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Etiqueta: Math

How to Create a GRE Problem Log for Quant

Manhattan Prep GRE Blog - How to Create a GRE Problem Log for Quant by Chelsey Cooley

Having a GRE problem log is like having a budget: sort of a pain sometimes, but much smarter than the alternative. Skeptical? Check out this article first—then come back here when you’re ready to roll.

1. Choose a format that inspires you.

Are you a gel-pen-loving bullet-journal enthusiast? Or would you rather something plain but practical, like a nice Excel spreadsheet? Your GRE problem log won’t work at all if you don’t write in it or look at it. A GRE problem log can be in any format that lets you record information in an organized way.

2. Light, heavy, or in between?

Some of us are natural self-analyzers. Some of us would rather just skip straight to the action. It’s okay if your GRE problem log is very simple. An elaborate problem log is great too. What matters is that you choose something that won’t feel like a burden.

3. The world’s simplest GRE problem log…

At the heart of it, the point of a GRE problem log is to remember what you’ve learned and to help you learn in the future. There are all kinds of little ‘aha’ moments that come from doing GRE problems: keeping a problem log makes sure those moments are recorded rather than vanishing.

With that in mind, here’s the world’s simplest GRE problem log:

Manhattan Prep GRE Blog - How to Create a GRE Problem Log for Quant by Chelsey Cooley

4. Not all takeaways are created equal.

The best takeaways are general. When you do a problem, you’re not going to see that same problem on your actual GRE. So, recording exactly how you did that specific problem is a waste of time. Your goal is to glean ideas from that problem that you could use on other problems.

The best takeaways remind you of not only what to do, but when to do it. Try to record not only which actions you took during a problem, but also how you knew what to do.

Here’s a problem from the 5 lb. Book of GRE Practice Problems:

If y≠0, what percent of y percent of 50 is 40 percent of y?

Here’s a quick solution:

  • Since y isn’t part of the answer, choose a number for y. We’ll choose 100, so we can read the problem like this:

What percent of 100 percent of 50 is 40 percent of 100?

  • Start by writing the equation as follows:

Manhattan Prep GRE Blog - How to Create a GRE Problem Log for Quant by Chelsey Cooley

  • Then, simplify the equation to solve for p:

Manhattan Prep GRE Blog - How to Create a GRE Problem Log for Quant by Chelsey Cooley

And here are some great takeaways:

  • If you see a variable percent (y%), but you aren’t solving for y, just choose 100 for y!
  • Translate ‘what percent’ as ‘p/100’ and translate ‘of’ as multiplication
  • If you see ‘100 percent’, you can just ignore it while doing math
  • Complicated percent problems can be easier to solve with fractions, rather than decimals

5. ‘Do it again?’

You don’t have to redo every single problem, or even every problem you missed. The best problems to redo are the ones that were right at the edge of your ability level. Don’t bother with the ones that were ridiculously hard, or the ones that you missed for a silly reason (although you should still write those ‘silly reasons’ down.) Redo the ones that you know you could get right with just a bit more studying.

6. Taking it up a notch…

Here’s some more information you may want to include in your GRE problem log:

  • What topic was the problem testing? This way, you can quickly skim your log to find all of the Algebra problems, or all of the Geometry problems, and so on.
  • What answer did you pick? This is useful when you redo a problem: compare your answer now to the one you got originally.
  • How long did it take? Log problems that take you a long time as well as the ones you got wrong. When you do them again, try to beat your previous time.

7. Take it up two notches.

You might not include this information for every single problem you do, but it can be useful for some problems!

  • If you got it wrong: what type of error was it? I like to think in terms of conceptual errors (you didn’t know how to do something), process errors (you knew how to do it, but didn’t choose the right approach), and careless errors (you added 2 plus 3 and got 7).
  • For Quantitative Comparison problems: what cases did you test? If you didn’t test cases… that may be a clue to why you missed the problem! What cases should you have tried?
  • Were there any interesting trap answers or easy mistakes to make in the problem – regardless of whether you fell for them yourself? What would be the easiest ways to get this problem wrong?
  • Is there a better or faster way to solve it – even if your approach worked?

8. Now what?

So, you’ve created this GRE problem log, and you’ve started filling it up with Quant problems. Now what? Twice per week, on the same days every week, read over your GRE problem log. On one of those two days, just reread it and look at your takeaways. On the other day, redo some or all of the problems you’ve decided to redo, and record whether you got them right this time. With time, you’ll find yourself thinking about lessons learned from old problems when you’re doing new ones—and that’s exactly what you need for test day. 📝


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Chelsey CooleyChelsey Cooley Manhattan Prep GRE Instructor is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post How to Create a GRE Problem Log for Quant appeared first on GRE.

