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A certain city with population of 132,000 is to be divided i

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A certain city with population of 132,000 is to be divided i [#permalink]

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New post 10 Oct 2008, 09:17
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-city-with-population-of-132-000-is-to-be-divided-76217.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 30 Jun 2014, 02:19, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: A certain city with population of 132,000 is to be divided i [#permalink]

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New post 10 Oct 2008, 09:52
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.

what is the OA
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Re: A certain city with population of 132,000 is to be divided i [#permalink]

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New post 10 Oct 2008, 10:31
EDIT : The correct OA is D
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Last edited by amitdgr on 10 Oct 2008, 11:24, edited 1 time in total.
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Re: A certain city with population of 132,000 is to be divided i [#permalink]

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New post 10 Oct 2008, 11:17
[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, 11:30, edited 2 times in total.
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Re: A certain city with population of 132,000 is to be divided i [#permalink]

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New post 10 Oct 2008, 11:17
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NO sir, Correct Answer is D :twisted:

(COME ON GUYS! Please be careful Official Answer. Incorrect OA can lead us to confusion and worst of all, waste our valuable time! )

After 30 min wasting my time trying to figure out why E is correct, I finally give up and look for other source. OA is in fact D.
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Re: A certain city with population of 132,000 is to be divided i [#permalink]

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New post 10 Oct 2008, 11:22
good thing about math is OA are not debatable..you can check the math :)

lets see..

in order to have a minimum population in one district than all the rest have to 1.1times biggers..

x+10(1.1x)=132K

12x=132K, x=11K...
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Re: A certain city with population of 132,000 is to be divided i [#permalink]

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New post 10 Oct 2008, 11:23
cityjoy92 wrote:
NO sir, Correct Answer is D :twisted:

(COME ON GUYS! Please be careful Official Answer. Incorrect OA can lead us to confusion and worst of all, waste our valuable time! )

After 30 min wasting my time trying to figure out why E is correct, I finally give up and look for other source. OA is in fact D.


Oops :) I have been posting too many questions lately. Got the OAs mixed up. Sorry for that. Will be more careful next time :)
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Re: A certain city with population of 132,000 is to be divided i [#permalink]

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New post 10 Oct 2008, 15:42
D - 11000

x+10(1.1x) = 132000
12x = 132000
x = 11000
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Re: A certain city with population of 132,000 is to be divided i [#permalink]

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

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New post 30 Jun 2014, 02:21
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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).

\(x+10*1.1x=132\) --> \(12x=132\) --> \(x=11\).

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-city-with-population-of-132-000-is-to-be-divided-76217.html
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Re: A certain city with population of 132,000 is to be divided i   [#permalink] 30 Jun 2014, 02:21
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