# LSAT Logic Games : Solving two-variable logic games

## Example Questions

### Example Question #31 : Solving Two Variable Logic Games

A car dealership is displaying vehicles in its showroom. The dealership will select six vehicles from seven models: A, B, C, D, E, F, and G.  Models A and B are trucks and all other models are cars. The vehicles must be displayed in the showroom in a row according to the following conditions:

If C is displayed, then both trucks also must be displayed

E always must be displayed first or last

If both D and F are displayed, there must be exactly two vehicles after D and before F

A and B cannot be next to each other

Which of the following could be the order of the vehicles in the showroom?

D, A, C, B, F, E

D, A, C, F, E, B

D, A, C, F, B, E

D, A, C, F, G, E

D, A, B, F, C, E

D, A, C, F, B, E

Explanation:

Each incorrect answer choice violates one or more conditions.  Carefully apply the rules to eliminate the incorrect answers.

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

A car dealership is displaying vehicles in its showroom. The dealership will select six vehicles from seven models: A, B, C, D, E, F, and G.  Models A and B are trucks and all other models are cars. The vehicles must be displayed in the showroom in a row according to the following conditions:

If C is displayed, then both trucks also must be displayed

E always must be displayed first or last

If both D and F are displayed, there must be exactly two vehicles after D and before F

A and B cannot be next to each other

If G and C are displayed, which of the following must be true?

Either D or F is not displayed

E is displayed first

Either A or B is not displayed

Either G or C is displayed third

E is immediately adjacent to either G or C

Either D or F is not displayed

Explanation:

When C and G are displayed, the display must include A, B, C, G, and E.  This leaves only one open space, which means that either D or F cannot be displayed.

### Example Question #33 : Solving Two Variable Logic Games

A car dealership is displaying vehicles in its showroom. The dealership will select six vehicles from seven models: A, B, C, D, E, F, and G.  Models A and B are trucks and all other models are cars. The vehicles must be displayed in the showroom in a row according to the following conditions:

If C is displayed, then both trucks also must be displayed

E always must be displayed first or last

If both D and F are displayed, there must be exactly two vehicles after D and before F

A and B cannot be next to each other

Which of the following models must be displayed?

C

B

D

A

E

E

Explanation:

The rules expressly state that E must be displayed either first or last. As a result, E must be displayed no matter which other vehicles are shown.  The other models are only required to be shown if certain conditions are met.

### Example Question #34 : Solving Two Variable Logic Games

A car dealership is displaying vehicles in its showroom. The dealership will select six vehicles from seven models: A, B, C, D, E, F, and G.  Models A and B are trucks and all other models are cars. The vehicles must be displayed in the showroom in a row according to the following conditions:

If C is displayed, then both trucks also must be displayed

E always must be displayed first or last

If both D and F are displayed, there must be exactly two vehicles after D and before F

A and B cannot be next to each other

If the rules are modified so that A and B must be displayed next to each other, and if A is displayed second and G is not displayed, which of the following must be true?

B is displayed first

F is displayed sixth

C is displayed fifth

D is displayed third

E is displayed first

C is displayed fifth

Explanation:

Under these conditions, there is only one possible arrangement.  Since E must be first or last and B must be adjacent to A, there only can be two cars between D and F if D is first and F fourth.  B must be third, which leaves only the fifth spot available for C.

### Example Question #301 : Linear Games

Four roommates – Aaron, Brad, Clark, and Dave – are deciding how to schedule their delivery laundry service for the week. They must all set one pickup day and one delivery day between Monday and Saturday. There may be only one pickup and one delivery that occur each day, subject to the following conditions:

A pickup day cannot be scheduled on Wednesday.
A delivery day cannot be scheduled on Tuesday.
There must be exactly two days in-between Aaron’s pickup day and his delivery day.
Brad’s delivery day must be scheduled before Thursday.
Clark’s delivery day must be scheduled before Dave’s pickup day.

Which one of the following could be an accurate list of the pickup and delivery days scheduled for the week?

Monday: Aaron (Pickup), Aaron (Delivery);
Wednesday: Aaron (Delivery);
Friday: Clark (Pickup), Clark (Delivery);
Saturday: Dave (Pickup), Dave (Delivery).

Thursday: Clark (Pickup), Clark (Delivery);
Friday: Dave (Pickup), Aaron (Delivery);
Saturday: Dave (Delivery).

