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The population of a bacteria culture doubles every 2 minutes
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11 Feb 2014, 01:00
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The Official Guide For GMAT® Quantitative Review, 2ND EditionThe 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: The population of a bacteria culture doubles every 2 minutes
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11 Feb 2014, 01:01
SOLUTIONThe 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 twominute intervals are needed, whcih is 18 minutes. Answer: E. Similar questions to practice: acertainbacteriacolonydoublesinsizeeverydayfor144013.htmlittakes30daystofillalaboratorydishwithbacteria140269.htmlacertaincultureofbacteriaquadrupleseveryhourifa52258.htmlthenumberofwaterliliesonacertainlakedoublesevery142858.htmlthepopulationoflocustsinacertainswarmdoublesevery90353.html
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Re: The population of a bacteria culture doubles every 2 minutes
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11 Feb 2014, 01:44
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 \(9*2=18\)
Ans is E




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Re: The population of a bacteria culture doubles every 2 minutes
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Updated on: 11 Feb 2014, 01:47
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
Therefore
\(Pn= Po*2^y\) \(500000 = 1000 * 2^y\) \(500 = 2^y\) \((4*125) = 2^y\)
As 125~128
\((4*128) = 2^y\) \((2^2*2^7) = 2^y\) \((2^9) = 2^y\) \(9 = y\) \(\frac{x}{2} = 9\) \(x = 18\)
Answer = E
Originally posted by ankitsachdev on 11 Feb 2014, 01:43.
Last edited by ankitsachdev on 11 Feb 2014, 01:47, edited 1 time in total.



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Re: The population of a bacteria culture doubles every 2 minutes
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11 Feb 2014, 01:48
We can ignore the thousands. So, basically, we are left with 1 and 500. Since, 2^9 = 512, approx minutes = 9*2 = 18. Answer (E).



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Re: The population of a bacteria culture doubles every 2 minutes
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21 May 2015, 20:15
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. 1k becomes 2k 4k 8k 16k 32k 64k 128k 256k 512k 9 "doubles" at 2 minutes each = about 18 minutes Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: The population of a bacteria culture doubles every 2 minutes
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05 May 2016, 21:42
I am confused here slightly ...
If I try to solve the question GP way, I get slightly different answer :
r = 2 ( as it doubles every 2 mins) a = 1000 nth term = 500,000
ar^n1 = 500,000 1000 * (2)^n1 = 500,000 2^n1 = 500 n1 = 9 n = 10
and since in every 2 mins it gets doubled ..therefore 2* 10 = 20 mins.
Where am I going wrong?



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Re: The population of a bacteria culture doubles every 2 minutes
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05 May 2016, 23:07
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). GMAT assassins aren't born, they're made, Rich
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Re: The population of a bacteria culture doubles every 2 minutes
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05 May 2016, 23:18
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



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Re: The population of a bacteria culture doubles every 2 minutes
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06 May 2016, 11:53
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. GMAT assassins aren't born, they're made, Rich
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Re: The population of a bacteria culture doubles every 2 minutes
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06 May 2016, 12:59
[quote="Bunuel"] The Official Guide For GMAT® Quantitative Review, 2ND EditionThe 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



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Re: The population of a bacteria culture doubles every 2 minutes
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10 May 2016, 23:22
ravisinghal wrote: I am confused here slightly ...
If I try to solve the question GP way, I get slightly different answer :
r = 2 ( as it doubles every 2 mins) a = 1000 nth term = 500,000
ar^n1 = 500,000 1000 * (2)^n1 = 500,000 2^n1 = 500 n1 = 9 n = 10
and since in every 2 mins it gets doubled ..therefore 2* 10 = 20 mins.
Where am I going wrong? Bunnuel, I am still not happy with the explanation provided on why the above calculation is wrong? please help. GP starts with 1000 and last term is 500,000.Therefore a has to be 1000 ..I don't understand why this should not be counted?



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Re: The population of a bacteria culture doubles every 2 minutes
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11 May 2016, 01:46
ravisinghal wrote: I am confused here slightly ...
If I try to solve the question GP way, I get slightly different answer :
r = 2 ( as it doubles every 2 mins) a = 1000 nth term = 500,000
ar^n1 = 500,000 1000 * (2)^n1 = 500,000 2^n1 = 500 n1 = 9 n = 10
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 Ans : 18 Min E



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Re: The population of a bacteria culture doubles every 2 minutes
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25 Mar 2018, 08:21
Bunuel wrote: SOLUTIONThe 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 twominute intervals are needed, whcih is 18 minutes. Answer: E. Similar questions to practice: http://gmatclub.com/forum/acertainbac ... 44013.htmlhttp://gmatclub.com/forum/ittakes30d ... 40269.htmlhttp://gmatclub.com/forum/acertaincul ... 52258.htmlhttp://gmatclub.com/forum/thenumberof ... 42858.htmlhttp://gmatclub.com/forum/thepopulatio ... 90353.html how should i know that 2^9 is 512... what if i have no idea about it and what does 500 mean



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Re: The population of a bacteria culture doubles every 2 minutes
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25 Mar 2018, 08:54
dave13 wrote: Bunuel wrote: SOLUTIONThe 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 twominute intervals are needed, whcih is 18 minutes. Answer: E. Similar questions to practice: http://gmatclub.com/forum/acertainbac ... 44013.htmlhttp://gmatclub.com/forum/ittakes30d ... 40269.htmlhttp://gmatclub.com/forum/acertaincul ... 52258.htmlhttp://gmatclub.com/forum/thenumberof ... 42858.htmlhttp://gmatclub.com/forum/thepopulatio ... 90353.html how should i know that 2^9 is 512... what if i have no idea about it and what does 500 mean Hey dave13, remembering certain powers of 2 can be very helpful ( and easy !) You can start with 2^10 = 1024 ( or 1 MB  from data storage devices.. as all data storage devices have capacity in powers of 2 *fun fact* ) From here it is easy to get to other powers as we can always round off to nearest number of 1000. Such numbers almost always arise in geometric series ( which this Q is an example of ). Best, Gladi
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Re: The population of a bacteria culture doubles every 2 minutes
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23 Nov 2018, 11:22
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
Therefore
\(Pn= Po*2^y\) \(500000 = 1000 * 2^y\) \(500 = 2^y\) \((4*125) = 2^y\)
As 125~128
\((4*128) = 2^y\) \((2^2*2^7) = 2^y\) \((2^9) = 2^y\) \(9 = y\) \(\frac{x}{2} = 9\) \(x = 18\)
Answer = E My understanding was that to find Tn in case of geometric progression was a*r^n1 Accordingly, 500=2^n1 So, n1 =9 So n=10 Can you point out where am I making a mistake?



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Re: The population of a bacteria culture doubles every 2 minutes
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23 Nov 2018, 14:41
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionThe 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 MINUTES ELAPSED  POPULATION0  1,000 2  2,000 4  4,000 6  8,000 8  16,000 10  32,000 12  64,000 14  128,000 16  256,000 18  512,000 DONE!! Answer: E Cheers, Brent
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Re: The population of a bacteria culture doubles every 2 minutes
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07 Jul 2019, 07:51
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
Let's say t is the number of times the population needs to grow The question is 1000∗2t=5000001000∗2t=500000 Or 2t=5002t=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=189∗2=18
Ans is E _




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