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# A scientist is studying bacteria whose cell population doubles at cons

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A scientist is studying bacteria whose cell population doubles at cons [#permalink]

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15 Nov 2011, 14:39
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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.
[Reveal] Spoiler: OA

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Re: A scientist is studying bacteria whose cell population doubles at cons [#permalink]

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16 Nov 2011, 02:42
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Here's the explanation.

We're told that the population doubles after a certain interval of time. So until that time is reached, the number of bacteria remain the same as it was at the start.

Statement 1 says that since the population divided two hours ago, the population has quadrupled increasing by 3750 cells.
Let's assume that the number of cells two hours ago was 'x'. Since this number quadrupled after 2 hours, the number of cells currently would be 4x.
We are told that the difference in the number of cells is 3250 cells. i.e. 4x - x = 3750
i.e. 3x = 3750
so x = 1250.

Using this, we can calculate the number of cells that would be present. Since the cells quadruple in 2 hours, 4 hours from now, it would be 16 times the number as it is now.
hence statement 1 is sufficient.

Statement 2 says that the population will double to 40000 with one hour remaining i.e. after 3 hours, the population will be 40000. So we can definitely say that the population will double again after the next 3 hours.
So, 4 hours from now, the population will still be 40000, which is the required number.
Hence this statement is sufficient by itself.

Hence the answer is option D.

The solution to this problem depends on the understanding that the cells won't double until and unless a specific amount ot time has passed. For e.g. say the number of cells at 07:00 AM is 1000 and the cells split/double in every 2 hours, then the number of cells will become 2000 only at 09:00 AM. This means that the number of cells will remain 1000 until 08:59:59 AM.

Hope this helps

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Re: A scientist is studying bacteria whose cell population doubles at cons [#permalink]

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16 Nov 2011, 07:23
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Given
Four hours from now, the population will double and then be destroyed immediately.

Statement 1
SUFFICIENT: If the population quadrupled during the last two hours, it doubled twice during that interval, meaning that the population doubled at 60 minute intervals. Since it has increased by 3,750 bacteria, we have:

Population (Now) – Population (2 hours ago) = 3750
Population (Now) = 4·Population (2 hours ago)

Substituting, we get 4·Population (2 hours ago) – Population (2 hours ago) = 3750
Population (2 hours ago) = 1250.
The population will double 6 times from that point to 4 hours from now

Population (4 hours from now) = (2^6)*1,250=80,000.

Statement 2
One hour before it is destroyed (or, in other words, three hours from now), the population will double to 40,000 cells. We need to determine the population from the sample at the time it is destroyed.

3 hours from now--population will double to 40,000
4 hours from now--population will double again then be destroyed

It's possible that the population doubles every hour, thus at 4 hours from now the population would be 80,000. But it is possible that the population doubles every half hour.
We could have:
3 hours from now--population will double to 40,000
3.5 hours from now--population will double to 80,000
4 hours from now--population will double to 160,000 and be destroyed.

So we can't obtain the exact number of bacteria before it is destroyed and Statement 2 is Insufficient.
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Re: A scientist is studying bacteria whose cell population doubles at cons [#permalink]

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16 Nov 2011, 08:49
it is only A

1 is sufficient as from the explanation above

2 is not sufficient because we only know the statistics till 3rd hour and but the bacteria is always destroyed at the end of 4th hour and we don't know what is the exact count of bacteria between 3rd and 4th hour so we cannot get the exact count, so 2 not sufficient

Plz correct me if i am wrong.
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Re: A scientist is studying bacteria whose cell population doubles at cons [#permalink]

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17 Nov 2011, 21:39
looks like the OA is wrong here. The question has been discussed before. Please find bunnel's solution to the prob:

Quote:
I think this one was the toughest. I've already given the solution for this one previously, so here it is:

Before considering the statements let's look at the stem:
A. Population doubles at constant intervals, but we don't know that intervals.
B. Experiment will end in 4 hours from now.
C. We don't know when bacteria divided last time, how many minutes ago.

(1) Population divided 2 hours ago and increased by 3750 cells. Note that this statement is talking that bacteria quadrupled during 2 hours before NOW. So, starting point 2 hours ago, end of experiment 4 hours from now. Total 6 hours.
This statement gives ONLY the following info:
A. population of bacteria TWO hours ago - 1250.
B. population of bacteria now - 5000.

But we still don't know the interval of division. It can be 45 min, meaning that bacteria divided second time 30 min ago OR it can be 1 hour, meaning that bacteria just divided. Not sufficient.

(2) An hour before the end of experiment bacteria will double 40.000. Clearly insufficient.

(1)+(2) We can conclude that in 5 hours (2 hours before now+3 hours from now) population of bacteria will increase from 1250 to 40.000, will divide 5 times, so interval is 1 hour. The population will contain 40.000*2=80.000 cells when the bacteria is destroyed. Sufficient.

The point is that from (1) we can not say what the interval of division is, hence it's not sufficient.
Please, tell me if you find this explanation not convincing and I'll try to answer your doubts.

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Re: A scientist is studying bacteria whose cell population doubles at cons [#permalink]

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15 Jan 2018, 08:48
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Re: A scientist is studying bacteria whose cell population doubles at cons   [#permalink] 15 Jan 2018, 08:48
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# A scientist is studying bacteria whose cell population doubles at cons

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