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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # The population of a bacteria culture doubles every 2 minutes  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 50544 The population of a bacteria culture doubles every 2 minutes [#permalink] ### Show Tags 11 Feb 2014, 00:00 6 22 00:00 Difficulty: 35% (medium) Question Stats: 68% (01:29) correct 32% (01:44) wrong based on 792 sessions ### HideShow timer Statistics The Official Guide For GMAT® Quantitative Review, 2ND Edition 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project Each 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! _________________ ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 50544 Re: The population of a bacteria culture doubles every 2 minutes [#permalink] ### Show Tags 11 Feb 2014, 00:01 4 13 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. Answer: E. Similar questions to practice: a-certain-bacteria-colony-doubles-in-size-every-day-for-144013.html it-takes-30-days-to-fill-a-laboratory-dish-with-bacteria-140269.html a-certain-culture-of-bacteria-quadruples-every-hour-if-a-52258.html the-number-of-water-lilies-on-a-certain-lake-doubles-every-142858.html the-population-of-locusts-in-a-certain-swarm-doubles-every-90353.html _________________ ##### General Discussion Intern Joined: 05 Feb 2014 Posts: 4 Location: Singapore Concentration: Strategy, General Management GMAT 1: 610 Q48 V27 GMAT 2: 730 Q49 V41 GPA: 2.8 WE: Sales (Energy and Utilities) Re: The population of a bacteria culture doubles every 2 minutes [#permalink] ### Show Tags Updated on: 11 Feb 2014, 00:47 2 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, 00:43. Last edited by ankitsachdev on 11 Feb 2014, 00:47, edited 1 time in total. Intern Joined: 30 Jan 2014 Posts: 17 Re: The population of a bacteria culture doubles every 2 minutes [#permalink] ### Show Tags 11 Feb 2014, 00:44 4 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 _________________ Please +1 KUDO if my post helps. Thank you. Manager Joined: 04 Jan 2014 Posts: 118 GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35 Re: The population of a bacteria culture doubles every 2 minutes [#permalink] ### Show Tags 11 Feb 2014, 00:48 2 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). EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12841 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The population of a bacteria culture doubles every 2 minutes [#permalink] ### Show Tags 21 May 2015, 19:15 1 3 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 _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Joined: 11 Aug 2013
Posts: 44
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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05 May 2016, 20:42
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^n-1 = 500,000
1000 * (2)^n-1 = 500,000
2^n-1 = 500
n-1 = 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  [#permalink]

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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).

GMAT assassins aren't born, they're made,
Rich
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Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 11 Aug 2013 Posts: 44 Re: The population of a bacteria culture doubles every 2 minutes [#permalink] ### Show Tags 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 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12841 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The population of a bacteria culture doubles every 2 minutes [#permalink] ### Show Tags 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. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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06 May 2016, 11:59
1
[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

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
Intern
Joined: 11 Aug 2013
Posts: 44
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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10 May 2016, 22:22
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^n-1 = 500,000
1000 * (2)^n-1 = 500,000
2^n-1 = 500
n-1 = 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?
Intern
Joined: 10 May 2016
Posts: 9
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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11 May 2016, 00:46
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^n-1 = 500,000
1000 * (2)^n-1 = 500,000
2^n-1 = 500
n-1 = 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  [#permalink]

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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.

Answer: E.

Similar questions to practice:
http://gmatclub.com/forum/a-certain-bac ... 44013.html
http://gmatclub.com/forum/it-takes-30-d ... 40269.html
http://gmatclub.com/forum/a-certain-cul ... 52258.html
http://gmatclub.com/forum/the-number-of ... 42858.html
http://gmatclub.com/forum/the-populatio ... 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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Joined: 16 Sep 2016
Posts: 359
GMAT 1: 740 Q50 V40
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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25 Mar 2018, 07:54
1
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.

Answer: E.

Similar questions to practice:
http://gmatclub.com/forum/a-certain-bac ... 44013.html
http://gmatclub.com/forum/it-takes-30-d ... 40269.html
http://gmatclub.com/forum/a-certain-cul ... 52258.html
http://gmatclub.com/forum/the-number-of ... 42858.html
http://gmatclub.com/forum/the-populatio ... 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
Re: The population of a bacteria culture doubles every 2 minutes &nbs [#permalink] 25 Mar 2018, 07:54
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# The population of a bacteria culture doubles every 2 minutes

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