 [Voiceover] So in any given GRE math section, the first eight questions will probably be what they call quantitative comparison. In other words, you'll have to determine which of two quantities is larger, whether they're equal, or whether it can not be determined. In this video, I'll show you what these questions look like and give you some basic technique. So on the screen we have a couple of examples of quantitative comparison questions. They're always gonna kinda look like this with a Quantity A and a Quantity B. Sometimes, above the quantities you'll see some rules.
So for that second example, a is equal to three, b is equal to negative five. And sometimes these questions are just straight up math problems like a little word problem or something, but the technique that I'm gonna point out specific to this type, which is gonna happen when there's algebra going on, in other words, when you see a variable in the quantities. Cause if it's a normal word problem, you can just usually do the math without testing numbers. But what we're gonna do here for this first one, we've got Quantity A and Quantity B. We're gonna test numbers to make sure that what we think is true is consistently true.
So good numbers to test are often gonna be one, zero, and negative one. Not only are these easy to test cause they're small, but they produce sometimes different results and that's what we want. We want to make sure that if Quantity A is bigger that it remains consistently bigger no matter what we pick. So let's start off with by testing one. Quantity A would be one squared, minus one. That is gonna turn into zero. Then Quantity B is gonna be seven times one, plus one.
So that's seven plus one, which is eight. So we would think it would be Quantity B, however, let's test negative one just to make sure. See if we can shake things up. So Quantity A we would have negative one squared, minus one, which would be one minus one, which again would be zero. Then Quantity B would have seven times negative one, plus one, which is negative seven plus one, which is negative six.
So look at that. This time, Quantity A is bigger cause zero is bigger than negative six. So now, since Quantity A was bigger for one test, Quantity B was bigger for the other test, we know that the answer is, in fact, D, which means that we can't determine it. So on the real test, you're gonna see choice A for Quantity A is bigger, choice B for Quantity B is bigger, choice C for if they're equal, and choice D, like this one, you just can't tell. So in this example over here on the right, let me point out another beneficial thing to do.
Think logically. So when you're doing these, we always wanna look for opportunities to compare without doing necessarily tons and tons of calculation. Sometimes using logic can help us do that. So let's think about this scenario here. Quantity A, let's just simplify this so we can see what it's gonna look like. It's gonna be three minus negative five to the sixth power. And then Quantity B would be three to the sixth, minus negative five to the sixth.
OK, hopefully you can read that. Three to the sixth minus negative five to the sixth. So before we go and calculate that, first of all, calculating most numbers to the sixth power is gonna take awhile. So we might save ourselves. Let's see if we notice anything going on here. Well you might remember that anything raised to an even exponent will be positive. So if we think about this situation in here, three minus negative five, well we might as well just do that. That's eight. We'll have eight to the sixth, which is a huge number and then on the right, before we even calculate, we're gonna have three to the sixth minus and then this negative five to the sixth that's gonna turn into, get a positive number.
So I'm gonna say that it's gonna be three to the sixth minus a big number. And a number bigger than three to the sixth, cause we have negative five to the sixth, which is definitely gonna be bigger than three to the sixth. So we don't need to really think about what that number exactly is gonna be. We know it's gonna be a negative number. So at that point, we're done. The thing on the left is gonna be a big positive number. The thing on the right is gonna be a big negative number. So we're done. That's it. We know that it's gonna be Quantity A.
So we want to use logic when we can to see if we can avoid doing heavy, time consuming calculations. So look for ways to compare without calculating and look for ways to simplify things so that they can more easily be compared. And, for algebraic quantitative comparisons, just like we did for the first example, think about adding numbers to test different scenarios.
Author
Vince KotchianReleased
3/11/2016 Setting your GRE goals
 Preparing a study timeline and choosing materials
 Analyzing sample GRE essay prompts
 Learning easier ways to solve GRE math problems
 Studying arithmetic, algebra, geometry, and data analysis
 Improving vocabulary and reading comprehension skills
 Using technique for sentence equivalence and text completion questions
 Reading difficult passages
 Learning methods to solve different kinds of comprehension questions
 Developing effective testtaking strategies
Skill Level Beginner
Duration
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Introduction

