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A cockroach population doubles every 3 days. In 30 days, by

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CEO
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A cockroach population doubles every 3 days. In 30 days, by [#permalink] New post 02 Jun 2018, 03:39
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Question Stats:

42% (00:18) correct 57% (01:13) wrong based on 7 sessions
A cockroach population doubles every 3 days. In 30 days, by what percent would a cockroach population increase?

(A) 900%
(B) 1,000%
(C) 9,999%
(D) 102,300%
(E) 102,400%
[Reveal] Spoiler: OA

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Re: A cockroach population doubles every 3 days. In 30 days, by [#permalink] New post 10 Jun 2018, 07:04
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sandy wrote:
A cockroach population doubles every 3 days. In 30 days, by what percent would a cockroach population increase?

(A) 900%
(B) 1,000%
(C) 9,999%
(D) 102,300%
(E) 102,400%


Given every 3 days population doubles and this continues for 30 days.

This double increase overall happens for 10 times. (30/3)

Now let's take the initial population is 10.

Now for every 3 days population doubles and total 10 times.

10 - 20 - 40 - 80 - 160 - 320 - 640 - 1280 - 2560 - 5120 - 10240.

Exactly after 10th time i.e. 30 days , population is 10240.

Now take the percentage increase = 10240 - 10 / 10 = 10230 / 10 = 1023 = 102300%.

Option D.
CEO
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Joined: 07 Jun 2014
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Re: A cockroach population doubles every 3 days. In 30 days, by [#permalink] New post 11 Jul 2018, 13:36
Expert's post
Explanation

The percent increase is the difference between the amounts divided by the original, converted to a percent. If the population doubles, mathematically the increase can be written as a
power of 2. In the 30-day interval, if the original population is 1, it will double to 2 after three days —so, 21 represents the population after the first increase, the second increase would then be 22 and so on. Since there are 10 increases, the final population would be 210 or 1,024. Therefore, the difference, 1,024 – 1, is 1,023. Use the percent change formula to calculate percent increase:

Percent Change=(\frac{Difference}{original} \times 100)
Percent Change=(\frac{1023}{1} \times 100)=102300 \%

Note that the new number is 102,400% of the original, but that was not the question asked—the percent increase is 102,300%.
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Re: A cockroach population doubles every 3 days. In 30 days, by   [#permalink] 11 Jul 2018, 13:36
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