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

## Example Questions

### Example Question #51 : Solving Four And Five Variable Logic Games

During an international academic conference that will take place over a six-day period, six different speakers will deliver lectures to the entire assembly.  The speakers come from different countries and each country has two lecturers who are eligible to be speakers.  The countries are:  France, Greece, Haiti, Iceland, Nigeria, and Tunisia.  The following restrictions apply:

Nigeria may not put forth a speaker for day 2 or 4.

A speaker from Iceland may not deliver a lecture unless a speaker from Nigeria delivers a lecture the next day.

A speaker from Greece may not deliver a lecture unless a speaker from Iceland delivers a lecture the next day.

Which one of the following is an acceptable order of countries from whom a speaker will be selected to deliver lectures to the assembly at the conference, from day 1 through day 6?

France, Haiti, Iceland, Nigeria, France, Haiti

Tunisia, France, Nigeria, Haiti, France, Tunisia

Nigeria, Tunisia, Haiti, Iceland, France, Tunisia

Haiti, France, Nigeria, Greece, Nigeria, Iceland

France, Greece, Iceland, Tunisia, Nigeria, Haiti

Tunisia, France, Nigeria, Haiti, France, Tunisia

Explanation:

Use each rule singly to eliminate rule-violators.  The one answer choice that remains is, by definition, a non-violator and therefore the correct answer.

### Example Question #52 : Solving Four And Five Variable Logic Games

Five dogs are finalists in a dog-show competition:  Fifi, Glee, Haley, Jo, and Kay.  They will appear on a platform singly and only once during the final phase of the competition.  The order of their appearance must accord with the following rules:

Glee must appear earlier than Fifi.

Kay must appear earlier than Haley and Jo.

Haley must appear either immediately before or immediately after Fifi.

If Jo appears earlier than Glee, then which one of the following could be true?

Kay appears second.

Glee appears second.

Jo appears third.

Fifi appears fourth.

Haley appears third.

Fifi appears fourth.

Explanation:

Given the added stipulation, the sequence must be this:

K --- J --- G --- F/H (either order).

This reveals that the only issue is whether F or H is fourth or fifth.  K, J, and G are fixed at slots 1, 2, and 3.  So the correct answer is F appears fourth.

### Example Question #52 : Solving Four And Five Variable Logic Games

Five dogs are finalists in a dog-show competition:  Fifi, Glee, Haley, Jo, and Kay.  They will appear on a platform singly and only once during the final phase of the competition.  The order of their appearance must accord with the following rules:

Glee must appear earlier than Fifi.

Kay must appear earlier than Haley and Jo.

Haley must appear either immediately before or immediately after Fifi.

Which one of the following CANNOT be true?

Jo appears immediately before Glee.

Glee appears immediately before Haley.

Haley appears immediately before Glee.

Kay appears immediately before Haley.

Fifi appears immediately before Jo.

Haley appears immediately before Glee.

Explanation:

Because this is an open-ended question, there is no option other than testing out the answer choices.  But with a good sequencing diagram, that testing can be done efficiently.

G --- F/H (either order)

K --- F/H

K --- J

From these relationship rules, it is clear that H cannot appear before G.

### Example Question #51 : Four & Five Variable

During an international academic conference that will take place over a six-day period, six different speakers will deliver lectures to the entire assembly.  The speakers come from different countries and each country has two lecturers who are eligible to be speakers.  The countries are:  France, Greece, Haiti, Iceland, Nigeria, and Tunisia.  The following restrictions apply:

Nigeria may not put forth a speaker for day 2 or 4.

A speaker from Iceland may not deliver a lecture unless a speaker from Nigeria delivers a lecture the next day.

A speaker from Greece may not deliver a lecture unless a speaker from Iceland delivers a lecture the next day.

If two speakers from Iceland are delivering lectures, one on day 2 and one on day 5, then the speaker on day 1 could be from any one of the following countries EXCEPT:

France

Greece

Tunisia

Haiti

Nigeria

Nigeria

Explanation:

The rules specify that if I is in play, then the sequence must be IN.  The question specifies that I is in slots 2 and 5.   That means N must be in slots 3 and 6.  Therefore, N could not be in slot 1.

### Example Question #51 : Solving Four And Five Variable Logic Games

During an international academic conference that will take place over a six-day period, six different speakers will deliver lectures to the entire assembly.  The speakers come from different countries and each country has two lecturers who are eligible to be speakers.  The countries are:  France, Greece, Haiti, Iceland, Nigeria, and Tunisia.  The following restrictions apply:

Nigeria may not put forth a speaker for day 2 or 4.

A speaker from Iceland may not deliver a lecture unless a speaker from Nigeria delivers a lecture the next day.

A speaker from Greece may not deliver a lecture unless a speaker from Iceland delivers a lecture the next day.

If two of the speakers are from Iceland, which one of the following CANNOT be true?

A speaker from Haiti delivers a lecture on day 6.

A speaker from Nigeria delivers a lecture on day 5.

A speaker from Tunisia delivers a lecture on day 4.

A speaker from Greece delivers a lecture on day 1.

A speaker from France delivers a lecture on day 3.

A speaker from France delivers a lecture on day 3.

