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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

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 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

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! 📝


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 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

You can attend the first session of any of our online or in-person GRE courses absolutely free. Crazy, right? Check out our upcoming courses here.


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

common denominators, GRE Quantitative Comparison Questions Clases particulares en Chile grechile.com

GRE Quantitative Comparison Questions Clases particulares en Chile grechile.com

0 < xy

Quantity A
Quantity B
5/2x – 2/2y
\frac{5y-2x}{2x-2y}

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

 

Clases particulares GRE QUANT and GRE SUBJECT MATH
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Clases particulares GRE QUANT and GRE SUBJECT MATH, en todo CHILE.
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correo : admin@grechile.com
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Answer: D

 

Resolución paso a paso:

Este es un ejercicio del item “comparision” del GRE QUANT.
Debemos prestar atención a ¿qué nos piden comparar?
Debemos comparar, el o los valores de x, con 6

Dado:
Cantidad A: 5 / 2x – 2 / 2y
Cantidad B: (5y-2x) / (2x-2y)

Veamos qué pasa si reescribimos la cantidad A como una gran fracción.
En primer lugar obtener denominadores comunes …
Cantidad A: 5y / 2xy – 2x / 2yx
Cantidad B: (5y-2x) / (2x-2y)

Combine para obtener:
Cantidad A: (5y-2x) / 2yx
Cantidad B: (5y-2x) / (2x-2y)

¡¡BONITO!! Estos numeradores son los mismos para ambas fracciones.

Puedo ver que si elijo un valor xyy que hace que los numeradores sean cero, esto acelerará mi solución. Verás por qué en breve.

Puedo ver que, si x = 5 ey = 2, entonces podemos conectar estos valores en las cantidades para obtener:
Cantidad A: [5 (2) -2 (5)] / (2) (2) (5)
Cantidad B: [5 (2) – 2 (5)] / [2 (5) – 2 (2)]

Evaluar:
Cantidad A: 0
Cantidad B: 0

Así, cuando x = 5 ey = 2 las cantidades son iguales.
La respuesta correcta es C o D

En este punto, todos los pares de valores de xy yy o bien darán iguales cantidades o no.
Vamos a conectar números super fáciles.
Vamos a conectar x = 1 yy = 1
Obtenemos:
Cantidad A: [5 (1) -2 (1)] / (2) (1) (1)
Cantidad B: [5 (1) – 2 (1)] / [2 (1) – 2 (1)]

Evaluar:
Cantidad A: 3/2
Cantidad B: 3/0
Estas cantidades no son definitivamente IGUALES.

Respuesta correcta D) 

Clases particulares GRE QUANT and GRE SUBJECT MATH
En grechile.com, ofrecemos Programas para que rindas con ventaja tu GRE QUANT, enfocados en preguntas de alta puntuación.
Clases particulares GRE QUANT and GRE SUBJECT MATH, en todo CHILE.
Reserva con tiempo tus clases.
contacto: claudio hurtado
correo : admin@grechile.com
whatsapp +56999410328
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perfect square, GRE Quantitative Comparison Questions Clases particulares en Chile grechile.com, Complete perfect square x(4 – x)

GRE Quantitative Comparison Questions Clases particulares en Chile grechile.com

Quantity A
Quantity B
x(4 – x)
6

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

 

 

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Answer: B

 

Resolución paso a paso:

Este es un ejercicio del item “comparision” del GRE QUANT.
Debemos prestar atención a ¿qué nos piden comparar?
Debemos comparar, el o los valores de x, con 6

Voy a convertir x (4 – x) en un cuadrado perfecto
Antes de hacer eso, aquí hay otros cuadrados perfectos:
X² + 6x + 9 = (x + 3) ²
X² – 10x + 25 = (x – 5) ²
X² – 4x + 4 = (x – 2) ²
Etc …

Dado: x (4 – x) = 4x – x²
= -x² + 4x
= -1 (x  ²  – 4x)

¿Qué necesitamos agregar a x² – 4x para que sea un cuadrado perfecto?
Necesitamos añadir 4 a ella para obtener x² – 4x + 4, que es igual a (x – 2) ²
Por supuesto, no podemos agregar aleatoriamente 4 a la expresión dada, ya que eso cambia totalmente la expresión.
En su lugar, vamos a añadir 0 a la expresión dada. Esto está bien, ya que agregar 0 no cambia nada.
SIN EMBARGO, vamos a añadir 0 de una manera muy especial. Vamos a añadir + 4 – 4 a la expresión.
Esto está bien, ya que agregar + 4 – 4 a la expresión es lo mismo que agregar 0 a la expresión.

Obtenemos: x (4 – x) = 4x – x²
= -x² + 4x
= -1 (x  ²  – 4x)
= -1 (x  ²  – 4x + 4 – 4)
= -1 (x² – 4x + 4) + 4 [para eliminar -4 de los corchetes, tuve que multiplicarlo por -1, ya que estamos multiplicando todo en los corchetes por -1]
= -1 (x – 2) ² + 4

Así pues, ahora podemos escribir lo siguiente:
Cantidad A: -1 (x – 2) ² + 4
Cantidad B: 6

En este punto, debemos reconocer que 4 es el mayor valor posible de -1 (x – 2) ² + 4
Sabemos esto, porque (x – 2) ² es siempre mayor o igual a 0
Por lo tanto, -1 (x – 2) ² es siempre menor o igual a 0
Por lo tanto, el mayor valor de -1 (x – 2) ² es 0. Esto ocurre cuando x = 2
Si 0 es el mayor valor posible de -1 (x – 2) ², entonces 4 es el mayor valor posible de -1 (x – 2) ² + 4

Entonces, tenemos:
Cantidad A: algún número menor o igual a 4
Cantidad B: 6

Respuesta correcta B) 

Clases particulares GRE QUANT and GRE SUBJECT MATH
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distance = speed*time, GRE Quantitative Comparison Questions Clases particulares en Chile grechile.com, The distance that Bob drives in 3 hours at an average speed of 44 miles per hour

GRE Quantitative Comparison Questions Clases particulares en Chile grechile.com

Quantity A
Quantity B
The distance
that Bob drives in
3 hours at an average
speed of 44 miles per
hour
The distance that Inez
drives in 2 hours and 30
minutes at an average
speed of 50 miles per
hour

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

 

 

 

Clases particulares GRE QUANT and GRE SUBJECT MATH
En grechile.com, ofrecemos Programas para que rindas con ventaja tu GRE QUANT, enfocados en preguntas de alta puntuación.
Clases particulares GRE QUANT and GRE SUBJECT MATH, en todo CHILE.
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contacto: claudio hurtado
correo : admin@grechile.com
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Answer: A

 

Resolución paso a paso:

Este es un ejercicio del item “comparision” del GRE QUANT.
Debemos prestar atención a ¿qué nos piden comparar?
Debemos comparar, ambas distancias

Bob maneja 3 horas a una velocidad promedio de 44 millas por hora
Distancia = (velocidad) (tiempo)
= (44) (3)
= 132 millas

Inez maneja 2 horas y 30 minutos a una velocidad promedio de 50 millas por hora
Distancia = (velocidad) (tiempo)
= (50) (2,5)
= 125 millas

Obtenemos:
Cantidad A: 132 millas
Cantidad B: 125 millas

Respuesta correcta A) 

Clases particulares GRE QUANT and GRE SUBJECT MATH
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GRE Quantitative Comparison Questions, solved exercises step by step; clases particulares GRE en Chile, tutor, tutorials, class, course, The units digit of

entrenamieno

 

GRE Quantitative Comparison Questions

x is a positive integer.

Quantity A
Quantity B
The units digit of 6^x
The units digit of 4^{2x}

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

 

 

 

 

 

Clases particulares GRE QUANT and GRE SUBJECT MATH
En grechile.com, ofrecemos Programas para que rindas con ventaja tu GRE QUANT, enfocados en preguntas de alta puntuación.
Clases particulares GRE QUANT and GRE SUBJECT MATH, en todo CHILE.
Reserva con tiempo tus clases.
contacto: claudio hurtado
correo : admin@grechile.com
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sitio web: www.grechile.com

 

 

Answer: C

 

Resolución paso a paso:

