Hidden Mirrors and Broken Mirrors in Data Sufficiency on the GMAT

Last week, we introduced the idea of “mirroring” in data sufficiency, and this week we’ll continue on that subject and look at different types of mirrors. “Mirroring” is my way of speaking about a technique called “manipulate algebraically” where the test taker attempts to manipulate either the statement or the question itself (or both) in order to get those statements to match each other exactly.

Sometimes it is not obvious that mirroring can be attempted on a particular question. I call these questions “hidden mirrors.”

Try the following example from the Veritas Prep Data Sufficiency Book:

Is x – y > r – s?

1)      x > r  and y  < s

2)      y =2, s = 3, r = 5, and x = 6

Clearly statement 2 is sufficient since it gives you values for all of the variables. Statement 1 can be approached a couple of different ways. You could plug in numbers of your own choosing to see if statement 1 is sufficient enough to guarantee a consistent answer to the question. But mirroring might just be the most efficient way to approach this statement.

If you have inequalities with signs pointing in the same direction those inequalities can be added together. If you leave “x > r” as it is and multiply “y < s” by a (-1) you get “– y > – s” now you can add these two inequalities as the signs are both “greater than”. On the left side of the sign you get “x – y” on the right side you get “r – s” so the expression becomes “x – y > r – s”. This exactly mirrors the question stem and so is absolutely sufficient. The correct answer is therefore D: each statement alone is sufficient. Watch for hidden mirrors, remember, if you have the same variables at the same power in a statement you can attempt to mirror without fear.

Broken Mirrors

Of course, “attempt to mirror without fear” does not mean that you should do so carelessly! We all know it is bad luck to break a mirror. Be sure to watch out for “broken mirrors” on the GMAT. A broken mirror is the exact opposite of a hidden mirror; it is situation in which mirroring seems to be the obvious technique, and yet it is actually a trap.

Try the following question and statement:

Is 5a > 2b?

1)      5a/b  >  2

This is appears to be an obvious exercise in mirroring, right? Simply multiply both sides by b and you get 5a > 2b. This means that statement 1 is sufficient alone. But wait! This is only true if b is a positive number. If b is a negative number the sign changes and 5a < 2b! Statement 1 is not sufficient alone and you would be looking to statement 2 for additional information.

Be careful when you see obvious mirroring situations. It may certainly still be the case that you should mirror, but run through the common number properties such as “positive / negative” and “integer/ non integer” to make sure that you are not dealing with a “broken mirror.”

Mirroring is a powerful technique on the GMAT. In some situations it can save time and in other situations it is indispensable. So long as you follow the rules and watch out for traps you can count on mirroring as a powerful tool in your Veritas Prep “Data Sufficiency Toolkit.”

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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!