Walkthrough of three GRE quantitative comparison problems

Tyler York
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Clay Daniel, founder of Clayborne Test Prep and Tutoring, to share his best practices for handling GRE quantitative comparison questions. In this podcast, Clay goes through three GRE quantitative comparison problems in a set from the ETS practice PDF here. Follow along as Clay walks you through how to work through this unique question type.

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Full Walkthrough of three GRE quantitative comparison problems video transcript:

Welcome to GRE snacks, snackin episodes by the GRE exam and graduate school admissions. I'm Tyler. Founder of achievable.me. Our affordable $199 GRE course includes everything you need to Ace your GRE Exam: Full textbook. Tons of GRE questions or backed by our memory-enhancing algorithm, and full-length practice exams. Try it for free at achievable.me and if you like it, use the code podcast to get 10% off at check out. Also, if you have a question topic, you'd like to discuss in a future episode. Please contact me at Tyler at achievable.me with the subject line podcast, topic. Now, let's get started today. We have claimed Daniel with us and he's going to walk us through some jewelry, questions. But before we do that play, do you want to just quickly introduce yourself?

GRE personal trainers for the test, everything that you need your, your study schedule but also a relation 12-10 program over weeks and months that I'll be dressed in some weaknesses and I say

Yeah, thanks so much and speaking of problems we are going to do a problem walk through today at 3 GRE Quant problems and all three of which are quantitative comparison since you want to just give me the overview what that means. First love to kind of problem on the GRE and not. Not many other test that that I'm aware of that involves not too much arriving at final values. So you're always going to have a quantity and a quantity be. And then I'll just read the choices that are presented to the test. Taker choose a day of quality as greater is greater. See if the two quantities are equal and G really interesting relationship, cannot be determined from the information given

Yeah, it doesn't itch it's not like a typical question where you figure out the the hypotenuse is 5 and then usually usually you actually can't figure out the answer without doing a lot of meth really. From some of these other ones, you can kind of like you just it's more like a logic related thing. Value-adding, how long is this going to take me and is there even if it takes a long time to sell, maybe there's a quick way to compare or as The Surreal buzzword or Buzz phrase for this is compared don't calculate either way to compare them so that that'll be something that will look at it and said these questions. And so also the questions that were working off of our official ets.org official GRE practice test, at says, I think the 2011 on the PDF, I think I'll try to

Put a link to it and the podcast description so that people can follow along. But we're starting here on page 71 of this document with question. Number one, if you want to follow along or otherwise, I'll be just listening to all sorts of problems because they're always going to get some sort of advanced set of information. Particularly if the quantities simply say what they say, here, we just want to be as has a quality he says why we're probably going to get there right triangle by the little, right angle symbol one of them is labeled at 4 and ask for the legs. You familiar with that terminate for the hypotenuse.

Or ax and age, the other has legs 4 and 4. And then why is the hypotenuse

as we think about how to compare these,

this is an example of a somewhat more straightforward problem in getting to a calculation. May not take that long but what's especially going out but not take long is familiar territory of a test. Like the GRE they love. The special cases. In this case, what we call special, right triangles

Anybody have a study to GRE and using a pulled out their flashcards and there's a 30-60-90 on there in the 45 45 90.

Well, recognized the pattern that is presented here even though the other angles besides 90° on given to us we can tell from the relationship between the sides of a triangle with shortest. The short side for and longest sigh date is a 30-60-90. And the triangle with legs for is a 45-45 isosceles, right triangle, right? Cuz they're the same foreign for us or two legs both of these problems, but that would not be the most efficient way and we're looking for the most efficient way.

Before we get all the way to the solution, that's a great place to pause. Tyler, just say, what does that mean for the choices? Remember that choice D says, the relationship cannot be determined is really the key in my view to Quality comparison. Question on some I seem pressed for DD is on. You can prove you don't want to prove G or disprove it.

