LSAT Logic Games : Linear Games

Study concepts, example questions & explanations for LSAT Logic Games

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Example Questions

Example Question #81 : Linear Games

Seven runners, Allen, Beth, Calli, Drew, Erin, Fred, and Gary, are being timed running a mile.  Only one runner can run at a time.  The following conditions apply:

Calli cannot run first or last

At least one person must run between Fred and Gary

Erin can only run directly before or after Drew if Allen runs first

Beth must run before Gary

If Allen runs first, Fred fifth, and Erin seventh, which of the following must be true?

Possible Answers:

Gary runs second

Drew runs fourth

Calli runs third

Beth runs second

Drew runs third

Correct answer:

Beth runs second

Explanation:

To allow for at least one runner between Gary and Fred, Gary must run second or third.  Since Beth must run before Gary, Beth must run second.  Drew must run sixth, and Calli must run fourth.

Example Question #81 : Linear Games

Seven runners, Allen, Beth, Calli, Drew, Erin, Fred, and Gary, are being timed running a mile.  Only one runner can run at a time.  The following conditions apply:

Calli cannot run first or last

At least one person must run between Fred and Gary

Erin can only run directly before or after Drew if Allen runs first

Beth must run before Gary

Which of the following could be the order of the runners from first to last?

Possible Answers:

Allen, Beth, Gary, Drew, Erin, Fred, Calli

Allen, Beth, Drew, Fred, Erin, Calli, Gary

Allen, Drew, Calli, Erin, Gary, Beth, Fred

Erin, Calli, Beth, Drew, Gary, Fred, Allen

Drew, Erin, Calli, Beth, Gary, Allen, Fred

Correct answer:

Drew, Erin, Calli, Beth, Gary, Allen, Fred

Explanation:

By using the process of elimination, you can eliminate each incorrect answer.  If you accurately apply the rules, you will find that each incorrect answer directly contradicts one or more of the conditions.

Example Question #81 : Linear Games

Jennifer is a high school student with five classes—Art, English, History, Math, and Spanish—and those classes meet at some point during the day according to the following time slots: 8:00 a.m., 9:00 a.m., 10:00 a.m., 11:00 a.m., 1:00 p.m., and 2:00 p.m. Jennifer also has a “free block” which she can use to do homework.

The following conditions must apply:

Jennifer has English before her free block.

Jennifer has History after her free block.

Jennifer has Spanish either immediately before or immediately after her free block.

Jennifer has Math before Art.

Which one of the following could be the order of the classes, from earliest to latest?

Possible Answers:

English, Math, Art, Spanish, History

English, Math, History, Spanish, Art

Math, Spanish, English, Art, History

English, Spanish, Art, History, Math

Math, Art, English, History, Spanish

Correct answer:

English, Math, Art, Spanish, History

Explanation:

The key here is to see that "free block" is not represented in the sequence but that it must still be accounted for. 

Math, Spanish, English, Art, History:  This sequence violates the rule that English must precede the free block, which immediately precedes or follows Spanish.

Math, Art, English, History, Spanish:  This sequence violates the rule that History must follow the free block.

English, Spanish, Art, History, Math:  This sequence violates the rule that Math must precede Art.

English, Math, History, Spanish, Art:  This sequence violates the rule that History must follow the free block, which immediately precedes or follows Spanish.

That leaves the following sequence, which violates no rules or conditions:  English, Math, Art, Spanish, History

Example Question #81 : Determining Sequence In Linear Games

Jennifer is a high school student with five classes—Art, English, History, Math, and Spanish—and those classes meet at some point during the day according to the following time slots: 8:00 a.m., 9:00 a.m., 10:00 a.m., 11:00 a.m., 1:00 p.m., and 2:00 p.m. Jennifer also has a “free block” which she can use to do homework.

The following conditions must apply:

Jennifer has English before her free block.

Jennifer has History after her free block.

Jennifer has Spanish either immediately before or immediately after her free block.

Jennifer has Math before Art.

How many of the classes are possible for the 8:00 a.m. time slot?

Possible Answers:

One

Four

Three

Two

Five

Correct answer:

Two

Explanation:

From the sequencing rules, we can eliminate the following from the first slot (the 8 a.m. slot):

free block (it must follow English)

Spanish (it, too, must follow English, since it must immediately precede or follow the free block)

History (it must follow English, Spanish, and free block)

Art (it must follow Math).

