...there are questions like this one:
Which is larger (or are they both the same, or is there not enough information to determine which is larger)?
(99^9)/(9^99) or (11^9)/(9^90)
The answer turned out to be C (equal), and 22 percent of test takers got it correct (which is actually what would be expected if pretty much everyone guessed at the answer).
It's understandable that almost everyone would simply guess since it would take a long time to solve it mathematically, and of course this is a timed test with barely enough time to finish even if you take the test quickly. The part I don't understand, however, is how then can so many people get 800 on the Quantitative with questions like this on the test? Are they partly lucky? Does getting an 800 require being very good and very lucky? Or are they extremly smart and can do the calculation quickly? Or is there a strategy? Or is there some other explanation that I can't think of?
Thanks for any feedback.
How is an 800 Quantitative possible when...?

 Posts: 9
 Joined: Sun Jun 21, 2009 1:14 pm
Re: How is an 800 Quantitative possible when...?
I don't think this is too difficult to solve... just a little bit tricky. If the given quantities involve square root or power, I usually divide one by the other. This way I can know whether it is less than, equal to, or greater than 1.
Divide (99^9)/(9^99) by (11^9)/(9^90)
And use (ab)^c = a^c * b^c rule.
= ((11*9)^9)/ (9^99)) * ((11^9)/(9^90))
= ((11^9 * 9^9)/ (9^99)) * ((11^9)/(9^90))
= 1
Hence, the answer is C.
Divide (99^9)/(9^99) by (11^9)/(9^90)
And use (ab)^c = a^c * b^c rule.
= ((11*9)^9)/ (9^99)) * ((11^9)/(9^90))
= ((11^9 * 9^9)/ (9^99)) * ((11^9)/(9^90))
= 1
Hence, the answer is C.

 Posts: 20
 Joined: Thu Aug 28, 2008 2:01 pm
Re: How is an 800 Quantitative possible when...?
99=9x11
cancel powers up and down.
took less than a minute, didnt it?
were u honestly trying to multiply everything?
cancel powers up and down.
took less than a minute, didnt it?
were u honestly trying to multiply everything?
Re: How is an 800 Quantitative possible when...?
Thanks for the feedback higgs_boson and sonikajohri. To answer your question, sonikajohri, I looked at it for a few seconds, then skipped it and did the rest of the 30 question paper practice test. At the end I decided I obviously couldn't do that one so I counted it as wrong and then I graded my test. I scored a 750 on the test (which I imagine to be below average for an aspiring Physics grad student). I then lamented (again) that I am below average and wondered how the rest of you get 800 or very close to it.
Follow up question: After I graded my exam I thought about that one for a long time (on and off for a couple of hours). I simply didn't see the solution that the two of you saw (And when I give myself a 30 question practice paper exam, I sometimes miss one or two due to not seeing an answer, and typically miss one to three others due to a simple math error like accidentally seeing something like "(x  4)" as "x 4" when it should be "x + 4". It's very easy, for me at least, to make one to three obvious errors like that, particularly when I am in a rush due to a timed exam. This is why I get a 740 or 750 instead of a 780 or 800 like so many of you.). How did you know the answer? Should I simply ascribe it to a lack of intelligence on my part and just accept that I may not have what it takes to be a Physicist? (Yes, I know, I could still get into a PhD program with a 750, or even a little lower, on the Quantitative GRE, it will simply be harder, and maybe it wont be a top school.). Or is there a way to train myself to be able to answer questions like this one? Thanks for your help.
Follow up question: After I graded my exam I thought about that one for a long time (on and off for a couple of hours). I simply didn't see the solution that the two of you saw (And when I give myself a 30 question practice paper exam, I sometimes miss one or two due to not seeing an answer, and typically miss one to three others due to a simple math error like accidentally seeing something like "(x  4)" as "x 4" when it should be "x + 4". It's very easy, for me at least, to make one to three obvious errors like that, particularly when I am in a rush due to a timed exam. This is why I get a 740 or 750 instead of a 780 or 800 like so many of you.). How did you know the answer? Should I simply ascribe it to a lack of intelligence on my part and just accept that I may not have what it takes to be a Physicist? (Yes, I know, I could still get into a PhD program with a 750, or even a little lower, on the Quantitative GRE, it will simply be harder, and maybe it wont be a top school.). Or is there a way to train myself to be able to answer questions like this one? Thanks for your help.

