Problem Solving

Interesting question. OA after a few reply. 10 points to the person who
arrives at final value in the least number of steps

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have 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

I will vote for the process of elimination

Choice B - wrong - 132000-10800 = 121200. Thus average of other 10 districts would be 12,120 which is more than 10% of 10800
Choice A - wrong (it's lesser than choice B)
Choice C - wrong - 132000-10900 = 121100. Thus average of other districts would be 12110 which is more than 10% of 10900
Choice D - Right - 132000-11000 = 121000. Thus average of other districts is 12100 which is exactly 110% of 11,000. Hence correct

Let the population of the district with the least population be "x"

x + (110/110)x * 10 = 132000

Solving for x, x = 11000

Yup, OA is D