# LSAT Logic Games : Solving two-variable logic games

## Example Questions

### Example Question #11 : Solving Two Variable Logic 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?

P

S

R

T

Q

Q

Explanation:

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 #11 : Solving Two Variable Logic 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?

S, T

P, T, R

P, S, T, R

P, S, T

P, S, R

P, S, T

Explanation:

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 #13 : Solving Two Variable Logic 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 more shows than Adrian.

Brett hosts both Q and S.

Calvin hosts more shows than Brett.

Calvin hosts both T and P.

Explanation:

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:

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.

### Example Question #11 : Solving Two Variable Logic 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 Q is aired after Brett’s first show, which of the following could be true?

Brett hosts both Q and R.

R is aired from 7:00-8:00.

Adrian hosts both P and S.

Calvin hosts the 9:00-10:00 show.

Brett hosts the shows aired at 8:00-9:00 and 9:00-10:00.

Brett hosts the shows aired at 8:00-9:00 and 9:00-10:00.

Explanation:

Since the latest spot that Q can air is the 7:00-8:00 slot, it follows that it will air then and Brett will host P, the only show that can air before Q, at 6:00-7:00. In order to satisfy the rule that Adrian's first show must have two shows in between it and Calvin's first show, Adrian must host Q at 7:00-8:00 and Calvin will host the 10:00-11:00 slot. Working off the Q - R - (S/T) order, that puts R in the 8:00-9:00 slot and leaves T and S in the last two spots in any order. That gives us the following model:

6:00-7:00: P: Brett
10:00-11:00: T/S: Calvin

Using this model, we can identify all of the incorrect answers as claims that must be false within the context of the question. The correct answer points out correctly that Brett can host both of the shows in the 8:00-9:00 and 9:00-10:00 slots.

### Example Question #15 : Solving Two Variable Logic Games

A cruise line company is preparing the itinerary for its upcoming global tour. The cruise will last five months and travel to exactly one of seven countries – C, D, E, F, G, H, I – each month. No country may be visited more than once. The following conditions must hold:

C or D is part of the itinerary, but not both.
If F is part of the itinerary, G is also included.
If E is part of the itinerary, it is visited earlier in the cruise than D and G.
If F is part of the itinerary, it is visited later in the cruise than both E and H.
I is part of the itinerary and must be visited during either the first or fifth month.

Which of the following could be an accurate itinerary, going chronologically from the first month to the fifth?

E, C, F, G, I

C, E, F, D, I

I, E, D, F, H

C, G, E, F, I

H, C, E, F, G

E, C, F, G, I

Explanation:

Each of the incorrect answers violates one of the stated conditions:

(C, G, E, F, I) - E is visited earlier in the cruise than G.

(I, E, D, F, H) - H is visited earlier in the cruise than F.

(C, E, F, D, I) - C and D cannot both be part of the itinerary.

(H, C, E, F, G) - I must be part of the itinerary in either the first or the fifth month.

The correct answer does not violate any of the stated conditions.

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

A cruise line company is preparing the itinerary for its upcoming global tour. The cruise will last five months and travel to exactly one of seven countries – C, D, E, F, G, H, I – each month. No country may be visited more than once. The following conditions must hold:

C or D is part of the itinerary, but not both.
If F is part of the itinerary, G is also included.
If E is part of the itinerary, it is visited earlier in the cruise than D and G.
If F is part of the itinerary, it is visited later in the cruise than both E and H.
I is part of the itinerary and must be visited during either the first or fifth month.

Which of the following CANNOT be the country visited in the fifth month of the tour?

D

H

E

F

G

E

Explanation:

There is no possible scenario in which E can be visited in the fifth month. Since D, G, and F can only be included if they are visited after E, that leaves only I, C, and H to fill the itinerary, insufficient for a full itinerary.

### Example Question #17 : Solving Two Variable Logic Games

A cruise line company is preparing the itinerary for its upcoming global tour. The cruise will last five months and travel to exactly one of seven countries – C, D, E, F, G, H, I – each month. No country may be visited more than once. The following conditions must hold:

C or D is part of the itinerary, but not both.
If F is part of the itinerary, G is also included.
If E is part of the itinerary, it is visited earlier in the cruise than D and G.
If F is part of the itinerary, it is visited later in the cruise than both E and H.
I is part of the itinerary and must be visited during either the first or fifth month.

