The population of a bacteria culture doubles every 2 minutes. Approxim

Solution =

Let x be the total number of minutes. As the population doubles every 2 minutes, the number of times population doubles is \(y = \frac{x}{2}\)
Let Po be the Original Population of bacteria. = 1,000
Let Pn be the Final Population of bacteria. = 500,000

Therefore

\(Pn= Po*2^y\)
\(500000 = 1000 * 2^y\)
\(500 = 2^y\)
\((4*125) = 2^y\)

As 125~128

\((4*128) = 2^y\)
\((2^2*2^7) = 2^y\)
\((2^9) = 2^y\)
\(9 = y\)
\(\frac{x}{2} = 9\)
\(x = 18\)

Answer = E

The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?

(A) 10
(B) 12
(C) 14
(D) 16
(E) 18

Lets say t is th number of times the population needs to grow
The question is \(1000*2^t=500000\)
Or \(2^t=500\)
2^6=64
2^7=128
2^8=256
2^9=512 BINGO.

So it needs to grow 9 times. If it grows every 2 min so \(9*2=18\)

Ans is E

We can ignore the thousands. So, basically, we are left with 1 and 500. Since, 2^9 = 512, approx minutes = 9*2 = 18. Answer (E).

Hi All,

This prompt can be solved with a bit of "brute force" - you can essentially "count doubles" and find the answer. This method is probably faster than any other approach that you might take. You can even speed up by ignoring the last 3 zeroes.

1k
becomes
2k
4k
8k
16k
32k
64k
128k
256k
512k

9 "doubles" at 2 minutes each = about 18 minutes

Final Answer:

GMAT assassins aren't born, they're made,
Rich

I am confused here slightly ...

If I try to solve the question GP way, I get slightly different answer :-

r = 2 ( as it doubles every 2 mins)
a = 1000
nth term = 500,000

ar^n-1 = 500,000
1000 * (2)^n-1 = 500,000
2^n-1 = 500
n-1 = 9
n = 10

and since in every 2 mins it gets doubled ..therefore 2* 10 = 20 mins.

Where am I going wrong?

Hi ravisinghal,

It looks like your work includes all of the terms (and it "counts" the 1st term, when that is technically the 'starting' term - so it should NOT be counted).

GMAT assassins aren't born, they're made,
Rich

can you please elaborate?

what I understand is 1000 should not be considered as 'a' ?? But that's the first term as per ques

Hi ravisinghal,

The question asks approximately how many minutes it takes for that increase to happen. If you START with 1,000 then no time has passed yet. If you're going to approach the question in the way that you did, then you can't include that first term since it requires NO time.

GMAT assassins aren't born, they're made,
Rich

[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?

(A) 10
(B) 12
(C) 14
(D) 16
(E) 18


2^9*1000=512000
answer 18 minutes.
solved in 20 secs

Bunnuel,

I am still not happy with the explanation provided on why the above calculation is wrong? please help.

GP starts with 1000 and last term is 500,000.Therefore a has to be 1000 ..I don't understand why this should not be counted?

Dear Ravi, u are right on your approach...
According to GP way 10th term would be 512000
So between 1st and 10th term there are 9 intervals of 2 min each means 18 Min

Ans : 18 Min E

how should i know that 2^9 is 512... what if i have no idea about it

and what does 500 mean

Hey dave13,

remembering certain powers of 2 can be very helpful ( and easy !)

You can start with 2^10 = 1024 ( or 1 MB - from data storage devices.. as all data storage devices have capacity in powers of 2 *fun fact* )

From here it is easy to get to other powers as we can always round off to nearest number of 1000.

Such numbers almost always arise in geometric series ( which this Q is an example of ).

Best,
Gladi

My understanding was that to find Tn in case of geometric progression was a*r^n-1
Accordingly, 500=2^n-1
So, n-1 =9
So n=10
Can you point out where am I making a mistake?

The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria?

(A) 10
(B) 12
(C) 14
(D) 16
(E) 18

Let's say t is the number of times the population needs to grow
The question is 1000∗2t=5000001000∗2t=500000
Or 2t=5002t=500
2^6=64
2^7=128
2^8=256
2^9=512 BINGO.

So it needs to grow 9 times. If it grows every 2 min so 9∗2=189∗2=18

Ans is E
_

I tried to solve this using geometric progression formula of AR^n-1 = d, after which I am getting n-1 as approximately 9. So, n is approximately 10. Could you please help me understand how this question is different from a geometric progression/sequence question?

Hi afra94,

Your question is actually answered in bits-and-pieces earlier in this thread, but the simple answer is that since you START with 1,000 then no time has passed yet (meaning that you shouldn't include that first number in your sequence since it requires NO time to pass). This IS technically a Geometric sequence (since each term is fixed multiple of the number that immediately comes before it in the sequence), but you have to adjust your work to account for what the question actually asks for. Here, it takes 9 two-minute 'steps' (NOT 10) to go from 1,000 to approximately 500,000 - and since the question asks for the total number of MINUTES involved, the answer is (9)(2) = 18.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com