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!
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 about combinations – it’s one of my favorite topics, and hopefully you’re feeling more confident about it after learning the tricks discussed. Today, let’s follow up with a look at how to tackle permutations, also known as “those terrible questions that ask me to arrange number and letters”.
I set up permutations using the “slot method”: Line up as many “slots” as you are arranging items, and fill in each slot with the number of items that could possibly go in that place. In this case, we’re arranging 5 items, so I’ll set up 5 slots: ___ ___ ___ ___ ___
Since NEUTRAL has 7 letters, and any of them could go in the first space, we put a 7 there:
7 ___ ___ ___ ___
Once one letter is “placed” in that first slot, there are 6 remaining options for what can go in the second slot:
7, 6 ___ ___ ___
Hopefully you’re starting to see the pattern here – we’re just decreasing the number in each slot by 1, as there will be 1 fewer letter to “place” as each slot gets filled. Our completed chart looks like this:
7, 6, 5, 4, 3. To calculate the number of permutations, we just multiply each of these numbers together: 7*6*5*4*3 = 2,520, and answer choice (D) is correct.
The slot method applies no matter how many rules or restrictions a problem gives you on where certain items can be placed. Let’s look at a tougher example:
First, let’s ignore the restriction about David and Alice and see how many arrangements of 6 people there are: 6*5*4*3*2*1 = 720. Now we need to figure out how many of those arrangements include David and Alice standing next to each other. It’ll be easier here to figure out how many scenarios actually have them standing next to each other, and subtract that from the total of 720.
We can draw a couple of sketches to visualize:
Al, Da, ___ ___ ___ ___
___ Al, Da, ___ ___ ___
And so on, and so forth, until we see that there are a total of 10 scenarios in which David and Alice are next to each other: 5 in which Alice is to the left of David, and 5 in which David is to the left of Alice.
For each “placement” of David and Alice, we can’t forget to arrange the other 4 people:
Al, Da, 4* 3* 2* 1. In each instance in which these two are standing next to each other, there are 24 arrangements of the other people .
(10 scenarios in which David and Alice are next to each other) * (24 arrangements of the remaining 4 people) = 240 total “prohibited” permutations. (720 total arrangements) – (240 prohibited permutations) = 480 scenarios in which Alice and David are not next to each other, and Quantity B is greater.
Permutations provide a great opportunity to pick up points that the vast majority of test-takers leave on the table – use the slots to your advantage and see the impact that it has on your score!
A couple of months ago, my fellow blogger Boris wrote an entry entitled “A Math Test: What the GRE Quantitative Section Isn’t”. In it, he explains that the GRE is test of your logic skills, not your ability to do complicated math. There are lots of math shortcuts that will get you points while saving you time and energy on the GRE quant section. Here are the key shortcuts to know when working with percentages, on which students tend to do far more calculations than necessary:
- If you’re comparing percentages from the same total value, you can just compare the percentages without calculating the real values. Consider this problem:
Yes, you could set up an equation to find the value of c, and then take 47% of that. But since we’re comparing two percentages that are taken from the same total, we can save time. We know that the value of 21% of c is 840, and we’re looking for the value of 47% of c.
47 is a little more than twice 21, so the correct answer must be a little more than twice 840. 840*2 = 1,680, and only one choice is larger than that: Choice (E), 1,880. Problem solved with one calculation.
- x% of y = y% of x. This is true because of the commutative property of multiplication – thank me when you now have something to talk about at your office holiday party. Here’s how it can help you on the GRE:
Based on the commutative property, we can tell that these two quantities are equal without making a single note or doing a single calculation. Since you have an average of 1.5 minutes per quantitative comparison, you just banked approximately 1 minute and 20 seconds to spend on a tougher problem. This concept pops up in more convoluted questions as well; be on the lookout to use it whenever possible.
