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Intro to Quantitative Comparison

Now, we can start talking about the Quantitative Comparison questions. So, back in the Intro to the GRE section, there was a video, Math Section Breakdown, and in that video my friend Chris Leilei talked about the math section, and pointed out that there are four question types. So just to review here are the four question types. The first one, Multiple Choice, some people call this problem solving.

This is just ordinary five answer multiple choice. You have seen this kind of multiple choice question on every standardized test you have taken since infancy. So this should not be brand new. This is a relatively familiar standardized test format. Multiple Answer, this is a little bit different it’s like multiple choice.

They give you the choices, but you are allowed to pick more than one answer if more than one answer is okay. And typically there are a few more choices, instead of five there might be six, seven or eight or something like that. You have to pick all the answers that work for the particular question. Numeric Entry, you have to come up with the answer yourself.

And so that’s the basic idea, and this is not very much like standardized tests but this is very much like all the math you’ve done throughout grade school and in high school all the math where you had to come up with the answer yourself. So this is just come up with the answer do yourself math, so that’s numeric entry. Those three are usually relatively intuitive for students. Its not all that different from what they’ve done before.

By contrast, the quantitative comparisons, these are a little bit different. These are questions that are unique to the GRE, they don’t appear on any other standardized test, they don’t appear in any other format, and so these deserve a special discussion. Now course right now, at this point if you’re watching these lessons in order, we haven’t learned any of the math yet.

All the math lessons are yet to follow, and so what we’re gonna have here, we just have three introductory videos, just to give you kind of the gist of the question, so that you can get started on your own practice. In other words, when you see the question you’ll have a basic idea of what the format is about, at least. At the end of the math module after all the other lessons, then we’ll have a section Advanced QC strategies.

And there we’ll talk about how the different content areas are tested in the QC questions. How do the quantitative comparisons test Geometry, how do these test Algebra, et cetera, et cetera. Obviously we can’t talk about that here because we haven’t talked about geometry or algebra yet.

So this is just about the basic, how does the format work? And then we’ll talk more about strategy at the end of the math module. So what are these questions about? The Quantitative Comparison questions. This question format will present entries in two different columns labeled Quantity A and Quantity B.

In each column there will either be a number or something that could take a numerical value. It might be a variable or some word problem formulation, it might be x, it might be the area of the triangle, it might be the number of employees. Obviously, if it’s a word problem thing we’d have to have a little context for that as part of the question.

Our job is to compare these two quantities, trying to figure out which one is bigger. That’s the big idea of Quantitative Comparison. It is a comparison of two quantities. The four answer choices are always the same. So it’s very important to get familiar with these answer choices.

Answer choice A, means Quantity A is greater. Answer choice B, means Quantity B is greater. Answer choice C, means the two quantities are equal. Answer choice D, means the, the relationship cannot be determined from the information given. So the first thing I’ll say about these answer choices is you should commit them to memory as soon as possible.

Many people actually find them intuitive. In other words, you pick A when A is greater, you pick B when B is greater, when you see that they’re equal, you pick C and when you don’t know, you pick D. Many people just can remember them but it’s very important to get familiar with these because again these are the answer choices on every single quantitative comparison question.

And I want to clarify that A means that Quantity A is always greater, in every way, in all cases. Similarly, B means that Quantity B is always greater, it couldn’t possibly be anything other than greater than Quantity A. C means that, at all times, in all ways, for all possible values of a relevant variable, the two quantities are always equal.

In other words, A, B and C implicitly have the word always in them. By contrast, choice D means that things don’t always stay one way. In other words, different values of the variable or different number choices within the specified range allow for different choices that produce different results. For example, one choice of numbers might make Quantity B bigger, and another choice might make the two columns equal.

If it is possible to make different choices that produce different relationships, then the answer is D. D means essentially, some relationships may be greater than shows up sometimes, less than shows up sometimes, equal shows up sometimes. If there’s any sometimes attached to any of these, then it’s answer choice D. So I’m gonna give you a few elementary practices questions now.

And again, these questions in this video are much, much easier than anything you would actually see on the GRE. I’m keeping the math relatively simple because a more important in just stressing how the question type works, rather than going into detail about mathematical ideas. So here we have a comparison, we have to compare 8 to the fraction 53 over 7.

Well, of course, the easiest way to compare two things and put them in the same form. In other words we can write 8 as 56 over 7. Well 56 over 7 is bigger than 53 over 7. So right away that means column A is bigger, because column A is bigger the answer is A.

That was a very straightforward question. Here’s another question. Pause the video for a moment and then we’ll talk about this. Okay, so we’re given a geometric figure. So notice, incidentally, this is, this is standard for the quantitative comparison.

