Positively Uncertain – Prognosis Negative

(This is one of a series of GMAT tips that we offer on our blog.)

One of the greatest contributions that Jerry Seinfeld has made to society is his array of fake movie titles from his sitcom. Mention the terms “Chunnel”, “Sack Lunch”, or “The Muted Heart” to any Seinfeld fan and he’ll have spent at least a few hours imagining what the plot for that movie could have been. Perhaps the one that inspired the greatest enthusiasm for the characters on the show was the faux film “Prognosis Negative” — which should also serve as a warning to you when you take the GMAT…

A common theme, particularly on Data Sufficiency questions, is the use of variables with inequalities. For example, a question might ask:

Is x>y/z?

And provide you with the statement:

(1) xz>y

Performing the algebra quickly, many might simply divide both sides by z, creating the given equation and proving, presumably, that the answer is yes.

Upon closer examination, however, we cannot know for sure that z is a positive number. If z is, in fact, negative, we would need to flip the inequality to demonstrate that x<y/z. Consider possible values for x, y, and z:

A) x=2, y=1, z=1. This satisfies statement 1, (2*1 > 1), and when manipulated algebraically, gives us the answer “yes” (2 > 1/1).

B) x = -2, y=1, z=-1. This also satisfies statement 1 (-2 * -1 > 1), but gives us the answer “no” to the overall question (-2 is not > 1/-1).

When inequalities use variables, you need to keep in mind that each variable could very well be negative unless specified otherwise. In other words, if you assume that a variable is positive, your prognosis is negative.

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