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Math 4AB/Mr. Hanlon

Logic Project 2

An amusement park roller coaster includes five cars, numbered 1 through 5 from front to back. Each caraccommodates up to two riders, seated side by side. Six people — Tim, Gill, Loren, Mike, Peter and John — are riding the coaster at the same time.
Loren is sharing a car.
Mike is not sharing a car and isseated immediately behind an empty car.
Tim is not sharing a car with either Gill or Peter.
Gill is riding in either the third or fourth car.

Which of the following groups of riders could occupythe second car?
[pic](A) Loren only
[pic](B) Tim and Gill
[pic](C) Loren and Mike
[pic](D) John and Tim
[pic](E) John, Gill, and Peter

If Gill is riding immediately behind Loren's car andimmediately ahead of Tim's car, all of the following must be true EXCEPT:
[pic](A) Gill is riding in the fourth car.
[pic](B) Peter is riding in the third car.
[pic](C) Tim is riding in the fifthcar.
[pic](D) Loren is riding in the third car.
[pic](E) The first car is empty.

Which one of the following statements CANNOT be true?
[pic](A) Neither Tim or Gill is sharing a car withanother rider
[pic](B) Neither Mike or John is sharing a car with another rider.
[pic](C) Tim is sharing a car, and John is sharing a car.
[pic](D) Gill is sharing a car, and Peter is sharing a car.[pic](E) Tim is sharing a car, and Gill is sharing a car.

If Peter is riding in the second car, how many different combinations of riders are possible for the third car?
[pic](A) one
[pic](C) three
[pic](D) four
[pic](E) five

Assume that a seventh rider is riding with John in the first car, but that all other rules remain unchanged. Which of the following is a completeand accurate list of the riders who might be riding in the fifth car?
[pic](A) Mike
[pic](B) Gill, Peter
[pic](C) Tim, Loren, Peter
[pic](D) Tim, Loren, Mike
[pic](E) Tim, Peter, Loren, Mike
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