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

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08 Oct 2012, 04:57

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71% (01:34) correct
29% (01:10) wrong based on 329 sessions

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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.

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 \(2^{x+1}=2^{30}\) --> \(x+1=30\) --> \(x=29\).

Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]

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10 Oct 2013, 21:29

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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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 \(2^{x+1}=2^{30}\) --> \(x+1=30\) --> \(x=29\).

Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]

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24 Oct 2014, 14:04

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]

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22 Jan 2015, 10:20

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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

Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]

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15 May 2016, 14:08

If we understand the question statement properly this question can be solved in under 30 seconds If the bacteria in the dish double every day and in 30 days the dish is full,just 1 day before it the dish will be exactly half - full on 29th day the dish would be half full Correct answer - D

Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]

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15 Oct 2016, 12:46

I found this formula to be easy to apply.

Final population growth = S * P ^ (t/l) S = starting population P = progression (doubles = 2, triples = 3 etc.) t/l = total amount of iterations t = time I = intervals

In our question, let the final population be x, in which case ---- x = 1 * 2 ^ (30 days/1 day)

Question, 1/2 * x = 1 * 2^ ( t days / 1 day), we know that x = 2^30...substitute and we get 1/2 * 2^30 = 2 ^ t, from here we can calculate t which is = 29 days

gmatclubot

Re: It takes 30 days to fill a laboratory dish with bacteria
[#permalink]
15 Oct 2016, 12:46

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