# LSAT Logic Games : Solving three-variable logic games

## Example Questions

### Example Question #41 : Three Variable

A large storage bin has six storage compartments called "Units" numbered 1 through 6.  The Unit numbers go in sequence from left to right.  Each Unit contains a particular type of item in need of storage:  albums, books, clothes, dishes, electronics, and folders.  The placement of the items in the appropriate Unit must comply with the following rules:

The Unit holding books is to the right of the Unit holding clothes.

The Unit holding clothes is to the right of the Unit holding folders.

The Unit holding electronics is to the right of the Unit holding albums.

The Unit holding folders is next to the Unit holding electronics.

Which one of the following sequences could accurately identify the items stored in the first three Units?

dishes, folders, electronics

dishes, clothes, albums

books, dishes, albums

dishes, folders, albums

albums, dishes, folders

albums, dishes, folders

Explanation:

Apply each rule singly to elminate rule violators.  The sequence "albums, dishes, folders" does not violate any of the rules.  Accordingly, it is the correct answer.  Each of the other options violates one of the rules.

### Example Question #412 : Lsat Logic Games

A large storage bin has six storage compartments called "Units" numbered 1 through 6.  The Unit numbers go in sequence from left to right.  Each Unit contains a particular type of item in need of storage:  albums, books, clothes, dishes, electronics, and folders.  The placement of the items in the appropriate Unit must comply with the following rules:

The Unit holding books is to the right of the Unit holding clothes.

The Unit holding clothes is to the right of the Unit holding folders.

The Unit holding electronics is to the right of the Unit holding albums.

The Unit holding folders is next to the Unit holding electronics.

Which one of the following CANNOT be the item type that is stored in Unit 4?

books

clothes

electronics

folders

dishes

books

Explanation:

Blending all of the rules together, we get the following loose sequence:

albums ---- electronics & folders (either order) ---- clothes ---- books.

The floater:  dishes.

From this sequence, it is clear that books could never occupy the 4th slot.  Books could only occupy slots 5 or 6.

### Example Question #413 : Lsat Logic Games

A large storage bin has six storage compartments called "Units" numbered 1 through 6.  The Unit numbers go in sequence from left to right.  Each Unit contains a particular type of item in need of storage:  albums, books, clothes, dishes, electronics, and folders.  The placement of the items in the appropriate Unit must comply with the following rules:

The Unit holding books is to the right of the Unit holding clothes.

The Unit holding clothes is to the right of the Unit holding folders.

The Unit holding electronics is to the right of the Unit holding albums.

The Unit holding folders is next to the Unit holding electronics.

If there is exactly one Unit between the Unit containing dishes and the Unit containing books, then for exactly how many of the six Units is the type of item that Unit is holding completely determined?

six

four

two

three

five

four

Explanation:

The question posits that there is one slot between books and dishes.  That means books would have to be in slot 6 and dishes in slot 4.  Albums would be in slot 1 and clothes in slot 5.  The only thing unresolved is the positioning of electronics and folders because the rule pertaining to them doesn't specify their relative position but only mandates that they be next to each other.  Therefore, four of the six slots are fully resolved.

### Example Question #412 : Lsat Logic Games

A large storage bin has six storage compartments called "Units" numbered 1 through 6.  The Unit numbers go in sequence from left to right.  Each Unit contains a particular type of item in need of storage:  albums, books, clothes, dishes, electronics, and folders.  The placement of the items in the appropriate Unit must comply with the following rules:

The Unit holding books is to the right of the Unit holding clothes.

The Unit holding clothes is to the right of the Unit holding folders.

The Unit holding electronics is to the right of the Unit holding albums.

The Unit holding folders is next to the Unit holding electronics.

Which one of the following could be the Unit holding clothes?

Unit 3

Unit 2

Unit 1

Unit 5

Unit 6

Unit 5

Explanation:

Blending the rules leads to the following loose sequence:

A ---- EF/FE ---- C ---- B.  D is a floater.

The question asks about C.  C must have at least three entities before it, so the answer cannot be Units 1, 2, or 3.  C must have at least one entity after it, so the answer cannot be Unit 6.  It can fit into slot 5, which means the correct answer is "Unit 5."

### Example Question #41 : Three Variable

A large storage bin has six storage compartments called "Units" numbered 1 through 6.  The Unit numbers go in sequence from left to right.  Each Unit contains a particular type of item in need of storage:  albums, books, clothes, dishes, electronics, and folders.  The placement of the items in the appropriate Unit must comply with the following rules:

The Unit holding books is to the right of the Unit holding clothes.

The Unit holding clothes is to the right of the Unit holding folders.

The Unit holding electronics is to the right of the Unit holding albums.

The Unit holding folders is next to the Unit holding electronics.

If the Unit containing electronics is next to the Unit holding clothes, then each of the following could be true EXCEPT:

Unit 4 contains folders.

Unit 5 contains dishes.

Unit 2 contains albums.

Unit 5 contains books.

Unit 4 contains electronics.

Unit 4 contains folders.

Explanation:

The added information supplied by the question solidifies the sequence in the following way:

A --- FE --- C --- B.    D remains a floater.

