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Manager
Joined: 28 Aug 2004
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A certain city with a population of 132,000 is to be divided [#permalink]
 13 Aug 2005, 06:19
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?
1. 10,700
2. 10,800
3. 10,900
4. 11,000
5. 11,100
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Manager
Joined: 14 Jul 2005
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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...
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Manager
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yes it should be D
to make x min; we should consider max population for 10 districts i.e 1.1X
x+10*1.1x=13200
x= 11000
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Senior Manager
Joined: 04 May 2005
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D
the strategy is to have one (let's say x) smallest and the rest 10 equal (let's say y)
x + 10y = 132000
y=1.1x
x = 11000
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SVP
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minimum = x
maximum = 1.1x
total = x+10(1.1x)=132000
so x = 11,000
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Director
Joined: 13 Nov 2003
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i will vote for 10 800 which is 10% less than the average-12000
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