A scientist is studying bacteria

[Ruben]

Hi Stacey,

I couldn't understand why the statement number one is not sufficient. The statement (1) AND (2) SUFFICIENT: Statement (1) indicates that the cells divided two hours ago. Let x equal the population immediately after that division and 4x the population after two hours

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.

[RonPurewal]

Hi -

The reason statement #1 is insufficient is that we are not told that another division has JUST occurred. So there is a range of possibilities:
* One possibility: The population JUST divided again NOW, meaning that the population divides every two hours. Therefore there will be 2 more divisions before the sample is destroyed.
* Another possibility: The population divided again a half-hour ago (every 1.5 hours). Therefore, there will be three more divisions before the sample is destroyed.
* Another possibility: The population divided again 48 minutes ago (every 1.2 hours). Therefore, there will be four more divisions before the sample is destroyed.

Notice that the possibilities are restricted by the fact that an integer # of divisions must occur in six hours (we know that a division occurred two hours ago, and we also know that one will occur 4 hours in the future).

One thing I don't like about this question is the phrase 'Since the population divided two hours ago' - to me, it isn't clear whether this population count refers to the population immediately BEFORE that division* or to the population immediately AFTER that division. The wording should therefore be changed to 'Since the time immediately before the population divided 2hrs ago' (in the former case), or to 'Since the time immediately after the population divided 2hrs ago' (in the latter case). I will address this problem.

*This is the assumption behind your answer, and therefore behind my explanations.

[Ruben]

Thank you Ron!

[SRIKANT]

Ron, I think question is clear. In fact after reading your explanation I understood the flaw in my answer.

Question clearly mentions that "Since the population divided two hours ago, the population has quadrupled." This quadruple means that population has doubled 2 times in last 2 hours "after the population divided 2 hours ago." Therefore there are only 2 possibilities.
Either it got divided at every 1 hour or every 45 minutes as there is one division happening exactly 4 hours from now (this statement plays a big role in making the intervals divided in such a way that in 6 hours division happens at the ends also i.e. at the beginning and at the end, and of course there cannot be more than 2 divisions within 2 hours excluding the one in the beginning!).

[StaceyKoprince]

We had some debates about this one as it was going through committee - some people thought the wording was too ambiguous and some people thought it was just ambiguous enough to make it a nice hard question. I'm sure GMAC has these debates on questions sometimes, too! :)

[vietst]

I think it is clear and very nice question.

[StaceyKoprince]

It's a nice, challenging question, yes - I agree!

[asharma8080]

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) The population just divided and, 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.

So, I came across this thread as I google searched the responses on this one...

Is the answer Not A? The official answer in MGMAT is A.

Given: The population doubles at constant intervals and immediately divides. So essentially the population goes 2x and then +2x again.

Now, the question is asking what is the population after 4 hours when the bacteria is destroyed. The moment in time when the bacteria is destroyed is right after it doubles (Not divides). So we need to know what was the population after the doubling at 4 hours. To figure this out, we need to know what was the rate of doubling and a previous population.

1) Statement 1 says the bacteria just divided
This means that if we had a chart like this
-2h = x
-1h
Now = 4x
1h
2h
3h
4h

Given that x + 3750 = 4x
x = 1250

Now, we know the population is 1250 at -2h, and 4x at at Now, so the population is doubling every hour?

-2h = x
-1h = 2x
Now = 4x
1h = 8x
2h = 16x
3h = 32x
4h = 64x

Therefore, 4 hours from now it will be 64 x ???
But that still does not give us what the doubling rate is. This is where I get stuck...How do I calculate the rate of doubling (not dividing) from this information?

[jnelson0612]

Please see my explanation on this thread and let us know if we can help further: a-scientist-is-studying-bacteria-t11381.html

[nocheivyirene]

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.

1. We know that the bacteria doubles but we don't know how frequently, every year, every hour, every minute. We also don't know the last cell population before it doubles.
2. Test STATEMENT 1: 4x = x + 3750 This will help us calculate the last cell population and thus, the quadrupled value. SUFFICIENT!
3. Test STATEMENT 2: We know that x became 40,000. Then it says there is one hour remaining. Perhaps, there is time to double again. Perhaps, there is not. INSUFFICIENT!

Answer: A

[jlucero]

Correct.

[anna.chaldysheva]

3. Test STATEMENT 2: We know that x became 40,000. Then it says there is one hour remaining. Perhaps, there is time to double again. Perhaps, there is not. INSUFFICIENT!

Answer: A

I just ran into this question and i don't understand why the second statement is insufficient.

the question stem says: Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample.

I understood this to mean that the population DEFINITELY will double exactly 4 hours from now, we just don't know how many times it will double before that and what the number of cells in population will be when scientist discards the bacteria.
Therefore i thought the second statement meant that 3 hours from now the population will double to 40k. (and since we know that 4 hrs from now bacteria will double again, the information is sufficient to determine that the population will contain 80k cells after 4 hours.)

The answer key and this thread say statement 2 is NOT Sufficient. Could someone please clarify why not.

[RonPurewal]

statement 2:
you're correct that the population will reproduce itself at t = 3 hours and also at t = 4 hours.
however, you're assuming, without justification, that no additional reproduction will occur BETWEEN these two times.

e.g., there's no reason why the bacteria couldn't reproduce every half-hour, or every 1/3 hour, or ... any 1/n hour, for whatever integer n.
thus the population could be 80,000 cells. but it could also be 160,000, or 320,000, etc.

[RonPurewal]

i'm going to lock this thread, since it's unnecessarily confusing: it includes both older and newer versions of the same problem.

if anyone has further questions about the currently existing version of this problem, please start a new thread. thanks.