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A certain city with population of 132,000 is to be divided i [#permalink]
10 Oct 2008, 08:17

2

This post was BOOKMARKED

00:00

A

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D

E

Difficulty:

65% (hard)

Question Stats:

45% (02:17) correct
55% (01:34) wrong based on 57 sessions

A certain city with 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?

Re: A certain city with population of 132,000 is to be divided i [#permalink]
10 Oct 2008, 08:52

amitdgr wrote:

Source : GMATPrep

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

I got stumped by the wording.

the answer is D

dividing 132000 by 11=12,000 I am picking answer choices to solve suppose we take answer choice D. assuming 10 districts have equal population of 12,000 each and the 11th district has population of 11,000 then the remaining 1,000 can be equally divided amongst all the 10 districts. now each of the 10 districts will have a population of 12,100. this population is exactly 10% of 11,000. if the population of the 11th district goes below 11,000 then the population of other districts will be more than 10% of 11th district.

therefor the minimum possible population that the least populated district can have is 11,000.

Re: A certain city with population of 132,000 is to be divided i [#permalink]
10 Oct 2008, 10:17

[quote="amitdgr"]Source : GMATPrep

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

minimum possible for the least is when it is max for all others AND ALL OTHERS ARE EQUALL( ie ; 10% bigger)

132,000/11 =12,000

12,000

THE ANSWER IS A BIT LESS THAN 12,000

USE ANSWER CHOICES 11,000 *1.1 = 12,100 ,

Last edited by yezz on 10 Oct 2008, 10:30, edited 2 times in total.

Re: A certain city with population of 132,000 is to be divided i [#permalink]
29 Jun 2014, 20:56

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Re: A certain city with population of 132,000 is to be divided i [#permalink]
30 Jun 2014, 01:21

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Expert's post

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amitdgr wrote:

A certain city with 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

As "no district is to have a population that is more than 10 percent greater than the population of any other district", then the populations of 11 districts should be in the range: \(x\) and \(1.1x\).

So we want to minimize \(x\). To minimize \(x\) we should make only one district to have that # of population (minimum possible) and the rest 10 districts to have \(1.1x\) # of population (maximum possible).

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