# LSAT Logic Games : Solving two-variable logic games

## Example Questions

### Example Question #71 : Solving Two Variable Logic Games

Eight students – Alice, Ben, Carl, Daisy, Earl, Frank, Gretchen, and Hailey – are sitting at the front of a school bus in four seats, with one student sitting on the right side and one student on the left side of each seat.  The seats are numbered sequentially 1 through 4, with Seat 1 at the front of the bus and Seats 2, 3, and 4 immediately behind, in that order.  The following conditions apply to the seating arrangement:

Ben must sit on the right side of whatever seat he sits in.

Frank and Gretchen sit closer to the front of the bus than Daisy.

Carl and Daisy do not sit in the same seat.

Earl and Hailey sit exactly one seat apart from each other, and on the same side of the seat.

If Carl and Hailey sit in the same seat, Frank and Ben also sit in the same seat.

If Hailey sits in Seat 1 on the right side of the seat, which one of the following could be true?

Carl and Hailey sit in the same seat.

Alice and Ben sit in the same seat.

Daisy and Earl sit in the same seat.

Daisy and Hailey sit in the same seat.

Ben and Earl sit in the same seat.

Carl and Hailey sit in the same seat.

Explanation:

Carl and Hailey can sit in the same seat in this scenario.  With Hailey sitting on the right side of Seat 1, Earl must sit in seat 2 (on the right side).   Further, since Carl and Hailey are sitting together, Ben and Frank must sit together, and it must be in Seat 3.  This means Daisy must sit in Seat 4 with Alice, and Gretchen can take the remaining spot in Seat 2.  The remaining answer choices violate one or more conditions under these circumstances.

### Example Question #71 : Solving Two Variable Logic Games

A consultant has agreed to see each of his nine clients-- L, M, N, O, P, Q, R, S, T--  once in the next six days, from Monday through Saturday. He arranges his schedule so that he can see at least one of his clients each day, while maintaining the following conditions:

O is always scheduled on a day before R and M.

P is not scheduled for Saturday.

If T is scheduled on a day after O, then S is scheduled on a day after N.

If T is scheduled on a day before O, then R is scheduled on a day before L.

The consultant always sees fewer clients on Friday and Saturday combined than he sees on any other two days of the week combined.

If the consultant sees O on Wednesday, what is the maximum number of clients that he can see after Wednesday?

5

2

3

4

1

4

Explanation:

The correct answer is 4 clients. Placing O on Wednesday does not lead to any particularly unique diagrams. This game is fairly loose-- there are a lot of possible diagrams. The key insight here is the fact that Friday and Saturday can accommodate, at most, two clients total and any other day accommodates at most two.

Here is a possible diagram that maximizes clients after Wednesday:

Mon: T

Tues: Q, P

Wed: S, O

Thurs: R, N

Fri: M

Sat: L

### Example Question #73 : Solving Two Variable Logic Games

A gym teacher wants his 6 students to line up in height order, from shortest to tallest. Corrin and Theresa are girls. Ben, Jonathan, Will, and Dan are the boys.

- Will is neither the tallest nor the shortest

- No girl is taller than Jonathan

- Dan is shorter than Corrin, but taller than Theresa

- Ben is the tallest

If Jonathan is the 2nd tallest, what must be true?

Dan is the 2nd tallest.

Will is 4th tallest.

Will is 2nd shortest.

Will is 5th tallest.

Corrin is not the shortest or second shortest.

Corrin is not the shortest or second shortest.

Explanation:

If Jonathan is 2nd tallest, that means Will can go anywhere but 6th, 2nd or 1st tallest positions. Since Corrin is taller than Dan, and Theresa is shorter than Dan, each of their positions can be altered by Will. Thus, the only certainty, is that Corrin cannot be the first or second in line, because Theresa and Dan must precede her.

### Example Question #74 : Solving Two Variable Logic Games

Daniel, Fiona, Ivette, Kevin, Marge and Polly are in line to get their cars washed, and all of their cars are washed only once. The order in which their cars recieve a wash is restricted by the following stipulations:

-Ivette's wash is separated from Daniel's wash by 3 other washes

-Fiona's wash is separated from Kevin's wash by one other wash

-Polly's car is washed before Daniel's

How many different spots in the line can Fiona occupy?

6

4

2

3

5

6

Explanation:

This is a time-consuming problem in that you must test to see if F can be in any position. There are two things to consider as far as time restraints: first, use the test thus far to your advantage. look at all your old sequences and see where F has occupied successfully. Second, every spot K occupies can be occupied by F.

