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# Population increase

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Population increase [#permalink]  20 Sep 2010, 09:10
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Question Stats:

56% (02:26) correct 44% (00:49) wrong based on 11 sessions
The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?

A. 1650
B. 1700
C. 1750
D. 1800
E. 1850
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Re: Population increase [#permalink]  20 Sep 2010, 09:20
Expert's post
cano wrote:
The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?

A. 1650
B. 1700
C. 1750
D. 1800
E. 1850

Increase by 50% = times 1.5, so if the population at a certain year were 10 then in 50 years it would be 10*1.5 and in 50*2=100 years it would be 10*1.5*1.5=10*1.5^2 --> $$160*1.5^n=810$$, where $$n$$ is the # of 50-year periods --> $$(\frac{3}{2})^n=\frac{81}{16}=(\frac{3}{2})^4$$ --> $$n=4$$, so there were 4 50-year periods --> 1950-4*50=1750.

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Re: Population increase [#permalink]  20 Sep 2010, 11:43
4 50 yrs to reach 810
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Re: Population increase [#permalink]  20 Sep 2010, 12:42
I just worked this one backwards until I reached 160. If the population increases by 50% then you're multiplying the previous number by 3/2. So to work backwards, divide by 3/2 (which is the same as multiplying by 2/3).

So we have:

1950: 810
1900: 810*(2/3) = 540
1850: 540*(2/3) = 360
1800: 360*(2/3) = 240
1750: 240*(2/3) = 160

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Re: Population increase [#permalink]  20 Sep 2010, 16:50
redjam wrote:
I just worked this one backwards until I reached 160. If the population increases by 50% then you're multiplying the previous number by 3/2. So to work backwards, divide by 3/2 (which is the same as multiplying by 2/3).

So we have:

1950: 810
1900: 810*(2/3) = 540
1850: 540*(2/3) = 360
1800: 360*(2/3) = 240
1750: 240*(2/3) = 160

How long did it take you to work it like that?
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Re: Population increase [#permalink]  20 Sep 2010, 17:41
55 sec to work forward for C

160 -> 240 -> 360 -> 540 -> 810
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Re: Population increase [#permalink]  21 Sep 2010, 05:35
cano wrote:
How long did it take you to work it like that?

Didn't specifically time myself but it wasn't longer than 2 mins. I would say around 1.5 mins. They are all numbers easily divisible by 3.
Re: Population increase   [#permalink] 21 Sep 2010, 05:35
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# Population increase

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