# LSAT Logic Games : Solving three-variable logic games

## Example Questions

### Example Question #11 : Solving Three Variable Logic Games

Chef Henri has six dinner specialties, A, B, C, D, E, and F. One dinner specialty, and only one dinner specialty, is presented on the menu for each evening the restaurant is open, which is Monday through Saturday (closed Sunday).

The following conditions must hold:

Free wine is served with C or D, but not for both, and free wine is served only on Tuesday or Wednesday.

A must be served earlier in the week than B or C.

If B is served on Thursday, then B is served earlier in the week than E and F.

If B is not served on Thursday, then B is served later in the week than E and F.

Either D or E is served on Friday.

Which one of the following must be true?

A is served earlier in the week than F.

A is served earlier in the week than E.

E is served earlier in the week than B.

E is served earlier in the week than C.

C is served earlier in the week than B.

C is served earlier in the week than B.

Explanation:

C must be served earlier in the week than B.  A key insight in this problem is that B can only be served on Thursday or Saturday.  This follows from the fact that if B is not served on Thursday, E and F must precede B.  But this particular condition precludes B from being served on Monday, Tuesday, or Wednesday because there are insufficient slots to accommodate E, F, and the free-wine meal (C or D).  These latter dinners must precede B if B is served on a day other than Thursday.  Therefore, the only non-Thursday slot available for B is Saturday (Friday is reserved strictly for D or E).  All this leads to the conclusion that C must be served earlier in the week than B.

### Example Question #12 : Solving Three Variable Logic Games

Chef Henri has six dinner specialties, A, B, C, D, E, and F. One dinner specialty, and only one dinner specialty, is presented on the menu for each evening the restaurant is open, which is Monday through Saturday (closed Sunday).

The following conditions must hold:

Free wine is served with C or D, but not for both, and free wine is served only on Tuesday or Wednesday.

A must be served earlier in the week than B or C.

If B is served on Thursday, then B is served earlier in the week than E and F.

If B is not served on Thursday, then B is served later in the week than E and F.

Either D or E is served on Friday.

If D is the dinner specialty served with free wine, then which one of the following must be true?

B is served on Thursday.

E is served on Friday.

F is served on Monday.

C is served on Tuesday.

D is served on Wednesday

E is served on Friday.

Explanation:

Dinner E must be served on Friday because only Dinners D or E can be served on Friday and the stipulation in the question requires D to be served on either Tuesday or Wednesday.  That leaves dinner E as the only option for Friday.

### Example Question #382 : Lsat Logic Games

Seven retired professional football players---identified as A, B, C, D, E, F, and G to preserve their anonymity from the press---received votes to the Hall of Fame. Because only four can actually be inducted in this particular year, they must be ranked in terms of votes from lowest to highest. The ranking accords with the following specifications:

If B gets more votes than C, and F gets more votes than D, then which one of the following must be true?

Explanation:

We know that B or C must be second, based upon all of our deductions:

A . . . B/C

A . . . C . . . F/G

B . . . E . . . D/F

By combining the latter two sequences, we can establish that B or C must take the second slot. Since the question posits that B received more votes than C, we can quickly arrive at the correct answer: B must be second.

### Example Question #383 : Lsat Logic Games

A creative writing professor is creating a set list for a poetry reading. She is choosing five poems from those written by eight students - Alan, Belle, Charlie, Dorian, Ernest, Xue, Yardley, and Zack. The poem's chosen and the order in which they are presented must conform to the following restrictions:

If Alan is chosen, Belle is also chosen

If Charlie is chosen, Dorian is not chosen

Ernest is chosen if and only if Xue is chosen

If Belle and Yardley are both chosen, Belle must read before Yardley

If Zack is chosen he must read first

If Charlie and Alan are both chosen, Charlie must read before Alan

Which of the following must be false?

Explanation:

If Yardley reads first, Belle cannot be in the game because she cannot read before Yardley. If Belle is not in the game, Alan is not in the game either. And if Yardley is in the first spot, Zack cannot be in the game at all. This leaves only Charlie, Dorian, Ernest and Xue to fill the remaining four spots. Since Charlie and Dorian can never read together, this scenario can never happen.

### Example Question #383 : Linear Games

A baker is making three pizzas, one at a time, each with two toppings. The baker has six available toppings--anchovies, bacon, mushrooms, peppers, sausage, tomatoes. No topping can be put on more than one pizza. The pairings of toppings must conform to the following rules:

Anchovies cannot be paired with peppers

Mushrooms and tomatoes must be on the same pizza

Sausage must be on the second pizza if mushrooms are on the first

Peppers must be on a pizza made after the pizza with sausage

If mushrooms and tomatoes can be on different pizzas, but all other conditions remain the same, which of the following could be true when peppers are on the second pizza?

Anchovies and sausage are on the third pizza

Sausage and anchovies are on consecutive pizzas

Tomatoes are on the first pizza

Mushrooms are on the first pizza

Tomatoes are on the second pizza and bacon and anchovies are on the same pizza

Tomatoes are on the first pizza

Explanation:

The important thing to note here is that, under the new conditions, mushrooms cannot be on the first pizza but tomatoes could be.  If mushrooms are on the first pizza, sausage must be on the second, but peppers and sausage may not be on the same pizza.

### Example Question #391 : Linear Games

A professor is selecting students to work in pairs on four separate parts of a final presentation. There are eight students in the class. Lisa, Marc, Nina and Oliver are seniors; William, Xavier, Yolanda and Zoe are juniors. The pairs will present their sections in a specific order, first through fourth. The assignments of partners and sections must conform to the following restrictions:

Each pair must consist of one senior and one junior

Lisa must be paired with William

Nina cannot be paired with Yolanda

William must present in an earlier group than Zoe

Marc can only present first if Oliver presents third

Which of the following is a complete and accurate list of how the final could be presented?

