LSAT Logic Games : Linear Games
Study concepts, example questions & explanations for LSAT Logic Games
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Example Questions
Example Question #3 : Solving Two Variable Logic Games
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 must be true?
If Dan is 2nd in line, Corrin must be 3rd.
If Will is 5th in line, Dan is 2nd in line.
If Theresa is shortest, Corrin is 2 spots behind her.
If Jonathan is 3rd tallest, Will is 4th tallest.
If Ben is tallest, Corrin is the 3rd tallest.
If Will is 5th in line, Dan is 2nd in line.
This can be answered by process of elimination. Ben being in 6th doesn't effect anyone, as he is always there. If Jonathan is 3rd tallest, the only one who can be the 5th spot is Will - thus, that answer is wrong. Theresa must be the first person in line, so she doesn't affect any positioning. Thus, Corrin could be 3rd, or 4th in line, despite Theresa's position. Finally, if Dan is 2nd in line, Corrin is not guaranteed to be at the 3rd position. Will can be at the third position, pushing Corrin to the 4th.
Example Question #2 : Solving Two Variable Logic Games
A librarian is organizing seven categories of books on seven shelves, numbered one to seven from top to bottom. The categories are art, botany, calculus, food, sports, theology, and zoology. The librarian places one category of books on each shelf, and does so according to the following rules:
Food must always be on either the top or bottom shelves
Art must be directly above or below calculus
Theology is never on the top or the bottom shelves
Calculus and botany must be separated by exactly one category
Which of the following is a possible order of the book categories on the shelves, from top to bottom?
S, C, A, B, T, Z, F
F, C, A, B, S, Z, T
F, A, C, B, T, S, Z
S, B, T, C, A, F, Z
A, C, S, Z, B, T, F
S, C, A, B, T, Z, F
Answers can be quickly eliminated when F is not the first or last letter or when T is the first or last letter. Other answers can be eliminated when A is not directly next to C. Finally, there must be precisely one letter between B and C. Remember, A can be the letter that separates B and C.
Example Question #1 : Solving Two Variable Logic Games
A librarian is organizing seven categories of books on seven shelves, numbered one to seven from top to bottom. The categories are art, botany, calculus, food, sports, theology, and zoology. The librarian places one category of books on each shelf, and does so according to the following rules:
Food must always be on either the top or bottom shelves
Art must be directly above or below calculus
Theology is never on the top or the bottom shelves
Calculus and botany must be separated by exactly one category
If calculus is assigned the spot directly below the top shelf, then each of the following could be true EXCEPT
Food is on the top shelf
Theology is one shelf above botany
Art is one shelf above botany
Sports is directly below food
Zoology is on a shelf directly above or directly below sports
Sports is directly below food
Sports could be directly above food if food is on the bottom shelf, but it could never be below food because food must either be on the top shelf or the bottom shelf. No category can be directly below food when it is on the bottom shelf and we know that calculus is directly below the top shelf.
Example Question #271 : Linear Games
A librarian is organizing seven categories of books on seven shelves, numbered one to seven from top to bottom. The categories are art, botany, calculus, food, sports, theology, and zoology. The librarian places one category of books on each shelf, and does so according to the following rules:
Food must always be on either the top or bottom shelves
Art must be directly above or below calculus
Theology is never on the top or the bottom shelves
Calculus and botany must be separated by exactly one category
When calculus is on the bottom shelf, which of the following could be true, but is not required to be true?
Botany is on a shelf above art
Food is on the top shelf
Zoology is on the fifth shelf
Art is on the shelf directly below sports
Zoology is on a shelf directly above theology
Zoology is on a shelf directly above theology
When calculus is on the bottom shelf, food must be on the top shelf and botany and art must occupy the fifth and sixth shelves. The remaining categories, however, can be in any order on shelves two, three, and four. Zoology could be on the shelf directly above theology, but it does not have to be.
