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

Question

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%

alldaytestprep · Answer

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 %

Answer: D

Shobhit7 · Answer

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

EgmatQuantExpert · Answer

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.

Answer: D

KSBGC · Answer

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.

hero_with_1000_faces · Answer

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 ?

pushpitkc · Answer

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!

hero_with_1000_faces · Answer

pushpitkc

Thanks Man, silly mistake :D

saynchalk · Answer

Doubles ever 3 days, and 30 days is 3 * 10

Let OG number be x

Increased number after 30 days (x)*(2)^10

Percent increase ends up being (2^10 - 1) * 100

which is (2^5 - 1) (2^5 + 1) * 100

which is 31*33*100

which is 102300

pralmall · Answer

Assume no of cockroaches on day = 1
After 3 days count will be = 1x 2 = 2 
Similarly after 30 days (every 3 days doubles) so 1 x 1024 ( as 2 exponent 10 times will be the increase in 30 days) 
Percentage increase = 1024 - 1 = 1023 > 1023 / 1 x 100 = 102300 % is the answer

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards