How To Get Better at the GMAT (or Anything Else)
Imagine two students sit down to study GMAT questions together. The first takes out 100 addition questions and gets all of them right. The other takes out 100 of the most-difficult, 800-level GMAT questions one can find, and gets all of them wrong. Who benefits more from this type of studying? It’s an absurd thought experiment since it’s fairly obvious that neither of these students is benefitting much from their study method. But over my years of teaching the GMAT, I’ve seen far too many students who fit too closely into one of these two camps. Students who are great at quant but not at verbal, yet spend all of their time doing quant questions because they are “more fun”. Other students are determined to score 750 and spend all of their time and effort doing as many 700-800 level questions as they can find, not seeing an improvement, and thinking that the solution is to see more 700-800 level questions. This isn’t some profound discovery, but too many students miss this critical point:
You get better at the GMAT by identifying a weakness, learning a better/faster method to attack that weakness, and practicing that method until it becomes habit. Repeat.
Note that this doesn’t mean that you have to do 50 rate questions and by question 50, you’ll be a master at determining the train schedule between two different towns. Nor do you need to do every question in every GMAT-related book you can get your hands on. If you’ve been to a Manhattan class, you’ve seen first-hand that our instructors’ goal is not to do as many questions as we can cram into a class. There are some topics in class where we only look at 4-5 questions, but we spend an hour breaking down the methods, key words, traps, and wrong answer choices that will be similar to the methods, key words, traps, and wrong answer choices that students will one day see on the real test. The goal is never to see why Answer Choice E is a trap answer. It’s to see why Answer Choice E fits into a certain category of trap answers and learn how to avoid that category of trap answers come test day.
So how does this relate to your own studying? Let’s talk about what a productive 1-hour study session might look like by examining what many of my own study sessions looked like while I was studying for my GMAT.
Another Way To Solve Median & Mean Questions
This is the second of a series of posts that offer alternate ways to solve certain GMAT problems (check out the first here: DS Value Problems). Just like last time, if you like the method, steal it! And if you don’t, I promise not to lose any sleep. There’s a lot of ways to solve most questions on the GMAT and the best way will always be the way that works best for you. So without further ado, let’s check out a GMATPrep question and see how fast you can solve:
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?
I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than $130,000 and less than $150,000.
III. At least one of the homes was sold for less than $130,000.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
First things first, if you answered this question using algebra, you’re in great company. Another one of our instructors, Stacey Koprince, has a great write up on the algebra in this question, and it’s definitely worth a read-through right here. But a lot of questions on the GMAT, including this one, can be solved by thinking of extremely simple scenarios, rather than the algebra that determines all of them.
The first thing I noticed on this question is that this is one of those awful questions where there’s a whole lot of wiggle room with the information that they give you. What was the cheapest house? What was the cost of the third most expensive house? Were any of the houses all the same price? If the second cheapest house is half as expensive as the most expensive, how does that affect the cost of the other houses? It’s easy to get lost when you start to think about how little you know in this scenario.
But before I jump around and start picking values out of thin air, the most important part of this problem are the (few) things that MUST be true. In this case, there are two: the 15 house prices have a mean of $150,000 and a median of $130,000. And on my paper, I would write out a few slots to represent the house prices like this: (note- I wouldn’t write out all 15 slots. Just the first few, the last few, and, since this is a median problem, one in the middle.)
____ |
____ |
… |
____ |
… |
____ |
____ |
1 |
2 |
7 |
14 |
15 |
Again, there are two things that they tell me here, but I want to start with the most restrictive element in this problem. There are lots of different ways to get a mean of $150,000, but in order to get a median of $130,000, I would need at least one house to cost EXACTLY $130,000. So I add that to my chart (ignoring the $ sign and extra zeroes):
4 Kinds of Questions to Review
What’s the difference between a real GMAT and a practice one? On the real GMAT, you’re finished after three and a half hours, give or take. But while you are preparing for the GMAT, finishing a practice test is much different than being finished with it. As I’ve written about before, practice tests are great assessment tools but not necessarily great learning tools. Practice tests tell you what you would likely score on the real GMAT if you answered 37 quant and 41 verbal questions with the same level of aptitude that you had on the questions you just saw. But if you want to see your GMAT score improve, you’re going to have to spend some time reviewing what you did, how you did it, and how you could do it better. To help you on that quest to get better, here are four kinds of questions that you can use to help improve your score.
