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Math Expert V
Joined: 02 Sep 2009
Posts: 58434
A cockroach population doubles every 3 days. In 30 days, by what perce  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 55% (01:40) correct 45% (01:48) wrong based on 130 sessions

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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%

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

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Bunuel 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%

Assume cockroach population now is x

Now =x
Day 3 = 2x
Day 6 = 4x
Day 9 = 8x
Day 12 = 16x
Day 15 = 32x
Day 18 = 64x
Day 21 = 128x
Day 24 = 256x
Day 27 = 512x
Day 30 = 1024x

% increase = $$\frac{(New - Old)}{(Old)}$$ * 100 = $$\frac{(1024x - x)}{x}$$* 100 = 1023 * 100 ----> 102300 %

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Manager  P
Joined: 01 Feb 2017
Posts: 242
A cockroach population doubles every 3 days. In 30 days, by what perce  [#permalink]

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Using Exponent formulae and given data, we get constant k=2^1/3

So, after 30 days, k^30= 2^10= 1024.

Let initial population be y.
Then final population will be 1024y. And increase in population will be 1023y.

% increase= (1023y/y)*100= 102300%

Ans D
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Re: A cockroach population doubles every 3 days. In 30 days, by what perce  [#permalink]

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1
1

Solution

Given:
• A cockroach population doubles in every 3 days

To find:
• The percentage increase in the cockroach population in 30 days

Approach and Working:
If we assume that initially (at the beginning of 30 days) the population was p, then
• Population after $$3 * 1$$ days = $$p * 2^1$$
• Population after $$3 * 2$$ days = $$p * 2^2$$
• Population after $$3 * 3$$ days = $$p * 2^3$$
Similarly, we can say
• Population after $$3 * 10$$ days = $$p * 2^{10}$$ = 1024p
• Therefore, the percentage increase = $$\frac{(1024p – p)}{p} * 100$$ = 102300%

Hence, the correct answer is option D.

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

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Bunuel 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%

Doubling activities will be taken place for 10 times as cockroach doubles every 3 days. This can be expressed as follows:

no. of cockroach * $$2^{10}$$
=C*1024
=1024C..........................C for cockroach

Percentage change in Cockroach ={ (1024C - C)/C}*100
= 1023*100
= 102300%, which is option D.
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Re: A cockroach population doubles every 3 days. In 30 days, by what perce  [#permalink]

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egmat in this question I tried number picking and picked "2", it did not work.

2^10 = 1024, therefore 1024-2/2*100 = wrong answer

why doesnt this approach works ?
Senior PS Moderator V
Joined: 26 Feb 2016
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Re: A cockroach population doubles every 3 days. In 30 days, by what perce  [#permalink]

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hero_with_1000_faces wrote:
egmat in this question I tried number picking and picked "2", it did not work.

2^10 = 1024, therefore 1024-2/2*100 = wrong answer

why doesnt this approach works ?

hero_with_1000_faces

So what you have assumed is that the cockroach population was 2. It doubled every 3 days
and on the 30th day, it would have doubled for the 10th time. The population would be 2048
on the 30th day.

So, the percentage change in the number of cockroaches will be $$\frac{2048 - 2}{2}$$ or $$1023$$%

Hope this helps you!
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Re: A cockroach population doubles every 3 days. In 30 days, by what perce  [#permalink]

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pushpitkc

Thanks Man, silly mistake :D Re: A cockroach population doubles every 3 days. In 30 days, by what perce   [#permalink] 10 Aug 2018, 02:14
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