GMAT Tip of the Week: Seeing Data Sufficiency Through the Proper Prism

This week, the 24-hour news cycle is focusing on the NSA’s PRISM surveillance program, which taps the data collection of cell phone carriers, search engines, and internet service providers to amass huge volumes of information. And regardless of your politics or opinions, you have to recognize one thing about the PRISM program – NSA is using any and all available information to do its job. Which is exactly the prism through which you should look at Data Sufficiency problems.

Data Sufficiency is in large part about leveraging assets – taking account of all the information you’re provided and finding a way to use it to solve a problem. When students miss Data Sufficiency problems, it’s usually because of one of two reasons:

1) They thought they had more information than they really did (often this comes down to an assumption – you assume that something is positive or an integer when it doesn’t have to be)

2) They didn’t realize they had as much information as they did. This is where you want to employ your own personal PRISM program – use all the information that you can get your hands on! Here’s an example:

Line M is tangent to a circle, which is centered on point (3, 4). Does Line M run through point (6, 6)?

(1) Line M runs through point (-8, 6)

(2) Line M is tangent to the circle at point (3, 6)

Now, most people can see quickly that both statements together are sufficient to answer the question. If you have two points on that line, you can calculate the slope (Change in Y / Change in X would lead you to a slope of 0 here), and then apply that slope to the two points you’re given to plot out the line. A majority of students answer C to this problem…and even if they don’t know the geometric principle that makes the answer something else, they’re guilty of making a management mistake that NSA would never make:

They leave valuable information untapped.

Let’s go back to the question stem and look at the information that you don’t use if you pick C.

Line M is tangent to a circle, which is centered on point (3, 4). Does Line M run through point (6, 6)?

If you pick C because “the statements together give me two points on the line which lets me plot the whole line,” you’re leaving a big chunk of information on the table. You never use the circle at all!! This should be a clue to you – it’s extremely rare that entire portions of a Data Sufficiency question don’t matter. You may find that they’re not quite sufficient, but if there are pieces of information that you haven’t used you should *always* consider why they’re there. That circle information, if you picked C, is a golden ticket invitation to spend a little time considering why it’s important that the line is tangent to that circle.

As it turns out, the correct answer is B – the rule goes that, at the point of tangency, a line is perpendicular to the diameter of the circle. So you can get the slope just by knowing statement 2. But even if you’ve forgotten (or never considered) that rule, you should be thinking about why that tangent/circle information is important, and you can even prove to yourself that it’s B by just drawing a circle and trying to draw two lines that are tangent at the same point. You can’t. So statement 2 alone is sufficient, but even more important is this:

Much like NSA, you should seek to find and utilize every piece of information you can on Data Sufficiency problems. If the problem gives you a number, relationship, or definition that you haven’t used or considered, you’re probably answering incorrectly. So view Data Sufficiency through this prism – all information is important.