# LSAT Logic Games : Solving three-variable logic games

## Example Questions

### Example Question #21 : Solving Three Variable Logic Games

Annie is packing her things to move. She has six objects left to pack: a globe, a microscope, a telescope, a fossil, a Bunsen burner, and an hourglass. She has three boxes left and wants to put exactly two objects in each box. Her packing choices are restricted to the following limits:

The microscope and the telescope cannot be in the same box.
The hourglass must be placed in the box directly after the globe.
If the fossil is in the second box, the Bunsen burner must be in the first box.
The first box cannot contain the fossil.

If the globe is in the same box as the fossil, what must be true?

Possible Answers:

The hourglass must be in the first box.

The globe must be in the third box.

The telescope must be in the first box.

The microscope must be in the fourth box.

The Bunsen burner must be in the first box.

Correct answer:

The Bunsen burner must be in the first box.

Explanation:

We know that the fossil and the globe are in the same box, and we know that the fossil cannot be in the first box. We also know that the hourglass must be placed in the box directly after the globe, so the globe cannot be placed in the last box, either. This means that the fossil and globe must be placed in the second box. Then, if the fossil is placed in the second box, we know that the Bunsen burner must be placed in the first box. Thus, we have our answer.

### Example Question #22 : Three Variable

Annie is packing her things to move. She has six objects left to pack: a globe, a microscope, a telescope, a fossil, a Bunsen burner, and an hourglass. She has three boxes left and wants to put exactly two objects in each box. Her packing choices are restricted to the following limits:

The microscope and the telescope cannot be in the same box.
The hourglass must be placed in the box directly after the globe.
If the fossil is in the second box, the Bunsen burner must be in the first box.
The first box cannot contain the fossil.

If the microscope is in the second box, what must be true?

Possible Answers:

The fossil is in the third box.

The telescope is in the first box.

The globe must be in the first box.

The hourglass must be in the second box.

The Bunsen burner is in the third box.

Correct answer:

The fossil is in the third box.

Explanation:

We know that the microscope is in the second box. We also know that the globe must be in the first or second box. This is because the hourglass is in the box directly after the globe, so the globe cannot be in the third box. If the globe is in the first box, then the hourglass must be in the second box with the microscope. If the globe is not in the first box, it must be in the second box with the microscope. So the second box is full.

We also know that the fossil cannot be in the first box. And since the second box is full, that leaves only the third box for the fossil. Thus, the fossil must be in the third box.

### Example Question #23 : Three Variable

Annie is packing her things to move. She has six objects left to pack: a globe, a microscope, a telescope, a fossil, a Bunsen burner, and an hourglass. She has three boxes left and wants to put exactly two objects in each box. Her packing choices are restricted to the following limits:

The microscope and the telescope cannot be in the same box.
The hourglass must be placed in the box directly after the globe.
If the fossil is in the second box, the Bunsen burner must be in the first box.
The first box cannot contain the fossil.

If the fossil is in the second box, which of the following could be true?

Possible Answers:

The globe is in the first box.

The telescope is in the second box.

The microscope is in the second box.

The hourglass is in the second box.

The microscope is in the first box.

Correct answer:

The microscope is in the first box.

Explanation:

Since the fossil is in the second box, that means that the Bunsen burner must be in the first box.

Let's now look at our answer choices. If the globe is in the first box with the Bunsen burner, that means that the hourglass must be in the second box with the fossil, and thus the microscope and telescope would be in the third box together. But we know that the microscope and telescope cannot be in the same box, so we see that two of our answer choices are not possible.

Now let's put the telescope in the second box with the fossil. That means that the globe is either in the first box with the Bunsen burner or the third box. But since the hourglass must be placed in the box directly after the globe, we know that the globe cannot be placed in the third box; so it must be placed in the first. But that is also impossible, because the hourglass would then have to go in the third box, meaning that it is not placed in the box directly after the globe. The same problem arises when we place the microscope in the second box. The hourglass does not directly follow the globe.

