This question annoys me beyond belief. It reminds of taking a test and getting a question where no information is covered during the semester. Like I'm magically supposed to predict what random piece of information I need to know to answer a ridiculously out of scope question.
The missing piece that everyone is looking for is knowing how an electric circuit works. I can't imagine you'd even know this if you didn't take physics at any point in your life and if you're like me, I couldn't even tell you one equation from my physics class in high school much less a whole array of concepts surrounding circuits.
Resistance in Parallel For resistors connected in parallelTotal Resistance = 1/R
total = 1/R
1 + 1/R
2 + 1/R
3 .... + 1/R
nThis is why you calculate the reciprocal of r instead of simply using r.
"In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y?" - There is no way to understand that r is referring to reciprocal of r without knowing that to calculate the total resistance for connected parallel resistors means calculating the reciprocal of r and the reciprocal of the resistors being connected. You simply would have needed to just trust your gut here and done the math with the information given.