Source : Webster's Revised Unabridged Dictionary (1913)

Unanswerable \Un*an"swer*a*ble\, a.
   Not answerable; irrefutable; conclusive; decisive; as, he
   have an unanswerable argument. -- {Un*an"swer*a*ble*ness}, n.
   -- {Un*an"swer*a*bly}, adv.

Source : WordNet®

unanswerable
     adj : impossible to answer; "an unanswerable argument"