It is currently 14 Dec 2017, 15:03

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If a certain culture of bacteria increases by a constant

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 27 Aug 2012
Posts: 1184

Kudos [?]: 1984 [3], given: 152

If a certain culture of bacteria increases by a constant [#permalink]

### Show Tags

29 Aug 2013, 12:31
3
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

54% (01:07) correct 46% (01:16) wrong based on 295 sessions

### HideShow timer Statistics

If a certain culture of bacteria increases by a constant factor of x every y minutes, how long will it take for the culture to increase to ten-thousand times its original size?

1. $$x=10^y$$
2.In two minutes, the culture will increase to one hundred times its original size.
[Reveal] Spoiler: OA

_________________

Kudos [?]: 1984 [3], given: 152

Intern
Joined: 31 Jan 2013
Posts: 17

Kudos [?]: 56 [0], given: 18

Schools: ISB '15
WE: Consulting (Energy and Utilities)
Re: If a certain culture of bacteria increases by a constant [#permalink]

### Show Tags

29 Aug 2013, 22:44
1
This post was
BOOKMARKED
My take:

We need to find y, when xy=10^4.

1) When x=10^y, y*(10^y)=10^4
or could also be written as y = 10^(4-y)
By using substitution, we could say y could be between 3 and 4 (~=3.4). Hence st1 is Sufficient
( And Options B,C,&E could be eliminated)

2) (2)*x=100 i.e. x=50. By substituting value of x in xy=10^4, we could find the time taken. Hence st2 is Sufficient

Hence the solution is
[Reveal] Spoiler:
D

/SM

Kudos [?]: 56 [0], given: 18

Retired Moderator
Joined: 27 Aug 2012
Posts: 1184

Kudos [?]: 1984 [0], given: 152

Re: If a certain culture of bacteria increases by a constant [#permalink]

### Show Tags

01 Sep 2013, 21:05
Hi Bunuel,
It'd be really helpful if you could provide an explanation for this problem to help me understand it.

_________________

Kudos [?]: 1984 [0], given: 152

Manager
Status: Persevering
Joined: 15 May 2013
Posts: 218

Kudos [?]: 101 [3], given: 34

Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: If a certain culture of bacteria increases by a constant [#permalink]

### Show Tags

08 Sep 2013, 04:40
3
KUDOS
bagdbmba wrote:
Hi Bunuel,
It'd be really helpful if you could provide an explanation for this problem to help me understand it.

Maybe this will help

from 1 we are given x=10^y, let initial quantity be m

So after y minutes the quantity => m*x =>m*10^y , now we need the new value to be 10,000 times the original => m*10^y=m*1000 => y=4 minutes
hence statement 1 is sufficient.

from statement 2

In 2 minutes the culture will increase to 100 times this can be interpreted as follows
1) every 1 minute the quantity is multiplied by 10
or
2) every 2 minutes the quantity is multiplied by 100

Either ways after 4 minutes the quantity will be multiplied by 10,000 hence y=4 minutes

Hence statement 2 is sufficient.
Hope the solution is clear.
_________________

--It's one thing to get defeated, but another to accept it.

Kudos [?]: 101 [3], given: 34

Intern
Joined: 17 Jun 2014
Posts: 27

Kudos [?]: 26 [0], given: 229

Location: India
WE: Information Technology (Computer Software)
If a certain culture of bacteria [#permalink]

### Show Tags

08 Sep 2014, 12:40
1
This post was
BOOKMARKED
If a certain culture of bacteria increases by a factor of x every y minutes, how long will it take for the culture to increase to 10000 times its original amount ?
1) (x)^1/y = 10
2) In 2 minutes the culture will increase to 100 times its original amount.

Please could you explain an how to solve such questions which involves population increasing by certain factors

Kudos [?]: 26 [0], given: 229

Director
Joined: 25 Apr 2012
Posts: 721

Kudos [?]: 872 [1], given: 724

Location: India
GPA: 3.21
Re: If a certain culture of bacteria [#permalink]

### Show Tags

08 Sep 2014, 19:45
1
KUDOS
ankitaprsd wrote:
If a certain culture of bacteria increases by a factor of x every y minutes, how long will it take for the culture to increase to 10000 times its original amount ?
1) (x)^1/y = 10
2) In 2 minutes the culture will increase to 100 times its original amount.

Please could you explain an how to solve such questions which involves population increasing by certain factors

Stem 1 is interesting..

Consider x=10 and y=1...so Initial bacteria (K) will increase by a factor of 10 in 1 minute...so after 1 minute there will be K+10K=11K...so we can find the time it will take for culture to increase to 10000 times

So after 1 minute, we have 11K
After 2 minutes, 11K+110K=121K
After 3 minutes= 121K+1210K=1331K
After 4 minutes...

