## Problem solving

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### Problem solving

by sakshis » Sun Sep 23, 2012 11:47 pm
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

[spoiler]OA: d[/spoiler]

What is the best approach to solve this question?
I tried to pick an option such as 11,000 and then divide the remaining population by 10(considering the population of rest of the districts equal)

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by vk_vinayak » Mon Sep 24, 2012 12:53 am
sakshis 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 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

[spoiler]OA: d[/spoiler]

What is the best approach to solve this question?
I tried to pick an option such as 11,000 and then divide the remaining population by 10(considering the population of rest of the districts equal)
Let s be the smallest population of any district. Then the maximum population other districts could have is 10% more than s ie 1.1s. And there are 10 other such districts

s + 1.1s * (10) = 132,000
12s = 132,000
s = 11,000
- VK

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by GMATGuruNY » Mon Sep 24, 2012 3:12 am
sakshis 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 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

[spoiler]OA: d[/spoiler]

What is the best approach to solve this question?
I tried to pick an option such as 11,000 and then divide the remaining population by 10(considering the population of rest of the districts equal)

To MINIMIZE the smallest population, we need to MAXIMIZE the other 10 populations.
Thus, each of the other 10 districts must have the maximum allowed population: 10% greater than the smallest population.
Since the total population of the city is 132,000 -- a multiple of 1,000 -- the correct answer choice is almost certainly a multiple of 1,000.

Each of the other 10 districts = (132,000 - 11,000)/10 = 12,100.
Difference between the populations = 12,100 - 11,000 = 1100, which is 10% of the smallest population.
Success!