Write rights on this case. We can look at it. We say, what information is given we have we definitely have two sides of one, right, triangle and two lengths of the other one is clearly we're going to get final value. There's going to be some relationship and he can be safely ruled out, right? So just remained, just use the most efficient tool. Not would beat to note that in the 30-60-90, we take the shortest side and x √ 3 to get the middle. So accident in Times Square to 3, but in the 45 45 90 to get the hypotenuse. We take the legs of x squared, it is to notice the right part of the answer is he similar or identical quantity, a for Route 32

Calculator it is tricky to because you might think to yourself man square into is smaller than 3 to the square, root of smaller, right?

Right? Well, and that's not that is the way that you can. You can reason through this one for re 3 is larger and it is it is one of the are some things that might seem obvious, the GRE are not to be careful that square root 3 is larger, which you know, makes sense. Then that would put us at quantity a in the answer Choice, a to 28th grader and you can think about the two quantities. I like to pretend that they're working with equations. If you have an equal sign has like a balance and it says, nothing as identical on both sides or just going to drop it before.

Question. A lot of times you do have variables on both both of your answer. So yeah, you got to do that now to problem number 5 for the bottom of page 72 so if you want to walk us through this certainly switching content of an arithmetic base question we can put before the listener of mine that idea of pressing toward Choice be almost imagine that you're on a quest and your goal is to prove two different relationship as we did last time. It's a great strategic way to think. About the question, we have the prior information given is that the value of x

Is larger than 6 and smaller than 7/6 and 7, an integer whole number. Why is 8 equals 8 and axes basically six-point? Something the task is to compare quantities a which is x / y a six-point something over eight the quantity. Which is 2.85 or helpful to hear first office. Start with the most specific information especially if you're given to it given it in the quantity of the colonists. 25 is a great friend to you, here is your reference point. So why not start there and say,

What would it take in quantity, a for me to get 25 as a result?

Asian don't want to think about, we know that. Why is 8 so it's really something over eight equals 25x. /, 8 equals 25.

calculator can help us there, but what can be really interesting about the answers at when we divide that out or we going to get something between 6 and 7

We're going to get something bigger than 7 or smaller than 6.

And that will determine everything about the answer that we end up at.

Was it turns out we do if you divide divide X by or I should say Point 85 x, 8, he is going to be between 6:00 and 7.8 when you put it into the calculator.

That makes the problem much more interesting than it would be. If it was like 7.2, we would know quantity, be would have to be greater because we're making a comparison here with .85. If x to be to make .85 would have to be exactly. 6.8 it raises the question. Well, is x / y, bigger than 185 or smaller.

And here we kind of remind ourselves. Our goal is to press toward point B. If we got that hinge exactly where we could quite the value. And let's just do a little bigger and a little smaller. What is 6.9 + 6.7?

Break out your day on screen calculator, 6.9 / 86.7 /, 86 smaller than a 8.5 / 0.85. Sorry, we've established in a sense actually, too many relationship even more than we had. Maybe it's quantity are equal to 80 is greater than b. We're already done. At that point. I can Thursday. So we really confirm it when we say last.

Is that explanation makes sense?

Yeah. Yeah, just make sense. I mean it's interesting because it doesn't strike you this way when you first look at the problem. But the answer actually really is is always going to be.

Like in essentially, it's always going to be d d, if that equation works at all right, right? If I make sense like if if you can if you can put you know, the two things equal to each other and then it comes out as X is between 6 and 7. And the answer is always, do you write it. That's really interesting. One of just getting concrete, I like to talk to you now. Letters. Plug-in number numbers are more concrete and you got to get your hands dirty. Let's just try some numbers and see what happens that often takes you. Most of the way there.

Right. And in this case, they were nice enough to actually give you the ranges for the numbers. So you know what's plug-in yeah. Alright so for the third one, you got to cover today. I'm quite comparison. I'm moving on to question 9 at the bottom of page. 74 is fine as general truth here is that X is not equal zero. Got a little line over the equal sign so she's not equal 0, we're supposed to compare absolute value of x.

Plus the absolute value of -2.

The quantity B, which is the absolute value of x - 2.

It almost as you're not looking, like I said, the same thing, but in the first case, there are two separate quantities, insiders, absolute value bars.

