The post GRE Math for People Who Hate Math: Right Triangles appeared first on GRE.

]]>Geometry is one of the most polarizing topics on the GRE. If you think it’s great, this article isn’t for you! This set of tips and tricks is for those of us who would rather have a root canal than calculate the length of a hypotenuse.

Check out this Quantitative Comparison problem:

Quantity A: The length of side AB

** Quantity B:** 6

You might be tempted to start applying right triangle rules. Plugging the sides into the Pythagorean Theorem (a^{2} + b^{2} = c^{2}), you’d find:

So, the answer is (A), correct? No! The answer is actually (D), because **this problem isn’t about right triangle rules.** It doesn’t actually specify that ABC is a right triangle, even though it looks like one. It’s really trying to test you on a totally different triangle rule, the rule that governs the possible side lengths of a triangle.

According to that rule, every side of a triangle must be shorter than the other two sides put together. Otherwise, you’d end up with a triangle that couldn’t ‘close’:

The only rule here is that AB must be shorter than 9, and longer than 1. It can be longer or shorter than 6, so the correct answer is (D).

The lesson here isn’t about the math, though. It’s that even if you know all of the right triangle rules, you should also know **whether those rules apply. **

The most powerful right triangle rule is the Pythagorean Theorem. It always works on **any right triangle**. However, there are two mistakes I’ve seen geometry-hating GRE students make over and over, and I’d like you to avoid them. First, remember that **in a ^{2} + b^{2} = c^{2 }, c is always the longest side**. It’s always the side opposite the right angle. If your number instincts aren’t great, it’s easy to plug the two known sides into the wrong spots in the equation and calculate a value that doesn’t make sense.

Second, **not every right triangle is a special right triangle**. The ‘special’ right triangles — the 45-45-90 triangle and the 30-60-90 triangle — only represent a very small number of right triangles. The Pythagorean Theorem works on all right triangles, but the ‘special right triangles’ rules only work if you already know the angles (or the sides). Here are the most common situations in which those rules apply.

– If a right triangle has **two equal legs**, its angles are 45-45-90, and vice versa.

– If a right triangle has a **hypotenuse twice as long as the shorter leg**, its angles are 30-60-90, and vice versa.

Those might not look like the ‘special right triangles’ rules that you’ve memorized already. That’s because I’ve left out the parts that you can calculate using the Pythagorean Theorem, to make the rest easier to remember. Here’s the neat trick: if you don’t exactly remember the ratio of side lengths for a special right triangle, just use the Pythagorean Theorem!

You can memorize the rule that states that the third side length is:

Or, you can just plug in the two sides you know:

The same applies to the 45-45-90 triangle:

Memorize the bullet points above, which tell you how to recognize special right triangles and what you’re allowed to do with them. You can also memorize the side length ratios —

— but those are super easy to work out on your own, in case you forget.

My last piece of advice to Geometry haters is to **know what you’re solving for**. If you’re solving for the **area** of a triangle, you don’t need to know its angles. In general, you don’t even have to know the side lengths. In a right triangle, the side lengths can be used as a base and a height, but that’s just a coincidence.

If you’re solving for an **angle**, you don’t need to know the side lengths. Instead, start by applying the rules you know about angles: the sum of the three angles in **any** triangle is 180 degrees. The only exceptions are the special right triangles, which have a specific relationship between side lengths and angles.

Finally, if you’re solving for a **side length**, look for right triangles! If you find a right triangle, use the Pythagorean Theorem. Ignore the other angles, unless it’s a special right triangle. And if you can’t find or create a right triangle, consider using different rules, like the one from the first problem in this article.

**In short: **

- Don’t use right triangle rules unless you’re sure the triangle has a right angle!
- The most powerful right triangle rule is the Pythagorean Theorem, but it’s only useful for finding side lengths.
- The only time that side lengths and angles are related on the GRE, is when you’re handling a special right triangle. Memorize the super-easy versions of the special right triangle rules shown above, to help you recall when and how to use them.
- If you’re solving for one thing — an area, a length, or an angle — focus on rules that address that. Don’t get hung up on angle rules if you’re trying to find the length of a hypotenuse.
- Don’t panic! Solving a Geometry problem isn’t a magic trick. It’s just a series of inferences. If you make them carefully and one at a time, and keep your scratch work neat, you can conquer GRE Geometry with style.

For comprehensive guidance on all things GRE Geometry, check out our Geometry GRE Strategy Guide.

*Want more guidance from our GRE gurus? You can attend the first session of any of our online or in-person GRE courses absolutely free! We’re not kidding. Check out our upcoming courses here. *

**Chelsey Cooley 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 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post GRE Math for People Who Hate Math: Right Triangles appeared first on GRE.

]]>The post Hack the GRE Vocab: Use Spaced Repetition to Get Maximum Results with Minimum Time Investment appeared first on GRE.

]]>Your time is a limited commodity. Studying vocabulary for the GRE can be tedious and time-consuming, and worst of all…inefficient.

