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

Question

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

Bunuel · Accepted Answer

SOLUTION

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

\(1000 * 2^t = 500,000\);

\(2^t = 500\).

Since \(2^9 = 512\), then \(t\approx{9}\). Thus, approximately 9 two-minute intervals are needed, which is 18 minutes.

Answer: E.

Similar questions to practice:
https://gmatclub.com/forum/a-certain-ba ... 44013.html
https://gmatclub.com/forum/it-takes-30- ... 40269.html
https://gmatclub.com/forum/a-certain-cu ... 52258.html
https://gmatclub.com/forum/the-number-o ... 42858.html
https://gmatclub.com/forum/the-populati ... 90353.html

_________________

New to the GMAT Club?

Question Bank

Bunuel's Signature Collection

Reading Comprehension

Ultimate Quant Guide

All You Need for Quant

Quantitative

Verbal

Signature Read More

BrentGMATPrepNow · Answer

When we scan the answer choices (ALWAYS scan the answer choices BEFORE deciding on the approach you'll take), we see that the number of population "doublings" will be between 5 and 9. 
Given these relatively small values, we might solve this question by creating a  growth table

MINUTES ELAPSED | POPULATION  
0 | 1,000
2 | 2,000
4 | 4,000
6 | 8,000
8 | 16,000
10 | 32,000
12 | 64,000
14 | 128,000
16 | 256,000
18 | 512,000 DONE!!

Answer: E

Cheers,
Brent

ankitsachdev · Answer

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 P o  be the Original Population of bacteria. = 1,000
Let P n  be the Final Population of bacteria. = 500,000

Therefore

P n = P o *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

liranmaymoni · Answer

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

Donnie84 · Answer

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).

EMPOWERgmatRichC · Answer

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:  E

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

ravisinghal · Answer

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?

EMPOWERgmatRichC · Answer

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

ravisinghal · Answer

can you please elaborate?

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

EMPOWERgmatRichC · Answer

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

Himanshu9818 · Answer

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

ravisinghal · Answer

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?

UttamGiet · Answer

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

dave13 · Answer

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

and what does 500 mean

Gladiator59 · Answer

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

sviral90 · Answer

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?

kavach · Answer

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 
_

afra94 · Answer

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?

EMPOWERgmatRichC · Answer

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

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

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

GMAT Problem Solving (PS) Questions

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

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