This is a quadratic equation. The best thing to do with these is shove all terms to one side, setting it equal to zero, and then factor. Usually. In this case we don't need to factor. But let's shove. So
x^2  9x = 36
becomes
x^2  9x  36 = 0
This is now in the same format as the classic ax^2  bx + c equation. Now it's good to know that the roots of an equation will always multiply to make c. And they will always add to make
negative b. Notice the negative! Crucial! Anyway since Quantity A is adding the roots, that should be 9, which is 9. And since Quantity B is multiplying them, we'll get c, which is 36. So A is the answer.
In case you have doubts, let's actually factor this thing to show why the roots multiply to c but add to negative b. Factoring x^2  9x  36 gets us (x  12)(x + 3). Thus, the roots are 12 and 3. Notice that they multiply to 36, (just like 12 and 3 would multiply to 36), but they add to 9, which is negative b. On the other hand 12 and 3 would add to 9, which is b. Important distinction between the roots and the numbers you see in the factored quadratic.
_________________





Need help with GRE math? Check out our groundbreaking books and app.