If you’re like most students, you flip through flashcards (either premade or hand-made) and quickly try to remember what was on the back. After a few dozen repetitions over a few weeks you probably remember many of them. But…you don’t retain that information for long, and you might not recognize the words when used in a slightly different context.

Vocabulary is a significant component of GRE verbal, but it’s not actually something that you should invest a significant portion of your time studying! That’s because there’s no way to determine which words you’ll see on test day – you might see a dozen of the words you studied, or you might not see any at all.

So, you want to learn as many words as you reasonably can between now and test day with the minimum time spent studying!

**The power of forgetting**

It’s a waste of time to study the same word every single day. That word will still be there in your short-term memory from the day before, but you can’t be sure that you’ve actually converted it into a long-term memory.

Letting yourself *almost* forget something before you recall it – the “it’s on the tip of my tongue!” feeling – actually *strengthens* neural connections. As Gabriel Wyner, author of *Fluent Forever *explains:

Memory tests are most effective when they’re challenging. The closer you get to forgetting a word, the more ingrained it will become when you finally remember it.

So, don’t study that same word every day. You want to **space out** how often you see it to maximize your ability to ultimately remember it.

Without any review, we forget most of what we learn:

But if we review at spaced intervals – *just *before we would have forgotten – we change that curve completely:

**How to space out your studying**

First, get organized. Create a set of 5 index card boxes (or piles, or folders, or whatever works for you.

**Directions:**

- Make a memorable flashcard, then place it in Deck 1.

- Quiz yourself on Deck 1 words every day.

- If you get a word right, move it to Deck 2.

- When you quiz yourself on Deck 2, any that you get right move to Deck 3.

- Any that you get wrong – from any deck – you move back to Deck 1.

- If you’ve moved a card back to Deck 1 more than once, you have to improve your definition: Add a new personalized sentence, rhyme, picture, etc.

- Once you get a word right in Deck 5, you’ll (ideally) remember it forever!

**Create a study calendar**

You’ll need to stay organized to know which decks to study on which days. Here is an example:

**Can I do this online?**

Yes! If you’re too tech-savvy for the pen-and-paper method, there are websites & apps with algorithms that create this same spacing effect. Here are some free ones that I recommend:

The principles will be the same whether you use an app or make your own physical study toolbox.

**How this helps**

Okay, yes. It takes extra time to organize all of this, and to keep track of what you’re reviewing when. But after that initial investment of a little bit of extra time, you’ll save yourself a lot of time in the long run. After you’ve reviewed a card 5 times (or maybe a few extras if you have to return it to Deck 1), you’ll know it forever! Rote memorization, on the other hand, usually takes twice as many repetitions.

More importantly, though, spacing out your study is more effective at convert short-term memories into long-term memories. This will do more to ensure that you actually remember the words on test day.

And bonus – you just might retain an impressive vocabulary for the rest of your life!

*Want more guidance from our GRE gurus? You can attend the first session of any of our online or in-person GRE courses absolutely free! We’re not kidding. Check out our upcoming courses here. *

**Céilidh Erickson is a Manhattan Prep instructor based on New York City.** When she tells people that her name is pronounced “kay-lee,” she often gets puzzled looks. Céilidh is a graduate of Princeton University, where she majored in comparative literature. After graduation, tutoring was always the job that bought her the greatest joy and challenge, so she decided to make it her full-time job. Check out Céilidh’s upcoming GMAT courses (she scored a 760, so you’re in great hands).

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]]>The post GRE Percentage Problems – Part 2: Percent Increase and Percent Decrease appeared first on GRE.

]]>If you’ve been following this blog for a while, you’ve probably read our article on how to handle GRE percentage problems. That article teaches you an ultra-simple approach for “percent of” Quant problems — that is, problems like the following:

*xy* is 20% of *z*. In terms of *y*, what **percent of** *x* is *z*?

Unfortunately, not every percentage problem is a “percent of” problem. Some of the toughest problems take things one step further, asking questions like the following:

*February’s profits were what percent higher than January’s? *

* By what percent did the number of students in the school decrease from 2010 to 2011? *

Luckily, these problems also have an easy approach. Let’s talk numbers.

It’s finally warming up and getting sunnier here in Seattle, and winter clothes are going on sale. Imagine that a department store originally sold a coat for $100, and it’s just been marked down by 20%. To calculate the sale price, you can do one of two things.

- You can subtract 20% from 100%, learning that the coat’s current price is 80% of the original price. Then, multiply $100 by 80% to find that the current price is $80.
- Or, you can find 20% of $100, which is $20. That’s the amount of the discount. Subtract this from $100 to find the current price. Again, it’s $80.

So, when you **decrease** $100 by 20%, you get $80. In other words, 80 is 20% **less than** 100.

Now, imagine the opposite situation. A coat is originally priced at $80. Then, it’s marked up by 20%. Again, you can do one of two things.

- You can add 20% to 100%, learning that the coat’s current price is 120% of the original price. Multiply $80 by 120% to learn that the current price is $96.
- Or, you can find 20% of $80, which is $16. That’s the amount of the markup. Add this to $80 to find the current price, which is $96.

