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# It takes 30 days to fill a laboratory dish with bacteria

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It takes 30 days to fill a laboratory dish with bacteria [#permalink]  08 Oct 2012, 03:57
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Question Stats:

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It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill one half of dish?

A) 10 days
B) 15 days
C) 24 days
D) 29 days
E) 29.5 days

It is a fairly simple problem, but I am struggling to express what happens here algebraically. Please help on algebra here.
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
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Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]  08 Oct 2012, 04:22
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ikokurin wrote:
It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill one half of dish?

A) 10 days
B) 15 days
C) 24 days
D) 29 days
E) 29.5 days

It is a fairly simple problem, but I am struggling to express what happens here algebraically. Please help on algebra here.

Since it takes 30 days to fill the dish and the population doubles each day, then the dish will be half full after 29 days: 1 day later (so after 30 days) the population will double again and the dish will be full.

Answer: D.

Algebraic approach:

Say initial population occupies 1/n of the disch.
Given: $$\frac{1}{n}*2^{30}=1$$
Question: if $$\frac{1}{n}*2^{x}=\frac{1}{2}$$, then $$x=?$$

$$\frac{1}{n}*2^{x}=\frac{1}{2}$$ --> $$\frac{1}{n}*2^{x}*2=1$$ --> $$\frac{1}{n}*2^{x+1}=1$$. Since we know that $$\frac{1}{n}*2^{30}=1$$, then $$2^{x+1}=2^{30}$$ --> $$x+1=30$$ --> $$x=29$$.

Hope it helps.
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Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]  10 Oct 2013, 20:29
Hello from the GMAT Club BumpBot!

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Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]  11 Oct 2013, 01:22
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Bunuel wrote:
ikokurin wrote:
It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill one half of dish?

A) 10 days
B) 15 days
C) 24 days
D) 29 days
E) 29.5 days

It is a fairly simple problem, but I am struggling to express what happens here algebraically. Please help on algebra here.

Since it takes 30 days to fill the dish and the population doubles each day, then the dish will be half full after 29 days: 1 day later (so after 30 days) the population will double again and the dish will be full.

Answer: D.

Algebraic approach:

Say initial population occupies 1/n of the disch.
Given: $$\frac{1}{n}*2^{30}=1$$
Question: if $$\frac{1}{n}*2^{x}=\frac{1}{2}$$, then $$x=?$$

$$\frac{1}{n}*2^{x}=\frac{1}{2}$$ --> $$\frac{1}{n}*2^{x}*2=1$$ --> $$\frac{1}{n}*2^{x+1}=1$$. Since we know that $$\frac{1}{n}*2^{30}=1$$, then $$2^{x+1}=2^{30}$$ --> $$x+1=30$$ --> $$x=29$$.

Hope it helps.

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Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]  24 Oct 2014, 13:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]  22 Jan 2015, 09:20
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It takes 30 days to fill a laboratory dish with bacteria. If the size of the bacteria doubles each day, how long did it take for the bacteria to fill one half of dish?

A) 10 days
B) 15 days
C) 24 days
D) 29 days
E) 29.5 days

SOLUTION:

2^30 = 2^x, where x = # of days for full plate
we need growth half of 2^30
i.e. (1/2)(2^30) = 2^x
i.e. 2^30 = (2)(2^x)
i.e. 30 = 1 + x
i.e. x = 29

ANSWER:D
Re: It takes 30 days to fill a laboratory dish with bacteria   [#permalink] 22 Jan 2015, 09:20
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# It takes 30 days to fill a laboratory dish with bacteria

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