Fuente https://www.manhattanprep.com

Using Smart Numbers for GRE Quant

Manhattan Prep GRE Blog - Using Smart Numbers for GRE Quant by Chelsey Cooley

Here’s a quick cheat sheet on how, when, and why to use Smart Numbers to solve GRE Quant problems.

What is Smart Numbers?

Smart Numbers is a strategy for certain GRE Quant problems, usually word problems. It’s not a guessing method—in other words, using Smart Numbers will give you the exact right answer, just like doing algebra will.

When can you use Smart Numbers on GRE Quant?

You’ll decide whether to use Smart Numbers by looking at the answer choices (so, it’s most often useful on Discrete Quant problems, which have answer choices!).

If you see the following in the answer choices, you can definitely use Smart Numbers:

  • Expressions with variables in them, such as 3x or 4y + z.

You can also usually use Smart Numbers if you see the following in the answer choices:

  • Percents
  • Ratios
  • Fractions

If you see percents, ratios, or fractions, here’s how to make the decision. Read the whole problem, and decide whether you’re dealing with specific numbers, or just with relationships between numbers.

For instance, does the problem say that x equals 12, or that Beryl has sixteen cats? Those are specific numbers, and you probably can’t use Smart Numbers.

On the other hand, if x is 50% more than y, or if Beryl has twice as many cats as Jane, those are relationships—and you probably can use Smart Numbers.

There are a few other special situations, so I’ll also give you a rule that covers everything—although it takes a little bit more thinking to apply it. If a GRE Discrete Quant problem doesn’t tell you the numbers, but just tells you how they relate to each other, you can use Smart Numbers. If it does tell you specific numbers, you can’t.

How does Smart Numbers work?

Suppose you’ve decided to use Smart Numbers because there are variable expressions in your answer choices. For instance, the problem looks like this:

If a, b, c, and d are consecutive integers and a < b < c < d, what is the average (arithmetic mean) of a, b, c, and d in terms of d?

A) d – 5/2
B) d – 2
C) d – 3/2
D) d + 3/2
E) (4d – 6)/7

In this situation, start by choosing numbers that fit all of the facts the problem gives you. In this one, the four numbers you choose have to be consecutive, with a being the smallest, and d being the largest.

As long as the numbers fit the facts, you should use the easiest numbers you can think of. For this problem, let’s go for 1, 2, 3, and 4.

The next step is probably the most important one: everywhere you see a variable in the problem—including the answer choices!—replace it with the number you chose. You can use a combination of mental math and scratch work to do this, depending on how complex the problem looks.

By the way, during this step, you should forget about the phrase “in terms of d.” “In terms of” only matters when you’re using variables. Since we’re replacing our variables with numbers, we can just drop it.

Here’s what that problem would look like, once we’re finished with this step:

If 1, 2, 3, and 4 are consecutive integers and 1<2<3<4, what is the average of 1, 2, 3, and 4?

A) 4 – 5/2
B) 4 – 2
C) 4 – 3/2
D) 4 + 3/2
E) (4*4 – 6)/7

Next, answer the question. What is the average of 1, 2, 3, and 4? It’s 2.5.

Which of the answer choices equals 2.5? Only (C) does. (By the way, you can often figure this out without doing too much math—for instance, you should eliminate (B) quickly, since it won’t result in a decimal.)

Let’s try another one. This time, suppose you’re using Smart Numbers because you noticed percents in the answer choices. Your problem might look like this:

Aloysius spends 50% of his income on rent, utilities, and insurance, and 20% on food. If he spends 30% of the remainder on video games and has no other expenditures, what percent of his income is left after all of the expenditures?

A) 30%
B) 21%
C) 20%
D) 9%
E) 0%

Pick a number that fits everything you’re told in the problem. This problem doesn’t really give us any constraints on the number—except that it’s a dollar amount, so it shouldn’t be negative—so we can pick more or less any number we want. Let’s say that Aloysius’s income is $100.

You don’t have to replace the variables with numbers in this scenario, because there aren’t any variables! If the problem only has percents or ratios, not variables, you can skip that step. Go right ahead and solve the problem.

50% of $100 is $50, and 20% of $100 is $20. That leaves $30 remaining. Aloysius spends 30% of that $30, or $9, on video games. His total expenditures are $50+$20+$9, or $79, with $21 left over. Since $21 is 21% of his original income, the right answer is (B).

Why should you use Smart Numbers?

In some situations, using Smart Numbers takes more time than just doing the algebra. If you’re fast and confident with algebra, there will be problems where you’ll save time by “just doing the math.” However, there are other advantages to using Smart Numbers:

  • It’s easier to check your work with numbers than with variables.
  • It makes it easier to convert between different units. It’s much easier to convert 100 pennies to dollars than to convert 4x pennies to dollars.
  • It makes it easier to work with percentages. I know that 3 is 50% of 6, but it’s not nearly as obvious that 3xy is 50y% of 6x.
  • It’s often an easier way to solve a very tough word problem. If you’re having a hard time setting up equations based on a word problem, it may become clearer when you try using specific numbers.

