Welcome back. As I mentioned before, each week we are going to feature a problem breakdown here on the blog. Last week we dove into probability. We’ll revisit that topic in the weeks to come. This week we are going to start moving into combinations and permutations. These can be some of the toughest problems on the test. However, since I can feel your pain on this topic, we are going to start slow. Instead of diving in, we’ll start by getting our big toe wet first, or maybe our little toe. For those who are at an advanced level on this topic, check back in a few weeks. We’ll be up to speed and breaking down some tough GMAT problems. For now, let’s use a problem to get a feel for how we handle these things.
Kim has four trophies, which she wishes to display in a … Read full post
One of the most important techniques to solving algebra problems, on the GMAT quantitative section or otherwise, is factoring. This technique, taking advantage of the “distributive property” of multiplication, lets you pull a common factor outside of a sum of terms, or to distribute it across those terms. In other words:
2x + 2y + 2z ↔ 2(x + y + z)
But did you know that the distributive property applies to grammar?
Well, not literally. But for quant experts confused by Parallelism in Sentence Correction, it can be helpful to imagine it as a distribution problem. When a sentence has a list of items, auxiliary verbs such as the “had” in “had been,” and prepositions such as “by” and “in,” can be “distributed” or “factored” across the list.
…by name, by date, or by subject ↔ …by (name, date, or subject)
Of … Read full post
The key to many GMAT coordinate geometry questions is to remember that coordinate geometry is just another way of expressing the possible solutions to a two variable equation. Each point on the line in a coordinate plane corresponds to a solution for the equation of that line.
The base equation for a line is y = mx + b, where b is the y intercept, or the point at which the line crosses the y-axis, and m is the slope, or the steepness of the line. More specifically, the slope of a line is the change in the y coordinates divided by the change in the x coordinates between any two points on the line.
While understanding the basic format for an equation of a line can be very useful on the GMAT quantitative section, you will encounter GMAT problems in which it is faster and easier to think … Read full post
Piecing together the time to study for the GMAT can be challenging. In today’s blog, I’m going to talk about three students (whose names I’m changing to protect their identities). Each had a major obstacle to studying, and each overcame it in a different way. I hope these students’ examples can help some of you reach your GMAT and MBA goals.
Case Study 1: Vincent, the Entrepreneur
The Challenge: Vincent was a busy man when I was tutoring him. His schedule was very flexible—his main source of income was a business that he started and ran himself—but he was distracted at all hours by emails and phone calls related to his work.
The Solution: Vincent needed a time and place where he could study in peace.
Because of his flexible work schedule, it was easier for Vincent to find time than it is for some other students. He … 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
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
Recently, I took a trip to the Metropolitan Museum of Art in New York. As I perused the galleries, I noticed that not all of the painting were equally easy to understand. In the works by Da Vinci, that were made to look realistic, I could clearly tell what was depicted. The Monet’s were a bit tougher, but with the explanation provided by the museum, I could clearly see the subject. At the Picasso’s the subject was a bit harder to find, even with the explanations. Finally, I came across the Pollock’s, which required me to depend entirely on the explanation to understand what was happening on the canvas.
In art, I realized, just as is the case on the GMAT, the more abstract the presentation of a concept is, the harder it is to understand. Luckily, the curator at the museum had written blurbs for each painting – blurbs … 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
Students regularly question me about the applicability of GMAT questions to the business world. While the critical thinking skills required by the GMAT certainly have real world applications, the content of the questions is often only tangentially related to scenarios that students will encounter in their careers.
However, one type of question is a clear exception to this rule: problems about pay rates. Take a look at the question below. The specific numbers will never show up again, but the principle could be important to many actual businesses.
On one hand, if you are deciding which of these jobs to take, knowing the number of hours at which you will be making the same amount of money will be essential to deciding which job to choose. If you are going to work more than that number of hours, the lower hourly rate with overtime pay is the better option, but … Read full post