GMAT Data Sufficiency: Get 5 Extra Minutes
What if I told you that you could have five extra minutes on the quantitative section of the GMAT? Would you be interested?
Good, because this is going to get a little technical. I’m also going to assume you’ve had some experience with Data Sufficiency problems on the GMAT Math section. You should also have practiced testing cases to solve these problems: here’s a good introduction to that strategy in case you’re unfamiliar.
Part 1: Practical Application
Now, to save yourself the five minutes I promised, you have to understand something I’m naming the Moliski Theorem. Though I’ve heard it discussed by several people, I’m naming it after my colleague Liz Moliski, who was the first person I saw actually float this idea while teaching a class. The theorem applies to any Data Sufficiency question that has a yes/no answer. For example, the theorem is applicable to this Data Sufficiency question:
Did Rocky the dog eat more dog treats this year than he did last year?
- …
- …
It is not, however, applicable to this question, since the question asks for a specific value:
How many dog treats did Rocky the dog eat this year?
- …
- …
Here’s the Moliski theorem, put simply: Attempt to find one concrete example of the statement where the answer to the question is “no.” If you can find such an example, the statement is not sufficient. If you can’t find such an example, the statement is sufficient.
That’s it! Is your mind blown yet? Cause mine is.
You see, up until I saw Liz teach, I’d always assumed you needed two concrete examples of the statement that got you two different answers to the question in order to show that the statement is not sufficient. Defining those examples was time-consuming. The Moliski theorem not only obviates the need for the second example, it also makes it extremely simple to define the single example you’re looking for. Since I now only need to define and find half the examples than I did before, I have been able to solve Data Sufficiency problems in half the time that it took me previously, going from two minutes (on average) down to one. I have seen at least five yes/no Data Sufficiency questions on each of my practice tests, meaning this idea has bought me at least five full minutes of extra time.
I’m going to show you a Data Sufficiency problem. Try to solve it on your own first. Then we’ll apply the Moliski theorem.
If x and y are integers, is the product xy even?
- x – y < 3
- x + y is odd
Remember, the Moliski theorem says we should attempt to find examples where the answer to the question is “no.” In this case, that means we don’t actually want the product xy to be even; we want that product to be odd.
Now let’s find our examples. Can I find an example of statement (1), which says x – y < 3, where the product xy is odd? Sure I can: 7 and 5, for example. 7 – 5 is 2, that’s less than 3. The product 7 · 5 is 35, which is odd. Statement (1) is therefore not sufficient.
Moving on to statement (2): I want to find numbers where x + y is odd, and also where the product xy is odd. Well that’s impossible, since if x + y is odd, then one or the other must be even, meaning when I multiply them together, there’s no way I’ll ever get an odd number. Since I couldn’t find my example, statement (2) is sufficient. Now we know that the correct answer is (B).
Are you excited yet? Try this super-tough problem:
Is x > 0?
- x² < 9
- x³ > x
The Moliski theorem tells us we don’t want x to be greater than 0; we want it to be less than 0. In other words, we want x to be negative.
Try to find a negative number x that would make statement (1) true. So, I know that x² < 9. Can x be negative? Sure, as long as it’s a negative fraction like –1/2. Statement (1) is not sufficient.
Now try to find a negative number for x that would make statement (2) true. If x³ > x, can x be negative? There’s no reason to reinvent the wheel, let’s just use x =–1/2 again. If you cube that, it’s greater than what you started with. So statement (2) is also not sufficient.
And oh, by the way, since –1/2 is an example that satisfies both statements, and gives us the “no” answer we’re looking for, the correct answer to this question is (E).
LET’S GOOOOOOO
Part 2: A Small Caveat and Other Non-Essential Nerdy Stuff That You Can Read If You’re Interested, but I’m Mostly Writing It Because I Don’t Want Liz to Get in Trouble
Occasionally, the Moliski theorem fails. Here’s an example:
Is x > 10?
- x < 5
- x² < 25
Both of these statements are sufficient on their own to answer the question, so the correct answer is (D), but the Moliski theorem would lead you to decide they are not (and would therefore lead you to incorrect answer (E)). These statements are each sufficient because the answer to the question is always “no,” meaning they technically do provide us enough information to answer that question. Liz mentioned this possibility in her class, noting that if you want to be thorough and precise, you should find a “yes” case after you’ve found a “no” case.
Don’t, however, let the rain fall on your parade quite yet. The “always no” situation is exceedingly rare; in my professional experience, it shows up on roughly 1% of all Data Sufficiency questions (probably even fewer, to be honest). So, we are still looking at a strategy that works 99+% of the time and saves you 5+ minutes: personally, I’m willing to accept that risk.
Finally, here’s what I think is the true genius of the Moliski theorem: It sidesteps the single most common error I see my students make when tackling Data Sufficiency problems, which is to misinterpret the question as a rule. By explicitly hunting for a “no” answer, the Moliski theorem forces you to consider that negative possibility right upfront, so that you don’t have to remember to look for it later when you’re already knee-deep in a fog of calculations and algebra.
Epilogue
When I first started teaching the GMAT, I never dreamed I’d see a day when I could get away with testing just one case per Data Sufficiency statement as opposed to two. Now that day is upon us. I hope your life is as changed as mine.
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Ryan Jacobs is a Manhattan Prep instructor based in San Francisco, California. He has an MBA from UC San Diego, a 780 on the GMAT, and years of GMAT teaching experience. His other interests include music, photography, and hockey. Check out Ryan’s upcoming GMAT prep offerings here.