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
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 At the risk of blowing all the secrets too early, let’s do this at the beginning. If you can answer three Core Questions, you’ll be able to answer any Combinatorics question that the GMAT decides to throw at you. Here they are: How Many Spaces? How Many Choices? Does Order Matter? … 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 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 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