LSAT Logic Games › Two-Variable
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
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.
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
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.
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:
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.
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 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.
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.
A photographer is hanging six portraits on the wall in a straight line. The portraits are of six family members: Lily, Mildred, Nancy, Owen, Peter and Quentin. The order in which the portraits are hung must conform to the following restrictions:
Mildred's portrait must be either first or last
There must be exactly one portrait between Nancy and Quentin
Nancy's portrait must come after Lily's but before Quentin's
Which of the following is an acceptable order in which the portraits could be hung?
Mildred, Lily, Owen, Nancy, Peter, Quentin
Lily, Mildred, Nancy, Owen, Quentin, Peter
Lily, Nancy, Quentin, Peter, Owen, Mildred
Mildred, Nancy, Lily, Quentin, Owen, Peter
Lily, Quentin, Peter, Nancy, Owen, Mildred
Any option without Mildred being first or last is immediately taken out. Any option without one space between Nancy and Quentin is taken out, and any option that has Quentin appearing before Nancy is taken out. Any option that doesn't have Lily appearing before Nancy is taken out, leaving only the correct answer as an option.
A photographer is hanging six portraits on the wall in a straight line. The portraits are of six family members: Lily, Mildred, Nancy, Owen, Peter and Quentin. The order in which the portraits are hung must conform to the following restrictions:
Mildred's portrait must be either first or last
There must be exactly one portrait between Nancy and Quentin
Nancy's portrait must come after Lily's but before Quentin's
Which of the following is an acceptable order in which the portraits could be hung?
Mildred, Lily, Owen, Nancy, Peter, Quentin
Lily, Mildred, Nancy, Owen, Quentin, Peter
Lily, Nancy, Quentin, Peter, Owen, Mildred
Mildred, Nancy, Lily, Quentin, Owen, Peter
Lily, Quentin, Peter, Nancy, Owen, Mildred
Any option without Mildred being first or last is immediately taken out. Any option without one space between Nancy and Quentin is taken out, and any option that has Quentin appearing before Nancy is taken out. Any option that doesn't have Lily appearing before Nancy is taken out, leaving only the correct answer as an option.
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?
garlic is fourth
mint is first
cumin is fourth
pepper is fifth
mint is second
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.
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
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 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?
oregano is fifth
mint is second
garlic is second
cumin is fifth
oregano is second
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.
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
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.