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# If a certain culture of bacteria increases by a constant

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If a certain culture of bacteria increases by a constant [#permalink]

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29 Aug 2013, 13:31
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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.
[Reveal] Spoiler: OA

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Re: If a certain culture of bacteria increases by a constant [#permalink]

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29 Aug 2013, 23:44
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My take:

We need to find y, when xy=10^4.

1) When x=10^y, y*(10^y)=10^4
or could also be written as y = 10^(4-y)
By using substitution, we could say y could be between 3 and 4 (~=3.4). Hence st1 is Sufficient
( And Options B,C,&E could be eliminated)

2) (2)*x=100 i.e. x=50. By substituting value of x in xy=10^4, we could find the time taken. Hence st2 is Sufficient

Hence the solution is
[Reveal] Spoiler:
D

/SM

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Re: If a certain culture of bacteria increases by a constant [#permalink]

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01 Sep 2013, 22:05
Hi Bunuel,
It'd be really helpful if you could provide an explanation for this problem to help me understand it.

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Re: If a certain culture of bacteria increases by a constant [#permalink]

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08 Sep 2013, 05:40
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bagdbmba wrote:
Hi Bunuel,
It'd be really helpful if you could provide an explanation for this problem to help me understand it.

Maybe this will help

from 1 we are given x=10^y, let initial quantity be m

So after y minutes the quantity => m*x =>m*10^y , now we need the new value to be 10,000 times the original => m*10^y=m*1000 => y=4 minutes
hence statement 1 is sufficient.

from statement 2

In 2 minutes the culture will increase to 100 times this can be interpreted as follows
1) every 1 minute the quantity is multiplied by 10
or
2) every 2 minutes the quantity is multiplied by 100

Either ways after 4 minutes the quantity will be multiplied by 10,000 hence y=4 minutes

Hence statement 2 is sufficient.
Hope the solution is clear.
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If a certain culture of bacteria [#permalink]

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08 Sep 2014, 13:40
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If a certain culture of bacteria increases by a factor of x every y minutes, how long will it take for the culture to increase to 10000 times its original amount ?
1) (x)^1/y = 10
2) In 2 minutes the culture will increase to 100 times its original amount.

Please could you explain an how to solve such questions which involves population increasing by certain factors

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Re: If a certain culture of bacteria [#permalink]

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08 Sep 2014, 20:45
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ankitaprsd wrote:
If a certain culture of bacteria increases by a factor of x every y minutes, how long will it take for the culture to increase to 10000 times its original amount ?
1) (x)^1/y = 10
2) In 2 minutes the culture will increase to 100 times its original amount.

Please could you explain an how to solve such questions which involves population increasing by certain factors

Stem 1 is interesting..

Consider x=10 and y=1...so Initial bacteria (K) will increase by a factor of 10 in 1 minute...so after 1 minute there will be K+10K=11K...so we can find the time it will take for culture to increase to 10000 times

So after 1 minute, we have 11K
After 2 minutes, 11K+110K=121K
After 3 minutes= 121K+1210K=1331K
After 4 minutes...

Consider $$x=\sqrt{10}$$, and y =1/2 or 30 seconds, So after 30 seconds, no. of bacteria will increase by $$(10^{1/2})^{2}$$ or by a factor of 10...in 1 minute it will increase by factor $$\sqrt{10}$$
At 0 seconds=K
After 30 seconds= K+10K=11K
After 1 minute, by a factor$$\sqrt{10}$$ so after 1 minute you will have $$11K+\sqrt{10}*11K$$-----> Now here the problem is the increase every y minute is not the same so this case will not be considered...

So St1 is sufficient

St2 is straight forward...

Can you post the Official Explanation to question.
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Re: If a certain culture of bacteria increases by a constant [#permalink]

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09 Sep 2014, 06:50
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Bunuel wrote:
ankitaprsd wrote:
If a certain culture of bacteria increases by a factor of x every y minutes, how long will it take for the culture to increase to 10000 times its original amount ?
1) (x)^1/y = 10
2) In 2 minutes the culture will increase to 100 times its original amount.

Please could you explain an how to solve such questions which involves population increasing by certain factors

Merging topics. Please search before posting. Thank you.

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Re: If a certain culture of bacteria increases by a constant [#permalink]

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20 Mar 2016, 03:00
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Re: If a certain culture of bacteria increases by a constant [#permalink]

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19 May 2017, 05:27
Hello from the GMAT Club BumpBot!

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Re: If a certain culture of bacteria increases by a constant [#permalink]

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24 Jun 2017, 04:17
Hi... Pls throw more light about the 1st statement...
i solved it like this...
Initial at time=0, let it be P
after y min, xP
after 2y min, x^2P
after ny min, x^nP

from question x^nP = 10000P
x^n=10^4
from statement 1, x=10^y
10^(yn)=10^4
yn=10
2 unknown and 1 equation, not sufficient

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Re: If a certain culture of bacteria increases by a constant [#permalink]

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25 Jun 2017, 11:51
JJSHHShank wrote:
Hi... Pls throw more light about the 1st statement...
i solved it like this...
Initial at time=0, let it be P
after y min, xP
after 2y min, x^2P
after ny min, x^nP

from question x^nP = 10000P
x^n=10^4
from statement 1, x=10^y
10^(yn)=10^4
yn=10
2 unknown and 1 equation, not sufficient

keyword is "by a factor of ", is used commonly to mean the same as "multiplied by" or "divided by." If x is INCREASED by a factor of 4, it becomes 4x. If x is DECREASED by a factor of 4, it becomes x/4. The key word is the direction of change i.e. (increased / decreased) by a factor of. so here from both the points, we can derive that every y minute(s) (the number increases/multiplies by a factor of 10) or in case of (2) we straightaway know that at 2 minutes we have 100, so 10^2 = 100 means that the number became 10 at 1 minute and 100 at 2 minutes. Hope it helps

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Re: If a certain culture of bacteria increases by a constant [#permalink]

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25 Jun 2017, 11:58
thanks smitsharma...
overlooked that... always of the notion that the factor doubles and it remains in the exponential form...

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Re: If a certain culture of bacteria increases by a constant   [#permalink] 25 Jun 2017, 11:58
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