We invite you to test your GMAT knowledge for a chance to win! Each week, we will 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 a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:

In the figure above, ABC is a right triangle with AC as its hypotenuse, and PQRS is a square. What is the area of the square?

(1) AC is 70 units long.

(2) The product of the length of AS and the length of RC is 396.

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Try to solve the following question, and time yourself:

If the volume of a big cube is 64 times that of a small cube, how many times bigger is the surface area of the big cube than that of the small cube?

If you cannot answer the above (classic GMAT) question in under 20 seconds, continue reading and you will learn a concept that will be super useful in your quest to crush the GMAT!

I was watching Austin Powers the other day and it suddenly hit me: Dr. Evil and Mini-Me are similar shapes! You know, like similar triangles, where the proportion between any two matching sides is always maintained “ if Mini-Me’s fingers are exactly half the length of Dr. Evil’s fingers, then Mini-Me’s eyes, ears, nose, and feet must also be exactly half their counterparts in Dr. Evil’s body. It got me thinking “ what other kinds of similar shapes could be out there? I will investigate that thought further in the second half of this post, but first let’s see why that might be useful

We know triangles are similar whenever they have the same three angles. If the base of the bigger triangle is exactly twice that of the smaller triangle, then each side in the bigger triangle will also be twice as big as its matching side in the smaller triangle.
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There was a lot of confusion and anxiety regarding last week’s Challenge Problem Showdown. And for good reason; it was a difficult problem! In fact, only 15% of submitted answers were correct, making this the most difficult Challenge Problem Showdown in several years (by the way, you can purchase our complete Challenge Problem Showdown Archive here).

With this in mind, here is the solution to the Challenge Problem.

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This 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 IR question from the Two-Part prompt category. First, give yourself up to 2.5 minutes to try the below GMATPrep problem.

An architect is planning to incorporate several stone spheres of different sizes into the landscaping of a public park, and workers who will be applying a finish to the exterior of the spheres need to know the surface area of each sphere. The finishing process costs $92 per square meter. The surface area of a sphere is equal to 4Ï€r², where r is the radius of the sphere.

In the table, select the value that is closest to the cost of finishing a sphere with a 5.50-meter circumference as well as the cost of finishing a sphere with a 7.85-meter circumference. Make only two selections, one in each column.

Circumference 5.50 m	Circumference 7.85 m	Finishing cost
		$900
		$1,200
		$1,800
		$2,800
		$3,200
		$4,500

After trying the problem, checking the answer, and reading the given solution (if any), I then try to answer the questions listed below. First, I’ll give you what I’ll call the standard solution (that is, one we might see in an Official Guide book if this were an official guide problem “ a correct solution but not necessarily one that shows us the easiest way to do the problem). Then we’ll get into the analysis.

Standard solution: The formula for circumference is C = 2Ï€r. We can use this to calculate the radii of the two spheres (note that the problem asks us to find the closest values, so we can estimate):

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Our 8 Strategy Guides, organized by topic, have been around for several years.  However, we were seeing some students who hadn’t looked at math in a LONG time and wanted a refresher.

So, after months of development, we are very happy and proud to announce the publication of our brand new Strategy Supplement, the Foundations of GMAT Math!  This book starts from the basics to give students those “Oh yeah, NOW I remember how to FOIL” moments.  We start with Order of Operations/PEMDAS and algebra, and go from there to fractions, geometry, exponents, divisibility and other flashback-inducing topics.  If you’re confident in your math skills, you may not need this book at all.  But otherwise, you may like it a great deal.  You know who you are . . .

All Manhattan GMAT Course Students will receive this book for free as part of their course materials.  If you’ve already started your course and want this book, contact studentservices@manhattanprep.com/gmat/ and they’ll hook you up (you may have to pay shipping depending on your location, but the book will be free).

Kudos to our curriculum wizards for their latest contribution to the best in GMAT Prep!

About 2 years ago, one of our L.A. Instructors, Mike Kim, suggested that we provide a math curriculum  for students who want a refresher on fundamental math topics (e.g.  fractions, algebra, etc.).  We thought it was a fantastic idea.  Being an extraordinarily productive guy, Mike went on to author the Foundations of GMAT Math Workshops I and II which take place online (it turns out there are too many fundamental math topics to teach in one sitting).

Now, the Foundations of Math Workshops will be available for free to any Manhattan GMAT course student.  If you are a course student, you can simply go to the website and add the Foundations workshops to your account.  You will immediately receive access to dozens of practice problems in your student center as well as class recordings, and you can attend the next scheduled Foundations workshops live.

For non-students, the Foundations of Math Workshops will each be available for only $95.  Additionally, if you end up signing up for a course after taking the Workshops, we’ll credit you whatever you spent on the workshops, so they’ll essentially wind up being free for you too.

Remember, these workshops review foundational math topics such as algebra, basic geometry, fractions, etc.  They’re very useful if you need a refresher because you haven’t seen the math in a long while, but if you’re comfortable with the math already you can feel free to go straight to the Official Guides, Strategy Guides, etc.

P.S.  The Foundations of GMAT Math Book is due out this Fall, as Mike’s original idea is taking multiple forms to reach as many people as possible.

Application season is starting to heat up again! For those of you just getting started, here’s an overview of “what’s what” with the GMAT.

What Is The GMAT?

The Graduate Management Admissions Test is a standardized test that many English-speaking business schools require applicants to take. The test is called a CAT, or Computer Adaptive Test, both because it is administered on a computer and because the test actually changes based upon how we answer the questions. The computer chooses what test questions to give us based upon our performance up until that point in the test. In a sense, we all take a different test, because the specific mix of questions any one person sees is based on that person’s performance during the test.

To register for the test or learn more information straight from the testwriters, go to www.mba.com.

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