Medwin,
I think I see where your confusion is coming from.
In your response to Canadian Beech you said that the correct anwer was: "longer runway is required".
"Longer runway" was not one of the options.
Using the definition of take-off distance that I cited previously, the consideration includes the distance required to achieve a screen height (usually) of 35 feet. Some of the "distance" required can be beyond the end of the runway!
If you were departing off a runway that was limiting because of field length with a lower flap setting , you may think about using a higher flap setting to "get off" a little quicker. But, because you are required to be able to climb to a prescribed screen height within a certain distance you
may jeopordize that by lowering you climb gradient. In other words, you have shortened your take-off roll but increased your take-off distance.
So you were thinking =runway length= required but the question was relating to =take-off distance= required.
OK, now my head hurts!
G'night