Absolute value. Actually, I figured out what that is. + absolute value negative to. We got to figure out what that has quantity. Instead, it's almost like, it's all inside, parentheses hear, whatever it is, we're tracking to, and then applying the absolute value, which let's start by decide to find that they will remember kind of like the absolute value. Does that it's helpful to add that the definition of absolute value is the distance, 20 on the number line,

I've asked you, how far is -7 from zero on the number line. You wouldn't say -7, right?

Yeah, 79 cents to say when you're asking for a distance that I can help. That's so interesting. So like that's the official definition. I've always just used it. Functionally is like it should always positive but that's not actually, right? It's really great to pull the last thing we said about the last problem. That is the value of plugging in numbers.

so what I'd like to do on this question is talk a little bit more about

How do I know there's literally Infiniti of numbers from which, to choose? How do I know what to plug in here? Aside from the fact that I'm not allowed to plug in 08? They did tell. I find to think of numbers you'll plug in in categories first. And by that, I mean, sick. Sick of different kinds of the most natural is positive integers. 1 to 3 etcetera, but there are also negative integer whole numbers on the negative side.

There is a number zero which behaves and very odd ways that which is disallowed from this problem. So they will toss that aside.

And then they're basically not, there's things between numbers between whole numbers on the number line, but especially interesting in that regard is the rain between 0 + 1 + 0. + -1

notice that if you multiply something by half,

smaller instead of larger opposite of what he would think of my X half a pizza and then half of it again, the pizza is continually getting smaller if you take half and half,

all I have to say if we if you plug in the number of each of these categories, you're probably going to be in pretty safe shape by the time you identified, all the relations

50, it's pretty safe to do with two negative to positive 1/2. + -1

Attempts to touch on behave different way. They have different characteristics. So let's start with the most straightforward one. And let's, let's also shortened the process by saying there is one thing here. We can simplify right away. Always good to do. Want to be in a house as part of it actually value of -2. What's the number to, which is much simpler.

What's up with positive to you? Because we intend to deal most easily with positive integers.

Why didn't you call? And by the way, that won't require us to do anything with an absolute value. If it's already positive at work or at least, absolute value of 2, + 2,

Parties at resting 2, - 2 has to happen first. So it's the absolute value of 0. What, how far is 0 from 0?

Yeah, I guess it's zero not in Trinity, right? Yeah. Yeah. It's absolute value. Always positive or negative

So he's found one relationship. I want to be a larger. You can make a note on her scratch paper to put a little a there or something. Now, right, this is fast as possible.

Let's be strategic. Is there a way we can think about the other numbers thinking we'll work might give me a different results.

It's okay. If you don't immediately, have an answer to this question, but because absolute value changes negatives to positives, probably best to try a negative number next time. I really changed what happened with that negative number

because it's easier to plug in the -1/2. We can always do the fraction of her.

ETA is once again. Yep. -2 + absolute value of -2, right? We already said that that is too so it's really just two plus two.

The quantity B is now inside the absolute value, negative 2 - 2 as a place. A lot of things are going to go wrong, it's very easy to go wrong. If you have a doubt yourself a little number 15 - 2 on it and then remind yourself. I'm contracted to from there. I'm going. Even more negative or to the left.

4 - 20 - 4 inside the absolute value.

Would Sunday, positive for?

Noticed a relationship. We have already arrived at our goal of our Quest because now the relationships are identical.

Right? So you have one, where is larger and that one where they're equal. So I basically confirms be right there.

Yes, that's not a problem. You can try the fractions if you need to, you know. But I will add that because there are 21 questions and you need to try to get to all of them 90% certain that you can always put a little on the test, the market. I guess it says Mama to come back to it and look at it later if you want, if you were only 90% sure instead of a hundred but seems will typically ask at this point, should I try the third number just to make sure?

Cancer. That is usually no from a strategic point of view, unless you have time tomorrow.

Yeah. And unless you think there could be a place for your math went wrong but in this case probably a checkered here. How many how many GRE to does it take to do 2 + 2 + 5?

Well, thanks very much. That was great. This has been Siri snacks with play Daniel from Claiborne test prep and hosted by Tyler from a chief. You can try achievable GRE course for free at achievable.me. And then you can use the code podcast to get 10% off at checkout.
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