LSAT Logic Games : Linear Games
Study concepts, example questions & explanations for LSAT Logic Games
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Example Questions
Example Question #1 : Linear Games
A library is holding a special five-day event honoring successful local writers. One writer will be invited to be a guest speaker for each night from Monday through Friday, and no writer will be asked to participate twice. The writers have each written books in only one of four different genres—science-fiction, mystery, historical fiction, and non-fiction. A, J, and X are all science-fiction writers. B and Y are both mystery writers. C and Z are both historical fiction writers. L is a non-fiction writer. The following conditions apply without exception:
At least one writer from each of science-fiction, mystery, historical fiction, and non-fiction will all be invited to speak on at least one night.
No two authors from the same genre will be invited to speak on the following night.
If C is invited to speak, then X is invited to speak on the following night.
If Y is invited to speak, then neither C nor A are invited to speak.
If X and J are both invited to speak, then neither will speak on either the first or last night.
If L and B are both invited to speak, then neither will speak on either the first or last night.
If A is invited to speak on Thursday, how many different writers could possibly be the invited speaker for Wednesday?
2
4
3
1
5
2
If A is invited, then we know that Y is NOT invited. If Y is NOT invited, we know that B MUST be invited, because he is the only remaining mystery writer. L is always invited.
Since B and L are both invited, they cannot speak on the first or last day. They must thus occupy two of either Tuesday, Wednesday, or Thursday. Since A is scheduled to speak on Thursday, they must both speak on either Tuesday or Wednesday and either L or B can speak on Wedneday.
Example Question #2 : Linear Games
A library is holding a special five-day event honoring successful local writers. One writer will be invited to be a guest speaker for each night from Monday through Friday, and no writer will be asked to participate twice. The writers have each written books in only one of four different genres—science-fiction, mystery, historical fiction, and non-fiction. A, J, and X are all science-fiction writers. B and Y are both mystery writers. C and Z are both historical fiction writers. L is a non-fiction writer. The following conditions apply without exception:
At least one writer from each of science-fiction, mystery, historical fiction, and non-fiction will all be invited to speak on at least one night.
No two authors from the same genre will be invited to speak on the following night.
If C is invited to speak, then X is invited to speak on the following night.
If Y is invited to speak, then neither C nor A are invited to speak.
If X and J are both invited to speak, then neither will speak on either the first or last night.
If L and B are both invited to speak, then neither will speak on either the first or last night.
If it is no longer necessary to invite at least one writer from every genre, which of the following is FALSE?
It is possible to invite ALL of the mystery writers.
It is possible to invite ALL of the science fiction writers.
It is possible to invite ALL of the non-fiction writers.
It is possible to invite ALL of the historical fiction writers.
It is possible to invite more historical fiction writers than writers of any other genre.
It is possible to invite ALL of the science fiction writers.
Writers of the same genre may not speak on consecutive nights. With only five slots to fill, two of the three science fiction writers must speak on Monday and Friday (e.g. A_J_X). If both X and J are invited (and they are, if we are inviting all of the science fiction authors), then at least one will be forced to speak on Monday or Friday, which is not allowed.
The modification of the rules is actually just a bit of a red herring, since all of the answer choices except for the one regarding science fiction writers is true regardless.
Example Question #3 : Linear Games
The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
Which of the following lists of five stops is a possible order of stops that the F train made at passenger stops in a single day?
Habermark, Terroire, Aberdeen, Ramrock, Basilica
Aberdeen, Basilica, Terroire, Ramrock, Habermark
Aberdeen, Basilica, Ramrock, Habermark, Terroire
Terroire, Basilica, Ramrock, Habermark, Aberdeen
Basilica, Habermark, Terroire, Aberdeen, Ramrock
Aberdeen, Basilica, Ramrock, Habermark, Terroire
The key insight necessary in order to answer this question is to realize that the question is asking about the stops the F train makes in an ENTIRE day (i.e. two complete loops of its route) rather than just a single route. Thus, you are not simply identifying a legal order of stops in a route, e.g. 1, 2, 3, 4, 5, but are also identifying possible orders BETWEEN the two routes, e.g. 3, 4, 5, 1, 2, 3. The question also specifies passenger stops, so the railyard is not really a consideration here.
[Habermark, Basilica, Terroire, Aberdeen, Ramrock]
Habermark and Basilica can never be consecutive stops.