Welcome1m 3s

What you should know1m 30s


1. Welcome to the GRE

Structure of the GRE2m 21s

GRE scoring1m 35s


2. Preparation and TestTaking Strategies

Prepare a study timeline2m 2s

Build your study sequence1m 44s

3. The GRE Analytical Writing Assessment

Overview of the GRE essays1m 52s

Issue essay examples1m 57s

Argument essay flaws2m 44s

Analyze an issue essay2m 55s

Analyze an argument essay2m 42s


4. GRE Quantitative Introduction

Build math concepts2m 2s

Testtaking math skills2m 15s

Build mental math skills3m 30s

5. GRE Quantitative Techniques

Using the calculator2m 19s

Estimation technique3m 8s

Backsolving technique3m 21s

Translation technique2m 25s

Adding numbers technique2m 41s

Find patterns technique3m 43s

Trialanderror technique3m 27s


6. GRE Arithmetic

Number properties3m 46s

Decimals3m 9s

Mental percents2m 55s

Percent change3m 36s

Ratios and proportions4m 20s

Exponents2m 7s

More exponents2m 7s

Fake exponent rules2m 10s

Scientific notation3m 32s

Square roots3m 45s

Cube and fourth roots2m 34s

7. GRE Algebra

Operations with expressions3m 46s

Multiplying expressions1m 42s

Algebraic identities3m 5s

Linear equations2m 1s

Quadratic equations4m 5s

Linear inequalities1m 37s

Functions4m 6s

Symbol functions58s

Coordinate geometry4m 26s

Function graphs1m 5s

Distance between points2m 56s

Equation of a line3m 16s

Finding intercepts2m 15s

Special slopes3m 2s

Circle equations2m 47s


8. GRE Word Problems

Averages3m 29s

Mixtures2m 24s

Rate3m 21s

Work3m 53s

System of equations2m 53s

Interest4m 46s

Number lines1m 39s

Sequence word problems3m 18s


9. GRE Geometry

Angles2m 4s

Parallel lines2m 19s

Polygons2m 37s

Triangles4m 2s

Pythagorean theorem3m 11s

Special right triangles3m 51s

Area of a triangle2m 30s

Congruent triangles2m 17s

Similar triangles2m 40s

Quadrilaterals4m 30s

Circles3m 6s

Boxes5m 1s

Cylinders3m 26s

10. GRE Data Analysis and Statistics

Frequency1m 22s

Standard deviation2m 48s

Normal distribution2m 21s

Venn diagram problems2m 15s

Permutations3m 23s

Combinations3m 35s

Basic probability3m 21s

Either/or probability3m 42s

Graph and chart questions2m 33s


11. GRE Verbal Reasoning

Overview of verbal reasoning2m 10s

How to build vocabulary3m 7s

Reading efficiently2m 35s


12. Question Type: Text Completion

Overview of text completions2m 30s

Use signposts2m 23s

Tripleblank text completion4m 22s

Analyze complex sentences2m 23s

Review text completions1m 23s


13. Question Type: Sentence Equivalence

14. Question Type: Reading Comprehension

Read for the big picture5m 49s

Read critically3m 48s

Basic question technique3m 27s

Detail questions2m 33s

Whole passage questions3m 26s

Wordincontext questions2m 29s

Inference questions3m 41s

Wrong answer types1m 55s

15. Question Type: Function

Review function questions1m 15s

16. Question Type: Logic

Overview of logic questions1m 42s

Logic question technique1m 26s

Weaken an argument technique3m 39s

Explain a paradox3m 36s

Wrong answer types1m 30s

Review logic questions1m 6s


Conclusion

GRE testtaking strategies2m 34s

Conclusion and next steps1m 25s

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Video: Quantitative comparison technique