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by das.ashmita » Tue Oct 02, 2012 5:41 am
In 2010, City X urban planners expected the city's population to increase by 20% per year over the three years that followed. If that projection were to come true, the population in 2012 would be exactly triple the population in 2009. Which of the following is the approximate percent population increase in City X from 2009 to 2010?

20%
45%
72%
108%
124%

OA D
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by anuprajan5 » Tue Oct 02, 2012 6:19 am
Ashmita,

Solution is

Assume population in 2010 to be x

2010 - x
2011 - 1.2x
2012 - 1.2(1.2x) = 1.44x


2009 population is 1/3 of 2012 population. Therefore 2009 is 0.48x

% change = (2010 - 2009)/2009 = (x-0.48x)/0.48x = 52/48 = [spoiler]108%[/spoiler]

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by Brent@GMATPrepNow » Tue Oct 02, 2012 6:45 am
das.ashmita wrote:In 2010, City X urban planners expected the city's population to increase by 20% per year over the three years that followed. If that projection were to come true, the population in 2012 would be exactly triple the population in 2009. Which of the following is the approximate percent population increase in City X from 2009 to 2010?

20%
45%
72%
108%
124%

OA D

Let the 2010 population be 100
2011 population = 120 (added 20% of 100)
2012 population = 144 (added 20% of 120)

We're told that the 2012 population is 3 times the 2009 population.
If the 2012 population is 144, then the 2009 population is about 50.

Important: I could have been more precise and calculated the 2009 population as 144/3, but I'd rather not work with such a clunky value. Since the answer choices are sufficiently spread apart, I can be somewhat aggressive with my estimation.

So, the 2009 population is about 50, and the 2010 population is 100.
This represents a 100% increase from 2009 to 2010.

When I check the answer choices, I see that only D is close to 100%. So, the correct answer must be D.

Cheers,
Brent

For more information on when to estimate (and other strategies for tackling math questions) we have this free video: https://www.gmatprepnow.com/module/gener ... es?id=1111
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by GMATGuruNY » Tue Oct 02, 2012 9:22 am
das.ashmita wrote:In 2010, City X urban planners expected the city's population to increase by 20% per year over the three years that followed. If that projection were to come true, the population in 2012 would be exactly triple the population in 2009. Which of the following is the approximate percent population increase in City X from 2009 to 2010?

20%
45%
72%
108%
124%

OA D
From 2010 to 2012, the population increases by 1/5 twice.
To make the math easy, let the population in 2010 = 5*5 = 25.

Population in 2011 = 25 + (1/5)25 = 30.
Population in 2012 = 30 + (1/5)30 = 36.
Since the population in 2012 is 3 times the population in 2009, the population in 2009 = (1/3)36 = 12.

Thus, from 2009 to 2010 the population increases from 12 to 25, a bit more than 100%.

The correct answer is D.
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by eski » Tue Oct 02, 2012 3:57 pm
Its very simple , draw a line

48 100 120 144
-----------------------
2009 10 11 12

so 100-48 / 48 % is 108%
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