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

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Manager
Joined: 28 Aug 2004
Posts: 205
A certain city with a population of 132,000 is to be divided [#permalink]

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13 Aug 2005, 06:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Manager
Joined: 14 Jul 2005
Posts: 104
Location: Sofia, Bulgaria

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13 Aug 2005, 07:10
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

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...
Manager
Joined: 28 Jun 2005
Posts: 214

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13 Aug 2005, 07:25
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
Senior Manager
Joined: 04 May 2005
Posts: 279
Location: CA, USA

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13 Aug 2005, 16:41
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
SVP
Joined: 05 Apr 2005
Posts: 1710

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14 Aug 2005, 20:38
minimum = x
maximum = 1.1x

total = x+10(1.1x)=132000
so x = 11,000
Director
Joined: 13 Nov 2003
Posts: 789
Location: BULGARIA

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15 Aug 2005, 05:18
i will vote for 10 800 which is 10% less than the average-12000
15 Aug 2005, 05:18
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