Rich is one of the stellar teachers in Knewton’s GMAT course, in whch he loves helping students rock the Quantitative section.
In any GMAT prep course, one of the first things taught about the Data Sufficiency section is that the two statements are true and do not contradict one another. It’s a point that’s easy to gloss over and completely overlook during the hustle and bustle of your test prep.
But this supposedly self-evident point gets many students into trouble when dealing with YES/NO questions, because they mistakenly try to prove or disprove the statements rather than the prompt.
I’ll explain: Recall that a YES/NO question is one in which the answer will be “Yes” or “No.” For example, “Is x even?” or “Are the distances equal?” This is in contrast to VALUE questions, for which you must come up with one particular value (e.g. “What is x?”, “What is the average of a and b?”).
If a statement produces both a YES and a NO, then it is insufficient. If the statement (or combination of statements) always produces a YES or always produces a NO, then it is sufficient. (Remember, a NO is not the same thing as INSUFFICIENT; so if you’re asked “Is x even?” and a statement lets you know that x is always odd, then that is SUFFICIENT, because you can answer NO with certainty.)
Is x odd?
(1) x is a multiple of 3.
(2) x is a multiple of 5.
For Statement (1), x could be 3, which would lead to a YES, but x could also be 6, which would lead to a NO. Insufficient.
For Statement (2), x could be 5, which would lead to a YES, but x could also be 10, which would lead to a NO. Also insufficient.
Combining the statements, we see that x could be 15, which would lead to a YES, but x could also be 30, which would lead to a NO. Final answer, E: the statements together are not sufficient to answer the question.
This is a simple example that would not likely appear on the GMAT, but it’s great for illustrating a basic mistake students make: trying to disprove the statements.
It might be tempting to look at Statement (1) and try to find a YES or a NO to the statement itself, rather than the prompt. So you try to prove/disprove “x is a multiple of 3″, rather than prove/disprove the real question, “Is x odd?”
This would result in you picking, let’s say, x = 3, because it answers YES to “x is a multiple of 3″. Then you might pick x = 5, because it answers NO to “x is a multiple of 3.”
But of course, both 3 and 5 answer YES to the question in the prompt, and you may erroneously conclude that Statement (1) is sufficient, when in actuality, it is not.
Obviously, this approach can get you into trouble, because you may get an incorrect answer. But there’s an even more basic error behind this mistake: You’re wasting valuable time trying to prove/disprove something that is already known to be true!
And thus I return to that basic maxim of Data Sufficiency questions:
The statements are always true and never contradict one another. Again, it seems like a trivial point, but as the aforementioned example demonstrates, you’d be surprised how forgetting the basics can lead to unnecessary wasted time!
So, in conclusion, recognize that the statements are true, and use their information to address what really matters: the question in the prompt.