Antibiotic

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Antibiotic

by N:Dure » Tue Mar 08, 2011 6:34 pm
An antibiotic is added to a culture of bacteria and is found to kill 1/3 of the bacteria in the culture every 30 seconds. If a lab assistant checks the culture after 2 minutes, what fraction of the original bacteria will have been killed?

a) 16/81
b) 8/27
c) 19/27
d) 65/81
e) 80/81

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by 4GMAT_Mumbai » Tue Mar 08, 2011 6:52 pm
Hi,

At start, # of bacteria = x

After 30 seconds, # of bacteria left = (2/3) * x

After 60 seconds, # of bacteria left = (2/3) * (2/3) * x

After 90 seconds, # of bacteria left = (2/3) * (2/3) * (2/3) * x

After 120 seconds, # of bacteria left = (2/3) * (2/3) * (2/3) * (2/3) * x = (16/81) x

Those killed = x - (16/81)x = (65/81) * x

Is it D ? OA please ... Thanks.
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by GMATGuruNY » Tue Mar 08, 2011 6:54 pm
N:Dure wrote:An antibiotic is added to a culture of bacteria and is found to kill 1/3 of the bacteria in the culture every 30 seconds. If a lab assistant checks the culture after 2 minutes, what fraction of the original bacteria will have been killed?

a) 16/81
b) 8/27
c) 19/27
d) 65/81
e) 80/81
We can plug in a value for the bacteria.

Let bacteria = 81.
After first 30 seconds, 1/3*81 = 27 killed, 81-27 = 54 left.
After next 30 seconds, 1/3*54 = 18 killed, 54-18 = 36 left.
After next 30 seconds, 1/3*36 = 12 killed, 36-12 = 24 left.
After next 30 seconds, 1/3*24 = 8 killed, 24-8 = 16 left.
Since only 16 are left, 81-16 = 65 were killed.
Killed/Total = 65/81.

The correct answer is D.
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by N:Dure » Tue Mar 08, 2011 7:57 pm
Alf shokr.