GMAT Data Sufficiency

To understand GMAT Data Sufficiency, one should try to think about how these questions are written.  While popular novice strategy says to “only look at each statement individually, and only consider them together once you’ve determined that they’re insufficient independently,” those who score well into the 700s tend to think far beyond the 1-2-TEN, AD/BCE structures and really play the game embedded within Data Sufficiency. 

Contrary to what you might believe from basic DS strategy, Data Sufficiency statements are not written independently in a vacuum, and so on difficult questions you probably cannot solve them by seeing them this way either.  The author of each question carefully crafts a question and two statements together, using the way that students tend to think to set traps and build in clever rewards.

To excel with Data Sufficiency, be aware of those traps but focus your energy on the rewards.  Data Sufficiency questions really are a lot like a game, in which knowing the rules and playing strategically can be fun and successful.  What may be a trap to someone can be a great opportunity for you to claim a reward.  Take a look at a couple of questions that demonstrate what we mean:

As rational human beings, we’re predisposed to wanting to see more information before making a decision. We go to multiple doctors for second opinions, consult multiple review websites before making purchases, and triple-check our work before selecting answers.  So the GMAT authors know that you’ll be tempted by the answer choice C, which allows you to use both statements together.  But the second portion of answer choice C’s description is arguably more important:  both statements together are sufficient but NEITHER ALONE is sufficient.  You only “get to” use both statements if you “have to” use them both.  You’re essentially paying for each statement; if you could have done the project cheaper, you’ll be punished for using too many resources.  Consider the question:

This should be C, right?  The first equation factors into multiple solutions:

The second qualifies that only the odd value, 9, counts, so both statements together are sufficient.  But wait – do we really know that neither alone is sufficient?  Could we have a negative number of students?  That’s impossible; -2 students could never attend a movie together.  So statement 1 alone is sufficient – C was the trap here, making you think that you needed both statements.  But knowing that an “easy C” is often a trap, you should be aware of that.  And as a strategic point, being aware of that trap can help you on questions with tougher math involved.

The Game:  If C seems too good to be true, it probably is; reconsider the statements, particularly if one clearly gives more information than the other.

Consider this question (note: I took this from the Data Sufficiency forum here and I love this question – but if I’m borrowing another instructor’s question please let me know and I’ll cite you!!)

Again, C looks pretty good!  If we are given two points on any line, we can determine the slope of the line.  So both statements together are clearly sufficient.  BUT – we’re smarter than that.  We also need to know that neither alone is sufficient in order to pick C, and it’s unlikely that the GMAT would do that here.  Why?  Play the game – in just using those two points:

1) The question is a little too easy…

2) In arriving at C you’re leaving information on the table – we haven’t even used the circle.  As a Data Sufficiency game theorist, you have to suspect that something is up here – why would the author have written about the circle/tangency if the correct answer is both kind-of-easy and doesn’t use that at all?

So those are your clues.  And even if you don’t know the rule upon which the correct answer is based (at the point of tangency, the diameter and tangent are perpendicular) you should be leaning toward choice A. Choice A has more information (it’s not just “a point on the line” but rather “the point of tangency,” and it’s the statement that links the line to the circle given in the stimulus).  And if you do your own crude test – draw a circle and try to draw more than one line tangent to it at the same point..you can’t! – you can probably become well over 90% confident that A is correct. As it turns out, mathematically it’s certain that choice A is correct, but even without having memorized that one particular rule, you can play the game en route to a correct answer.

Often we become so concerned by Data Sufficiency “traps” that we fail to play the game.  Each trap is also an opportunity for you – you know that C is often a trap answer and that negative numbers (or nonintegers) are often the not-so-fast-my-friend catch.  So use those things to your advantage – you know exactly how the GMAT likes to play the game, so anticipate that and play the game right back.