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A certain state with a population of 130,000 is to be divided into 11

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A certain state with a population of 130,000 is to be divided into 11  [#permalink]

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New post 30 Mar 2019, 13:12
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Question Stats:

29% (01:29) correct 71% (03:01) wrong based on 17 sessions

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A certain state with a population of 130,000 is to be divided into 11 new districts, and no district has a population that is more than 20 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

A. 9,900
B. 10,000
C. 10,200
D. 10,400
E. 10,600

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Re: A certain state with a population of 130,000 is to be divided into 11  [#permalink]

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New post 30 Mar 2019, 13:31
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As per the question, since "no district has a population that is more than 20 percent greater than the population of any other district", then the populations of 11 districts should be in the range of x and 1.2x

To minimize the value of x, we should make only one district to have the minimum number of population and the rest 10 districts to have 1.2x of population.

x + (10 ∗ 1.2x) = 130,000
13x = 130,000
x = 10,000

Answer is B.

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Senior Manager
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Joined: 24 Oct 2016
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A certain state with a population of 130,000 is to be divided into 11  [#permalink]

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New post 30 Mar 2019, 13:15
dabaobao wrote:
A certain state with a population of 130,000 is to be divided into 11 new districts, and no district has a population that is more than 20 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

A. 9,900
B. 10,000
C. 10,200
D. 10,400
E. 10,600


Solution



As "no district has a population that is more than 20 percent greater than the population of any other district", then the populations of 11 districts should be in the range: x and 1.2x.

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 1.2x # of population (maximum possible).

x+10∗1.2x = 130,000
13x = 130,000
x = 10,000

Answer: B.

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Premium Member
Re: A certain state with a population of 130,000 is to be divided into 11  [#permalink]

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New post 30 Mar 2019, 13:32
2
As per the question, since "no district has a population that is more than 20 percent greater than the population of any other district", then the populations of 11 districts should be in the range of x and 1.2x

To minimize the value of x, we should make only one district to have the minimum number of population and the rest 10 districts to have 1.2x of population.

x + (10 ∗ 1.2x) = 130,000
13x = 130,000
x = 10,000

Answer is B.

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GMAT Club Bot
Re: A certain state with a population of 130,000 is to be divided into 11   [#permalink] 30 Mar 2019, 13:32
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A certain state with a population of 130,000 is to be divided into 11

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