Solving two-variable logic games - LSAT
Card 0 of 864
A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:
- Package E must be the only package delivered between packages C and D
- Package A cannot be the first, third or fifth package delivered
- Package D must be delivered sometime before Package C
- Package F must be either the first or last package delivered
If Package A is delivered second, which of the following could be true?
A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:
- Package E must be the only package delivered between packages C and D
- Package A cannot be the first, third or fifth package delivered
- Package D must be delivered sometime before Package C
- Package F must be either the first or last package delivered
If Package A is delivered second, which of the following could be true?
If Package A is delivered second, there are only two spots where the DEC block can fit: either in spots three, four and five, or four, five and six. Leaving us with two possible set ups:
_ A D E C _ OR _ A _ D E C
Leaving us to place F and B. In the first solution, F and B are interchangeable - since the only rule we are working with is that F must go either first or last. In the second solution, F must go first, leaving us with only one way to solve. Therefore, the following three solution are the only possibilities:
F A D E C B; B A D E C F; F A B D E C
If Package A is delivered second, there are only two spots where the DEC block can fit: either in spots three, four and five, or four, five and six. Leaving us with two possible set ups:
_ A D E C _ OR _ A _ D E C
Leaving us to place F and B. In the first solution, F and B are interchangeable - since the only rule we are working with is that F must go either first or last. In the second solution, F must go first, leaving us with only one way to solve. Therefore, the following three solution are the only possibilities:
F A D E C B; B A D E C F; F A B D E C
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A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:
- Package E must be the only package delivered between packages C and D
- Package A cannot be the first, third or fifth package delivered
- Package D must be delivered sometime before Package C
- Package F must be either the first or last package delivered
Which of the following, if true, would determine the order in which every package must be delivered?
A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:
- Package E must be the only package delivered between packages C and D
- Package A cannot be the first, third or fifth package delivered
- Package D must be delivered sometime before Package C
- Package F must be either the first or last package delivered
Which of the following, if true, would determine the order in which every package must be delivered?
If Package C is third, the we know that package D and E must be second and third, respectively.
_ D E C _ _
Package A cannot go first or fifth, so we must place it last.
_ D E C _ A
F must then go first, and we fill in B in the second spot.
F B D E C A
If Package C is third, the we know that package D and E must be second and third, respectively.
_ D E C _ _
Package A cannot go first or fifth, so we must place it last.
_ D E C _ A
F must then go first, and we fill in B in the second spot.
F B D E C A
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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 accurate order in which the women dance during the week starting with Monday?
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 accurate order in which the women dance during the week starting with Monday?
The key is to figure out where Olivia and Nicole can go based on where Carlos and Ben can be placed with one day in between them. For example:
The men being ordered B __ C __ A means the women would be ordered __ O N __ __
Additionally, Olivia and Nicole could be placed as follows:
__ __ O N __
__ N __ __ O
N __ __ O __
Using this information, one finds only the correct answer conforms to one of these placement patterns.
The key is to figure out where Olivia and Nicole can go based on where Carlos and Ben can be placed with one day in between them. For example:
The men being ordered B __ C __ A means the women would be ordered __ O N __ __
Additionally, Olivia and Nicole could be placed as follows:
__ __ O N __
__ N __ __ O
N __ __ O __
Using this information, one finds only the correct answer conforms to one of these placement patterns.
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A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
Which of the following could be true?
A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
Which of the following could be true?
Only the statement that B is assigned to the sixth slot can be true. If A is in the third slot, and since B and C cannot be consecutive, neither can go in slots one and two. This means E and F must go in the first two slots. This scenario only leaves B being in the sixth slot as the only possibility.
If C is in the third slot, since B cannot immediately follow it, again E and F must go in the first two slots. Because A must come before D, it cannot be in the sixth slot. Again, only B being in the sixth slot is a possibility.
Only the statement that B is assigned to the sixth slot can be true. If A is in the third slot, and since B and C cannot be consecutive, neither can go in slots one and two. This means E and F must go in the first two slots. This scenario only leaves B being in the sixth slot as the only possibility.
If C is in the third slot, since B cannot immediately follow it, again E and F must go in the first two slots. Because A must come before D, it cannot be in the sixth slot. Again, only B being in the sixth slot is a possibility.
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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 accurate order in which the men dance during the week starting with Monday?
