Help me (with your math genius) to do the least amount of prep possible for this exam!

June 10, 2010 2:12 AM

I have a list of 10 questions to help prepare for an exam. Of these 10 questions, 6 will be selected for the exam paper. Of the 6 on the exam paper I need to choose 3 to write an essay on. How many do I ACTUALLY need to research to be okay on the day?

Okay, so I have an exam next week. For the exam I need to write 3 essays.

We have been given a list of 10 questions to help prepare. Of these 10 questions, 6 will be selected for the exam paper. Of the 6 on the exam paper I need to choose 3 to write an essay on.

My question is: how many of the original 10 questions do I need to study up on, to ensure that I have covered at least 3 out of the 6 that will be included on the paper.
Those numbers again:
10 possible qns
6 included on paper
3 to write about

I am sure there is some (very simple) formula to work this out but it is breaking my brain!

posted by nothing too obvious to grab bag (8 answers total)

Assuming you don't study them all, but you study just enough to cover 3 of the 6 that are used in the exam (as you hope to), the most questions you can get out of the 6 that do come up that you haven't studied is 3. If 4 questions come up that you haven't studied, you can only do 2 of the 6, so you're screwed.

Therefore the maximum number of questions from the original 10 that you can skip is 3, and you have to study at least 7 of the original 10.
posted by EndsOfInvention at 2:17 AM on June 10, 2010

EndsOfInvention is right. Think of worst possible scenario, and how to avoid it. Worst case is you waste four of the questions you studied on the four that aren't shown. So you need those four plus three of those on the exam. That makes seven.
posted by kingjoeshmoe at 2:21 AM on June 10, 2010

If you are okay with a passing (50%) grade,then you need to:

Study 7 of the 10 possible questions

In Exam:
3-6 of the questions you've studied will be on the 6-question exam

mark:

Assuming you got 100% on the three relevant questions you studied, you'll get 60%.
Because, however, it is unlikely you will get 100% on the only three questions you studied (and were asked), you'll likely get less than 60% on those three questions but perhaps will gain a few percentages on other questions that were asked that DID his your study program.

Good luck!
posted by salmonking at 2:23 AM on June 10, 2010

Seven. The first 4 you revise might not be on the paper so you need to do another three to give you a 100% chance of being able to answer 3 questions properly.
posted by biffa at 2:25 AM on June 10, 2010

To put it a different way, you can use the "evil overlord argument." Assume you study only 6 questions. Then pretend your professor is an evil overlord— he wants to maximize the number of unstudied problems on the exam. He will deliberately place the four unstudied questions on your exam. In other words, you won't know 4/6 of the questions on the final exam, and your score will be 2/6. Lame.

Now, let's try to repeat this argument if you study 7 questions. Again, pretend your professor is an evil overlord that wants to trip you up. He will deliberately place the three unstudied questions on your exam. You won't know 3/6 questions on the final exam, and your final score will be 2/6. So it won't matter!
posted by yaymukund at 2:26 AM on June 10, 2010

*and your final score will be 3/6. So it won't matter!
posted by yaymukund at 2:28 AM on June 10, 2010

Sorry - confusing explanation. There will be 6 qns on the paper but I am only required to choose 3 of them to write on. So those 3 total are worth 100%

I enjoyed reading the responses and yes, I am pretty sure my lecturer is an evil overlord.

Thanks all! Off to study 7 of the 10!
posted by nothing too obvious at 2:33 AM on June 10, 2010

Now for that simple formula you're looking for. If it's a straight pick X out of Y (which is already pulled from Z number of questions you were given to study) number of questions then you can just study Z-(Y-X). Or in normal person, take the number of questions you get to skip and subtract it from the total number of questions you've been given.

Of course, this is assuming the test is like this:

Pick 3 of these questions:
A
B
C
D
E
F

If the test is instead done like this:

Pick 1 of these 2
A
B

Pick 1 of these 2
C
D

Pick 1 of these 2
E
F

you have to think about it differently. Even skipping 2 questions means you have the possibility of getting a set where you skipped both questions.

I'm sure there's something that I'm missing. But if my thinking is correct, you can take the group with the smallest number of question you can skip, and skip studying the number of questions you get to skip for that group. So in my first scenario (Which looks an awful lot like your question doesn't it?) you'd get to skip 3. In my second you'd get to skip one. If you skip two then you run the risk of having to pick between two questions that you didn't study for.

The danger is in not making that distinction, nor not knowing that that is how the test will be laid out (I've had some professors pull that on me).
posted by theichibun at 10:58 AM on June 10, 2010