However, I do have one warning: don’t think of Smart Numbers as a last resort! If you wait until you’ve already spent two minutes on the GRE Quant problem, using Smart Numbers isn’t going to help you. Try using it first—after all, there’s no rule saying you have to try algebra before you can do something else. On the GRE, you’re free to use whichever approach works, even if your middle school algebra teacher would disapprove! 📝


See that “SUBSCRIBE” button in the top right corner? Click on it to receive all our GRE blog updates straight to your inbox!


Chelsey CooleyChelsey Cooley Manhattan Prep GRE Instructor is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post Using Smart Numbers for GRE Quant appeared first on GRE.

Fuente https://www.manhattanprep.com

Can You Ace GRE Quant if You’re Bad at Math? (Part 3)

Manhattan Prep GRE Blog - Can You Ace GRE Quant if You're Bad at Math? (Part 3) by Chelsey Cooley

If you have a complicated relationship with math, you need to be especially careful about how you study. Some GRE Quant study techniques might seem to make perfect sense, but can actually leave you frustrated and demoralized in the long run. For painless studying, try these next few ideas instead.

(If you’re just joining us now, check out the previous two articles in this series before you keep reading. In the first one, we dispel the “bad at math” myth. In the second, we go over some simple approaches to gain momentum and learn the basics.)  

The When and Why of GRE Quant Rules

Part of the “bad at math” mindset is the feeling that math is sort of like magic. When you watch an expert solve a math problem, it’s like watching someone pull a rabbit out of a hat: you can see what’s happening, but you don’t know what they actually did.   

That’s compounded by the way that a lot of us learn math in school. Unless you had great elementary school math teachers, you probably learned math as a long list of rules and operations. You probably spent a lot of time learning to apply each rule correctly, and much less time learning when to use each rule.

So, if you took a test on multiplication in elementary school, you’d pass as long as you multiplied the numbers correctly. That doesn’t work on GRE Quant. To ‘pass’ the GRE, you have to not only multiply correctly, you have to decide whether to multiply in the first place.

That’s a skill that you won’t get from memorizing rules. You also won’t get there by drilling one problem type over and over until you can perform it perfectly, then moving on to the next one. If you don’t also know the “when and why,” the real test will seem much harder than your practice sessions.

So, what can you do? My first piece of advice is to create “when I see this, do this” flashcards. Those are discussed in detail here. Every time you do a GRE Quant problem, try to spot clues that you could use in other problems. Then, identify what you’re supposed to do when you notice one of those clues. Put those two things on the front and back of a flashcard, and keep it handy. Periodically, go through all of these flashcards and test your “what to do next” knowledge.

Second, regularly set aside time to do random sets of actual GRE Quant problems. This is more and more important the closer you get to test day. It forces you to not only solve the problems, but also figure out what they’re testing in the first place, and what approach to take. Instead of just skimming through your mental cheat sheet on a single topic, you have to choose from among everything you know about GRE Quant. That’s not something that comes naturally, but it will improve if you start practicing it!

Take GRE Quant Step by Step

Think of your GRE Quant knowledge as a jigsaw puzzle. Each time you learn a new fact or skill, someone hands you a new puzzle piece. If you already have the surrounding pieces in place, it’ll be easy to fit the new one in. But if you’re just getting started, and someone hands you a random piece from the middle of the puzzle, it’s almost impossible to decide where it goes.

Don’t start your GRE Quant studies by picking random pieces from the middle of the puzzle. Start with the corners and the edges: the math foundations. Check out the previous article for a list of starting places and some ideas on how to approach them.   

From there, aim to “push your GRE Quant score up from below,” rather than “dragging it up from above.” You’ll gain more points by really mastering the easy or moderate problems than you will by conquering the very hardest problems—and this will take less of your limited study time and build your confidence as well. Spend a little more of your time on the problems that are just a bit too hard for you—the ones where you have all of the surrounding puzzle pieces in place, but you haven’t quite placed the very last one. And avoid wasting time on the very toughest problems, unless those are really the only ones that are challenging for you.

It may seem satisfying to continue drilling one topic until you’re comfortable with it, but this can also lead to frustration when it doesn’t work out. Worse, it’s a poor strategy for memory formation. You’re better off moving around the jigsaw puzzle, changing which bit you’re working on in order to stay fresh. (This means that even if you’re spending almost all of your study time on GRE Quant, a little work on Verbal can be good for both your morale and your score.)

It’s fine to not understand things, to make mistakes, and to get problems wrong, even all the way up until test day. Focus on learning the material that’s most within your grasp right now, and learning it in the most efficient and effective way you can. Why not check out GRE Interact to get started? 📝


See that “SUBSCRIBE” button in the top right corner? Click on it to receive all our GRE blog updates straight to your inbox!


