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

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Joined: 07 Jun 2014
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A cockroach population doubles every 3 days. In 30 days, by [#permalink]  02 Jun 2018, 03:39
Expert's post
00:00

Question Stats:

55% (00:44) correct 44% (01:13) wrong based on 9 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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Sandy
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Joined: 29 May 2018
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Kudos [?]: 75 [1] , given: 2

Re: A cockroach population doubles every 3 days. In 30 days, by [#permalink]  10 Jun 2018, 07:04
1
KUDOS
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.
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4473
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 80

Kudos [?]: 1478 [0], given: 346

Re: A cockroach population doubles every 3 days. In 30 days, by [#permalink]  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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