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If you’ve ever taken a GRE, you’ve encountered something like this:
This is a good ole GRE Quantitative Comparison question—a “QC” for short. They’re always the first questions you see on the test. And they always have the same answer choices.
A, B, and C are fairly straightforward. Is quantity A bigger? Quantity B? Or are they both equal?
Answer choice D, on the other hand, has a way of driving test-takers mad on the GRE. If you took even the most benign question in the world and stuck on an answer choice that said “it cannot be determined from the information given,” that choice would sow the seeds of uncertainty. I can picture it now:
Question 1: What’s 4 + 5?
(D) It cannot be determined from the information given.
“Ah! I don’t know! I mean, I thought I knew how to add. But now that I see answer choice D, I just don’t know anymore!”
To D or not to D on the GRE – that is the question: Whether ‘tis nobler in the mind to suffer the slings and arrows of proving an answer choice like A, B, or C, or to take arms against a sea of certainty, and pick D.
Okay, okay… I’ll stop. And if you’re thinking this way, so should you. There is no need to wax poetic and become the Hamlet of standardized tests, paralyzed between D and the other choices. A good GRE test-taker is pretty skeptical—but not too skeptical. Fail to exercise enough skepticism and you fall for a trap answer. Exercise too much skepticism and you never get done with any of the questions.
Seems Like = Wrong Answer
How do you tell the difference between one with enough information and one without? Compare these two problems. One of them is D. The other is not. Can you tell the difference?
Take a look at that triangle problem; we’ll come back to the other one afterwards.
I don’t know about you, but something immediately pops into my head when I see this triangle. My flashcard memory sees “triangle…3…4…” and immediately thinks “5!” A 3-4-5 triangle is one of the very famous Pythagorean triples. Sure enough, if you square 3 and add it to 4 squared, you get 5 squared—it gets the Pythagorean stamp of approval. Pick C and move on.
Actually, wait a second. If you do that, you miss the question.
A 3-4-5 triangle is in fact a famous right triangle. If you were tempted to pick C here, ask yourself what you were assuming. They never told you this was a right triangle. It could just as easily be something else. Geometric figures are not necessarily drawn to scale on the GRE. Just because something “looks like” a right triangle doesn’t mean it is. If you’re ever answering a question because it “looks like” or “seems like” something, you’re getting it wrong.
Admittedly, this problem is pretty annoying, but the GRE is a pretty nit-picky test. I picture a pedantic little gremlin, cackling to himself, writing questions like this one. He might be pretty irritating, but you can learn to play his game. Remember: If it feels too easy, it probably is. All it takes is a brief, skeptical self-check to make sure you’re on solid ground before you answer.
It’s Not You, It’s Me
Now, look at the second question. This one is definitely not going to be D. Why not?
First, note that many people mistake “I can’t solve it” with “It’s unsolvable.” Notice how they give you incredibly difficult math to solve in quantity A? I imagine most folks solving this problem—especially on a timed test—will look at it in befuddlement, realize their calculator won’t help them, and eventually give up and guess.
Many of them will guess D—and they’ll get it wrong. If you look a little deeper at quantity A, you’ll see it refers to an actual value that you could theoretically find if you had a giant calculator with a 3-foot-long screen. This kind of situation always results in a correct answer of A, B, or C. (Take that great big number, divide it by 11, and you’ll end up with some specific amount left over. It’ll be 4, or something a little bigger or smaller.)
It takes some guts to throw in the towel on a difficult question, and it takes some humility to distinguish an inability to solve on your part from the general “unsolvability” of a problem. If it seems impossible to solve, ask yourself if it’s the problem that’s making it impossible or if it’s you not knowing how to do it. If it’s you, a reasonable guess is anything other than D.
