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A strain of bacteria reproduces @ 25% every 12 min. In how m

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Re: PERCENTAGES - CONCEPTUAL  [#permalink]

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New post 07 Feb 2014, 04:28
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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.

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Re: A strain of bacteria reproduces @ 25% every 12 min. In how m  [#permalink]

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New post 08 Feb 2014, 22:28
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Bunuel,

How were you able to calculate to find x, in the formula (1.25)^x=3 so easily??
1.25^x=(5/4)^x=3.
Would have imagined x would be some irrational number, since 5/4 is not a multiple of 3.
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Re: A strain of bacteria reproduces @ 25% every 12 min. In how m  [#permalink]

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New post 10 Jul 2014, 01:31
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 25% every 12 min. In how m  [#permalink]

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New post 17 Sep 2014, 23:41
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 25% every 12 min. In how m  [#permalink]

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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 25% every 12 min. In how m  [#permalink]

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New post 18 Sep 2014, 21:21
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.

These two posts will help you understand this concept fully:
http://www.veritasprep.com/blog/2011/02 ... rcentages/
http://www.veritasprep.com/blog/2011/02 ... e-changes/
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Re: A strain of bacteria reproduces @ 25% every 12 min. In how m  [#permalink]

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New post 16 May 2018, 18:33
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 @ 25% every 12 min. In how m  [#permalink]

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New post 17 May 2018, 03:39
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 @ 25% every 12 min. In how m  [#permalink]

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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 @ 25% every 12 min. In how m  [#permalink]

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New post 17 May 2018, 05:56
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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Karishma
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Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

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Re: A strain of bacteria reproduces @ 25% every 12 min. In how m &nbs [#permalink] 17 May 2018, 05:56
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