 Posts: 20
 Joined: Thu Aug 28, 2008 2:01 pm
Re: How is an 800 Quantitative possible when...?
Its kind of to do with having a feel of numbers, which I guess comes from experience.
Like when you see 99 and 9 and 11 floating around in a problem, you should make the connection that 99=9x11 and then the problem practically solves itself.
So I guess you should practice A LOT. And concentrate on doing the stuff you don't know how to do. Don't go on solving problems which you know you can do (is there a contradiction there? ).
And studying for GRE and PGRE won't be a total waste of time like a lot of people claim since the skill comes in useful when you are solving reallife physics problems too. Like seeing that an integrand is even, so you can put one of the limits as zero and save on calculation time; or when you are solving some equations and you can do a bit of trial and error solving instead of doing the whole matrix thing; or while designing or analysing a circuit, you can reduce a lot of things by symmetry.
Recently, the research paper I was referring to for a problem had a set of boundary conditions which I needed to use, but they were in a different basis from mine, but I noticed that while converting from one to the other stepbystep would get pretty involved, I could easily multiply a phase factor in a certain way to my variables and the condition would be satisfied. And then when I thought about it, the phase factor made sense physically too.
I don't know how to put this, but the socalled tricks are something which is happening physically (though what does physically mean if its a maths problem?). Its different from the kind of trick involved in questions like, "In a room, there's a short rope on the ceiling with a man hanging from it and water on the floor? How did he get up there?" You CAN learn to appreciate them and of course, they make life a whole lot easier.
I don't think anyone could truly answer what it takes to be a top physicist. Luck, maybe?
Like when you see 99 and 9 and 11 floating around in a problem, you should make the connection that 99=9x11 and then the problem practically solves itself.
So I guess you should practice A LOT. And concentrate on doing the stuff you don't know how to do. Don't go on solving problems which you know you can do (is there a contradiction there? ).
And studying for GRE and PGRE won't be a total waste of time like a lot of people claim since the skill comes in useful when you are solving reallife physics problems too. Like seeing that an integrand is even, so you can put one of the limits as zero and save on calculation time; or when you are solving some equations and you can do a bit of trial and error solving instead of doing the whole matrix thing; or while designing or analysing a circuit, you can reduce a lot of things by symmetry.
Recently, the research paper I was referring to for a problem had a set of boundary conditions which I needed to use, but they were in a different basis from mine, but I noticed that while converting from one to the other stepbystep would get pretty involved, I could easily multiply a phase factor in a certain way to my variables and the condition would be satisfied. And then when I thought about it, the phase factor made sense physically too.
I don't know how to put this, but the socalled tricks are something which is happening physically (though what does physically mean if its a maths problem?). Its different from the kind of trick involved in questions like, "In a room, there's a short rope on the ceiling with a man hanging from it and water on the floor? How did he get up there?" You CAN learn to appreciate them and of course, they make life a whole lot easier.
I don't think anyone could truly answer what it takes to be a top physicist. Luck, maybe?
Re: How is an 800 Quantitative possible when...?
cooper, A key thing to remember is that the QGRE (and PGRE) problems are only intended to take at most a few minutes. Many can be solved in your head, or at worst with a few lines on scratch paper. You'd never have to expand a large polynomial or divide out 7.18 / 5.93 explicitly. So if you find yourself doing a lot of work, you're probably missing the gist of the problem, and you should look at it again and try something else before continuing your work.
This fact helped me with those tests. For instance, if I saw the problem (99^9)/(9^99) or (11^9)/(9^90), on a math contest I'd be feebly trying all kinds of exotic *** to try to get an answer, knowing that a simple solution would never work... But if I saw it on the QGRE, I'd know it was supposed to be a joke, and I'd know to just divide the numbers, factor the 99's and 90's, and cancel. The same confusion would happen if I saw one of the Lagrangian PGRE problems in an endofchapter problem in ThorntonMarion.
So my advice is, instead of looking at a problem and immediately starting with the first idea that comes to mind, think about it until a straightforward solution presents itself... since you know there has to be one.
This fact helped me with those tests. For instance, if I saw the problem (99^9)/(9^99) or (11^9)/(9^90), on a math contest I'd be feebly trying all kinds of exotic *** to try to get an answer, knowing that a simple solution would never work... But if I saw it on the QGRE, I'd know it was supposed to be a joke, and I'd know to just divide the numbers, factor the 99's and 90's, and cancel. The same confusion would happen if I saw one of the Lagrangian PGRE problems in an endofchapter problem in ThorntonMarion.
So my advice is, instead of looking at a problem and immediately starting with the first idea that comes to mind, think about it until a straightforward solution presents itself... since you know there has to be one.
Re: How is an 800 Quantitative possible when...?
quizivex wrote:cooper, A key thing to remember is that the QGRE (and PGRE) problems are only intended to take at most a few minutes. Many can be solved in your head, or at worst with a few lines on scratch paper. You'd never have to expand a large polynomial or divide out 7.18 / 5.93 explicitly. So if you find yourself doing a lot of work, you're probably missing the gist of the problem, and you should look at it again and try something else before continuing your work.
This fact helped me with those tests. For instance, if I saw the problem (99^9)/(9^99) or (11^9)/(9^90), on a math contest I'd be feebly trying all kinds of exotic *** to try to get an answer, knowing that a simple solution would never work... But if I saw it on the QGRE, I'd know it was supposed to be a joke, and I'd know to just divide the numbers, factor the 99's and 90's, and cancel. The same confusion would happen if I saw one of the Lagrangian PGRE problems in an endofchapter problem in ThorntonMarion.
So my advice is, instead of looking at a problem and immediately starting with the first idea that comes to mind, think about it until a straightforward solution presents itself... since you know there has to be one.
Thanks, I actually do that, try to find the simple trick. Usually, I am successful, but sometimes, this time, I couldn't see it. It's possible I was panicking and that's why I couldn't see it. Or maybe I was right about the intelligence thing, who knows.
Edit: My goodness, it seems you didn't panic when you took the test: 800 Q, 770 V (even your verbal score is higher than mine, up till now I took consolation that at least my Verbal score is higher than everyone else's here ), 4.00 GPA. Impressive. I never understood that. No matter how hard I try, I can't get a perfect GPA (typically, my GPA's are around 3.7, 3.8 ), if nothing else there is always some teacher who wont give me an A for some crazy reason (When I went for my Masters degree in Psychology, for example, I had a teacher that only gave out an A if the final paper was good enough to publish. To make matters worse, he claimed that published papers have to be written in formal English, I didn't even have a clue what formal English is. When I disproved his claim by bringing him some samples of papers written in informal English, he still stuck to his position. I later found out through another teacher that they gave up formal English in published papers decades ago. The first Professor probably hasn't read anything in a long time . He certainly didn't put in too much effort to teach his classes.).