Math Strategies for GRE
In this section we provide some general strategies to get you thinking in the right direction regarding GRE math. Here’s a preview:
- Change Your Math Mindset
- Use Scratch Paper
- Avoid Careless Mistakes
Change Your Math Mindset
The GRE tests only basic math from junior high or early high school. However, since the concepts tested are basic and predictable, those wily test makers have to resort to certain tricks and traps to throw you off; otherwise, most test takers would ace the section. This fact has one very important ramification:
You need to change the way you’ve typically approached math questions in the past.
Think about the typical math tests you took in high school. Many were accompanied by three dreaded and imposing words: SHOW YOUR WORK. This mandate implies a slogging mentality: You’re taught to do a problem a certain way, and then required to spit back that exact method to get full credit.
GRE math, however, rewards cleverness to combat the traps the test makers set. It doesn’t matter whether you answer the question using a traditional or untraditional method. It doesn’t matter if you use algebra or don’t use algebra, draw a diagram or don’t draw a diagram, or simply get into the ballpark through approximation instead of calculating an answer precisely. All that matters is whether you answer the question correctly. Three elements of your new math mindset will be looking for shortcuts, approximating when possible, and keeping your eyes open for “common trap” and “left-field” answer choices. Let’s have a look at each one.
As discussed above, your high school math experience may have instilled in you an instinct to jump into math problems with your sleeves rolled up, ready to slog away. And yes, sometimes that is the only way, or at least the only way you can see at the moment. Unless you perform math calculations lightning fast, however, you’ll probably need to sneak your way around at least some GRE Math problems to get to all 28 questions; that’s simply how the section is constructed. If you find yourself up against a real monster calculation that you think you need to work through to get the right answer, think again: Chances are the question is testing your math reasoning skills—that is, your ability to spot a more elegant solution that doesn’t require hacking through the math. Consider, for example, the following problem:
If x = 33.87, what is the value of ?
Is it really likely that they expect you to plug such an unwieldy number such as 33.87 in for all those x’s in the equation, especially given the fact that calculators aren’t allowed on the test? No, of course not, although that’s exactly what some people will attempt. Not you. Once you change your math mindset, you’d know instinctively that there must be some sort of shortcut here, and indeed there is.
If you multiply out the (x + 1) and (3x + 15) in the top part of the fraction (the “numerator”), you get 3×2 + 18x + 15, which cancels out the entire bottom part (the “denominator”), leaving the simplified value of the equation at (x – 2). Alternatively, you may have factored the bottom into (3x + 15)(x + 1) and then canceled out those terms from the numerator, again reducing the entire fraction to (x – 2). No matter which shortcut you employ, all that’s left is to substitute the given value for x into (x – 2) to get 33.87 – 2 = 31.87, and you’re done.
FOIL, factoring quadratic equations, and canceling are the concepts in play here, and if you need to brush up on them, don’t worry—we’ll get to these and plenty more bits of math minutiae soon enough in the following chapter. The point is simply to understand that many GRE math questions are written with shortcuts in mind, so begin right now to look for shortcuts as part of your new GRE math mindset.
Approximating (When Possible)
Another habit that may be ingrained in you from your math background is to “get the right answer.” Well duh, you may be saying; this is math, after all, so naturally you’ll want to solve the problems. Well, yes and no: yes in Problem Solving and Data Interpretation, but no in Quantitative Comparison questions where your job is not necessarily to solve the problems but rather to learn enough about quantities A and B to compare them. So especially in QCs—but also in the other question types—approximating values may save time. (Some DI questions even ask flat out for an approximate answer.)
Let’s see how we might use approximation on a sample QC question:
|Column A||Column B|
|48% of 54||11% of 273|
(A) The quantity in Column A is greater.
(B) The quantity in Column B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
There’s no doubt that some test takers with an old-fashioned high school math mentality would wear down their pencils grinding out calculations to precisely determine the value of each quantity. Then they could say with complete confidence which column is greater, or if they’re the same. (Note that with only numbers and no variables in the question, the answer cannot be D. More on that in chapter 4.) Will this method get the right answer? Maybe, if they don’t botch the math—a not-so-unlikely prospect when dealing with awkward numbers like these. Even if this method does yield the right answer, it may take a good chunk of time.
Approximating is the way to go. Observe: 48% is pretty close to 50%, or one-half, so let’s work with that figure instead. Half of 54 is 27, so a little less than half of 54 (remember, the real figure is 48%, not the full 50%) must be a little less than 27, which is a fine approximation for Column A. Similarly, 11% is awfully close to 10%, an extremely manageable percentage. To take 10% of anything, we simply move the decimal point one place to the left. The value in Column B is therefore a little more than 27.3, since 11% of a number is larger than 10% of that same number. Since the quantity in Column A is less than 27, and the quantity in Column B is more than 27.3, Column B must be larger than Column A, which means that choice B is correct.
It would actually take a quick test taker less time to approximate the two values and settle on choice B than it took us to explain the method above. And, needless to say, it would take way less time (with less risk of careless mistakes, to boot) than it would take to actually do the math.
Common Traps and Left-Field Choices
One more element of your new math mindset concerns how you interact with the answer choices. The test makers prefer that you don’t stumble upon the right answer accidentally and therefore construct the choices accordingly. Let’s first discuss “common trap” and “left-field” choices individually, and then we’ll get to some examples.
Remember, the test makers often spice up what would otherwise be basic problems. That means that you should assume that they go out of their way to trap unwary test takers into selecting appealing wrong answer choices, sometimes called “distractors” since they’re meant to distract you from the correct choice. What might make a wrong choice appealing? Three main things:
- It repeats a number used in the problem itself.
