Mkappa wrote:
Quote:
You are interpreting this as the first and only doubling period
I am not. I am saying it is a point in time where doubling occurs, however. If it also occurs at the 3hr mark (as the second statement would suggest), then the second statement is sufficient, because you can infer the doubling period as 1 hour.
Quote:
Does it double again at 6:00 pm? Maybe, we don't know.
But we do know, because the destruction occurs
immediately after a doubling!
Here's an example:
Immediately after I take a bite of salad, I take a sip of water (and I never sip water without taking a bite of salad).
I took a bite of salad an hour ago. Right now I am taking a sip of water.
From that you can infer that I have taken a bite of salad just a moment ago (as well as an hour ago, and also that I took a sip of water an hour ago), because I take a sip of water
immediately after a bite of salad. Given these facts, there is not a "we don't know" of whether I took a bite of salad or not.
Quote:
So now I am confused about the usefulness of
MGMAT.
Here, I was just asking a question. Thanks for answering it. You're right that I was being a little too critical.
However, I would appreciate it very much if you could look at what I am actually saying, without making assumptions, and then tell me what you think.
I also appreciate the rest of your advice, but I'm really focusing on the question here.
Dear
Mkappa,
My friend, yes, my fault, you are quite right.
The question explicitly says that the last "doubling" occurs
immediately before the population was destroyed. Let's look careful at the text. I will provide some clock times just to make things clear.
The prompt:
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?OK, let's say right now is 2:00 pm. We know that, at 6:00 pm, there will be a final doubling event, followed immediately by the destruction of the sample. At this point we have absolutely no idea of absolute counts of the cells, and we don't know the doubling period.
I will look only at the second statement, since your question concerns that.
(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample. Now, we know that at 5:00 pm, a doubling event occurred, and after this event, there were 40K cells. We know have pegged an exact count at one point in time. BUT, do we
know the doubling period?
Interpretation #1: The 5:00 pm doubling was the last doubling event until the 6:00 pm event. The doubling period is 1 hour. There will be 80K after the 6:00 pm doubling event.
Interpretation #2: The doubling period is 30 minutes, and so there will doubling events at 5:30 pm and at 6:00 pm. There will be 160K after the 6:00 pm doubling event.
Interpretation #3: The doubling period is 20 minutes, and so there will doubling events at 5:20 pm, 5:40 pm, and 6:00 pm. There will be 320K after the 6:00 pm doubling event.
etc.
It's true that that this statement places a mathematical limit on the doubling period --- for example, the doubling period could not be, say, 45 minutes, because then it couldn't happen at exactly 5:00 pm and exactly 6:00 pm. Nevertheless, the text of the statement does not give us any basis of deciding between these and similar interpretations. The statement literally tells us that there's a doubling event at 5:00 pm, which is one hours before the final doubling event. It doesn't indicate anything about whether other doubling events came between 5:00 pm and 6:00 pm. That's the ambiguity left open by Statement #2, which prevents us from determining a definitive answer to the prompt question. This is why Statement #2 is insufficient.
Does this analysis answer your question about Statement #2?
Finally, my friend, I will apologize about any unwarranted assumptions. I will simply caution you: questions are always fantastic, genuine questions about individual problems or open-ended questions about the quality of a particular company or source, but as soon as you shift from the curious & open question mode to a judgmental & critical mode, especially criticism about a universally respected source, it shifts everything, and at times can obscure the precise content of your question itself. It is a tremendous art to ask excellent questions, an art not to be underestimated, and the skills involved are both cognitive and affective. See:
http://magoosh.com/gmat/2014/asking-exc ... questions/I share this, because it is one of the habits of excellence, and I hope it helps you thrive in all your studies.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)