I have posted the following question three times already, but I have not understand any of the explanations that have been provided. Thus, if you know how to solve the following problem and you know how to explain it in a simple way, please let me know. Thanks!



A certain city with 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 percent 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

The correct answer should be 11,000 which is D.

NOTE: my explanation may make the question appear too complex; well it's not. THat's just because I'm trying to provide a thorough and detailed explanation.


My Approach:
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First, I would divide 132,000 by 11 = 12,000 (the average)

Now you have a list of 11 distrcits of equal population. Time to use logic and minor changes to this list to get to the minimum possible population of one of these districts. We can take a specific amount of people of the target district and spread that equally over all other districts. We can keep doing that untill we reach one district with minimum population and 10 equal districts, all of which's population are each 110% times the minimum district's population.


Method 1: Reasoning
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Let's assume that we have one district with unkown population, the minimized one, and 10 other districts all with 12,000 people.
12,000 is 110% of what number ? 12,000 /1.1 = 10,909

Well, then the minimized population should be at least 10,909. However, since in this case the other districts will have populations larger than 12,000, this minimized population will be slightly larger than 10,909.

It's either D or E. D is smaller so D is the minimum


Method 2: Back solving
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Start with B and D
using B, 10,800

the difference now is 1,200 --> about 120 per district.
is 11,420=< 1.1 x 10,800?
NO

Try D, 11,000
the difference now is 1,000, or 100 per district
is 11,300=< 1.1x 11,000 ?
YES