Hi All,
If you don't see the 'elegant' approach to this question, then you can still solve it with some 'brute force' math (and a bunch of multiplication) - it's not 'pretty', but if you're comfortable doing math by hand then you can still get to the correct answer in 2 minutes:
We're told that the sum of two squares is 1000 and that the two numbers (before they are squared) differ by 8. Since the answer choices to the question are integers, it's likely that the two side lengths of the two squares are also integers. Let's list out some perfect squares and get a sense of how big the numbers can get...
20^2 = 400
30^2 = 900
Since the larger square is clearly bigger, it's area will be more than half of the 1000, so it's side length will fall into the range of 20-30. The side length of the smaller triangle will be 8 LESS... Now let's try to narrow things down a bit...
15^2 = 225
25^2 = 625
17^2 = does NOT end in a 5, so there's no way the sum would be 1000, but this example probably isn't too far away from the correct answer...
26^2 = 676
18^2 = 324
This IS the sum that we're looking for, so these MUST be the dimensions of the two squares. By extension, the dimensions of the two white rectangles are 26x18 and the area of each is 468. Since there are two of those rectangles, their total area = 468(2) = 936.
Final Answer:
GMAT assassins aren't born, they're made,
Rich