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Math Expert V
Joined: 02 Sep 2009
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The population of a bacteria culture doubles every 2 minutes  [#permalink]

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45 00:00

Difficulty:   45% (medium)

Question Stats: 67% (01:33) correct 33% (01:44) wrong based on 966 sessions

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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

Problem Solving
Question: 90
Category: Arithmetic Estimation
Page: 73
Difficulty: 600

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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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5
13
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, whcih is 18 minutes.

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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
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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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
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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2
1
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

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

Originally posted by ankitsachdev on 11 Feb 2014, 01:43.
Last edited by ankitsachdev on 11 Feb 2014, 01:47, edited 1 time in total.
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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2
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).
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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2
4
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

GMAT assassins aren't born, they're made,
Rich
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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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?
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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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,
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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EMPOWERgmatRichC wrote:
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

what I understand is 1000 should not be considered as 'a' ?? But that's the first term as per ques
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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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,
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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[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
solved in 20 secs Intern  B
Joined: 12 Aug 2013
Posts: 45
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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ravisinghal wrote:
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?

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?
Intern  Joined: 10 May 2016
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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ravisinghal wrote:
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?

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
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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Bunuel wrote:
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, whcih is 18 minutes.

Similar questions to practice:
http://gmatclub.com/forum/a-certain-bac ... 44013.html
http://gmatclub.com/forum/it-takes-30-d ... 40269.html
http://gmatclub.com/forum/a-certain-cul ... 52258.html
http://gmatclub.com/forum/the-number-of ... 42858.html
http://gmatclub.com/forum/the-populatio ... 90353.html

how should i know that 2^9 is 512... what if i have no idea about it and what does 500 mean Senior PS Moderator D
Status: It always seems impossible until it's done.
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GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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1
dave13 wrote:
Bunuel wrote:
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, whcih is 18 minutes.

Similar questions to practice:
http://gmatclub.com/forum/a-certain-bac ... 44013.html
http://gmatclub.com/forum/it-takes-30-d ... 40269.html
http://gmatclub.com/forum/a-certain-cul ... 52258.html
http://gmatclub.com/forum/the-number-of ... 42858.html
http://gmatclub.com/forum/the-populatio ... 90353.html

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,
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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ankitsachdev wrote:
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

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

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?
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Posts: 4217
Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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Top Contributor
Bunuel wrote:
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

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!!

Cheers,
Brent
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Re: The population of a bacteria culture doubles every 2 minutes  [#permalink]

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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
_ Re: The population of a bacteria culture doubles every 2 minutes   [#permalink] 07 Jul 2019, 07:51
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