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A certain city with a population of 132000 is to be divided

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A certain city with a population of 132000 is to be divided [#permalink] New post 01 Aug 2006, 10:00
A certain city with a population of 132000 is to be divided into 11 voting districts and no district is to have population that is more than 10% greater thant he population of any other district. what is the minimum possible population that the least populated district could have?

a. 10700
b. 10800
c. 10900
d. 11000
e. 11100
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 [#permalink] New post 01 Aug 2006, 10:03
D

Let x is minimum. To take the worst case one is x and all other 10 are 1.1x.

So x+10(1.1x) = 132000
12x = 132000
x = 11000
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 [#permalink] New post 01 Aug 2006, 12:32
D

Let x is the minimum population for a district. Remaining all 10 districts can have the max population allowed ie 10% greater than x i.e., 11x/10 for each OR 11x total for remaining 10 districts.

But the total of all 11 districts must be 132000

So x+11x=132000
=> 12x=132000
=> x=11000
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Re: Population [#permalink] New post 01 Aug 2006, 13:13
positive_energy wrote:
A certain city with a population of 132000 is to be divided into 11 voting districts and no district is to have population that is more than 10% greater thant he population of any other district. what is the minimum possible population that the least populated district could have?

a. 10700
b. 10800
c. 10900
d. 11000
e. 11100


Tough for me, but D is my choice.

The way to make the 11th district smallest is to put as many people as possible in the others. Let the 11th have a pop. of x. Then all the other 10 can at most be 1.1x

=>x + 10(1.1x) = 132000
x= 11000
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 [#permalink] New post 02 Aug 2006, 02:36
Clear D.

Lets say the district with the least population has x people.
The other ten districts should not be greater than 10%

x + 10(1.1x) = 132000
12x = 132000
x = 11000
  [#permalink] 02 Aug 2006, 02:36
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