Chelsey CooleyChelsey Cooley Manhattan Prep GRE Instructor is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post Can You Ace GRE Quant if You’re Bad at Math? (Part 3) appeared first on GRE.

Fuente https://www.manhattanprep.com

Can You Ace GRE Quant if You’re Bad at Math? (Part 2)

Manhattan Prep GRE Blog - Can You Ace GRE Quant if You're Bad at Math? (Part 2) by Chelsey Cooley

You’re here because you’re bad at math, and you want to ace GRE Quant but aren’t sure how. But if you read the previous article, you know that you weren’t born without a “math organ,” and your brain is just as suitable for learning GRE Quant as anybody else’s. That doesn’t mean you don’t have challenges to overcome. But you should really be asking, How can I ace the GRE with limited math experience? Or How can I ace the GRE when I don’t know how to study math? Or even How can I get over my math anxiety and get excited about the GRE?

Don’t Panic

There’s a lot of common sense involved in solving GRE Quant problems. If the price of a couch is marked up by 15%, it shouldn’t end up costing $180,000. If you want to know how many eighth-graders are in a classroom, you shouldn’t end up with 2/3 of a student. But when you let math anxiety get the better of you, it’s easy to lose that common sense.

When you start a GRE Quant problem, take a deep breath. This reduces anxiety—and gives your brain some oxygen. Read the problem slowly and calmly. Don’t immediately start asking yourself which equations to use. When you start trying to do the math immediately, you stop trying to understand the story the problem is telling you.

It’s okay to slow down at the beginning of a GRE Quant problem. On the GRE, you don’t run out of time because you read math problems too carefully! You run out of time because you don’t understand the problem, but you try to solve it anyway.

If you struggle with math anxiety—and a lot of people do!—you probably won’t fix it by studying more. Actually, things tend to work the opposite way: studying and practice will be far more effective if you reduce your math anxiety first. Staying calm makes you better at GRE Quant, not the other way around. Here’s another article with some great tips for reducing test anxiety.

Don’t Go from Zero to a Hundred

One huge study mistake I see from “bad at math” students is this: you choose one topic, say, solving linear equations. You drill away at that topic during a killer multi-hour study session, or even over a period of days. You watch videos, read articles, and do practice problems. When you’re finished, you’re exhausted, but confident that you totally understand how to solve an equation. So, you move on to the next topic.

Then you see a linear equation on your practice GRE a week later, and you get it wrong.

The study style described above is called “blocking.” I’ll be the first to admit that there’s something satisfying about it. It’s nice to feel like you’re finally done with a topic that’s challenged you for a long time. But your brain hates it.

This analogy might be a little crude, but just work with me: teaching yourself GRE Quant is a little bit like training a dog. If you want your dog to learn to sit, you start when it’s calm and relaxed, and you don’t try to get it to master the trick in a single marathon session. Instead, you interleave, which is what you should do when you study basic math.

Here’s a great rundown on interleaving. (The article is from our GMAT blog, but everything there applies to the GRE as well!)

In short, give yourself permission to walk away without 100% mastering something. In the long run, that’s actually better for your brain.

Where Should You Start on GRE Quant?

Some math-phobes get along just fine in our 8-week GRE course. If you have a lot of time to devote to the GRE, and you’re confident that you’ll pick up the basics quickly—for instance, if you always did well in math in school, but you’ve gotten rusty—go ahead and dive in!

However, if you’re weak on the math foundations, you might struggle to get as much as possible out of the course and the homework. Consider starting with something like Khan Academy, which has great videos and problem sets on all of the topics covered on the GRE. Good math topics to start with:

  • Working with fractions, decimals, percents, and ratios
  • Writing, simplifying, and solving basic equations
  • Working with equations that have exponents or quadratics
  • Knowing some basic statistics definitions: average, median, range, quartile, and standard deviation
  • Basic geometry formulas, dealing with circles, triangles, squares, and rectangles

You could even begin with the Foundations of GMAT Math Strategy Guide: it’s written for GMAT students, but the content heavily overlaps with what’s on GRE Quant, and the book is a fantastic guide to math basics for adults.

Also, start developing your “math instincts” as soon as you can. You get a calculator on the GRE, but the more confident you are with numbers, the better. Take every opportunity to do simple math or estimation: guess the number of people in a large auditorium, or calculate your tip at dinner in your head, or estimate how much it’ll cost to fill your car up with gas at a certain price. Try out some arithmetic games, like this one. Download the Manhattan Prep GRE app, and start getting in the habit of thinking about math every day.

