If a certain culture of bacteria increases by a constant

Question

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.

ramannanda9 · Accepted Answer

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. 
  therefore the answer is D   
Hope the solution is clear.

Bunuel · Answer

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 a-certain-culture-of-bacteria-quadruples-every-hour-if-a-52258.html

Smallwonder · Answer

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   D  
/SM

bagdbmba · Answer

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

Thanks in advance.

ankitaprsd · Answer

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

WoundedTiger · Answer

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.

JJSHHShank · Answer

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

Thanks in advance

smitsharma · Answer

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

JJSHHShank · Answer

thanks smitsharma...
overlooked that... always of the notion that the factor doubles and it remains in the exponential form...

guireif · Answer

The question asks "how long it will take for the culture to I NCREASE 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

Raksat · Answer

To understand what the question stem is telling us, let's pick some numbers: the bacteria
culture begins with an initial quantity of I = 100 and increases by a factor of x = 2 every y = 3
minutes.
 
In 3 minutes bacteria population = 2*100
In 6 minutes bacteria population = 2^2*100
.
. 
. 
.
In 3n (t) minutes bacteria population = 2^n*100

n represents the number of growth periods, and n = t/y where t is time in minutes. For example, the
4th growth period in our chart above ended at 12 minutes, and 4 = 12 minutes/3 minutes.
From this example, we can generalize to a formula for the quantity of bacteria, F:
F = I(x)^t/y 
This question asks us how long it will take for the bacteria to grow to 10,000 times their original
amount. In other words, “What is t when F = 10,000 I ?”
F = 10,000 I = I(x)^t/y
10,000 = (x)^t/y
Thus, our final rephrased question is “What is t when 10,000 = (x)^t/y ?”
(1) SUFFICIENT: Note that the yth root of x is equivalent to x to the 1/y power. This statement tells
us that x^1/y = 10. If we plug this value into the equation we can solve for t.
10,000 = (x)^t/y
10,000 =  ^t
10,000 = (10)^t
10^4 = 10^t
t = 4
(2) SUFFICIENT: The culture grows one-hundredfold in 2 minutes. In other words, the sample
grows by a factor of 10^2. Since exponential growth is characterized by a constant factor of growth
(i.e. by a factor of x every y minutes), in another 2 minutes, the culture will grow by another factor of
102. Therefore, after a total of 4 minutes, the culture will have grown by a factor of 10^2 × 10^2 = 10^4,
or 10,000.
The correct answer is D.
OE

Deshnajain · Answer

Simply explained:

Let the number of bacteria initially be N
Given N increases by factor of x every y minutes : 
 Y minutes -> Nx
2Y minutes-> NX^2
3Y Minutes -> NX^3

Statement 1 -> X=10^Y thus:

Y Minutes -> N 10^Y

so for N 10^4 -> Y=4 minutes (Sufficient)

Statement 2 -> When Y=2 , X= 100

2 minutes -> N 10^2
4 minutes -> N 10^4 (Sufficient)

Hence D is the answer

HarshG7 · Answer

i believe there exists some problem in regards to the wordings of the question. I personally faced it. For starters the "increased by a factor of" made me ponder if it is multiplied or being increased by x. Furthermore in the statement 2: "In two minutes, the culture will increase to one hundred times its original size", i was struck at the fact "in two minutes" at first i thought to interpret it as "every two minutes" but later in doubted that contention thinking it would be wrongful to assume so. Or maybe i am just over analyzing

Bunuel · Answer

Bacteria increases by a constant factor of x every y minutes means that  every y minutes, the culture multiplies by x . For example, if x = 2 and y = 1, then every minute the culture doubles: starting from 1, after 1 minute it becomes 2, after 2 minutes it becomes 4, after 3 minutes it becomes 8, and so on.

Now, statement (2) says that in 2 minutes the culture increases to 100 times its original size.  Since the rate is constant , this means that  every 2 minutes the culture multiplies by 100 . So after 2 minutes it is 100 times, after 4 minutes it is 100 * 100 = 10,000 times, and so on.

Check the links to the similar questions given above to practice more such questions.

If a certain culture of bacteria increases by a constant

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If a certain culture of bacteria increases by a constant

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards