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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! 📝


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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 Using Smart Numbers for GRE Quant appeared first on GRE.

Fuente https://www.manhattanprep.com

This Simple Visualization Exercise Will Help You Beat the GRE

Manhattan Prep GRE Blog - This Simple Visualization Exercise Will Help You Beat the GRE by Chelsey Cooley

When I’m not teaching the GRE or writing this blog, I like riding my bicycle absurdly long distances. For the last five months, I’ve been training for one of the hardest bike races of my life: the 206-mile, 14-plus-hour Dirty Kanza. And now I want to share the best piece of advice I was given while training, because it applies to GRE test day just as much as it applies to bike racing.

A couple of months ago, I was lucky enough to get to chat with a woman who’s won Dirty Kanza a couple of times—including a win on her very first attempt. The conversation turned to the strategies she uses to succeed on race day. When she brought up visualization, I immediately assumed that I was supposed to visualize myself winning. If you want to overcome an obstacle, whether it’s a 200-mile bike race or the GRE, you should picture yourself overcoming it, right?

Maybe not. Instead of picturing myself succeeding, she invited me to picture myself failing. I was supposed to imagine rolling across the finish line hours late, having had a terrible race. “Now,” she said, “try to think of all of the excuses you might be making if you don’t do well.”

I imagined trying to explain that my back was bothering me, that my bike had gotten a flat tire, or that I had forgotten to bring enough water. Any number of things could send my race completely off the rails.

Each of those imaginary excuses, she explained, was actually something that I could fix right now, before race day. If I thought I might run out of water, I should start measuring how much water I needed during my training rides. If I was worried about back pain, I should start stretching and work on my posture on the bike. Almost anything that could put an end to my race could be prevented, if I started working on it before race day.

So, let me extend the same invitation to you. Imagine finishing the GRE, and getting a score that you’re really unhappy with. What excuses can you imagine making? Make a list on paper. For each excuse, there’s probably something you could do to help right now, before test day.  

For instance, here’s one I often hear: “I didn’t have enough time to finish a section.” That doesn’t mean the GRE should have given you more time on test day. Running out of time isn’t something that happens to you—it’s a consequence of actions you take on and before test day. It means you didn’t guess enough, or you should have practiced your pencil-and-paper arithmetic, or you didn’t identify the problem types that take you the longest. There’s so much you can do prior to test day to avoid having to make this excuse!

Or, you might picture yourself saying, “I got really anxious during the test, and it threw me off.” A little anxiety might be unavoidable, but you can take steps now to ensure that it doesn’t derail your GRE. Read this article about anxious reappraisal and give it a try. Check out these tricks for staying calm during the GRE, and plan to use one or more of them on test day.

Something could happen during your GRE that you can’t predict. For all you know, a meteor might fall through the roof of the testing center! But it’s more likely that if you start thinking of the excuses you might make if you fail, you’ll come up with the situations that are most likely to cause you problems on test day. If those situations are unexpected, they could hurt your score. But if you anticipate them ahead of time, you can make sure they won’t cause you any problems.

What are you most worried about on test day? Feel free to share or offer your own advice 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 This Simple Visualization Exercise Will Help You Beat the GRE appeared first on GRE.

Fuente https://www.manhattanprep.com

Interact for GRE, Our New Adaptive & Interactive GRE Prep, is Here!

Manhattan Prep GRE Blog - Interact for GRE, Our New Adaptive & Interactive GRE Prep, is Here! by Manhattan Prep

We’re extremely excited to announce that Interact for GRE—our on-demand, interactive GRE self-study experience that’s been in the works for years—has officially launched. 🎉

Starting at just $249, Interact for GRE is a revolutionary learning experience made just for you, the busy grad school applicant who needs flexible and comprehensive GRE prep. Using branching video technology, Interact for GRE adapts to your performance by providing you with prompts and delivering customized feedback based on your responses.

With Interact for GRE, you will:

  • learn from top 1% GRE scorers with years of teaching experience
  • be an active participant in the study experience—you won’t just watch instructors lecture you from slides.
  • work with videos that adapt to your strengths and weaknesses so that you spend the right amount of time on each topic.
  • get all the practice problems you could ask for (100,000+) to ensure that the lessons did their job.

Check out Interact for GRE here—you can learn what it’s all about, see what’s included, and even try it out for free. 📝

The post Interact for GRE, Our New Adaptive & Interactive GRE Prep, is Here! appeared first on GRE.

