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Boomtown

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by j_shreyans » Sun Oct 12, 2014 9:22 am
Boomtown urban planners expect the city's population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year?

A)20%
B)40%
C)50%
D)65%
E)75%

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by [email protected] » Sun Oct 12, 2014 11:06 am
Hi j_shreyans,

This question can be solved with algebra or by TESTing THE ANSWERS. Here's how you can use the answers to your advantage:

We're essentially asked to keep track of 4 years of data:

Last year
This year
Next year
2 yrs from now

We're told about the percentage increases in population over the last two years (10% each), but we're asked for the percentage increase from last year to this year (with the goal that the population has to DOUBLE over the course of all of these years).

Let's make last year's population = X

Now, let's TEST Answer B....40%

Last year = X
This year = 1.4X
Next year = 1.54X
2 years = 1.694X
This is an increase of 69.4%, which is TOO SMALL. We need a bigger percentage increase...


Let's TEST Answer D...65%

Last year = X
This year = 1.65X
Next year = 1.815X
2 years = 1.9965X
This is an increase of 99.65%, which is just about DOUBLE. This is a MATCH for what we're looking for.

Final Answer: D

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by GMATGuruNY » Sun Oct 12, 2014 5:33 pm
j_shreyans wrote:Boomtown urban planners expect the city's population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year?

A)20%
B)40%
C)50%
D)65%
E)75%

OAD
Let the population today = 100.

Since the population increases by 10% each year, we get:
Population after 1 year = 100 + 10% of 100 = 100 + 10 = 110.
Population after 2 years = 110 + 10% of 110 = 110 + 11 = 121.

Since the population after 2 years is equal to twice the population 1 year ago, the population 1 year ago = 121/2 = 60.5 ≈ 60.
Percent increase from 1 year ago to today = Difference/Original * 100 = (100-60)/60 * 100 = 200/3 ≈ 66%.

The correct answer is D.
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by Matt@VeritasPrep » Sun Oct 12, 2014 8:09 pm
Let's say that

This year = x
Next year = 1.1x
Two years = 1.21x

Since 1.21x is DOUBLE last year's population, last year's population = .605x.

Since we've gone from .605x (last year) to x (this year), our percent increase is

(x - .605x)
---------- * 100
.605x

or

.395x
------ * 100
.605x

.395/.605 is close to 4/6, or 2/3, which is ≈ 66%, making D the best answer.
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by pooja181 » Sun Oct 12, 2014 8:18 pm
Let's make last year's population = X

Now, let's TEST Answer B....40%

Last year = X
This year = 1.4X
Next year = 1.54X
2 years = 1.694X
This is an increase of 69.4%, which is TOO SMALL. We need a bigger percentage increase...


Let's TEST Answer D...65%

Last year = X
This year = 1.65X
Next year = 1.815X
2 years = 1.9965X
This is an increase of 99.65%, which is just about DOUBLE. This is a MATCH for what we're looking for.

Final Answer: D
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by gmatdriller » Fri Jan 09, 2015 8:48 am
The question did not indicate the percentage increase between last year
and any specific year.

Did we just assume last year and this year?

Pls assist to clarify.
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by GMATGuruNY » Fri Jan 09, 2015 9:03 am
gmatdriller wrote:The question did not indicate the percentage increase between last year
and any specific year.

Did we just assume last year and this year?

Pls assist to clarify.
From the prompt:
The population two years from now would be exactly double the population of one year ago.
To DOUBLE a value is to increase it by 100%.
Since the population two years from now must be double the population of one year ago, the percentage increase from last year to two years from now = 100%.
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by gmatdriller » Sun Jan 11, 2015 7:22 am
I understand, but my question is:

Granted that Last year = say Y(60.5)
This year = 100
Next year = 110
Next 2 years = 121

So, the question is asking for Percent increase btw Last year AND
which particular year?
This Yr(100); Next Yr(110); or Next 2Yrs(121)?
Last edited by gmatdriller on Sun Jan 11, 2015 7:38 am, edited 1 time in total.
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by GMATGuruNY » Sun Jan 11, 2015 7:26 am
gmatdriller wrote:I understand, but my question is:

Granted that Last year = say Y(60.5)
This year = 100
Next year = 110
Next 2 years = 121

So, the question is asking for Percent increase btw Last year AND
which particular question? This Yr(100), Next Yr(110), or Next 2Yrs(121)?
Question stem:
Which of the following is closest to the percent population increase in Boomtown OVER THE LAST YEAR?
OVER THE LAST YEAR means from LAST YEAR TO THIS YEAR.
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