Next time, we’ll take a deeper look at how to study GRE Quant. You may have been studying inefficiently for your whole life! That could have a lot to do with why you aren’t a math expert—and with a few simple changes, you can start becoming one. 📝


See that “SUBSCRIBE” button in the top right corner? Click on it to receive all our GRE blog updates straight to your inbox!


Chelsey CooleyChelsey Cooley Manhattan Prep GRE Instructor is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post Can You Ace GRE Quant if You’re Bad at Math? (Part 2) appeared first on GRE.

Fuente https://www.manhattanprep.com

Can You Ace GRE Quant if You’re Bad at Math? (Part 1)

Manhattan Prep GRE Blog - Can You Ace GRE Quant if You're Bad at Math? (Part 1) by Chelsey Cooley

First, let’s get on the same page about what being “bad at math” really means. In my experience, GRE students who say that they’re bad at math tend to fall into these categories:

  1. People who don’t think math is interesting or fun.
  2. People who got bad grades in math as kids—or people who got good grades, but had to work harder than everybody else.
  3. People to whom math doesn’t feel natural or intuitive.
  4. People who feel anxious about math.

Instead of saying that you aren’t a math person, get specific. Which one of those groups describes you? Or, like many of my GRE students, do you fall into more than one of those categories? The more clearly you can describe the challenge you’re facing, the more power you have over it.

People Who Don’t Think Math is Interesting or Fun

It’s fine to think that math is boring—I think Reading Comprehension is soul-crushingly boring, and I’ve managed to make a career out of teaching the GRE. Learning to enjoy the GRE will make studying more fun, but I’ve also had a lot of successful students who thought of studying for the GRE as a boring but worthwhile job—or even as an annoying obstacle.

People Who Got Bad Grades in Math as Kids

As an adult learning middle-school and high-school math for the GRE, you’re in a strange position. You’re studying things that you once learned in grade-school math class. But you’re learning them from a totally different perspective: you’re smarter, more introspective, and have access to better resources. Getting bad grades in math as a kid says a lot about your middle-school math teacher, a little about your childhood level of patience and study skills, and not much at all about your “math aptitude.”

People to Whom Math Doesn’t Feel Natural or Intuitive

The idea that math should come naturally (or not at all!) is one of the nastiest myths in modern education. Math isn’t natural, and it isn’t intuitive. There’s actually a lot of evidence—which we’ll look at later in this article—that there’s no such thing as a “math person,” at least when it comes to GRE-level math.

Most people are more or less equally equipped to learn GRE math. But some people start the GRE process with more math experience, some people start out with more math confidence, and some people start out with both. Those people who seem to “get it” right away? It’s more likely that they’re just a little more familiar with the material than you are. Maybe they use math every day in their work; maybe they had a fantastic middle-school algebra teacher.

Think about it: when teachers and parents decide that a student is “good at math,” what do they do? They give them more and harder math to work on, creating a self-perpetuating cycle. Some people end up getting a lot of positive and varied experiences with math, which strengthens their abilities even further. The rest of us fall behind and focus on other topics.

People Who Feel Anxious about Math

A lot of us have had negative experiences with bad math teachers, bad grades, or seemingly impossible math problems. More of my students seem to have math anxiety than, say, “vocabulary anxiety”—probably because of the pervasive myth that some people are doomed to suck at math. Hopefully, by examining and rejecting that myth, you’ll find your anxiety being replaced by determination. Keep reading!

Bad at Math: The Evidence

This is the point where you stop saying that you’re “bad at math.” The language you use to describe yourself, even in your own head, makes a difference. It’s fine to say that you’re scared of math, or that you dislike math, or that you haven’t taken a math class in fifteen years, or that you absolutely hated your eighth-grade Algebra teacher. Those are facts! “Bad at math,” though, is a myth—here’s some evidence to prove that.

Here’s a chart summarizing the math performance of 15-year-olds around the world in 2012. If high-school math was always intuitive for some of us, and counterintuitive for others, we’d expect to see similar rates of high- and low-performers regardless of location. But the chart makes it clear that some ways of teaching and learning make almost everybody “good at math,” while other ways work for almost nobody. (So, why not sign up for GRE Math in a Day?)

There’s a common misconception, although fortunately it’s becoming less common as time goes on, that girls are naturally more likely to be bad at math than boys. But there are strong arguments to be made that this gap is completely explained by other factors, and when some of those factors are mitigated—as in single-sex schools—the gap begins to disappear.  

Twin studies have tried to determine whether mathematical ability is genetic. Here’s a study that leans more towards the “bad at math” side than what we’ve looked at so far. On the one hand, it suggests that genetics makes a “moderate” contribution to math ability at age 10. On the other hand, differences in mathematical ability due to social factors tend to be smaller for elementary school students than for older students—it’s possible that with older students, the pattern would change.

