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

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Senior Manager
Joined: 05 Aug 2005
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A certain city with population of 132,000 is to be divided [#permalink]

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04 Nov 2005, 13:35
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58% (01:33) correct 42% (02:07) wrong based on 85 sessions

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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

Last edited by Bunuel on 13 Apr 2014, 06:22, edited 1 time in total.
Renamed the topic, edited the question and the OA.

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04 Nov 2005, 13:44
gmacvik wrote:
A certain city with a population of 132,000 is to be divided into 11 voting districts is to have
a populationn that is more than 10% greater than the population of any other district. What is
the minimum possible population that the least populated district could have?

10,700
10,800
10,900
11,000
12,000

population that is 10% greater than the population of any other district..

11000.. 10% of 11000 = 1100.. so the next population will be 12100..
10*12,100 + 11000 = 132000.
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Manager
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04 Nov 2005, 13:45

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Director
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04 Nov 2005, 18:58
bewakoof,

how any why you assumed that the population of the reaming 10 districts will be same ..... Pls explain ....i am kina lost

bewakoof wrote:
gmacvik wrote:
A certain city with a population of 132,000 is to be divided into 11 voting districts is to have
a populationn that is more than 10% greater than the population of any other district. What is
the minimum possible population that the least populated district could have?

10,700
10,800
10,900
11,000
12,000

population that is 10% greater than the population of any other district..

11000.. 10% of 11000 = 1100.. so the next population will be 12100..
10*12,100 + 11000 = 132000.

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Senior Manager
Joined: 29 Aug 2005
Posts: 498

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04 Nov 2005, 21:15
There is not mention that population would be different. This is PS and not CR where the number can be from 1 to 12100. When the division is stated and unless a exception is mentioned it is considered an equal distribution/division.

cool_jonny009 wrote:
bewakoof,

how any why you assumed that the population of the reaming 10 districts will be same ..... Pls explain ....i am kina lost

bewakoof wrote:
gmacvik wrote:
A certain city with a population of 132,000 is to be divided into 11 voting districts is to have
a populationn that is more than 10% greater than the population of any other district. What is
the minimum possible population that the least populated district could have?

10,700
10,800
10,900
11,000
12,000

population that is 10% greater than the population of any other district..

11000.. 10% of 11000 = 1100.. so the next population will be 12100..
10*12,100 + 11000 = 132000.

Kudos [?]: 14 [0], given: 0

Intern
Joined: 10 Apr 2014
Posts: 33

Kudos [?]: 22 [0], given: 3

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

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12 Apr 2014, 06:32
gmacvik wrote:
A certain city with a population of 132,000 is to be divided into 11 voting districts is to have
a populationn that is more than 10% greater than the population of any other district. What is
the minimum possible population that the least populated district could have?

10,700
10,800
10,900
11,000
12,000

The question doesn't seem to complete/correct...
guess it is 11 voting districts is to have
a population that is not more than 10% greater than the population of any other district.

Kudos [?]: 22 [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128562 [0], given: 12180

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

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13 Apr 2014, 06:23
Expert's post
1
This post was
BOOKMARKED
ind23 wrote:
gmacvik wrote:
A certain city with a population of 132,000 is to be divided into 11 voting districts is to have
a populationn that is more than 10% greater than the population of any other district. What is
the minimum possible population that the least populated district could have?

10,700
10,800
10,900
11,000
12,000

The question doesn't seem to complete/correct...
guess it is 11 voting districts is to have
a population that is not more than 10% greater than the population of any other district.

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).

$$x+10*1.1x=132$$ --> $$12x=132$$ --> $$x=11$$.

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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Kudos [?]: 128562 [0], given: 12180

Re: A certain city with a population of 132,000 is to be divided   [#permalink] 13 Apr 2014, 06:23
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