GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jan 2019, 16:13

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# The population of a bacteria culture doubles every 2 minutes

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52231
The population of a bacteria culture doubles every 2 minutes  [#permalink]

### Show Tags

11 Feb 2014, 00:00
6
31
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:08) correct 32% (01:23) wrong based on 873 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:
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!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52231
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.

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
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

$$(4*128) = 2^y$$
$$(2^2*2^7) = 2^y$$
$$(2^9) = 2^y$$
$$9 = y$$
$$\frac{x}{2} = 9$$
$$x = 18$$

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: 117
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: 13331
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

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 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, 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? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13331 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 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 _________________ 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
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

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: 13331
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
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Manager
Joined: 13 Apr 2016
Posts: 59
Location: India
GMAT 1: 640 Q50 V27
GPA: 3
WE: Operations (Hospitality and Tourism)
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

### Show Tags

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
solved in 20 secs
Intern
Joined: 11 Aug 2013
Posts: 44
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

### Show Tags

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]

### Show Tags

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
VP
Joined: 09 Mar 2016
Posts: 1287
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

### Show Tags

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.

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
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 652
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

### Show Tags

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.

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,
_________________

Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

Intern
Joined: 07 Apr 2018
Posts: 3
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

### Show Tags

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

Therefore

$$Pn= Po*2^y$$
$$500000 = 1000 * 2^y$$
$$500 = 2^y$$
$$(4*125) = 2^y$$

As 125~128

$$(4*128) = 2^y$$
$$(2^2*2^7) = 2^y$$
$$(2^9) = 2^y$$
$$9 = y$$
$$\frac{x}{2} = 9$$
$$x = 18$$

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?
CEO
Joined: 11 Sep 2015
Posts: 3331
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

### Show Tags

23 Nov 2018, 13:41
Top Contributor
Bunuel wrote:
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

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 | POPULATION
0 | 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!!

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com

Re: The population of a bacteria culture doubles every 2 minutes &nbs [#permalink] 23 Nov 2018, 13:41
Display posts from previous: Sort by