Is there a strategy for solving this?

cooper
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Is there a strategy for solving this?

Postby cooper » Sun Aug 23, 2009 4:09 am

A question on the practice computer GRE test is:

A) the value in column A is greater
B) the value in column B is greater
C) the values are equal
D) there is not enough information given to solve the problem

column A: the greatest prime factor of 3^5

column B: the greatest prime factor of 5^3

(the correct answer turns out to be B)

I simply couldn't figure out how to answer this one, or properly prepare myself to answer this if I encounter something like it when I take the exam. In preparation for the exam, should I take the time to memorize the first several prime numbers? How many should I memorize? (It sounds like a lot of work) Then, when I take the test, should I try each prime number till I find the answer? That could take a while and we don't have much time. What should I do? Thanks for any help anyone can give me.

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grae313
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Re: Is there a strategy for solving this?

Postby grae313 » Sun Aug 23, 2009 11:39 am

Just remember that there is only one set of prime factors for any number.

a) 3^5 = 3*3*3*3*3
b) 5^3 = 5*5*5

Those are the prime factors and prime factorization is unique, so b has the largest prime factor.

Oh, and if you can't rattle off the first ten or so prime numbers then yeah, that's something you're supposed to just know. It's not hard to figure them out, either

cooper
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Re: Is there a strategy for solving this?

Postby cooper » Sun Aug 23, 2009 5:43 pm

Thanks for the response Jessie. I thought I knew all of the math that I need to know for the GRE (as you said several times, it’s all high school math), but it sounds like I don’t know everything I need to know (I think I am starting to understand part of the reason why I can’t get a perfect score on the Quantitative GRE). I am not sure I understand your response, however. What do you mean by “only one set of prime factors for any number”? It sounds like you are saying that any number has a group of numbers that are its prime factors. That makes sense, but are you saying that if a certain number can be expressed as one number to the power of another number (for example, the number 243 can be expressed as 3^5, with 3 being, I believe, the base, and 5 being the exponent), then the group of prime factors for that number is the base (in other words, for example, since 243 = 3^5, then the group of prime factors for 243 would be the base of 3^5, which is the number 3)? I DID NOT KNOW THAT! I already know, or at least thought I know (high school) math pretty well, and I reviewed the math in ETS’s book, “Practicing To Take The GRE, General Test, 10th Edition”, but I never learned the fact that you are explaining. I do appreciate the help. I wonder if there is anything else I am missing? What did you mean by prime factorization is unique? More generally, how can I prepare myself for this kind of question on the GRE? In other words, how do I find the group of prime factors for any number? Thanks for your help (it’s actually quite impressive that you can moderate this forum, and constantly answer my questions WHILE AT THE SAME TIME be a full time Physics graduate student. I would think you would barely have time to eat and sleep while being a full time graduate student).

Yes, I can rattle off the first ten or so prime numbers, I was afraid you would say I should memorize the first 30 numbers (I didn’t think ETS expected us to memorize that, but I couldn’t understand how they expected us to solve this type of problem otherwise).

meno
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Re: Is there a strategy for solving this?

Postby meno » Sun Aug 23, 2009 6:13 pm

Cooper,

Get a GRE book by the Princeton Review or Kaplan--I used the Princeton Review and got an 800. These books will not only jog your memory on the math involved in some of the trickier questions, but will also help you work out a good strategy for taking this kind of test. It sounds like you are spending too much time worrying about details and questioning your own abilities. Looking at a GRE book that is NOT manufactured by ETS may help put a lot of your fears to rest.

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grae313
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Re: Is there a strategy for solving this?

Postby grae313 » Sun Aug 23, 2009 7:23 pm

When I say prime factorization is unique, what I mean is that each number has one and only one set of prime factors. So of course you know that you could factor 5^3 as 5*5*5, but you might be wondering if 5^3 has another, larger prime factor. The fact that prime factorization is unique rules this out.

"It sounds like you are saying that any number has a group of numbers that are its prime factors." Yes... this is what you learn in 4th grade. :D And of course, if you have a number X^n, and X is a prime number, then X is the largest, greatest, and only prime factor of X^n. This isn't something you need to memorize or some strange thing about math that you don't know, it's just obvious if you know how to factor a number and if you know that each number has only one set of prime factors. I'm not trying to be unduly harsh here, just perhaps unduly frank.

cooper
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Re: Is there a strategy for solving this?

Postby cooper » Mon Aug 24, 2009 3:37 am

meno wrote:Cooper,

Get a GRE book by the Princeton Review or Kaplan--I used the Princeton Review and got an 800. These books will not only jog your memory on the math involved in some of the trickier questions, but will also help you work out a good strategy for taking this kind of test. It sounds like you are spending too much time worrying about details and questioning your own abilities. Looking at a GRE book that is NOT manufactured by ETS may help put a lot of your fears to rest.


When I first prepared for the GRE's many years ago (around 1995, in fact I was one of the first to do the Computer Adaptive GRE) because I needed them to get into a Psychology PhD program (In my "previous life" I was a Psychologist. What a waste of time that was, PSYCHOTHERAPY IS NOT EFFECTIVE!!!! :roll: I should have went with my first thought when I was in college, and studied Physics right away. :( ), I decided not to use non ETS material (with the exception that Barron's had a nice vocabulary list and math review, but I recently found the same review in an ETS book). I found the tests that supposedly simulated actual GRE's to be different from the actual GRE tests (although my complaint was mostly against the Psychology GRE test, Barron's simulated exam, for example, was much harder than the actual test put out by ETS, and included material not found on the actual test.). So, when I recently started studying for the GRE's again, I immediately went right for ETS study material. However, maybe you're right, maybe one of the sources you mentioned could help me with the trickier problems, so I guess I will check those sources out of the library. Thanks for the suggestion.

cooper
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Re: Is there a strategy for solving this?

