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A strain of bacteria reproduces at the rate of 25% every 12 min.

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Bunuel
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A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   07 Feb 2014, 04:28
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A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

(A) 96 min
(B) 72 min
(C) 60 min
(D) 48 min
(E) 40 min
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C
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Bunuel
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   08 Feb 2014, 22:28
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A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

(A) 96 min
(B) 72 min
(C) 60 min
(D) 48 min
(E) 40 min

The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

1.25^x = 3 --> x = ~5 --> five 12 minute periods = 60 minutes.

Answer: C.
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   10 Jul 2014, 01:31
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Hi Bunnel,

I used rounding off method. Is that right?
1.25 approx 1.3
\(1.3^2\) = 1.69
\(1.7^2\) = 2.89 or approx 3

Since we squared twice and 1.3>1.25, we need more than 4, or at least 5.
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   17 Sep 2014, 23:41
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Bunuel wrote:

The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

a) 96 min

b) 72 min

c) 60 min

d) 48 min

e) 40 min



Responding to a pm:

If initial amount of bacteria is X, we need it to become 3X. How many 12 min time intervals does it need? Let's assume we need n time intervals.

X*(5/4)^n = 3X
(5/4)^n = 3

Now note that the options are 12*4, 12*5, 12*6 etc. So this gives us some ideas.

(5/4)^4 = 625/256 -> this is much less than 3 since 256*3 is more than 750.
(5/4)^5 = 3125/1024 -> this is a tiny bit more than 3 and hence is out answer since 1024*3 is a bit more than 3000.

Hence n is 5 and time required = 12*5 = 60 mins
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   18 Sep 2014, 20:13
Responding to a pm:

If initial amount of bacteria is X, we need it to become 3X. How many 12 min time intervals does it need? Let's assume we need n time intervals.

X*(5/4)^n = 3X
(5/4)^n = 3

Now note that the options are 12*4, 12*5, 12*6 etc. So this gives us some ideas.

(5/4)^4 = 625/256 -> this is much less than 3 since 256*3 is more than 750.
(5/4)^5 = 3125/1024 -> this is a tiny bit more than 3 and hence is out answer since 1024*3 is a bit more than 3000.

Hence n is 5 and time required = 12*5 = 60 mins

--------------
i could not understand the solution at all. could you please explain as to how did you get the fraction 5/4?
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   Updated on: 17 Oct 2022, 01:03
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arshu27 wrote:
Responding to a pm:

If initial amount of bacteria is X, we need it to become 3X. How many 12 min time intervals does it need? Let's assume we need n time intervals.

X*(5/4)^n = 3X
(5/4)^n = 3

Now note that the options are 12*4, 12*5, 12*6 etc. So this gives us some ideas.

(5/4)^4 = 625/256 -> this is much less than 3 since 256*3 is more than 750.
(5/4)^5 = 3125/1024 -> this is a tiny bit more than 3 and hence is out answer since 1024*3 is a bit more than 3000.

Hence n is 5 and time required = 12*5 = 60 mins

--------------
i could not understand the solution at all. could you please explain as to how did you get the fraction 5/4?


If a number has to be increased by 25%, you effectively multiply it by 5/4.

n + n*25/100 = n + n/4 = n(1 + 1/4) = n*5/4

Similarly, if you want to increase a number by 20%, you multiply it by 6/5 and so on...

Since the colony increases by 25% every 12 mins, you keep multiplying it by 5/4 till it becomes 3 times.

Originally posted by KarishmaB on 18 Sep 2014, 21:21.
Last edited by KarishmaB on 17 Oct 2022, 01:03, edited 1 time in total.
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   16 May 2018, 18:33
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Bunuel wrote:
aimlockfire1 wrote:
A strain of bacteria reproduces @ 25% every 12 min. In how much time will it triple itself ??

a) 96 min

b) 72 min

c) 60 min

d) 48 min

e) 40 min


The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

1.25^x = 3 --> x = ~5 --> five 12 minute periods = 60 minutes.

Answer: C.

P.S. Please do not shorten or reword the questions.


How are you able to see that (1.25)^x = 3 yields x = 5? Are you completing this calculation in your head? Thank you.
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   17 May 2018, 03:39
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GMAT2645 wrote:
Bunuel wrote:
aimlockfire1 wrote:
A strain of bacteria reproduces @ 25% every 12 min. In how much time will it triple itself ??

a) 96 min

b) 72 min

c) 60 min

d) 48 min

e) 40 min


The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

1.25^x = 3 --> x = ~5 --> five 12 minute periods = 60 minutes.

Answer: C.

P.S. Please do not shorten or reword the questions.


How are you able to see that (1.25)^x = 3 yields x = 5? Are you completing this calculation in your head? Thank you.


Approximate.

(1.25)^2 = 1.5625 (square of a number ending in 5 is easy to find.

