# LSAT Logic Games : Solving two-variable logic games

## Example Questions

### Example Question #51 : Solving Two Variable Logic Games

Three English runners--Albert, Barry, and Carl--are competing in a race with three German runners--Dieter, Franz, and Hans. The order in which the six runners will finish the race is subject to the following conditions:

Hans will finish the race before Carl and Dieter.

Franz will finish the race immediately after Barry.

Carl will finish the race sometime before Barry.

A German runner will finish the race first.

No English runner will be the last to finish the race.

Which of the following is a complete and accurate list of runners, any one of which could finish the race immediately after Albert?

Hans, Barry, Carl, Dieter

Barry, Carl, Dieter

Barry, Dieter, Franz

Hans, Dieter, Carl

Barry, Carl

Barry, Carl, Dieter

Explanation:

Barry, Carl, and Dieter could all finish the race immediately after Albert. Remember that the question asks for a “complete and accurate list,” so a partial list (Barry, Carl) is insufficient. Franz cannot finish immediately after Albert because he finishes immediately after Barry. Hans, because he is a German runner and must finish before Dieter and Carl (and by extension, Barry and Franz), must finish before Albert.

### Example Question #52 : Solving Two Variable Logic Games

Three English runners--Albert, Barry, and Carl--are competing in a race with three German runners--Dieter, Franz, and Hans. The order in which the six runners will finish the race is subject to the following conditions:

Hans will finish the race before Carl and Dieter.

Franz will finish the race immediately after Barry.

Carl will finish the race sometime before Barry.

A German runner will finish the race first.

No English runner will be the last to finish the race.

If Carl finishes the race third, each of the following could be true EXCEPT:

Carl finishes the race before Franz.

Dieter finishes the race before Carl.

Albert finishes the race after Dieter.

Barry finishes the race before Albert.

Franz finishes the race before Dieter.

Barry finishes the race before Albert.

Explanation:

Under this scenario, Barry cannot finish the race before Albert. Carl finishing third restricts the finishing positions significantly. Hans must finish first. Because of the condition that Franz must finish immediately after Barry, the only possible runners who could finish the race second are Albert and Dieter. If Albert finishes second, Barry must finish after him. If Dieter finishes second, then Albert must finish fourth, Barry fifth, and Franz last.

### Example Question #53 : Solving Two Variable Logic Games

Three English runners--Albert, Barry, and Carl--are competing in a race with three German runners--Dieter, Franz, and Hans. The order in which the six runners will finish the race is subject to the following conditions:

Hans will finish the race before Carl and Dieter.

Franz will finish the race immediately after Barry.

Carl will finish the race sometime before Barry.

A German runner will finish the race first.

No English runner will be the last to finish the race.

The runner who finishes the race fourth could be any one of exactly how many of the runners?

Five

Six

Two

Three

Four

Five

Explanation:

Five of the runners could finish fourth. Hans is the only runner who could not. Under the conditions, Hans must finish before Dieter and Carl. Carl must finish before Barry. Under these two conditions alone, Hans cannot finish in fourth place or later.

### Example Question #51 : Solving Two Variable Logic Games

Three English runners--Albert, Barry, and Carl--are competing in a race with three German runners--Dieter, Franz, and Hans. The order in which the six runners will finish the race is subject to the following conditions:

Hans will finish the race before Carl and Dieter.

Franz will finish the race immediately after Barry.

Carl will finish the race sometime before Barry.

A German runner will finish the race first.

No English runner will be the last to finish the race.

Which one of the following, if substituted for the condition that no English runner will be the last to finish the race, would have the exact same effect in determining the finishing order?

Albert must finish the race fifth or earlier.

Dieter must finish the race fifth or later.

Dieter must finish the race before Carl.

Franz must finish the race before Albert.

Barry must finish the race fourth or earlier.

Albert must finish the race fifth or earlier.

Explanation:

Because Albert is the only English runner who could possibly finish last if the proposed condition is removed, his finishing the race fifth or earlier effectively forces a German runner to finish last. Carl still cannot finish last due to the condition that he must finish before Barry. Barry still cannot finish last due to the condition that he finish immediately before Franz. Therefore, if Albert does not finish last, a German runner must do so.

### Example Question #55 : Solving Two Variable Logic Games

Tania will be taking seven business trips over seven weeks.  Each trip will be to one of four destinations.  She must visit each destination at least one time.  The four locations are Indiana, Kansas, Louisiana, and Missouri.  The following conditions apply:

She cannot travel to Missouri in the fourth week

She must travel to Kansas during the first or seventh weeks

Any time she travels to Louisiana, she must travel to Missouri the next week

She cannot travel to Missouri and Indiana on consecutive weeks

She must travel to at least one location on consecutive weeks, but cannot travel to any location three weeks in a row

Which of the following could be the order in which Tania travels to the destinations?

Kansas, Indiana, Indiana, Louisiana, Missouri, Kansas, Indiana

Kansas, Indiana, Kansas, Louisiana, Missouri, Kansas, Indiana

Louisiana, Kansas, Missouri, Kansas, Indiana, Indiana, Kansas

Missouri, Kansas, Kansas, Louisiana, Missouri, Kansas, Indiana

Louisiana, Missouri, Indiana, Indiana, Missouri, Indiana, Kansas

Kansas, Indiana, Indiana, Louisiana, Missouri, Kansas, Indiana

Explanation:

Each incorrect answer directly contradicts one or more rules.  Carefully apply the rules to eliminate incorrect answers.

