275: Subtracting a series.

If you're a junior or senior, you've seen versions of this problem before, perhaps on the SAT (the source of this problem). As I've said before, the SAT is designed in a way that calculators are not necessary and each question must be solvable in less than a minute. Often, the student is expected to change the form of the question: text to algebra, or algebra to visual (graphical); or rearrange the terms, or work backwards from the known. 

The sum of the positive odd integers less than 200 is subtracted
from the sum of the positive even integers less than or equal to 200.
What is the resulting difference?

As it stands, that question would take you far too long to find an answer for, so it must have a simplification somewhere.

What can we do to make this quicker to answer?
Or simpler to understand?

How can we change it?