LSAT Logic Games : Solving two-variable logic games

Study concepts, example questions & explanations for LSAT Logic Games

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Example Questions

Example Question #61 : Two Variable

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

Which of the following could be the order of the spices on the shelf?

Possible Answers:

mint, garlic, salt, cumin, oregano, pepper, basil

cumin, salt, pepper, oregano, basil, mint, garlic

salt, pepper, cumin, basil, oregano, garlic, mint

cumin, salt, pepper, mint, garlic, oregano, basil

cumin, salt, pepper, oregano, basil, garlic, mint

Correct answer:

cumin, salt, pepper, oregano, basil, mint, garlic

Explanation:

Each of the incorrect answer choices directly contradicts one of the rules.  Apply the rules to eliminate the incorrect answers.

Example Question #62 : Two Variable

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

Which of the following cannot be true?

Possible Answers:

salt is fourth

pepper is sixth

garlic is sixth

basil is fourth

oregano is fifth

Correct answer:

salt is fourth

Explanation:

Because salt must be the first large jar, garlic, oregano, and pepper must come after salt.  Basil must come after pepper and, therefore, also must come after salt.  There is no way that four spices can come after salt when salt is fourth.

Example Question #61 : Two Variable

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

Basil can be in each of the following places, EXCEPT

Possible Answers:

fourth

fifth

sixth

third

directly after pepper

Correct answer:

third

Explanation:

Basil cannot be third because it must come after cumin, pepper, and salt.

Example Question #61 : Solving Two Variable 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

Which of the following could be first?

Possible Answers:

basil

oregano

mint

garlic

pepper

Correct answer:

mint

Explanation:

Mint could be first but the other options all must come at some point after salt.

Example Question #62 : Solving Two Variable 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

When pepper is third, which of the following could be true?

Possible Answers:

cumin is fifth

oregano is fifth

mint is second

garlic is second

oregano is second

Correct answer:

oregano is fifth

Explanation:

When pepper is third, salt and cumin are the only spices to come before it.  As a result, oregano, garlic, and mint cannot be second.  Further, cumin must come before pepper and, therefore, cannot be fifth.  Oregano could be fifth.

Example Question #66 : 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.

Which one of the following could be a complete and accurate matching of students to their seats?

Possible Answers:

Seat 1: Carl, left side, Earl, right side; Seat 2: Frank, left side, Hailey, right side; Seat 3: Gretchen, left side, Ben, right side; Seat 4: Alice, left side, Daisy, right side

Seat 1: Alice, left side, Ben, right side; Seat 2: Carl, left side, Earl, right side; Seat 3: Frank, left side, Gretchen, right side; Seat 4: Daisy, left side, Hailey, right side

Seat 1: Earl, left side, Frank, right side; Seat 2: Hailey, left side, Gretchen, right side; Seat 3: Alice, left side, Ben, right side; Seat 4: Daisy, left side, Carl, right side

Seat 1: Frank, left side, Alice, right side; Seat 2: Carl, left side, Hailey, right side; Seat 3: Gretchen, left side, Earl, right side; Seat 4: Daisy, left side, Ben, right side

Seat 1: Alice, left side, Hailey, right side; Seat 2: Frank, left side, Earl, right side; Seat 3: Gretchen, left side, Daisy, right side; Seat 4: Carl, left side, Ben, right side

Correct answer:

Seat 1: Carl, left side, Earl, right side; Seat 2: Frank, left side, Hailey, right side; Seat 3: Gretchen, left side, Ben, right side; Seat 4: Alice, left side, Daisy, right side

Explanation:

The correct answer choice is the only one that does not violate the listed conditions.  Each of the incorrect answer choices either has Daisy not sitting behind Frank and Gretchen, has Carl and Daisy sitting in the same seat, has Earl and Hailey not sitting one seat from each other, or failing to have Frank and Ben sit together when Carl and Hailey are sitting together.

Example Question #61 : Two Variable

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 Daisy sits in Seat 2 on the right side of the seat, which one of the following must be true?

Possible Answers:

Gretchen sits on the right side of her seat.

Hailey sits in Seat 2.

Ben sits in Seat 4.

Alice sits on the left side of her seat.

Earl sits on the left side of his seat.

Correct answer:

Earl sits on the left side of his seat.

Explanation:

With Daisy sitting in Seat 2, Frank and Gretchen must both sit in Seat 1 to be closer to the front than Daisy.  This means there is no room for Earl or Hailey (who must sit on the same side) to sit on the right side of their seats, because Ben must also sit on the right side of his seat.  The remaining answer choices could be true, but do not have to be.

Example Question #68 : 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 Carl and Ben sit in Seat 2, then each of the following could be true EXCEPT

Possible Answers:

Gretchen and Alice sit in Seat 1.

Frank and Gretchen sit in Seat 1.

Daisy and Earl sit in Seat 3.

Frank and Hailey sit in Seat 3.

Alice and Frank sit in Seat 3.

Correct answer:

Alice and Frank sit in Seat 3.

Explanation:

With Carl and Ben in Seat 2, either Earl or Hailey must sit in Seat 3, and whoever of the two does not sit in Seat 3 must sit in Seat 4.  Otherwise, there is no way they can sit one seat away from each other, since Carl and Ben occupy Seat 2.  Thus, Alice and Frank cannot sit in Seat 3.  The remaining answer choices could be true.

Example Question #69 : 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 Gretchen sits exactly two seats apart from Frank, which one of the following must be true?

Possible Answers:

Carl sits closer to the front of the bus than Daisy.

Hailey sits closer to the front of the bus than Daisy.

Alice sits closer to the front of the bus than Hailey.

Ben sits closer to the front of the bus than Earl.

Gretchen sits closer to the front of the bus than Carl.

Correct answer:

Carl sits closer to the front of the bus than Daisy.

Explanation:

Since Gretchen and Frank must both sit closer to the front of the bus than Daisy, under this scenario Daisy must sit in Seat 4 (with Gretchen or Frank in Seat 1, and the other in Seat 3).  Since Carl cannot sit next to Daisy, he cannot sit in Seat 4.  Thus, he must sit closer to the front of the bus than Daisy.  The remaining answer choices, while they could be true, do not have to be.

Example Question #70 : 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 Carl sits in the same seat as Frank, exactly how many different students could sit in Seat 4?

Possible Answers:

four

eight

five        

seven

six

Correct answer:

five        

Explanation:

This question is simpler than it appears.  Under normal circumstances, the only students who cannot sit in Seat 4 are Frank and Gretchen (since they must always sit in front of Daisy).  With Carl and Frank sitting in the same seat, Carl obviously cannot sit in Seat 4 either.  However, any of the remaining five students could sit in Seat 4 under these circumstances, if properly arranged.

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