See if F can be first (and consequently third, the spot K must occupy)

Place F first and follow though all the restrictions

(F, _, _, _, _, _) --> (F, _, K, _, _, _) --> (F, I, K, _, _, D) I choose to put D last to leave more flexibility with the placement of P. See rule 3. --> (F, I, K, (M/P),(M/P) , D). F and K are replaceable so F can occupy spot 1 and 3.

Place F second and work it through

(_, F, _, _, _, _) --> (_, F, _, K, _, _) --> (I, F, _, K, D, _) --> (I, F, P, K, D, _) --> (I, F, P, K, D, M). F and K are interchangeable so F works in both 2 and 4.

Next test F in 5.

(_, _, _, _, F, _) --> (_, _, K, _, F, _) --> (_, (I/D), K, _, F, (I/D)) --> (P, (I/D), K, _, F, (I/D)) --> (P, (I/D), K, M, F, (I/D)). F can work in 5.

Next test F in 6.

(_, _, _, _, _, F) --> (_, _, _, K, _, F) --> (_, (I/D), _, K, (I/D), F) --> (P, (I/D), _, K, (I/D), F) --> (P, (I/D), M, K, (I/D), F). F can work in 6.

F can work in any spot, so since there are 6 spots, the answer is 6.

### Example Question #341 : Lsat Logic Games

A chef is arranging spices on a shelf.  Four of the spices are in large jars: garlic, oregano, pepper, and salt.  Three of the spices are in small jars: basil, cumin, and mint.  The following conditions apply:

A large jar must be first or fourth

Pepper must come after cumin but before basil

The jar of salt must be the first large jar in the line

Basil cannot be immediately before or after garlic

If the rules are changed so that basil must come directly after garlic, and if all other rules remain the same, which of the following cannot be true?

pepper is fifth

garlic is fourth

mint is first

cumin is fourth

mint is second

garlic is fourth

Explanation:

If garlic and basil must be next to each other, then there are now five spices that must come after salt.  Only four spices can come after salt when salt is third, so salt cannot be third.

### Example Question #71 : Solving Two Variable Logic Games

Three circus performers—Flo, Genie, and Kyle—will perform the following six circus acts: acrobatics; ball juggling; clowning; dunking; elephant demonstrations; fire twirling. Each act is performed only once in any given show, and only one act is performed at a time. The following conditions dictate the sequencing of these acts:

• Flo performs exactly one act before Genie performs any of her acts
• Flo does not perform first and he does not perform last
• Genie does not do acrobatics and ball juggling
• Kyle does not do acrobatics and elephant demonstrations
• Ball juggling is performed immediately after the elephant demonstrations

Which one of the following is an acceptable list of the performers and their circus acts, in order from first to last in the show?

Kyle: fire twirling; Flo: elephant demonstrations; Genie: dunking; Kyle: ball juggling; Flo: acrobatics; Genie: clowning

Kyle: clowning; Flo: acrobatics; Flo: elephant demonstrations; Kyle: ball juggling; Genie: dunking; Genie: fire twirling

Kyle: clowning; Flo: dunking; Genie: elephant demonstrations; Kyle: ball juggling; Flo: acrobatics; Genie: fire twirling

Kyle: dunking; Kyle: fire twirling; Flo: clowning; Genie: acrobatics; Flo: elephant demonstrations; Genie: ball juggling

Flo: fire twirling; Genie: elephant demonstrations; Kyle: ball juggling; Kyle: dunking; Flo: acrobatics; Genie: clowning

Kyle: clowning; Flo: dunking; Genie: elephant demonstrations; Kyle: ball juggling; Flo: acrobatics; Genie: fire twirling

Explanation:

This is a sequence and matching game. The following are deductions we can make from the list of conditions (and thus are added to those conditions to guide our handling of the questions):

Kyle must perform first because Flo is eliminated from the first slot by virtue of an explicit rule and Flo must go before Genie by virtue of an explicit rule, (which means Genie can't go first, as well).

Flo must do acrobatics because neither Kyle nor Genie can do it.

If we go rule by rule, including these new rules we have deduced, and apply each of them one by one to the answer choices, we can eliminate all but the credited response.

### Example Question #77 : Solving Two Variable Logic Games

Three circus performers—Flo, Genie, and Kyle—will perform the following six circus acts: acrobatics; ball juggling; clowning; dunking; elephant demonstrations; fire twirling. Each act is performed only once in any given show, and only one act is performed at a time. The following conditions dictate the sequencing of these acts:

• Flo performs exactly one act before Genie performs any of her acts
• Flo does not perform first and he does not perform last
• Genie does not do acrobatics and ball juggling
• Kyle does not do acrobatics and elephant demonstrations
• Ball juggling is performed immediately after the elephant demonstrations

Which of the following must be true?

Flo does ball juggling.

Genie does fire twirling.

Flo does elephant demonstrations.

Genie does clowning.

Flo does acrobatics.

Flo does acrobatics.

Explanation:

Because neither Genie nor Kyle can do acrobatics, by virtue of explicit rules, the only performer left to do acrobatics is Flo.

### Example Question #78 : Solving Two Variable Logic Games

Three circus performers—Flo, Genie, and Kyle—will perform the following six circus acts: acrobatics; ball juggling; clowning; dunking; elephant demonstrations; fire twirling. Each act is performed only once in any given show, and only one act is performed at a time. The following conditions dictate the sequencing of these acts:

• Flo performs exactly one act before Genie performs any of her acts
• Flo does not perform first and he does not perform last
• Genie does not do acrobatics and ball juggling
• Kyle does not do acrobatics and elephant demonstrations
• Ball juggling is performed immediately after the elephant demonstrations

If Kyle performs fourth in the circus show, then when could acrobatics be performed?

Second

First

Fourth

Third

Sixth

Second

Explanation:

Since Flo is the only one who does acrobatics, and Flo cannot go first, we can immediately eliminate "first" as an answer choice. Likewise, we can eliminate "sixth," since Flo can't go last. "Fourth" is also out since Kyle doesn't do acrobatics. "Second" is the only viable option because Flo must come before Genie, which means acrobatics is second.

### Example Question #71 : Solving Two Variable Logic Games

Three circus performers—Flo, Genie, and Kyle—will perform the following six circus acts: acrobatics; ball juggling; clowning; dunking; elephant demonstrations; fire twirling. Each act is performed only once in any given show, and only one act is performed at a time. The following conditions dictate the sequencing of these acts:

• Flo performs exactly one act before Genie performs any of her acts
• Flo does not perform first and he does not perform last
• Genie does not do acrobatics and ball juggling
• Kyle does not do acrobatics and elephant demonstrations
• Ball juggling is performed immediately after the elephant demonstrations

If Genie does clowning immediately before Flo does elephant demonstrations, which one of the following must be true?

Kyle does fire twirling as first act.

Genie performs fourth.

Genie does dunking as the fifth act.

Flo does acrobatics as the second act.

Kyle performs sixth.

Flo does acrobatics as the second act.

Explanation:

We can deduce the following sequence: Kyle . . . Flo (acrobatics) . . . then :Genie (clowning); Flo (elephant demonstrations); Kyle (ball juggling)—the latter three forming a block.

Because Flo (acrobatics) must come before any act by Genie, it must come early in the sequence (earlier than the block of three—GFK). If Flo (acrobatics) does not occupy slot two, then the sequencing necessarily breaks down. That means Flo doing acrobatics must be the second act performed.

### Example Question #80 : Solving Two Variable Logic Games

Three circus performers—Flo, Genie, and Kyle—will perform the following six circus acts: acrobatics; ball juggling; clowning; dunking; elephant demonstrations; fire twirling. Each act is performed only once in any given show, and only one act is performed at a time. The following conditions dictate the sequencing of these acts:

• Flo performs exactly one act before Genie performs any of her acts
• Flo does not perform first and he does not perform last
• Genie does not do acrobatics and ball juggling
• Kyle does not do acrobatics and elephant demonstrations
• Ball juggling is performed immediately after the elephant demonstrations

Which one of the following could be true?

Ball juggling is the second act performed.

Fire twirling is the first act performed.

Acrobatics is the first act performed.

Elephant demonstrations is the last act performed.

Elephant demonstrations is the first act performed.

Fire twirling is the first act performed.

Explanation:

Flo does acrobatics, so it cannot come first.

For ball juggling to go second, elephant demonstrations would have to first.  But elephant demonstrations can't go first because Kyle must go first and he doesn't do elephant demonstrations.

Finally, elephant demonstrations can't go last because ball juggling must follow.

Consequently, the only option left is fire twirling going first---and that is the credited response.

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