The “variable trap” in Data Sufficiency
- March 29, 2017
- Posted by: gmatdudes
- Category: Strategies and Tips
For many people, Data Sufficiency is one of the areas in which they suffer most when preparing for the GMAT. And these questions are, by far, the ones in which the test maker tries to play tricks on you the most, trying to lure you into the wrong answer choice. They have over five decades of experience doing this, and they are very good.
Most of the time one tries to use logic: “can I get an answer with the statement?” The problem is that most students do not always focus on the real question, but on an implicit question that is not always what is asked: what is the value of each variable? And the result is that people dismiss a statement because “x has too many values”, not noticing that the real question does not ask about an exact value, but maybe whether that value is positive or negative.
The best method to overcome this (and it hasn’t failed me yet), is to enforce the following definition of “sufficiency”:
- Sufficient: The statement gives me a unique answer to the question.
- Not Sufficient: The statement gives me two or more answers to the question.
Never dismiss a statement unless you have concrete answers, or values, or a property that satisfies the definition.
Consider the following example:
If x, y and z are positive integers, is x(y+z) odd?
- x + yz is even
- x is even
Looking at statement 1, if the sum is even, that means either (even + even) or (odd + odd). If the sum is (even + even), then x is even and yz is even (meaning that one or both are even). If the sum is (odd + odd), then x is odd and yz is odd (meaning that both are odd). Usually at this point, we just throw our hands in the air and say “there are too many options! It’s not sufficient!” But wait! If you try them out, they all answer NO. It is sufficient and the answer is unique (a no). You must decide if the statement is sufficient or not in the question (not in the statements).
Let’s look at statement 2. It says that x is even. At this point many people think “oh, I just have one variable, y and z could be anything! So, it is not sufficient!” Wrong again. If x is even, in the question, the result is always going to be even and therefore the answer would be no. The answer is unique, making the statement sufficient.