If a certain culture of bacteria increases by a constant factor of x every y minutes, how long will it take for the culture to increase to ten thousand times its original size.

1- x^(1/y)= 10
2 - In two minutes, the culture will increase to one hundred times its original size.

Statement 1: x^(1/y) = 10.
[x^(1/y)]^y = 10^y.
x = 10^y.
Since 10,000 = 10�, x=10,000 when y=4.
Thus, it will take y=4 minutes for the culture to increase by a factor of x=10,000.
SUFFICIENT.

Statement 2: In two minutes, the culture will increase to one-hundred times its original amount.
Thus, in 4 minutes, the culture will increase to 100*100 = 10,000 times its original size.
SUFFICIENT.

The correct answer is D.

Dear Experts/Moderators,

I am comparatively weak in such concepts(relative increases in populations). Request you to please post few similar questions solving which I can master this topic.
Thanks a lot in advance!

-RR1

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If a certain culture of bacteria increases by a constant factor of x every y minutes, how long will it take for the culture to increase to ten-thousand times its original size?

1. x=10^y
2.In two minutes, the culture will increase to one hundred times its original size.


Since there are 2 variables (x,y) in the original condition, we need 2 equations to match the number of variables and equations. We have 1 each in 1) and 2), therefore C is likely the answer.
Using both 1) & 2) together,
In case of 1), x=10^6. Since the value is multiplied by 10^6 every 6 minute, the answer is 6 minute.
In case of 2), since the value is multiplied by 100 every 2 minute, it's 10,000times for 4 minutes and 1,000,000 for 6 minutes. Since 1) = 2), The answer is D.


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