If E is the country visited in the fourth month of the tour, which of the following could be true?

F is the country visited in the fifth month.

H is the country visited in the third month.

I is the country visited in the fifth month.

D is the country visited in the fifth month.

C is the country visited in the first month.

H is the country visited in the third month.

Explanation:

Each of the incorrect answers must be false in the above scenario. If E is fourth, that means that there must be three countries visited beforehand and as D, G, F can only be after E, that leaves I, C, and H as the first three countries. I is the first country visited since it can only be visited in the first or fifth month and H or C can go in the second or third months in any order.

This gives us the following model:

I (1) - H/C (2) - C/H (3) - E (4) - (5)

For the fifth month, we can eliminate D since both C and D cannot be part of the itinerary. F can also be eliminated since that would force G to be included as well and there is only one spot after E, where G would have to be placed. That leaves the only possible country that can be visited in the fifth month as G and provides the following model:

I (1) - H/C (2) - C/H (3) - E (4) - G (5)

Looking at the answers, H being visited in the third month is the only one that is possible in this scenario.

### Example Question #18 : Solving Two Variable Logic Games

A cruise line company is preparing the itinerary for its upcoming global tour. The cruise will last five months and travel to exactly one of seven countries – C, D, E, F, G, H, I – each month. No country may be visited more than once. The following conditions must hold:

C or D is part of the itinerary, but not both.
If F is part of the itinerary, G is also included.
If E is part of the itinerary, it is visited earlier in the cruise than D and G.
If F is part of the itinerary, it is visited later in the cruise than both E and H.
I is part of the itinerary and must be visited during either the first or fifth month.

Which of the following must be false?

F is the country visited in the first month.

D is the country visited in the first month.

G is the country visited in the second month.

H is the country visited in the fourth month.

C is the country visited in the fifth month.

F is the country visited in the first month.

Explanation:

The correct answer cannot occur in any scenario. If F is the first country visited, that eliminates both E and H from the itinerary since they must be visited before F. That leaves C, D, G, and I as the remaining countries, but C and D are mutually exclusive. As a result, there are not enough countries to make a full itinerary.

The incorrect answers are all possible under certain conditions.

### Example Question #13 : Solving Two Variable Logic Games

A cruise line company is preparing the itinerary for its upcoming global tour. The cruise will last five months and travel to exactly one of seven countries – C, D, E, F, G, H, I – each month. No country may be visited more than once. The following conditions must hold:

C or D is part of the itinerary, but not both.
If F is part of the itinerary, G is also included.
If E is part of the itinerary, it is visited earlier in the cruise than D and G.
If F is part of the itinerary, it is visited later in the cruise than both E and H.
I is part of the itinerary and must be visited during either the first or fifth month.

If H is the country visited in the fifth month of the tour, which of the following pairs of countries must be part of the itinerary?

E and G

E and F

F and G

C and I

D and E

E and G

Explanation:

If H is the country visited in the fifth month, that means that I is the country visited in the first month. Furthermore, F cannot be part of the itinerary since it must be after H and there are no possible spots. That leaves E, G, and one of C or D to fill the slots in the second through fourth months. Neither C or D individually must be part of the itinerary, however, so that leaves E and G as the only two countries that must be visited in this scenario.

### Example Question #20 : Solving Two Variable Logic Games

A cruise line company is preparing the itinerary for its upcoming global tour. The cruise will last five months and travel to exactly one of seven countries – C, D, E, F, G, H, I – each month. No country may be visited more than once. The following conditions must hold:

C or D is part of the itinerary, but not both.
If F is part of the itinerary, G is also included.
If E is part of the itinerary, it is visited earlier in the cruise than D and G.
If F is part of the itinerary, it is visited later in the cruise than both E and H.
I is part of the itinerary and must be visited during either the first or fifth month.

If C is the country visited in the first month of the tour, each of the following could be true EXCEPT:

G is the country visited in the third month.

E is the country visited in the third month.

G is the country visited in the second month.

H is the company visited in the fourth month.

F is the country visited in the second month.