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A certain city with a population of 132,000 is to be divided [#permalink]
13 Aug 2005, 06:19
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A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
I think it's best to choose one district and designate it to be the smallest one. We make all the big districts of identical size, with enough capacity to accommodate exactly 110% of the population of the smallest one.
x + 10*1.1x=132k
x = 132k / 12 = 11k
Is (D) the right answer?
I can't really explain the solution clearly, but I'll try. We are looking for the case where the average of the 10 large districts is exactly 110% of the population of the smallest district. But if the population of 1 of the 10 is greater than their average, this would break condition of "not greater than 10%", so the 10 big ones must be of equal size.
I am sure someone can do better with the explanation...