1) Questions You Got Wrong
This one is the obvious one- if you want to get better at the GMAT, you need to find questions that you got wrong and learn how to get them right. But this isn’t as simple as finding an explanation online and memorizing it. Studying for the GMAT is more than just trying to read and memorize a bunch of facts- it’s about changing the way that your brain thinks about how to manipulate an equation or dissect an argument. And what better way for your brain to learn how to tackle a challenge than to give your brain more time to do so. In the middle of a test, your brain is rushed. You might have had to give up on the question halfway through or guessed on it immediately to save yourself time. But when you give your brain more time to discover that A-HA! moment, your brain is much more likely to recognize what to do the next time you see a similar hurdle. After you spend some time trying to solve it on your own, feel free to search for an explanation or a better way of solving a problem. However, you have to make sure that the explanation you read is something that you can do in your own head or your own paper come test day.
Another Way to Solve Data Sufficiency Value Problems, The Goldilocks Method, & Finding a Number That’s Just Right
One of the hardest parts about becoming an instructor with Manhattan GMAT was relearning how to solve GMAT questions. That sounds absurd, considering I had already scored a 780 on the GMAT when I applied to become an instructor, but it’s true. During the interview process, I went through online and in-person classroom simulations with 99th percentile instructors playing students, testing my ability to explain a question using algebra instead of plugging numbers or using a rate chart instead of adding rates. Over the years, I’ve found that many of our instructors felt the same way: overwhelmed by how hard it is to go along with someone else’s preferred method without skipping a beat. Ultimately, I realized that teaching the GMAT is a hundred times harder than taking the GMAT because every question has several valid ways of being solved.
Which leads to the problem of what solution is the BEST solution. Any student who has worked with me over the years has heard me say the following- I don’t care what method you use to solve a problem. But I do care that you get great at that method. It’s the reason why the Official Guide has an explanation for each quant problem and Manhattan has an OG Companion with different explanations, along with online video explanations that will sometimes differ from either of those methods. With so many different ways of solving a question, it’s important to not get bogged down finding the best way to solve a problem, but instead focus on finding the fastest way from start to submit.
So with that said, over the next few months, I’d like to share a few methods that I personally use when solving a few different types of GMAT questions. Some of these methods might click for you, and I hope you practice them. Some of them won’t and I hope you stick with a method that works better for you. So without further ado- let’s take a look at a fairly straightforward GMATPrep problem and think about how you would attack this question:
A sum of $200,000 from a certain estate was divided among a spouse and three children. How much of the estate did the youngest child receive?
(1) The spouse received 1/2 of the sum from the estate, and the oldest child received 1/4 of the remainder.
(2) Each of the two younger children received $12,500 more than the oldest child and $62,500 less than the spouse.
The first two things that I notice about this problem is that it is a word problem, giving us a real-world scenario, and a value Data Sufficiency question, asking us to find a single value for the amount that the youngest child received. And if I wanted to set this up algebraically, I could assign variables (s = spouse, x, y, z = oldest, middle, youngest child), write out several equations (s + x + y + z = 200,000. (1) s = 1/2*200,000; x = 1/4 * (1/2*200,000); y + z = 75,000. (2) y = z; z = x + 12,500; z = s âˆ’ 62,500), and eventually solve for z using Statement 2: the correct answer is (B). Different students at different levels of comfort with Data Sufficiency will be able to stop at different points after realizing that there either will or will not be a single variable in the equation that they’ve set up.
The Power(s) of 2
Even though the NCAA tournament finished up earlier this month, for the next ten months I will be thinking about college basketball whenever I see the first several powers of two. No matter what type of GMAT question you are dealing with, our minds are better able to work through topics that we are already familiar with. Probability problems make me think of gambling, weakening a GMAT argument becomes shooting down an argument from that crazy relative you only see at Thanksgiving, and anything dealing with the number 64 comes down to rounds in a basketball tournament. Here’s a few tricks on the GMAT where knowing your powers of two can save you some time and brainpower.
