Advice on Quant Section, strategic input needed

[stock2007]

I got my basics down in quant.

i got some days to go for the test.

what are the tough quant questions that the 700 plus scores get.

should i focus on sets, probability, permutatiion and combination, co-ordinate geometry..

any tips.. i want to get a good quant score.

[mayonnai5e]

Generally at the 700 level you'll see questions from the end of the PS and DS sections of the OG books. The Kaplan 800 book also has pretty good quant questions that I think are in the 700s area. Personally, I believe you should focus on getting the fundamentals down pat because you'll need to do flawlessly on them to get a really high quant score.

[Stacey Koprince]

Even at the high end, probability and comb / perm are just not that common. I've had several students in the past 6 months score 700+ and tell me that they did not see a single prob. or comb. problem on the entire test.

Number properties problems are very common, however, even at the high end, as are quadratics, rates & work, ratios, and weighted averages. At the very high end, it's also common to see more pattern-recognition type problems - things that seem to involve impossible calculations for the 2-min-with-no-calculator setup of the test but, if you spot the pattern, they become much easier to solve.

[II]

Even at the high end, probability and comb / perm are just not that common. I've had several students in the past 6 months score 700+ and tell me that they did not see a single prob. or comb. problem on the entire test.

Number properties problems are very common, however, even at the high end, as are quadratics, rates & work, ratios, and weighted averages. At the very high end, it's also common to see more pattern-recognition type problems - things that seem to involve impossible calculations for the 2-min-with-no-calculator setup of the test but, if you spot the pattern, they become much easier to solve.

The quant section covers the following topics:
Number properties
Statistics
Permutations & Combinations
Geometry
Exponents
Algebra - equations
Word problems

How would you prioritise these in order of importance for someone aiming for 700+ score ?

[II]

Even at the high end, probability and comb / perm are just not that common. I've had several students in the past 6 months score 700+ and tell me that they did not see a single prob. or comb. problem on the entire test.

Number properties problems are very common, however, even at the high end, as are quadratics, rates & work, ratios, and weighted averages. At the very high end, it's also common to see more pattern-recognition type problems - things that seem to involve impossible calculations for the 2-min-with-no-calculator setup of the test but, if you spot the pattern, they become much easier to solve.

Also you mention the "more pattern-recognition type problems - things that seem to involve impossible calculations for the 2-min-with-no-calculator setup of the test but, if you spot the pattern, they become much easier to solve". Are there examples of these questions in the OG11 books ?

Thanks.

[Stacey Koprince]

I'm traveling and don't have my books with me this week but look at the last 50 of so questions in each math section in the book. Look for things that could be solved pretty easily with a calculator (eg, something that has 2^30 power or something ridiculous like that) but that require a different approach if you don't have a calculator.

[mayonnai5e]

Even at the high end, probability and comb / perm are just not that common. I've had several students in the past 6 months score 700+ and tell me that they did not see a single prob. or comb. problem on the entire test.

I got a 720 with a 49 raw Q score and saw 0 prob/perm/comb questions.

For II, I believe all the topics you listed are important at the 700 level (with the exception of P&C since you may not see any even at the 700 level). I don't think there's a particular order that you should focus on because, to be honest, at the 700 level you pretty much need to have a mastery of each and every one.

Number properties
Statistics
Permutations & Combinations
Geometry
Exponents
Algebra - equations
Word problems

I also agree with Stacy on her comment about pattern-recognition problems. I never referred to them as "pattern-recognition" problems, but basically there are certain mathematical manipulations and rules that a 700 test taker will very quickly recognize and utilize to finish a problem within 2 minutes whereas a 600 test taker will take much longer to see it or may not recognize it at all.

[II]

Thanks Mayonnai5e !

When you say "there are certain mathematical manipulations and rules that a 700 test taker will very quickly recognize and utilize to finish a problem within 2 minutes" ...

Do you have any examples of these certain mathematical manipulations and rules ?

Thanks.

[Stacey Koprince]

I'll let mayonnai5e address this directly, but I'd also like to suggest something else - there's a first level that you have to master before you can handle the ones mayonnai5e is talking about.

We're basically talking about the difference between someone who can look at a problem and recognize what to do based on making connections with past problems s/he has done and someone who has to figure out what to do every time or almost every time.