With those four eliminated as options for the 8 a.m. slot, we are only left with Math and English as eligible options.  So the answer is TWO.

Example Question #81 : Linear Games

Jennifer is a high school student with five classes—Art, English, History, Math, and Spanish—and those classes meet at some point during the day according to the following time slots: 8:00 a.m., 9:00 a.m., 10:00 a.m., 11:00 a.m., 1:00 p.m., and 2:00 p.m. Jennifer also has a “free block” which she can use to do homework.

The following conditions must apply:

Jennifer has English before her free block.

Jennifer has History after her free block.

Jennifer has Spanish either immediately before or immediately after her free block.

Jennifer has Math before Art.

Jennifer cannot have Math at which one of the following times?

Possible Answers:

1:00 p.m.

8:00 a.m.

11:00 a.m.

10:00 a.m.

9:00 a.m.

Correct answer:

10:00 a.m.

Explanation:

Math cannot be at 10:00 a.m. because the remaining three slots (11 a.m., 1 pm, and 2 pm) must be occupied by Spanish, free block, and History, thus leaving no space for Art, which must follow Math.  The reason Spanish, free block, and History are forced into the final three slots is that Spanish and free block operate in tandem and thus cannot occupy the 8 a.m. and 9 a.m. slots, since they must follow English.  And since History must follow Spanish and free block, the latter two are locked into the 11 a.m. and 1 pm slots, with History then occupying the 2 pm slot, leaving no slot for Art.

Example Question #81 : Linear Games

Jennifer is a high school student with five classes—Art, English, History, Math, and Spanish—and those classes meet at some point during the day according to the following time slots: 8:00 a.m., 9:00 a.m., 10:00 a.m., 11:00 a.m., 1:00 p.m., and 2:00 p.m. Jennifer also has a “free block” which she can use to do homework.

The following conditions must apply:

Jennifer has English before her free block.

Jennifer has History after her free block.

Jennifer has Spanish either immediately before or immediately after her free block.

Jennifer has Math before Art.

If English takes place the hour before Spanish, then each of the following could be true, EXCEPT:

Possible Answers:

Art is at 9:00 a.m.

History is at 2:00 p.m.

History is at 11:00 a.m.

Spanish is at 1:00 p.m.

Spanish is at 10:00 a.m.

Correct answer:

Spanish is at 1:00 p.m.

Explanation:

The key here is to see that the added restriction creates the following sequencing block:  English-Spanish-free block.  History must follow this sequencing block since one rule specifies that History follows the free block.  Therefore, if Spanish occupied the 1:00 p.m. slot, there would be no room for free block and History.

Example Question #81 : Determining Sequence In Linear Games

Jennifer is a high school student with five classes—Art, English, History, Math, and Spanish—and those classes meet at some point during the day according to the following time slots: 8:00 a.m., 9:00 a.m., 10:00 a.m., 11:00 a.m., 1:00 p.m., and 2:00 p.m. Jennifer also has a “free block” which she can use to do homework.

The following conditions must apply:

Jennifer has English before her free block.

Jennifer has History after her free block.

Jennifer has Spanish either immediately before or immediately after her free block.

Jennifer has Math before Art.

If History is at 11:00 a.m., then which one of the following must be true?

Possible Answers:

Spanish is at 10:00 a.m.

Art is at 1:00 p.m.

Spanish is at 9:00 a.m.

Free block is at 9:00 a.m.

Math is at 1:00 p.m.

Correct answer:

Math is at 1:00 p.m.

Explanation:

With History occupying the 11:00 a.m. slot, the three preceding slots must be occupied by English, Spanish, and free block, since those subjects must precede History, according to the rules.  That leaves the 1:00 p.m. and 2:00 p.m. slots for Math and Art.  Math must precede Art, so it must occupy the 1:00 p.m. slot. 

Example Question #82 : Linear Games

A boy band (composed of Henry, Ralph, and Viktor) will play one song a day in a six-day music festival from Sunday to Friday.  They have 10 total songs and will play a different song each day.  Two songs will be chosen from among the three songs written by Henry – 1, 2, and 3: two from among the four songs written by Ralph – 4, 5, 6, and 7; and two from the songs written by Viktor – 8, 9, and 10. The following rules also apply:

  1.   If song 5 is selected, then song 2 is also selected.
  2.   If song 4 is selected, then neither songs 2 nor 6 can be selected.
  3.   If song 8 is selected, then neither songs 10 nor 7 can be selected.
  4.   If both songs 2 and 6 are selected, then song 2 is played at some time before song 6.
  5.   Song 8 cannot be played on Thursday unless one of Ralph’s songs is played on Sunday.

