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If you’ve been preparing at all for GMAT data sufficiency, you’ve probably been confronted with situations in which the information in the statement seems inscrutable. You know that it’s telling you something, but you’re not quite sure what, if any, relevance the information has to the question in the prompt. This, in and of itself, is a fairly common situation. Even though almost all Data Sufficiency statements can be understood conceptually or algebraically, even Quant wizards will sometimes have difficulty understanding what a statement actually implies. The difference between these high scorers and people trying to break it into the upper echelon is how they deal with this situation. A student who hasn’t internalized proper DS strategy will deal with a weird statement in the following way: “Hmmm, this doesn’t make a lot of sense. I guess this isn’t sufficient!” Whereas more advanced test-takers will deal with difficult statements by saying: “Hmmm, this doesn’t make sense. Time to test cases!”
To understand how these tendencies play out, take a look at the below question:
If x and y are positive integers, is x divisible by 6?
1) x = y(y+1)(y-1)
2) y – 1 is a multiple of 3
If you’re up to speed on your advanced Number Properties rules, you can answer this question pretty quickly, but let’s assume you don’t know the rule that’s relevant here or that you forgot it. The important point is that you can still determine whether the statements are sufficient!
Our lower-scoring test-taker will look at statement 1 and implement the sub-optimal reasoning discussed above: “Well, I have no idea what statement 1 means. I don’t know how to deal with it, so it must not be sufficient.”
But our higher-scoring test-taker will say: “Well, I have no idea what statement 1 means. But I know that there are only certain values that satisfy the conditions in the statement. Let me find some values that satisfy the statement and see whether I get a consistent Yes/No answer to the question or a Maybe”. And this test-taker will move on to testing cases. If you’re not familiar with testing cases, look at the methodology below:
Step 1: Choose a set of values that satisfy the conditions in the prompt.
We’ll start by choosing a value for y: y = 2. Now, substitute that value for y in statement 1: x = (2)(3)(1) = 6. So, when y = 2, x = 6.
Step 2: Determine what answer the given values yield to the question in the prompt: If x = 6, is x divisible by 6? The answer is: YES
Step 3: Plug in a new set of values that will give you a different answer to the question: Since the values we chose in step 1 yielded a “Yes” answer to the question, our new goal is to choose values that will yield a “No” answer to the question. To yield a different answer to the question, choose numbers with properties different from the numbers that you chose in step 1. Different properties can be: even vs odd; positive vs negative; fraction vs non-fraction. Since the prompt specifies that x and y must be positive integers, a “different” number for y would be an odd number. So, let y = 3. When y = 3, x = (3)(4)(2) = 24.
Step 4: Repeat step 2: If x = 24, is x divisible by 6? The answer is: YES
So, our smart test-taker recognized that she didn’t understand statement 1, but went a step further. Instead of simply saying that the statement is not sufficient because she doesn’t understand it, she used concrete evidence to test whether the statement yielded a consistent answer to the question. Whether y is odd or even, statement 1 yields a Yes answer to the question, so we can conclude that statement 1 is sufficient.
The above is a purely strategic way to determine sufficiency. There is a conceptual reason explaining sufficiency in statement 1, but you should realize that an absence of a conceptual or algebraic approach toward a statement doesn’t doom you on the question. The GMAT is an evidence-based test, so when concluding that a statement is or is not sufficient, you should focus on finding concrete evidence to justify your conclusion. This is one of the key skills that differentiates 700+ scorers from other scorers, and keeping this fact in mind will go a long way toward helping you see steady improvements in your preparation.