In other words, when you **increase** $80 by 20%, you get $96. **You don’t get $100. **

That’s sort of counterintuitive. It seems like you should be able to decrease a number by 20%, then increase it by 20%, and end up back where you started. **The first key to percent increase/decrease problems is to remember that you can’t use ‘increase’ and ‘decrease’ interchangeably. **It’s true that 80 is 20% less than 100. But it **isn’t** true that 100 is 20% greater than 80.

If you aren’t careful enough with this, you’ll end up missing problems like the following:

10% more students scored an A on the final exam than scored an A on the midterm. If 110 students scored an A on the final exam, how many students scored an A on the midterm?

If you take 110 and decrease it by 10%, you’ll get the wrong answer, 99. Why? Because ‘percent more than’ and ‘percent less than’ aren’t interchangeable. The problem specifies that 110 is 10% *more* than the number of the students who scored an A on the midterm. You can’t take 10% *less* than 110 and expect to get the same result.

Instead, use a variable, *m*, for the number of students who scored an A on the midterm. Then, translate the problem into math. Increasing *m* by 10% corresponds to multiplying *m* by 1.1.

1.1*m* = 110

*m* = 110/1.1 = 100

The correct answer is 100, not 99. Double-check your work by plugging the value back into the problem, and confirming that everything makes sense. If 100 students scored an A on the midterm, then 10% more than that would be 110. That’s the number of students who scored an A on the final exam.

It boils down to this: when you write out the math, you have to use exactly what’s written in the problem, including the ‘more than’ or ‘less than’, ‘increase’ or ‘decrease’. The problem above specifies “10% more than”, so no matter what, you’ll have to increase some value in the problem by 10%, rather than decreasing it. Don’t know what that value is? Use a variable to stand in for it. Solve for that variable, and you’ll have your answer.

Now, try this one:

Pat’s average weekly income from her part-time job was 15% more in September than it was in July. Her average weekly income in July was 10% less than it was in August. If her average weekly income in September was $207, what was her average weekly income in August?

Use variables to stand in for the unknown values. Pat’s weekly income in July was *j*, and her weekly income in August was *a*.

The first sentence specifies “15% *more than*“, so you’ll need to increase *j* by 15%. That is, 1.15*j* = 207, so *j* = 180.

The next sentence specifies “10% *less than*“, so you’ll need to decrease *a* by 10%. That is, 0.9*a* = 180, so *a* = 180/0.9 = 200. The correct answer is $200. To review, plug that value back into the problem and confirm that all of the numbers work out correctly.

For even more insight into percentage problems, check out our Fractions, Decimals, and Percents Strategy Guide.

*Want more guidance from our GRE gurus? You can attend the first session of any of our online or in-person GRE courses absolutely free! We’re not kidding. Check out our upcoming courses here. *

**Chelsey Cooley 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 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

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]]>The post GRE Math for People Who Hate Math: Data Interpretation appeared first on GRE.

]]>Math is unavoidable on the Quantitative sections of the GRE. But it isn’t *all *about math. By leveraging your strengths — and learning just a couple of ultra-simple math rules — you can gain the advantage over certain Quant problem types, even if you’re more of a Verbal person. Here’s how to apply that idea to Data Interpretation.

**Read the graph first. **

Reading a Data Interpretation graph or chart is like reading a Reading Comprehension passage. Look for major, structural points, and strike a balance between understanding and taking too much time. For most of my students, this means **spending more time examining the graph than you think you should**. If you understand the story the graph is telling, the questions will be less overwhelming and you’ll be more efficient.

How do you work out the story? Read the title of the graph, if it has one. If it has axes, carefully read their labels as well. Examine the key or legend. Understanding a graph means being able to describe, in general terms, **what types of information you could learn from it**.

At this stage, also check whether you’re given any totals or overall values. A pie chart might include a legend telling you the total number of dollars (or people, or households, etc.). A table might include a row providing the total of each column. If you don’t “get” the graph, move on! You can always return to the problem later if you have time. Trying to answer questions about a graph you aren’t sure how to read is a waste of your time and energy.

**Write more than you think you need. **

It’s easy to get distracted or confused while solving a DI problem. If you read the question, then immediately jump to the graph and start gathering information, you risk forgetting (or getting confused about) the question in the meantime. So, take advantage of your strong language skills, and your scratch paper! First, write the question down on your paper, in shorthand if necessary. Many DI questions aren’t even mathematical: “# of days w/ mean temp. above 80.” But if the question *does* ask for a mathematical calculation, now is the time to think through the data you’ll need to perform it. For instance, if you’re asked for the percent change in mean temperature from 2006 to 2010, transcribe it like this: “100(2010 temp – 2006 temp)/(2006 temp).” This is more intuitive than working with numbers right away, and makes it totally clear what data you’ll need to gather.

Always write down the data you’re using to answer the question, rather than pulling it directly from the graph and plugging it straight into the calculator. If you miss or misread a piece of data, you’ll have a record of your work to double-check. And if you need to change your approach, you won’t have to gather all of the data again.