- If you decrease a number by a certain percentage, and increase the result by that same percentage, you will not get your starting number as a result. Let’s look at a problem to explain exactly what this means:
We need to use the centered information to find the values of x and y to get a value for Quantity A. We know that after a 25% discount, the sweater cost $36. So can we take 25% of 36, add that to 36, and get our answer? No, because of the principle stated above – decreasing something by 25% is not the same thing as increasing that result by 25%. Instead, think of it this way: Since we decreased x by 25%, the remaining $36 represents 75% of the pre-discount cost. So 75% of x = 36, and we can solve for x this way.
I’m going to leave the rest of this problem for you to do on your own – let me know what answer you get in the comments! Keep these percentages tricks in mind, and you’ll save precious time on test day.
In my last couple of posts here and here, I’ve discussed strategies to tackle Data Interpretation problems. For the most part, test-takers find these question types straightforward and easy to handle, but there are some difficult questions sprinkled amongst the easy ones. As you tackle Data Interpretation problems, be cognizant of the fact that it’s very easy to get into a groove and become over-confident. The test-makers love to present a tough problem right at the moment when you think you’re crushing all of the questions. However, as long as you stay alert and on the lookout for difficult or oddly worded problems, you’ll be okay.
Let’s take for example the following pie charts. As I discussed in my earlier posts, the first thing you want to do when faced with Data Interpretation questions is take a quick moment to familiarize yourself with the different diagrams and data being presented. Here, the pie chart on the left shows us the distribution of the TOTAL amount of National Park Land, while the pie chart on the right is simply a breakdown of the “Acreage of National Parks”.
The test-makers will first ask a few straightforward questions. Let’s imagine that they ask you to determine the land area of National Monuments. If you look to the pie chart on the left, you’ll notice that the land area of National monuments is 6% of 79.6 million acres. Using rounding, you can determine that 6% of 80 million is 4.8 million, so the correct answer will be right around that amount.
Next, they might increase the difficulty level just a bit by asking you to determine the land area of Glacier Bay and Everglades. Here, you will need to deploy a two-step process to answer the question. Since Glacier Bay and Everglades are on the chart on the right, which is a representation of National Park acreage, you’ll need to find the total acreage of National Parks. Looking to the left, you’ll see that 59% of 79.6 million acres is the total land amount of National Parks; using rounding, you can say that that amount is about 48 million acres. The acreage of Glacier Bay (7%) and Everglades (3%) is a combined 10% of National Parks. Therefore, 10% of 48 million is around 4.8 million acres.
It’s around this point that the test-makers love to throw a curveball. Since they’ve been having you calculate values based off of percent values, they’re hoping that they’ve lulled you into a habit of simply finding a specific percent on the chart and calculating a value quickly. So if you’re given a question like this, be careful.
How much larger is the acreage of National Monuments than the acreage of National Recreation Areas, as a percent?
It’s very easy to look to the pie chart on the left and jump to the conclusion that because National Monuments are 6% of Total Acreage and National Recreation Areas are 5% of Total Acreage, then National Monuments must be 1% larger than National Recreation Areas. Makes sense, right? I mean, there is a 1% difference in the size of the two acreages. But the test-makers aren’t asking you to compare the acreage of Monuments and the acreage of Recreational Areas to the Total Acreage – they’re asking you to compare those two areas to each other. So in order to figure out how much larger the acreage of National Monuments is compared to the acreage of Recreational Areas, you need to find the difference between the two, then divide that amount by the smaller of the two values. Using the values presented on the chart, we can determine that the acreage of Monuments is around 4.8 million, while the acreage of Recreational Areas is 4 million. So there are .8 million more acres of land that make up National Monuments. If we divide that value by 4 million, we get a value of .2, or 1/5. Therefore, the size of the acreage of the National Monuments is actually 20% larger than the size of the acreage of the National Recreation Areas.
Don’t get lulled into a false sense of security or overconfidence when tackling Data Interpretation problems. Though many DI questions are easy and straightforward, be on guard when you notice a question that looks too easy. Always slow down, pause, and double check what the question is asking.
Do you have questions about Data Interpretation problems on the GRE? Ask them here!
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