Answer
All three Gaussian surfaces have the same magnitude of the electric field at any point on the surface.
Work Step by Step
We can use Equation (23-15) to find an expression for the electric field at each Gaussian surface.
radius $R$:
$E = \frac{1}{4\pi~\epsilon_0}~\frac{Q}{R^2}$
radius $2R$:
$E = \frac{1}{4\pi~\epsilon_0}~\frac{4Q}{(2R)^2} = \frac{1}{4\pi~\epsilon_0}~\frac{Q}{R^2}$
radius $3R$:
$E = \frac{1}{4\pi~\epsilon_0}~\frac{9Q}{(3R)^2} = \frac{1}{4\pi~\epsilon_0}~\frac{Q}{R^2}$
When we can rank the Gaussian surfaces according to the magnitude of the electric field at any point on the surface, all three Gaussian surfaces have the same magnitude of the electric field at any point on the surface.