Let's place the microscope in the first box. Then we can place the globe in the second box with the fossil, and the hourglass in the third box in the telescope. This works. Thus, it is the correct answer.

### Example Question #21 : Three Variable

Annie is packing her things to move. She has six objects left to pack: a globe, a microscope, a telescope, a fossil, a Bunsen burner, and an hourglass. She has three boxes left and wants to put exactly two objects in each box. Her packing choices are restricted to the following limits:

The microscope and the telescope cannot be in the same box.
The hourglass must be placed in the box directly after the globe.
If the fossil is in the second box, the Bunsen burner must be in the first box.
The first box cannot contain the fossil.

If in the Bunsen burner is in the same box as the hourglass, which of the following must be true?

Possible Answers:

The globe cannot be in the first box.

The fossil cannot be in the second box.

The telescope cannot be in the first box.

The microscope cannot be in the fourth box.

The Bunsen burner cannot be in the second box.

Correct answer:

The fossil cannot be in the second box.

Explanation:

So we know that the Bunsen burner and the hourglass are in the same box. We also know that the hourglass is in the box directly following the globe, so the hourglass cannot be in the first box; it must be in either the second or the third box. Since the hourglass is not in the first box, the Bunsen burner also cannot be in the first box. Since the Bunsen burner is not in the first box, the fossil cannot be in the second box. We have our answer.

### Example Question #21 : Three Variable

Last week, Sara, Tony, Ulrich, Victor, and Wynne each saw La Traviata once at the opera house. The group divided up five tickets—one for the Thursday performance, one for the Friday performance, two for the Saturday performance, and one for the Sunday matinee—according to the following conditions:

• Neither Sara nor Victor attend Saturday performances
• If Wynne sees the opera before Victor, Wynne sees the first performance.
• Ulrich does not see a performance until Tony has also seen a performance.

Which one of the following could be a complete and accurate matching of the theatre-goers to the days on which they saw the opera?

Possible Answers:

Thursday: Tony

Friday: Victor

Saturday: Ulrich, Wynne

Sunday: Sara

Thursday: Wynne

Friday: Sara

Saturday: Tony, Victor

Sunday: Ulrich

Thursday: Wynne

Friday: Tony

Saturday: Ulrich, Sara

Sunday: Victor

Thursday: Tony

Friday: Wynne

Saturday: Ulrich, Sara

Sunday: Victor

Thursday: Victor

Friday: Sara

Saturday: Ulrich, Wynne

Sunday: Tony

Correct answer:

Thursday: Tony

Friday: Victor

Saturday: Ulrich, Wynne

Sunday: Sara

Explanation:

The correct answer satisfies the conditions that neither Sara nor Victor attend Satuday. Wynne in this case does not attend before Victor, so need not be first. Ulric sees the show after Tony has gone. This is a possible distribution of opera tickets.

### Example Question #21 : Three Variable

Last week, Sara, Tony, Ulrich, Victor, and Wynne each saw La Traviata once at the opera house. The group divided up five tickets—one for the Thursday performance, one for the Friday performance, two for the Saturday performance, and one for the Sunday matinee—according to the following conditions:

• Neither Sara nor Victor attend Saturday performances
• If Wynne sees the opera before Victor, Wynne sees the first performance.
• Ulrich does not see a performance until Tony has also seen a performance.

Which of the following is a complete and accurate listing of the people who can attend the Thursday show?

Possible Answers:

Sara, Tony, Wynne

Sara, Tony, Victor, Wynne

Sara, Tony, Victor

Sara, Tony, Ulrich, Victor, Wynne

Sara, Tony, Ulrich, Wynne

Correct answer:

Sara, Tony, Victor

Explanation:

Ulrich cannot see the first performance by the third rule in the problem. Neither can Wynne: if Wynne sees the Thursday show, there are only two non-Saturday tickets, which must be used by Sara and Victor. This leaves Ulrich and Tony to see the show at the same time, which violates this third rule again.

