# LSAT Logic Games : Solving two-variable logic games

## Example Questions

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### Example Question #101 : Solving Two Variable Logic Games

A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:

• E and F must occupy consecutive time slots.
• Either A or C must occupy the third time slot.
• A must audition before D.
• B must audition after C.
• B and C cannot occupy consecutive time slots.

If D is assigned to the fifth slot, then which of the following must be assigned to the sixth slot?

B

F

C

A

E

B

Explanation:

With D in the fifth slot, E and F must be in the first two slots. If A is in the third slot, and since B must come after C, this leaves C in the fourth slot and B in the sixth slot. If C is in the third slot, and since B and C cannot be consecutive, again B must be in the sixth slot.

### Example Question #101 : Solving Two Variable Logic Games

A human resources manager must schedule a round of interviews during a particular day. Six different time slots are available in the afternoon and are numbered one through six in sequential order. Six candidates - Joe, Jim, Mary, Bob, Jess, and Sue - must be scheduled during the afternoon. Only one candidate can occupy each interview slot. The assignment of interview slots is subject to the following restrictions:

• Either Mary or Bob must occupy the second time slot.
• Joe must occupy the sixth time slot.
• Mary and Bob cannot occupy consecutive time slots.
• Jim and Mary must occupy consecutive time slots.
• Sue must be interviewed before Jess.

If Jim is assigned to the fourth slot, which of the following must be true?

Sue must occupy the third slot.

Mary must occupy the third slot.

Jess must occupy the first slot.

Mary must occupy the fifth slot.

Bob must occupy the third slot.

Mary must occupy the fifth slot.

Explanation:

The only restriction that involves Jim is that he and Mary must occupy consecutive slots. Therefore, if Jim occupies the fourth slot, Mary must occupy the third or fifth slot. Since Mary can't be in the second slot, Bob must be assigned to this slot. Lastly, Mary and Bob cannot occupy consecutive slots. So if Bob is in the second slot, Mary cannot be in the third slot. Mary must be in the fifth time slot. Now the 2nd, 4th, 5th, and 6th slots are all accounted for. Finally, since Sue must be interviewed before Jess, Sue must be 1st and Jess must be 3rd.

### Example Question #103 : Solving Two Variable Logic Games

A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:

• E and F must occupy consecutive time slots.
• Either A or C must occupy the third time slot.
• A must audition before D.
• B must audition after C.
• B and C cannot occupy consecutive time slots.

If C is assigned to the third time slot, then which of the following must be true?

E must be assigned to the fifth time slot.

B must be assigned to the sixth time slot.

F must be assigned to the fifth time slot.

A must be assigned to the second time slot.

A must be assigned to the fourth time slot.

A must be assigned to the fourth time slot.

Explanation:

The only statement that must be true is that A must be assigned to the fourth time slot. B cannot be consecutive with C but must come before C, which leaves only the fifth or sixth slots for B. Because E and F must be consecutive, they must be in slots one and two. Since A must come before D, D must either be fifth or sixth. Therefore, A must be in the fourth slot.

### Example Question #101 : Solving Two Variable Logic Games

A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:

• Package E must be the only package delivered between packages C and D
• Package A cannot be the first, third or fifth package delivered
• Package D must be delivered sometime before Package C
• Package F must be either the first or last package delivered

Which of the following is a complete and accurate order in which the packages could be delivered?

F, A, C, E, D, B

F, A, D, B, E, C

D, E, C, A, B, F

B, F, D, E, C, A

A, D, E, C, B, F

D, E, C, A, B, F

Explanation:

F must be first or last, which eliminates one answer. D must come before C, which eliminates another. E must be immediately surrounded by D and C, which eliminates yet another. And the last we take out because A cannot be first.

### Example Question #105 : Solving Two Variable Logic Games

A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:

• Package E must be the only package delivered between packages C and D
• Package A cannot be the first, third or fifth package delivered
• Package D must be delivered sometime before Package C
• Package F must be either the first or last package delivered

Which of the following must be true?

Package A cannot be delivered last

If Package F is delivered first, then Package A is delivered last

Package B must be delivered sometime before Package C

Package B cannot be delivered first

If Package B is delivered third, then Package E is delivered fifth

If Package B is delivered third, then Package E is delivered fifth

Explanation:

If Package B is delivered third, then the only place the DEC block can fit is in spots four, five and six, respectively. Therefore we know the only place E could go is in spot five, which means it must be true.

### Example Question #106 : Solving Two Variable Logic Games

A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:

• Package E must be the only package delivered between packages C and D
• Package A cannot be the first, third or fifth package delivered
• Package D must be delivered sometime before Package C
• Package F must be either the first or last package delivered

If Package A is delivered second, which of the following could be true?

Package B is delivered fourth

Package D is delivered fifth

Package C is delivered fourth

Package E is delivered third

Package B is delivered first

Package B is delivered first

Explanation:

If Package A is delivered second, there are only two spots where the DEC block can fit: either in spots three, four and five, or four, five and six. Leaving us with two possible set ups:

_ A D E C _     OR    _ A _ D E C

Leaving us to place F and B. In the first solution, F and B are interchangeable - since the only rule we are working with is that F must go either first or last. In the second solution, F must go first, leaving us with only one way to solve. Therefore, the following three solution are the only possibilities:

F A D E C B;  B A D E C F;  F A B D E C

### Example Question #107 : Solving Two Variable Logic Games

A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:

• Package E must be the only package delivered between packages C and D
• Package A cannot be the first, third or fifth package delivered
• Package D must be delivered sometime before Package C
• Package F must be either the first or last package delivered

Which of the following, if true, would determine the order in which every package must be delivered?

Package A is delivered last

Package C is delivered third

Package E is delivered fourth

Package F is delivered last

Package F is delivered first

Package C is delivered third

Explanation:

If Package C is third, the we know that package D and E must be second and third, respectively.

_ D E C _ _

Package A cannot go first or fifth, so we must place it last.

_ D E C _ A

F must then go first, and we fill in B in the second spot.

F B D E C A

### Example Question #101 : Solving Two Variable Logic Games

A photographer is hanging six portraits on the wall in a straight line. The portraits are of six family members: Lily, Mildred, Nancy, Owen, Peter and Quentin. The order in which the portraits are hung must conform to the following restrictions:

Mildred's portrait must be either first or last

There must be exactly one portrait between Nancy and Quentin

Nancy's portrait must come after Lily's but before Quentin's

If Mildred's portrait is first, which is a complete and accurate list of all the possible portraits that could appear second?

Owen, Peter

Owen, Lily

Owen, Lily, Peter

Nancy, Owen Peter, Lily

Nancy, Owen, Peter