Davis: Hey everybody, this is GRE Bites. My name is Davis, and I’m an educator with over ten years of experience.
Orion: And I’m Orion, the founder of StellarGRE.
Davis: We’re here to bring you your weekly bite-sized episode on GRE prep and grad school admissions. Check out our top-rated GRE self-study program at stellargre.com. And don’t forget, you can use the code “BITES” for 10% off any membership.
Alright, let’s get to it. We’ve previously tried an in-person live walkthrough of a problem from the verbal section. Now, we’re going to try one on the quant section. We look forward to any feedback from our users and listeners. So, let’s dive right in. Orion, we’ve got a question prepped for you. I can read it, or you can.
Davis: And then, let’s discuss the strategies.
Davis: So, let’s try to do a live run-through of a quantitative reasoning problem here on air. It’s a bit challenging because you can’t see the question with me, but I’m here to walk you through my thought process. Hopefully, that’s not too much of a handicap. When this question pops up, I notice it’s only two sentences long. So, it’s not a paragraph. Looking at the answer choices, I see it’s a “choose one” type, and there are no graphs. I’m going to tackle this right then and there.
Orion: It seems to be a “choose one” type. There are clearly variables in the answer choices; I see x, y, and w variables. This means that, within a few seconds, I can already anticipate that I should be plugging in values for this problem. With that in mind, I’ll begin to read the question, plugging in concrete values for variables as needed and solving continuously as I go.
Davis: What’s the first number you’re going to plug in?
Orion: Let’s find out. It kind of depends on the question itself. So let’s take a look. It says a certain movie theater sells W adult tickets for X dollars. Okay. Because I’m doing this even in my head, we’re going to use some numbers that are really simple. Let’s say that the theater sold 10 adult tickets for $4 each. So, 10 for $4 each. Okay. And Y child tickets for 25% less than the adult price. Okay. So, 25% less is a quarter less than $4. A quarter of $4 is $1. So, 25% less would be $3. So they sold those child tickets for $3 each. And let’s say they sold two child tickets for $3 each. So, all told, 10 adults at $4 each is $40. Two child tickets at $3 each comes to $6. Let’s keep going. Which of the following expressions represents the theater’s total income? That would be $40 plus $6, or $46. That’s the answer to the question.
So, now all I have to do is go to these answer choices and plug those values into the variables to see which of these five answer choices is really my target number, or $46 in disguise.
Let’s take a look. The first one says wx + 0.25xy. Okay, so xy would be 4×2, that’s 8.25% of that is 2, plus wx which is 4×10, that’s 40. So, 40 plus 2 is 42. That doesn’t work.
Orion: Next, we have x×(w+1.25y). y is 2, and 1.25 is going to be a fractional amount, which probably won’t work because we have integer values here. So, we can pass on that for now.
Let’s move on to the next one: wx+0.75xy. Okay, so that would be 4×2, that’s 8.75% of 8 is 6. w×x is 10×4, which equals 40. So, 40 plus 6 is 46. Bing, bing, bing! That’s the number we’re looking for.
But because we’re plugging in values, we do have to go through all the answer choices just to be sure. Let’s keep going. The next one is x×(w+1.75y). y again is 2, and 1.75×2 is a non-integer, so that’s not going to work. Finally, we have 1.25wxy. w×x is 40, and 40×2 is 80, which is way too big.
We can stop right there. So, C is the only answer choice that correctly gives us back our target number. I did that only reading the question once, with fairly easy, small positive integers. I could do all of the math in my head. I also stopped solving for some of these problems once I realized that it was unlikely to give me back my target number.
And, you know, I spoke that in complete English sentences too. So, with a little practice, you can certainly accomplish this in less than 60 seconds.
Davis: And for a question like this, can you briefly explain why? This question seems easy enough that if someone was familiar with algebra, they could go in and say, “Oh, I know W represents this, X represents this, and Y represents that, and 25% is 0.25.” So, they might think they can solve it without ever plugging in. But can you give us a hint as to why that type of mindset might lead someone astray?
Orion: Yeah, that’s a good question. The algebra here is not super advanced. However, it might be complex for some students. For those students, we’re definitely going to sidestep the algebra and move to plugging in as quickly as possible. But here’s the thing: even for more advanced students who feel quite comfortable with the algebra, I generally say this: I have yet to meet a student who is more accurate and efficient with algebra than with arithmetic.
No matter who you are, or how proficient you are with algebra, you’ve been doing arithmetic longer. If we’re aiming for top percentile scores, which these high performers can certainly achieve, and if you can get the algebra correct 98% of the time under a time limit but can get the arithmetic right 99% of the time under the same limit, why not choose arithmetic? We’re trying to find the solution that uses the fewest cognitive resources and is the most reliably accurate over the greatest number of questions to ensure efficiency.
Lastly, when we try to solve questions by creating algebra from scratch, dealing with abstractions can sometimes lead to overlooking details. This is less likely when working with concrete, actual numbers. Using algebraic abstractions may increase the likelihood of careless errors.
Davis: I think that’s a great response. Going straight to algebra might be enticing for people who feel comfortable with it. However, as you mentioned, it’s more mentally energy-intensive and can be prone to errors due to the level of abstraction you’re discussing. This discussion also underscores that the GRE isn’t necessarily testing understanding of concepts. Instead, as you pointed out, it’s evaluating efficient and accurate problem-solving within a time limit. Having a clear, delineated strategy, like the one demonstrated today, can alleviate much of the mental strain and indecision.
Orion: I hope everyone found this beneficial.
Davis: Thanks, everybody, for tuning in. We’ll be back next week with another bite-sized episode of GRE Bites. If you have a topic you’d like discussed on a future episode, let us know at firstname.lastname@example.org. And if you’re ready to take your prep to the next level, check out our top-rated GRE self-study program at stellargre.com. You can use the code “BITES” for 10% off all memberships there. Talk to you soon.