This applies across ALL math topics, so there won't ever be a short list of items here.

A 700 level tester will be able to recognize what to do on approx. every other or every third problem. A 750+ level tester will recognize what to do on all but a few problems. A 600 level tester will recognize parts of maybe every 3rd to 4th problem, but may only recognize 5 or so complete problems in the section.

* Note that, when I say recognize, I don't mean you'll see a problem you've seen before. You won't. But you'll see problems with the same or very similar structures or set-ups; even if they look very different on the surface, they are testing the same things or some of the same things. *

For instance, if you have these books, compare these two problems:
OG Quant review #39
OG 11th ed. #153

The first one is much easier than the second but both are testing the same concept: prime. (In fact, both questions can be rephrased: is this variable prime?) The statements are much harder to deal with in #153 and statement 2, in particular, requires some additional knowledge to solve, beyond what you need for #39. But the bones of the two problems are nearly identical (I'd be willing to bet money that the same person wrote both problems and was looking at or thinking about the first one when s/he wrote the second one).

Master this first to lift yourself to 700+ questions consistently - know that you won't slip on any of these or you won't have to worry about the crazy-hard problems because you won't see them. Then, this mastery is also the foundation that allows you to recognize and know what to do with even harder problems.

[II]

Stacy,

Excellent points !
This is exactly the type of thing I want to master. The question is how best to master this ?

Using your example questions. You are saying that both of these questions are testing the same concepts: prime numbers. Both questions are asking if the variable is a prime number. How would I identify this and make the connection ?

#39 from OG Quant DS section:
Can positive integer p be expressed as the product of 2 integers, each of which is greater than 1?
(1) 31 < p < 37
(2) p is odd

#153 from OG 11 DS section:
Does integer k have a factor p such that 1 < p <k> 4!
(2) 13! + 2 &#8804; k &#8804; 13! + 13

Currently, the way I would have answered this question is to plug-in values and work from there. I would then potentially start seeing the whole "prime" number thing appearing, whilst working it through.

thanks again for your kind assistance.

[Stacey Koprince]

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.

[beatthegmat]

Moved to GMAT Math area...

[II]

Thanks Stacey ... that is useful advice.

For me it was pretty straightforward to recognise that the first question was asking for a prime ... but not as straightforward for the second question.

Are there any drills or methods which I can use to practice this and master this ?

Thanks again.

[Stacey Koprince]

Any time you do a problem, figure out what it's really about and then ask yourself "what is the language or the setup in this problem that indicates that this is really what the problem is about?"

Once you figure out, for prime, that a defining factor is whether there are factors between 1 and the number (not prime) or not (prime), then any time you see language indicating the same thing (even if slightly different language / setup is used), you know prime is an issue for the problem.

If you use our books, go take a look at the problem sets at the back of each book. Look at, say, all of the divisibility and prime problems over a couple of days (there are a lot) and try to make connections between them. Which problems are really asking the same thing? Which problems have some overlap? Work from the easier ones to the harder ones, because you use your understanding of the easier ones to build your ability to do the harder ones.

By the way, that second statement in the harder problem - you're also never going to figure out from scratch how to deal with that in 2 minutes. You either recognize what to do with it (and part of that is recognizing that the problem is dealing with prime), in which case you can execute in the time you have, or you're going to have to make an educated guess.

If you know it's about prime, you should be able to eliminate A and D. That leaves you with B, C, and E. At the least, you should also figure out not to choose C for a very simple reason: C says that both statements must be used together. In other words, each statement brings something valuable to the final solution. Statement 1 simply tells us that k>24. Statement 2 tells us a range of possible numbers for k, starting with 13! + 2. So does statement 1 tell us anything new and useful? No - I already know that 13! + 2 is greater than 24. So C can't be the right answer. Now I'm down to two answers even though I don't know how to deal with statement 2.

So, my short answer: you have to do the work. You have to study from the point of view of: what do I want to remember from this problem that I can use on later problems, and how will I recognize that later problems are similar? That means stripping problems down to the bare bones and really understanding what's being tested.

[II]

Thanks Stacey ... that makes absolute sense. Will start practicing using that school of thought, and will see how I get on.