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 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
Ultimate Guide to GMAT Geometry, Part II: Polygons, Perimeter and Area, Parallelograms Chapter 5: Polygons in GMAT Geometry Remember how I’ve mentioned like ten times about how a straight line creates a 180-degree angle? If not, well, it does. Now, think about this. What happens if we were to magically fracture that line? If we … Read More
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 Combinatorics Questions: Permutations vs. Combinations (plus Shorthand!) As noted above, this is simply a clipped factorial. Let’s take the case from above and modify it slightly. Three paintings, from a group of seven total paintings, are chosen to be hung on a wall. In how many ways can these three paintings be arranged? So: … Read More
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 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 Combinatorics: an Introduction Ever wonder why GMAT Permutations and Combinations seem to hard to learn? There’s no good reason–that’s just because they tend to be explained in a terrible way. It’s time for us to fix that! At the risk of blowing all the secrets too early, let’s do this at the beginning. If … Read More
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: 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