I’ve spoken with multiple students lately who received a disappointing (lower than they were expecting) score on the quant section and who all said that the quant felt relatively easy or straightforward. How is that possible?

First of all, thinking that a test like the GRE is easy is actually a warning sign: unless you are poised to get a perfect score, chances are you’re missing something. Some of the questions are really very challenging and they should feel hard even to someone like me (who did get a perfect score on this test! 🙂 ).

Second, the test writers are phenomenal at writing questions that don’t seem all that complicated but are in fact your worst nightmare. My worst nightmare is not an impossible question “ I know I can’t do it, so I just pick an answer and move on. My worst nightmare is a question that I think I can do, and I spend a decent chunk of time doing it, and then I get it wrong anyway “ even though I’m sure I got it right!

The problem I’ve chosen is actually a GMAT problem; I chose it because it perfectly illustrates the point that I’m trying to make, and it is actually in the same form as GRE problems. Try this GMATPrep problem and you might see what I mean. Set your timer for 2 minutes. and GO!

*  Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/3, what percent of the total number of the remaining employees would then be clerical?

 

(A) 25%

(B) 22.2%

(C) 20%

(D) 12.5%

(E) 11.1%

What’s hard about this one? It looks completely straightforward!

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Most people dislike absolute value, and inequalities can tie us up into knots. Put them together, and we can have some major headaches! Let’s test one out.

Set your timer for 1 minute and 15 seconds for this Quantitative Comparison problem and GO! Read more

Many word problems seem to require us to write formulas in order to solve. Certain problems, though, qualify for a neat technique: Smart Numbers. We can actually pick our own real numbers and use them to solve!

Set your timer for 2 minutes for this Fill-In problem and GO! (© ManhattanPrep)

* Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate, Carrie, who earns twice as much as Lisa, spends ¼ of her monthly paycheck on rent and ½ on food. If the two women decide to donate the remainder of their money to charity each month, what fraction of their combined monthly income will they donate? (Assume all income in question is after taxes.)

 

(No answer choices given; this is a fill-in-the-blank)

 

We’ve got two women, Lisa and Carrie, and they each spend a certain proportion of income on rent and on food. Annoyingly, the fractions don’t have the same denominators; even more annoyingly, the two women don’t make the same amount of money. All of that will make an algebraic solution challenging.

Here’s what an algebraic solution would look like. Let’s call Lisa’s income x. She spends (3/8)x on rent and (5/12)x on food. Add these together:

(3x/8) + (5x/12) = (9x/24) + (10x/24) = 19x/24

Subtract from 100%, or x:

24x/24 “ 19x/24 = 5x/24

Lisa donates 5/24 of x, her income, to charity. What about Carrie?

Carrie’s income is equal to 2x (because she makes twice as much as Lisa). How much does she spend on rent and food?
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Recently, we discussed various strategies for translating word problems into math. Let’s put that knowledge to the test on a challenging problem from a category that everybody hates: Rates.

Set your timer for 2 minutes and GO! (© ManhattanPrep)

*  A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 300 miles apart, at what time will the trains pass each other?

(A) 12:40pm

(B) 12:49pm

(C) 12:55pm

(D) 1:00pm

(E) 1:05pm

One of the strategies we discussed in the translation article was make the situation real. Put yourself into the situation and imagine you’re the one doing whatever the problem is describing. That will help you to set things up cleanly and correctly.

So what’s going on in this particular situation? First, you’re the conductor on the Kyoto train. At noon, you pull out of the station (instantly and magically traveling 240 miles per hour from the very start!). The track is 300 miles long; after one hour, where are you?

After one hour, it’s 1pm and you’ve gone 240 miles, so you’re just 300 “ 240 = 60 miles from Tokyo.

Okay, now switch jobs. You’re the Tokyo train conductor and you leave Tokyo at 12:10pm. After one hour, where are you? You’re going 160 miles an hour, so after 1 hour, it’s 1:10pm and you’re 300 “ 160 = 140 miles from Tokyo.

By 1:10p, have the two trains passed each other? Definitely, because train K (for Kyoto) is even further towards Tokyo at that point. Now, make a guess: do you think that the trains had already passed each other by 1p? Think about it before you read the next paragraph.
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In addition to the long, boring reading comprehension passages (that everyone hates!), we will also see quite short passages that are perhaps more appropriately called arguments. We might be asked to strengthen or weaken the conclusion, find the conclusion, articulate the role of a specific piece of information, and so on. Today we’re going to talk about Analyze the Argument Structure questions.

We’re going to use the analysis process that we discussed in a previous article; please take a look at that article first if you haven’t already.

We want to average about 1.5 to 2 minutes on RC questions in general, so set your timer for either 1.5 minutes (if RC is a strength) or 2 minutes (if RC is a weakness). (© ManhattanPrep)

(1) Local authorities are considering an amendment to the litter law that would raise the fine for littering in the community picnic area to $1,000. (2) Advocates say that raising the fine will make people take notice of the law. (3) They may be correct that higher fines get more attention. (4) Since the inception of the litter law, incremental increases in the littering fine have proven to be consistently effective at further reducing the amount of litter in the community picnic area. (5) However, raising the fine to $1,000 would actually have the unintended effect of increasing the amount of litter in the picnic area. (6) Picnic area users would perceive this fine to be unreasonable and unenforceable, and would disregard the litter law altogether.

