Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.

For all values, [x] denotes the least integer greater than or equal to x.  If -2.5 < x < 1.5, what is the least possible value of [2x] + [x²]?

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I remember in a high school chemistry class, my teacher said, There are a few magic numbers. One of them is pi. One of them is e. Anyone know another one? Jane? I had no idea what he was talking about. Eight? I guessed. Obviously I missed the point.

But today’s magic number is seven. While there are lots of different ways to classify numbers, there are seven categories of numbers that make all the difference when trying to move quickly and correctly through the Quantitative Comparison section of the GRE.

Seven Important Categories of Numbers

Picture a number line. In the middle, you’ve got zero. (Okay, I know the number line doesn’t have a middle. But you get the idea.) On either side of that, you have positive and negative proper fractions. (For the rest of this post, I’m just going to use fractions to refer to proper fractions, meaning fractions with an absolute value less than one.) Next, moving outward, you hit one and negative one. And then, you hit positive and negative integers other than one.

While there are other categories of numbers that matter (primes, perfect squares, odds, evens, etc.), these are the seven that come to my mind fastest when I’m trying to come up with two alternative results in a QC questions.  When we’re trying to find two different results, we always look to try numbers that are fundamentally different. And these categories churn out some fast differences that are important in matters that QC cares about testing.

When are these sets of numbers most helpful? I’m glad you asked.

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Happy Friday! It’s time to take a break from GRE prep to catch up on some of the top grad school tips and news links from the week:

8 Steps for Making the Most of Your Summer Internship (Brazen Life)

It’s almost summertime! Here are some great tips to help you maximize your summer internship experience.

Yes, Guys, Graduate School in the Humanities is Still a Worthwhile Investment (Policymic)

Graduate school, especially in the humanities, has been receiving very bad press for a long time, but 2013 has already produced a bumper crop of essays about the Ph.D. process.

Get Research Experience for Graduate Admissions (About.com Graduate School)

Graduate programs, especially PhD programs, highly value research experience. Without it, it’s unlikely that you’ll gain admission, regardless of your GPA.

Grad School May Not be for Everyone (Daily Sundial)

A current student argues that grad school is a good idea, but only if you’re 100 percent ready for the challenges that await.

Did we miss your favorite article from the week? Let us know what you’ve been reading in the comments or tweet @ManhattanPrep

Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.

Two different children are to be selected at random from a group of 12 students. If the probability that both students selected are girls is greater than , there must be at least how many girls among the 12 students?

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Are you feeling incredibly stressed out when you sit down to study for the GRE? (Or maybe I should ask, who isn’t?) Do you find it hard to concentrate on the task at hand?

Researchers at the University of California at Santa Barbara recently published the results of a study following 48 undergrads preparing for the GRE. Jan Hoffman details the research in a blog post over at The New York Times; here’s a summary:

The Motivation

We had already found that mind-wandering underlies performance on a variety of tests, including working memory capacity and intelligence, said Michael D. Mrazek, (quoted from the NYT blog post)

Ah, yes, mind-wandering. We’ve all had this experience. We’re taking a test, the clock is ticking, and we keep finding ourselves thinking about something other than the question we’re supposed to be answering right now. Maybe we’re stressing about our score. Maybe we’re thinking about applications. Maybe we’re even distracted by work, significant others, family, or other issues that have nothing to do with the test!

How do we stop fixating on other things and concentrate on the task at hand? This study tried to find out.

The Study

First, the students were given one verbal reasoning section from the GRE. They also completed a task that measured their working memory. These tests are the baseline results.

The students were split into two groups; let’s call them Group M and Group N.

Group M attended meditation classes four times a week; these students learned lessons on mindfulness, which focuses on breathing techniques and helps to minimize distracting thoughts.

Group N attended nutrition classes, designed to teach these students healthy eating habits.

Afterwards, the students were given another GRE verbal section and another task to measure working memory. The performance of students in group N stayed the same; the nutritional studies didn’t make a difference.

Group M students, however, improved their GRE scores by an average of 12 percentile points! Here’s the best part: the study took just two weeks. You read that correctly: these students improved their verbal scores by 12 percentile points in just two weeks.

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Here are the free GRE events we’re holding this week (All times local unless otherwise specified):

5/13/13– Online –Mondays with Jen– 9:00- 10:30PM (EDT)

5/19/13– New York, NY- Free Trial Class– 2:00PM – 5:00PM

Looking for more free events? Check out our Free Events Listing Page.

Anyone who’s taken my GRE class can tell you that I’m not a vocab girl. I never took Latin, I pretty much don’t know any roots, and I’m terrible at learning foreign languages. So how did I get a perfect score on the GRE? For vocab, the biggest skill for me is mnemonic devices.

All for the game

I think it’s great that some teachers want to use the GRE as a way to inspire a love of learning in students. You’ll use this vocab all your life! You’ll sound so smart! Start reading the Economist every day! I just really? You’re an adult. You have infinite things you could learn about, and infinite resources to learn about them, and finite time to do it in. If you were passionate about vocab and wanted to learn more of it, you already would be! And who is really ever going to care if you can use puerile or penumbra in a sentence?

For me, studying for the GRE is all about the game, and the game here is getting GRE points. That’s it. I don’t need to know this word for life. I need to know it to get it right on the exam. And I like that mindset, because I feel like it presents me with a defined challenge that I can win. And I like to win.

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Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.

Within rectangle ACDF, both ABGH and BCDE are squares, and 3x > y > 2x.

 

Quantity A

The ratio of the area of ACDF to the area of HGEF

Quantity B

5

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Here are the free GRE events we’re holding this week (All times local unless otherwise specified):

5/6/13– New York, NY- Free Trial Class– 6:30PM – 9:30PM

5/6/13– Online – Free Trial Class– 2:00PM – 5:00PM

5/6/13– Online –Mondays with Jen– 9:00- 10:30PM (EDT)

5/8/13– Los Angeles, CA- Free Trial Class– 6:30 – 9:30PM

5/12/13– Berkeley, CA- Free Trial Class– 6:00 – 9:00PM

Looking for more free events? Check out our Free Events Listing Page.

I have a GRE class that’s right now winding down to our couple final classes, and the first panicked email has just come in. This always happens in GRE (and GMAT and LSAT) classes as the end approaches. People start freaking out, because they’re studying, and they’re learning things, and they know more than they did before “ but the score isn’t budging. Or if it is budging, it’s not increasing enough! Or worst, it’s going down! And they start to lose hope. But they’re just in the dip.

The Studying Dip

When Seth Godin wrote about The Dip, he was talking about the time in a business where you feel like things will never improve, but they’re just about to get better. He was trying to quantify, or at least clarify, when you should stick with it despite the obstacles, versus when you are just on a steady downward streak.

When we talk about the dip, we’re talking about that time in studying for a standardized test when you’re working, and working, and working, and you wonder, Is this working?

The Bad News

Let’s start with the bad news first. The bad news is that if what you’re doing isn’t making your score go up, after a number of weeks, you have to change it. But this section is very short because that’s the only bad news.

The Good News

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