Explanation:

I is precluded from slots 1, 3, and 6 by virtue of the rule that if I is used, it must immediately precede N.  N cannot be in slots 2 and 4 according to one rule.  So, if I is used twice in the sequence, then it must be in slot 2, 4, or 5.  No matter what, I must appear in slot 2, which entails N being in slot 3.  Therefore F cannot be in slot 3.

### Example Question #52 : Solving Four And Five Variable Logic Games

During an international academic conference that will take place over a six-day period, six different speakers will deliver lectures to the entire assembly.  The speakers come from different countries and each country has two lecturers who are eligible to be speakers.  The countries are:  France, Greece, Haiti, Iceland, Nigeria, and Tunisia.  The following restrictions apply:

Nigeria may not put forth a speaker for day 2 or 4.

A speaker from Iceland may not deliver a lecture unless a speaker from Nigeria delivers a lecture the next day.

A speaker from Greece may not deliver a lecture unless a speaker from Iceland delivers a lecture the next day.

Which one of the following is a complete and accurate list of the days, any one of which is a day on which a speaker from Iceland could deliver a lecture?

day 2, day 4, day 5

day 2, day 5, day 6

day 1, day 3, day 5

day 2, day 4

day 1, day 3

day 2, day 4, day 5

Explanation:

I must immediately precede N whenever I appears.  N cannot be in slots 2 and 4.  Combining these two rules leads to the deduction that I cannot be in slots 1, 3, and 6.  That means I can only be in slots 2, 4, and 5.

### Example Question #54 : Solving Four And Five Variable Logic Games

During an international academic conference that will take place over a six-day period, six different speakers will deliver lectures to the entire assembly.  The speakers come from different countries and each country has two lecturers who are eligible to be speakers.  The countries are:  France, Greece, Haiti, Iceland, Nigeria, and Tunisia.  The following restrictions apply:

Nigeria may not put forth a speaker for day 2 or 4.

A speaker from Iceland may not deliver a lecture unless a speaker from Nigeria delivers a lecture the next day.

A speaker from Greece may not deliver a lecture unless a speaker from Iceland delivers a lecture the next day.

If two speakers are from France, one lecturing on day 3 and the other on day 5, which one of the following is a pair of countries that could offer speakers to deliver lectures on day 1 and day 6, respectively?

Tunisia and Greece

Nigeria and Tunisia

Greece and Haiti

France and Tunisia

Iceland and Nigeria

Nigeria and Tunisia

Explanation:

F is stipulated to be in slots 3 and 5.  That means I can't be in slots 2 and 4 because N must come immediately after I (slots 3 and 5 are taken now).  G can't be in slot 1 because I cannot appear in slot 2.  I can't be in slot 1 because N can't be in slot 2.  G can't be in slot 6 because it must precede I and N.  F can't be in slot 1 because it already occupies two slots.  These deductions serve to eliminate all the answer choices except the correct one:  N in slot 1 and T in slot 6.

### Example Question #52 : Solving Four And Five Variable Logic Games

During an international academic conference that will take place over a six-day period, six different speakers will deliver lectures to the entire assembly.  The speakers come from different countries and each country has two lecturers who are eligible to be speakers.  The countries are:  France, Greece, Haiti, Iceland, Nigeria, and Tunisia.  The following restrictions apply:

Nigeria may not put forth a speaker for day 2 or 4.

A speaker from Iceland may not deliver a lecture unless a speaker from Nigeria delivers a lecture the next day.

A speaker from Greece may not deliver a lecture unless a speaker from Iceland delivers a lecture the next day.

If a speaker from Greece delivers a lecture at some time after a speaker from Nigeria delivers a lecture, then a speaker from Nigeria must deliver a lecture on:

day 5

day 3 or else day 5

day 1 or else day 3

day 1

day 3

day 1 or else day 3

Explanation:

G must come after N, so the sequence must abide by this sequence:

N --- GIN.

We already know that N cannot be in slots 2 and 4.  Given the sequence noted here, N cannot be in slots 5 and 6 because G is precluded from slots 5 and 6.  That leaves only 1 and 3 open for N.  So N could only appear in one of those two slots, but not both.  Hence, the correct answer is:  day 1 or else day 3.

### Example Question #51 : 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 products aired during week 3.

Which one of the following could be the schedule for the airing of the television shows?

week 1: K, M; week 2: H, J; week 3: O, G; week 4: K, L

week 1 H, L; week 2: J, M; week 3: O, G; week 4: K, L

week 1: H, K; week 2: J, G; week 3: O, L; week 4: M, K

week 1: H, K; week 2: J, M; week 3: O, L; week 4 G, M

week 1: G, J; week 2: K, L; week 3: O, M; week 4: H, L

week 1: H, K; week 2: J, G; week 3: O, L; week 4: M, K

Explanation:

This is an acceptability question, so the approach is to use each rule singly to eliminate answer choices that violate that specific rule. Applying each of the rules to the choices leaves the correct answer standing as the only non-rule violator.

### Example Question #491 : Linear 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 products aired during week 3.

Which one of the following is a pair of products that CANNOT be advertised during the same week as each other?

L and M

H and K

K and L

H and M

J and O