GMAT Data Sufficiency Strategy - Prove Insufficiency

Perhaps no GMAT item is as symbolic of the test as is a Data Sufficiency question.  It is an iconic question format, unique to the GMAT and true to the aims of this specific test: to reward those who show the higher-order reasoning skills that will lead to success in business.

The corporate world is full of “yes men” and “groupthink” – of the kind of inertia that leads companies to think in the same direction without considering alternate points of view.  To combat that, employers and business schools seek those who can see the entire array of possibility, and the GMAT tests for that in many Data Sufficiency problems.  Consider a problem like:

Is the product jkmn = 1?

(1) jk/mn = 1

(2) j, k, m, and n are integers

Considering statement 1 it’s quite easy to get the answer “NO”.  Using 1, 8, 2, and 4, for example, satisfies statement 1?s constraints but clearly gives a product unequal to 1.  So does 1, 20, 5, and 4.  But having just one “NO” should immediately change your focus toward getting the other answer.  A series of nos using similar numbers (1, the product of two integers, and those two integers is the formula we used to create both options thus far) doesn’t do you any good. 

You need to either prove that the statement is sufficient in all cases or find the case or two that doesn’t give the same answer, rendering the statement insufficient.  And in either case you need to try different types of numbers.  With that as your guide, you might be persuaded to try nonintegers as at least a few values:  1/2, 2, 1/4, 4 satisfies statement 1, but also provides the product 1 and the answer “YES”.  We can prove the statement insufficient using these not-as-obvious nonintegers, and that’s why having a goal of insufficiency is so helpful: it forces you to try unique numbers.

Statement 2, however, renders our non-integer choices obsolete.  We can use the same integers as before (1, 8, 4, 2) t o get “YES”, but now we need to try harder to get “NO” as the fractions don’t work.  Here, again, the key to unlocking this one may be in our goal: we want the statement to be insufficient!  So we should push the limits of possibility.

Does the statement say that we can’t repeat numbers? 

No!  So we can say that j, k, m, and n are 1, 1, 1, and 1, rendering both statement 2 and both statements together insufficient.   A major component of Data Sufficiency is that it rewards you for playing devil’s advocate – for noting the few unique cases in which a likely conclusion is invalid.  By making that your goal, you can ensure that you’re working toward those unique case numbers (like negatives, fractions, primes, 0) that tend to produce different results.