A certain city with a population of 132000, is divided into 11 voting districts, and no district is to have a 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) 10700
B) 10800
C) 10900
D) 11000
E) 11100

Total population = 132000 & no. of districts = 11.

If divided equally, the population of each district = 132000/11 = 12000

The condition to satisfy = no district can have the population > 10% of any other district.

For ex - assume district (A) has the least population, now the only way to get the min. population of (A) so that no other district can have population > 10% of (A) is to reduce the population of (A) to minimum and add the reduced amount equally into the rest 10 districts.

If you look at the answer choices the least possible population of (A) when no other district will have pop > 10% of A would be (11000)

If A = 11000 the reduced pop = 1000. so 1000 can be increased in rest of 10 districts, so the population of rest of the 10 district= 12100

10 % of (A's population) = 10% of 11000 = 1100. So rest of the districts have exactly 10% more population than (A)

Hence the answer is (D)

Hope it helps.

GMAT 2007

Great explanation.

Question for MGMAT - What would be the difficulty level of questions like this? I guess this is a 700+ level question.