LSAT Logic Games › Determining sequence in 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 genre will 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 L is invited to speak on Friday, then on what days MUST a science fiction writer be invited?
Tuesday and Thursday
Monday and Wednesday
Monday and Thursday
Monday and Tuesday
Only Wednesday
If L is the speaker on Friday, then B cannot be a guest speaker at all, since if L and B are both guest speakers then neither can speak on Monday or Friday. If B is not a speaker, then Y must be a speaker, in order for there to be a mystery writer guest speaker. If Y is a guest speaker, then C must not be a guest speaker. Thus, Z must be a guest speaker in order to have a historical fiction writer.
We thus know so far that Y and Z and L are three out of five possible guest speakers (from Monday through Friday). That means the remaining two MUST be science fiction writers. Furthermore, because Y is a guest speaker, A cannot be a guest speaker. Thus, the two science fiction guests are X and J and they both are invited. They must be invited for Tuesday and Thursday, because any other day would force one of them to speak on Monday, which is not possible if both X and J are invited.
Y/Z, X/J, Y/Z, X/J, L
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 genre will 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.
Which of the following is an acceptable list of guest speakers for the library's special event from Monday to Friday?
L, J, Z, X, Y
L, J, C, X, Y
A, C, B, J, Z
X, L, C, B, Z
A, X, Y, J, L
This question is actually a combination of sequencing and grouping. The test-taker must determine both which variables will be involved in the sequence and the order in which the variables are placed in sequence. Answering this particular question is simply a matter of checking the rules in the question stem. Each incorrect answer breaks one or more rules.
L, J, C, X, Y is incorrect because C may not be invited if Y is invited. Z must be invited instead.
A, C, B, J, Z is incorrect because L is not invited. L is the only non-fiction writer and thus MUST be one of the five invited speakers.
X, L, C, B, Z is incorrect because X must follow C.
A, X, Y, J, L is incorrect because A and X are both science-fiction writers, and they are not allowed to speak on consecutive nights.
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 genre will 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.
Which two writers cannot BOTH be invited to speak?
C and J
C and B
A and X
J and Z
B and C
Since X always follows C and J is participating, we have the pair of X and J. X and J are both science fiction, so there must be at least one space between them. Neither can speak in either the first or last slot. C must come directly before X. Thus, we have either CX_J_ or _JCX_.
We know that L must be part of any correct diagram, and we still need a mystery writer, either B or Y. Y cannot fit because Y and C can't both be part of the diagram. B cannot fit because There is no way to fit L and B without either one or both speaking first or last.
In a new strip mall, six vacant store spaces will be used to open new stores by six companies: Fisk, Gourd, Hack, Jipp, Lux, and Mort. Each of the six companies will open exactly one new store in one of the spaces, numbered 1-6. No two companies can share an individual store space. The stores will choose their store space based on the following rules:
Hack must open a store space numbered higher than the one opened by Jipp.
Lux’s space number is lower than the space number of Gourd.
Hack cannot use the fifth or the sixth store space.
Jipp must open a store space numbered higher than the one opened by Fisk.
Which of the following could be a list of companies, ordered 1-6 by the store spaces they use for their stores?
Lux, Fisk, Jipp, Hack, Gourd, Mort
Fisk, Hack, Jipp, Lux, Mort, Gourd
Fisk, Jipp, Gourd, Hack, Lux, Mort
Jipp, Lux, Mort, Hack, Fisk, Gourd
Mort, Fisk, Jipp, Lux, Hack, Gourd
For this question, you will need to eliminate wrong answers using the rules given in the stimulus.
The first global rule tells you that Jipp must be listed before Hack. With this deduction, you can eliminate the following sequence as a wrong answer: Fisk, Hack, Jipp, Lux, Mort, Gourd.
The second global rule tells you that Lux must be listed before Gourd. With this deduction, you can eliminate the following sequence as a wrong answer: Fisk, Jipp, Gourd, Hack, Lux, Mort.
The third global rule tells you that Hack must be in either the first, second, third, or fourth space. With this deduction, you can eliminate the following sequence as a wrong answer: Mort, Fisk, Jipp, Lux, Hack, Gourd.
The fourth global rule tells you that Fisk must be listed before Jipp. With this deduction, you can eliminate the following sequence as a wrong answer: Jipp, Lux, Mort, Hack, Fisk, Gourd.
The correct answer is: Lux, Fisk, Jipp, Hack, Gourd, Mort. This sequence conforms to all four global rules.
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?
Aberdeen, Basilica, Ramrock, Habermark, Terroire
Basilica, Habermark, Terroire, Aberdeen, Ramrock
Aberdeen, Basilica, Terroire, Ramrock, Habermark
Terroire, Basilica, Ramrock, Habermark, Aberdeen
Habermark, Terroire, Aberdeen, Ramrock, Basilica
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.
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 C and A are both invited to speak, which two writers CANNOT speak on consecutive nights?
A and C
X and L
B and C
A and L
Z and B
If C is invited to speak, then we know that C and X will be speaking on consecutive nights. Since C and A are invited to speak, then we know that Y is NOT invited to speak, which means that B IS invited (because at least one of the two mystery writers must speak. L always speaks.
