This is the latest in a series of “How To Analyze” articles that began with the general “How To Analyze A Practice Problem” article (click on the link to read the original article). This week, we’re going to analyze a specific Data Sufficiency question. The GMATPrep® problem we’re using this week is one that we’ve already discussed how to solve in a previous article; click here to read that article and try the problem first.

Here’s the problem again; if you didn’t read the first article and try the problem already, then try this problem now (2 minutes):

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Data Sufficiency questions, which will comprise approximately half of your quantitative section, are a format unique to the GMAT.  As you become familiar with this unique type of question, you’ll find it challenging, frustrating, confusing, infuriating, but hopefully in the end satisfying as you master the many challenges that these questions present.

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Over these past few months of writing articles for Beat The GMAT, you’ve probably noticed that I like to associate important GMAT concepts with common situations.  Well, with regards to pacing on data sufficiency questions, the best way to approach them is to know the material and content through and through.  However, while on the actual GMAT and as you practice with CAT tests, keep in mind the words of Kenny Rogers, The Gambler:

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Though they’ll never admit to using “dirty tricks” to keep your score down, the authors of the GMAT can be shrewd in the way that they word questions to prey on the inefficiencies of human nature.  Previously in this space, we talked about the “Simon Says” nature of Data Sufficiency questions, in which the authors know that you will often make assumptions about variables – that they’re integers, or positive – without being explicitly told so.   Data Sufficiency questions contain another, perhaps even more devilish, example of this need for perfect precision, embedded deeply in the way that these questions are written.  Consider this fragment of a GMAT question:

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In any GMAT course, one of the very first things taught about the Data Sufficiency section is that the two statements are true and do not contradict one another.  It’s a point that’s easy to gloss over and completely overlook during the hustle and bustle of your test prep.

But this supposedly self-evident point gets many students into trouble when dealing with YES/NO questions, because they mistakenly try to prove or disprove the statements rather than the prompt.

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Inequalities on the GMAT should be approached in the same way as regular equations.  We can manipulate inequalities the same way that we can manipulate equations.  And just like equations on the GMAT, you first must simplify the equation in order to answer the question presented.

The title of this post is: Flipping the sign to inequalities.  The only difference to simplifying inequalities compared to normal equations is the times when we have to flip the sign.  There are two consistent times when we must always flip the sign:

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One of the hallmark points of confusion on the GMAT is the dreaded Yes/No Data Sufficiency question.  In a Value question, such as “What is the value of x?” the question of sufficiency is a familiar one: if you can solve for x, you have sufficiency.  But in a Yes/No question, especially when variables are involved, finding a solid answer can be a much cloudier process.

The best way to clear this fog is with a concrete example.  Let’s look at this Data Sufficiency question, along with its first statement:

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While recuperating from Arthroscopic knee surgery, I decided to write a piece on Data Sufficiency questions. Then I visited the website and saw that Ben Leff had done something on that just a few days ago.* I decided to alter the focus a bit and talk more generally about the nature of the point he was making and expand to talk about the distinctions between Data Sufficiency (DS) and Multiple Choice (MC) questions, with most of the focus on the DS questions.

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To succeed on the GMAT, there is a general rule of Algebra that you should know: to solve for all variables in a system of equations, you need as many distinct linear equations as variables.  So if you get 2 variables, you need two equations; three variables, three equations, and so on.  With that in mind, think about this Data Sufficiency question:

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Sets, matrices and Venn Diagram – they are all the same. It’s really a matter of preference; some students like to use Venn diagrams, and others make matrices. Personally, I prefer a matrix format, but there is no “better” way.

On your GMAT, you will encounter 1-3 questions that contain overlapping groups with specific characteristics. You will almost never see more than two characteristics (since you can’t draw 3D on your scratch paper). For illustration, let’s take a look at the following Data Sufficiency example:

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GMAT data sufficiency questions test your ability to analyze a quantitative problem and recognize which information is necessary to figure out the solution.  What a data sufficiency question does NOT test you on is your ability to calculate and number-crunch.  A simpler way of addressing this might be to ask yourself a question as you work through a data sufficiency problem: “Is this enough?”  Keep this in mind as you evaluate (and on test day, avoid) two specific common errors that test-takers make while taking the GMAT:

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Welcome back to this week’s Challenge Problem! As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 750+ level question, so do not worry if you cannot solve the problem in a 2 minute time frame. If you are up for the challenge, however, set your timer for 2 minutes and go!

Question

How many factors does x have, if x is a positive integer?

(1) x = , where p is a prime number.
(2) = n + n, where n is a positive integer.

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Even though Data Sufficiency questions test the same math content as Problem Solving questions, most GMAT students find that they can’t use the same strategies on both question types. One of the common errors students make in their approach to Data Sufficiency questions is jumping to the two statements without analyzing the question first and figuring out what information is missing. You wouldn’t start hunting for a jigsaw puzzle piece without first looking at the shape of the hole you’re trying to fill, would you? Most Data Sufficiency questions can be simplified with the Pieces of the Puzzle approach, and some would be nearly impossible to solve without it.

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The best way to think of inequalities is as equations with slightly less specific information. Instead of providing an exact location, they provide a range of locations, all of which are satisfactory. With “=” instead of“<”, we can solve for the exact number. In an inequality, that number will be used as an endpoint.

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FACT: So many students get caught up in the idea that one must solve a problem to get the correct answer.  Well that is not the case for many questions on the GMAT.  Sometimes it actually slows you down to fully work out a problem.

Let’s go to the board to check out my point with DATA SUFFICIENCY.

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