Select the sentence, by clicking on the passage itself, that provides support for the author’s position in the passage.

Note: the real test will not number the sentences; we’ll just be able to click on a specific sentence to highlight it. We can’t do that in this article, though, and it’s a lot easier to talk about the sentences if we number them, so voila. I inserted numbers. : )

The first thing everybody does is check the answer “ so I’ll tell you that the answer is Sentence 6. Even if you answered correctly, though, you’re not done! You still need to analyze the problem.
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This is the second part of a two-part article on the topic of translating wordy quant problems into the actual math necessary to set up and solve the problem. Click here for the first part.

Last time, we discussed the basics as well as these two tactics:

1. Translate everything and make it real
2. Use a chart or table to organize info

Today, we’re going to dig a bit deeper into how the test writers can make translation really challenging.

Task 3: finding hidden constraints

The higher-level the problem, the more likely it will be to contain some kind of constraint that is not stated explicitly in the problem. For instance, I could tell you explicitly that x is a positive integer. Alternatively, I could tell you that x represents the number of children in a certain class. In the latter case, x is still a positive integer (at least I hope so!), even though I haven’t said so explicitly.

Here’s another example, from page 35 of our Word Problems book:

If Kelly received 1/3 more votes than Mike in a student election

If we say that M equals the number of votes case by Mike, then how would we represent the number of votes cast for Kelly?
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I’ve spoken with several students recently who are struggling with translating wordy quant problems into the actual math necessary to set up and solve the problem. Some people make too many mistakes when doing this, and others find that, though generally accurate, they take more time than they can afford. In the next two articles (this is part 1!), we’re going to talk about how to translate efficiently and effectively.

We’re going to do this by example: I’ll provide short excerpts from actual problems, and then we’ll discuss how to know what to do, how to do the actual translation, and how to do everything efficiently. Note that I’m not necessarily going to provide the full text of problems “ and, therefore, we’re not going to solve fully. That’s not our goal today.

The Basics

Before we dive into more advanced issues, there are some basics we all need to know. We’re not going to spend a lot of time on the basics because all GRE books out there already explain this; I’ll give a quick introduction and, if you need more, seek out one of the standard books on this topic (in Manhattan Prep’s books, you’ll find this info in the Algebraic Translations chapter of the Word Problems Strategy Guide).

First, when the problem introduces certain people, objects or other things, we will likely need to assign variables. Cindy can become C and Bob can become B. Next, the words will give us some kind of relationship between variables.
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Have you started studying Number Properties yet? Most people find this topic on the more difficult side in general, particularly the area of divisibility and prime. We did learn all of these basic concepts years ago, when we were about 8 or 10 years old “ number properties refers to all of the building blocks we use later in school to do algebra, geometry, and more advanced math.

However, most of what we learned in school was at a much more basic level (we were only 10 after all!) and we also didn’t have to understand the number properties theory or answer questions that were anything like some of the bizarre-seeming questions we find on standardized tests.

Let’s try this problem first (© Manhattan Prep) from our GRE Number Properties Strategy Guide. Set your timer for 2 minutes.

The quantity 3³4⁴5⁵6⁶ “ 3⁶4⁵5⁴6³ will end in how many zeros?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 9

Got your answer? Great, let’s get started. You want to know what the correct answer is? Let me ask you a couple of questions first.

Are you confident about your answer? Did you end up having to guess? Did you give up without guessing? (If the last, make a guess right now. You can’t keep reading till you do. Well, obviously I can’t stop you, but I’m serious “ make a guess.)

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Did you know that 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.

Did you know that you can find everything you ever wanted to know about Reading Comprehension here on our blog? Well, okay, perhaps I’m exaggerating just a little but not that much! Follow the links! Read more

How much did you study for the GRE this past week-end? For how many hours? Over how many sittings? What did you study and how did you study it?

Most importantly: how many breaks did you take and how long were they?

Time Magazine just published a fascinating little article: To Boost Memory, Shut Your Eyes and Relax. Go take a look at it. Don’t worry, I’ll wait. : )

Has this happened to you? You have ambitious plans to study a ton of things this week-end. You get tired, but you’re determined to push through, so you keep studying. You begin to get a bit anxious because you feel you aren’t learning well (and you’re not!), so you study even more. You get even more tired, and that makes it even harder to learn. By the end of the week-end, you’re exhausted, frustrated, and demoralized.

You may have already heard me say this (many times on various forums or in blog posts!), but I’m saying it again because it’s so important: your brain makes better memories when it’s not tired.

The Time article quotes Michaela Dewar, the lead author of a new research study on this topic. She notes that we are at a very early stage of memory formation when we first start to study new information, and further neural processes have to occur after this stage for us to be able to remember this information at a later point in time.

The italics are mine. Note what Ms. Dewar has said: more stuff has to happen in our brains after we have studied this info in order for us to be able to recall that information later on.

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