himu wrote:A group of 9 people is traveling in two taxis from one destination to another. If the taxis have different passenger capacities, how many different ways can this group divide itself among the two taxis?
(1) The larger of the two taxis can hold no more than 5 people.
(2) The smaller of the two taxis can hold no more than 4 people.
To determine how many ways the group can be divided, we need to know the MAXIMUM capacity of each taxi.
Statement 1: The larger of the two taxis can hold no more than 5 people.
By definition, the LARGER taxi must be able to hold more people than the SMALLER taxi.
The maximum capacity of the LARGER taxi is 5.
Thus, the maximum capacity of the SMALLER taxi must be less than 5.
Since a total of 9 people are traveling, the maximum capacity of the SMALLER taxi must be 4; otherwise, it is not possible for all 9 people to be traveling.
SUFFICIENT.
Statement 2: The smaller of the two taxis can hold no more than 4 people.
It's possible that the maximum capacity of the smaller taxi = 4, while the maximum capacity of the larger taxi = 5.
It's possible that the maximum capacity of the smaller taxi = 3, while the maximum capacity of the larger taxi = 6.
Since different combinations are possible, INSUFFICIENT.
The correct answer is
A.
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