This is from MGMAT CAT 5

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%

I understand their explanation except for one thing. If you choose a smart number of 100 as the original population, and then it's 110 in the 2nd year, and 121 in the third year, how can it then be that the population in the 3rd year is double the 2nd year? Can't we see from our smart numbers that the population in the 2nd and 3rd years is 110 and 121 respectively?

Thanks!

You are slightly mis-reading the question.

Lets assign years.
Questions says that in 2009 the projection is for next 2 years population will increase @ 10% per year. So lets assume its x today.

2009 = x
2010 = 1.1x
2011 = 1.21x

so far so good, thats what you have done as well, only your x=100.

Now the question is saying that that 2011 population will be twice of 2008 (population one year ago with reference to today i.e 2009).

so lets say 2008 = y

so 1.21 x = 2y
y = 0.605 x

you need to calcuate how much should 0.605x must increase to get to x
1/0.605 = ~65%.

Thanks a lot - that really helps! I totally didn't get that.

we like when posters help each other out.

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I have a problem understanding the below statement,

Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years.

I interpret the statement as

Today - 100

Two years from now 10% increase so 110

it could be 102 in the 1st year and and reach to 110 the 2nd year so there is a total 10 % increase for the two yrs.

So one year ago population say y therefore

110 = 2y
y = 55

Since the question say approximate growth so 55 ¬ 50 % increase.

I took the question to say 10 % increase for next 2 year and and the official answer here suggests that I have to take it as - 10% increase for each of the next 2 yrs ?

Could you please help.

10% PER YEAR. I hope the phrase PER YEAR is sufficient to convey what the intent of the question is. Please let me know if you have any further questions..

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Tim Sanders
Manhattan GMAT Instructor