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

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Math Expert
Joined: 02 Sep 2009
Posts: 52431

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07 Feb 2014, 03:28
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Difficulty:

55% (hard)

Question Stats:

64% (02:21) correct 36% (02:17) wrong based on 200 sessions

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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.

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

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Joined: 12 Feb 2012
Posts: 125
Re: A strain of bacteria reproduces @ 25% every 12 min. In how m  [#permalink]

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08 Feb 2014, 21:28
1
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.
Manager
Joined: 04 Jan 2014
Posts: 103
Re: A strain of bacteria reproduces @ 25% every 12 min. In how m  [#permalink]

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10 Jul 2014, 00:31
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.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8810
Location: Pune, India
Re: A strain of bacteria reproduces 25% every 12 min. In how m  [#permalink]

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17 Sep 2014, 22:41
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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Joined: 25 Jan 2014
Posts: 15
Concentration: Technology, General Management
Re: A strain of bacteria reproduces 25% every 12 min. In how m  [#permalink]

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18 Sep 2014, 19:13
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?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8810
Location: Pune, India
Re: A strain of bacteria reproduces 25% every 12 min. In how m  [#permalink]

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18 Sep 2014, 20:21
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.

http://www.veritasprep.com/blog/2011/02 ... rcentages/
http://www.veritasprep.com/blog/2011/02 ... e-changes/
_________________

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 01 Jan 2016
Posts: 21
Re: A strain of bacteria reproduces @ 25% every 12 min. In how m  [#permalink]

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16 May 2018, 17:33
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.

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.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8810
Location: Pune, India
Re: A strain of bacteria reproduces @ 25% every 12 min. In how m  [#permalink]

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17 May 2018, 02:39
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.

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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Karishma
Veritas Prep GMAT Instructor

Director
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
GMAT 1: 700 Q50 V33
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Re: A strain of bacteria reproduces @ 25% every 12 min. In how m  [#permalink]

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17 May 2018, 04:04
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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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8810
Location: Pune, India
Re: A strain of bacteria reproduces @ 25% every 12 min. In how m  [#permalink]

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17 May 2018, 04:56
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.
_________________

Karishma
Veritas Prep GMAT Instructor

Re: A strain of bacteria reproduces @ 25% every 12 min. In how m &nbs [#permalink] 17 May 2018, 04:56
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