Finally, here’s one of my favorite articles addressing the “bad at math” issue. It contains a great description of where the “bad at math” myth comes from, and it’s worth a read just for that. It also introduces the idea that your beliefs about math influence how well you perform. People who believe that math ability can be improved, will improve! People who believe that they’re stuck where they are, won’t.

So, as you start or continue your GRE Quant studies, strive to convince yourself that you can get better at math. That belief alone may be enough to improve your performance. And remember that while you may feel anxious towards math or may dislike math, that won’t stop you from improving your Quant score. Want to know how to get better at Quant when you’re math-phobic? That’s coming up in the next article. 📝


See that “SUBSCRIBE” button in the top right corner? Click on it to receive all our GRE blog updates straight to your inbox!


Chelsey CooleyChelsey Cooley Manhattan Prep GRE Instructor is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post Can You Ace GRE Quant if You’re Bad at Math? (Part 1) appeared first on GRE.

Fuente https://www.manhattanprep.com

Math and the Growth Mindset

Manhattan Prep GRE Blog - Math and the Growth Mindset by Tom Anderson

Do you consider yourself a “math person?”

Actually—hold on a second. Whether you answer yes or no, you’re expressing a potentially harmful thought. Such thoughts reflect a fixed mindset about oneself—a belief that you’re born good at some things and bad at others. Carry that line of thinking a little further:

“Math people” grew up solving quadratic equations in their heads as toddlers. They always just “got it.” Everyone else had to work hard to get there. “Non-math people” could more easily run 10 miles backwards than calculate a tip at a restaurant. If you’re a “math person,” congrats on the easy grades and high GRE scores for the rest of your life. If you’re not, then too bad. It’s hopeless.

I believe that such thoughts are not just untrue, but downright harmful. There’s a growing body of research on this issue. Many readers of this blog entry will no doubt have heard of Carol Dweck, her book Mindset, and her TED talk, which currently has over 7 million views. Dweck argues that the way you view yourself has a huge impact on your success. It’s not just those who think they’re “naturally bad at something” who are at risk, by the way. One of the most negatively-impacted groups seems to be very high-performing students who think it’s all about being “naturally good at something.” I would encourage you to leave behind those fixed ideas of being a “math person” and instead adopt a mindset of growth.

In this entry, I’ll share with you a few ideas from research in educational psychology about growth mindsets and what you can do to develop one. In particular, I’ve been reading a book called Mathematical Mindsets by Jo Boaler. I’ll share with you some ideas from this book.

You Can Rewire Your Brain (to Become a “Math Person”)

First of all, know that your brain can be changed. In one intriguing study, researchers looked at the brains of cab drivers in London who had to memorize over 25,000 streets and 20,000 landmarks in order to qualify for their jobs. During the intensive training process, cab drivers showed dramatic growth in the hippocampus—the area of the brain that is used to acquire spatial information. Their brains were so affected by their practice that they showed measurable growth in the very brain matter inside their heads.

This concept that the brain can change and adapt in dramatic ways is called neuroplasticity. There are abundant examples of it. Stroke victims can sometimes regain their speech by rewiring a new region of their brain. People paralyzed in accidents can sometimes regain their movement; in one extreme case, an individual even lost the entire left hemisphere of her brain and was then able to regrow its functions in the remaining right hemisphere.

Aside from these extreme examples, we all experience neuroplasticity when we learn. Your brain is more like a muscle that can grow with exercise than like a computer that’s stuck with the processor it was built with.

Mistakes Matter

Take a few minutes and watch this video of a Swiss watchmaker who has been making watches by hand for 50 years. He tells us, “It’s not easy because you learn all your life. Even at my age, I learn every day and very often by making mistakes.” An expert in nearly any field will tell you the same thing: they’ve made their most significant learning through mistakes rather than successes.

The research backs them up. Not only do experts learn from making an incredible number of mistakes, they seem to learn more when making mistakes than when doing something correctly. Jo Boaler summarizes some research on the issue:

“Students’ brains reacted with greater […] electrical activity when they made mistakes than when their answers were correct. Second […] brain activity was greater following mistakes for individuals with a growth mindset than for individuals with a fixed mindset. The study also found that individuals with a growth mindset had a greater awareness of errors than individuals with a fixed mindset, so they were more likely to go back and correct errors.” Mathematical Mindsets (p.12)

It may not always feel this way, but mistakes are not something that should make you cringe. They’re probably the most worthwhile tidbits from any study session. And they’re even better for you if you open yourself up to growth, log them, and go back to correct them.

Think of it this way: your brain grows a synapse every time you make a mistake. A good practice session shouldn’t be easy. Get out there and start making some mistakes!

Process > Product

A good teacher will make it clear: the route to a right answer is much more important than the right answer itself. Of course, on an exam like the GRE, you want to get as many points as possible. But you get those points by carefully thinking about the problem in front of you and the solution paths it beckons you to use.

