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Word Problem - DS

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Word Problem - DS [#permalink] New post 18 May 2007, 15:03
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How would you solve?

A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed?

(1) Since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.

(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample.
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 [#permalink] New post 18 May 2007, 21:18
Pn = Po (1+100/100)^n = Po (2)^n

From (1)

4Po = Po (2)^n => n = 2
Since this was a 2 hours period, so each cycle happens in 1 hour

Also 4Po - Po = 3750 => Po = 1250

Sufficient to find what the number will be with n = 2 + 4 = 6

So, A
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 [#permalink] New post 21 May 2007, 17:31
(1) Since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.

(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample.

Need 2 more pieces of info to solve problem:
How often does the population double?
What is the pop. size immediately following the doubling of a population?

(1) If there was a quadrupling of the pop. in last 2 hrs, this means that the pop. doubled 2X in that time span - not necessarily meaning that the doubling occurred in 60 min. intervals. Since the frequency of the population's doubling cannot be determined here, this is - INSUFFICIENT

(2) No info on the frequency of the population's doubling - INSUFFICIENT

Try combining:
(1) cells divided 2 hrs ago
4x = x + 3750
3x = 3750
x = 1250

Since the pop. doubled to 1250 cells exactly 2 hrs ago and will multiply 2X to 40k cells in 3 hrs, the frequency is established.

Answer C

Anyone agree??
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 [#permalink] New post 21 May 2007, 20:51
above:

statement one tells us 1: that *two hours ago the cells divided* (so we have a reference point to calculate future divisions- remeber they divide at a constant rate) it goes on to tell us that 2: it has quadrupled in the past two hours since that division, so we know it doubles every hour. it also tells us the amount of the increase due to the quadrupling. I am too tired to calculate the population, but I know this is all the info we need, since they divide at a constant rate, to figure out what the population will be in 4 hours.

statement II: doesn't give us a starting point to figure out how often the cells divide.

so answer is A
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 [#permalink] New post 23 May 2007, 15:20
It's a Manhattan GMAT problem and they actually provide "C" as the answer.
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 [#permalink] New post 24 May 2007, 02:23
Since division occurs at constant interval , I guess A should be the answer. But as mentioned above , C seems to be the correct answer. Any thoughts?
  [#permalink] 24 May 2007, 02:23
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