A scientist is studying bacteria whose cell population doubles at

Question

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

mikemcgarry · Accepted Answer

I'm happy to help with this. :-)

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? We know destruction is four hours from now. We don't know either (a) the number of cells, i.e. the size of the population, either now or at any point in time, or (b) the period of doubling, the size of the "constant interval". Both these must be ascertained to answer the prompt question. (1) The population just divided and, since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells. Since the division two hours ago and the division just now, the population quadrupled -- that's two doubling periods, so each doubling period is about an hour. That's piece (b). Since two hours ago, it quadrupled, increasing by 3,750 ---- this means 3750 is three times what it was two hours ago. We don't need to calculate, but this means we could figure out how much there was two hours ago, how much now, and therefore how much four hours from now. This statement, alone and by itself, is sufficient . (2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample Well, now we have an (a) piece of information, a population at one point in time, but we know nothing about the doubling interval, and without that, we cannot answer the prompt. This statement, alone and by itself, is insufficient . Answer = A Does all this make sense? Mike :-)

mikemcgarry · Answer

Dear Mkappa , I'm happy to respond. :-)

First of all, I believe you are interpreting the first quote incorrectly. The stem indeed says Four hours from now, immediately after the population doubles , the scientist will destroy the entire sample . You are interpreting this as the first and only doubling period, which is not justified by the context. Let's say, right now, it's 2:00 pm. Let's say that the doubling period is every 30 minutes. That means it will double at 2:30 pm, then at 3:00 pm, etc. It will double at 5:30 pm, and the scientist will destroy the sample at six, but this statement explicitly lets us know that the destruction at 6:00 pm will take place after the doubling at 6:00 pm. In other words, the amount destroyed at 6:00 pm is the amount after the 6:00 doubling, not the amount after the 5:30 doubling. That was a potential ambiguity in the statement, and the MGMAT folks wisely clarified this subtle point with this statement. You are also misinterpreting the second statement you quote: The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample . Say, the time of destruction is 6:00 pm. Say, there's a doubling event at 5:00 pm, and after this doubling event, there 40,000 cells. Does it double again between 5:00 pm and 6:00 pm? Maybe, we don't know. Does it double again at 6:00 pm? Maybe, we don't know. Does it double more than once between 5:00 pm and 6:00 pm? Maybe, we don't know. We can't infer the doubling period from this statement. My friend, I gather that you are a non-native English speaker, and it's perfectly understandable that the sophisticated and subtle wording of a word problem confuses you. It's important to be patient with yourself as you learn. I will suggest this blog: https://magoosh.com/gmat/2014/how-to-imp ... bal-score/ I want you to consider something very important. GMAT Club is a public forum, so anyone could see your words here. Other readers of GMAT Club now might one day be your boss, your co-worker, your business partner, your customer, your supplier, your consultant, etc. You never know where you meet some of these people again in the business world. It's very important to focus on making a very good first impression: psychologist tell us of the tremendous power of first impressions, and you never get another chance once you made one. In your post, you were very critical of MGMAT: So now I am confused about the usefulness of MGMAT. Plus it has some nonsense questions where non-convex polygons come into play . Professionally, the MGMAT folks are competitors of my company, Magoosh, but I will unreservedly say that MGMAT is one of the best GMAT prep companies in existence. Those people at MGAMT are truly brilliant individuals and wonderfully gifted teachers. They command universal respect in the GMAT preparation space. You misunderstood some of the statements in this question, but rather than assume that perhaps your reading was not perfectly correct, you immediately went to criticism and blame. To be honest, my friend, this does not make you look good: it does not look good at all when you misinterpret a shortcoming on your own part as a reason to blame somebody who is widely held in respect. I am telling you this, because I want you to be successful. I want you to make a good impression on others professionally and have a wonderfully prosperous career. Especially when you are in the position of a student, humility and cautious questioning go a lot further than automatically criticizing and blaming. It's somewhat anti-intuitive, but genuine humility can allow you to go very far in the business world: in many ways, for example, Warren Buffet is a genuinely humble man, and he's one of the richest men in the world. My friend, I hope you understand that I am pointing out this difficult things precisely because I want to see you thrive and be successful in all aspects of your business school application and your business career. Sincerely, Mike

mun23 · Answer

Hi mikemcgarry thanks a lot.wonderful explanation......... :lol:

Mkappa · Answer

The OA doesn't make any sense, because the stem states:

That means the population doubles at the 4 hour mark. So, from the second statement:

We can infer that the doubling period is 1 hour.

