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The first thing I would suggest if you're at all math-challenged is to get the Kaplan GRE & GMAT Exams Math Workbook. Work your way through the entire book from cover to cover (skip the one chapter that applies only to GRE). Do all the drills and all the problems, read the explanations, make sure you understand exactly what they're talking about before you move on. This is also a good book if you used to be pretty good at math, but have just become very rusty. The quant review section in [tooltip=Official Guide]OG[/tooltip] is good, but it's pretty dense. It just summarizes everything you're supposed to know, but I didn't find it all that helpful until I had already gone through the Kaplan book for a more thorough refresher course.

You are correct that you need to multiply by 6. The reason for this is that if you use the probabilities approach, you need to take into account all the ways in which a favourable outcome can occur. Notice that the question doesn't say you must choose R first, then G, then B. To be systematic, you would need to list all of the favourable outcomes like this: p(R G B)=2/9 * 3/8 * 4/7 p(G R B)=3/9 * 2/8 * 4/7 p(G B R)=... p(B R G)= p(B G R)= p(R B G)= Note that on each line you have the same numerators and denominators, just lined up in different ways. So when you add them all up you end up with just 6 * (2/9*3/8*4/7). By the way, this is similar to rolling a total of 11 using 2 dice. You need a 5 and a 6. You could get a 5 on the first die and a 6 on the second, or the other way around. Both events are favourable outcomes, so you need to add up their probabilities to arrive at the total probability of rolling 11.

Hi haddock, Congratulations on joining the 700 club! [banana] [banana] [banana] I don't see any reason to consider retaking - you've cleared the 80%ile hurdle that some of the top schools are rumored to use, so I really don't think there is anything to be concerned about. In fact, most schools like to see a good quant/verbal balance, so a 710 based on fairly even Q/V percentiles should be viewed a bit more favourably than a 710 based on a stellar quant but below 80th percentile verbal score. Keep in mind that your GMAT score alone will not get you admitted anywhere - it can keep you out, but can't get you in. I would say you've cleared the GMAT hurdle for any school you might consider, and should move on to the other parts of your application. These are just my personal opinions - you may want to post your stats and your list of planned schools in the AskAdmissionConsultants thread for a more reasoned response.

Hey Matrix, Congratulations on exceeding your personal target by 100 points! :tup: People here sometimes become too focused on absolute scores (such as crossing the magic 700), but what really counts is whether you can reach the target you need to have a shot at the school(s) where you would like to apply. In spite of some serious anxiety, you've done that and more, so you should be very proud of yourself! Best of luck with your application!

See whether you can identify your "careless errors" more specifically. For example, after some analysis I found a couple of categories: 1) Transcription errors from mind to paper - e.g. thinking "26" but writing down "22" 2) Mind racing ahead of pen - e.g. thinking "A+B+C", but only writing down "A+B", because in my head I was already thinking about how to rearrange the equation, before I had actually finished writing it down 3) Arithmetic mistakes - even with simple addition or subtraction 4) Trying to rearrange equations in my head instead of bothering to write down that extra step on the scratch paper 5) Rushing too much in reading the question, and overlooking an important detail (e.g. *positive* integers, or *all* divisors). For 1 and 2, the only thing that worked was to slow myself down a bit. For 3, the best thing for me was just lots of manual practice, because I had become too used to working with a calculator. For 4 it was understanding that saving 5 seconds wouldn't help me if I ended up with the wrong answer (sometimes I would actually take *more* time, because the wrong answer was not on the list, so I'd have to backtrack and redo some of the work anyway). For 5, I developed the habit of taking one deep breath right after reading the question, before starting to solve it - just to focus my mind and make sure I didn't try to jump in too quickly. (Think of AWA: The worst thing to do is to read the topic and immediately start writing. You need time to gather your thoughts and figure out how to approach the question first.) I don't necessarily agree with people who say that you shouldn't work more slowly - it really depends on the type of careless errors you make. Performance in the quant section comes down to striking the optimal balance between doing it fast and doing it right. That balance point is different for everybody, so if you find that you're making more than the occasional careless mistake, you need to adjust your strategy.

Thanks for your kind words, vingmat! :o You have certainly proven once again how critical it is to believe in yourself, and I'm very happy that I was able to contribute to your success. I wish you all the best in your future endeavours. I'm sure you'll do great, no matter what you decide to do - just follow your heart! As you may have guessed from my reduced posting frequency, I'm well into the first term of my MBA program now, with piles of unfinished readings, multiple assignments due this week, cases, term projects, presentations, not to mention midterms starting in a couple of weeks... I'm starting to see now that the GMAT was just a warm-up for the main event :)

Congratulations on a great job! :tup: [clap] :tup: I was quite certain you'd be able to knock this thing past 750 if you were able to keep your nerves in check - glad to hear you kept it all together and didn't decide to cancel your score :D

Build a table of pairs, starting with the factors 1 and the number itself. Keep incrementing the first number, and if it's a divisor, add another line to the table. You only need to go up until in the first column you reach the square root of the original number, because any factors above that will already have appeared in your second column earlier: 1 x 441 3 x 147 7 x 63 9 x 49 21 x 21 In this case, you get a total of 9 numbers (8 unique numbers from the pairs in the first four lines, plus the "twin" 21 on the last line, since 441 is a perfect square). By the way, for a small number you don't need to do prime factorization first - you can just build the table. For a large number it's probably best to do the prime factorization first. For example, otherwise you would waste time in this example checking for possible additional divisors between 9 and 21. Prime factorization would tell you that there aren't any.

