GMAT Prep 1 - Arithmetic

[ruthm_24]

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 per cent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

Answer is 11,000.

[Rahul@gurome]

We need to find the minimum possible population that any district can have.
Let the districts be given by d1, d2,......d11.
Let d1 have the minimum population. So districts d2, d3,....d11 should have maximum population.
But no district is to have a population that is more than 10 per cent greater than the population of any other district.
So if population of d1 is n, population of d2, d3,...d11 <= 1.1n each.
Or the maximum possible population of d2, d3,....d11 is 1.1n each.
Or n + 1.1n +1.1n......(10 times) = n + 10*(1.1n) = n + 11n = 12n = 132,000.
Or n is 11, 000.
So the minimum possible population that the least populated district can have is 11,000.