If song 6 is played on Sunday, which song must also played during the band’s six-day music festival?

Possible Answers:

Song 4

Song 5

Song 3

Song 8

Song 2

Correct answer:

Song 3

Explanation:

Since song 6 is played first, song 2 must not be chosen at all (See Rule 4).  Without song 2, the other two Henry songs, 1 and 3, must be played, which means that either song 1 or song 3 could be the correct answer choice.  Here, only one of these songs, song 3, is listed as an answer choice; and song 3 is the correct choice. 

Example Question #81 : Determining Sequence In Linear Games

Madeline, Natalie, Rachel, Stacey, Ursula, and Valerie are six kindergarten students on a picnic with their teacher. The teacher is seated in the center with the children seated on six separate cushions arranged in a clock-wise circular fashion around their teacher.  The cushions are numbered 1 through 6 with cushion 1 at the 12 o’clock position, cushion 2 at the 2 o’clock position, cushion 3 at the 4 o’clock position, cushion 4 is at the 6 o’clock position, cushion 5 at the 8 o’clock position, and cushion 6 at the 10 o’clock position.  The following rules apply:

  1.   “Adjacent” cushions are those cushions that are consecutively numbered. Cushions 1 and 6 are also considered adjacent.
  2.   Stacey and Rachel are not sitting in adjacent cushions
  3.   Natalie is sitting in cushion 1 or cushion 4
  4.   Ursula and Stacey are sitting in adjacent cushions on either the left of right side of the clock-wise circle (i.e. cushions 2 and 3, or cushions  5 and 6)

If Valerie and Stacey are sitting in adjacent cushions, then Madeline could be sitting in any of the following cushions except:

Possible Answers:

Cushion 5

Cushion 3

Cushion 2

Cushion 1

Cushion 6

Correct answer:

Cushion 1

Explanation:

The question stem informs us that Stacey and Valerie are next to each other.  Likewise, Stacey and Ursula are also next to each other (Rule 3). Therefore, Valerie and Ursula are on opposite sides of Stacey respectively.  Rule 3 specifically states that Valerie and Stacey are on either the left of right side of the clock-wise circle, at cushions 2 and 3, or cushions 5 and 6.  Therefore, Valerie must be either at cushion 1 or 4.  The opposite end of the clock-wise circle is reserved for Natalie (Rule 2). Looking at the answer choices, the choice for cushion 1 is the correct choice, as cushion 1 must be reserved for either Valerie or Natalie. 

Example Question #81 : Linear Games

A boy band (composed of Henry, Ralph, and Viktor) will play one song a day in a six-day music festival from Sunday to Friday. They have 10 total songs and will play a different song each day.  Two songs will be chosen from among the three songs written by Henry – 1, 2, and 3: two from among the four songs written by Ralph – 4, 5, 6, and 7; and two from the songs written by Viktor – 8, 9, and 10.  The following rules also apply:

  1.   If song 5 is selected, then song 2 is also selected.
  2.   If song 4 is selected, then neither songs 2 nor 6 can be selected.
  3.   If song 8 is selected, then neither songs 10 nor 7 can be selected.
  4.   If both songs 2 and 6 are selected, then song 2 is played at some time before song 6.
  5.   Song 8 cannot be played on Thursday unless one of Ralph’s songs is played on Sunday. 

If the six songs to be played are songs 2, 3, 5, 6, 9, and 10 and if song 5 is to be played on Sunday, then which one of the following songs CANNOT be played on Monday?

Possible Answers:

Song 3

Song 6

Song 10

Song 2

Song 9

Correct answer:

Song 6

Explanation:

Here, the grouping aspect is provided which means that the sequencing element has to be dealt with.  Rules 4 provide us with the appropriate sequencing rule. Rule 4 states that if songs 2 and 6 are selected (as they are in this question), then song 2 has to be played before song 6.  The question provides us that song 5 will be played first on Sunday.  Therefore, song 6 cannot be played on the next day, Monday, because that would place song 6 before song 2, a violation of Rule 4.

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