I would simply concentrate on the following extract.... I think it is enough to answer the question.
....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?
right. (SunShine - you have the correct answer too)
But what about "r is the combined resistance of these two resistors"
Wouldn't that say r = x+y? I understand that the solution wouldn't be that simple, but I couldn't grasp how r could be the combination of the resistances, while the reciprocal of r is equal to the sum of the reciprocals of the resistances.
It does not matter. You should concentrate on the sentence that says that reciprocal of r is equal to the sum of reciprocals of x and y. It is a stated fact so we can construct a simple equation and solve it....