GMAT Combinatorics: The Ultimate Guide to GMAT Factorials — the Three-Question Method If we don’t get the concept of Factorials straight, the rest of this–Permutations and Combinations, quite a lot of advanced GMAT fatoring, etc.–is never going to work. How to Think About GMAT Factorials in a Broad Sense The idea of a Factorial is … Read More
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, 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 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