Make your scratch work **neat but verbose**. Data Interpretation questions usually don’t include tough math. The difficulty is in keeping everything straight in your head and avoiding simple mistakes, such as counting data points incorrectly or dividing by the wrong value. Take advantage of your strong reasoning skills — and your scratch paper — to avoid this.

**Get a handle on percents and statistics (but don’t forget the calculator!)**

Learning a handful of simple math rules can have a huge payoff on Data Interpretation questions. The toughest math on DI problems often involves either percents or statistics (such as averages or ranges). Devote some study time *outside* of Data Interpretation to mastering these two math concepts. The 5 lb. Book of GRE Practice Problems has some great questions at the beginning of the Percents chapter, which challenge you to quickly calculate both *percent of* and *percent change*. For a tutorial on *percent of* problems, you can also check out this earlier blog article. For real mastery, learn to prevent the most common errors you make on these problem types. For instance, on *percent change* problems, it’s easy to set up the initial equation incorrectly. Always structure your percent change equations as “change/old value”, not “change/new value”!

You’re often invited to **estimate** on Data Interpretation questions. Take advantage of this, because simplifying the numbers might make the math more intuitive for you. But beware of potential pitfalls, like estimating incorrectly because you’ve misunderstood the scale of a graph or the way its axes are labeled. That’s yet another reason to read the graph thoroughly before you start.

A lot of the math on the GRE isn’t that mathematical at all. (And you probably aren’t as bad at math as you think you are, either!) Admissions committees don’t care very much whether you’re great at calculating the hypotenuse of a triangle or finding the average height of a class of students. They’re more interested in your **organization** and **reasoning** skills — skills that you already have. Take advantage of them, and master some of the toughest GRE Quant problem types.

**Chelsey Cooley 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 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post GRE Math for People Who Hate Math: Data Interpretation appeared first on GRE.

]]>The post Answer Any Weighted Average Problem in One Minute or Less appeared first on GRE.

]]>**A group consists of both men and women. The average (arithmetic mean) height of the women is 66 inches, and the average (arithmetic mean) height of the men is 72 inches. If the average (arithmetic mean) height of all the people in the group is 70 inches, what is the ratio of women to men in the group?**

This is a *weighted average* problem. There are two groups, and each group has a different average height. When the two groups are combined, the average height changes. In problems like this, you might be asked to find the size of one group, the relationship between the two groups, the average height of one of the groups, or something else entirely. If you try to memorize a mathematical formula to use, you’ll find yourself stumped as soon as the problem differs from what you’ve memorized. But with a little creativity and logical reasoning, you can solve any weighted average problem quickly. Here’s how.

Imagine the overall average height as the pivot point of a seesaw.

Figure out how each group compares to the average height. In this case, the women are on average **4 inches shorter**, and the men are on average **2 inches taller**. So, the women will stand 4 inches to the left of the pivot point, and the men will stand 2 inches to the right.

If you’ve ever played on a seesaw before, you know that the further you are from the pivot point, the more your weight ‘counts’. Someone who’s all the way out at the very edge will be able to balance out a much heavier person who’s closer to the center. The image should actually look like this:

The women are twice as far from the center as the men. Their weight counts for twice as much. To balance them out, you’ll need twice as many men as women.

Now, the seesaw is balanced, and the problem is solved. The ratio of women to men is **1:2**.

What if you don’t know how far each group is from the center? Here’s another problem:

**The average (arithmetic mean) of 13 numbers is 70. If the average of 10 of these numbers is 90, what is the average of the other 3 numbers?**

Draw out your seesaw. There are 10 numbers on the right, and 3 numbers on the left. Because the average of the 10 larger numbers is 90, and the average is 20, they’ll stand 20 away from the center. You don’t know just yet how far from the center the numbers on the left are. (However, because there are fewer of them, you know they need to be *more* than 20 units from the center in order to balance the seesaw!)

How far away from the center are the three numbers on the left, when the seesaw is balanced? Well, there are only 3/10 as many of them. So, in order to balance everything out, each of them must count for 10/3 times as much. They have to be 10/3 times as far from the center.

10/3 * 20 is 200/3. However, that’s not the answer — it’s just how far away from the middle the three values are. If they’re 200/3 away from the center, their average value must be 70 – 200/3, or **10/3**.

You can even use this strategy on some percentage problems. Here’s a final example. Try it on your own before reading onwards.

*Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon combines an amount of the two cereals in a single bowl of mixed cereal that is 65% fiber. If the bowl contains a total of 12 ounces of cereal, how much of the cereal, in ounces, is Fiber X? *

Here’s how you’d set up the seesaw:

Fiber X is twice as far from the middle, so its weight counts for twice as much. There must be half as much of it in order for the seesaw to balance. If the bowl contains 12 ounces of cereal, **4 ounces** will be Fiber X, and the remaining 8 ounces will be Fiber Max.

