Patterns in Divisibility Problems

Today we’re going to tackle a couple of tough divisibility problems from GMATPrep. The two problems I’ve chosen share some interesting characteristics. Here’s your first one; set your timer for 2 minutes and go!

If n is a multiple of 5 and n = p ² q , where p and q are prime numbers, which of the following must be a multiple of 25?”
(A)  p ²

(B)  q ²

(C) p q

(D) p²q²

(E) p³q^“

Hmm. So p and q are primes. They could be 2, 3, 5, 7 or so on. It doesn’t say that p and q are different prime numbers, so they could also be the same number. And I’m going to use some theory here: if p²q equals n and n is a multiple of 5, then that 5 must be contained in either p or q. And since those two numbers are primes, either p or q is 5. (Or maybe both are!)

Read more

In this article, we’re going to tackle a challenging GMATPrep problem solving question from the topic of Percents.  (The GMATPrep software can be downloaded for free at MBA.com)

Let’s start with the problem.

Set your timer for 2 minutes… and… GO!

*Before being simplified, the instructions for computing income tax in country R were to add 2 percent of one’s annual income to the average (arithmetic mean) of 100 units of country R’s currency and 1 percent of one’s annual income. Which of the following represents the simplified formula for computing the income tax, in country R’s currency, for a person in that country whose annual income is I?

Read more

This week, we’re going to tackle a challenging GMATPrep problem solving question from the topic of Rates & Work.

Let’s start with the problem. Set your timer for 2 minutes. and GO!

*Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 15

Given info about two different gears, P and Q, we have to figure out something about how quickly they move relative to each other. In particular, we’re supposed to figure out when this is true: (# of Gear Q revolutions) = (# of Gear P revolutions) + 6.

Read more

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.

GMAT Strategies for the Math-Challenged

by Chris Ryan, Director of Instructor and Product Development, ManhattanGMAT

The thought of algebra gives you hives. You’d rather discuss any topic but prime numbers. And you bitterly wonder why geometry is tested on the GMAT “ the Graduate Management Admissions Test, after all. It’s not like you want to be an architect.

Well, the GMAT is what it is: a hoop to jump through for business school. Whether knowing rate times time equals distance translates to academic and financial victory (or not!) is a moot question. You want to get an MBA. And crouching between you and that degree is the giant spider of middle- and high-school math.

You’re not alone. Many other b-school candidates share your apprehension. But in order to beat the GMAT, you’re going to have to revisit some math skills that you likely haven’t had to use in 5 “ 10 years.

What are math skills? There are three types, all tied together:

Read more