I hear this from a lot of you. Unfortunately, as I explained recently, having more time on the GRE wouldn’t actually help you get a higher score, since the GRE is a scaled test. So let’s leave the complaining to our competition, shall we? Instead of moaning about the clock, strive be as awesome as you can at solving problems. If you’re great, you’ll also be fast. Here’s a quantitative comparison that’s pretty simple, but also a nice illustratration of the fact that speed isn’t something that comes independently of problem solving skill.
This problem, like several I’ve been looking at recently, comes from our GRE Bootcamp event:
Quantity A: The sum of all integers from 9 to 29, inclusive
Quantity B: The sum of all integers from 12 to 30, inclusive
At a glance, the “math” way to solve this problem is time-consuming but direct: add up the sums in both columns, then compare. Since there’s an on-screen calculator on the GRE, some of your competition will solve the problem this way. And boy does it take a long time.
Let me be very clear: directly totaling both columns isn’t just a slow way to solve the problem. It’s a BAD way. Someone who solves the problem in this head-on, brute force fashion, then says to themselves, “I’m fine with the problems, it’s the timing that kills me,” is being dishonest with themselves. They are not ”fine with the problems.” They are very much unfine!
Instead, when you have to compare two quantities, start by eliminating what they have in common. If a quantity appears in both columns, then it isn’t helping either one to be bigger than the other.
Here, both columns include the range of numbers 12-29. Thus, totaling that range would be a waste of time. Ignore it and look instead at what’s different:
Quantity A: The sum of all integers from 9 to 11, inclusive
Quantity B: The of all integers from … never mind, it’s just 30!
And since 9 + 10 + 11 clearly equals 30, you can click choice (C) — “The two quantities are equal” — in under 10 seconds and score the point. That’s the beauty of the GRE: if you’re awesome, speed comes for free. Practice will get you there!
For anyone who ate too much chocolate last week and is looking for a sweet treat that won’t add to his or her waistline, look no further: How would you like a quick way to solve rate & speed problems that have lots of variables? It probably doesn’t sound quite as good as a box of truffles does, but truffles unfortunately aren’t going to get you into grad school.
The beautiful thing about rate problem is that they virtually always are written as a fraction. Think about it: Any rate – miles/gallon, cookies/jar, heartbeats/minute – is just one term divided by another term. So when you’re setting up a rate problem in which you have variables without real numbers, figuring out where each variable goes in the fraction – the numerator or the denominator – will often get you directly to the correct answer. Let’s look at an example to demonstrate this:
Sweetheart Candies sells boxes holding p pieces of chocolate each. The boxes are shipped in crates, each holding b boxes. What is the price charged per piece of chocolate, in cents, if Sweetheart Candies charges m dollars for each crate?
What’s this question asking us for? We’re looking for the price per piece of chocolate, in cents. The keyword “per”, along with the fact that the answer choices are all fractions, clue us into the fact that this is a rate problem. We have three variables, so let’s see where we can put them in the fraction.
Anything that comes before the “per” will go in the fraction’s numerator. In this case, that’s the price. m is the only variable that has anything to do with money, so it must be on top. If we glance back up at the answer choices right now, which answer choices can we eliminate because they don’t correctly place m? That’s right: (A), (C), and (E) are now gone.
The only difference between (B) and (D), the two remaining choices, is that (B) multiplies m by 100. Is that extra 100 a necessary component of the rate that we’ve been asked to set up? Let’s think: The problem asks for the price, in cents, but m represents a number of dollars. So yes, we absolutely need to multiply m by 100 to get from dollars to cents. And voila – choice (D) is out, and we’ve determined that (B ) is the correct answer.
The next time that you’re confronted with a tough rate problem that involves multiple variables, don’t despair – just figure out whether each variable belongs on the top of the bottom of the fraction. On Test Day, you’ll have nailed points and moved on before your competition is even done reading the problem!
In my last entry, about quick arithmetic tricks, I mentioned that you should never try to do extensive math calculations in your head. This bears further explanation, as it’s counterintuitive to many students. After all, why wouldn’t it save time to do a few steps in your head, instead of writing them down? The short answer is this: Trying to do more than one step mentally, without writing anything down, will end up taking you more time and will lead to more errors.
Think about the last time that you tried to do multiple steps in your head, and the questions that it ended up raising: Did I remember to divide by 2 at the end? Did I end up with x in the denominator, or was it x2? And once those questions start coming, there are only two options: Proceed with the result you got and hope that it’s correct, or backtrack and run through all of the steps again. Do you like either of those routes? Neither do I. If you instead write down the steps as you’re doing them, you’ll not only avoid a lot of calculation errors, but you’ll also have work to refer back to in case you end up with a result that doesn’t match an answer choice.
Process of elimination is an important part of test-taking success, but it’s not effective to mentally remember which choices you’ve already eliminated, and it’s inefficient to write out the letters “ABCDE(F)” out 80-100 times. Add a new column to this chart each time you need to keep track of which answers you’ve eliminated, and you’ll save precious minutes on each section – as you’ve learned by now (and as my “arithmetic tricks” entry began driving home), it’s the confluence of many small factors that lead to Test Day confidence and success.
What strategies have you been applying in your studies to work through problems and tests smoothly and accurately? Let us know in the comments!
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!
As a Kaplan instructor, one of my primary goals is to make students comfortable with a variety of methods and strategies that will help them on test day, and build up their confidence in their ability to apply these strategies. For example, take this problem:
Employee X is paid $19.50 an hour no matter how many hours he works per week. Employee Y is paid $18 an hour for the first 40 hours she works in a week and is paid 1.5 times the hourly rate for every additional hour she works. On a certain week, both employees worked the same number of hours and were paid the same amount. How many hours did each employee work that week?
This problem looks like it’ll take a lot of calculation to solve, but let’s think critically. If each employee worked a regular 40-hour week, could they be paid the same amount? No – until we get past the 40-hour mark, employee X will always out-earn employee Y. Employee Y thus has to work more than 40 hours and get some overtime pay to even things out. So without putting pencil to paper or using the calculator, we’ve eliminated 3 out of the 5 answer choices. Now, we can just test out either choice (D) or choice (E) – if the one that we choose to test out gives us the same weekly pay for both workers, then great! We’ve found the answer. And if it doesn’t, then (still) great! We know that the other choice must be correct.
Inevitably, whenever I teach this, at least one student says, “But I could just set up an equation and solve this algebraically – what’s the point of even trying to solve this way?” Here’s why: Pacing. In each quantitative section, you have to complete 20 questions in 35 minutes. Overall, that’s less than an average of 2 minutes per problem, and some problems will take far longer than the average to complete. And don’t forget: The better you get at the first quant section, the more difficult the second section becomes.
To save time for the really tough questions, you need to bank as much time as possible on any problem that can be solved by applying a strategy and critical thinking instead of doing a slew of calculations. And when you practice, you want to ask yourself not only “How can I find the correct answer?”, but also “How could I eliminate as many incorrect answers as possible if I saw this problem with 15 seconds left in the section?” If you do so consistently, you’ll put yourself miles ahead of the competition and add points to your GRE score on Test Day.