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# A scientist is studying bacteria whose cell population

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

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01 Jul 2008, 13:32
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95% (hard)

Question Stats:

24% (01:56) correct 76% (01:58) wrong based on 88 sessions

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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.

DISCUSSED HERE: collection-of-12-ds-questions-85441-20.html#p646479
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01 Jul 2008, 13:40

given: population double every constant time interval.
1) population has quadrupled (double * double) in last two hours. => popuoation doubles every hr
lets say original population was x then now it is x+3750
and 3x=3750
therefore current population = 3750*4/3
hence the current population is know at the time interval when it double is known=1hr
therefore we can guess the population after 4hrs

2) if the population doubles 1 hr before the destruction then the constant time interval at which population increases is 3hr.
so the next split would be after 6hrs.... but the destruction was to happen aftr 4hr???
there is a contradiction over here. and hence we should ignore point (2

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01 Jul 2008, 13:56
agree with A. I misinterpreted condition 1 again ...
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01 Jul 2008, 14:00
maratikus wrote:
agree with A. I misinterpreted condition 1 again ...

actually don't agree. what if interval is 45 min -> condition 1 still holds but results are going to be different
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01 Jul 2008, 14:06

1) number of bacteria two hours ago was 1,250 and interval c: c > 2/3 and c <=1 -> insufficient
2) bacteria doubles at 3 hours, the number is equal to 40,000 -> insufficient

1&2: since bacteria doubles 2 hours before 0 and 3 hours after 0 -> 5*c = integer -> c = integer/5

since 40,000/1,250 = 32 = 2^5 -> bacteria doubled 5 times in 5 hours -> c = 5 -> sufficient
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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
1
2
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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Re: A scientist is studying bacteria whose cell population doubles at cons  [#permalink]

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16 Nov 2011, 02:42
2
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

Cheers!
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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
1
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  [#permalink]

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19 Aug 2013, 11:19
1
Question mentions about events 2 hours ago, now, and 4 hours from now… So the total time we’ll consider here will be 6 hours

(1) Let population 2 hours ago be P.

Population increases by 3750 and becomes 4 times in last 2 hours. (But we don’t know exactly when it divided)

4P = P + 3750
P = 1250
And, 4P = 5000

This means the population after 2 hours have passed is 5000.

Can we find how much the population will be in next 4 hours? No we can’t; Because we don’t know whether the population doubles every 0.5 hours, 1 hours, 2 hours, etc.

Insufficient.

(2) With 1 hour remaining, it means it’s been 6 – 1 = 5 hours.

In 5 hours, the population is 40000.

Can we find how much the population will be in next 4 hours? No we can’t; Because we don’t know whether the population doubles every 0.5 hours, 1 hours, 2 hours, etc.

Insufficient.

Consider 1 and 2 together.

In 2 hours, population = 5000
…..
…..
In 5 hours, population = 40000

And we know that the population always doubles. It never becomes 1.2 or 1.5 times. It ALWAYS becomes 2 times.

Using this information, can we fill in the blanks above?

Yes we can,

In 2 hours, population = 5000
In 3 hours, population = 10000
In 4 hours, population = 20000
In 5 hours, population = 40000

This shows that the population doubles every 1 hour.

So in 6 hours (before the sample is destroyed), population will be 2 * 40000 = 80000.

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

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19 Aug 2013, 17:20
A
two hrs ago 1250 ....now 5000...as the ques says it doubles at constant time period....
if it has bcum 4 times in two hrs means it doubles every hour
so aftr 4 hr 5000 *2^4+= 80,000- SUFFICIENT
B
only tells the number of cell after 3 hrs ....the rate at wich it doubles no info-insuffcient

ANS is A
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Re: A scientist is studying bacteria whose cell population  [#permalink]

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19 Aug 2013, 17:26
ashishbakshi9 wrote:
Question mentions about events 2 hours ago, now, and 4 hours from now… So the total time we’ll consider here will be 6 hours

(1) Let population 2 hours ago be P.

Population increases by 3750 and becomes 4 times in last 2 hours. (But we don’t know exactly when it divided)

4P = P + 3750
P = 1250
And, 4P = 5000

This means the population after 2 hours have passed is 5000.

Can we find how much the population will be in next 4 hours? No we can’t; Because we don’t know whether the population doubles every 0.5 hours, 1 hours, 2 hours, etc.

Insufficient.

(2) With 1 hour remaining, it means it’s been 6 – 1 = 5 hours.

In 5 hours, the population is 40000.

Can we find how much the population will be in next 4 hours? No we can’t; Because we don’t know whether the population doubles every 0.5 hours, 1 hours, 2 hours, etc.

Insufficient.

Consider 1 and 2 together.

In 2 hours, population = 5000
…..
…..
In 5 hours, population = 40000

And we know that the population always doubles. It never becomes 1.2 or 1.5 times. It ALWAYS becomes 2 times.

Using this information, can we fill in the blanks above?

Yes we can,

In 2 hours, population = 5000
In 3 hours, population = 10000
In 4 hours, population = 20000
In 5 hours, population = 40000

This shows that the population doubles every 1 hour.

So in 6 hours (before the sample is destroyed), population will be 2 * 40000 = 80000.

Isnt the first statement enough to tell us that the population
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Re: A scientist is studying bacteria whose cell population  [#permalink]

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20 Aug 2013, 00:46
DISCUSSED HERE: collection-of-12-ds-questions-85441-20.html#p646479
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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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