In the same way that you don’t improve your free throws by focusing on the “whoosh” a basketball makes when it goes through the net, you shouldn’t try to improve your problem-solving process by going straight to an answer key. Instead, focus on the steps to get there.

When you practice on your own, try thinking of your answer keys and explanations less like the finish line and more like consultants to whom you can turn for feedback along the way. Rather than just checking the right answer, peek at the explanation to see if the work you’ve done is on the right track. If so, continue onward. If not, go back and revise. Try to lead yourself to the correct answer rather than just reading what it is.

Believing You Can Grow is Part of the Recipe for Growth

On the first day of my GRE class, I often ask my students a similar question to the one I asked at the beginning of this blog entry—I ask them to raise their hand if they’ve come into my classroom with an idea floating around in their subconscious that they are “bad at math.” Every time I ask this question, a few reluctant hands pop into the air, followed by an avalanche of others, until a huge majority of hands silently confess this belief.

It’s easy for me to believe that there is no such thing as being “bad at math”—for years, I’ve seen my students bring up their GRE Math scores, sometimes to levels they never thought possible. That said, I’m well aware many folks have been traumatized by math in their prior education. Even many well-meaning teachers may have conveyed the notion that math is a gift, and either you have it or you don’t. Take heart and do what you can to throw out these “fixed” notions that may be rummaging around in your brain. Just like your math ability can be changed, so can your mindset.

Believing that you can get smarter is part of the process in doing so. 📝


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tom-andersonTom Anderson is a Manhattan Prep instructor based in New York, NY. He has a B.A. in English and a master’s degree in education. Tom has long possessed an understanding of the power of standardized tests in propelling one’s education and career, and he hopes he can help his students see through the intimidating veneer of the GRE. Check out Tom’s upcoming GRE courses here.

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Fuente https://www.manhattanprep.com

GRE Math for People Who Hate Math: Cracking the GRE Code

Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Cracking the GRE Code by Chelsey Cooley

The GRE will never lie to you—but it doesn’t always tell you what you really want to know. The GRE is a little bit like my friend in this exchange:

Me: “What do you think of this outfit?”

My friend: “Well, it’s very… creative.”

Sure, it’s not like she lied (zebra-striped leggings are pretty creative). But she also didn’t come right out and call me a fashion victim. In order to work that out, I had to crack the code.

You already know how to “crack the code” in English. Codebreaking is how we figure out what people really mean, even though we exaggerate, simplify, avoid touchy topics, and change the subject. And on the test, codebreaking is how you start to understand a GRE Math problem.

Here’s an example of a GRE Math problem that’s full of code:

What is the largest integer n such that 5n is a factor of 10!?

1. …

2. …

This problem looks fairly intimidating, but if it just said what it meant in plain English, it’d be a lot easier. The people who write GRE Math problems want to intimidate you a little, if they can—that way, they can reward people who calm down, take a deep breath, and focus on what the problem really means. Let’s do exactly that right now.

10! is pronounced as “10 factorial,” and it’s code for a very large number: the number you’d get by multiplying 10, times 9, times 8, times 7, and all the way down to 1.

If something is a factor of 10!, you can divide 10! evenly by that number. For instance, 2 is a factor of 10!. So is 20.

We really want to know whether 5n divides evenly into this large number. 5n is code too. An exponent just refers to a number such as 5, 5×5, 5x5x5, 5x5x5x5, or any number of 5s multiplied together. Since the problem asks about the largest integer n, you’re looking for the largest number of 5s that you can possibly divide evenly into 10!.

So, here’s what the problem says now:

10x9x8x7x6x5x4x3x2x1 can be evenly divided by 5x5x…x5. What is the largest number of 5s that can be evenly divided into the larger number?

“Divisible” or “evenly divided” is code as well. If you want to know if one number is divisible by another number, here’s a great way to do it. Write a fraction, with the bigger number on the top and the smaller number on the bottom. Start simplifying that fraction, a little bit at a time. If you can cross off the entire bottom of the fraction, you know the number is divisible. If you can’t, it isn’t divisible.

If we were solving this problem, we’d write our fraction like this:

Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Cracking the GRE Code by Chelsey Cooley

How many 5s can be crossed off on the bottom? As many 5s as there are on the top. Notice that 10 can be rewritten as 5 times 2.

Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Cracking the GRE Code by Chelsey Cooley

So, there are exactly two 5s on the top of the fraction. The answer to the problem is 2: 10! is divisible by 5².

Here’s what the GRE Math problem really said, ignoring all of the code:

In total, how many 5s can be divided out of the numbers 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1?

You aren’t supposed to go through all of that codebreaking on GRE test day. There just isn’t time. If you see a GRE Math problem that has code you don’t know how to translate, consider guessing and moving on. But, here’s why codebreaking is still important: if you do it ahead of time, you’ll recognize the code quickly when you see it on the test.

