# LSAT Logic Games : Solving three-variable logic games

## Example Questions

### Example Question #401 : Lsat Logic Games

Sarah is planting flowers in each of her three window boxes from the following varieties: Azaleas; Carnations; Daffodils; Gardenias; Marigolds; Petunias. She plans to plant two varieties of flowers in two of the boxes and three varieties in the third. She plants the flower seeds according to the following conditions:

• No flower variety may appear in all three window boxes, and up to one variety may be planted in two window boxes.
• If Petunias are planted with two other varieties, Sarah does not plant any Gardenias.
• Carnations may not be planted in the same window box as Daffodils.
• If Marigolds are not planted next to Azaleas, then the only place they must be planted is in the same box as two other flowers.

How many different types of flowers could be planted in a small window box next to Petunias?

Three

One

Five

Two

Four

Four

Explanation:

Carnations, Daffodils, Gardenias, and Azaleas may be planted with Petunias. Marigolds cannot in either case because they would either be in the large window box or with Azaleas.

### Example Question #32 : Solving Three Variable Logic Games

Sarah is planting flowers in each of her three window boxes from the following varieties: Azaleas; Carnations; Daffodils; Gardenias; Marigolds; Petunias. She plans to plant two varieties of flowers in two of the boxes and three varieties in the third. She plants the flower seeds according to the following conditions:

• No flower variety may appear in all three window boxes, and up to one variety may be planted in two window boxes.
• If Petunias are planted with two other varieties, Sarah does not plant any Gardenias.
• Carnations may not be planted in the same window box as Daffodils.
• If Marigolds are not planted next to Azaleas, then the only place they must be planted is in the same box as two other flowers.

Each of the following could be true EXCEPT __________.

Azaleas are planted in two different boxes.

Carnations are planted in two different boxes.

Sarah does not plant any Gardenias.

Daffodils and Azaleas are planted together.

Petunias are planted in one box only.

Sarah does not plant any Gardenias.

Explanation:

Note that if Gardenias cannot be planted, there are not enough varieties to fill the boxes.

### Example Question #31 : Three Variable

Sarah is planting flowers in each of her three window boxes from the following varieties: Azaleas; Carnations; Daffodils; Gardenias; Marigolds; Petunias. She plans to plant two varieties of flowers in two of the boxes and three varieties in the third. She plants the flower seeds according to the following conditions:

• No flower variety may appear in all three window boxes, and up to one variety may be planted in two window boxes.
• If Petunias are planted with two other varieties, Sarah does not plant any Gardenias.
• Carnations may not be planted in the same window box as Daffodils.
• If Marigolds are not planted next to Azaleas, then the only place they must be planted is in the same box as two other flowers.

Which one of the following could represent the locations of each flower Sarah planted?

Box 1: Azaleas, Marigolds, Carnations

Box 2: Carnations, Daffodils

Box 3: Gardenias, Azaleas

Box 1: Azaleas, Gardenias, Carnations

Box 2: Petunias, Daffodils

Box 3: Marigolds, Azaleas

Box 1: Azaleas, Petunias, Carnations

Box 2: Marigolds, Azaleas

Box 3: Petunias, Daffodils

Box 1: Daffodils, Gardenias, Carnations

Box 2: Azaleas, Marigolds

Box 3: Petunias, Daffodils

Box 1:Petunias, Daffodils, Azaleas

Box 2: Marigolds, Gardenias

Box 3: Carnations, Marigolds

Box 1: Azaleas, Gardenias, Carnations

Box 2: Petunias, Daffodils

Box 3: Marigolds, Azaleas

Explanation:

Only one option does not break one of the conditions. Notice that Petunias may not be planted in the large window box, and one variety must be planted in two boxes.

### Example Question #32 : Three Variable

Sarah is planting flowers in each of her three window boxes from the following varieties: Azaleas; Carnations; Daffodils; Gardenias; Marigolds; Petunias. She plans to plant two varieties of flowers in two of the boxes and three varieties in the third. She plants the flower seeds according to the following conditions:

• No flower variety may appear in all three window boxes, and up to one variety may be planted in two window boxes.
• If Petunias are planted with two other varieties, Sarah does not plant any Gardenias.
• Carnations may not be planted in the same window box as Daffodils.
• If Marigolds are not planted next to Azaleas, then the only place they must be planted is in the same box as two other flowers.

Marigolds are planted in one of the two small window boxes, which of the following must be true?

Azaleas are planted in the large window box.

Carnations are planted in two window boxes.

Daffodils are planted in a small window box.

Gardenias are planted in a small window box.

Carnations are planted in a small window box.

Azaleas are planted in the large window box.

Explanation:

Either Carnations or Daffodils may fill one slot in the large window box, and the variety not planted in the large box is planted in the small window box. No neither statement regarding Carnations or Daffodils must be true; however, Azaleas must be planted in the large window box in this case.

