In the Veritas Prep Data Sufficiency book, we have a section called the “Data Sufficiency Toolkit.” This toolkit contains a technique called “Manipulate Algebraically.” This technique involves “manipulating” either the statement or the question stem (or both) so that they exactly match each other.
Here is a simple example from the Veritas Prep Data Sufficiency book:
Is 2x = 3y + 2z?
Statement 1) x – z = 3y / 2
Either the statement or the question can be manipulated until they are identical to each other. For this example let’s work with the statement to get it to match the question stem. If you simply multiply the number 2 times the equation in statement 1, you get 2x – 2z = 3y and then you can add 2z to both sides and arrive at 2x = 3y + 2z. Since the statement now exactly matches the question, statement 1 is sufficient.
Some test takers wonder if this really is sufficient. After all, is this not just repeating the question? No it is not repeating the question. An analogy would be to ask the question, “Is he tall?” and get the answer, “He is tall.” You can see that this is the most direct way of answering the question and is absolutely sufficient.
I call this technique of matching the question and the statement “Mirroring.” “Manipulate Algebraically” as it is called in the Veritas Prep book describes HOW you do this, and “Mirroring” describes WHAT you are attempting to do. Taken together, these names present the “how” and the “why” of a valuable strategy for data sufficiency.
Mirroring is Indispensable
Manipulating or mirroring is a technique that there is simply no substitute for! There is no other way to find that a single equation with three variables is sufficient (as we did above). If not for the mirroring technique you would be trying to find the values for x, y and z. Embrace the inevitable and learn to manipulate the statement and the question stem so that they mirror each other.
When to Attempt Mirroring
It is very important that you understand when you can attempt the mirroring technique and when you should not. The rule is a simple one: “If the question stem and the statement each have the same variables and if those variables are at the same powers, you can safely attempt to mirror.”
Take the following example:
Is y > z?
1) Y2 > Z2
2) y – z > 0
Of these two statements, only the second one is a candidate for mirroring. Simply, add z to both sides and you get y > z. The first statement is tempting, yet it is not a good idea to try to match equations or inequalities if the exponents are different. In the question you have y and z as variables. In the statement you have y squared and z squared. Simply taking the square root of both variables in statement 1 might appear to give you the desired result, but that is without taking “positive and negative” into account. Y could be smaller than z and yet y2 be larger than z2 if y is negative!
Remember the rule, if you have the same variables at the same powers in the statement and in the question then you can attempt to mirror without fear. The worst that can happen is that you fail to mirror and have to run through the rest of your “tool box” when analyzing the question.
Learn to embrace this powerful technique: in some cases it is helpful and in others it is essential. Stay tuned for part 2 of this article where you will learn about “hidden mirrors” and “broken mirrors.”
David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star!