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by fangtray » Wed Apr 04, 2012 6:03 am
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 is more than 10% greater than the population of any other district. What is 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
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by GMATGuruNY » Wed Apr 04, 2012 6:14 am
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by Pharo » Wed Apr 04, 2012 6:36 am
let the smallest district have 100x votes. That means 10 other districts will have 110x votes.

Total votes = 132000 = 100x + 10 * 110x --> x = 110 --> smallest district = 100x = 11000 :)

D is the answer :)
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by Anurag@Gurome » Wed Apr 04, 2012 6:59 pm
fangtray wrote: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 is more than 10% greater than the population of any other district. What is 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
Let us assume that the minimum possible population of the least populated district be P.

It is given that "no district is to have a population that is more than 10% greater than the population of any other district."

Then the population of 11 districts should be between P and (P + 10% of P) = 1.1P
Now we have minimize P. For this we should make only one district to have minimum possible population and the remaining 10 districts should have maximum possible population.
So, P + (10 * 1.1P) = 132,000
12P = 132,000
P = 11,000

The correct answer is D.
Last edited by Anurag@Gurome on Fri Apr 13, 2012 5:24 pm, edited 1 time in total.
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by amit28it » Wed Apr 04, 2012 9:10 pm
I have just solve your question and the answer given by Anurag@Gurome and Pharo is absolutely correct and the explanation given by Anurag@Gurome is more simple to understand.
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