# LSAT Logic Games : Solving four- and five-variable logic games

## Example Questions

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### Example Question #71 : Four & Five Variable

Over the course of four weeks, each of seven television programs will be aired to a focus group for help in coming up with a title. The programs are identified as G, H, J, K, L, M, and O. A different pair of these programs will be aired each week. Exactly one of the programs will be a member of two of these four pairs. The following constraints must be observed:

J is not aired during a given week unless H is aired during the week immediately preceding J’s airing.

The show that is aired during two of the weeks is aired during week 4 but is not aired during week 3.

G is not aired during a given week unless either J or else O is also aired during that week.

K is aired during one of the first two weeks.

O is one of the programs aired during week 3.

Which one of the following CANNOT be the show that is aired during two of the weeks?

K

L

G

H

M

G

Explanation:

If a show is aired during two weeks, then, according to the second rule, that show must be aired during week 4.  Making appropriate deductions (see below), we can see that G, J, and O cannot be aired in week 4.

Note:  H cannot be aired in weeks 2 or 3 due to the second rule.  J cannot be doubled since that would also require H to be doubled (no two doubles).  Therefore, J can be eliminated from weeks 1, 3, and 4.  Since G must be aired with either J or O, and since J and O cannot be doubled, G must be aired during week 2 or 3 but not week 1 or 4.

### Example Question #72 : Solving Four And Five Variable Logic Games

Over the course of four weeks, each of seven television programs will be aired to a focus group for help in coming up with a title. The programs are identified as G, H, J, K, L, M, and O. A different pair of these programs will be aired each week. Exactly one of the programs will be a member of two of these four pairs. The following constraints must be observed:

J is not aired during a given week unless H is aired during the week immediately preceding J’s airing.

The show that is aired during two of the weeks is aired during week 4 but is not aired during week 3.

G is not aired during a given week unless either J or else O is also aired during that week.

K is aired during one of the first two weeks.

O is one of the programs aired during week 3.

Which one of the following is a program that could be aired in any of the four weeks?

H

J

K

L

O

L

Explanation:

This question can be effectively attacked by using deductions that are required to answer the other questions associated with this game.  Based on the rules and the deductions, the following entities have restrictions attached to them:  G, H, J, K, and O.  Accordingly, L is the correct answer.

### Example Question #73 : Solving Four And Five Variable Logic Games

Over the course of four weeks, each of seven television programs will be aired to a focus group for help in coming up with a title. The programs are identified as G, H, J, K, L, M, and O. A different pair of these programs will be aired each week. Exactly one of the programs will be a member of two of these four pairs. The following constraints must be observed:

J is not aired during a given week unless H is aired during the week immediately preceding J’s airing.

The show that is aired during two of the weeks is aired during week 4 but is not aired during week 3.

G is not aired during a given week unless either J or else O is also aired during that week.

K is aired during one of the first two weeks.

O is one of the programs aired during week 3.

Which one of the following is a pair of shows that could be aired during the same week as each other?

G and H

M and O

H and O

H and J

K and O