GRE数学选择题精炼
Petworld has exactly fourteen animals (three gerbils, three hamsters, three lizards, five snakes) that are kept in four separate cages (W, X, Y, Z) according to the following conditions:
Each cage contains exactly two, four, or six animals. Any cage containing a gerbil also contains at least one hamster; any cage containing a hamster also contains at least one gerbil. Any cage containing a lizard also contains at least one snake; any cage containing a snake also contains at least one lizard. Neither cage Y nor cage Z contains a gerbil. Neither cage W nor cage X contains a lizard.
(1). Which one of the following could be a complete and accurate list of the animals kept in cages W and Y?
(A) W: one gerbil and one hamster; Y: two lizards and two snakes
(B) W: one gerbil and two hamsters; Y: one lizard and three snakes
(C) W: two gerbils and two hamsters; Y: one lizard and four snakes
(D) W: two gerbils and two hamsters; Y: three lizards and one snake
(E) W: two gerbils and two lizards; Y: two hamsters and two snakes
(2). If there are exactly two hamsters in cage W and the number of gerbils in cage X is equal to the number of snakes in cage Y, then the number of snakes in cage Z must be exactly
(A) one
(B) two
(C) three
(D) four
(E) five
(3). If cage Z contains exactly twice as many lizards as cage Y, which one of the following can be true?
(A) cage Y contains exactly two lizards.
(B) Cage Y contains exactly two snakes.
(C) Cage Y contains exactly four animals.
(D) Cage Z contains exactly three snakes.
(E) Cage Z contains exactly two animals.