### Example Question #21 : Solving Three Variable Logic Games

Last week, Sara, Tony, Ulrich, Victor, and Wynne each saw La Traviata once at the opera house. The group divided up five tickets—one for the Thursday performance, one for the Friday performance, two for the Saturday performance, and one for the Sunday matinee—according to the following conditions:

• Neither Sara nor Victor attend Saturday performances
• If Wynne sees the opera before Victor, Wynne sees the first performance.
• Ulrich does not see a performance until Tony has also seen a performance.

Which of the following is a complete and accurate listing of all of the shows that Victor can see?

Possible Answers:

Friday, Saturday

Thursday, Friday, Saturday

Thursday, Friday, Sunday

Thursday, Friday, Saturday, Sunday

Thursday, Friday

Correct answer:

Thursday, Friday

Explanation:

We know that Wynne cannot see the Thursday show because it would leave Ulrich and Tony to see the opera at the same time. As a result, Wynne must always see the opera after Victor. Victor cannot attend the Saturday performance, nor can he attend Sunday if Wynne has to see the show after him. As a result, Victor can only see the Thursday or Friday shows.

### Example Question #402 : Linear Games

Last week, Sara, Tony, Ulrich, Victor, and Wynne each saw La Traviata once at the opera house. The group divided up five tickets—one for the Thursday performance, one for the Friday performance, two for the Saturday performance, and one for the Sunday matinee—according to the following conditions:

• Neither Sara nor Victor attend Saturday performances
• If Wynne sees the opera before Victor, Wynne sees the first performance.
• Ulrich does not see a performance until Tony has also seen a performance.

If Tony sees the opera first, which of the following must be true?

Possible Answers:

Sarah sees the show last.

Wynne sees the show after Ulrich.

Sarah sees the show before Victor.

Either Sarah or Victor could see the opera second.

Neither Victor nor Wynne see the Saturday show.

Correct answer:

Sarah sees the show last.

Explanation:

If Tony sees it first, there is only one possible order: T,V,UW,S

### Example Question #24 : Three Variable

Last week, Sara, Tony, Ulrich, Victor, and Wynne each saw La Traviata once at the opera house. The group divided up five tickets—one for the Thursday performance, one for the Friday performance, two for the Saturday performance, and one for the Sunday matinee—according to the following conditions:

• Neither Sara nor Victor attend Saturday performances
• If Wynne sees the opera before Victor, Wynne sees the first performance.
• Ulrich does not see a performance until Tony has also seen a performance.

Which of the following would have the same effect as the rule that says if Wynne sees the opera before Victor, Wynne sees the first performance?

Possible Answers:

Sarah must see the opera either first or last.

Wynne must either see the Saturday or Sunday performance.

Victor must see the Friday performance, and Wynne cannot see the last performance.

Ulrich must see the Saturday performance.

Victor must see the opera before Ulrich, and Wynne must see the Saturday performance.

Correct answer:

Victor must see the opera before Ulrich, and Wynne must see the Saturday performance.

Explanation:

There are only four total arrangements that satisfy the rules given. Only one of the options keeps the four arrangements as tickets as is.

### Example Question #25 : Three Variable

Last week, Sara, Tony, Ulrich, Victor, and Wynne each saw La Traviata once at the opera house. The group divided up five tickets—one for the Thursday performance, one for the Friday performance, two for the Saturday performance, and one for the Sunday matinee—according to the following conditions:

• Neither Sara nor Victor attend Saturday performances
• If Wynne sees the opera before Victor, Wynne sees the first performance.
• Ulrich does not see a performance until Tony has also seen a performance.

How many total arrangements of tickets to people are there?

Possible Answers:

6

3

4

5

1

Correct answer:

4

Explanation:

The only people who can see the first show are Tony, Sarah, and Victor. Of these initial choices, there is only one arrangement each if Tony or Sarah sees the first show, and two if Victor sees the first show.