So, on the first one (assuming you see this one first), you would probably start by plugging in numbers but, during study, you wouldn't leave it at that - you'd keep working at it till you figured out the principal behind it, which in this case is prime.
Then, you'd look at the wording of the problem and think "what specific words here are necessary in order for them to ask me about prime without using the word prime?"
Well, they need to make a distinction between a number that has only itself and 1 as factors (prime) and a number that has factors between itself and 1 (not prime). In the first problem, "product of two integers" means factors (when you multiply two numbers together to get a third number, your first two numbers are automatically factors of the third number). Then, the problem also had to specify that these factors were "greater than 1" - otherwise, the two integers I multiplied together might be 1 and whatever prime number I'm talking about.
So now I know one way the test can ask about prime without using the word prime. (And, if you think about it, there's a limit to how many ways they can ask about a certain concept without naming the concept. Essentially, they have to provide the definition of the concept, and that's a static thing.)
Then, when you get to the second (harder) problem, you recognize that the question is basically asking the same thing, though it's worded a little differently. (By the way, you have a typo in your post. Okay, it's not a typo - when I tried to type it in correctly and submitted it, it formatted the same way yours did - something weird with the software, I guess. So let me write it out. The question ends with "1 is less than p is less than k." Then, the first statement says k is less than 4!.)
But the statement essentially says is there another factor between 1 and k (in which case it is not prime) or is there not another factor between 1 and k (in which case it is prime). Same thing.
Now, the second question is MUCH harder, so if I want to have a hope of answering it, I have to recognize very quickly that this is a prime question - maybe 15 seconds, instead of taking 60 seconds of my precious 2 minutes to figure out that it's a prime question. I'm going to need the time I save to deal with the statements (especially statement 2). If I need to do all the work to figure out that the question is really asking about prime, I'm never going to get this question done in 2 minutes.
Plus, even if I can't finish the question, if I know it's asking about prime, then I can probably deal at least with statement 1, even if I have no idea what to do with statement 2. That narrows it down to 2 or 3 choices right off the bat, so I can make an educated guess within 2 minutes even if I can't deal with statement 2. If I don't know that it's about prime, I may not even be able to figure out how to deal with statement 1 in my available time.
Last edited by
Stacey Koprince on Wed Jan 09, 2008 7:26 am, edited 2 times in total.
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