Here is the long explanation for this answer I posted in an earlier thread:
The correct answer is D. I used picking numbers.
Before starting, realize that aside from the lowest populated district, the other 10 disctricts will all have the same size. This will maximize the difference between the least and 2nd least populated districts.
Starting with C:
-If you choose 10,900 as the lowest possible population, then the remaining ten districts will have an average population of 12,100 [(132,000-10,900)/10].
-12,100 is more than 10% higher than 10,900
Be careful on this option. 10,900 is 10% less than 12,100. However, the question says that "no district is to have a population that is more than 10% greater than the population of any other district."
So... looking at answer D:
-If the lowest district has 11,000 people, then the average of the remaining 10 districts is 12,100 [(132,000-11,000)/10]
-12,100 is 10% greater than 11,000.
Better yet, here is the short, algebraic solution:
1.1x = (132,000-x)/10
11x = 132,000-x
12x = 132,000
x = 11,000