If a certain culture of bacteria increases by a constant : GMAT Data Sufficiency (DS)
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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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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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New post 29 Aug 2013, 22:44
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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

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

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New post 01 Sep 2013, 21:05
Hi Bunuel,
It'd be really helpful if you could provide an explanation for this problem to help me understand it.

Thanks in advance.
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Re: If a certain culture of bacteria increases by a constant [#permalink]

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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.

Thanks in advance.



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.
therefore the answer is D
Hope the solution is clear.
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If a certain culture of bacteria [#permalink]

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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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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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New post 09 Sep 2014, 05:49
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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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] 20 Mar 2016, 02:00
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