## Ultimate Guide to GMAT Geometry Part V: GMAT Triangles 1

Chapter 11: GMAT Triangles All the basic stuff for triangles is probably going to be fairly obvious. First, of course, a triangle is a three-sided object. Second is that all of the angles of a triangle add to 180 degrees.  Third is that the angle opposite any side of the triangle is proportional to that … Read More

## The Ultimate Guide to GMAT Geometry III: Trapezoids, Rectangles, Squares

The Ultimate Guide to GMAT Geometry, Part III: Trapezoids, Rectangles, and Squares Chapter 8: Trapezoids (Trapeziums (Trapeziae?)) in GMAT Geometry If you were paying attention to the footnotes, then you’d recognize this as the extra credit answer.  In essence, a trapezoid is sort of a dodgy parallelogram, where only two of the opposite sides got … Read More

## GMAT Grammar Tips for Sentence Correction: the Ultimate Guide

GMAT Grammar Tips for Sentence Correction: the Ultimate Guide GMAT Grammar is an odd concept. I mean, how could it possibly be different from normal English grammar?  HAHAHAHAHAHAHA! The problem, then, becomes one of how one defines “normal English grammar.” The problem is that there’s not really one particular type or book of grammar that … Read More

## The Ultimate Guide to GMAT Geometry: Introduction and Lines (Part I)

The Ultimate Guide to GMAT Geometry (Part I) Geometry has a really weird relationship with the GMAT. It’s the one place where quite a bit of memorization is necessary, which causes a big problem: imperfect memorization will lead to wrong results. For that reason, I think memorization of rote formulae is mostly a waste of … Read More

## GMAT Probability Question SOLVED: An Exception to the “At Least” Rule?

A GMAT Probability Question Fully Solved: An Exception to the “At Least” Rule? It’s difficult to say that there’s really an exception–after all, you can do any Probability question multiple ways, forward, backward, or even sideways. The question is just which of these ways will be most effective in the given situation. What is the … Read More

## GMAT Probability: Prob. per Distribution and Equal Likelihoods

GMAT Probability per Distribution and Equal Likelihoods A bag contains red and blue balls. Exactly half of the balls are red, and the other half are blue. If four balls are removed from the bag, then replaced, what is the Probability that exactly three blue balls will be among those selected? First, let’s figure out … Read More

## GMAT Probability: a Step-by-Step Guide Through a Complex Problem

A GMAT Probability Problem with Too Many Moving Parts — How to Deal With a Complex Problem by Isolating its Constituent Parts This problem is so complicated that it’s unlikely to be seen as an actual GMAT Probability question–that is, something you would see in such a complex form on the exam itself–but bear with … Read More

## Collapsing Probabilities in GMAT Probability: Part Deux

Collapsing Probabilities: Part Deux — for Part Un, Click Here This one I’m only doing with the “Collapsing Probabilities” technique. You’re welcome to do it by making your choice first, then multiplying by the number of potential choices. It’s just that I won’t. You can e-mail me if you need your hand held. Here’s the … Read More

## Collapsing Probabilities in GMAT Probability

Collapsing Probabilities in GMAT Probability Unsurprisingly, there’s more than one way to look at this phenomenon. Let’s take a look at this straightforward case… Bag 1 contains forty marbles numbered consecutively from 11 to 50. Bag 2 contains fifty marbles numbered consecutively from 41 to 90. If one marble is selected from each bag, what … Read More

## GMAT Probability: Number of Distributions x Probability per Distribution

GMAT Probability and Number of Distributions x Probability per Distribution The Independent Probability Case for GMAT Probability Now, let’s go back to the example from the previous page, which we can rephrase as this:If a coin is flipped five times, what is the Probability that it will land on Heads only once?That gives us a … Read More