Think Inside the Box on Tricky GMAT Questions

When dealing with questions that ask us to compartmentalize information, there are two major sorting methods that we can use on the GMAT. The first, and perhaps more familiar concept, is the Venn diagram. This categorization is very useful for situations where information overlaps, as it allows a visual representation of multiple categories at once. However, if the information provided has no possible overlap, such as indicating whether something is made of gold or silver, or if they’re male or female (Bruce Jenner notwithstanding), the preferred method of organization is the matrix box.

The advantage of the matrix box is that it highlights the innate relationships that must be true, but that are not always easy to keep track of. For instance, if a box contains 100 paperclips, some of which are metallic and some of which are plastic, then if we find 40 paperclips made of metal, there must necessarily be 60 that are made of plastic. The binary nature of the information guarantees that all the elements will fall into one of the predetermined categories, so knowing about one gives you information about the other.

The matrix box allows you to catalogue information before it becomes overwhelming. Anyone who’s studied the GMAT for any length of time (five minutes is usually enough) knows that the exam is designed to be tricky. As such, questions always give you enough information to solve the problem, but rarely give you the information in a convenient manner. Setting up a proper matrix box essentially sets you up to solve the problem automatically, as long as you know what to do with the data provided.

Let’s look at an example and what clues us into the fact that we should use a matrix box.

Of 200 students taking the GMAT, all of them have college degrees, 120 have been out of college for at least 3 years, 70 have business degrees, and 60 have been out of college for less than 3 years and do not have business degrees. How many of them have been out of college for at least 3 years and have business degrees.

A) 40
B) 50
C) 60
D) 70
E) 80

The principle determinant on whether we should use Venn diagrams or matrix boxes is whether the data has any overlap. In this example, it’s very hard to believe that a student could both have a business degree and not have a business degree, so it looks like the information can’t overlap and a matrix box approach should be used. Before we set up the matrix box, it’s important to know that the axes are arbitrary and you could put the data on either axis and end up with essentially the same box. We can thus proceed with whichever method we prefer. The box may look like what we have below:

 Business Degree No Business Degree Total At least 3 years Less than 3 years Total

Without filling out any information, it’s important to note that the “Total” column and row will be the most important parts. They allow us to determine missing information using simple subtraction. If we have the total figures, as little as one piece of information in the inside squares would be enough to solve every missing square (like the world’s simplest Sudoku). Let’s populate the total numbers provided in the question:

 Business Degree No Business Degree Total At least 3 years 120 Less than 3 years Total 70 200

With these three pieces of information, we can fill out the remaining “Total” squares by simply subtracting the given totals.

 Business Degree No Business Degree Total At least 3 years 120 Less than 3 years 80 Total 70 130 200

Now all we would need to reach the correct answer is one piece of information: any of the remaining four squares. Luckily the question stem will always provide at least one of these, as the problem is unsolvable otherwise. Problems may be tricky and convoluted on the GMAT, but they will never be impossible. Looking back at the question, there are 60 students who have been out of college for less than 3 years and do not have business degrees. Plugging in this value we get:

 Business Degree No Business Degree Total At least 3 years 120 Less than 3 years 60 80 Total 70 130 200

Using a little bit of basic math we can turn this into:

 Business Degree No Business Degree Total At least 3 years 70 120 Less than 3 years 20 60 80 Total 70 130 200

And finally the completed:

 Business Degree No Business Degree Total At least 3 years 50 70 120 Less than 3 years 20 60 80 Total 70 130 200

The question was asking for how many students have been out of college for at least 3 years and have business degrees, but using this method we could solve any potential question (Other than “What is the meaning of life”?). Since the number of students with business degrees who have been out of college three years or more is 50, the correct answer will be answer choice B.

In matrix box problems, setting up the question is more than half the battle. Correctly setting up the parameters will ensure that the rest of the problem gets solved almost automatically, and all you have to do is avoid silly arithmetic mistakes or getting ahead of yourself too quickly. Remember that if the information doesn’t overlap, it will likely make for a good matrix box problem. On these types of questions, don’t be afraid to think inside the box.

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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.