The lesson here is that you don’t need to memorize a bunch of mathematical formulas to succeed on the GRE. In fact, trying to memorize formulas makes you less flexible and less likely to spot your own mistakes. Work through weighted average problems like the three in this article using logical reasoning, instead. There are many more problems to try in the *Averages, Weighted Averages, Median, and Mode* chapter of the 5lb. Book of GRE Practice Problems!

**Chelsey Cooley 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 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post Answer Any Weighted Average Problem in One Minute or Less appeared first on GRE.

]]>The post Easy Answers Are Lousy Answers on the GRE appeared first on GRE.

]]>There are a few different types of wrong answers on the GRE. Some wrong answers are just there in hopes that you’ll guess incorrectly: they actually don’t make much logical sense, but if you don’t know what you’re looking for, they look just as good as any other option. Other wrong answers are meant to trick test-takers who make particular mistakes. If you pick an answer on a Text Completion problem that’s exactly the opposite of the correct one, because you missed a critical word like *despite* or *although*, this is the type of wrong answer you’ve fallen for.

The third type is more interesting than either of those, and that’s the type we’ll discuss in this article. This type of wrong answer is designed, intentionally, to look **easy**. A hard problem will sometimes have an easy answer or two, designed to tempt test-takers who aren’t quite sure what to do. In order to make the best guesses, and improve the confidence of your answers, learn to spot these “too easy” answer choices and stay away from them.

**Idioms**

*Prodigal son*. *Grand gesture*. *Foreign reporter*. *Proceeded by rote*. All of these are common, idiomatic English expressions that you’ve likely heard before. When you spot them in a Text Completion or Sentence Equivalence problem, watch out!

Imagine that the sentence includes the phrase ______ *son*, and one of the answer choices is *prodigal*. It might be correct, but it also could be a “too easy” trap. The writers know that you’ve heard the expression *prodigal son *before, and that it probably sounds good to you. To fool test-takers who simply choose whatever sounds best, instead of deeply understanding the sentence, they include it alongside the worse-sounding, but technically correct, right answer. On TC or SEq problems, never choose an answer *just* because it seems to go well with the words close to it: instead, base your answer on a careful reading of the entire sentence. If you decide to guess, don’t go straight for an answer choice that creates a common idiom. And remember that TC and SEq problems aren’t testing writing ability! An option that makes the sentence sound awkward or poorly written could be correct, if it’s the only choice that logically fits.

**Quantitative Comparisons**

The easiest guess to make on a QC problem is often (D). Here’s an example, from our 5lb. Book of GRE Practice Problems:

*a*, *b*, and *c* are positive even integers such that 8 > *a* > *b* > *c*.

** Quantity A**: The range of

** Quantity B**: The average (arithmetic mean) of

At first glance, it seems like you have too little information to decide which quantity is greater. After all, *a*, *b* and *c* could be anything — right? Nonetheless, (D) is a lousy answer to pick on this problem. It’s just too easy. In fact, the problem was designed to look like you lack information, while secretly giving you enough information to solve. That happens often enough that you should look out for it.

The solution is to never choose (D) without formally proving it, and to avoid guessing (D) on problems that look like this, even if you’re really pressed for time. In order to prove (D), show that Quantity A could be greater, or Quantity B could be greater, depending on the values you test. (Check out our recent article on QC case testing for much more info!) When you try that with this problem, you’ll notice quickly that the only case that seems to work is *a *= 6, *b* = 4, and *c* = 2. The problem doesn’t make that restriction obvious, but it’s there. And with those three values, the two quantities will be equal, making the right answer (C).

**Reading Comprehension**

Reading Comp passages are tough to understand. It’s easy to miss the really important stuff — the way that ideas in the passage relate to each other — in favor of the useless but flashy stuff, particularly *jargon*. The test writers throw a ton of jargon into Reading Comp passages, to disguise what usually is a very simple structure. (Since the longest passages are only a few paragraphs, there isn’t room for complicated rhetoric.) They want you to miss the forest for the trees.

In Reading Comp questions, particularly general questions, avoid answer choices that use a lot of fancy terms and phrases directly from the passage. If one of these answer choices seems correct to you, be skeptical. Don’t fall for an answer choice that actually reverses, or subtly changes, what the passage is saying. And never guess an answer choice that repeats a lot of technical terms from the passage. It could be right, but it’s probably just there to tempt you.

**What to do next**

There are two ways to use the information in this article.

First, use it to step up your guessing! Inevitably, you’ll make guesses on the GRE. Your goal is to get as many problems right as possible, but some problems are much harder than others. The smartest way to approach each section is to solve the easiest problems, then only attempt the more time-consuming ones if you have extra time. On the remainder, make the best guesses you can. If an answer choice looks too simple at first glance, *don’t* pick it: the GRE is a tough test designed for intelligent people, and it’s unlikely that the test writers will give you a question you can solve without any work.

Second, use this article to double-check your work and improve your review. If you’re tempted to choose (D) on a QC problem, always prove it first. If you’re thinking about selecting a jargon-filled RC answer, spend an extra few seconds to be certain you aren’t missing anything. Step up your standards for proof when the answer to a TC or SEq problem looks ‘too good to be true’. Keep your eyes open, and get ready to outwit the GRE.