So now I am confused about the usefulness of MGMAT. Plus it has some nonsense questions where non-convex polygons come into play.

Mkappa · Answer

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.

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.

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.

mikemcgarry · Answer

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: https://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 :-)

Mkappa · Answer

Thanks for your patience, Mike! I understand that I was misinterpreting it.

dimson · Answer

Hi Michael,

Could you please provide a numerical example and explanation for (1)?

I failed to understand this part  "The population just divided and, since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells. 
Since the division two hours ago and the division just now, the population quadrupled -- that's two doubling periods, so each doubling period is about an hour. That's piece (b). 
Since two hours ago, it quadrupled, increasing by 3,750 ----  this means 3750 is three times what it was two hours ago . We don't need to calculate, but this means we could figure out how much there was two hours ago, how much now, and therefore how much four hours from now. "

Quadrupled means - 4 times as great, so i assumed that if 3750 is not divisible by 4, then the answer can not be found.

at 1h ....
at 2h the population is x+937.5 
at 3h the population is x+1875 
at 4h the population is x+3750

Because the population doubles at constant intervals, it means that the population will quadruple in exactly 2hours. In other words, doubling period is about 1hour.

I cant understand where i am going wrong. Please help.

Thank you.

mikemcgarry · Answer

Dear dimson , I'm happy to respond. Please call me "Mike."

There is a subtle idiomatic issue that I believe is causing the confusion. Consider these two statements. (a) By the end of 2017, the population increased to 50,000. (b) By the end of 2017, the population increased by 50,000. Those two mean very different things. Sentence (a) is giving us the final amount, the end result. It's telling us that, at the end of 2017, the size of the population was 50,000. Sentence (b) is giving us something very different. It is tell us the increase, the change in population. This one tells us that, before some unspecified start time, there was some "beginning" value of the population--call it P--and by the end of 2017, the new value for the total number in the population is (P + 50,000). Version (b) is simply telling us the size of the change, but without more information, we won't be able to calculate the total value right now. In this problem, Statement #1 says: The population just divided and, since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells. In other words, two hours ago, before that doubling period, the population was x now, after that doubling and this one, the population is 4x this value, 3750, is the amount of change: 4x - x = 3x thus, 3x = 3650 Does all this make sense? Mike

thejosem · Answer

mikemcgarry

This all makes sense, but how do we know that the period mentioned in Statement 1 refers to period 3? How do we know it does not take place in period 4?

In the examples below, both change by 3750 from 2 periods ago: 
- Pd 3 example: hour 3 vs hour 1 
- Pd 4 example: hour 4 vs hour 2

We could stretch this out back to period zero as well. Thoughts?

Hour 1 Hour 2 Hour 3 Hour 4
Pd 3 1250 2500 5000 10000
Pd 4 625 1250 2500 5000

mangamma · Answer

OFFICIAL EXPLANATION

We need two additional pieces of information to solve this problem, which can be rephrased as "How frequently does the population double, and what is the population size at any given time immediately after it has doubled?"

(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) = 3,750
Population (Now) = 4·Population (2 hours ago)

Substituting, we get 4·Population (2 hours ago) – Population (2 hours ago) = 3,750
Population (2 hours ago) = 1,250.
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.

(2) INSUFFICIENT: This statement does not give any information about how frequently the population is doubling.

The correct answer is A.

A scientist is studying bacteria whose cell population doubles at

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A scientist is studying bacteria whose cell population doubles at

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