Linear Games
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A school is holding tryouts for seven athletes – Eric, Fred, Greg, Ian, John, Kevin, and Merlin – for the varsity and JV track teams. Which team the athletes can join is determined by their 40 yard dash time; the three fastest will join the varsity team and the four slowest the JV team, subject to the following conditions:
Fred has a faster time than Ian.
Eric has a faster time than Ian, but a slower time than Greg
Greg has a faster time than Fred, but a slower time than John.
Kevin is part of the JV team.
Which of the following could be an accurate list of the team rosters, arranged from fastest to slowest?
Varsity: John, Merlin, Greg;
JV: Fred, Eric, Kevin, Ian.
Varsity: John, Fred, Greg;
JV: Merlin, Eric, Ian, Kevin.
Varsity: Merlin, John, Greg;
JV: Kevin, Eric, Ian, Fred.
Varsity: Greg, John, Fred;
JV: Eric, Ian, Kevin, Merlin.
Varsity: John, Merlin, Ian;
JV: Greg, Fred, Eric, Kevin.
Explanation
Each of the incorrect answers violates one of the stated conditions:
(Varsity: John, Fred, Greg;
JV: Merlin, Eric, Ian, Kevin.) - Greg has a faster time than Fred.
(Varsity: Merlin, John, Greg;
JV: Kevin, Eric, Ian, Fred.) - Fred has a faster time than Ian.
(Varsity: Greg, John, Fred;
JV: Eric, Ian, Kevin, Merlin.) - John has a faster time than Greg.
(Varsity: John, Merlin, Ian;
JV: Greg, Fred, Eric, Kevin.) - Ian has a slower time than both Fred and Greg.
The correct answer does not violate any of the conditions.
The directors of a movie festival are deciding the lineup of their six films: Causes, Brothers, Willow, Above, Forged, and Monarchy. The festival will span Friday, Saturday, and Sunday evenings. At least one movie must be played each night, and there can be no more than three played the same evening. No movie is played more than once. The directors have decided on the following:
Monarchy is played on the night directly after Brothers.
Willow is played on the same night as Above.
If Causes is played on Saturday, then Above is played on Friday.
Brothers and Forged do not play on the same night.
Forged does not play by itself.
What is the possible order of the six films?
Friday: Above, Willow
Saturday: Causes, Brothers
Sunday: Monarchy, Forged
Friday: Brothers, Forged
Saturday: Causes, Monarchy
Sunday: Above, Willow
Friday: Brothers, Above, Willow
Saturday: Causes, Monarchy
Sunday: Forged
Friday: Causes, Brothers
Saturday: Willow, Above
Sunday: Monarchy, Forged
Friday: Brothers, Above
Saturday: Monarchy, Causes
Sunday: Forged, Willow
Explanation
First, consider what we're given. Forged cannot be played on a night by itself; we can delete that answer. Willow and Above must be played on the same evening, so we can delete the answer where they're not. Monarchy must be played directly after Brothers, so delete the answer where that is not the case. And lastly, Brothers and Forged cannot be played on the same evening. Delete that. We are left with the correct answer choice.
A library is holding a special five-day event honoring successful local writers. One writer will be invited to be a guest speaker for each night from Monday through Friday, and no writer will be asked to participate twice. The writers have each written books in only one of four different genres—science fiction, mystery, historical fiction, and non-fiction. A, J, and X are all science fiction writers. B and Y are both mystery writers. C and Z are both historical fiction writers. L is a non-fiction writer. The following conditions apply without exception:
At least one writer from each genre will be invited to speak on at least one night.
No two authors from the same genre will be invited to speak on the following night.
If C is invited to speak, then X is invited to speak on the following night.
If Y is invited to speak, then neither C nor A are invited to speak.
If X and J are both invited to speak, then neither will speak on either the first or last night.
If L and B are both invited to speak, then neither will speak on either the first or last night.
Which of the following is an acceptable list of guest speakers for the library's special event from Monday to Friday?
