It is currently 21 Oct 2017, 02:00

### 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 June
Open Detailed Calendar

# A certain bacteria colony doubles in size every day for 20

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 24 Apr 2012
Posts: 38

Kudos [?]: 16 [0], given: 35

GMAT 1: 660 Q48 V33
WE: Information Technology (Health Care)
A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

12 Dec 2012, 13:42
16
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

65% (00:58) correct 35% (01:22) wrong based on 292 sessions

### HideShow timer Statistics

A certain bacteria colony doubles in size every day for 20 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?

A. 6.33
B. 7.5
C. 10
D. 15
E. 19
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Dec 2012, 02:50, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 16 [0], given: 35

Current Student
Joined: 24 Apr 2012
Posts: 38

Kudos [?]: 16 [0], given: 35

GMAT 1: 660 Q48 V33
WE: Information Technology (Health Care)
A certain bacteria colony doubles in size every day for 20 days, [#permalink]

### Show Tags

12 Dec 2012, 13:55
samsonfred76 wrote:
simultaneous grow = same amount of time

In 20 days we should expect to have P(2)^20

So if we have two things doing the job of getting us there then;

2^x + 2^x = 20

2(2)^x=2
2^(x+1)=2^20

x+1 = 20

x = 19

More often than not, if you start thinking the question is wrong chances are you are wrong!

If the colony doubles every day then on 20th day the size should be P 2^19 and not P 2^20..right ?

Kudos [?]: 16 [0], given: 35

Intern
Joined: 10 Apr 2012
Posts: 23

Kudos [?]: 41 [1], given: 0

Concentration: Finance, Economics
GMAT 1: 760 Q50 V44
Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

12 Dec 2012, 15:09
1
KUDOS
Let the size at the colony at the start of 20 days be = 1
At the end of the first day it would be 2...At the end of the second day it would be 2(2) and the day after that (2)(2)(2)...You can see then that following the same pattern at the end of 20 days you have (2)^20 since the population doubles...
Hope this helps...

Kudos [?]: 41 [1], given: 0

VP
Joined: 24 Jul 2011
Posts: 1347

Kudos [?]: 642 [1], given: 20

GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: A certain bacteria colony doubles in size every day [#permalink]

### Show Tags

12 Dec 2012, 21:10
1
KUDOS
1
This post was
BOOKMARKED
Let a be the number of bacteria in the colony at start of day 1.

a * 2^(20) = 2a * 2^(x)
=> x = 20 -1 = 19

Option E
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Kudos [?]: 642 [1], given: 20

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17374 [9], given: 232

Location: Pune, India
Re: A certain bacteria colony doubles in size every day [#permalink]

### Show Tags

12 Dec 2012, 21:17
9
KUDOS
Expert's post
8
This post was
BOOKMARKED
gmatgeek wrote:
A certain bacteria colony doubles in size every day
for 20 days, at which point it reaches the limit of its
habitat and can no longer grow. If two bacteria
colonies start growing simultaneously, how many
days will it take them to reach the habitat’s limit?
 6.33
 7.5
 10
 15
 19

Say the colony has x bacteria in the beginning.
1st day - 2x bacteria
2nd day - $$2^2x$$ bacteria
3rd day - $$2^3x$$ bacteria
.
20th day - $$2^{20}x$$ bacteria

If we start with 2 bacteria colonies, it means there are already 2x bacteria (equal to number of bacteria at the end of the first day in the first case). In how many more days will they reach $$2^{20}x$$ ? Another 19 days!
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17374 [9], given: 232

Intern
Joined: 12 Dec 2012
Posts: 3

Kudos [?]: [0], given: 0

Re: A certain bacteria colony doubles in size every day [#permalink]

### Show Tags

12 Dec 2012, 21:24

If the bacteria doubles its size everyday and takes 20 days to fill up its habitat, then the previous day it filled up half the habitat.

So if it takes 1 bacteria 19 days to fill up half its habitat, it takes 2 bacteria 19 days to fill up the habitat.

Kudos [?]: [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129069 [2], given: 12194

Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

13 Dec 2012, 02:58
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
gmatgeek wrote:
A certain bacteria colony doubles in size every day for 20 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?

A. 6.33
B. 7.5
C. 10
D. 15
E. 19

If there is one bacteria colony, then it will reach the limit of its habitat in 20 days.

If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 19 times.

Similar questions to practice:
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

Hope it helps.
_________________

Kudos [?]: 129069 [2], given: 12194

Manager
Joined: 28 Feb 2012
Posts: 115

Kudos [?]: 52 [3], given: 17

GPA: 3.9
WE: Marketing (Other)
Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

15 Dec 2012, 06:34
3
KUDOS
2
This post was
BOOKMARKED
I am not sure whether ny nethod works for everybody but this is how i did.

