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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

65% (00:58) correct
35% (01:22) wrong based on 290 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?

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

Show Tags

12 Dec 2012, 15:09

1

This post received 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...

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!
_________________

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.

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

Show Tags

15 Dec 2012, 06:34

3

This post received 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. E is the answer.

Hope thats helpful!
_________________

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

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).
_________________

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.
_________________

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.
_________________

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.
_________________

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

Show Tags

08 Apr 2016, 20:25

1

This post received 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 2833 times ]

_________________

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

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

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...