Example Question #3 : Two Variable
A librarian is organizing seven categories of books on seven shelves, numbered one to seven from top to bottom. The categories are art, botany, calculus, food, sports, theology, and zoology. The librarian places one category of books on each shelf, and does so according to the following rules:
Food must always be on either the top or bottom shelves
Art must be directly above or below calculus
Theology is never on the top or the bottom shelves
Calculus and botany must be separated by exactly one category
If a condition is added that sports must always be on a shelf between botany and calculus, and if all other conditions remain the same, which of the following cannot be true?
Zoology is on the last shelf and sports are on the fifth
Botany is on the sixth shelf and art is on the third
Calculus is on the fourth shelf
Theology is on the second shelf
Zoology is on the second shelf and calculus is on the fourth shelf
Zoology is on the second shelf and calculus is on the fourth shelf
When calculus is on the fourth shelf, botany must be on the second or sixth. Since zoology is on the second shelf, botany must be on the sixth. Sports must be on the fifth shelf to be between botany and calculus, and art must be on the second to be adjacent to calculus, which leaves only the top or bottom for theology.
Example Question #1 : Two Variable
A media company is determining the lineup for its programming tonight. There are five hour long shows – P, Q, R, S, T – that must be aired one after another from 6:00 to 11:00. Each show must be paired with one of three newscasters – Adrian, Brett, Calvin – subject to the following conditions:
Each newscaster must host at least one show.
Adrian cannot host a show after 9:00.
There must be exactly two shows in between Adrian’s first show and Calvin’s first show.
Q is aired before R.
R is aired before both S and T.
Which one of the following could be an accurate and complete list of the order the shows air along with the newscasters assigned to host them?
P: Adrian, Q: Adrian, R: Adrian, S: Calvin, T: Calvin
P: Brett, Q: Adrian, S: Adrian, R: Brett, T: Calvin
Q: Brett, R: Adrian, T: Adrian, P: Brett, S: Calvin
Q: Adrian, R: Brett, T, Brett, P: Calvin, S: Adrian
P: Adrian, Q: Brett, R: Adrian, S: Brett, T: Calvin
Q: Brett, R: Adrian, T: Adrian, P: Brett, S: Calvin
The incorrect answers all violate one of the stated conditions:
(P: Adrian, Q: Brett, R: Adrian, S: Brett, T: Calvin) - Adrian's first show must have exactly two shows in between it and Calvin's first show. This has three.
(Q: Adrian, R: Brett, T, Brett, P: Calvin, S: Adrian) - Adrian cannot have any shows after 9:00; the last slot would be 10:00-11:00, a violation of the rule.
(P: Brett, Q: Adrian, S: Adrian, R: Brett, T: Calvin) - R is aired before both S and T; it is aired after S in this case.
(P: Adrian, Q: Adrian, R: Adrian, S: Calvin, T: Calvin) - All of the newcasters must host at least one show, so Brett's absence here is a violation.
The correct answer does not violate any of the stated conditions.
Example Question #2 : Two Variable
A media company is determining the lineup for its programming tonight. There are five hour long shows – P, Q, R, S, T – that must be aired one after another from 6:00 to 11:00. Each show must be paired with one of three newscasters – Adrian, Brett, Calvin – subject to the following conditions:
Each newscaster must host at least one show.
Adrian cannot host a show after 9:00.
There must be exactly two shows in between Adrian’s first show and Calvin’s first show.
Q is aired before R.
R is aired before both S and T.
If P is aired from 6:00-7:00 with Brett as the host, which of the following must be true?
Brett hosts the 8:00-9:00 show.
Adrian hosts the 9:00-10:00 show.
S is aired from 10:00-11:00
Calvin hosts the 10:00-11:00 show.
S is aired from 9:00-10:00.
Calvin hosts the 10:00-11:00 show.