Este es un ejercicio del item “comparision” del GRE QUANT.
Debemos prestar atención a ¿qué nos piden comparar?
Ojo: a pesar de que en el enunciado hablan de una variable “x”, que se mueve en los valores de los enteros positivos. lo que nos piden comparar, es el valor de la unidad, al desarrollar dos expresiones, una en A y otra en B, en ambas expresiones aparece la variable “x”. Esto es un ejercicio que nos pide “trabajo en la ambigúedad” (no se define un valor fijo para “x”, dado que lo único que se afirma, es que es un entero positivo, esto quiere decir que puede tomar cualquier valor entero positivo).
Además para responder correctamente el alumno debe saber trabajar con potencias y sus propiedades.
No se nos pide comparar “x”, sino la consecuencia de actuar como exponente en una potencia de base entera (6), para ver que resulta en la unidad del número obtenido.

En A, se nos presenta  6^x, debemos ver que ocurre con el valor de la unidad al desarrollar para los distintos valores de exponente entero positivo, haciendo una inspección nos damos cuenta que 6^x, para x=1, es 6 (valor de la unidad 6) , para x=2, es 6*6=..6, es 6 (valor de la unidad), para x=3, es el valor de la unidad de x=2, multiplicado 6, es 6 (valor de la unidad y así sucesivamente.
Conclusión: independiente del valor entero positivo que tome x, el valor de la unidad de 6^x, siempre será 6.

En B, se nos presenta 4^{2x}, debemos ver que ocurre con el valor de la unidad al desarrollar para los distintos valores de exponente entero positivo.
Aplicando una propiedad de potencias, tenemos que    4^{2x}=( 4²)^x= 16^x, para ver el valor de la unidad de 16^x, vasta con analizar cómo se comporta 6^x, este hecho fue analizado en A, es decir estamos en la misma situación de A.

Luego, lo afirmado en A, es igual a lo afirmado en B, ya que en ambos casos, se obtiene un valor único para la unidad, esto es 6.

Respuesta correcta C) 

Clases particulares GRE QUANT and GRE SUBJECT MATH
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Clases particulares GRE QUANT and GRE SUBJECT MATH, en todo CHILE.
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Exercises solved Data interpretation, GRE QUANT, During how many of the months in which City Y’s average rainfall exceeded 3 inches was City X’s average low temperature greater than or equal to 30 degrees?

average monthly rainfall for cities x and y

average temperature highs and lows for city x

Question 1 During how many of the months in which City Y’s average rainfall exceeded 3 inches was City X’s average low temperature greater than or equal to 30 degrees?
A. One
B. Two
C. Three
D. Four
E. All

Question 2 The “monthly midpoint” is calculated by taking the average (arithmetic mean) of a month’s average high and low. Which of the following is the average monthly midpoint in City X for the 3-month period from July to September?
A. 55.3
B. 60.0
C. 64.7
D. 69.3
E. 74.0

answers  1b   2c

 

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Explicacion y desarrollo, lectura de graficos, interprertacion de tablas
Data Interpretation GRE QUANT

Pregunta 1. En primer lugar, mira en el gráfico de barras para averiguar qué meses tuvieron una precipitación media superior a 3 pulgadas y luego aplicar esa información a la tabla de temperatura. Según el gráfico de barras, los únicos meses que tuvieron una precipitación media superior a 3 pulgadas fueron enero, febrero, marzo, octubre, noviembre y diciembre. De acuerdo con el gráfico de líneas, sólo dos de esos meses tuvieron bajas promedio superiores a 30 grados: octubre y noviembre.
Por lo tanto la opción B es correcta.

Pregunta 2. Este es un problema de varios pasos, por lo que debe tomar un paso a la vez. Primero, determine el punto medio mensual para cada mes. La alta en julio es 78 y la baja es 59, por lo que el punto medio mensual es: 78 + 59 = 137 ÷ 2 = 68,5. Del mismo modo, el punto medio de agosto es: 76 + 57 = 133 ÷ 2 = 66,5. El punto medio de septiembre es: 68 + 50 = 118 ÷ 2 = 59. El promedio de los tres puntos medios es: 59 + 66.5 + 68.5 = 194 ÷ 3 = 64.7, opción (C)

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