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by gmat740 » Mon Jun 15, 2009 8:26 am
A certain city with 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 population district could have?
A 10700 B 10800 C 10900 D 11000 E 11100


Please provide explanation
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Source: — Data Sufficiency |
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Re: Population

by jakesing » Mon Jun 15, 2009 9:04 am
How's this sound:

The minimum possible population would be if one district "gave up" an equal chunk to each of the others, such that each of the others is exactly 10% bigger than the sacrificial district. If they were all equal, each district would have 12,000 people. In our situation, each of the 10 receiving ones would have 12,000+x people, and the smallest one would have 12,000-10x people. Then you can set up an equation:

12,000+x=110%*(12,000-10x)=1.1(12,000-10x)

x=100

Now to find the value of the smallest one, you swap it back in:

[spoiler]12,000-10(100)=11,000 and the answer is D[/spoiler]
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by nitya34 » Mon Jun 15, 2009 9:27 am
Let the least one is X

When other 10 populations have the greatest value, X will have the
minimum value.

X+10*1.1X=132000
get X :)

Good Q, Thanks for posting

I believe source is GMATPrep?
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