourth, and Fifth.  California cannot be in second, because then New York would be first and the two cannot be consecutive to each other.

### Example Question #22 : Solving Four And Five Variable Logic Games

A popular band is preparing for a nationwide music tour.  The tour must include the following five states: California, Florida, Illinois, New York, and Texas.  The tour will conclude in one state before moving to the next state.  The following restrictions apply to the tour dates:

The tour must start in New York or California.

Texas cannot be the final state.

Texas and Illinois must be consecutive, with either coming first.

Florida must be after New York.

New York and California must not be consecutive to each other.

Which state(s) may not be in the third position in the tour sequence?

Florida only

New York and Florida

Texas and Illinois

New York only

Illinois only

New York and Florida

Explanation:

New York and Florida cannot be in the third position.  If New York is in the third position, then California must be first, and either Florida will not be after New York or Texas and Illinois will not be consecutive to each other.  Florida cannot be in the third position because then either New York or California will be consecutive to each other, or Texas and Illinois will not be consecutive to each other.

### Example Question #21 : Four & Five Variable

A popular band is preparing for a nationwide music tour.  The tour must include the following five states: California, Florida, Illinois, New York, and Texas.  The tour will conclude in one state before moving to the next state.  The following restrictions apply to the tour dates:

The tour must start in New York or California.

Texas cannot be the final state.

Texas and Illinois must be consecutive, with either coming first.

Florida must be after New York.

New York and California must not be consecutive to each other.

Which state(s) can be in the most possible positions in the tour sequence?

California only

Illinois and California

New York only

Florida only

Florida and California

Illinois and California

Explanation:

Illinois and California can be in the most possible positions.  Both Illinois and California may be in four possible positions.

### Example Question #22 : Solving Four And Five Variable Logic Games

A popular band is preparing for a nationwide music tour.  The tour must include the following five states: California, Florida, Illinois, New York, and Texas.  The tour will conclude in one state before moving to the next state.  The following restrictions apply to the tour dates:

The tour must start in New York or California.

Texas cannot be the final state.

Texas and Illinois must be consecutive, with either coming first.

Florida must be after New York.

New York and California must not be consecutive to each other.

If California is the first tour date, which position(s) can Florida be in?

Fourth or fifth

Fourth only

Fifth only

Second or fifth

Second only

Fifth only

Explanation:

If California is the first tour date, then Florida cannot be second, third, or fourth.  Therefore, Florida may only be in the fifth position.

### Example Question #23 : Solving Four And Five Variable Logic Games

Four baseball players are the leaders in five statistical categories.  Each player is the leader in at least one category.  The players are Howard, Jennings, Robinson, and Sanchez.  The categories are home runs (HR), runs batted in (RBI), runs scored (R), doubles (2B), and stolen bases (SB).  You are aware of the following facts regarding the players' statistics:

Howard hit more home runs than Robinson.

Sanchez had more runs scored than Howard.

Jennings finished last in the categories of home runs and runs batted in.

Robinson had twice as many stolen bases as Jennings.

Sanchez hit more doubles than Robinson and Howard.

Which player could potentially be the leader in any (not each) category?

Robinson

Jennings

Sanchez

Howard

None of the players