75^2 = _(7*8)_ 25 = 5625
35^2 = _(3*4)_25 = 1225
105^2 = _(10*11)_25 = 11025

Now round up 1.5625 to 1.6
1.6^2 = 2.56 (so this is about 1.25^4)

So we are close to 3 but not quite there yet.
Round down 2.56 to 2.5 and 1.25 to 1.2

2.5*1.2 = 3.00 = about 1.25^5
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   17 May 2018, 05:04
VeritasPrepKarishma wrote:
Bunuel wrote:

The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

a) 96 min

b) 72 min

c) 60 min

d) 48 min

e) 40 min



Responding to a pm:

If initial amount of bacteria is X, we need it to become 3X. How many 12 min time intervals does it need? Let's assume we need n time intervals.

X*(5/4)^n = 3X
(5/4)^n = 3

Now note that the options are 12*4, 12*5, 12*6 etc. So this gives us some ideas.

(5/4)^4 = 625/256 -> this is much less than 3 since 256*3 is more than 750.
(5/4)^5 = 3125/1024 -> this is a tiny bit more than 3 and hence is out answer since 1024*3 is a bit more than 3000.

Hence n is 5 and time required = 12*5 = 60 mins


Hi VeritasPrepKarishma,

Why cant we use GP Series here?? Can you please clarify.

Let x be initial bacteria. Now, we have

x + 5x/4 + 25x/16 + ... = 3x
(5/4)^n = 7/4..

However, I am not able to get value of n here.
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   17 May 2018, 05:56
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rahul16singh28 wrote:
VeritasPrepKarishma wrote:
Bunuel wrote:

The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

a) 96 min

b) 72 min

c) 60 min

d) 48 min

e) 40 min



Responding to a pm:

If initial amount of bacteria is X, we need it to become 3X. How many 12 min time intervals does it need? Let's assume we need n time intervals.

X*(5/4)^n = 3X
(5/4)^n = 3

Now note that the options are 12*4, 12*5, 12*6 etc. So this gives us some ideas.

(5/4)^4 = 625/256 -> this is much less than 3 since 256*3 is more than 750.
(5/4)^5 = 3125/1024 -> this is a tiny bit more than 3 and hence is out answer since 1024*3 is a bit more than 3000.

Hence n is 5 and time required = 12*5 = 60 mins


Hi VeritasPrepKarishma,

Why cant we use GP Series here?? Can you please clarify.

Let x be initial bacteria. Now, we have

x + 5x/4 + 25x/16 + ... = 3x
(5/4)^n = 7/4..

However, I am not able to get value of n here.


This is a compounding situation.

x becomes (5/4)x which becomes (5/4)^2x which then becomes (5/4)^3x and so on...

We cannot add these terms since once x becomes (5/4)x, we don't have x anymore.
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   01 Jan 2020, 00:34
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Let's assume x (initial bacteria strain) = 100
x (final bacteria strain) = 300 [Triples itself]
Time interval, T=12.
At T=12, X (final) = 25%(100) = 125.
At T=24, X (final) = 25%(125) = ~156.
At T=36, X (final) = 25%(156) = ~195. [25% or 1/4x156 + 156]
At T=48, X (final) = 25%(195) = ~244.
At T=60, X (final) = 25%(244) = ~305, which is closest to 300. Therefore at T=60 mins, X(final) = 300 = 3X.
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   13 May 2021, 13:23
VeritasKarishma wrote:
rahul16singh28 wrote:
VeritasPrepKarishma wrote:

The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

a) 96 min

b) 72 min

c) 60 min

d) 48 min

e) 40 min



Responding to a pm:

If initial amount of bacteria is X, we need it to become 3X. How many 12 min time intervals does it need? Let's assume we need n time intervals.

X*(5/4)^n = 3X
(5/4)^n = 3

Now note that the options are 12*4, 12*5, 12*6 etc. So this gives us some ideas.

(5/4)^4 = 625/256 -> this is much less than 3 since 256*3 is more than 750.
(5/4)^5 = 3125/1024 -> this is a tiny bit more than 3 and hence is out answer since 1024*3 is a bit more than 3000.

Hence n is 5 and time required = 12*5 = 60 mins


Hi VeritasPrepKarishma,

Why cant we use GP Series here?? Can you please clarify.

Let x be initial bacteria. Now, we have

x + 5x/4 + 25x/16 + ... = 3x
(5/4)^n = 7/4..

However, I am not able to get value of n here.


This is a compounding situation.

x becomes (5/4)x which becomes (5/4)^2x which then becomes (5/4)^3x and so on...

We cannot add these terms since once x becomes (5/4)x, we don't have x anymore.[/quote]

Hey Karishma, I didn't understand this explanation. Why is there no x anymore?

I have the same doubt as Rahul. The question stem is not clear and the 25% increase could be from the newly acquired value after every new 12 min iteration, making it a GP/Compound Interest sorta problem. Why can't it be interpreted in that way?
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink] New post   25 Apr 2023, 09:40
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Re: A strain of bacteria reproduces at the rate of 25% every 12 min. [#permalink]
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