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Math Articles

Knewton Weekly Quant Challenge – Week 1

We’re happy to introduce the Knewton Weekly Math Challenge. Every Wednesday we’ll post a very difficult quant question. The first person to answer correctly in the comment field below will win the new Knewton T-shirt. After the right answer appears in the comments (you can only post one answer, and you must explain how you arrived at your answer — so take your time), we’ll post a full explanation. Here’s the first question. Good luck!

In a certain game, a player begins with a bag containing tiles numbered 1 through 10, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?

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How to Analyze a GMATPrep Data Sufficiency Question

Close Up of Pen on Paper excerptThis is the latest in a series of “How To Analyze” articles that began with the general “How To Analyze A Practice Problem” article (click on the link to read the original article). This week, we’re going to analyze a specific Data Sufficiency question. The GMATPrep® problem we’re using this week is one that we’ve already discussed how to solve in a previous article; click here to read that article and try the problem first.

Here’s the problem again; if you didn’t read the first article and try the problem already, then try this problem now (2 minutes):

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Manhattan GMAT Challenge Problem of the Week – 11 Mar 10

Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!

Question

A circle is inscribed in an equilateral triangle, such that the two figures touch at exactly 3 points, one on each side of the triangle. Which of the following is closest to the percent of the area of the triangle that lies within the circle?

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Interest and Compound Interest Problems

percentageThere are two types of interest problems on the GMAT, and they include simple interest and compound interest. Simple interest is the most basic and is a function of P, the principle amount of money invested, the interest rate earned on the principle, i, and the amount of time the money is invested, t (this is usually stated in periods, such as years or months). The resulting equation is:

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GMAT Insider: The GMAT Case Method

numbersMany business schools teach using the famous “case method”, in which you will analyze the real-world situation of a specific business at a time of crisis/transition/decision in order to gain practical knowledge of business theory as applied to an actual situation.  The theory behind the case method is that, by analyzing how, for example, Kodak needed to transition from a conventional (film) to a new (digital) business model, you will gain large-scale comprehension of a business principle in general, and not just an intimate understanding of one business.  With this experience, you can then apply your theoretical-and-practical understanding of a vast array of business principles to whatever situations will arise in your future role as a manager.

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Right Answer / Wrong Question

The GMAT is notorious for many reasons.  As you continue to study with relevant books and materials, you’ll find that one aspect of the test will continue to frustrate you – getting the correct answer, but not answering the right question.

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Manhattan GMAT Challenge Problem of the Week – 4 Mar 10

Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!

Question

Skier Lindsey Vonn completes a straight 300-meter downhill run in t seconds and at an average speed of (x + 10) meters per second. She then rides a chairlift back up the mountain the same distance at an average speed of (x – 8 ) meters per second. If the ride up the mountain took 135 seconds longer than her run down the mountain, what was her average speed, in meters per second, during her downhill run?

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The Importance of Prime Factorization on the GMAT

Prime Factorization: My single favorite topic on the GMAT. Hands down.

My passionate (some would say evangelical!) advocacy of prime factorization results not only from my finding prime numbers so intrinsically fascinating in and of themselves, but also from the plain and simple truth that prime factorization proves surprisingly useful on questions on which prime numbers aren’t even mentioned.

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My 2 Keys to GMAT Quant Success

Math HomeworkEveryone has their own strategies for these tests, but to me the GMAT quantitative test came down to two main components, i) knowing the underlying math and ii) question identification.

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GMAT Insider: To Beat the GMAT, Be the GMAT

InvestigateData Sufficiency questions, which will comprise approximately half of your quantitative section, are a format unique to the GMAT.  As you become familiar with this unique type of question, you’ll find it challenging, frustrating, confusing, infuriating, but hopefully in the end satisfying as you master the many challenges that these questions present.

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Manhattan GMAT Challenge Problem of the Week – 26 Feb 10

Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!

Question

x^8 – y^8 =

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Know When to Hold ‘Em: Pacing on Data Sufficiency

Texas Hold 'EmOver these past few months of writing articles for Beat The GMAT, you’ve probably noticed that I like to associate important GMAT concepts with common situations.  Well, with regards to pacing on data sufficiency questions, the best way to approach them is to know the material and content through and through.  However, while on the actual GMAT and as you practice with CAT tests, keep in mind the words of Kenny Rogers, The Gambler:

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GMAT Insider: Memorization – The 2,000-Pound Elephant in the Room

elephantThey say that “elephants never forget”, but, when you think about it, how much do elephants really have to remember?  Aspiring graduate students, however, have quite a bit to keep track of: dozens of passwords, bank account and phone numbers,  and years’ worth of academia that we’ve collected over time.  Human ingenuity, however, has created computer memory – we carry gigabytes of storage space in our pockets everywhere we go – so that we don’t need to rely on our more-limited natural capacity for memory. (Note to elephants: Now who’s impressed?)

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Manhattan GMAT Challenge Problem of the Week – 18 Feb 10

Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 minutes and go!

Question

Set S consists of 5 values, not necessarily in ascending order: {4, 8, 12, 16, x}. For how many values of x does the mean of set S equal the median of set S?

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Save Time on Math Questions… Estimate Rather Than Calculate

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At Magoosh, we believe that Beating The GMAT often comes down to answering questions in the most efficient way possible.  This post outlines a way to save time on math problems.  The key is to know when to estimate.  Here’s a typical arithmetic question on the GMAT:

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