Is there a faster way?

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[email protected]: Master | Next Rank: 500 Posts; Posts: 117; Joined: Mon Oct 27, 2008 5:08 pm; Thanked: 1 times

Is there a faster way?

by [email protected] » Mon Dec 29, 2008 7:23 pm

The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1000 to 500000?

18

Does anyone know a faster way?

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Source: Beat The GMAT — Problem Solving | Mon Dec 29, 2008 7:23 pm

Sachindh: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Wed Sep 17, 2008 8:17 pm; Location: India; Thanked: 4 times

Re: Is there a faster way?

by Sachindh » Mon Dec 29, 2008 7:33 pm

[email protected] wrote:The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1000 to 500000?

18

Does anyone know a faster way?

I dont know it is fast or not but I solved this without paper.

you can interpret this ques as
500000 = 1000( 1 + 2*1 + 2*2*1 + 2*2*2*1 +.. )
500 = (1 + 2 + 4 + 8 + .. till nth minute ) (sum of GP series)
500 = (2^n - 1)/(2-1)
500 = 2^n -1 or 501 = 2^n
now value of n for which 2^n closest to 501 shall be 9 because 2^9=512
Therefore total time shall be 9 times 2 minutes which is equal to 18 mins.

I hope it helps.

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pm; Thanked: 33 times; Followed by:4 members

by vittalgmat » Tue Dec 30, 2008 12:55 am

Whenever we see a problem which has doubling(tripling, multiplying) every x time units, then it implies that the problem is a geometric series problem.
If sum of the geometric series is asked, then use the following formula:

S = a (1 -r^n)/(1 - r)
where
a: starting value
r: common ratio
n: the nth term.

Thanks Sachindh for the nice explanation of the solution.

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vivek.kapoor83: Legendary Member; Posts: 833; Joined: Mon Aug 04, 2008 1:56 am; Thanked: 13 times

by vivek.kapoor83 » Tue Dec 30, 2008 2:06 am

it can be cal verbally , no need to cal and it took me 30 sec approx

current 1000
2000
4000
8000
16000
32000
64000
128000
256000
512000 ----- 9 instance...earc instance 2 mins ...So 9*2 =18mins