Is it permissible to seek out a "wasta" (mediation/favor) for a job promotion, knowing that the number of those promoted is limited and that this might be considered illicit gain?

If promotion in a job is based solely on passing an exam without other considerations, then it is not permissible to seek intercession (wasta); because it leads to obtaining what one does not deserve and is considered an injustice to the one who does deserve it.