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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das.ashmita
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anuprajan5
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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]
Regards
Anup
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]
Regards
Anup
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Brent@GMATPrepNow
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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
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From 2010 to 2012, the population increases by 1/5 twice.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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