prat_agl wrote:A certain city with a population of 132,000 is to be divided into 11 voting districts and no district is to have a population that is more than 10% greater than the population of any other district. what is the minimum possible population that the least populated district could have?
a) 10,700
b) 10,800
c) 10,900
d) 11,000
e) 11,100
An alternate approach is to plug in the answer choices, which represent the minimum possible population.
To MINIMIZE the smallest population, we need to MAXIMIZE the other 10 populations.
Thus, each of the other 10 districts must have the maximum allowed population: 10% greater than the smallest population.
Since the total population of the city is 132,000 -- a multiple of 1,000 -- the correct answer choice is almost certainly a multiple of 1,000.
Answer choice D: 11,000.
Maximum value of each of the other 10 districts = 11,000 + .1(11,000) = 12,100.
Sum of the 11 districts = 11,000 + 10(12,100) = 132,000.
Success!
The correct answer is
D.
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