If anything about the problem we just did was surprising or challenging for you, take a moment to make some flashcards. On the front of the flashcard, write a piece of code you could see in a problem. On the back, write out what it really means. Here are the flashcards that I’d make for this GRE Math problem:

Manhattan Prep GRE Blog - GRE Math for People Who Hate Math: Cracking the GRE Code by Chelsey Cooley

Let’s practice some codebreaking and get a few more flashcards made. Here are some snippets of “GRE code.” Take your time and work out what they’re really saying, in plain English. Then, make a flashcard or two for each one.

  1. xy ≠ 0
  2. x is divisible by 6, but not by 12
  3.  + 1 is odd
  4. p has exactly two factors
  5. p has an odd number of factors
  6. /b < 0

Try it out, and let us know what you think in the comments! 📝


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Chelsey CooleyChelsey Cooley Manhattan Prep GRE Instructor is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post GRE Math for People Who Hate Math: Cracking the GRE Code appeared first on GRE.

Fuente https://www.manhattanprep.com

GRE Math Misconceptions

Manhattan Prep GRE Blog - GRE Math Misconceptions by Chelsey Cooley

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Math can be counterintuitive. There are a few GRE Math misconceptions that really seem like they should be true—but actually aren’t. Being prepared for them will keep you aware on test day.

Mistake: 1 is prime.

Fact: 1 isn’t prime. In fact, the smallest prime number is 2.

Why?: It seems like 1 should be prime, because you can’t divide it by any other integers. However, mathematicians have agreed to say that 1 isn’t a prime. This makes certain mathematical theorems much simpler and more intuitive. Even though you won’t use those theorems on the GRE (phew!), you have to deal with their consequences by remembering that 1 isn’t prime.

Mistake: 3-4-5 and 30-60-90 triangles are the same thing.

Fact: A right triangle can be 3-4-5 or 30-60-90, but not both.

Why?: Here’s a couple of 3-4-5 triangles next to a couple of 30-60-90 triangles. Even if the triangles get bigger or smaller, the triangles on the left all have different proportions from the triangles on the right. So, if the sides of a right triangle have the ratio 3-4-5, you know the angles aren’t 30-60-90, and vice versa.

Manhattan Prep GRE Blog - GRE Math Conceptions by Chelsey Cooley

Mistake: If the ratio of teachers to students at a school is 1 to 4, then 1/4 of the people at the school are teachers.

Fact: In this scenario, only 1/5 of the people at the school are teachers!

Why?: A fraction always represents a part of a particular whole. In this case, the part is the number of teachers, and the whole is all of the people at the school. So, the denominator of the fraction has to be the sum of the teachers and the students, not just the students alone.

Try it out with numbers to confirm. If there are 10 teachers and  40 students, then 10 out of the 50 people at the school, or 1/5, are teachers.

Mistake: The average of the numbers from 1 to 10 is 5.

Fact: The average of the numbers from 1 to 10 is 5.5.

Why?: Intuition tells you that 5 is halfway from 1 to 10. However, to find the average of a bunch of consecutive numbers, you need to average the smallest and largest numbers together. The right answer will be the average of 1 and 10, which is (1+10)/2 = 11/2 = 5.5.

Confirm this by actually averaging the numbers from 1 to 10. Here’s the sum:

1+2+3+4+5+6+7+8+9+10 = 55

There are 10 terms, so the average is 55/10, which equals  5.5.

Mistake: If x is 25% greater than y, then y is 25% less than x.

Fact: If x is 25% greater than y, then y is only 20% less than x.

Why?: This is one of the most counterintuitive math facts out there, but the numbers back it up. Suppose that a coat costs 25% more than a sweater. If the sweater costs $100, the coat would cost 1.25($100), or $125.

However, if a sweater costs 25% less than a coat, and the coat costs $125, the sweater only costs 0.75($125) = $93.75.

‘Percent more than’ and ‘percent less than’ aren’t interchangeable. Pay close attention to which term the problem actually uses. If it says ‘percent more’ or ‘percent greater,’ then use a decimal greater than 1, such as the 1.25 figure from the example above. If it says ‘percent less’ or ‘percent smaller,’ then use a decimal lower than 1, such as 0.75.

You can also prove this specific example using fractions. If x is 25% greater than y, then x is 5/4 of y. Use algebra rules to get y by itself:

x = 5/4 y

4x = 5y

4/5 x = y

y is fourth-fifths as large as x. Since the missing 1/5 is equivalent to 20%, y is only 20% smaller than x. 📝


See that “SUBSCRIBE” button in the top right corner? Click on it to receive all our GRE blog updates straight to your inbox!


Chelsey CooleyChelsey Cooley Manhattan Prep GRE Instructor is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post GRE Math Misconceptions appeared first on GRE.

Fuente https://www.manhattanprep.com