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 accurate order in which the men dance during the week starting with Monday?
The question gives enough information to figure out where Adam, Ben, and Carlos can possibly go. Thus listing out of the possibilities we get:
__ B __ C A
__ C __ B A
B __ C __ A
C __ B __ A
Using this information, one finds that only the correct answer conforms to one of these placement patterns.
The question gives enough information to figure out where Adam, Ben, and Carlos can possibly go. Thus listing out of the possibilities we get:
__ B __ C A
__ C __ B A
B __ C __ A
C __ B __ A
Using this information, one finds that only the correct answer conforms to one of these placement patterns.
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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.
If Adam and Olivia dance on the same day, what must not be true?
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.
If Adam and Olivia dance on the same day, what must not be true?
If Adam and Olivia dance on the same day (Friday), then Ben dances on Thursday (one day before Olivia) and Carlos and Nicole must dance on Tuesday (they dance on the same day and there is a day in-between Ben and Carlos). Thus it must not be true that Nicole dances on Wednesday.
If Adam and Olivia dance on the same day (Friday), then Ben dances on Thursday (one day before Olivia) and Carlos and Nicole must dance on Tuesday (they dance on the same day and there is a day in-between Ben and Carlos). Thus it must not be true that Nicole dances on Wednesday.
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A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
If E is assigned to the first time slot, then each of the following could be true EXCEPT:
A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
If E is assigned to the first time slot, then each of the following could be true EXCEPT:
The only statement that cannot be true is that B can occupy the fourth slot. If C is in the third slot, B cannot occupy the fourth slot because it cannot be consecutive with C. If A is in the third slot, E and F must be in the first two slots. Since B must be after C and in this scenario C must be fourth or later, B cannot occupy the fourth slot.
The only statement that cannot be true is that B can occupy the fourth slot. If C is in the third slot, B cannot occupy the fourth slot because it cannot be consecutive with C. If A is in the third slot, E and F must be in the first two slots. Since B must be after C and in this scenario C must be fourth or later, B cannot occupy the fourth slot.
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A family is having a yard sale and pricing each type of item at $0.25, $0.50, $1.00, or $2.00. The types of items they sell are: books, CDs, dolls, flowerpots, paintbrushes, and towels.
- Flowerpots cost at least as much as dolls.
- The total price of one doll with one CD is less than the total price of one doll with one book.
- Books are the same price as paintbrushes.
- Towels cost $2.00.
If books cost $0.50 and dolls cost more than books, which of the following could be true?
A family is having a yard sale and pricing each type of item at $0.25, $0.50, $1.00, or $2.00. The types of items they sell are: books, CDs, dolls, flowerpots, paintbrushes, and towels.
- Flowerpots cost at least as much as dolls.
- The total price of one doll with one CD is less than the total price of one doll with one book.
- Books are the same price as paintbrushes.
- Towels cost $2.00.
If books cost $0.50 and dolls cost more than books, which of the following could be true?
Since dolls cost more than books, dolls must cost either $1.00 or $2.00.
- If dolls cost $1.00, flowerpots cost either $1.00 or $2.00 because flowerpots cost at least as much as dolls.
- If dolls cost $2.00, flowerpots cost $2.00 for the same reason.
In either case, flowerpots could cost $2.00 (the same price as towels).
Since dolls cost more than books, dolls must cost either $1.00 or $2.00.
- If dolls cost $1.00, flowerpots cost either $1.00 or $2.00 because flowerpots cost at least as much as dolls.
- If dolls cost $2.00, flowerpots cost $2.00 for the same reason.
In either case, flowerpots could cost $2.00 (the same price as towels).
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A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
If B is assigned to the fifth time slot, then which of the following is a complete and accurate list of possible slots for D?
A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
If B is assigned to the fifth time slot, then which of the following is a complete and accurate list of possible slots for D?
If B is assigned to the fifth slot, then E and F must occupy the first two slots. If A is in the third slot, then C would have to be either fourth or sixth. Since B and C cannot occur consecutively, A cannot be in the third slot in this scenario. Therefore, C must be in the third slot. Since A must come before D, A must then be in the fourth slot and D in the sixth slot. This is the only possible position for D when B is fifth.