**Chelsey Cooley 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 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

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]]>The post A Step-By-Step Guide to ‘Multiple Workers’ GRE Rates problems appeared first on GRE.

]]>*Nine identical machines, each working at the same constant rate, can stitch 27 jerseys in 4 minutes. How many minutes would it take 4 such machines to stitch 60 jerseys?*

First, take a deep breath. In this article, you’ll learn a methodical approach that will work on this problem type every single time. On test day, it’ll be tempting to throw away your new habits and go back to old ones. Try to do the opposite. You’ve done all of this studying for a reason!

On problems like this, don’t try anything fancy. A lot of GRE test-takers will try to logically reason their way through this problem, saying something like “well, if 9 machines stitch 27 jerseys in 4 minutes, then 3 machines stitch 9 jerseys in 12 minutes…” That approach is valid but dangerous. Whenever you choose not to write something down, you’re taking away your ability to check your work for mistakes. (By the way, where’s the mistake in the logic described above?)

To start the problem, make a table. Your scratch paper should look like this:

Using the table, figure out how quickly a single machine is working. Solve the equation 9 * ? * 4 = 27 to learn that ?, the unknown value, equals 3/4. Add it to the table.

Once the first line is completely filled in, add a second line with the remaining information:

Finally, solve for the unknown value**. **In this case, we’re looking for the time. Solve the equation 4 * 3/4 * ? = 60 to find that ? equals 20. The answer is 20 minutes.

If you’re creating a cheat sheet for Rates & Work problems, add the steps that we took to solve this one:

- Create a table
- Fill in the first line
- Find the rate of one worker
- Fill in the second line
- Solve for the unknown value

Always follow these steps, and you won’t go wrong. The advantage of filling out a table is that you can see which values you’ve calculated already and which values you still need to find. An unknown variable is just a blank space in the table.

There’s another, very similar type of problem in which the workers *aren’t* all identical. These problems look like this:

*Jenny takes 3 hours to sand a picnic table; Laila can do the same job in 1/2 hour. Working together at their respective constant rates, Jenny and Laila can sand a picnic table in how many hours? *

This is a ‘working together’ rates problem, and the solution process is similar. Again, always start by creating a table. Since you aren’t worrying about identical workers, there’s no need to consider the rate of a single worker. Label the rows with the workers’ names, and fill in everything you know.

Once again, calculate the rate for each worker by solving the equations. In this case, Jenny’s rate is 1/3 tables per hour, and Laila’s rate is 2 tables per hour. (It feels a little silly to think in terms of ‘tables per hour’ or ‘violins per minute’, but it’s necessary in order to solve this type of problem). Then, create a third row to represent both workers’ combined efforts.

The rate of both workers combined is always the sum of their individual rates. That lets you fill in one more square in the table: Jenny and Laila’s rate when working together is 1/3 + 2, or 7/3 tables per hour.

Now there’s only one unknown. Solve the equation 7/3 * time = 1 to find that Jenny and Laila sand the table together in 3/7 hours.

Here are the steps:

- Create a table
- Fill in the first 2 (or 3, or 4) lines
- Find the rate of each worker
- Add the workers’ rates together to find the combined rate
- Fill in the last line
- Solve for the unknown value

Some GRE problems require creativity. Others require a methodical approach. These two Rates & Work problems fall into the second category. If you struggle with Rates & Work, practice and review these strategies using simpler problems, then move on to tougher problems that might require other skills as well, such as unit conversions or percent calculations. The Rates & Work chapter of the 5lb. Book of GRE Practice Problems (where both of these problems came from) is a great place to start!

**Chelsey Cooley 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 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.

The post A Step-By-Step Guide to ‘Multiple Workers’ GRE Rates problems appeared first on GRE.

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]]>The *Your Dream MBA* series webinars will be held on consecutive Tuesdays from April 12th through May 10th, 2016 from 7:30 to 9:30 p.m. EDT.

We hope you will join us for this special series. Please sign up for __each__ part separately via the links below—space is limited!

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**Part 4: May 3, 2016:** Advanced GMAT: 700+ Level Quant and Advanced GMAT: 700+ Level Sentence Correction Strategy

**Part 5: May 10, 2016:**

Admissions officers on this panel include:

Additional admissions officers yet to be announced!

All attendees of these events will also receive:

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]]>The post Here’s What to Do When You Don’t Know What to Do on GRE Vocab appeared first on GRE.

]]>While you’re taking the GRE, you’ll encounter words that you just haven’t learned. It happens to everyone: I’ve gotten a perfect score on the GRE (twice!), and both times, I saw multiple Text Completion and Sentence Equivalence answer choices that I couldn’t define. What does a smart test-taker do when this happens?