Fuente https://www.manhattanprep.com

Why Bother Predicting a GRE Verbal Answer?

Manhattan Prep GRE Blog - Why Bother Predicting a GRE Verbal Answer? by Chelsey Cooley

One habit of Verbal high-scorers is predicting the GRE Verbal answer before checking the answer choices. Here’s why this works, and how you can do it yourself.

1. Predicting the GRE Verbal answer makes sure you really read the sentence (or the passage).

Think about how you read in the real world.

When you read a book or an article, you usually don’t do a deep read of every single sentence. Unless you’re a lawyer, small misunderstandings don’t matter that much.

You have to read more closely to succeed on the GRE. You’re not only trying to get the basic idea, you’re also trying to answer questions, some of which can be downright nitpicky. But close reading doesn’t come naturally to a lot of us.

One way to force yourself to read closely, especially on Text Completion and Sentence Equivalence problems, is to predict the right GRE Verbal answer after you read. On these two problem types, we call this prediction a “fill-in”—you fill in the blank(s) in the sentence with your own word(s), before you look at the actual answer choices.

If you finish reading the sentence and you can’t come up with a fill-in, your brain is letting you know that you didn’t really “get” the sentence!

If you can’t predict the GRE Verbal answer at all, reread the sentence more closely. You may have missed an important clue. Sure, looking at the answer choices can give you a nudge in the right direction—but you shouldn’t rely on them as a crutch. Instead, practice reading closely. After all, looking at the answer choices can be dangerous…

2. Predicting the GRE Verbal answer protects you from “confirmation bias.”

Have you ever noticed that sometimes, certain answer choices just “look right”?

Sometimes, these great-looking answer choices are actually right. However, a great-looking answer could also be a really smart wrong answer.

Confirmation bias is the cognitive bias that makes us look for support for what we already think is correct. If you look at the answer choices too soon, and one of them looks great, your brain will start looking for evidence to prove that answer and ignoring evidence that supports other answers.

If the GRE Verbal answer you noticed is the right one, this is a good thing! But if you got tricked by a nice-looking wrong answer, it’s easy to talk yourself into picking it, even if it’s not really correct. Once you decide which answer is right, it’s hard to change your mind.

When you predict a GRE Verbal answer ahead of time, you’re protecting yourself against confirmation bias. By the time you look at the answer choices, you already know what the right answer should look like. Since you’ve already done the thinking, you (hopefully) won’t talk yourself into a wrong answer. You’ll go straight to the right answer that best matches your prediction.

Of course, sometimes our predictions are wrong or don’t match any of the answer choices. Prediction is a skill that you can practice. Every time you do a GRE Verbal problem in practice, predict an answer before you check the choices—if it helps, you can even write down your prediction. Once you check the answer choices, evaluate your prediction. Gradually, you’ll get better at anticipating right GRE Verbal answers.

3. Predicting the GRE Verbal answer protects you from some of the most common traps.

What makes a wrong GRE Verbal answer a “trap”? A trap is any wrong answer that you’d arrive at by making a common, simple mistake.

For instance, on Verbal, you might get overwhelmed and focus too much on the jargon in a sentence, ignoring the underlying structure. There’s a trap for that: it’s called a “theme trap.” Here’s an example:

Contrary to the assumptions that many Westerners hold about mindfulness practices, meditation is often anything but ____________; while using various methods to calm the mind, meditators frequently experience intense periods of restlessness and doubt.

Manhattan Prep GRE Blog - Why Bother Predicting a GRE Verbal Answer? by Chelsey Cooley

The theme trap here is mystical. The sentence talks about mindfulness and meditation, which can be somewhat mystical practices. If you focus too much on what the sentence is about, and not enough on what it says, you could fall for this trap. (By the way, the right answer is idyllic, which means peaceful and joyous.)

If you predict the GRE Verbal answer first, though, you hopefully won’t even notice mystical. After all, there isn’t much evidence in the sentence that would lead you to mystical before you look at the answer choices. You should fill in the blank with something like restful or relaxing, which are great matches for the right answer.

Hopefully this has convinced you to try predicting the right GRE Verbal answer, if you weren’t already! It might feel a bit unnatural or time-consuming at first, but there are a lot of good reasons to keep working on it. If you can master this skill, you’ll be on your way to improving your GRE Verbal score. 📝


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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 Why Bother Predicting a GRE Verbal Answer? 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