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# Four hours from now, the population of a colony of bacteria

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Director
Joined: 10 Feb 2006
Posts: 636
Four hours from now, the population of a colony of bacteria  [#permalink]

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04 May 2008, 08:06
Four hours from now, the population of a colony of bacteria will reach
1.28 * 10 ^ 6. If the population of the colony doubles every 4 hours, what was the popluation 12 hours ago?

6.4 * 10 ^ 2
8.0 * 10 ^ 4
1.6 * 10 ^ 5
3.2 * 10 ^ 5
8.0 * 10 ^ 6

NOW = x
4 hours from now = 2x = 1.28 * 10 ^ 6
x = (1.28 * 2 ^ 6 * 5 ^ 6)/2
x = 1.28 * 2 ^ 5 * 5 ^ 6

x/16 = 1.28 * 2 ^ 5 * 5 ^ 6 / 2 ^ 4 = 1.28 * 2 * 5 ^ 6

128/100 * 2 * 5 ^ 6
128 /50 * 5 ^ 6
(64/25) * 5 ^ 6
(64 /5 ^ 2) * 5 ^ 6
64 * 5 ^ 4

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Manager
Joined: 31 Oct 2007
Posts: 112
Location: Frankfurt, Germany

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04 May 2008, 08:15
1
Four hours from now, the population of a colony of bacteria will reach
1.28 * 10 ^ 6. If the population of the colony doubles every 4 hours, what was the popluation 12 hours ago?

6.4 * 10 ^ 2
8.0 * 10 ^ 4
1.6 * 10 ^ 5
3.2 * 10 ^ 5
8.0 * 10 ^ 6

4hrs later - 1.28 * 10^6
Now - 0.64 * 10^6
4hrs ago - 0.32 * 10^6
8hrs ago - 0.16 * 10^6
12hrs ago - 0.08 * 10^6

0.08 * 10^6 = 8/10^2 * 10^6
= 8.0 * 10^4

Ans: B
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Jimmy Low, Frankfurt, Germany
Blog: http://mytrainmaster.wordpress.com
GMAT Malaysia: http://gmatmalaysia.blogspot.com

Intern
Joined: 21 Mar 2008
Posts: 22

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04 May 2008, 08:20
Four hours from now, the population of a colony of bacteria will reach
1.28 * 10 ^ 6. If the population of the colony doubles every 4 hours, what was the popluation 12 hours ago?

6.4 * 10 ^ 2
8.0 * 10 ^ 4
1.6 * 10 ^ 5
3.2 * 10 ^ 5
8.0 * 10 ^ 6

NOW = x
4 hours from now = 2x = 1.28 * 10 ^ 6
x = (1.28 * 2 ^ 6 * 5 ^ 6)/2
x = 1.28 * 2 ^ 5 * 5 ^ 6

x/16 = 1.28 * 2 ^ 5 * 5 ^ 6 / 2 ^ 4 = 1.28 * 2 * 5 ^ 6

128/100 * 2 * 5 ^ 6
128 /50 * 5 ^ 6
(64/25) * 5 ^ 6
(64 /5 ^ 2) * 5 ^ 6
64 * 5 ^ 4

You need to divide the number given by 16. Why 16? Well, you account (2x) for the number itself, and then, 12 hours ago, 12/4 = 3. 2^3 = 8, multiply by the 2 from step one and it's 16.

1.28 / 16 move two decimals over so 128 / 16 = 8 and then it's now 10^4 not 10^6 because you moved those decimals over.
Current Student
Joined: 28 Dec 2004
Posts: 3255
Location: New York City
Schools: Wharton'11 HBS'12

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04 May 2008, 08:51
the question says 4 hours from now..the population is 1.28*10^6...

doubles every 4 hrs..so 12 hours ago..what was the population..well basically we need to go back 16 hours from the 1.28*10^6...

16/4=4...basically 2^4.. 128*10^4/2^4=2^3*10^4 or 8*10^4
Non-Human User
Joined: 09 Sep 2013
Posts: 8462
Re: Four hours from now, the population of a colony of bacteria  [#permalink]

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19 Nov 2017, 02:30
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Re: Four hours from now, the population of a colony of bacteria &nbs [#permalink] 19 Nov 2017, 02:30
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# Four hours from now, the population of a colony of bacteria

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