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Two months from now, the population of a colony of insects i

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Two months from now, the population of a colony of insects i

by alanforde800Maximus » Wed Oct 19, 2016 6:36 am
Two months from now, the population of a colony of insects in a remote area will reach 3.2 * 10^4. If the population of the colony doubles every two months, what was the population eight months ago?

a) 3.6 * 10^2
b) 1.0 * 10^3
c) 2.0 * 10^3
d) 1.6 * 10^4
e) 2.6 * 10^4


Please assist with above problem.
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by Brent@GMATPrepNow » Wed Oct 19, 2016 7:13 am
alanforde800Maximus wrote:Two months from now, the population of a colony of insects in a remote area will reach 3.2 * 10^4. If the population of the colony doubles every two months, what was the population eight months ago?

a) 3.6 * 10^2
b) 1.0 * 10^3
c) 2.0 * 10^3
d) 1.6 * 10^4
e) 2.6 * 10^4
Let's use a growth table to work backwards

If the population DOUBLES every 2 months we travel into the future, we can also say that the population is HALVED every 2 months we travel into the past

2 months from now: population = (3.2)(10^4)
Now: population = (1/2)(3.2)(10^4) = (1.6)(10^4)
2 months ago: population = (1/2)(1.6)(10^4) = (0.8)(10^4)
4 months ago: population = (1/2)(0.8)(10^4) = (0.4)(10^4)
6 months ago: population = (1/2)(0.4)(10^4) = (0.2)(10^4)
8 months ago: population = (1/2)(0.2)(10^4) = (0.1)(10^4)

(0.1)(10^4) isn't among the answer choices, so let's REWRITE it.

(0.1)(10^4) = (1)(10^-1)(10^4)
= (1)(10^3)

Answer: B

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- Growth tables: https://www.gmatprepnow.com/module/gmat ... /video/929
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by [email protected] » Wed Oct 19, 2016 10:03 am
Hi alanforde800Maximus,

Since the prompt involves Scientific Notation, you can either adjust each individual calculation (in terms of the Scientific Notation that would result) OR you could think in terms of what all of those 'doubles' would do to the total and do one adjustment right at the end:

We're told that a population doubles EVERY 2 MONTHS. If we go from 8 months ago to 2 months in the future, we would have:

8 months ago: X insects
6 months ago: 2X insects
4 months ago: 4X insects
2 months ago: 8X insects
Now: X insects: 16X
2 months in the future: 32X insects

So, in that time frame, the number of insects becomes 32 times what it started at. We can now divide (3.2 x 10^4) by 32 to figure out what the population was 8 months ago...

(3.2)(10^4)/(32) =
(.1)(10^4) =
(1)(10^3)

Final Answer: B

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