Apryl, Beth, and Carla are three remarkable women, each having some remarkable characteristics.
(1) Just two are intelligent, just two are beautiful, just two are artistic, and just two are rich.
(2) No one has more than three of those characteristics.
(3) Of Apryl it is true that: if she is intelligent, she is rich.
(4) Of Beth and Carla it is true that: if she is beautiful, she is artistic.
(5) Of Apryl and Carla it is true that: if she is rich, she is artistic.
Who is not rich?
show your reasoning