### Example Question #35 : Solving Three Variable Logic Games

Sarah is planting flowers in each of her three window boxes from the following varieties: Azaleas; Carnations; Daffodils; Gardenias; Marigolds; Petunias. She plans to plant two varieties of flowers in two of the boxes and three varieties in the third. She plants the flower seeds according to the following conditions:

• No flower variety may appear in all three window boxes, and up to one variety may be planted in two window boxes.
• If Petunias are planted with two other varieties, Sarah does not plant any Gardenias.
• Carnations may not be planted in the same window box as Daffodils.
• If Marigolds are not planted next to Azaleas, then the only place they must be planted is in the same box as two other flowers.

If Marigolds are NOT planted in the large window box, which of the following varieties could be planted in two different window boxes?

Carnations

Azaleas

Marigolds

Gardenias

Petunias

Azaleas

Explanation:

In this case, only one variety may be planted in two flower boxes, and that is Azaleas.

### Example Question #33 : Three Variable

Sarah is planting flowers in each of her three window boxes from the following varieties: Azaleas; Carnations; Daffodils; Gardenias; Marigolds; Petunias. She plans to plant two varieties of flowers in two of the boxes and three varieties in the third. She plants the flower seeds according to the following conditions:

• No flower variety may appear in all three window boxes, and up to one variety may be planted in two window boxes.
• If Petunias are planted with two other varieties, Sarah does not plant any Gardenias.
• Carnations may not be planted in the same window box as Daffodils.
• If Marigolds are not planted next to Azaleas, then the only place they must be planted is in the same box as two other flowers.

Which of the following, if substituted for the condition that

• If Petunias are planted with two other varieties, Sarah does not plant any Gardenias.

would have the same effect on the arrangement of flowers?

Carnations must not be planted in two boxes.

Gardenias must not be planted at all.

Marigolds and Azaleas must be planted together.

Petunias must be planted in a small window box.

Marigolds must not be planted in a large window box.

Petunias must be planted in a small window box.

Explanation:

The effect of this rule is that Petunias must be planted in a small box, as Gardenias must be used to fill all of the window boxes.

### Example Question #34 : Three Variable

A quarterback has time left in the game to call exactly seven plays—L, M, N, O, P, S, and T—one at a time and in any order according to the following conditions:

• Play P is called either first or last.
• The quarterback calls L at some point before calling N.
• The quarterback calls M at some point before calling T.
• The quarterback calls exactly one play between calling play L and play O.
• The quarterback calls exactly one play between calling play M and play P.

If N is called fourth, all of the following must be false EXCEPT __________.

L is called second

O is called fifth

M is called third

S is called first

L is called first

L is called first

Explanation:

L cannot be called second, because then O would have no place to go, placeholder 4 already being filled by N. M cannot be placed third because then P would come first and L would come in second which, as discussed above, does not work. O cannot be placed fifth because then M must be placed third, P first and thus L second which, again, does not work. If S is first, P comes last, M fifth, T sixth, and L and O must be placed next to each other in the second and third positions which again, violates our conditions. The only answer that violates no conditions is L in the first position.

### Example Question #31 : 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.

Which one of the following could be the assignment of the sports team to the floors of the gymnasium?

third floor:  baseball, football, and track

second floor:  golf, swimming, and track

first floor:  hockey

third floor:  hockey

middle floor:  golf, karate, and track

bottom floor:  baseball, football, and swimming

third floor:  baseball, football, karate, and track

second floor:  hockey

first floor:  golf and swimming

third floor:  football, karate, and track

second floor:  golf and swimming

first floor:  baseball and hockey

third floor:  football, karate, and track

second floor:  baseball, golf, and swimming

first floor:  hockey

third floor:  football, karate, and track

second floor:  baseball, golf, and swimming

first floor:  hockey

Explanation:

Apply each rule singly to the answer choices to strike all the "rule-violaters."  The correct answer remains intack, as it violates none of the rules.

### Example Question #31 : Three Variable

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.

Which one of the following CANNOT be the assignment of sports teams to floors of the gymnasium?

football, karate, swimming, and track

baseball, karate, swimming, and track

baseball, golf, karate, and track

golf, karate, swimming, and track

baseball, football, karate, and track

baseball, karate, swimming, and track

Explanation:

Karate and track must be with either football or golf, by virtue of rules one and two.  The correct answer violates this necessity.

### Example Question #32 : Three Variable

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 baseball conducts practices or workouts on the same floor as swimming, which one of the following could be true?

Exactly three sports teams conduct practices or workouts on the first floor.

Exactly four sports teams conduct practices or workouts on the second floor.

Exactly four sports teams conduct practices or workouts on the first floor.

Exactly one sports team conducts practices or workouts on the second floor.

Exactly two sports teams conduct practices or workouts on the first floor.