tito1545 wrote: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% grater 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
ANS D
Solution:
Let the 11 voting districts have populations d1, d2, d3, d4,....d11 respectively.
Let d1 be the least population.
So, d1+d2+d3+...+d11 = 132,000.
Now, according to question d2 <= 1.1*d1, d3 <= 1.1*d1,....d11<=1.1*d1.
Adding all inequality, we get that (d2+d3+d4...d11) <= 10*1.1*d1.
Or (d2+d3+d4...d11) <= 11d1.
Or (d1+d2+...+d11) <= 12d1.
Or 132,000 <= 12d1.
Or d1 => 11,000.
So, the minimum possible population of least populated district is 11,000.
) 12x=132,000, approximately 10,900 answer D (11,000)