That's the solution I would have used, too. Just to clarify, in case some of you were wondering about the line I've highlighted in red that determines the number of invalid permutations we need to subtract: The easiest way to look at that part is to consider the two P's to be a single block (just glue them together in your mind). So you're really only rearranging 4 items - hence the 4!

By the way, a good reflex to develop for probability questions is to quickly check whether the question can be solved more easily using the "complement" approach, i.e. P(x) = 1 - P(not x) For this question, the probability of Amber finishing ahead of George is 1 minus the probability of George finishing ahead of Amber. I immediately concluded that this wouldn't be any easier to solve than the original problem :) . However, that's the point where intuition kicked in and I realized that the symmetry of the situation would have to lead to a 50% probability.

That's the problem with intuition - it's hard to explain! Ok, let me try to back it up a bit more analytically: Pick any particular permutation P for George (G), Amber (A) and the other three guys (x,y,z). For example, let's pick: P = xGyzA This permutation has a "mirror" in which everything stays exactly the same, except that George's and Amber's positions are reversed, i.e. P' = xAyzG Since you can find exactly one "mirror" for any permutation you pick, you can conclude that half the possible permutations will have George ahead, while the other half will have Amber ahead.

You have to remember that the GMAT is only part of the application process. Beyond a certain point, your GMAT doesn't actually do much for you (other than an ego trip and bragging rights among your friends). If you check out the GMAT score brochure at http://www.mba.com/mba/TaketheGMAT/Tools/InterpretingYourScores.htm , you'll see that 750-800 is 99th percentile. But even people with perfect 800 scores (pretty rare, but possible) get rejected by top 10 schools, if they don't have a strong "package" (work experience, essays, recommendations, GPA). There is some element of luck involved on test day as well that determines whether you happen to get a tough question that stumps you or a tough question you can do. Also, keep in mind that according to GMAC stats, your real ability is within a margin of error of approx. 28 points two times out of three - so my 760 really reflects an ability level of 788 :D

Hi nonpareil, I think you're overcomplicating the question. If you ignore for a moment who's ahead, there are a total of 5! ways in which the race can finish (5 choices for first place, then 4 for second etc.). That's a total of 120 possible permutations. There is nothing special about Amber and George - in half of all the permutations Amber will finish ahead, in the other half George will finish ahead. So the probability is just 1/2, or 60/120 if you looked at all of the actual permutations. The danger with the exhaustive method in this case (apart from the time it takes) is that it's easy to make mistakes. For example, if Amber and George finish right next to each other, as in the first case you gave, you also need to take into account that Guy1, Guy2, and Guy3 can finish in 6 different orders for each of those 4 cases you listed, so already there are 24 possibilities (by the way, that first case can be thought of as 4! if you look at Amber+George as a single block). If you do a "semi-exhaustive" method like you did (where you ignore the internal arrangements of the other 3 guys) you're correct that you'd get 10 possible arrangements: GAxxx GxAxx GxxAx GxxxA xGAxx xGxAx xGxxA xxGAx xxGxA xxxGA However, if you then wanted to use this to determine the probability, you'll need to look at P = favourable outcomes / total outcomes. You need to be careful, though: In this case your total outcomes would be the number of permutations of 5 elements where 3 of them are indistinguishable: Total outcomes = 5! / 3! = 20 (For more on "indistinguishable elements", check out my post in this thread: http://www.www.urch.com/forums/showthread.php?p=61317#post61317 ) So the desired probability is 10/20 = 0.5 Where did you get 25 for your denominator? Still, the intuitive approach I mentioned first is far easier and faster...

Schools generally use your highest score. Just to be sure, you should check with the admissions offices of the schools you're considering. Often the policy is explicitly stated on a school's website.

Yes, GMAT-HELP's analysis is correct. From the words "steadily decreasing" we can conclude that the U.S. percentage never dropped below 2.2 (otherwise it would have had to increase at some point to get back up to its final value of 2.2% in 1978). Japan must have been somewhere below 1.6% to start with, and climbed up to 1.6 by 1978. So D is correct. By the way, I actually drew myself a little graph when I first encountered this question, just to visualize what was going on.