Consider $$x=\sqrt{10}$$, and y =1/2 or 30 seconds, So after 30 seconds, no. of bacteria will increase by $$(10^{1/2})^{2}$$ or by a factor of 10...in 1 minute it will increase by factor $$\sqrt{10}$$
At 0 seconds=K
After 30 seconds= K+10K=11K
After 1 minute, by a factor$$\sqrt{10}$$ so after 1 minute you will have $$11K+\sqrt{10}*11K$$-----> Now here the problem is the increase every y minute is not the same so this case will not be considered...

So St1 is sufficient

St2 is straight forward...

Can you post the Official Explanation to question.
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 872 [1], given: 724

Math Expert
Joined: 02 Sep 2009
Posts: 42607

Kudos [?]: 135660 [1], given: 12705

Re: If a certain culture of bacteria increases by a constant [#permalink]

### Show Tags

09 Sep 2014, 05:50
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
Bunuel wrote:
ankitaprsd wrote:
If a certain culture of bacteria increases by a factor of x every y minutes, how long will it take for the culture to increase to 10000 times its original amount ?
1) (x)^1/y = 10
2) In 2 minutes the culture will increase to 100 times its original amount.

Please could you explain an how to solve such questions which involves population increasing by certain factors

Merging topics. Please search before posting. Thank you.

Similar questions to practice:
a-certain-bacteria-colony-doubles-in-size-every-day-for-144013.html
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
the-population-of-locusts-in-a-certain-swarm-doubles-every-90353.html
the-population-of-a-bacteria-culture-doubles-every-2-minutes-167378.html
_________________

Kudos [?]: 135660 [1], given: 12705

Intern
Joined: 03 Jun 2017
Posts: 15

Kudos [?]: 0 [0], given: 13

Re: If a certain culture of bacteria increases by a constant [#permalink]

### Show Tags

24 Jun 2017, 03:17
Hi... Pls throw more light about the 1st statement...
i solved it like this...
Initial at time=0, let it be P
after y min, xP
after 2y min, x^2P
after ny min, x^nP

from question x^nP = 10000P
x^n=10^4
from statement 1, x=10^y
10^(yn)=10^4
yn=10
2 unknown and 1 equation, not sufficient

Kudos [?]: 0 [0], given: 13

Intern
Joined: 05 Apr 2017
Posts: 12

Kudos [?]: 3 [0], given: 5

Re: If a certain culture of bacteria increases by a constant [#permalink]

### Show Tags

25 Jun 2017, 10:51
JJSHHShank wrote:
Hi... Pls throw more light about the 1st statement...
i solved it like this...
Initial at time=0, let it be P
after y min, xP
after 2y min, x^2P
after ny min, x^nP

from question x^nP = 10000P
x^n=10^4
from statement 1, x=10^y
10^(yn)=10^4
yn=10
2 unknown and 1 equation, not sufficient

keyword is "by a factor of ", is used commonly to mean the same as "multiplied by" or "divided by." If x is INCREASED by a factor of 4, it becomes 4x. If x is DECREASED by a factor of 4, it becomes x/4. The key word is the direction of change i.e. (increased / decreased) by a factor of. so here from both the points, we can derive that every y minute(s) (the number increases/multiplies by a factor of 10) or in case of (2) we straightaway know that at 2 minutes we have 100, so 10^2 = 100 means that the number became 10 at 1 minute and 100 at 2 minutes. Hope it helps

Kudos [?]: 3 [0], given: 5

Intern
Joined: 03 Jun 2017
Posts: 15

Kudos [?]: 0 [0], given: 13

Re: If a certain culture of bacteria increases by a constant [#permalink]

### Show Tags

25 Jun 2017, 10:58
thanks smitsharma...
overlooked that... always of the notion that the factor doubles and it remains in the exponential form...

Kudos [?]: 0 [0], given: 13

Intern
Joined: 05 Jul 2016
Posts: 16

Kudos [?]: 9 [0], given: 366

Location: Brazil
Concentration: Finance, Entrepreneurship
WE: Analyst (Investment Banking)
Re: If a certain culture of bacteria increases by a constant [#permalink]

### Show Tags

27 Nov 2017, 05:52
bagdbmba wrote:
If a certain culture of bacteria increases by a constant factor of x every y minutes, how long will it take for the culture to increase to ten-thousand times its original size?

1. $$x=10^y$$
2.In two minutes, the culture will increase to one hundred times its original size.

The question asks "how long it will take for the culture to INCREASE to 10.000x its original size". We need to find "y" minutes.
1. x=10ˆy | If 10.000 = 10ˆ4; When x = 10ˆ4; y=4 minutes; Sufficient
2. 2min: x=100 ; 4 minutes: x=10000

Kudos [?]: 9 [0], given: 366

Re: If a certain culture of bacteria increases by a constant   [#permalink] 27 Nov 2017, 05:52
Display posts from previous: Sort by