If B is assigned to the fifth slot, then E and F must occupy the first two slots. If A is in the third slot, then C would have to be either fourth or sixth. Since B and C cannot occur consecutively, A cannot be in the third slot in this scenario. Therefore, C must be in the third slot. Since A must come before D, A must then be in the fourth slot and D in the sixth slot. This is the only possible position for D when B is fifth.
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A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
If D is assigned to the fifth slot, then which of the following must be assigned to the sixth slot?
A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
If D is assigned to the fifth slot, then which of the following must be assigned to the sixth slot?
With D in the fifth slot, E and F must be in the first two slots. If A is in the third slot, and since B must come after C, this leaves C in the fourth slot and B in the sixth slot. If C is in the third slot, and since B and C cannot be consecutive, again B must be in the sixth slot.
With D in the fifth slot, E and F must be in the first two slots. If A is in the third slot, and since B must come after C, this leaves C in the fourth slot and B in the sixth slot. If C is in the third slot, and since B and C cannot be consecutive, again B must be in the sixth slot.
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Five friends: Lenny, Monica, Nathan, Olivia, and Peter, take turns doing the following five chores: dishes, sweeping, mopping, dusting, and trash removal. Each person does exacly one chore, and each chore is done by exactly one person. To determine which friend does each chore, they apply the following rules:
- Lenny cannot sweep.
- Peter must either dust or mop.
- If Monica does dishes, then Lenny does trash removal.
- If Olivia does not do trash removal, then Peter dusts.
If Monica does dishes, which of the following must be true?
Five friends: Lenny, Monica, Nathan, Olivia, and Peter, take turns doing the following five chores: dishes, sweeping, mopping, dusting, and trash removal. Each person does exacly one chore, and each chore is done by exactly one person. To determine which friend does each chore, they apply the following rules:
- Lenny cannot sweep.
- Peter must either dust or mop.
- If Monica does dishes, then Lenny does trash removal.
- If Olivia does not do trash removal, then Peter dusts.
If Monica does dishes, which of the following must be true?
Since Monica does dishes, Lenny does trash removal. Therefore, Olivia does not do trash removal, so Peter dusts.
Since Monica does dishes, Lenny does trash removal. Therefore, Olivia does not do trash removal, so Peter dusts.
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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?
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?
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)
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)
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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?
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?
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.
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.
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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.
If Carlos dances on Monday, what must be true?
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.
If Carlos dances on Monday, what must be true?
If Carlos dances on Monday, then Ben dances on Wednesday. Since Olivia dances one day after Ben, she must dance on Thursday.
If Carlos dances on Monday, then Ben dances on Wednesday. Since Olivia dances one day after Ben, she must dance on Thursday.
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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
If a rule is added that requires exactly two boxes to be after French and before Green, which of the following could be true?
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
If a rule is added that requires exactly two boxes to be after French and before Green, which of the following could be true?
Since a tea must be fifth, Green cannot be fourth or sixth (otherwise it would be adjacent to another tea). As a result, Green could only be fifth or seventh. French could only be second or fourth.
Since a tea must be fifth, Green cannot be fourth or sixth (otherwise it would be adjacent to another tea). As a result, Green could only be fifth or seventh. French could only be second or fourth.
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A cruise line company is preparing the itinerary for its upcoming global tour. The cruise will last five months and travel to exactly one of seven countries – C, D, E, F, G, H, I – each month. No country may be visited more than once. The following conditions must hold:
C or D is part of the itinerary, but not both.
If F is part of the itinerary, G is also included.
If E is part of the itinerary, it is visited earlier in the cruise than D and G.
If F is part of the itinerary, it is visited later in the cruise than both E and H.
I is part of the itinerary and must be visited during either the first or fifth month.
Which of the following CANNOT be the country visited in the fifth month of the tour?
A cruise line company is preparing the itinerary for its upcoming global tour. The cruise will last five months and travel to exactly one of seven countries – C, D, E, F, G, H, I – each month. No country may be visited more than once. The following conditions must hold:
C or D is part of the itinerary, but not both.
If F is part of the itinerary, G is also included.
If E is part of the itinerary, it is visited earlier in the cruise than D and G.
If F is part of the itinerary, it is visited later in the cruise than both E and H.
I is part of the itinerary and must be visited during either the first or fifth month.
Which of the following CANNOT be the country visited in the fifth month of the tour?
There is no possible scenario in which E can be visited in the fifth month. Since D, G, and F can only be included if they are visited after E, that leaves only I, C, and H to fill the itinerary, insufficient for a full itinerary.
