Min/Max

[heshamelaziry]

*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 percent 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

Explanation for this is posted in articles. However, I am confused. I can't picture the city with the highest population being 10% more than the city with the lowest population. In reality, is the only why to minimize the population of one city is to have same population in each of the other 10 cities ? Can each city have different population from one another, but remain no more than 10% of the other population ?

I don't know why I can't reply to the article.

[Abdulla]

Hesham,

I think again using the Min/Max tool to solve this problem is the best and fastest way to get the answer.

we've got 11 districts in the city ..
Let's assign x for the first district, so we've got 10 districts left.
The key is ( NO district has greater than 10% of any other district ).
If you thought about it in this way x + x1.1 + (x1.1)1.1....etc then, it's not true because the third district will be greater than the first district.

The question asks for the minimum value.
The maximum we can have is 110% of x = 1.1x ... let's write our equation..

x+ 10(1.1x)= 132,000

12x= 132,000

x= 11,000

I hope this helps !!

[heshamelaziry]

thanks Abdulla. This is what i wanted to verify