**Triage the problem. Is it impossible, or just ugly?**

In this article, we discussed the difference between “bad” problems and* “*ugly” problems. A Text Completion or Sentence Equivalence problem that you just don’t understand, even after reading it twice, is probably a “bad” problem. If you don’t know what sort of word would fit in the blank, it doesn’t matter whether you know the vocabulary. When you see one of these problems, *guess randomly, don’t mark the problem, and move on.* If you’re way ahead on time, you can try some answer-choice analysis, but don’t get bogged down.

What if you understand the sentence, but you don’t know some or all of the words in the answer choices? It may be an “ugly” problem. If you’re behind on time when you see it, and you’re struggling to answer, *guess randomly, mark the problem, and come back to it later. *When you return to the problem — or if you decide that you have enough time to do it — use the strategies in the rest of this article.

Always prioritize the questions you can answer. You’re only judged on the total number of questions you answer correctly, not how difficult they are, so leave the tough questions for later (or ignore them entirely).

**Use your scratch paper wisely.**

On Sentence Equivalence and Text Completion, you only need to find the right answer(s). It doesn’t really matter whether you can define a word if it isn’t correct; at most, it may help you confirm your answer. Keep track of which answers are possibly right, which are definitely wrong, and which you can’t define. I like to jot down symbols to help me remember my analysis of each answer choice. My scratch work for a SEq problem might look like this:

In the problem above, I don’t recognize one of the words, so I’ve used a question mark. But I *do* see two words that fit the blank, so I’ll probably pick those and move on, ignoring the unknown word.

What if my work looked like this, instead?

I’ve eliminated three answer choices, so the second right answer must be one of the two words I don’t know. The rest of this article gives two ways to escape this predicament.

**Use context to jog your memory.**

GRE vocabulary words represent the vocabulary an educated person might see in scholarly writing. You’ve probably seen many of them before, even if you don’t remember them clearly. When you’re stuck on a word, if you have time, ask yourself if you’ve seen it in context. For instance:

– You might not remember the definition of *armada*, but have you read about the Spanish Armada in history classes?

– You might not remember the definition of *burgeon*, but have you seen a news article about the *burgeoning *national debt?

Don’t spend too much time doing this. But even if the definition of a word doesn’t come to you right away, you might still know it subconsciously. Consider whether you’ve ever heard the word in context, and whether you can infer its meaning.

**Use roots, prefixes, and suffixes cautiously.**

Etymology can sometimes give you a clue to the meaning of a word, and it’s a great memory tool for some students, but it’s also sometimes deceptive. For instance, a *sobriquet* has nothing to do with *sobriety*, and the prefix *un* means ‘one’ in the word *unanimity* but ‘not’ in the word *unseemly*.

That said, if you don’t have anything else to use, there’s nothing wrong with making a guess based on etymology. Maybe the word sounds very similar to another word that you do know. One safe way to use this technique is by guessing whether the unknown word has a positive or a negative connotation, and matching this to the connotation of the word that would fit in the blank. That’s often enough information to choose between two unknown words.

**You won’t know every word in every problem. **Know the core words by heart (try our 500 Essential Words GRE Vocabulary Flashcards as a starting point), but also have a clear strategy to use when you can’t define a word. Learn the four points above, and use them to keep moving quickly while practicing tough Text Completion and Sentence Equivalence problems. You may also develop other strategies on your own as you practice. If you do, share them with us and your fellow students in the comments!

**Chelsey Cooley 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 170/170 on the GRE.Check out Chelsey’s upcoming GRE prep offerings here.

The post Here’s What to Do When You Don’t Know What to Do on GRE Vocab appeared first on GRE.

]]>The post Want to Do Better on GRE Quant? Put the Pen Down! appeared first on GRE.

]]>Let’s do an experiment. This is one I do with all of my GRE classes and tutoring students. Grab a piece of paper, a pen, and a stopwatch (or use the stopwatch function on your mobile device).

When you’re ready, click “start” on the stopwatch and begin the following multiple choice Discrete Quant problem…

Solution A contains 20% alcohol by volume, and Solution B contains 50% alcohol by volume. If the two solutions are combined, the resulting mixture of A and B contains 32% alcohol by volume. What percent of the total volume of the mixture is Solution A?

(A) 35%

(B) 40%

(C) 50%

(D) 60%

(E) 70%

Ok, write down the answer you got, and how much time it took you.

Right now, though, I’m not interested in what answer you got. I just want to know 2 things:

- At what point did you start writing on your paper? 5 seconds into the problem? 10? 30?
- How long did you take on the problem overall?

Believe it or not, there is probably an *inverse correlation* between those two answers. Students who dive in and start writing equations right away will often spend 2:30 to 3:30 on a question like this – generally much longer than students who take their time before writing things down. They’re also much more likely to get the question wrong!

Savvy test takers don’t dive in and start solving right away. They know that slowing down at first (even though it seems counter-intuitive) can improve both timing and accuracy.

The *savvy* way to approach Discrete Quant questions is this:

**Read the entire problem, pen down.**

It’s not Reading Comprehension, so you don’t need to take notes! If you’re writing while you’re reading, you’re much more likely to miss key pieces of information. Think about the concept that’s being tested, and what information the problem is giving you.