L, J, Z, X, Y
L, J, C, X, Y
A, C, B, J, Z
X, L, C, B, Z
A, X, Y, J, L
Explanation
This question is actually a combination of sequencing and grouping. The test-taker must determine both which variables will be involved in the sequence and the order in which the variables are placed in sequence. Answering this particular question is simply a matter of checking the rules in the question stem. Each incorrect answer breaks one or more rules.
L, J, C, X, Y is incorrect because C may not be invited if Y is invited. Z must be invited instead.
A, C, B, J, Z is incorrect because L is not invited. L is the only non-fiction writer and thus MUST be one of the five invited speakers.
X, L, C, B, Z is incorrect because X must follow C.
A, X, Y, J, L is incorrect because A and X are both science-fiction writers, and they are not allowed to speak on consecutive nights.
Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:
Ben dances one day before Olivia.
Carlos and Nicole attend class on the same day.
Adam dances on Friday.
There is exactly one day between the days Ben and Carlos dance.
Which is a possible and acceptable partial schedule for the week?
Monday: Ben and Michelle
Tuesday: David and Olivia
Wednesday: Carlos and Nicole
Monday: Carlos and Nicole
Tuesday: David and Olivia
Wednesday: Ben and Patricia
Monday: David and Patricia
Tuesday: Carlos and Michelle
Wednesday: Eric and Nicole
Monday: David and Patricia
Tuesday: Ben and Michelle
Wednesday: Adam and Olivia
Monday: Eric and Michelle
Tuesday: Carlos and Nicole
Wednesday: Ben and Patricia
Explanation
All of the incorrect answers break one of the constraits placed on the order.
Monday: Carlos and Nicole
Tuesday: David and Olivia
Wednesday: Ben and Patricia
(Ben must dance one day before Olivia)
Monday: David and Patricia
Tuesday: Carlos and Michelle
Wednesday: Eric and Nicole
(Carlos and Nicole must dance on the same day)
Monday: David and Patricia
Tuesday: Ben and Michelle
Wednesday: Adam and Olivia
(Adam must dance on Friday)
Monday: Eric and Michelle
Tuesday: Carlos and Nicole
Wednesday: Ben and Patricia
(The must be one day between Ben and Carlos)
A library is holding a special five-day event honoring successful local writers. One writer will be invited to be a guest speaker for each night from Monday through Friday, and no writer will be asked to participate twice. The writers have each written books in only one of four different genres—science fiction, mystery, historical fiction, and non-fiction. A, J, and X are all science fiction writers. B and Y are both mystery writers. C and Z are both historical fiction writers. L is a non-fiction writer. The following conditions apply without exception:
At least one writer from each genre will be invited to speak on at least one night.
No two authors from the same genre will be invited to speak on the following night.
If C is invited to speak, then X is invited to speak on the following night.
If Y is invited to speak, then neither C nor A are invited to speak.
If X and J are both invited to speak, then neither will speak on either the first or last night.
If L and B are both invited to speak, then neither will speak on either the first or last night.
If L is invited to speak on Friday, then on what days MUST a science fiction writer be invited?
Tuesday and Thursday
Monday and Wednesday
Monday and Thursday
Monday and Tuesday
Only Wednesday
Explanation
If L is the speaker on Friday, then B cannot be a guest speaker at all, since if L and B are both guest speakers then neither can speak on Monday or Friday. If B is not a speaker, then Y must be a speaker, in order for there to be a mystery writer guest speaker. If Y is a guest speaker, then C must not be a guest speaker. Thus, Z must be a guest speaker in order to have a historical fiction writer.
We thus know so far that Y and Z and L are three out of five possible guest speakers (from Monday through Friday). That means the remaining two MUST be science fiction writers. Furthermore, because Y is a guest speaker, A cannot be a guest speaker. Thus, the two science fiction guests are X and J and they both are invited. They must be invited for Tuesday and Thursday, because any other day would force one of them to speak on Monday, which is not possible if both X and J are invited.
Y/Z, X/J, Y/Z, X/J, L
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?
Fire twirling is the first act performed.
