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

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Director
Joined: 24 Oct 2016
Posts: 535
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
A certain state with a population of 130,000 is to be divided into 11  [#permalink]

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30 Mar 2019, 13:12
4
00:00

Difficulty:

65% (hard)

Question Stats:

43% (01:43) correct 57% (02:50) wrong based on 30 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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Intern
Joined: 12 Jul 2016
Posts: 16
Location: India
GMAT 1: 690 Q50 V32
GPA: 3.74
Re: A certain state with a population of 130,000 is to be divided into 11  [#permalink]

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30 Mar 2019, 13:31
6
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

Posted from my mobile device
##### General Discussion
Director
Joined: 24 Oct 2016
Posts: 535
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
A certain state with a population of 130,000 is to be divided into 11  [#permalink]

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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

Similar Q to practice: https://gmatclub.com/forum/a-certain-ci ... 76217.html
_________________

If you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.
Intern
Joined: 12 Jul 2016
Posts: 16
Location: India
GMAT 1: 690 Q50 V32
GPA: 3.74
Re: A certain state with a population of 130,000 is to be divided into 11  [#permalink]

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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

Posted from my mobile device
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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