Imagine you are driving from Chicago to Los Angeles, and you want to know what your average speed needs to be to reach Los Angeles in a certain number of hours. You would probably start by determining the speed you will be able travel during certain parts of your journey. Since most of the distance will be covered by highway, you might plan to travel most of the distance at 70 miles per hour. However, you will also want to plan for some traffic when you are still in or near Chicago and when you get close to Los Angeles. During these parts of your journey let’s say you can plan to travel at 30 miles per hour.
When calculating the average speed at which you will be traveling, you need to avoid the trap of just averaging these speeds together and planning on an average speed of 50 miles … Read full post
The trickiest question type in the quantitative section of the GMAT for most students is yes/no data sufficiency questions. When approaching these problems, it is imperative that you keep in mind the purpose of data sufficiency.
Let’s start with a review of data sufficiency. On these questions, your goal is not to find the answer. Rather, it is to determine if you have enough information to find the answer, regardless of what the answer is. On value questions, this is fairly straightforward. If you are asked for the value of x and you know it is 4, that’s sufficient, but if it could be 4 or 6, that’s not sufficient. In the former case we could narrow down the possibilities to one answer. In the latter, we could not.
Now let’s see how this same concept applies to yes/no questions. If a question asks us if x is positive and … Read full post
Ever since I started teaching GMAT classes, I have taken note of any references to standardized tests I come across in television shows and movies. In the six years of doing so, I have found that these references almost always follow the same pattern. One of the characters needs to take a standardized test that they find difficult or boring. In order to illustrate this to the other characters, they will read an example of one of the questions on the exam. Invariably, the question they read involves two trains leaving two different stations at two different times and traveling towards each other.
Because of this, rate problems that feature two trains (or cars or people or anything else) have a bit of a bum rap. These questions are seen, unjustly, as difficult, time consuming and complicated. However, by learning only a few basic rules, you can handle these … Read full post
Everyone studying for the GMAT wants to identify the skills that will lead directly to the greatest point increases. While this can be difficult to do, given the adaptive nature of the exam, some skills definitely do come into play more often than others.
One of the most important skills to master for the GMAT is prime factorization. Finding prime factors can be useful on many different types of questions. On test day, if you are stuck on a question and unsure of how to solve, remember the big number rule. The big number rule is simply this: if you see a big number, one that is so large it is unreasonable to work with, find its prime factors. Once you have those factors, you should be able to simplify.
Every positive integer that is not prime, with the exception of 1, can be broken down into a … Read full post
Not surprisingly, most GMAT test takers have a background in the business world. As such, many readers have worked on a committee formed from a larger group of employees. Every time a committee is formed in this fashion, you are, in fact, doing a GMAT problem. More specifically, you are attempting one of the most dreaded question types on the GMAT quantitative section – combinations.
While these questions can be tough, by thinking about the real life experience of forming a committee, you can more easily understand exactly what a combinations question is asking you to do. Let’s say that your business has ten employees and needs to create a committee of four people. If you want to determine how many different possible committees you could create, you would use the combinations formula, n!/[k!(n - k)!], where n is the number of people with which you start (in this case … Read full post
One of the big GMAT skills that is often overlooked by students is translation. Any time you decide approach a word problem using algebra, you will need to translate the English in the question stem into an algebraic equation. While this seems as if it would usually be fairly straightforward, the GMAT will often find ways to make it more difficult. A translation error will often lead to a trap answer, so it is essential that you learn how to translate difficult statements before test day.
To understand why translation can be more difficult than it seems, think about translating a foreign language. If you only need to translate one word, you can usually just find the equivalent word in English. Similarly, if a GMAT problem uses the phrase “more than” you know that it must translate to addition.
However, when you try to translate an entire sentence from … Read full post
Most students learn that absolute value is the positive version of a number. Thus, the absolute value of 7 is 7 and the absolute value of -7 is also 7. While these absolute values are correct, many GMAT problems will be more straightforward if you learn the true definition of absolute value, which is the distance a number is from zero on a number line. Thus, the absolute values of 7 and -7 are 7 because both numbers are 7 away from zero on a number line.
To understand how absolute value works, imagine you live in a house right in the middle of a block. The street has 5 houses to the left of your house and 5 houses to the right of your house. Whether you walk two houses to the left or two houses to the right you will be 2 houses away from your home. Now, … Read full post
While preparing for the GMAT, you have probably heard that if you have multiple variables for which to solve, you need as many equations as you have variables to do so. However, as is the case with many GMAT topics, just knowing the rule will not be enough. You will also need to know three exceptions to this rule that regularly appear.
First, if you have two variables, but only one equation, you can solve for one of those variables if the other variable cancels out. Note that it is still not possible to solve for the variable that cancels – in fact, that variable would have an infinite number of solutions. Second, if you are asked to solve for an expression, such as x + y, rather than an individual variable, you may be able to do so with fewer equations than variables. In these cases make sure … Read full post
Think back to your childhood. Do you remember when you would scheme to throw a snowball, grab an extra cookie or give your broccoli to the dog? And do you also remember how, unlike in the movies, your parents would often seem to know what you were about to try to do and thwart your attempt? Sometimes the GMAT is like your parents – it knows what are are thinking even before you do.
One classic example of this is prime numbers. It is not a secret that knowing that a prime number is a positive integer with exactly two factors, itself and one, is essential to the GMAT. However, the test makers also know that some test takers, in an effort to save time, will not always make sure the number being tested is truly prime.
Two numbers, in particular, will show up regularly on the GMAT for … Read full post
The only thing you need to know about sequences is that a sequence is an ordered series of numbers. Really, that’s it. Many sequences are defined by specific mathematical formulae or properties, and most sequences of note continue on infinitely, but neither of those are necessary. All you need to have a sequence is an ordered list.
Of course, that raises the question of why they are tested at all. One might assume that the simplicity of sequences means that they should be trivial and a waste of the testmaker’s time. Conversely, it could seem that since simple definition covers an enormous range of possibilities, it would be impossible to expect students to understand them all. But in fact, sequences test a very specific skill: your ability to decode instructions.