Acrobatics is the first act performed.
Ball juggling is the second act performed.
Elephant demonstrations is the first act performed.
Elephant demonstrations is the last 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.
A school is holding tryouts for seven athletes – Eric, Fred, Greg, Ian, John, Kevin, and Merlin – for the varsity and JV track teams. Which team the athletes can join is determined by their 40 yard dash time; the three fastest will join the varsity team and the four slowest the JV team, subject to the following conditions:
Fred has a faster time than Ian.
Eric has a faster time than Ian, but a slower time than Greg
Greg has a faster time than Fred, but a slower time than John.
Kevin is part of the JV team.
Which of the following athletes CANNOT be on the varsity team?
Ian
Greg
Eric
Merlin
Fred
Explanation
Using the J - G - E/F - I combination of the first three rules, we can see that there are at least four athletes that must have faster times than Ian. As there are only three spots on the varsity team, it is impossible for Ian to be placed onto the varsity team in any scenario.
A barista has seven boxes of tea and coffee of varying types, which she places in a line behind the counter. There are four types of coffee: Colombian, Dark, Espresso, and French. There are three types of tea: Green, Herbal, and Vanilla. The following rules apply:
A box of tea must be fifth
No tea may be placed next to another tea
Herbal may not be next to either Colombian or Espresso
At least two boxes must be between Colombian and Dark
Which of the following cannot be true?
Coffee is both first and last
Coffee is both first and sixth
Two boxes of coffee are next to each other
Tea is both first and last
Coffee is third and fourth
Explanation
If coffee were first and last, then two boxes of tea would need to be next to each other. Since one box would need to be fifth and since we could not put tea first or seventh, there is no way to separate all the boxes of tea.
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 last, then which of the following must be true?
Genie performs some time after Kyle and Flo.
Genie performs second.
Genie performs immediately after Kyle.
Genie does elephant demonstrations immediately before Kyle performs.
Flo does ball juggling.
Explanation
This question calls for an answer that reflects what must happen, not what could happen. We know that Kyle must go first, so Kyle occupies slots 1 and 6. We know that Flo must go before Genie performs her first act. So Genie cannot occupy slot 2. That means Genie must perform after some time after Kyle and Flo, which is the credited response.
Exactly five men—Adam, Ben, Carlos, David, and Eric—and five women—Liza, Michelle, Nicole, Olivia, and Patricia—are scheduled to take ballroom dance classes. There is one class offered each day—Monday, Tuesday, Wednesday, Thursday, and Friday—for a total of five classes. Every class has exactly one man and one woman. Every person participates in exactly one class with the following conditions:
Ben dances one day before Olivia.
Carlos and Nicole attend class on the same day.
Adam dances on Friday.
There is exactly one day between the days Ben and Carlos dance.
Which is a possible and acceptable partial schedule for the week?
Monday: Ben and Michelle
Tuesday: David and Olivia
Wednesday: Carlos and Nicole
Monday: Carlos and Nicole
Tuesday: David and Olivia
Wednesday: Ben and Patricia
Monday: David and Patricia
Tuesday: Carlos and Michelle
Wednesday: Eric and Nicole
Monday: David and Patricia
Tuesday: Ben and Michelle
Wednesday: Adam and Olivia
Monday: Eric and Michelle
Tuesday: Carlos and Nicole
Wednesday: Ben and Patricia
Explanation
All of the incorrect answers break one of the constraits placed on the order.
Monday: Carlos and Nicole
Tuesday: David and Olivia
Wednesday: Ben and Patricia
(Ben must dance one day before Olivia)
Monday: David and Patricia
Tuesday: Carlos and Michelle
Wednesday: Eric and Nicole
(Carlos and Nicole must dance on the same day)
Monday: David and Patricia
Tuesday: Ben and Michelle
Wednesday: Adam and Olivia
(Adam must dance on Friday)
Monday: Eric and Michelle
Tuesday: Carlos and Nicole
Wednesday: Ben and Patricia
(The must be one day between Ben and Carlos)