Hi All,
In questions that ask for a minimum (or maximum) value of a variable, the typical way to solve it is to maximize (or minimize) the other variable(s) in the prompt.
Here, we're asked for the minimum population for one district, so we have to maximize all of the other districts. Based on the limitations of the question, the maximum value of the other 10 districts would be 12,100, so the minimum value would be 11,000 (Rahul provides an equation that proves it).
GMAT assassins aren't born, they're made,
Rich