Thus, we know our diagram will be some sequence of CX, A, B, and L. Since L and B are both invited, neither may speak first or last. Thus, a possible diagram may be something like C, X, L, B, A. L and B will always be surrounded on either side by the groups CX and A. Thus, there is no combination in which the A and CX blocks touch, and no consecutive grouping of those letters may take place.
Six fast-food restaurants at a food court are assigned to numbered lots---1 through 6---that are arranged in that order (i.e., lot 1 is on the far left and lot 6 is on the far right). The restaurants are A, B, C, D, E, and F. The following arrangement characterizes how these restaurants are situated in the food court:
A and B have one restaurant between them, which is to say, they are assigned to lots that are separated from each other by exactly one other lot.
A and D are not situated next to each other.
D is located in a higher-number lot than C.
F is in lot 3.
Which one of the following is a complete and accurate list of the positions any one of which can be the positon for restaurant A?
Slots 2, 4, 6
Slots 1, 2
Slots 2, 3
Slots 2, 4
Slots 2, 4, 5
This is a classic sequencing game. We know there are six slots and the task is to fit the entities into the correct slot. The problem gives us slot 3---F goes there. We can make several deductions here to facilitate quick answering of all the questions.
Because of the rule that C precedes D, we can deduce that C cannot go in slot 6 and D cannot go in slot 1.
Because F is in slot 3 and there is a rule that mandates that A and B be separated by one slot, neither A nor B can be in slot 1. Thus, we can rule out for slot 1 restaurants A, B, D, and F. So we know for sure that slot 1 must have either C or E.
Deeper investigation reveals that A cannot go in slot 5. If we try to put A in slot 5, we see that B cannot fit into a slot that is separated by one slot (slot 3 is occupied and there is no slot 7). Going even deeper, we see that E cannot go into slot 2, because if that were the case, we could not fit the other restuarants into slots 4, 5, and 6. In other words, with E in slot 2, C must occupy slot 1. That leaves A, B, and D for slots 4, 5, and 6. But notice: A cannot be next to D, according to the rules. Since A and B must be separated by one slot, this arrangement would force A to be next to D, which is not permissible.
From the explicit rules and our deductions, we can quickly eliminate slots 1, 3, and 5 as viable for restaurant A. So the only issue is whether only slots 2 and 4 are viable, as opposed to slots 2, 4, and 6. Nothing precludes A from occupying slot 6, so the correct answer is: Slots 2, 4, 6.
A piano teacher instructs six students -- Ralph, Sam, Thomas, Venna, Wanda, and Xavier. The students' lessons are held daily at six times: 1 pm, 2 pm, 3 pm, 4 pm, 5 pm, and 6 pm. Each lesson begins on the hour at one of the listed times, and only one student may be scheduled for each hour. Each student receives exactly one lesson per day. The following conditions govern the times at which students may be scheduled:
Ralph's lesson must be given at 1 pm or 3 pm.
Venna's lesson is given sometime before Sam's lesson but sometime after Wanda's lesson.
Thomas's lesson is given immediately after Sam's lesson.
If Xavier's lesson is at 4 pm, which one of the following must be true?
Sam's lesson is at 5 pm.
Wanda's lesson is at 1 pm.
Ralph's lesson is at 3 pm.
Venna's lesson is at 3 pm.
Wanda's lesson is at 2 pm.
Sam's lesson must be held at 5 pm under these circumstances. The remaining answer choices could be true, but do not have to be true. With Xavier at 4 pm, the only possible slots to accommodate Sam and Thomas are 5 pm and 6 pm (because Wanda and Venna must receive their lessons earlier than Sam). Wanda's lesson could be at either 1 pm or 2 pm. Venna's lesson could be at either 2 pm or 3 pm. Ralph's lesson could be at either 1 pm or 3 pm.
Seven runners, Allen, Beth, Calli, Drew, Erin, Fred, and Gary, are being timed running a mile. Only one runner can run at a time. The following conditions apply:
Calli cannot run first or last
At least one person must run between Fred and Gary
Erin can only run directly before or after Drew if Allen runs first
Beth must run before Gary
If the conditions are modified so that exactly one runner runs between Gary and Fred and so that Drew must run immediately before Calli, which of the following cannot be true?
Drew runs sixth
Beth runs between Fred and Gary
Gary runs before Fred
Allen runs first
Drew runs third
Under the new conditions, Calli would have to run seventh if Drew ran sixth. We know, however, that Calli cannot run seventh.
Five contestants in a speech-giving contest—Mort, Othello, Paul, Quinn, and Sue—will give their speeches in front of a judging panel during five consecutive time slots, one contestant per time slot. Each contestant will give his/her speech exactly once. The order of the contestants must adhere to the following conditions:
If Sue gives her speech first, Mort gives his speech last.
If Mort gives his speech second, Quinn gives her speech first.
Mort does not give his speech first.
Paul gives his speech immediately after Othello gives his speech.
Othello can give his speech in any of the five time slots EXCEPT
fifth
first
second
third
fourth
You can use your global rules to determine in which time slot Othello cannot give his speech.
The fourth global rule tells you that Othello must give his speech immediately before Paul gives his speech. This means that Othello can never give his speech fifth. Otherwise there would be no way for Paul to go immediately after him.
So your correct answer is fifth.