Monday: Aaron (Pickup);
Thursday: Dave (Pickup), Aaron (Delivery);
Friday: Clark (Pickup), Clark (Delivery);
Saturday: Dave (Delivery).

Tuesday: Aaron (Pickup);
Thursday: Clark (Pickup), Aaron (Delivery);
Friday: Dave (Pickup), Dave (Delivery);
Saturday: Clark (Delivery).

Monday: Aaron (Pickup);
Thursday: Clark (Pickup), Aaron (Delivery);
Friday: Clark (Delivery);
Saturday: Dave (Pickup), Dave (Delivery).

Monday: Aaron (Pickup);
Thursday: Clark (Pickup), Aaron (Delivery);
Friday: Clark (Delivery);
Saturday: Dave (Pickup), Dave (Delivery).

Explanation:

The incorrect answers all violate at least one of the stated rules:

Thursday: Clark (Pickup), Clark (Delivery);
Friday: Dave (Pickup), Aaron (Delivery);
Saturday: Dave (Delivery).

Tuesday cannot have a delivery day scheduled.

Monday: Aaron (Pickup);
Thursday: Dave (Pickup), Aaron (Delivery);
Friday: Clark (Pickup), Clark (Delivery);
Saturday: Dave (Delivery).

Wednesday cannot have a pickup day scheduled.

Monday: Aaron (Pickup), Aaron (Delivery);
Wednesday: Aaron (Delivery);
Friday: Clark (Pickup), Clark (Delivery);
Saturday: Dave (Pickup), Dave (Delivery).

Aaron must have exactly two days in-between his pickup and delivery days.

Tuesday: Aaron (Pickup);
Thursday: Clark (Pickup), Aaron (Delivery);
Friday: Dave (Pickup), Dave (Delivery);
Saturday: Clark (Delivery).

Clark's delivery day must be scheduled before Dave's pickup day.

The correct answer violates none of the stated rules.

### Example Question #36 : Solving Two Variable Logic Games

Four roommates – Aaron, Brad, Clark, and Dave – are deciding how to schedule their delivery laundry service for the week. They must all set one pickup day and one delivery day between Monday and Saturday. There may be only one pickup and one delivery that occur each day, subject to the following conditions:

A pickup day cannot be scheduled on Wednesday.
A delivery day cannot be scheduled on Tuesday.
There must be exactly two days in-between Aaron’s pickup day and his delivery day.
Brad’s delivery day must be scheduled before Thursday.
Clark’s delivery day must be scheduled before Dave’s pickup day.

Which one of the following must be true?

Chris’ delivery day is on Friday.

Aaron’s pickup day is on Tuesday.

Brad’s pickup day is on Monday.

Dave’s delivery day is on Saturday.

Brad’s delivery day is on Wednesday.

Dave’s delivery day is on Saturday.

Explanation:

The correct answer must be true in all scenarios. There are only two scenarios that can be constructed around the number of positions Aaron's pickup and delivery days can be created:

Monday: Aaron (Pickup);
Thursday: Aaron (Delivery);
Friday: Chris (Delivery);
Saturday: Dave (Delivery).

Chris' pickup day can be on either Thursday or Friday and Dave's pickup day can be on either Friday or Saturday and still satisfy all the conditions.

Tuesday: Aaron (Pickup);
Thursday: Chris (Pickup), Chris (Delivery);
Friday: Aaron (Delivery);
Saturday: Dave (Delivery).

Brad's delivery day can be on either Monday or Wednesday and Dave's pickup day can be on either Friday or Saturday and still satisfy all the conditions.

As seen, Dave's delivery deal must be on Saturday in all the possible scenarios. The remainder of the answers do not necessarily have to be true in all scenarios.

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

Four roommates – Aaron, Brad, Clark, and Dave – are deciding how to schedule their delivery laundry service for the week. They must all set one pickup day and one delivery day between Monday and Saturday. There may be only one pickup and one delivery that occur each day, subject to the following conditions:

A pickup day cannot be scheduled on Wednesday.
A delivery day cannot be scheduled on Tuesday.
There must be exactly two days in-between Aaron’s pickup day and his delivery day.
Brad’s delivery day must be scheduled before Thursday.
Clark’s delivery day must be scheduled before Dave’s pickup day.

