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A certain bacteria colony doubles in size every day for 20

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A certain bacteria colony doubles in size every day for 20 [#permalink] New post 30 Mar 2012, 01:35
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A certain bacteria colony doubles in size every day for 20 days, a 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 

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-bacteria-colony-doubles-in-size-every-day-for-144013.html
[Reveal] Spoiler: OA
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Re: A certain bacteria colony doubles in size every day for 20 [#permalink] New post 30 Mar 2012, 02:06
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Case 1: Consider the bacteria num to be B. As it doubles every day, number of bacteria at the end of each day would be
Day 1 – B
Day 2 – 2B
Day 3 – 4B
Day 4 – 8B
.
.
.
Day 20 – 2^19 B
It can be implied that the capacity of the habitat is 2^19 B.

Case 2: There are 2 bacteria which keep doubling every day. So, the count would be
Day 1 – 2B
Day 2 – 4B
Day 3 – 8B
.
.
.
Day 18 – 2^18 B
Day 19 – 2^19 B --> this is the point where the habitat is filled to its capacity.
Hence, 19 is the answer
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Re: A certain bacteria colony doubles in size every day for 20 [#permalink] New post 15 Dec 2012, 04:09
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GMATCan wrote:
Please explain fully! I don't get it!
:|


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.

Answer: E.

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
a-certain-culture-of-bacteria-quadruples-every-hour-if-a-52258.html

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-bacteria-colony-doubles-in-size-every-day-for-144013.html

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Re: A certain bacteria colony doubles in size every day for 20 [#permalink] New post 30 Mar 2012, 03:20
I think the question is incorrect as number of days is not mentioned

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Re: A certain bacteria colony doubles in size every day for 20 [#permalink] New post 13 Sep 2012, 23:55
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

We do not need additional information to answer this.
More often than not, if you start thinking the question is wrong chances are you are wrong!
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Re: A certain bacteria colony doubles in size every day for 20 [#permalink] New post 14 Dec 2012, 19:07
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


We do not need additional information to answer this.
More often than not, if you start thinking the question is wrong chances are you are wrong!



Please explain fully! I don't get it!
:|
Re: A certain bacteria colony doubles in size every day for 20   [#permalink] 14 Dec 2012, 19:07
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