Let be the voltage at a point between the two leftmost resistors in the figure. There are only two resistors that are on horizontal line segments. Let the voltage at a point between them. Let be the voltage at a point between two rightmost resistors in the figure. Then, using Kirchoff's junction rule, we have the following equations
When we multiply both sides of these equations by and then simplify, we obtain
The first two equations, when subtracted, imply that . Plugging this into equation (3) gives
We can plug in (from equation (1)) to solve for
and then plug this back into equation (4) to get
and the current through the battery is
Therefore, answer (D) is correct.