LSAT Logic Games : Four- & Five-Variable
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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.
Which racer could have potentially finished in first and potentially finished in last?
None of the other answers
Adam
Don
Eric
Bill
None of the other answers
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 #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.
What is the possible order of the six films?
Friday: Brothers, Forged
Saturday: Causes, Monarchy
Sunday: Above, Willow
Friday: Above, Willow
Saturday: Causes, Brothers
Sunday: Monarchy, Forged
Friday: Causes, Brothers
Saturday: Willow, Above
Sunday: Monarchy, Forged
Friday: Brothers, Above
Saturday: Monarchy, Causes
Sunday: Forged, Willow
Friday: Brothers, Above, Willow
Saturday: Causes, Monarchy
Sunday: Forged
Friday: Above, Willow
Saturday: Causes, Brothers
Sunday: Monarchy, Forged
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 #452 : Linear 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 Forged plays on Friday, what must be true?
Causes is played on Saturday.
Monarchy is played on Sunday.
Willow is played on Friday.
Brothers is played on Sunday.
Causes is played on Friday.
Monarchy is played on Sunday.
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 #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 Sunday night is cancelled, but the same restrictions apply, what could be the possible order of the six films?
Friday: Causes, Brothers, Forged
Saturday: Monarchy, Willow, Above
Friday: Brothers, Monarchy, Causes
Saturday: Forged, Willow, Above
Friday: Causes, Brothers
Saturday: Willow, Above, Forged, Monarchy
Friday: Brothers, Causes, Willow
Saturday: Forged, Above, Monarchy
Friday: Brothers, Willow, Above
Saturday: Causes, Monarchy, Forged
Friday: Brothers, Willow, Above
Saturday: Causes, Monarchy, Forged
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 #23 : 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
Two
One
Three
Four
Four
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 #24 : 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) may not be in the third position in the tour sequence?
Florida only
Texas and Illinois
New York and Florida
New York only
Illinois only
New York and Florida
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 #25 : 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
Florida and California
Florida only
Illinois and California
New York only
Illinois and California
Illinois and California can be in the most possible positions. Both Illinois and California may be in four possible positions.
Example Question #26 : 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.
If California is the first tour date, which position(s) can Florida be in?
Second or fifth
Fifth only
Fourth only
Second only
Fourth or fifth
Fifth only
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 #27 : Four & Five Variable
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?
Jennings
Sanchez
Howard
Robinson
None of the players
Sanchez
While no player could be the leader in each category at the same time, Sanchez could potentially be the leader in any category, including home runs, runs batted in, runs scored, doubles, and stolen bases.
Example Question #28 : Four & Five Variable
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.
In which category could any player potentially be the leader?
Runs
Doubles
Stolen Bases
None of the categories
Runs Batted In
None of the categories
There is no category in which any player could potentially be the leader. There is at least one player who could not be the leader in each category to choose from, as well as in home runs.
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