(This is one of a series of GMAT tips that we offer on our blog.)
As any good street hustler knows, the key to “Three-Card Monte” or any of its variations is to show the unsuspecting victim something that seems easy enough to recognize, and then obscure it through a series of distracting motions so that the mark loses track of it, and loses his money at the same time.
Such is the case with the GMAT and the seemingly-innocent number zero. Zero is the bane of the existence of many a GMAT test-taker precisely because it is harder than you might think to follow. Is it an integer (yes), even (yes), positive (no), negative (no), prime (no), divisible by 3 (yes)? When the GMAT asks a math question, it often does so with the exact goal of getting the test-taker to forget about the number zero. Consider the following:
Is x negative?
(1) IxI = -x
Upon initial inspection, it appears that x has to be negative. The absolute value of a number either keeps a positive number positive, or strips a negative number of its negative – absolute value measures “the distance from zero”, and is therefore never negative.
However, consider the number 0. Its absolute value is 0, and if you multiply it by -1 it is also 0. Therefore:
I0I = -(0)
And so zero satisfies statement (1), as well. Accordingly, zero is the lone number for which statement (1) doesn’t provide a negative value, and is the only reason that the statement is insufficient.
The GMAT knows that you’ll likely overlook the presence of zero – after all “zero” is “nothing”, so it’s easy to forget about.
If you’re following the college football season, you likely remember those special players like Reggie Bush, Percy Harvin, Charles Woodson, and others who could play a variety of positions, and for whom defensive coaches needed to always be looking. (Is he at receiver? In motion out of the backfield? Lining up under center?) Similarly, on the GMAT you should always be aware of the potential impact of zero — ask yourself whether zero has any bearing on the potential answer, because failure to account for it will often cost you.