GRE teachers have a love/hate relationship with the calculator that testers get on their quantitative section. It can be useful in certain situations – if you have to multiply 372 by 754, for example, then by all means take advantage of the calculator to get a quick answer. By and large, though, we find that the majority of our students, even the ones who use a lot of math as part of their jobs or classes, overuse the calculator on problems that they could solve much faster by hand. It’s not because they’re unintelligent or lazy – given how ubiquitous calculators and spreadsheets are in our daily lives now, a lot of people just don’t remember how to do quick scratch-paper arithmetic. (You’ll notice that I didn’t say “mental” arithmetic – do not do any steps in your head! Write your work down. But that’s a topic for another day.)
So, to help remedy this problem, here are some quick arithmetic tricks that you can use to save yourself time and energy on the GRE:
- To divide by 4: Divide the number by 2, and then divide by 2 again.
- To multiply by 4: Flip the last trick. Double the number, and then double again.
- To multiply by 5: Multiply the number by 10, and divide by 2. (For integers, this just means adding a 0 to the end of the number and taking half of the result.)
- To divide by 5: Again, flip the previous tip. Divide the number by 10 (take away a 0 or move the decimal point one unit to the left), and double it.
- Once you’ve multiplying and dividing by 4 and 5 down, working with other numbers becomes simpler as well: Multiplying by 6, for example, just involves doubling a number and then multiplying that by 3.
- To quickly find percentages, multiply the number by the integer value of the percent, and use logic to determine where the decimal point goes. For example: If you need to find 12% of 300, first multiply 12 and 300: That gives us 3600. But we’re looking for a value that’s just a bit bigger than 30 (which is 10% of 300), so our answer must be just 36.
Applying these tricks may feel like a poor use of time at first, but if you practice by doing just a couple of calculations a day this way, by Test Day you’ll be a scratch-paper math whiz – able to outpace both the calculator and everyone else in the testing room!
In my last blog entry, I wrote that knowing the Kaplan methods and strategies like the back of your hand, and being able to apply them without hesitation, will help prevent you from freezing in the face of tough problems on test day. To demonstrate exactly what I meant, I decided to devote today’s entry to an example:
If n is a non-negative integer such that 12n is a divisor of 3,176,793, what is the value of n12 – 12n ?
Well, what do we do? Panic? Let’s try some good old-fashioned critical thinking instead:
- What is this problem testing?
It’s testing divisibility – we know that 12n divides evenly into 3,176,793, which means that 3,176,793/12n is an integer. We need to find the value of n in order to get an answer to the question.
- What strategies have we used on previous divisibility problems?
If we know exactly what numbers we’re working with, we can use the divisibility rules (the rules that allow you to tell quickly whether a number is divisible by 3, 4, 6, etc). That won’t help in this case, since we don’t know the value of 12n.
We’ll have to use the other common approach to tackling divisibility problems: Prime factorization. Breaking both 3,176,793 and 12n apart into prime factors will allow us to cancel out common terms.
Let’s start with the denominator: 12n can be broken apart into 2n*2n*3n.
Now let’s look at 3,176,793: It might be divisible by 3, but is divisible by 2? No way – it’s odd, and no odd number can be evenly divisible by 2.
- So if 3,176,793 isn’t divisible by 2, how can it be divisible by 12n?
Now we’re getting somewhere: For that giant odd number to be divisible by 12n, 12n must be odd.
There’s only one value of n that will make 12n odd: If n = 0, then 12n will equal 1.
- So we just did all that work to determine that the correct answer is 0, answer choice (C)? My head hurts.
Actually, we’re not quite done yet – we weren’t asked for the value of n; we were asked for the value of n12 – 12n. We just need to plug in 0 for n: 012 – 120 = 0 – 1 = -1.
The strategic process of determining what approach would best serve us, based on the topic being tested, allowed us to sniff out the trick to this problem. If you consistently apply the same approach in your own work, you’ll be miles ahead of the competition on GRE test day!
I consider Sentence Equivalence the tougher of the two “short” question types of the GRE verbal section. That’s because in a Text Completion, all you have to do is pick the right words — but in a Sentence Equivalence, you have to pick the right words and make sure the words you pick have an equivalent effect on the sentence. It’s this “equivalent effect” requirement that can sometimes make SE’s so maddening to students, and the logic behind it is what I’d like to clarify in this entry.
Let’s start, as we often do, with an example problem:
The professor’s delivery was so _______ that no student was happy, and some walked out before the lecture was half over.
In short verbal problems, find clues in the sentence and try to predict the blank before looking at the choices. Here, you know that “no student was happy” and that some even walked out on the professor. Clearly, then, the professor’s delivery wasn’t very good. However, you can’t predict exactly what it was about the professor’s delivery that made her lecture so bad. There are many ways in which a lecture could displease students, and that’s where this problem gets tricky.
For starters, let’s kick out galvanizing (“energizing”) and enlightening, which are positive words. That leaves soporific, offensive, boring, and demoralizing.
If you’re a long-time reader of this blog, you might remember what soporific means. But let’s suppose you don’t. What can you do about offensive, boring, and demoralizing? You might get frustrated here because those all seem like reasonable words to put into the sentence. Lectures that offend, bore, or cause students to lose hope could all drive students out of the classroom. But those things are all very different. While all of those words produce a reasonable meaning in the sentence, no two of them produce the SAME meaning.
Thus, even if you don’t know what soporific means, you should be able to tell on GRE Test Day that it MUST be one of the correct answers, since no pairing of the other three satisfies the “equivalent effect” requirement. It so happens that soporific means “sleep-inducing,” so the partner word that yields the same effect is choice C, boring. Choices A and C are the winners.
Sometimes the hardest thing about solving a GRE problem is understanding its requirements. If you’re still confused about Sentence Equivalence, ask here!
Greetings! For the third part of this series, I took it to the camera:
If you’d like to take a practice test — but hopefully not a week before your actual Test Day — we do in fact do them for free.
If you’ve been studying your GRE vocabulary for any length of time, you’re probably familiar with the concept of word groups: A list of words that all have similar-enough meanings to be considered, for GRE purposes, interchangeable synonyms. I haven’t heard a single person argue against the benefits of learning word groups, but memorizing the lists themselves isn’t the easiest proposition. The trick to learning word lists efficiently is to work with your brain’s natural inclination to remember words that are associated with other things. For example, which of these two sentences is more likely to help you remember the definition of “perspicacious”?
- “Perspicacious” means “keen” or “intelligent”.
- The company’s perspicacious president solved many of the business’s problems by determining the issues underlying the flat-lining sales.
While the first sentence is just a recitation of the word’s definition, the second word gives you a context and some color that you can use to remember the word’s meaning. On Test Day, when you see “perspicacious” among the answer choices of a text completion, you’ll recall the company president’s accomplishments and remember that the word means “intelligent”.
Now comes the part in which you get to inject some creativity into your otherwise-straightforward GRE studies: Pick one of the word groups, and write a paragraph-long story in which you use as many of the words from the group as possible. Before you start writing, pick an overarching plotline that fits with the group you’re working with.
If you’re working with the “criticize” word group, for example, the story could be about a harangued child whose mother and teacher constantly deride him. He could even have an older brother, who also excoriates him. Or, if you’re in a lighter mood, you can tackle the “funny” word group and write about a comedy duo whose jocular performance was filled with droll raillery, and much riposte.
The act of writing a paragraph for each key word group will give you a clear association between the words and not just one sentence, but an entire paragraph with context that will allow you to recall the definition when you see any of the words on GRE Test Day. Now get your imaginative juices flowing – let us know in the comments what you end up writing about!