Since we are given Brett as the host of the first show, this means that Adrian must host the 7:00-8:00 show and Calvin must host the 10:00-11:00 show in order to put exactly two shows in between their initial shows. Moreover, the shows in between must be hosted by Adrian or Brett because Calvin must have his first performance in the 10:00-11:00 slot. This gives us the following order:
6:00-7:00: P: Brett
7:00-8:00: Adrian
8:00-9:00: Adrian/Brett
9:00-10:00: Adrian/Brett
10:00-11:00: Calvin
If one combines the last two rules, the following order in which the shows air is created:
Q - R - (S/T)
Applying this to the above model, we get:
6:00-7:00: P: Brett
7:00-8:00: Q: Adrian
8:00-9:00: R: Adrian/Brett
9:00-10:00: S/T: Adrian/Brett
10:00-11:00: T/S: Calvin
The correct answer is the only one that must be true. Every way the game is played requires Calvin to host the 10:00-11:00 show. The incorrect answers can happen, but do not necessarily have to in order for the game to work.
Example Question #271 : Linear Games
A media company is determining the lineup for its programming tonight. There are five hour long shows – P, Q, R, S, T – that must be aired one after another from 6:00 to 11:00. Each show must be paired with one of three newscasters – Adrian, Brett, Calvin – subject to the following conditions:
Each newscaster must host at least one show.
Adrian cannot host a show after 9:00.
There must be exactly two shows in between Adrian’s first show and Calvin’s first show.
Q is aired before R.
R is aired before both S and T.
Which of the following shows CANNOT be aired in the 8:00-9:00 slot?
T
P
Q
R
S
Q
Recall from the previous question that combining the last two rules produces the following order in which the shows air:
Q - R - (S/T)
There must be at least three shows that air after Q, so the latest it could possibly air is at 7:00-8:00.
Example Question #272 : Linear Games
A media company is determining the lineup for its programming tonight. There are five hour long shows – P, Q, R, S, T – that must be aired one after another from 6:00 to 11:00. Each show must be paired with one of three newscasters – Adrian, Brett, Calvin – subject to the following conditions:
Each newscaster must host at least one show.
Adrian cannot host a show after 9:00.
There must be exactly two shows in between Adrian’s first show and Calvin’s first show.
Q is aired before R.
R is aired before both S and T.
Which one of the following is an accurate and complete list of the shows that Calvin can host?
P, S, T
S, T
P, S, T, R
P, T, R
P, S, R
P, S, T
Because of the rule that two shows must air in between Adrian's first show and Calvin's first show, the only possible slots in which Calvin can host are 9:00-10:00 and 10:00-11:00.
Using the Q - R - (S/T) combination of the last two rules, that means that of these four, only S and T can occupy the last two slots and be hosted by Calvin as a result. Since P has no set rules, there is nothing stopping it from it being put in the last two spots and being hosted by Calvin either.
Example Question #273 : Linear Games
A media company is determining the lineup for its programming tonight. There are five hour long shows – P, Q, R, S, T – that must be aired one after another from 6:00 to 11:00. Each show must be paired with one of three newscasters – Adrian, Brett, Calvin – subject to the following conditions:
Each newscaster must host at least one show.
Adrian cannot host a show after 9:00.
There must be exactly two shows in between Adrian’s first show and Calvin’s first show.
Q is aired before R.
R is aired before both S and T.
If Calvin hosts exactly two shows, which of the following must be false?
Brett hosts both Q and S.
Adrian hosts exactly three shows.
Calvin hosts both T and P.
Calvin hosts more shows than Brett.
Brett hosts more shows than Adrian.
Adrian hosts exactly three shows.
In order for Calvin to host two shows, Adrian must host the first show in the 6:00-7:00 slot so that two shows can air before Calvin's first show at 9:00-10:00 and allow an opportunity for Calvin to host a second show at 10:00-11:00. That gives us the following model:
6:00-7:00: Adrian
7:00-8:00: Adrian/Brett
8:00-9:00: Adrian/Brett
9:00-10:00: Calvin
10:00-11:00: Calvin
The correct answer must be false in every scenario, which is the case for the assertion that Adrian hosts three shows. Along with Calvin hosting two shows, this would leave no room for Brett to host a show and violate the rule that each of the newcasters must host at least one show.
The incorrect answers all could be true under certain scenarios.
All LSAT Logic Games Resources