If Brad’s delivery day is on Monday, how many of the days’ schedules are completely determined?

One

Four

Five

Three

Two

Four

Explanation:

If Brad's delivery day is on Monday, it produces the following scenario:

Tuesday: Aaron (Pickup);
Thursday: Chris (Pickup), Chris (Delivery);
Friday: Aaron (Delivery);
Saturday: Dave (Delivery).

Since Dave's pickup day can be held on either Friday or Saturday, it means that four of the six days are completely determined.

### Example Question #38 : Solving Two Variable Logic Games

Four roommates – Aaron, Brad, Clark, and Dave – are deciding how to schedule their delivery laundry service for the week. They must all set one pickup day and one delivery day between Monday and Saturday. There may be only one pickup and one delivery that occur each day, subject to the following conditions:

A pickup day cannot be scheduled on Wednesday.
A delivery day cannot be scheduled on Tuesday.
There must be exactly two days in-between Aaron’s pickup day and his delivery day.
Brad’s delivery day must be scheduled before Thursday.
Clark’s delivery day must be scheduled before Dave’s pickup day.

Which one of the following is a complete and accurate list of the days on which Brad can have his laundry picked up?

Tuesday, Thursday

Monday, Friday, Saturday

Monday

Monday, Tuesday

Monday, Tuesday, Thursday

Monday, Tuesday

Explanation:

Going off the two scenarios mentioned earlier:

Monday: Aaron (Pickup);
Thursday: Aaron (Delivery);
Friday: Chris (Delivery);
Saturday: Dave (Delivery).

Chris' pickup day can be on either Thursday or Friday and Dave's pickup day can be on either Friday or Saturday and still satisfy all the conditions.

Tuesday: Aaron (Pickup);
Thursday: Chris (Pickup), Chris (Delivery);
Friday: Aaron (Delivery);
Saturday: Dave (Delivery).

Brad's delivery day can be on either Monday or Wednesday and Dave's pickup day can be on either Friday or Saturday and still satisfy all the conditions.

As seen in the scenarios presented, Brad's pickup day can only be on Monday or Tuesday.

### Example Question #302 : Linear Games

Four roommates – Aaron, Brad, Clark, and Dave – are deciding how to schedule their delivery laundry service for the week. They must all set one pickup day and one delivery day between Monday and Saturday. There may be only one pickup and one delivery that occur each day, subject to the following conditions:

A pickup day cannot be scheduled on Wednesday.
A delivery day cannot be scheduled on Tuesday.
There must be exactly two days in-between Aaron’s pickup day and his delivery day.
Brad’s delivery day must be scheduled before Thursday.
Clark’s delivery day must be scheduled before Dave’s pickup day.

If Aaron’s delivery day is on Thursday, which of the following must be false?

Clark’s pickup day is on Friday.

Dave’s pickup day is on Friday.

Aaron’s pickup day is on Monday.

Clark’s pickup day is on Thursday.

Brad’s delivery day is on Monday.

Brad’s delivery day is on Monday.

Explanation:

A Thursday delivery day for Aaron forces the following scenario:

Monday: Aaron (Pickup);
Thursday: Aaron (Delivery);
Friday: Chris (Delivery);
Saturday: Dave (Delivery).

Chris' pickup day can be on either Thursday or Friday and Dave's pickup day can be on either Friday or Saturday and still satisfy all the conditions.

As a result, there cannot be a scenario in which Brad has a delivery day on Monday, making it the correct answer.

### Example Question #33 : Solving Two Variable Logic Games

Four roommates – Aaron, Brad, Clark, and Dave – are deciding how to schedule their delivery laundry service for the week. They must all set one pickup day and one delivery day between Monday and Saturday. There may be only one pickup and one delivery that occur each day, subject to the following conditions:

A pickup day cannot be scheduled on Wednesday.
A delivery day cannot be scheduled on Tuesday.
There must be exactly two days in-between Aaron’s pickup day and his delivery day.
Brad’s delivery day must be scheduled before Thursday.
Clark’s delivery day must be scheduled before Dave’s pickup day.

If Aaron’s pickup day is on Monday, which of the following is a day without a delivery scheduled?

Friday

Thursday

Wednesday

Saturday

Monday

Monday

Explanation:

Aaron having a pickup day on Monday forces the following scenario:

Monday: Aaron (Pickup);