Postby cooper » Mon Aug 24, 2009 3:49 am

meno wrote:Cooper,

It sounds like you are spending too much time worrying about details and questioning your own abilities.


Yes, I spend a lot of time worrying about details, obsessing about them actually, and never feeling perfect enough, and obsessing that I need to be perfect. It's no wonder I was diagnosed as having Obsessive Compulsive Disorder (not that any of the many Psychologists I ever saw were able to help me overcome this problem :( ). On the other hand OCD does have its advantages, like when I spent several months back in 1995 obsessively driven to perfectly learn Barron's 3500 word list. It paid off, too. I obtained a very high score on the Verbal GRE, and that more than anything else is what caused the admissions committees at a number of schools to accept me into their Psychology PhD program :D .
Last edited by cooper on Mon Aug 24, 2009 4:21 am, edited 2 times in total.

cooper
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Re: Is there a strategy for solving this?

Postby cooper » Mon Aug 24, 2009 4:01 am

grae313 wrote:When I say prime factorization is unique, what I mean is that each number has one and only one set of prime factors. So of course...


Thanks for the help again Jessie. You just turned the hardest problem for me into the simplest :D . And no, I didn't think you were trying to be harsh over the fact that I clearly don't remember a principle that I was taught in grade school. After all, everyone knows that the success over the program "Are you smarter than a fifth grader?" is due to the fact that we tend to forget facts learned many years ago, that we haven't used in many years. Although, apparently you knew it, which is another example of your many abilities. I am sure you will go far in Physics :) .

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quizivex
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Re: Is there a strategy for solving this?

Postby quizivex » Mon Aug 24, 2009 5:26 am

A few comments based on the discussion here:

- Prep books are useful for describing the outline and content of the tests, but keep in mind that some of the strategies given (I recall one that showed you how to get an analogy correct when you don't know either of the 2 main words) may work for the specific examples they're presenting, but they'll apply to very few questions on the real test. There's no substitute for having a big vocabulary and reading effectively and knowing basic math well. ETS won't make many questions that can be answered by magical tricks without understanding the gist of the question.

-I'd only recommend using the official ETS practice tests for the general GRE. Those questions (almost) always have one fair answer. Kaplan and barron's books are riddled with flawed, unrealistic questions, especially in the verbal. I was getting really confused and losing confidence trying to see what I was doing wrong with the imitator tests until I encountered a problem that was so indisputably wrong I realized it wasn't me.

-Cooper seemed confused by the "uniqueness" property grae mentioned. While this property (called the fundamental theorem of arithmetic) is critical to the theory (you'd prove/learn it in number theory), you probably already "knew" this. When you took your first algebra class, you factored numbers by breaking them down into smaller factors until you can't anymore. You're left with the prime factors. Did you ever have the issue of multiple answers coming up in class? Nope. So instinctively, you knew the answer should be unique. So it just takes one more step to apply it to this problem, i.e. that 5, 7, 11 or any larger prime can't be a factor of 3*3*3*3*3. The answer follows. I'm not sure where exactly you got stuck, but I just wanted to reiterate that there's nothing profound you need to know for the QGRE.
cooper wrote:I would think you would barely have time to eat and sleep while being a full time graduate student).
Most people leave this forum because it's no longer useful for them. Some of us want to remain active to help future students and cuz it's often fun (remember garden? lol). If anyone's under so much pressure that they can't spend a few hours per week on non-work things, such as visiting this forum, they're straining themselves to the point of danger. Of course once in a while (finals week, paper submission deadline), we'll have some sleepless nights, but if that's a year-long ordeal they're in a very unhealthy situation. When you go to grad school, you'll find that most people are more normal and down-to-earth than you'd expect. They do normal things like go out to eat sometimes, talk with their parents on the phone, watch TV, get laid etc...

-The "5th grader" show's title is just for effect. There's nothing to feel stupid about if we forget who the 23rd president was, or the capital of Ecuador, or any of the other crap the 5th graders just learned. Intelligence and knowledge are distinct things.

cooper
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Re: Is there a strategy for solving this?

Postby cooper » Mon Aug 24, 2009 6:34 am

quizivex wrote:A few comments based on the discussion here...


Yes, I guess we are in agreement about not using non ETS material. When I initially studied for the Psychology GRE using Barron's as a guide, I thought the Psychology GRE was going to be extremely hard since Barron's simulated Psychology exams were very hard (and had information that never appeared in any of my Psychology classes). I imagined I would need to study for a long time. Then, when I got my hands on an ETS exam, I realized I was pretty much ready for the exam, and it was easier than the practice tests Barron's provided. So when it came time to study for the General GRE I pretty much went right to the ETS exams.

I was kind of only kidding about that remark about not having any time for anything else if you are in a PhD program. I didn't have time for anything else, but I can be "Obsessive" about over studing, as I kind of mentioned earlier.

The only thing I was confused about regarding what grae was talking about (aside from the fact that to my knowledge I never heard of what grae was talking about) is that her explanation about how to determine the prime factors was unclear (it was unclear to me at least). After reading her second post I understand perfectly why you know that the prime factors of 125 = 5^3 is 5*5*5.




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