There is no possible scenario in which E can be visited in the fifth month. Since D, G, and F can only be included if they are visited after E, that leaves only I, C, and H to fill the itinerary, insufficient for a full itinerary.
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Five friends: Lenny, Monica, Nathan, Olivia, and Peter, take turns doing the following five chores: dishes, sweeping, mopping, dusting, and trash removal. Each person does exacly one chore, and each chore is done by exactly one person. To determine which friend does each chore, they apply the following rules:
- Lenny cannot sweep.
- Peter must either dust or mop.
- If Monica does dishes, then Lenny does trash removal.
- If Olivia does not do trash removal, then Peter dusts.
If Peter mops, all of the following are possible except:
Five friends: Lenny, Monica, Nathan, Olivia, and Peter, take turns doing the following five chores: dishes, sweeping, mopping, dusting, and trash removal. Each person does exacly one chore, and each chore is done by exactly one person. To determine which friend does each chore, they apply the following rules:
- Lenny cannot sweep.
- Peter must either dust or mop.
- If Monica does dishes, then Lenny does trash removal.
- If Olivia does not do trash removal, then Peter dusts.
If Peter mops, all of the following are possible except:
Since Peter mops, he does not dust. Employing the contrapositive of the last statement (ie: P -> Q means ~Q -> ~P), if Peter does not dust, then Olivia does trash removal. This means that Lenny does not do trash removal, so (again, employing the contrapositive), Monica does not do dishes.
Since Peter mops, he does not dust. Employing the contrapositive of the last statement (ie: P -> Q means ~Q -> ~P), if Peter does not dust, then Olivia does trash removal. This means that Lenny does not do trash removal, so (again, employing the contrapositive), Monica does not do dishes.
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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?
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?
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.
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.
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A college is having an event for alumni who graduated in the years 2005-2010, inclusive. Six friends-- Harry, Inez, Jack, Katie, Lou, and Maria-- attend the event.
- Katie graduated in 2006.
- Harry and Maria graduated the same year.
- Nobody graduated in 2007.
- Katie graduated before Jack, but after Lou.
If Inez is the only person who graduated in 2010, and Jack did not graduate the same year as Maria, which of the following could be a correct assessment of each person's graduation year?
A college is having an event for alumni who graduated in the years 2005-2010, inclusive. Six friends-- Harry, Inez, Jack, Katie, Lou, and Maria-- attend the event.
- Katie graduated in 2006.
- Harry and Maria graduated the same year.
- Nobody graduated in 2007.
- Katie graduated before Jack, but after Lou.
If Inez is the only person who graduated in 2010, and Jack did not graduate the same year as Maria, which of the following could be a correct assessment of each person's graduation year?
Lou ('05), Katie ('06), Harry ('08), Maria ('08), Jack ('09), Inez ('10) is the only sequence of possibilities among the given choices that adheres to all the requirements.
Lou ('05), Katie ('06), Harry ('08), Maria ('08), Jack ('09), Inez ('10) is the only sequence of possibilities among the given choices that adheres to all the requirements.
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A family is having a yard sale and prices each type of item at $0.25, $0.50, $1.00, or $2.00. The types of items they sell are: books, CDs, dolls, flowerpots, paintbrushes, and towels.
- Flowerpots cost at least as much as dolls.
- The total price of one doll with one CD is less than the total price of one doll with one book.
- Books are the same price as paintbrushes.
- Towels cost $2.00.
Which of the following cannot be true?
A family is having a yard sale and prices each type of item at $0.25, $0.50, $1.00, or $2.00. The types of items they sell are: books, CDs, dolls, flowerpots, paintbrushes, and towels.
- Flowerpots cost at least as much as dolls.
- The total price of one doll with one CD is less than the total price of one doll with one book.
- Books are the same price as paintbrushes.
- Towels cost $2.00.
Which of the following cannot be true?
Since the total price of one doll with one CD is less than the total price of one doll with one book, CDs cost less than books. Given the prices, the most a book can cost is $2.00, so CDs must cost less than $2.00. Therefore, CDs cannot cost $2.00.
Since the total price of one doll with one CD is less than the total price of one doll with one book, CDs cost less than books. Given the prices, the most a book can cost is $2.00, so CDs must cost less than $2.00. Therefore, CDs cannot cost $2.00.
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