Choice A. No current will flow through the additional lightbulb because there is no potential difference across it.
Work Step by Step
Consider the bottom branch of the circuit to be at 0 V. The top branch will be at 20 V, and the point between the two batteries is at 10 V, as is the point between the two resistors. Both sides of the newly-added lightbulb are at the same potential of 10 V, so no current will flow.