Sometimes you’re just given, Quantity A and Quantity B, nothing else. Sometimes you’re given some text above the problem or you’re given a diagram, or some kind of explanation that sets up the question, and whatever appears above the question is relevant to both quantities. So, here we’re told that ABDE is a rectangle. And we want to compare the area of the triangle ACE, to half the area of the rectangle.

Well, let’s think about this, I’m gonna be reminding you of some geometry formulas. If this is unfamiliar, don’t worry. We’ll have a whole module on geometry coming up later. You don’t need to have this memorized inside out right now. Just kind of, a reminder. The area of a triangle, you may remember, is one half base times height.

Again, if this is unfamiliar to you, do not worry. You’ll see it in the geometry module coming up. The area of the triangle, the area of the rectangle would just be base times height, and so half of that would be one-half base times height. Well notice, both of those are equal. Another way to see this kind of visually incidentally, is if we imagine splitting it in half, well that area is equal to that area, and that area is equal to that area, and so looks like the triangle is exactly half the area of the rectangle.

You might do it visually, or you might do it with formulas, either way is fine, but either way it turns out that the answer is C. Here’s another practice question, pause the video and then we’ll talk about this. Okay, in this one, I threw you a real curve ball and this is actually typical, even though this question is a little easier than something that would appear on the GRE.

The curve ball that I threw you, is very typical of the kind of curve ball that the GRE will throw. So, N is not an odd integer and we know that N is between 6 and 10. And we want to know how does N compare to 8? Well, you see the mistake people make is, they think in terms of numbers that they can count on their fingers.

They think in terms of integers 1, 2, 3, 4, 5, 6, 7, 8. And they think well what are the numbers between 6 and 10? Well, 7, 8, and 9. And it’s not an odd integer, it’s not 7, it’s not 9, so it has to be 8. People forget that numbers is a much bigger category than numbers you can count on your fingers.

And we’ll be talking about this a lot in the math module. So this is your first notice of this, don’t get stuck in the trap of thinking only in terms of numbers you can count on your fingers, what we technically know as the positive integers because there are many, many other kinds of numbers. So yes, in terms of positive integers, 8 would be the only possibility for N. But, we have no guarantee that N is an integer.

We only know that it is not a odd integer. So it could be something like 6.5 or 9.1 or our old friend 53 over 7. The fraction that appeared a couple problems ago. So, all of these possible, all those are numbers they’re genuine bona-fide numbers on the number line. They are not odd integers, so if N is not an odd integer, it could be any of those numbers.

And some of them are bigger than 8, some of them are smaller than 8, so we have no way to determine whether N is bigger or smaller than 8. So, because we have no way to determine, the answer is D, and again, remember that trick. It’s one of the traps that, that is woven throughout the GRE Quant section. People, when they near the word number or when they see a variable, they think only in terms of numbers they can count on their fingers.

They forget about decimals, they get, forget about fractions, they forget about negatives. It’s very important to keep all the categories of numbers in mind. So, pause the video for this one, and then we’ll talk about it. Okay, so this is a question about probability.

If probability is something that you haven’t thought about in a while, or if it’s entirely new to you, don’t worry, we have an entire module on probability coming up later in the math module. So if this is, if the math here is something you haven’t seen before, do not worry. You will see it in depth later on.

But the probability of rolling a 6 twice, well if it’s a six-sided twice, the probability of rolling a 6 once is one-six. The probability of getting any particular side of the die is one-sixth. And then for it to happen twice, to roll 6 and roll 6 again, the word end means multiply in probability. So the probability of 2 sixes is one-sixth times one-sixth, so one-sixth times one-sixth, you may remember, when you multiply fractions, you just multiply numerators, multiply denominators.

And we get one-thirtysixth. One thirty-sixth is a smaller fraction, it is smaller than one-sixth. And so, the answer here is definitely B. So, some basic facts about the question, now that we talked a little about the format.

On the GRE, the four answer choices are equally likely. So in other words, the folks who write the test are careful so that on average, they produce about the same number of questions that have an answer choice of A or B or C or D. So you don’t get stuck thinking that one answer choice is more likely than the other.

Because the GRE is very careful to make sure that that doesn’t happen. Typically you’ll see somewhere in the neighborhood of about 7 or 9 quantitative questions on a math section. Typically, the math, the quant section opens with quantitative comparison questions. So they’re the first questions you see.

These tend to take less time than other math questions, for reasons that we’ll talk about a little bit later. Basically you’re only have to do a comparison, you don’t have to do a full calculation in many cases. When you get in practice with these, the easier ones may take only 45 seconds. So you, you may well find that you can race through some of these questions, compared to other question formats.

Although, especially if you’re doing some of the harder questions on the test, there are some hard quantitative comparison questions that may take up to 2 minutes. So just to keep in mind, it’s important to get comfortable with this format so at least the easy and medium questions you’re handling relatively efficiently.