Problem Solving

For how many set of natural number values of x and y, (xy^2)+y+7 will divide (x^2)y+x+y?

A)0

B)1

C)2

D)5

E)None of these

Let's say that n is a positive integer. We're given that

(x²y + x + y) / (xy² + y + 7) = n

or

x²y + x + y = nxy² + ny + 7n

Now notice that this will always be true if x = 7n² and y = 7n.

So we can simply pick a natural value of n and always find a solution. For instance, if n = 1, then x = 7, y = 7. If n = 2, then x = 28, y = 14, etc.

With that, we have an infinite number of sets of natural numbers {x, y}.

It goes without saying that this is galaxies beyond what the GMAT would ask you to do (on the GMAT scale, this is about difficulty 920!) The "none of these" option is particularly maddening.