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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]

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New post 08 Oct 2012, 04:57
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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.
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Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]

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New post 08 Oct 2012, 05:22
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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]

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New post 10 Oct 2013, 21:29
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Re: It takes 30 days to fill a laboratory dish with bacteria [#permalink]

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New post 11 Oct 2013, 02:22
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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 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).

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

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New post 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

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

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

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New post 05 Jun 2016, 04:12
Let x be the number of bacteria.

Then first day it will be 2x=1st day
2^2=2nd day
2^3=3rd day
....
....
.....

2^30=30th day-Full
These are all powers of 2(double the next day and half the previous day).So on the 29th day,number of bacteria would be just half.
Re: It takes 30 days to fill a laboratory dish with bacteria   [#permalink] 05 Jun 2016, 04:12
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