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# A scientist is studying bacteria whose cell population

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Senior Manager
Joined: 21 Jun 2006
Posts: 282
A scientist is studying bacteria whose cell population [#permalink]

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16 Jun 2007, 20:20
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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.
VP
Joined: 10 Jun 2007
Posts: 1439

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16 Jun 2007, 21:07
ArvGMAT wrote:
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.

Time,Quantity
0,x
t,2x
t+4,?

t = time which the quantity doubles

Find "?"

(1) Time, Quantity
t, x
t+2, 8x

We can find x by 8x - x = 3750. We also know that the amount doubles every hour since it is at constant rate and @t, quantity = x and @t+2, quantity = 8x; thus, @t+1, the quantity must be 4x. Therefore, we can find the amount at t+4. SUFFICIENT.

(2) Time,Quantity
0, x
t+3, 40,000
t+4, ?

We don't really know the amount at t+4 becasue the statement doesn't say when the amount divided, unlike statement 1. INSUFFICIENT.

My answer is A, but I want to know the OA...What is it?
Senior Manager
Joined: 21 Jun 2006
Posts: 282

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16 Jun 2007, 21:24
C
both are sufficient

A is insufficient because it does not give info about frequency for eg. it can double every 45 mins or 50 mins
B gives nothing about frequency but says that pop. is 40000 , 3hrs from now.

A & B give
A -----> x =1250 (population 2 hrs back)
B ------> x= 40000 (pop 4 hrs from now)
40000/1250=32=2^5
5 divisions in 5 hrs, which is population doubling every 60 minutes
VP
Joined: 10 Jun 2007
Posts: 1439

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16 Jun 2007, 21:26
Thanks. This was hard for me...confusing wording.
Director
Joined: 13 Mar 2007
Posts: 543
Schools: MIT Sloan

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16 Jun 2007, 22:05
ARV,

The Q says - each cells divides 'simultaneously' and the population doubles at constant intervals.

This means - if at time t, the pop is X, at time t+k, the pop instantaneously becomes 2X - i.e there is no linear increase in pop between t and t+k ('simultaneously')

If the above is right, then isnt A alone sufficient ?

at t = 2X
and now at t+2 = 4x ! so interval = 2hrs hence SUFF

so what is it I am missing here ?
Senior Manager
Joined: 21 Jun 2006
Posts: 282

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16 Jun 2007, 22:23
I think you are getting confused with the wording, just as I did.
It took me a few minutes to grasp the underlying meaning of the problem.

Let's analyze the sentence -
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?

fours hours from now, population doubles
that could mean that the interval was anything 1hr, 45 mins, 2 hrs, etc.

now since 2 hrs back the population has quadrapled, but it does not mean that the population quadrapled RIGHT now. it could have quadrapled 30 mins back and still be at the same population.

for eg.
2 hrs back pop = x
75 mins back pop = 2x (assuming 45 min interval)
30 mins back pop = 4x
0 mins(current) pop = 4x still
15 mins forward pop = 8x etc.
60 mins forward pop = 16x
similarly, 4 hrs forward pop = 256x (i.e has just doubled)

or interval could be 1 hr
2 hrs back pop = x
60 mins back pop = 2x
0 mins(current) pop = 4x
60 mins forward pop = 8x

so, even with statement one, there are two cases at least.
Hope it is clear.
16 Jun 2007, 22:23
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