[Aberdeen, Basilica, Terroire, Ramrock, Habermark]
There are at least two stops that the train stops at twice before stopping at Aberdeen for the second time. This is simply another way of saying that there are two stops that come before Aberdeen on a single loop of the route. This is a very useful insight for this game. If we rearrange the order of the stops so that Aberdeen is third, we get Ramrock, Habermark, Aberdeen, Basilica, Terroire. Aberdeen is earlier on the route than at least one of Ramrock or Habermark, but, with Aberdeen as third, both Ramrock and Habermark come before Aberdeen. Pushing Aberdeen to fourth or fifth does nothing to change this. Thus, this is an impossible list.
[Terroire, Basilica, Ramrock, Habermark, Aberdeen]
This is wrong for essentially the same reason as [Aberdeen, Basilica, Terroire, Ramrock, Habermark]. Rearranging this so that Aberdeen is third puts Ramrock and Habermark in an impossible position. These are both really exercises testing the understanding of there being two routes in a day versus one.
[Habermark, Terroire, Aberdeen, Ramrock, Basilica]
Habermark and Basilica are consecutive stops. Even if Habermark is actually the first stop and the order of the stops in the route is as listed, Habermark will be the next stop after Basilica when it starts the second loop. The conditions say that the train doesn't stop at the railyard-- it merely passes it-- and also specifies that the railyard is not considered a passenger stop. The question asks for passenger stops specifically.
Thus, [Aberdeen, Basilica, Ramrock, Habermark, Terroire] is the correct answer. It reflects the valid route of Habermark, Terroire, Aberdeen, Basilica, Ramrock.
Example Question #4 : Linear Games
The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
If Terroire is the fifth passenger stop, which of the following must be true?
There is exactly one stop between Habermark and Basilica.
Aberdeen is not the third stop.
Habermark is one of the first two stops.
Aberdeen and Ramrock are consecutive stops.
Basilica and Ramrock are consecutive stops.
Basilica and Ramrock are consecutive stops.
If Terroire is the fifth stop, then Ramrock and Basilica must be consecutive stops.
If Terroire is the fifth stop, then Aberdeen cannot be the fourth stop, because one of Ramrock or Habermark must come after Aberdeen. Aberdeen can never be earlier than the third stop. Thus, Aberdeen must be in the third stop.
_ _ A _ T
The fourth stop must be one of Habermark or Ramrock, because, again, at least one must come after Aberdeen.
_ _ A H/R T
That means that Basilica is one of the first two stops. However, because Basilica and Habermark are never consecutive stops, then Ramrock must be one of the first two stops as well, and Habermark is the fourth stop.
B/R B/R A H T
There is no more information to determine whether Basilica or Ramrock comes first, but it doesn't matter as they will be consecutive stops regardless. With this diagram, the other answers are obviously false. Habermark is always the fourth stop. Aberdeen is always the third stop. It is possible to make Basilica and Aberdeen consecutive instead of Ramrock and Aberdeen. It is possible for there to be two stops between Habermark and Basilica, by making Basilica be the first stop.
Example Question #5 : Linear Games
The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
What is the maximum possible number of passenger stops between Habermark and Basilica in a single day?
2
4
3
1
5
2
The maximum number of stops is 2. The largest distance around a circle is from a single point back to itself. In this case, the maximum possible number of stops is four. (Count how many numbers there are between the 1s: 1 2 3 4 5 1). The maximum possible number of stops between two different points is three; this is the case if the two are adjacent to each other (Count how many numbers there are between 1 and 2: 2 3 4 5 1).
Habermark and Basilica, however, cannot be adjacent. There must be at least one stop between them. This means that the maximum possible number of stops between them is two. (Count how many numbers there are between 1 and 3: 3 4 5 1 2 3).
Example Question #6 : Linear Games
The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
If the stops were numbered from 1 to 5 from earliest to latest, which stop has the least possibilities regarding which of the passenger stops it represents?
3
4
1
5
2
3
The 3rd stop is the most constrained by the conditions. Aberdeen MUST be in either the third or fourth position. If it is in the third position, then obviously nothing else can be in the third position. If it is in the fourth position, then the diagram for the game looks like the following:
B/H T H/B A R.
