Real Numbers

The GMAT official language mentions “real numbers.” The point is that all numbers on the GMAT are real numbers, and that, for the GMAT, you don’t have to worry about “imaginary numbers.” Most GMAT test takers would never have thought about imaginary numbers to begin with, and if you fall in that group you can skip this section and forget about it.

For the rest of you or the curious ones: all numbers on the GMAT are “real.” In other words, imaginary numbers, which involve i, the square root of -1, do NOT appear on the GMAT.

So, for example, when a GMAT question talks about an unknown quantity, some x, you can assume that it’s real. It may or may not be an integer, it may or may not be positive, but it’s definitely real. Another way to phrase this fact is that the number will lie somewhere on the number line.

To take another example, if you’re asked how many solutions an equation has on the GMAT, and the only solutions would involve taking the square root of a negative number, then the equation has “no solutions.”

Since you may recall, freshly or vaguely, the term “rational number,” we’ll clarify that term as well for GMAT purposes. A rational number is one that can be written as a fraction of two integers, say p/q. Not all numbers can be written this way. For example, the number pi and the square root of 2 cannot be written as a fraction of integers, so those are irrational numbers, but they are real numbers – hence, they are on the GMAT.

Again, the GMAT will not test you directly on whether you understand the terms “real” and “rational.” All you need to know is that, on the GMAT, all numbers are real, and they may or may not be rational (expressible as a fraction).