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# PS: voting districts

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Joined: 20 May 2006
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05 Oct 2006, 09:59
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Can somebody explain the math please.

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 i more than 10% greater than the population of any other district. What i 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
Senior Manager
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05 Oct 2006, 11:07
Hey govinam,

The population of one district will be minimum provided the population of all the other 10 districts is same.

i.e if x is the minimum population, then the population of all the other 10 districts must be 110% of x ie 11/10(x).

So x+ 10 (11/10)x = 132000.

hence x= 11000
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05 Oct 2006, 20:02
govinam wrote:
Can somebody explain the math please.

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 i more than 10% greater than the population of any other district. What i 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

another way to do is

the average is 12000 so all the 11 district could have a population of 12000. Now if a district needs to have a population lower than 12000, some other must have a population greater than 12000.

lets take C as the least population. then max population = 10900 + 10% of 10900 = 11990. If this were the case, we cann't have a average population of 12000.

so none of the values lower than this will work.

trying D = 11,000 gives max population 12100 ie above 12000 , so this is possible and the answer !
Re: PS: voting districts   [#permalink] 05 Oct 2006, 20:02
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