Electric Flux and Charges on the Surface of a Sphere

[lugita15]

Homework Statement

In the interior of a sphere is a charge -q. On the surface of the sphere are two charges, each q, as shown in this figure:

Homework Equations

Electric Flux through a Closed Surface=(Charge Enclosed)/Epsilon_0

The Attempt at a Solution

This was a question in the 1982 AP Physics C E&M Free problem 1, part c.
Unfortunately, I cannot find this test anywhere on the internet. I was, however, able to find the solution to the test. The solution given to this question is:

If anyone is able to find the AP Physics C test in question, I would greatly appreciate it.
What I do not understand is that since two charges are on the surface of the sphere, the electric field due to these charges at the points where they are located would be undefined, and thus the electric flux through the surface should also be undefined. According to the creators of the test, however, the charges *on* the sphere are considered to be "enclosed by the sphere."
I would think that the two charges on the sphere would neither be enclosed by it nor outside of it, therefore the flux would be undefined.
Any help would be highly appreciated.
Thank you in advance.

 

[learningphysics]

I agree with you. Are you sure the closed surface that are referring to is the surface of the sphere itself? The question might refer to a surface enclosing the sphere...

 

[lugita15]

I agree with you. Are you sure the closed surface that are referring to is the surface of the sphere itself? The question might refer to a surface enclosing the sphere...

No, I'm sure the question was to find the electric flux through the sphere.