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

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Manager
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A certain city with a population of 132000 is to be divided [#permalink]

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29 Sep 2007, 10:55
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A certain city with a population of 132000 is to be divided into 11 voting districts and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum population that the least populated district could have ?

a)10,700
b)10,800
c)10,900
d)11,000
e)11,100
Director
Joined: 03 May 2007
Posts: 886
Schools: University of Chicago, Wharton School
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29 Sep 2007, 11:45
tlntd42 wrote:
A certain city with a population of 132000 is to be divided into 11 voting districts and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum population that the least populated district could have ?

a)10,700
b)10,800
c)10,900
d)11,000
e)11,100

D. 1.1 (10x) + x = 132000
x = 132000/12
x = 11000
Director
Joined: 08 Jun 2007
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29 Sep 2007, 13:14
Fistail wrote:
tlntd42 wrote:
A certain city with a population of 132000 is to be divided into 11 voting districts and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum population that the least populated district could have ?

a)10,700
b)10,800
c)10,900
d)11,000
e)11,100

D. 1.1 (10x) + x = 132000
x = 132000/12
x = 11000

hey can you elaborate this solution.
VP
Joined: 08 Jun 2005
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29 Sep 2007, 13:34
132,000/11 = 12,000

What is the minimum population that the least populated district could have?

since we want the minimum we don't have to use 12,000 we can take for exsample 1,000 people from one district and move them to the other 10 districts (distributed evenly).

D1 = 12,000-1000 = 11,000
D2 = 12,000+(1000/10) = 12,100

D2/D1 = 12,100/11,000 = 121/110 = 110%

no district is to have a population that is more than 10 percent greater than the population of any other district.

true !

Director
Joined: 03 May 2007
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29 Sep 2007, 22:36
ashkrs wrote:
Fistail wrote:
tlntd42 wrote:
A certain city with a population of 132000 is to be divided into 11 voting districts and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum population that the least populated district could have ?

a)10,700
b)10,800
c)10,900
d)11,000
e)11,100

D. 1.1 (10x) + x = 132000
x = 132000/12
x = 11000

hey can you elaborate this solution.

similar work found here: http://www.gmatclub.com/forum/t29885?&h ... t=district
Manager
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04 Oct 2007, 12:07
Does the wording also mean that there is one with LEAST populated district?
So to get to the least others have to be max?
So x = population of the least poulated district then other 10 can ne maxed out at 1.1x

S0 x + 10(1.1 x) = 132000

GMAT makes the wording unneccessary complicated.
Intern
Joined: 03 Oct 2007
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04 Oct 2007, 17:46
D...
Population of the least poulated district is- x
Others are 10% greater than- 1.1x
x + 1.1 (10x) = 132000
x = 132000/12
x = 11000
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