F must have at least one entity before it (A) and possibly two entities before it (A and D).  That means F cannot be in slot 1.  F must have at least three entities after it (E, C, and B) and possibly four entities after it (E, C, B, and D).  That means F cannot be in slot 4, 5, or 6.  Therefore, answer choice "Unit 4 contains folders" is the correct one.

### Example Question #41 : Three Variable

A large storage bin has six storage compartments called "Units" numbered 1 through 6.  The Unit numbers go in sequence from left to right.  Each Unit contains a particular type of item in need of storage:  albums, books, clothes, dishes, electronics, and folders.  The placement of the items in the appropriate Unit must comply with the following rules:

The Unit holding books is to the right of the Unit holding clothes.

The Unit holding clothes is to the right of the Unit holding folders.

The Unit holding electronics is to the right of the Unit holding albums.

The Unit holding folders is next to the Unit holding electronics.

Which one of the following must be false?

The Unit containing books is next to the Unit containing dishes.

The Unit containing clothes is next to the Unit containing albums.

The Unit containing folders is next to the Unit holding albums.

The Unit containing electronics is next to the Unit holding clothes.

The Unit containing albums is next to the Unit containing dishes.

The Unit containing clothes is next to the Unit containing albums.

Explanation:

Blending the rules to create the loose sequence, we can see that A can never be next to C, as EF/FE must always come between them.  So the correct answer is:  "The Unit containing clothes is next to the Unit containing albums."

### Example Question #41 : Solving Three Variable Logic Games

A school has seven sports teams---baseball, football, golf, hockey, karate, swimming, and track.  The new school gymnasium has three floors.  Each floor can allow for a maximum of four sports teams to do indoor practicing or working out.  No sports team can practice or work out on more than one floor.  Assignment of the sports teams to the appropriate floor of the gym is subject to the following conditions:

Karate and track must conduct their practices or workouts on the same floor.

Football must conduct practices or workouts on the floor immediately above golf.

Hockey must conduct practices or workouts on its own floor without any other sports team.

If golf and track practice or workout on the second floor, which one of the following could be true?

Swimming practices or does workouts on the first floor.

Baseball practices or does workouts on the second floor.

Football practices or does workouts on the second floor.

Track practices or does workouts on the third floor.

Hockey practices or does workouts on the third floor.

Baseball practices or does workouts on the second floor.

Explanation:

With golf and track on the middle floor, football must be on the third floor by virtue of the second rule.  Hockey must occupy its own floor, so it must be on the ground floor with no other sports teams there.  Karate must be on the middle floor by virtue of the first rule.  With these deductions, the only answer choice that doesn't violate the setup is the one that places baseball on the middle floor.

### Example Question #41 : Solving Three Variable Logic Games

At an art exhibit six sculptures, identified by the first letter of the artist's last name, will be displayed sequentially, from front to back.  The sculptures are L, M, O, S, V, and Z.  The front-to-back display must accord with the following restrictions:

M must be displayed closer to the front than S.

S must be displayed closer to the front than both L and V.

V and Z each must be displayed closer to the front than O.

Which one of the following could be an accurate sequencing of the sculptures, displayed from front to back?

L third, V fourth, O fifth

Z second, V third, O sixth

M first, V fifth, and L sixth

S third, V fourth, Z fifth

M first, V third, L sixth

M first, V third, L sixth

Explanation:

This acceptability question deals only with a partial listing of the entities, so it is more difficult.  But fundamentally the technique is the same:  apply each rule to each answer choice and eliminate rule-violators.  The correct answer will emerge as the one that violates none of the rules.

### Example Question #42 : Solving Three Variable Logic Games

At an art exhibit six sculptures, identified by the first letter of the artist's last name, will be displayed sequentially, from front to back.  The sculptures are L, M, O, S, V, and Z.  The front-to-back display must accord with the following restrictions:

M must be displayed closer to the front than S.

S must be displayed closer to the front than both L and V.

V and Z each must be displayed closer to the front than O.

If V is fifth, then which one of the following must be true?

Z must be third

L must be fourth

S must be second

O must be sixth

M must be first

O must be sixth

Explanation:

If V is fifth, then according to the third rule, O must be sixth.  Hence, O is our answer.  The other answer choices could be true, but they need not be true.

### Example Question #42 : Three Variable

At an art exhibit six sculptures, identified by the first letter of the artist's last name, will be displayed sequentially, from front to back.  The sculptures are L, M, O, S, V, and Z.  The front-to-back display must accord with the following restrictions:

M must be displayed closer to the front than S.

S must be displayed closer to the front than both L and V.

V and Z each must be displayed closer to the front than O.

If L is third, then each of the following could be ture EXCEPT:

O is displayed immediately behind V.

O is displayed immediately behind Z.

V is displayed immediately behind L.

Z is displayed immediately behind V.

S is displayed immediately behind Z.

S is displayed immediately behind Z.

Explanation:

If L is third, then M must be first and S must be second.

Because either L or O must be last, and because L occupies slot 3, O occupies slot 6.

V and Z do not have a direct relationship, so either can occupy the 4th and 5th slots.

Based on this sequence, S can never be siituated immediately behind Z.