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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] New post 29 Aug 2013, 12:31
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53% (02:11) correct 47% (01:00) wrong based on 60 sessions
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] New post 29 Aug 2013, 22:44
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] New post 01 Sep 2013, 21:05
Expert's post
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] New post 08 Sep 2013, 04:40
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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.

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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Re: If a certain culture of bacteria increases by a constant   [#permalink] 08 Sep 2013, 04:40
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