From the course: Test Prep: GRE

Quantitative comparison technique

From the course: Test Prep: GRE

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Quantitative comparison technique

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- [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.

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