Question

Only one of the approaches to ethical reasoning has as its central tenet that actions are more right if they promote more happiness, more wrong as they produce unhappiness. which approach applies

Answer 1

I believe the answer is: End-result ethics. 

End-result ethics refers to a moral standard in which the standard of right or wrong would be determined by the final outcome of your actions rather than the process.
In End-result ethics, as long as the person feel happiness/positive benefits in the end, all of their actions would be considered as right even though it might cause some collateral damages along the way.