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# A certain city with a population of 132,000 is to be divided

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Intern
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A certain city with a population of 132,000 is to be divided [#permalink]  06 Jan 2008, 12:56
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
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: Population divided into 11 districts [#permalink]  06 Jan 2008, 13:40
Expert's post
D

z - district with maximum population
y - district with minimum population
T - total population (132,000)
z=1.1*y

I think the best configuration is: T=10*z+y
132,000=10*1.1*y+y=12y ==> y=11,000
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Re: Population divided into 11 districts [#permalink]  06 Jan 2008, 13:57
kamilaak 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

10(1.1x)+x=132000 --> 12x=132000 x=11000
Director
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Re: Population divided into 11 districts [#permalink]  06 Jan 2008, 16:31
I kinda of understand how you are solving. Can you break it down further in text how you are solving this?
Manager
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Re: Population divided into 11 districts [#permalink]  06 Jan 2008, 16:57
what does the "10" represent?
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Re: Population divided into 11 districts [#permalink]  06 Jan 2008, 18:23
walker wrote:
D

z - district with maximum population
y - district with minimum population
T - total population (132,000)
z=1.1*y

I think the best configuration is: T=10*z+y
132,000=10*1.1*y+y=12y ==> y=11,000

Walker,

you walk very quickly !

May I contact you for some talk! hihi
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Re: Population divided into 11 districts [#permalink]  06 Jan 2008, 19:01
jimmyjamesdonkey wrote:
I kinda of understand how you are solving. Can you break it down further in text how you are solving this?

We want the district with the LEAST possible population. The problem also tells us that no district can be 10% greater than the next. So what we do is make 10 districts all the same and 10% greater than the least populated district, which we can represent as X.

10 *1.1X (10 other districts)*(110% of X) ---> 10*1.1X +X=132000 12X=132000 X=11000
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Re: Population divided into 11 districts [#permalink]  06 Jan 2008, 21:23
Expert's post
sondenso wrote:
May I contact you for some talk! hihi

No problem
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Re: Population divided into 11 districts   [#permalink] 06 Jan 2008, 21:23
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