1. 64 = 2^6
Know how to translate larger numbers into their smaller factors
Since 1985, every team that has won the NCAA tournament has had to win six games. By multiplying two times itself, you can expand to each round of the NCAA tournament- 2, 4, 8, 16, 32, and 64. And because these numbers are all small and have a single prime factor, they commonly end up on the GMAT. Because of this, you should be able to recognize them and quickly put each one into its base of two: 2 = 2^1, 4 = 2^2, etc. Same for the powers of three- 3, 9, 27, 81. The number 81 is far more likely to show up on your GMAT than 83, because 81 is a power of 3 that can be broken down into small prime factors. Without a calculator, numbers that are easy to break down show up 2 x 5 times more often than they do in the real world.
Studying for the GMAT? There’s An App For That.
If you asked me where I learned my countries in Africa, I’d tell you that it was from watching Where In the World is Carmen Sandiego? My knowledge of state capitals? Animaniacs. My ability to find prime numbers while being hunted by cartoon monsters in a 6×5 grid? Number Munchers.
And while these and so many other skills that I learned in school also came largely from my grade school teachers, I think that there’s an underappreciated value to using videos and games to help supplement learning. Staring at a GMAT book for an hour isn’t helpful if you aren’t learning anything because your mind is checked out. But tricking your brain into getting faster at finding numbers that multiply to 24 might be, especially if you can make time to do so on your ride to work or while waiting for your dentist appointment. And for many of us, myself included, there’s no better place in the world to find 5-minute distraction than at the App Store. So if you have an iPhone or iPad (and many of these apps are also found on Android too) check out some of these apps below. And if you have any other apps that you use, type them up in the comments below!
Note: Listing here is not an endorsement by Manhattan GMAT.
Basic Computation Apps
Working Smarter, Not Harder
What’s more valuable on the GMAT? Saving 30 seconds on a question that took you 2:30 to solve? Or 30 seconds on a question that took you 1:30 to solve? Trick question. Either way, you have the same amount of extra time to use on some other question. So with that in mind, take out a timer, pen, and paper, and let’s try out a fairly straightforward GMATPrep problem.
District
Number of Votes
Percent of Votes for Candidate P
Percent of Votes for Candidate Q
1
800
60
40
2
1,000
50
50
3
1,500
50
50
4
1,800
40
60
5
1,200
30
70
The table above shows the results of a recent school board election in which the candidate with the higher total number of votes from the five districts was declared the winner. Which district had the greatest number of votes for the winner?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Now before we work through the problem. Ask yourself a few questions about what you just did:
- How confident are you in your answer?
- How much time did you take to answer?
- Looking back on your solution, was there shortcut you could have used to eliminate some of the work you did?
- If so, what specifically about this problem allows you to use your shortcut?
At this point, hopefully you either did the shortcut for this problem or discovered what the shortcut might be. Let’s start with the long method. If I wanted to calculate the number of votes for each candidate, it would look like this:
District |
Number of Votes |
Total Number of Votes for Candidate P |
Total Number of Votes for Candidate Q |
1 |
800 |
480 |
320 |
2 |
1,000 |
500 |
500 |
3 |
1,500 |
750 |
750 |
4 |
1,800 |
720 |
1,080 |
5 |
1,200 |
360 |
840 |
Total |
6,300 |
2,810 |
3,490 |
Twelve calculations later (ten products and two sums), we have all of our numbers calculated and can answer two questions:
- Who won the election? (Candidate Q)
- Which district had the most votes for that candidate? (District 4- answer D)
Let’s go back for a second though. Are there any calculations from above that we could have skipped? Let’s start by analyzing the first question from above. Who won the election?
5 Simple Math Tricks for Faster Computations
Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.