- It represents a number you derive along the way to the right answer choice.
- It represents the answer that results from a common misunderstanding of the problem.
You’ll see examples in just a bit, but first let’s discuss another kind of answer choice you should keep on your radar.
“Left-field” choices are just what they sound like—choices from way out in left field that simply make no sense in the context of the question. Say you get a complicated rate/time/distance problem in which you’re given a whole bunch of information and need to calculate how long it would take someone to drive from New York to Chicago. (Don’t worry—we’ll cover this kind of problem in chapter 2 along with every other essential math concept you need to know.) Say you forgot to divide by 100 at some point along the way and ended up with an answer of 1,500 hours. It seems ludicrous, but some people take the test with blinders on, and if they get 1,500, they get 1,500—period. So if that answer appeared among the choices, they’d choose it. This despite the fact that traveling even at a reasonably slow rate of 40 miles per hour, one could drive from New York to California twenty times in 1,500 hours. The answer just doesn’t make sense in the context of the question—it comes from left field. The test makers include some left-field choices to remind you that it’s not just a math test; it’s also a reasoning test, which means you can and should quickly eliminate choices that defy common sense.
Let’s now take a look at some traps and left-field choices in action. See what you can make of the following question:
Simone invests $10,000 in a bank account that pays 10% interest annually. If the interest is compounded quarterly, how much money will be in the account after two years assuming that no money is deducted from the account and no money other than interest and the initial investment is added to the account?
If you understand the formula for compound interest and can get the answer that way, that’s fine, although in this case we can eliminate choices to get there faster. Choice A repeats a number from the question, which makes it suspicious to begin with. Moreover, it contains shades of “left field” since it defies common sense. Does it sound reasonable that a bank account that receives interest will have the same amount it started with after two years, given that no deductions are made from it? No—it has to have more, so choice A bites the dust on this count as well. And speaking of left-field choices, we may as well cut E too: Does it seem logical that an account would more than double in two years at an interest rate of 10%? Any experience with an interest-bearing account should suggest that $21,000 is way out of the ballpark here, leaving only B, C, and D as contenders.
Ten percent of $10,000 is $1,000. If the problem were based on simple interest—which no doubt the test makers are hoping some people will think—then $11,000 would be in the account after one year, and $12,000 after two years. But neither of these takes into consideration that the interest is compounded quarterly. B and C are therefore traps, both written to tempt anyone who falls for this common misunderstanding. C, $12,000, is what results if you calculated simple instead of compound interest, while B, $11,000, represents a number on the way to that wrong answer. The correct answer is D, which is what we’d get if we plugged the numbers into the complicated equation for compound interest. In this case, we didn’t have to.
Your familiarity with distractors will help lead you to some quick and easy points, but that’s not the only use of this knowledge. Some questions are just downright tough, especially if you’re doing well and land yourself in the deep end of the question pool. Since in the computer-adaptive format you can’t move on to the next question until you answer the one in front of can never leave an answer blank. If you get stuck, you still have to pull the trigger on some choice or another. In those cases, eliminating even a few common traps or left-field choices will put the odds in your favor and allow you to guess intelligently.
Use Scratch Paper
On test day, you’ll receive at least three pieces of blank 8½ × 11 paper. Use them! Don’t try to solve equations in your head—you get no extra points, and the risk of error is high when you’re doing complex calculations or working with complicated strings of numbers. Some people even find it handy to jot down the letters A through E (or A through D for QC questions) on their scratch paper for each new question they face, allowing them to cross off choices they eliminate so they don’t get confused with which ones they chopped and which ones are still in contention. Try out this strategy to see whether it works for you.
If you use up your batch of paper, ask for more during the break between sections. The test center’s proctor will give you more, in batches of three sheets at a time. You’ll have to hand in your used scratch paper to the test proctor to get more, and you won’t be able to take the scratch paper with you when you leave the testing center.
Avoid Careless Mistakes
The bane of test takers at all levels is selecting the wrong answer to a question they know how to solve. Such mistakes are understandable, considering the pressure of the test and the timing restrictions which often force people to work faster than they’d like. But it doesn’t have to be this way. To avoid careless mistakes, follow these tips:
- Slow down. Although rushing may allow you to answer more questions, a multitude of wrong answers, especially in the beginning of the test, could send your score plummeting. Think through the questions before jumping in to solve them. Taking the necessary time to select the proper approach will help you get off on the right foot before investing tons of time in a fruitless direction.
- Read the question carefully. The test makers have a knack for asking strange or unexpected questions, the kind not usually asked in math class. Make sure that you answer the question asked rather than the question you think they might ask. If you have time, reread the question one last time before making your final selection to make sure you’re giving them what they want. For example, if they give you a question about boys and girls and ask for the number of boys, make sure you don’t accidentally go with the number of girls or the total number of boys and girls, things you very well may determine along the way. As we noted earlier, the test makers like to scatter such traps among the choices to catch the careless. Also pay attention to the units given in the problems: If they give you information in terms of minutes but ask for the answer in hours, you better take notice. In addition, if the test makers want you to round an answer, they’ll instruct you to do so, and when they’re looking for an approximate value (as is sometimes the case in DI questions), they’ll tell you that too. Listen for exactly what they want, and then give it to them.
- Study your practice sets. Don’t gloss over careless errors in your practice problems. Study them! It’s one thing to simply not know how to do a problem, and quite another to think you aced it only to find out otherwise. Figure out where you went wrong. Were you rushing? Did you mix up numbers or fall for a common trap? Perhaps you did all the right math but then selected something other than what they asked for? Determine where your mistake lies and figure out what you need to do to avoid making that same mistake again.