### Example Question #56 : Solving Two Variable Logic Games

Tania will be taking seven business trips over seven weeks.  Each trip will be to one of four destinations.  She must visit each destination at least one time.  The four locations are Indiana, Kansas, Louisiana, and Missouri.  The following conditions apply:

She cannot travel to Missouri in the fourth week

She must travel to Kansas during the first or seventh weeks

Any time she travels to Louisiana, she must travel to Missouri the next week

She cannot travel to Missouri and Indiana on consecutive weeks

She must travel to at least one location on consecutive weeks, but cannot travel to any location three weeks in a row

Which of the following cannot be true?

Tania travels to Indiana during the fourth and fifth weeks

Tania travels to Louisiana during the third week

Tania travels to Louisiana during the fourth week

Tania travels to Missouri on consecutive weeks

Tania travels to Kansas on consecutive weeks

Tania travels to Louisiana during the third week

Explanation:

If Tania traveled to Louisiana during the third week, then she would be required to travel to Missouri during the fourth week.  The rules directly prohibit her from doing that, however.

### Example Question #57 : Solving Two Variable Logic Games

Tania will be taking seven business trips over seven weeks.  Each trip will be to one of four destinations.  She must visit each destination at least one time.  The four locations are Indiana, Kansas, Louisiana, and Missouri.  The following conditions apply:

She cannot travel to Missouri in the fourth week

She must travel to Kansas during the first or seventh weeks

Any time she travels to Louisiana, she must travel to Missouri the next week

She cannot travel to Missouri and Indiana on consecutive weeks

She must travel to at least one location on consecutive weeks, but cannot travel to any location three weeks in a row

Each of the following could be true EXCEPT

Tania travels to one destination a total of four times

Tania travels to Kansas both first and seventh

Tania travels to Louisiana on consecutive weeks

Tania travels to both Missouri and Indiana two times

Tania travels to Indiana only once

Tania travels to Louisiana on consecutive weeks

Explanation:

Tania cannot travel to Louisiana on consecutive weeks.  If she were to do so, she would directly contradict the requirement that she travel to Missouri directly after traveling to Louisiana.

### Example Question #58 : Solving Two Variable Logic Games

Tania will be taking seven business trips over seven weeks.  Each trip will be to one of four destinations.  She must visit each destination at least one time.  The four locations are Indiana, Kansas, Louisiana, and Missouri.  The following conditions apply:

She cannot travel to Missouri in the fourth week

She must travel to Kansas during the first or seventh weeks

Any time she travels to Louisiana, she must travel to Missouri the next week

She cannot travel to Missouri and Indiana on consecutive weeks

She must travel to at least one location on consecutive weeks, but cannot travel to any location three weeks in a row

If Tania travels to Kansas during the second and third weeks, which of the following could be true?

Tania travels to Indiana on consecutive weeks

Tania travels to Louisiana first

Tania travels to Kansas sixth

Tania travels to Louisiana sixth

Tania travels to Kansas first

Tania travels to Kansas sixth

Explanation:

It is possible for Tania to travel to Kansas sixth even if she travels there second and third.  She would also need to travel to Kansas seventh.  In this situation, she would travel to Indiana first, Louisiana fourth, and Missouri fifth.

### Example Question #51 : Two Variable

Tania will be taking seven business trips over seven weeks.  Each trip will be to one of four destinations.  She must visit each destination at least one time.  The four locations are Indiana, Kansas, Louisiana, and Missouri.  The following conditions apply:

She cannot travel to Missouri in the fourth week

She must travel to Kansas during the first or seventh weeks

Any time she travels to Louisiana, she must travel to Missouri the next week

She cannot travel to Missouri and Indiana on consecutive weeks

She must travel to at least one location on consecutive weeks, but cannot travel to any location three weeks in a row

When Tania travels to Louisiana first, which of the following must be true?

Tania travels to Kansas or Indiana second

Tania travels to Indiana fifth

Tania travels to Kansas or Indiana third

Tania travels to Indiana sixth

Tania travels to Kansas or Missouri third

Tania travels to Kansas or Missouri third

Explanation:

When Tania travels to Louisiana first, she must travel to Missouri second.  She cannot then travel to Louisiana or Indiana third.  If she did, either she would travel to Indiana and Missouri consecutively or she would travel to Missouri fourth--both are prohibited.  As a result, she could only travel to Kansas or Missouri third.

### Example Question #51 : Solving Two Variable Logic Games

Tania will be taking seven business trips over seven weeks.  Each trip will be to one of four destinations.  She must visit each destination at least one time.  The four locations are Indiana, Kansas, Louisiana, and Missouri.  The following conditions apply:

She cannot travel to Missouri in the fourth week

She must travel to Kansas during the first or seventh weeks

Any time she travels to Louisiana, she must travel to Missouri the next week

She cannot travel to Missouri and Indiana on consecutive weeks

She must travel to at least one location on consecutive weeks, but cannot travel to any location three weeks in a row

If the rules are changed so that Tania must travel to Indiana directly after traveling to Missouri, and if all other rules remain unchanged, which of the following could be true?

Tania travels to Louisiana third

Tania travels to Louisiana on consecutive weeks

Tania travels to Missouri on consecutive weeks

Tania travels to Louisiana sixth

Tania travels to Missouri first