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The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?
(A) 10 (B) 12 (C) 14 (D) 16 (E) 18
Problem Solving Question: 90 Category:Arithmetic Estimation Page: 73 Difficulty: 600
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Re: The population of a bacteria culture doubles every 2 minutes
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11 Feb 2014, 00:01
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SOLUTION
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?
(A) 10 (B) 12 (C) 14 (D) 16 (E) 18
\(1000 * 2^t = 500,000\) --> \(2^t = 500\) --> since \(2^9 = 512\), then \(t\approx{9}\). Thus, approximately 9 two-minute intervals are needed, whcih is 18 minutes.
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Updated on: 11 Feb 2014, 00:47
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Solution =
Let x be the total number of minutes. As the population doubles every 2 minutes, the number of times population doubles is \(y = \frac{x}{2}\) Let Po be the Original Population of bacteria. = 1,000 Let Pn be the Final Population of bacteria. = 500,000
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11 Feb 2014, 00:44
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The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?
(A) 10 (B) 12 (C) 14 (D) 16 (E) 18
Lets say t is th number of times the population needs to grow The question is \(1000*2^t=500000\) Or \(2^t=500\) 2^6=64 2^7=128 2^8=256 2^9=512 BINGO.
So it needs to grow 9 times. If it grows every 2 min so \(9*2=18\)
Re: The population of a bacteria culture doubles every 2 minutes
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21 May 2015, 19:15
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Hi All,
This prompt can be solved with a bit of "brute force" - you can essentially "count doubles" and find the answer. This method is probably faster than any other approach that you might take. You can even speed up by ignoring the last 3 zeroes.
Re: The population of a bacteria culture doubles every 2 minutes
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05 May 2016, 22:07
Hi ravisinghal,
It looks like your work includes all of the terms (and it "counts" the 1st term, when that is technically the 'starting' term - so it should NOT be counted).
Re: The population of a bacteria culture doubles every 2 minutes
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05 May 2016, 22:18
EMPOWERgmatRichC wrote:
Hi ravisinghal,
It looks like your work includes all of the terms (and it "counts" the 1st term, when that is technically the 'starting' term - so it should NOT be counted).
GMAT assassins aren't born, they're made, Rich
can you please elaborate?
what I understand is 1000 should not be considered as 'a' ?? But that's the first term as per ques
Re: The population of a bacteria culture doubles every 2 minutes
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06 May 2016, 10:53
Hi ravisinghal,
The question asks approximately how many minutes it takes for that increase to happen. If you START with 1,000 then no time has passed yet. If you're going to approach the question in the way that you did, then you can't include that first term since it requires NO time.
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?
(A) 10 (B) 12 (C) 14 (D) 16 (E) 18
2^9*1000=512000 answer 18 minutes. solved in 20 secs
and since in every 2 mins it gets doubled ..therefore 2* 10 = 20 mins.
Where am I going wrong?
Dear Ravi, u are right on your approach... According to GP way 10th term would be 512000 So between 1st and 10th term there are 9 intervals of 2 min each means 18 Min
Re: The population of a bacteria culture doubles every 2 minutes
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25 Mar 2018, 07:21
Bunuel wrote:
SOLUTION
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?
(A) 10 (B) 12 (C) 14 (D) 16 (E) 18
\(1000 * 2^t = 500,000\) --> \(2^t = 500\) --> since \(2^9 = 512\), then \(t\approx{9}\). Thus, approximately 9 two-minute intervals are needed, whcih is 18 minutes.
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
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Re: The population of a bacteria culture doubles every 2 minutes
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25 Mar 2018, 07:54
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dave13 wrote:
Bunuel wrote:
SOLUTION
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?
(A) 10 (B) 12 (C) 14 (D) 16 (E) 18
\(1000 * 2^t = 500,000\) --> \(2^t = 500\) --> since \(2^9 = 512\), then \(t\approx{9}\). Thus, approximately 9 two-minute intervals are needed, whcih is 18 minutes.
Re: The population of a bacteria culture doubles every 2 minutes
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23 Nov 2018, 10:22
ankitsachdev wrote:
Solution =
Let x be the total number of minutes. As the population doubles every 2 minutes, the number of times population doubles is \(y = \frac{x}{2}\) Let Po be the Original Population of bacteria. = 1,000 Let Pn be the Final Population of bacteria. = 500,000
My understanding was that to find Tn in case of geometric progression was a*r^n-1 Accordingly, 500=2^n-1 So, n-1 =9 So n=10 Can you point out where am I making a mistake?
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?
(A) 10 (B) 12 (C) 14 (D) 16 (E) 18
When we scan the answer choices (ALWAYS scan the answer choices BEFORE deciding on the approach you'll take), we see that the number of population "doublings" will be between 5 and 9. Given these relatively small values, we might solve this question by creating a growth table
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68% (01:08) correct 