T and R cannot occupy the third position. Only A, B, and H can possibly occupy the third position. T cannot be in the third position, because then B and H would be forced into the first two stops. They are not allowed to be consecutive stops. R cannot occupy the third position, because A would have to go into to the fourth position and H would have to go into the fifth position. H cannot be in the fifth position if A is in the fourth position.
The first, second, and fifth positions are restricted only in that A cannot occupy these positions.
Example Question #7 : Linear Games
The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
If the ninth passenger stop of the day is made at Aberdeen, then for which of the following can you determine the exact positions on the route?
Ramrock and Habermark
Basilica and Habermark
Terroire and Ramrock
Habermark and Terroire
Basilica and Ramrock
Terroire and Ramrock
The correct answer is Terroire and Ramrock.
This is actually very similar to another question in this set. If the ninth stop is Aberdeen, then that means that on the route that the F train is taking, Aberdeen is the fourth stop. When Aberdeen is the fourth stop, then the diagram is always B/H T B/H A R. Only the positions of Basilica and Habermark are uncertain, and those are uncertain only in that we don't know which is first and which is third.
Example Question #8 : Linear Games
The Silvermine Railway's F train takes a loop through the region in which it operates. It stops at five passenger stops-- Aberdeen, Basilica, Habermark, Ramrock, and Terroire, although not necessarily in that order. The F train begins and ends each loop at the railyard, which is not considered a passenger stop. The order of the stops on the route must conform to the following conditions without exception:
The F train stops at each of the five passenger stops exactly once per loop and does exactly two complete loops per day. The railyard is where the train begins and ends each loop. After leaving the railyard at the beginning of the day, the train will stop at each of the five passenger stops before completing its loop by returning to the railyard. The train will then proceed to stop at each of the five passenger stops once again (in the same order it did the first time around) before once again stopping at the railyard and thus completing its second and final loop of the day.
The F train will never stop at Habermark and Basilica consecutively.
The F train will stop at at least two other passenger stops two times before stopping at Aberdeen for the second time.
If Terroire is the third stop, then Habermark is the second stop.
If Aberdeen is the fourth stop, then Habermark is not the fifth stop.
Aberdeen is earlier on the route than at least one of Habermark and Ramrock.
Which of the following could be added to the existing conditions and cause absolutely no changes whatsoever to the possible set of routes?
If Terroire is the third stop, then Ramrock is the fifth stop.
Basilica must come before Habermark.
Habermark must come before Ramrock.
Aberdeen is always the fourth stop.
Only one of Basilica or Habermark comes before Aberdeen.
If Terroire is the third stop, then Ramrock is the fifth stop.
[If Terroire is the third stop, then Ramrock is the fifth stop.]
This causes no changes, because Terroire is never the third stop. You can predicate anything on Terroire being the third stop, because it will never happen.
[Aberdeen is always the fourth stop.]
Aberdeen is sometimes the third stop. This removes that possiblity from the set of possible routes.
[Basilica must come before Habermark.]
Basilica can come after Habermark on several valid routes, such as H T B A R.
[Habermark must come before Ramrock.]
This removes the possibility of routes like R B A T H.
[Only one of Basilica or Habermark comes before Aberdeen.]
This removes the possibility of routes like B T H A R or H T B A R, as shown above.
Example Question #1 : Sequencing
A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.
- Will is not the tallest or the shortest.
- No girl is taller than Jonathan
- Dan is shorter than Corrin, but taller than Theresa.
- Ben is the tallest
Which of the following could be true?
Dan is the shortest.
Will is the shortest.
Jonathan is the 4th tallest.
Corrin is the 4th tallest.
Ben is the 5th tallest.
Corrin is the 4th tallest.
This can be solved by prcoess of elimination. Ben cannot be anything but 6th. Will cannot be 1st or 6th. Dan is taller than Theresa, so he could never be shortest. Jon can only be 2nd or 3rd tallest, because Theresa, Dan, and Corrin must precede him. Thus, he could not be 4th.
Example Question #2 : Sequencing
A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.
- Will is not the tallest or the shortest.
- No girl is taller than Jonathan
- Dan is shorter than Corrin, but taller than Theresa.
- Ben is the tallest
What must always be true?
Jonathan is 4th.
Jonathan is 5th.
Corrin is 3rd.
Theresa is 1st in line.
Will is 2nd.
Theresa is 1st in line.
Theresa must be shorter than Dan, Corrin, and Jonathan. Will cannot be the shortest. Ben is always the tallest.
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