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the population of Colorado was approximately half

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the population of Colorado was approximately half [#permalink] New post 20 Jan 2016, 18:44
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Question Stats:

72% (01:03) correct 27% (01:25) wrong based on 33 sessions
In year Y, the population of Colorado was approximately half that of New Jersey, and the land area of Colorado was approximately 14 times that of New Jersey. The population density (number of persons per unit of land area) of Colorado in year Y was approximately how many times the population density of New Jersey?

A 1/28
B 1/14
C 1/7
D 1/4
E 1/2

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Question: 10
Page: 459
Difficulty: medium
[Reveal] Spoiler: OA

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Re: the population of Colorado was approximately half [#permalink] New post 23 Jan 2016, 01:46
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Solution

The information given in the question can be rewritten algebraically as follows.

population of Colorado = \(\frac{1}{2}* population of New Jersey\)

land area of Colorado = \(14 * land area of New Jersey\)

Using the information given and the fact that population density is the number of persons per unit of land area, you can express the population density of Colorado in terms of the population density of New Jersey as follows.


population density of Colorado = \(\frac{population of Colorado}{land area of Colorado}\)


= \(\frac{1}{2}* (population of New Jersey))/ 14 * (land area of New Jersey)\)

= \(\frac{1}{2}*\frac{1}{14}*\frac{population of New Jersey}{land area of New Jersey}\)

= \(\frac{1}{28}* population density of New Jersey\)

Thus, the population density of Colorado was approximately \(\frac{1}{28}\) times the population density of New Jersey. The correct answer is Option A.
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Re: the population of Colorado was approximately half [#permalink] New post 14 Jul 2016, 14:36
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sandy wrote:
In year Y, the population of Colorado was approximately half that of New Jersey, and the land area of Colorado was approximately 14 times that of New Jersey. The population density (number of persons per unit of land area) of Colorado in year Y was approximately how many times the population density of New Jersey?

A 1/28
B 1/14
C 1/7
D 1/4
E 1/2



Another approach is to plug in some NICE VALUES that meet the given condition.

the population of Colorado was approximately half that of New Jersey
Say Colorado's population = 14 and New Jersey's population is 28

the land area of Colorado was approximately 14 times that of New Jersey
Say Colorado's area = 14 and New Jersey's area = 1

Colorado density = 14/14 = 1
New Jersey density = 28/1 = 28

Colorado's density is 1/28 that of New Jersey's density

Answer:
[Reveal] Spoiler:
A

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Re: the population of Colorado was approximately half [#permalink] New post 18 May 2018, 10:04
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sandy wrote:
In year Y, the population of Colorado was approximately half that of New Jersey, and the land area of Colorado was approximately 14 times that of New Jersey. The population density (number of persons per unit of land area) of Colorado in year Y was approximately how many times the population density of New Jersey?

A 1/28
B 1/14
C 1/7
D 1/4
E 1/2


We can let the population of Colorado = c and that of New Jersey = 2c.

We can let the land area of New Jersey = a and that of Colorado = 14a

Thus, the population density (number of persons per unit of land area) of Colorado in year Y is (c/(14a))/(2c/a) = ca/(28ac) = 1/28 times that of New Jersey.

Answer: A
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Re: the population of Colorado was approximately half [#permalink] New post 13 Aug 2018, 22:10
1/28
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Re: the population of Colorado was approximately half [#permalink] New post 14 Aug 2018, 02:53
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obinnauzo wrote:
1/28

Care to share your method?
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Re: the population of Colorado was approximately half   [#permalink] 14 Aug 2018, 02:53
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