Question to be asked = "If I ask you if this is the correct path to go, would you say ça" ? 4 possibilities:
ca = yes
path' correctness = yes
reply= yes (ca)
ca = yes
path' correctness = no
reply= no (ga)
ca = no
path' correctness = yes
reply= no (ca)
ca = no
path' correctness = no
reply= yes (ga)
Hence we see whenever reply is ga the path is incorrect, if the word asked in the question to the wise man was ca .