For every five hours of studying combinatorics-type questions, the average GMAT student increases their chances of being able to correctly answer a question type that is found only on the very difficult end of the GMAT spectrum. Meanwhile, the same student will have to compute hundreds of basic computations without the aid of a calculator. For students who know how to quickly do these computations, they are rewarded with extra minutes that can be spent double-checking their work and critically thinking about whether their answers make sense. As BenGMAT Franklin might say- a second saved is a second earned on the GMAT, but it doesn’t matter if those extra seconds come from being faster at doing combinatorics questions or quicker at computations. So check out these five math tricks, learn the ones that you like, and practice them daily to give yourself some extra time to finish off that 37th and final quant question.
Note: like everything else on the GMAT, being able to do something and being able to do something QUICKLY are two different tasks. If you like any of the following tricks, make sure you know it inside and out before you try using it during your test.
1. Add or Subtract 2 or 3 Digit Numbers
To add numbers that aren’t already a multiple of ten or one-hundred, round the number to the nearest tens or hundreds digit, add, and then add or subtract by the number you rounded off. Do the opposite when subtracting.
Examples:
144 + 48 = 144 + 50 – 2 = 192
1385 – 492 = 1385 – 500 + 8 = 893
Why?
This math trick comes down to the order of operations- adding and subtracting occur in the same step and can happen in either order. Like many other computation tricks, this one comes down to replacing one tricky computation with two simpler ones.
2. Multiply or Divide by 5
To multiply a number by 5, divide by 2 and then multiply by 10. To divide a number by 5, divide by 10 and then multiply by 2.
Example:
82 Ã— 5 = 82 Ã· 2 x 10 = 410
Why?
This math trick comes down to the order of operations- multiplying and dividing occur in the same step and can happen in either order. But instead of doing the (somewhat) difficult task of multiplying by 5, do the easier task of multiplying by the fraction 10/2. And since you can do this in either order, you can start by dividing a number by 2 or multiplying the number by 10. Starting with division is usually easier when you start with an even number (34 × 5 = 17 x 10 = 170) while starting with multiplication is easier when beginning with a non-integer (6.4 × 5 = 64 ÷ 2 = 32). And instead of thinking about dividing by 5, think about multiplying by 2/10 (455 ÷ 5 = 45.5 × 2 = 91).
3. Multiply Numbers Between 11 & 19
To multiply two numbers that are between 11 and 19, add the ones digit of one number to the other number, multiply by 10, and then add the product of the ones digits.
Example:
Why?
In the standard way that most American-students are taught to multiply numbers, you set up two numbers on top of one another like this:
This leads to a problem where you multiply 3 by 14, then multiply 10 by 14 and add the two products together. But you can rearrange this problem further to say you want to multiply 3 by 4, 3 by 10, and 10 by 14. Because you are multiplying both 3 and 14 by the same factor of 10 (which only happens when both numbers are between 11-19), you can combine this into one step. So instead of doing one tricky computation (3 × 14) and two easy ones (10 × 14 and 42 + 140), you make four easy computations (14 + 3, 17 × 10, 4 × 3, and 170 + 12).
4. Square Any Number Between 11 & 99
To square any number n, first find the nearest multiple of 10 and find out how much you would have to add or subtract (k) to get to that number. Then do the opposite function (addition or subtraction) to get two numbers that average out to n (i.e. n + k and n – k). Multiply those two numbers and add the square of k.
Examples:
23^{2} = (26 x 20) + 3^{2} = 529
97^{2} = (100 x 94) + 3^{2} = 9409
Why?
a^{2} – b^{2} = (a+b)(a-b)
a^{2} = (a+b)(a-b) + b^{2}
If this special product doesn’t look familiar to you, write it down right now and memorize it because there are a plethora of GMAT questions that test you on this very concept. But for this special trick, you are (once again) trading a difficult calculation (23 x 23) for a few simpler ones.
