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

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A certain city with a population of 132,000 is to be divided [#permalink]  04 May 2006, 21:29
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A certain city with a population of 132,000 is to be divided into 11 voting disticts, and no district is to have a population that is more than 10% greater than the population of any other disticts. What is the minimum possible population that the least populated district could have?
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Re: GMAT Prep PS [#permalink]  04 May 2006, 22:48
foolbox wrote:
A certain city with a population of 132,000 is to be divided into 11 voting disticts, and no district is to have a population that is more than 10% greater than the population of any other disticts. What is the minimum possible population that the least populated district could have?

11,000?

To make one of the city x minimum, we should consider max population for 10 other cities

x+10*1.1x=13,200

x= 11,000
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Let max population = x
Min population = y
Let 10 cities have maximum population. 1 city has min population.

ie 10x + y = 132000 ----------------------- 1)

Max population = 10% greater than min population

ie. x = 1.1y ----------------------------- 2)

Solving these two equations, we get y = 11000

Minimum population = 11000
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