Translating word problems into algebra is a staple skill of GMAT test-takers, one that underlies countless problems in practice and on Test Day. But some challenging translations occur as part of probability and combinatorics problems. That’s because a pair of the most basic words in the English language, “And” and “Or,” suddenly become overburdened with mathematical significance.
“And” is the simpler of the two. When “And” represents independent choices—cases in which one option or arrangement has no impact on the other choice—just multiply the outcomes. For instance:
“The number of ways to purchase three board games and two video games” is an independent choice. The board games we pick have no impact on the video games we pick. So, to translate: [The number of ways to purchase three board games] × [the number of ways to select two video games]. Of course, we’d need the combination … Read full post
Mixture problems show up frequently on the quantitative section of the GMAT and fall into two basic categories. As each type of mixture question will be approached in fairly different ways, it is important that you know the difference between them.
First, there are mixture problems that ask you to alter the proportions of a single mixture. These questions could, for example, tell you that you have a 200 liter mixture that is 90% water and 10% bleach and ask how much water you would need to add to make it 5% bleach. The key in this type of question is the part of the mixture that is constant – in this case the bleach. While we are adding water, the amount of bleach stays the same. First, determine how much bleach we have. 10% of 200 is 20 liters. Next, we know we want those 20 liters to equal … Read full post
Mastering ratio questions on the GMAT requires systematic organization of the individual pieces and a solid understanding of how ratios are typically presented and tested on test day. One of the most common presentations of ratios on test day is a question that presents a part:part or part:whole relationship and asks for the actual number of a part, the whole, or a difference between the parts.
The first thing to note about ratios is that they represent relationships between items. On the GMAT Quantitative Section, the ratio is usually in the simplest form; I call this multiple level 1 because it represents the smallest potential positive quantity for each aspect of the ratio. For instance, if a question tells you that the ratio of apples to oranges is 2:3, you know immediately that the minimum number of apples possible is 2 while the minimum number of oranges is … Read full post
In my years of teaching, I’ve seen all kinds of clever solutions to GMAT math problems. I’ve also seen all kinds of errors. Some are utterly bizarre—and fortunately, seldom repeated, because the students who make those mistakes usually face-palm when they review their tests and go on to learn from their missteps. But some errors are so common and so often repeated that they earned their own names. One such example is the “fencepost error.”
Here’s a simple example: Say we are setting up a straight fence that’s exactly 100 ft long, with posts every 10 feet. How many posts do we need?
Did you say 10? Tempting, but that’s the right answer to the wrong question. There are 10 sections of fence, each 10 feet long. But there are actually 11 fenceposts, because you start with a fencepost, at 0 feet!
This error can trap … Read full post
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
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
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