Marc and Yolanda; Lisa and William; Nina and Zoe; Oliver and Xavier

Nina and Xavier; Marc and Zoe; Lisa and William; Oliver and Yolanda

Oliver and Yolanda; Marc and Xavier; Lisa and William; Nina and Zoe

Marc and Xavier; Lisa and William; Oliver and Zoe; Nina and Yolanda

Lisa and Yolanda; Nina and William; Marc and Xavier; Oliver and Zoe

Oliver and Yolanda; Marc and Xavier; Lisa and William; Nina and Zoe

Explanation:

We can eliminate any answer that fails to pair Lisa and William. We can then eliminate any answer that has Zoe presenting before William. Then we eliminate any answer that pairs Nina with Yolanda. We then eliminate any answer that has Marc presenting first without Oliver presenting third. By going through all of the rules and eliminating in this fashion we are left with only the correct answer.

### Example Question #14 : Solving Three Variable Logic Games

A professor is selecting students to work in pairs on four separate parts of a final presentation. There are eight students in the class. Lisa, Marc, Nina and Oliver are seniors; William, Xavier, Yolanda and Zoe are juniors. The pairs will present their sections in a specific order, first through fourth. The assignments of partners and sections must conform to the following restrictions:

Each pair must consist of one senior and one junior

Lisa must be paired with William

Nina cannot be paired with Yolanda

William must present in an earlier group than Zoe

Marc can only present first if Oliver presents third

If Marc presents in the first group, what is a complete and accurate list of whom his partners could be?

Yolanda, Zoe

Xavier, Zoe

William, Xavier, Yolanda, Zoe

Xavier, Yolanda

Xavier, Yolanda, Zoe

Xavier, Yolanda

Explanation:

If Marc presents first, we know that Oliver must present third. Then we must put Lisa and William in the second slot, since William must present before Zoe, and that would not be possible if he and Lisa presented fourth. We are left with placing Xavier, Yolanda and Zoe. Zoe cannot go first, since she must present after William. Therefore the only possible juniors who could be paired with Marc are Xavier and Yolanda.

### Example Question #11 : Solving Three Variable Logic Games

A professor is selecting students to work in pairs on four separate parts of a final presentation. There are eight students in the class - Lisa, Marc, Nina and Oliver are seniors; William, Xavier, Yolanda and Zoe are juniors. The pairs will present their sections in a specific order, first through fourth. The assignments of partners and sections must conform to the following restrictions:

Each pair must consist of one senior and one junior

Lisa must be paired with William

Nina cannot be paired with Yolanda

William must present in an earlier group than Zoe

Marc can only present first if Oliver presents third

If Zoe presents in the second group, which of the following CANNOT be true?

Yolanda presents third

Nina presents second

Xavier does not present second

Marc presents first

Oliver presents third

Marc presents first

Explanation:

If Zoe presents second, we automatically know that William must present first. William must always be paried with Lisa, therefore the senior spot in the first group is filled, and Marc could never present first. *Note - Oliver can still present third even if Marc does not present first. The conditional states that Oliver must be third if Marc is first, but Oliver can still be third even if Marc is not first.

### Example Question #11 : Three Variable

A professor is selecting students to work in pairs on four separate parts of a final presentation. There are eight students in the class - Lisa, Marc, Nina and Oliver are seniors; William, Xavier, Yolanda and Zoe are juniors. The pairs will present their sections in a specific order, first through fourth. The assignments of partners and sections must conform to the following restrictions:

Each pair must consist of one senior and one junior

Lisa must be paired with William

Nina cannot be paired with Yolanda

William must present in an earlier group than Zoe

Marc can only present first if Oliver presents third

All of the following statements could be true EXCEPT:

Nina presents second and Oliver presents fourth

Lisa presents third and Xavier presents second

Oliver presents third and Lisa presents first

Marc presents first and Yolanda presents fourth

Zoe presents second and Yolanda presents third

Marc presents first and Yolanda presents fourth

Explanation:

If Marc presents first, we automatically put Oliver in the third spot. As previously discussed, Lisa and William fill out the second spot and Nina must go in the fourth. Nina cannot be paired with Yolanda - therefore, if Marc presents first, Yolanda cannot present fourth.

### Example Question #11 : 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.

Which is the possible order of the objects and their boxes?

Box 1: Globe, Bunsen Burner

Box 2: Fossil, Telescope

Box 3: Hourglass, Microscope

Box 1: Bunsen Burner, Microscope

Box 2: Fossil, Globe

Box 3: Hourglass, Telescope

Box 1: Telescope, Globe

Box 2: Fossil, Hourglass

Box 3: Bunsen Burner, Microscope

Box 1: Microscope, Telescope

Box 2: Globe, Bunsen Burner

Box 3: Fossil, Hourglass

Box 1: Fossil, Microscope

Box 2: Bunsen Burner, Globe

Box 3: Hourglass, Telescope

Box 1: Bunsen Burner, Microscope

Box 2: Fossil, Globe

Box 3: Hourglass, Telescope

Explanation:

Let's go through our restrictions one at a time. First, we know that the microscope and the telescope cannot be in the same box, so we can automatically delete one answer choice. Next, we know that the hourglass is in the box directly after the box with the globe in it. We can delete the answer choice where it is not. We also know that if the fossil is in the second box, the Bunsen burner must be in the first box. One of our answer choices does not follow this restriction; delete it. Finally, we know that the fossil cannot be in the first box.

We are left with one answer, and it follows all of our restrictions. It must be correct.