23^{2} – 3^{2} = (23+3)(23-3)
23^{2} – 3^{2} = (26)(20)
23^{2} = (26)(20) + 3^{2}
23^{2} = 529
Since multiplying by multiples of ten are usually easier than non-multiples of ten, you find the nearest multiple of ten. While this may be very confusing at first, it’s a neat trick if you can get quick with it and is especially helpful when squaring numbers ending in five, since you will always add 25 to the lower and higher multiple of 10:
45^{2} = (40 x 50) + 5^{2} = 2025
65^{2} = (60 x 70) + 5^{2} = 4225
5. Estimate Root 2 & Root 3
Example:
The length of some side of a figure is about equal to 13 and you are down to the following three options:
a) 9 √2
b) 9 / √2
c) 15 * (1 – 1/√2)
By estimating √2 ≈ 1.4 or even 3/2, you could quickly recognize that only answer (A) could be correct in this problem.
Why?
Because your calculator says so! But rather than trying to remember these two roots on test day, remember your two favorite holidays in the second and third months of the year- Valentine’s Day & St. Patrick’s Day, 2/14 and 3/17. Root of 2 is about 1.4 and Root of 3 is about 1.7. The above example is adapted from an old Official Guide problem and is a reminder of how the GMAT’s wrong answer choices aren’t there because they are close to correct value, but because they are some incorrect computational jumble of the numbers given in the problem. If you can estimate in this problem, you can find four incorrect answer choices and that’s just as good as finding one correct answer.
Of course, the most in-depth way to learn the ins-and-outs of the GMAT is to take a complete course with one of our master instructors. You can try out any first session for free! No strings attached. We promise.
Joe Lucero is a Manhattan Prep instructor based in Washington, DC. Joe teaches both the GMAT and the GRE for Manhattan Prep, owning scores of 780 on the GMAT and a 170Q/167V on the GRE. Joe graduated from the University of Notre Dame in 2005 with a degree in Biology and began his teaching career in math and science before managing the educational programming for the Fort Worth Zoo. Joe’s passion for teaching keeps classes engaged whether he’s holding an Expo marker or an American alligator. Check out Joe’s upcoming GMAT courses here.
How Would Nate Silver Take The GMAT?
Over the past several days, Nate Silver has gone from baseball and political forecasting guru to full-blown media darling. Since correctly forecasting the winning presidential candidate in 49 and 50 states in the last two elections, Silver has been seen everywhere from NBC to Comedy Central. All of this culminated Wednesday when Silver won the ultimate modern-day achievement: trending Twitter topic. And while #DrunkNateSilver has already predicted the next two presidential elections and the ending to Star Wars 7, his sober counterpart has lessons that we can apply to our GMAT studying.
The PECOTA System- Finding historical similarities
Nate Silver first became famous outside of his consulting job when he developed PECOTA, which sought to predict the statistics and career arc of major league baseball players, as well as projected team win totals. PECOTA wasn’t the first projection system for baseball, but it was the first to use other players’ previous performances instead of that player’s trends. By comparing each player with 20,000+ player’s seasons since World War II, Silver was able to make a probabilistic distribution for individual players and their teams.
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Sports Book Odds, How to Make Smart Bets, & Why You’ll Still (Probably) End Up Losing
On October 13, 2012, one of the major sports books in Las Vegas said that there was a 108.8% chance of one of the four teams left in the baseball postseason would win the World Series. Of course it didn’t actually say there was a 108.8% chance of this happening, but the odds that they released to bettors did and helped ensure that over the long run, Vegas wins and we, as a whole, lose.
If you haven’t already, check out Part 1 for a review of AND vs OR probability. Now let’s imagine that instead of betting on outcomes, like we did in the previous article, you’ve wised up and decided to open your own sports book, gMATH. You decide to start simple and offer bettors a chance to bet on which number, 1-4, randomly rolls out of a bingo cage. You realize that the probability of each number being selected is 25%, but you need a way to translate this for paying bettors. In a scenario where four different people each put down $1 on each of the four numbers, one person would win $3 ($4 total – $1 they bet). So you place the very first odds at gMATH’s number guessing game at 3 to 1.
In the long run, gMATH’s inaugural betting event may attract a clientele of people who enjoy watching ping pong balls with painted numbers roll around, but it won’t be bringing you the fortunes that you passed up on business school for. You realize that you need a new betting game that will attract more than just the bingo-loving crowd, involves a small amount of luck, and allow you to make a profit no matter which team wins. As there are exactly four teams left in the postseason, you decide that baseball would make a perfect switch.
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