# Blog (Free Videos!)

## The domain of the function f(x) = \frac(sqrt(x-1))(x+1) GMAT Quant Question

The domain of the function f(x) = \frac(x-1)(x+1) is the set of all real numbers that are:  Oof–that’s a huge chunk of code, which I had to put on here just so you could find it! Sorry–let’s try that one again in a way that actually makes some sense… The domain of the function f(x) … Read More

## A certain identification code consists of 6 digits: GMAT Counting Problem

A certain identification code consists of 6 digits, each of which is chosen from 1, 2, …, 9. …The same digit can appear more than once. If the sum of the 1st and 3rd digits is the 5th digit, and the sum of the 2nd and 4th digits is the 6th digit, how many identification … Read More

## If 3^x – 3^(x-3) = 2106, what is the value of x? GMAT Factoring Question

If 3^x – 3^(x-3) = 2106, what is the value of x? This is a fairly tricky factoring question, but it goes back to one of the general factoring principles: always factor out the common term. Here’s where we start:  In our case, the common term is 3^x. That leaves us with… …on the left … Read More

## At a picnic there were 3 times as many adults GMAT

At a picnic there were 3 times as many adults GMAT SOLUTION This question is more complicated than it needs to be, but it is simply an issue of careful substitution. Look at it this way: we need the number of men in terms of x, which would imply that we get all of the … Read More

## If the recommended weight w, in pounds, for a male… GMAT

If the recommended weight w, in pounds, for a male… GMAT Data Sufficiency Question Here’s the question for you: If the recommended weight w, in pounds, for a male is given in terms of his height h, in inches, by the formula w = 4.5h − 154, how much greater is Eric’s recommended weight than … Read More

## Last year the price per share of Company A’s stock — SOLUTION GMAT

Last year the price per share of Company A’s stock… is a pretty frustrating little question. That’s because this GMAT question is extra-sneaky in its wording. Make sure that you’re being careful about what is what. I personally recommend writing down all of your values relative to the original value, perhaps in a table. Last … Read More

## SIMPLE solution: For a certain race, 3 teams were allowed… GMAT

Here’s a simple solution to the classic “For a certain race, 3 teams were allowed to enter 3 members each” GMAT question. First, let’s look at the question text so you know what we’re talking about: For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n … Read More

## GMAT Combinatorics: The Ultimate Guide to GMAT Factorials (also useful for Probability!)

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

## 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