Word Problem on Percents - source: GmatPrep

[mathew.tony]

Q: 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 poulated district could have?

A: 10,700
B: 10,800
C: 10,900
D: 11,000
E: 11,100



Could someone explain if there is an easy method to solve this? I tried the tedious plug in method to arrive at the answer.

The answer is D.

[neerajbansal]

This is how I go about problems which have maxima and minima questions.

Its asking for minimum, so maximise all of the other.

Lets say the town A with minimum possible population is ---> x

So

x + ( maximize all the other 10 districts ) = 132000

The max the each of the 10 districts can have are 1.1x (more than 10 percent greater)

so

x + 1.1(10) = 132000

12x= 132000

x= 11000


Please share if there is any other way to solve this faster.

[mathew.tony]

hey neeraj,

Just wanted to be sure. If this question asked " What is the maximum possible population that the most poulated district could have?" how would your approach be?

Thanks

[neerajbansal]

Q: 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 maximum [/b]possible population that the populated district could have?



i guess the answer would be then
1.1*x

11000 * 1.1 =

12100