Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49915

Re: PERCENTAGES  CONCEPTUAL
[#permalink]
Show Tags
07 Feb 2014, 04:28
Question Stats:
65% (02:21) correct 35% (02:18) wrong based on 198 sessions
HideShow timer Statistics



Manager
Joined: 12 Feb 2012
Posts: 125

Re: A strain of bacteria reproduces @ 25% every 12 min. In how m
[#permalink]
Show Tags
08 Feb 2014, 22:28
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: 107

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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8385
Location: Pune, India

Re: A strain of bacteria reproduces 25% every 12 min. In how m
[#permalink]
Show Tags
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
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 25 Jan 2014
Posts: 15
Concentration: Technology, General Management
Schools: Kellogg '17, Booth '17, Ross '17, Haas '17, Stern '17, Duke '17, Anderson '17, Tepper '17, KenanFlagler '17, Marshall '17, LBS '17, Oxford, ISB '17, Georgia Tech '17, Merage '17, Schulich '17, NUS '17, UrbanaChampaign '17, NTU '17, SPJ GMBA '17

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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8385
Location: Pune, India

Re: A strain of bacteria reproduces 25% every 12 min. In how m
[#permalink]
Show Tags
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 ... echanges/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 01 Jan 2016
Posts: 21

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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8385
Location: Pune, India

Re: A strain of bacteria reproduces @ 25% every 12 min. In how m
[#permalink]
Show Tags
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
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Senior Manager
Joined: 31 Jul 2017
Posts: 477
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Re: A strain of bacteria reproduces @ 25% every 12 min. In how m
[#permalink]
Show Tags
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.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8385
Location: Pune, India

Re: A strain of bacteria reproduces @ 25% every 12 min. In how m
[#permalink]
Show Tags
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.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!




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






