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!
In honor of the upcoming weekend, I decided to devote this entry to some great math-themed movies that you can watch the next time you need a break from your GRE studies. Giving yourself time off is important, and there’s no reason that you can’t use that time to let some of these classic (and not-so-well-known) stories characters inspire you to knock your next study session out of the park.
In no particular order, here are my recommendations:
- 21: Several MIT students are trained to count cards, and go to Las Vegas to win millions playing blackjack. I’m always a fan of Kevin Spacey, who places a professor, and hey – you may come away from this movie with a completely new, very valuable skill set that you can take on your next trip to Vegas.
- Moneyball: While everyone who saw this movie focused on Brad Pitt (understandably so), there was a lot of fun discussion about how to use math to cut through bias and human, error-prone perception. If you’re a sports fan, you’ll enjoy this baseball-themed movie. If you’re not a sports fan, don’t worry – it has Brad Pitt and Jonah Hill in it, and is very well-written.
- Fermat’s Room: This Spanish movie is about several mathematicians who are trapped together in a room and forced to solve “enigmas” or risk being killed as the room becomes increasingly small, all while trying to determine who is trying to kill them – it’s a combination of “Clue” and the scene from Star Wars in which Luke Skywalker & company are trapped in the Death Star’s garbage compactor. At the very least, it’ll make you feel better about the fact that the GRE testing room won’t close on in you if you get an incorrect answer!
- Good Will Hunting: Matt Damon as a math prodigy who, with the guidance of mentor –therapist Robin Williams, must decide what to make of his life. Certainly a good pick-me-up for anyone who is at a crossroads (as many who are applying to grad school are!), but be warned: You might come out of this movie speaking with a Boston accent.
These are just a sampling of some of the great movies that you can use to motivate you in your GRE prep – what are your favorite math-themed movies? Let us know in the comments!
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!
Not too long ago, I used something called the “balance approach” to show you how to solve a mixtures problem. But the balance technique isn’t exclusive to mixtures. In fact, the most likely time for it to come up is when a problem deals with plain ol’ averages.
Here’s an example of the kind of GRE problem I’m talking about:
At a bowling tournament in which males and females competed, the average score of the participants was 154 points. If the average score of the 8 males was 148 points, how many females were in the tournament if the average female score was 158 points?
Most of your competition is going to try to use the average formula: average equals sum divided by number, or as I prefer to write it,
Average × Number = Sum
Using the above formula gives you this:
154(8 + x) = 8(148) + x(158)
There are a couple of problems here. One, you have to do some nasty arithmetic, such as 154×8 and 8×148. And perhaps more importantly, it takes a rather impressive feat of translation to set that baby up.
Try this instead.
The overall average is 154. Each man got 148 points, which is 6 points short of the average. There were 8 men, so altogether, they dragged down the average by 8×6 = 48 points.
This means the women need to make up a 48 point deficit. Each woman scores a 158, which is 4 points above the average. If each woman contributes 4 points to overcoming the 48 point shortfall, then there need to be 48/4 = 12 of them.
That sure was a lot easier than solving the equation. And if you’re a real critical thinking wizard, you might notice that even this was too much work. The ratio of the men’s deficit (-6) to the women’s surplus (+4) is 6 to 4, or 1.5. Thus, the ratio of women to men also needs to be 1.5, and that it is: 12÷8 = 1.5.
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!