So let say our limit is 5 days (just for easiness of calculation) and we have one collony with 1 bacterium in the first day, so in 5 days we have 1+2+4+8+16=31 bacteria, but if we have two colonies, then in order to fill the max capacity of 31 bacteria we need overall 4 days (1+2+4+8=15 and 1+2+4+8=15).

The same principle applies for 20 days, then we need 19 days to fill the max capacity with two colonies.

_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Kudos [?]: 52 [3], given: 17

Intern
Joined: 24 Apr 2012
Posts: 48

Kudos [?]: 24 [0], given: 1

Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

16 Dec 2012, 04:21
Ans:
If there is one bacteria colony, then it will reach the limit of its habitat in 20 days which is 2^19

If there are two bacteria colonies growing simultaneously, then they would multiply as 2, 2^2, 2^3 in order to reach the limit of habitat they would need one day less than normal which is 19 days. (E).
_________________

www.mnemoniceducation.com

Kudos [?]: 24 [0], given: 1

Manager
Joined: 12 Dec 2012
Posts: 156

Kudos [?]: 210 [1], given: 67

Location: Poland
Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

16 Dec 2012, 18:24
1
KUDOS
2
This post was
BOOKMARKED
Two colonies double every day, the given limit value is 2^20 (the asked growth, x - number of days (doublings)):

2(2^x)=2^20

Manipulate the exponent:
2^(x+1)=2^20

Solve for x:
x=19

_________________

If I answered your question with this post, use the motivating power of kudos!

Kudos [?]: 210 [1], given: 67

Manager
Joined: 25 Oct 2013
Posts: 169

Kudos [?]: 70 [0], given: 56

Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

20 Jan 2014, 06:27
Let the final amount of bacteria or the MAX size of the habitat on day 20 be 2x. With single colony doubling every day, the quantity of bacteria on day 19 will be 2x/2 which is x. Now we have another colony growing at the same pace, its size on day 19 is also going to be x. Therefore on day 19 colony 1 size is x and colony 2 size is also x. So total size on day 19 will be 2x. Which is the MAX size of the habitat. Hence E is the answer.

PS: The question seems a little ambiguous because we have to assume each bacteria colony starts with same amount in the beginning.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Kudos [?]: 70 [0], given: 56

Intern
Joined: 20 Jan 2014
Posts: 5

Kudos [?]: [0], given: 1

Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

20 Jan 2014, 06:43
19 days. Nice explanation buenel

Kudos [?]: [0], given: 1

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16611

Kudos [?]: 273 [0], given: 0

Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

22 Jan 2015, 09:36
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Intern
Joined: 29 Nov 2014
Posts: 1

Kudos [?]: 1 [1], given: 0

Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

27 Feb 2015, 11:06
1
KUDOS
20th day = 100%
19th day = 50% (coz it doubles every day)
so two colonies will take 19 days i.e 50% + 50% simultaneously.

Posted from my mobile device

Kudos [?]: 1 [1], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16611

Kudos [?]: 273 [0], given: 0

Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

17 Mar 2016, 02:57
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Senior Manager
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 404

Kudos [?]: 481 [1], given: 53

Location: United States (CA)
Age: 37
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)
A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

08 Apr 2016, 20:25
1
KUDOS
1
This post was
BOOKMARKED
Attached is a visual that should help. Technically the equation for "doubles in size x times" should be $$n(2^x)$$ because we do not know that the colony is necessarily doubling in integer form, i.e, 1,2,4,8 etc. But it's easier to eliminate that part since "n" would be on both sides of the equation, and we are not given a specific starting number so we might as well use the integer powers of two.
Attachments

Screen Shot 2016-04-08 at 8.24.37 PM.png [ 72.01 KiB | Viewed 3020 times ]

_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and via Skype, since 2002.

McElroy Tutoring

Kudos [?]: 481 [1], given: 53

Manager
Joined: 08 Sep 2015
Posts: 73

Kudos [?]: 40 [0], given: 29

Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

### Show Tags

15 Oct 2016, 12:56
I found this formula to be easy to apply.

Final population growth = S * P ^ (t/l)
S = starting population
P = progression (doubles = 2, triples = 3 etc.)
t/l = total amount of iterations
t = time
I = intervals

Let x be final population or habitat limit = > x = 1 bacteria * 2 ^(20 days/1 day) which is x = 2 ^20
if we have 2 bacterias, then each has to fill in half of the habitat => x/2 = 2^20 / 2 = > x/2 = 2 ^19 - so it will take 19 days for each bacteria to fill in half of the habitat, which mens that together they will reach habitat's limit in 19 days

Kudos [?]: 40 [0], given: 29

Re: A certain bacteria colony doubles in size every day for 20   [#permalink] 15 Oct 2016, 12:56
Display posts from previous: Sort by