Back to this particular problem. If I’m honest with you, I’ve never bothered to calculate n and divide it by 11—and I wouldn’t try to do so on a real test. Instead, solve a simpler problem as the key to unlocking the more difficult one. If you started testing these powers of 10 by adding 4 and then dividing them by 11, you’ll notice a pattern:
14… 104… 1004… 10004… 100004…
14/11 leaves a remainder of 3
104/11 leaves a remainder of 5
1004/11 leaves a remainder of 3
10004/11 leaves a remainder of 5
In the cases where 10 is raised to an even power, the remainder is 5. So the answer to this QC question is A.
Test Before You Guess
The question of whether or not to pick D remains a vexing one. In the middle of a tough QC question—one that just doesn’t seem to have all of the information you need—when is it best to solve through and get some kind of answer? And when is it best to just pick D and move on?
Take a look at this one. What does your gut instinct tell you the answer is?
There are definitely a lot of unknowns here. We don’t know exact values for any of our variables. At first glance, w, m, n, and z could be any positive integers.
But they gave you a line on a coordinate plane. Why on earth did they do that?
Here is a much simpler variation of this problem. Let’s try it and then come back. What would your answer be here?
With hardly any constraints at all, I’m almost 100% certain that this one will be D. For good measure, I’ll put a few numbers on my paper anyway. If c and d are 1 and 2, but a and b are 100 and 101, then B would be bigger. Reverse those values and A could also be bigger. The correct choice here would be D.
Now go back to the other problem. Try exactly the same thing. Put some numbers to your paper to confirm whatever intuition you had about the answer.
For this problem, it might seem like “anything goes.” But you’re actually limited to putting in only certain kinds of numbers for w, m, n, and z. For (w, m) your x value has to be bigger than your y value. (You ran further than you rose.) The opposite is true for (n, z). Try setting (w, m) equal to (4, 2). And set (n, z) equal to (2, 4). You’ll notice quantity B is asking you to add the smaller values together. A is adding the larger values. Thus, your answer is A.
Whatever your initial thought about this problem, you’ll likely find that you become a stronger problem solver if you combine an instinct about the answers with a simple number test. It’s much safer to pick a choice when you’ve proved it.
Sometimes you’re going to feel lazy. Or tired. Or rushed for time. It’s cases like these where a simple number test will save you from a bad guess.
In Order to Beat the GRE Gremlin, BE the Gremlin
Earlier, I mentioned that the GRE can often be a pedantic test—it loves to lead you into traps and test you on the limits of your knowledge. When I studied for the test, I found myself laughing out loud and thinking, “Hah! You thought you had me, you GRE gremlin-demon, you! I’m not falling for your trap!”
Yes, my roommates at the time were a little concerned. But I think this attitude helped me get the score I wanted.
If you can learn to see the GRE like a game—and particularly if you can learn to test the limits in that game—you’ll find that you become much more aware of the trap choices and how to avoid them.
Check out this problem from the Official Guide.
The problem tells you almost nothing about that quadrilateral. There are so many options. It certainly seems like the answer should be D. Pencil down. No math done.
But is that an answer or a guess? If I put my pencil down, am I being wise by saving some time? Or am I just being lazy and going on “math autopilot?”
This one does in fact happen to be D, but with a little change it could very well have another answer. Think about how you would rewrite it if you were that evil GRE gremlin, seeking to make it just a little bit harder. What would be a more deceptive value to write in for quantity B? I have an idea that would likely fool a lot of test-takers. What about you? If you’ve got a suggestion, write it in the comments below.
Thinking like a test-writer will hone your sense of skepticism. When you study, making moves like this will sharpen your sense of what’s D and what’s not.
Ay, There’s the Rub
I don’t know if I’ve got you thinking you’ve mastered QC or if I’ve got you questioning everything you thought you knew in math. In the long-run, a well-cultivated level of skepticism and a game-like approach to QC will make you a better test-taker. Get out there and crush some QC questions on the GRE. Happy studying! ?
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Tom Anderson is a Manhattan Prep instructor based in New York, NY. He has a B.A. in English and a master’s degree in education. Tom has long possessed an understanding of the power of standardized tests in propelling one’s education and career, and he hopes he can help his students see through the intimidating veneer of the GRE. Check out Tom’s upcoming GRE courses here.