Here’s what I’d be thinking while reading the problem above: “ok, this is a weighted average problem – we’re mixing 2 things together. They’re each different amounts of alcohol, and then we’re given a total.”

**Define what the question is asking for.**

Again, before writing equations down, just define the question. Is it asking us for a value, a sum, a difference, a proportion, a variable “in terms of” another variable, etc.?

This is the best way to ensure that you don’t accidentally solve for the wrong thing! The GRE loves to trick us into doing that. How many times have you looked back to realize that your algebra was correct, but you just answered the wrong question?

My thoughts: “The question is asking me about A as a percentage of the *total *of A and B. I bet they’ll include a trap if I accidentally solve for B!”

**Scan the answers & try to eliminate.**

Before picking up the pen, *do a common sense test *first! This isn’t high school, where you have to show all of your work before picking an answer. Think of the answers as part of the problem itself!

Scanning the answers first can give you powerful clues for how to solve a multiple choice problem. For example, if a geometry problem featured √3 in some of the answer choices, that’s your clue to think about 30:60:90 right triangles. If a ratio problem featured some ratios that were greater than 1 (e.g. 3:2) and some that were less than 1 (2:3), that’s your clue to assess which portion should be greater.

My thoughts on the problem above: “I notice that some of the answer choices are less than 50%, one is 50%, and the others are greater than 50%. If I can just figure out whether I have more A or more B in the mixture, I can narrow it down.”

“Since the 32% in the overall mixture is closer to A’s 20% than B’s 50%, that means that A must make up more of the overall mixture – in other words, more than 50%. I can eliminate (A), (B), and (C).”

**Look out for Traps**

As I mentioned before, the GRE loves to set traps for us. If you become aware of those traps, you can narrow down answer choices easily. Here are some common traps to watch out for:

**Numbers in the Problem**– these are rarely right answers. The GRE imagines that if a student didn’t know what to do, she would just say, “um, that number looks familiar. I guess I’ll pick it.” Don’t do that! We could eliminate (A) and (C) (if we hadn’t already) since they’re in the problem.

**One-Move Answers**– similar to the above. If you can get to one of the answers just by performing one operation (addition, subtraction, multiplication, division) to 2 of the numbers in the problem, that’s almost certainly a trap. 50 + 20 = 70, so (E) is almost certainly a trap answer.

**“Evil Twins”**– if we expect that the GRE is trying to trick us into answering the wrong question (for example, solving for B instead of A here), we should look for answers that form a pair. We know that the percentage of A + the percentage of B will add to 100%. So, look for 2 answers that add to 100: only (B) and (D) in this case. Since we know A has to be more than half of the total, that means that (B) is probably an “evil twin” trap!

If we eliminate all of the likely trap answers, that just leaves us with (D).

**Be Strategic**

In a situation like this, the best strategic move would be to pick (D) and move on. It’s a bad idea to get bogged down in a lot of algebra just to prove what you probably already know to be true. The savvy test-taker would say “90% sure of my answer in 40 seconds is better than 100% sure of my answer in 3 minutes.”

It’s an uncomfortable feeling not to know for sure, but the GRE is a time-constrained game! You don’t have time to be 100% sure of every answer.

If this question were different, and you weren’t able to eliminate all of the other answer choices, you would want to make a *strategic* decision about which approach would work best. Don’t just dive into doing algebra! Remember that there are other strategies that can often be faster: picking smart numbers, working backwards from answer choices, estimating, etc.

On this problem, *if *we wanted to solve, we could do a combination of strategies. Since we don’t have any concrete amounts given, we can pick our own numbers. Let’s say that the total mixture is 100 liters.

We could also work backwards from the answer choices, based on that 100L total. Since we suspect that the answer is (D), let’s then say A = 60 liters. The amount of alcohol in A would be 20% of 60, so 12L. If A is 60L, then B must be 40L. 50% of 40L would be 20L of alcohol. Thus the total amount of alcohol is 12 + 20 = 32 liters of alcohol out of 100 à 32%.

That works! So (D) must be the right answer.

**Saving time on Discrete Quant.**

If you did long or complicated algebra on this question, you probably took well over 2 minutes to solve. It’s also *far* more likely that you got the answer wrong! Putting the pen down and thinking through the problem in the way we outlined above will improve both your timing and your accuracy.

The next time you’re doing a set of Discrete Quant problems, write this on a post-it note and keep it next to you as you’re working:

- Read the entire problem, pen down
- Define what the question is asking for
- Scan answers & try to eliminate
- Look out for traps
- Be strategic (either in solving, or in guessing & moving on)

Good luck!

**Céilidh Erickson is a Manhattan Prep instructor based on New York City.** When she tells people that her name is pronounced “kay-lee,” she often gets puzzled looks. Céilidh is a graduate of Princeton University, where she majored in comparative literature. After graduation, tutoring was always the job that bought her the greatest joy and challenge, so she decided to make it her full-time job. Check out Céilidh’s upcoming GMAT courses (she scored a 760, so you’re in great hands).

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