This relies mostly on vocabulary knowledge: you know
that the blank needs a word that supports habitual lying. The only
one you can immediately throw out is selective because it does not imply
that Jessica would be even more of a liar than before. Perfidious
means dishonest and mean and doesn’t fit because it doesn’t say anything
of lying habitually. Rancorous means hostile and bitter, and that
wouldn’t fit for the same reason as perfidious. Arcane means secret
and private, so that definition has no relevance in the sentence.
Inveterate means chronic, so E works.