A scientist is studying bacteria whose cell population : GMAT Data Sufficiency (DS)
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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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22% (02:32) correct 78% (01:49) wrong based on 81 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
[Reveal] Spoiler: OA
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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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Re: A scientist is studying bacteria whose cell population [#permalink]

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19 Aug 2013, 11:19
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   [#permalink] 20 Aug 2013, 00:46
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