Electric Field due to Charged Sphere

1. The problem statement, all variables and given/known data

Refer to the attached photo for the problem statement.

2. Relevant equations

Electric Field Strength = 1/(4*pi*EpsilonNaught)*q/r^2

3. The attempt at a solution

So, I need to find the charge magnitude of q. Because the electric field strength is given at a point greater than the radius of the sphere, that should allow me to treat the entire sphere and point charge as a single point charge.

Using the above formula, I get the net charge to be -8.34 micro coulombs. I take this number and then subtract the charge from the sphere and should be getting the correct answer. However, I’m getting an answer not listed. Am I making an incorrect assumption somewhere?

Attached Images
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